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[ "(Last Updated On: March 17, 2019)\n\nThis week, we’re excited to share an interview with Brian Hoffman, puzzle master and owner of family-run, Just Escape Room in La Grange, IL. ", "Brian reveals his approach to escape room puzzle design.", "\n\nEnjoy!", "\n\nCan you provide me with a little history of Just Escape Room and what inspired you to start an escape room business?", "\n\nMy family started with an escape room that opened near us in West Chester, Ohio 4 years ago. ", "It was the type of activity that everyone loved: grandmother, high schooler, 6-year-old and we all had a blast. ", "We went on to do another 60 + rooms around the world. ", "Eventually, my wife was looking at going back to work, I had a background in control systems and IT, and it dawned on us that we could create an escape room. ", "We started creating a business plan and running the numbers. ", "In parallel, I had created most of the puzzles for our first to rooms in my garage, and five months later we opened our doors. ", "The business has grown nicely ever since.", "\n\nHow did you learn how to design puzzles for your escape rooms? ", "Did you have any previous experience with puzzle design?", "\n\nThe escape room was my first entry into puzzle design. ", "The only thing I was armed with is the vast number of puzzles I had tested myself against (escape rooms, books puzzles, online puzzle hunts, online and board games, etc.). ", "I knew what my family enjoyed and what we didn’t. ", "When creating the puzzles for Just Escape, I took the features I liked best from past experiences and kept out the ones I didn’t enjoy.", "\n\nThis included:\n\nThe puzzle flow – pattern of quick wins vs. harder challenges\n\nFocus on unique things not seen before.", "\n\nSurprise. ", "Reveals that are unexpected.", "\n\nKeep the excitement throughout the game, eliminate dead spots.", "\n\nPeople like to win, make sure they have a chance to win\n\nThe best puzzles are the one that you look back at and say “I should have gotten that sooner.”", "\n\nWhat is personally the most challenging aspect for you when it comes to escape room puzzle design? ", "What about running an escape room business overall?", "\n\nPuzzle design biggest challenge – Game Balance: Designing a room that both escape room veterans and newbies love and feel like it was an appropriate challenge. ", "I always find it interesting how the slightest change in a prop or clue can dramatically change how fast it is played. ", "In one room we changed a small version of the prop for a bigger one and that change allowed people to solve it ten mins faster. ", "That caused us to add another puzzle to fill in that ten mins and get the right balance.", "\n\nER business overall challenge: For me it is time. ", "Finding time to run the business, build new rooms, maintain existing rooms, advertise, create growth plans and execute those plans, etc. ", "It doesn’t help that this is a hobby company for us and I have a full-time day job also 🙂\n\nWhen designing puzzles and their accompanying stories and sets, do you find yourself having to quickly toggle between left (logical) and right-brained (creative) thinking?", "\n\nSet design is one of my biggest challenges. ", "I can build almost anything electronic or mechanical, but don’t have the same skills in making the set look amazing. ", "This is one area where I need to lean on others for help.", "\n\nWe were lucky in hiring game masters. ", "One of our game masters is an amazing artist, and another is a solid actor. ", "Both were amazingly helpful in set design and voiceover work.", "\n\nI am still looking for great contractors that can come in and help bring set design to the next level. ", "Further, I am still learning on how to best communicate the design I have in my head to these contractors for quoting purposes.", "\n\nAs a puzzle maker, do you ever find yourself feeling frustrated and reluctant to compromise when a puzzle doesn’t quite transfer from your head to real life? ", "If so, how do you decide when to compromise and to what extent?", "\n\nI have a storage unit of puzzles that didn’t make it into the final product. ", "Most of them were ambitious technology props that were not consistent enough to go into the room. ", "Some of them were cool puzzles but did not fit well into the story.", "\n\nMy biggest challenge is that I love unique technology that folks haven’t seen before. ", "I tend to lean toward tech or physical puzzles vs. paper. ", "Unfortunately, that also means that many puzzles never make it to prime time. ", "I’m ok with that because the ones that do make it out end up being pretty cool.", "\n\nWhen taking on the overwhelming task of designing an escape room, in your opinion, is it best to start with the story and build a puzzle around that, the converse, or something else?", "\n\nHere’s my approach:\n\nI collect a huge library of puzzle ideas, Physical, perspective, logic, pattern, old games, riddles, electronic sensors, science projects, and interesting ways to hide information, etc. ", "I come up with a story or concept theme that is interesting, and I haven’t heard of before. ", "I am not only thinking about the story but also the game flow. ", "I try to challenge myself with a way to build on the classic escape room flow of entering a room, find the secret room, and find the way out. ", "I love trying to find new ways of moving teams through the physical space in different ways. ", "With the story in place, I then start slotting puzzles that fit with the story theme. ", "I create the puzzle flowchart and a room layout. ", "With a story, puzzle flow, and room layout I then sketch out set design. ", "I may need to adapt earlier puzzles or flow to accommodate other design choices. ", "I go into construction. ", "I try to build as much of the puzzles and props offsite and then install into the room. ", "In parallel, I am building the base of the room, walls, electrical, control panel, doors, painting, etc. ", "Then I install puzzles and do initial testing. ", "Making sure the puzzles are stable and work consistently. ", "Beta testing. ", "Test with at least six teams of differing size and skill levels. ", "Make adjustments as needed for the game Launch game with a hyper care period to fix or adapt if any bugs are revealed.", "\n\nRegarding sprinkling in easy wins and feel good moments, have you found a formula that works? ", "Is there a magic number or ratio (time spent or quantity) that you feel hits the perfect sweet spot between boredom and frustration?", "\n\nI like to ramp up the energy at the start of the game. ", "This usually means an early phase of easy wins that results in a surprise reveal. ", "I equate it to the same equation online games use to hook people. ", "The first levels are easy, and the players acquire things quickly.", "\n\nFrom there I go into phase 2 which the players now know what to expect, and they go out and solve a bunch of medium difficulty puzzles. ", "This phase at a slightly slower pace with slightly higher difficulty. ", "Teams feel a sense of accomplishment at each win because they had to fight for it. ", "The risk is that this can become frustrating for the team and the energy level could go down as frustration raises. ", "To counter this, I try to put another major secret reveal in the phase. ", "Something that gives the team a whole new set of props to explore. ", "This helps keep the energy level high.", "\n\nIn the final puzzle phase, I put the most difficult puzzle chain. ", "Ideally, the team gets to this point with – ten mins left. ", "The clock ticking and the closeness to finishing the game provides the heightened energy level. ", "Ideally, the final puzzle solution triggers a theatrical climax (lights, sounds, etc.). ", "I don’t always achieve this.", "\n\nOn JustEscapeRoom.com , you mention that your rooms require players to use all of their senses. ", "Does this include smell and taste? ", "If so, how do you accomplish this?", "\n\nI have stayed away from taste so far (because it is either gross or a reset nightmare) although all other senses are fair game. ", "This goes back to finding unique ways to transfer information. ", "For example, there are a wealth of scented oils out there: everything from blue slushy to skunk. ", "You just need to find a way to build it into a puzzle. ", "I can’t reveal more without giving away too much info 🙂\n\nOn forums, when owners ask design or puzzle building questions, you tend to see answers like “it depends” since each situation is so different. ", "Given this, are there ANY universal truths that can be generalized across all escape rooms?", "\n\nHere are the major principles I use:\n\nAvoid red hearings . ", "Everyone hates them.", "\n\nWhen told the answer to the puzzle, people should feel like they should have gotten it. ", "If they are saying I would have never have gotten that it is a flaw in the design\n\nTech adds a great effect when it works. ", "When it doesn’t, it adds great frustration.", "\n\nDon’t repeat puzzles. ", "The first time is new, the second time feels like busy work.", "\n\nBe unique. ", "If you’re going to use common puzzles, put a new twist on them. ", "Don’t just make someone solve a sudoku puzzle. ", "Make them do it with a checkerboard or a giant version etc. ", "Anything different than the norm. ", "This goes with the room story also.", "\n\nMix your puzzle types. ", "This allows the diversity of the group to shine vs. having the same person solve all of the puzzles.", "\n\nHow do you use customer feedback and data to inform your design decisions and business decisions overall?", "\n\nAbsolutely critical. ", "We recently got our first 4-star review (Previously we were all 5 star). ", "Tracing back the reason it was because we had gotten so busy we weren’t able to give the full greeting and post-game celebration we had been doing previously. ", "These customer interaction moments are just as important as the game to have people leave loving the experience. ", "We immediately put in changes to address the issues.", "\n\nMultipart question time: Have you ever heard of anyone pulling off an escape room theme aimed to help people empathize with folks dealing with depression and mental illness? ", "Autism and intellectual disability too for that matter? ", "Do you think abstract or symbolic-based themes like this are feasible without being a total drag for customers? ", "How might you design puzzles for a room that tackles less concrete subject matter like this?", "\n\nI love this idea and haven’t heard of it before. ", "It sounds like a great way to grow awareness for a cause and would probably generate some PR. ", "If I would to go after a room like this, I might try to put the players in the mind of the hero character who has the disability. ", "The goal would be to overcome the challenges that these folks face to be successful in life. ", "I would probably look to partner with an organization familiar with the cause to make sure I was sensitive to the issues and to help me pick the puzzles that fit the theme. ", "You would also need to donate some of the profits to the cause. ", "Perhaps you could use the pay for hints approach with the money raised for hints donated to the cause. ", "Just some thought off the top of my head.", "\n\nFrom a puzzle & design perspective, what’s something that you think escape room owners put too much money & energy into that most customers don’t really care about?", "\n\nJust like video games, gameplay trumps the story/set. ", "Having a great story motivates people to pick your room. ", "Having a great set gives the room great bonus points. ", "At the end of the day, the room needs to have great puzzles and flow otherwise none of the other stuff matters.", "\n\nThe other calculus I am always wrestling with is how much to invest in set design. ", "The perfectionist in me wants a phenomenal set. ", "The practical side of me realizes that there are diminishing returns. ", "I don’t necessarily generate more traffic with a $100k room vs. a $10k room. ", "There is a sweet spot in there somewhere that is hard to nail. ", "It depends on where you’re located, how much competition is around. ", "What kind of foot traffic you have, etc.", "\n\nWhat mistakes do you see escape room owners making that is perhaps the most avoidable while also being highly detrimental? ", "This can be from a puzzle/design perspective, overall business or both.", "\n\nHmm, good question. ", "Some common mistakes I see:" ]

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[ "Q:\n\nHow can I find the amount of video Ram installed through a WMI call?", "\n\nDoes anyone know how to get the Video Ram of a PC from a WMI call?", "\nI've seen calls to the Win32_VideoController management object's AdapterRAM property, but that only gives the system memory, and is not representative of the video RAM at all.", "\n\nA:\n\nTurns out it was the adapter RAM returned, and through an unfortunate coincidence, the wrong conversion was used and gave the system RAM...on two different systems. ", "Thanks for pushing us to look again.", "\nFor what it's worth, in a C# WinForms app:\nint _ram = 0;\n\nManagementObjectSearcher searcher = new ManagementObjectSearcher(\"select AdapterRAM from Win32_VideoController\");\n\nforeach (ManagementObject mo in searcher.", "Get())\n{\n var ram = mo.", "Properties[\"AdapterRAM\"].Value as UInt32?;", "\n\n if (ram.", "HasValue)\n {\n _ram = ((int)ram/1048576);\n }\n}\n\nA:\n\nFrom The Microsoft Technet Script Center Script Repository under 'Hardware' then 'Video and Display' then 'List Video Controller Properties'.", "\nI would imagine you might have to work out something between AdapterRAM and 'VideoMemoryType'\nOn Error Resume Next\n\nstrComputer = \".\"", "\nSet objWMIService = GetObject(\"winmgmts:\\\\\" & strComputer & \"\\root\\cimv2\")\n\nSet colItems = objWMIService.", "ExecQuery _\n (\"Select * from Win32_VideoController\")\n\nFor Each objItem in colItems\n For Each strCapability in objItem.", "AcceleratorCapabilities\n Wscript.", "Echo \"Accelerator Capability: \" & strCapability\n Next\n Wscript.", "Echo \"Adapter Compatibility: \" & objItem.", "AdapterCompatibility\n Wscript.", "Echo \"Adapter DAC Type: \" & objItem.", "AdapterDACType\n Wscript.", "Echo \"Adapter RAM: \" & objItem.", "AdapterRAM\n Wscript.", "Echo \"Availability: \" & objItem.", "Availability\n Wscript.", "Echo \"Color Table Entries: \" & objItem.", "ColorTableEntries\n Wscript.", "Echo \"Current Bits Per Pixel: \" & objItem.", "CurrentBitsPerPixel\n Wscript.", "Echo \"Current Horizontal Resolution: \" & _\n objItem.", "CurrentHorizontalResolution\n Wscript.", "Echo \"Current Number of Colors: \" & objItem.", "CurrentNumberOfColors\n Wscript.", "Echo \"Current Number of Columns: \" & objItem.", "CurrentNumberOfColumns\n Wscript.", "Echo \"Current Number of Rows: \" & objItem.", "CurrentNumberOfRows\n Wscript.", "Echo \"Current Refresh Rate: \" & objItem.", "CurrentRefreshRate\n Wscript.", "Echo \"Current Scan Mode: \" & objItem.", "CurrentScanMode\n Wscript.", "Echo \"Current Vertical Resolution: \" & _\n objItem.", "CurrentVerticalResolution\n Wscript.", "Echo \"Description: \" & objItem.", "Description\n Wscript.", "Echo \"Device ID: \" & objItem.", "DeviceID\n Wscript.", "Echo \"Device Specific Pens: \" & objItem.", "DeviceSpecificPens\n Wscript.", "Echo \"Dither Type: \" & objItem.", "DitherType\n Wscript.", "Echo \"Driver Date: \" & objItem.", "DriverDate\n Wscript.", "Echo \"Driver Version: \" & objItem.", "DriverVersion\n Wscript.", "Echo \"ICM Intent: \" & objItem.", "ICMIntent\n Wscript.", "Echo \"ICM Method: \" & objItem.", "ICMMethod\n Wscript.", "Echo \"INF Filename: \" & objItem.", "InfFilename\n Wscript.", "Echo \"INF Section: \" & objItem.", "InfSection\n Wscript.", "Echo \"Installed Display Drivers: \" & _\n objItem.", "InstalledDisplayDrivers\n Wscript.", "Echo \"Maximum Memory Supported: \" & objItem.", "MaxMemorySupported\n Wscript.", "Echo \"Maximum Number Controlled: \" & objItem.", "MaxNumberControlled\n Wscript.", "Echo \"Maximum Refresh Rate: \" & objItem.", "MaxRefreshRate\n Wscript.", "Echo \"Minimum Refresh Rate: \" & objItem.", "MinRefreshRate\n Wscript.", "Echo \"Monochrome: \" & objItem.", "Monochrome\n Wscript.", "Echo \"Name: \" & objItem.", "Name\n Wscript.", "Echo \"Number of Color Planes: \" & objItem.", "NumberOfColorPlanes\n Wscript.", "Echo \"Number of Video Pages: \" & objItem.", "NumberOfVideoPages\n Wscript.", "Echo \"PNP Device ID: \" & objItem.", "PNPDeviceID\n Wscript.", "Echo \"Reserved System Palette Entries: \" & _\n objItem.", "ReservedSystemPaletteEntries\n Wscript.", "Echo \"Specification Version: \" & objItem.", "SpecificationVersion\n Wscript.", "Echo \"System Palette Entries: \" & objItem.", "SystemPaletteEntries\n Wscript.", "Echo \"Video Architecture: \" & objItem.", "VideoArchitecture\n Wscript.", "Echo \"Video Memory Type: \" & objItem.", "VideoMemoryType\n Wscript.", "Echo \"Video Mode: \" & objItem.", "VideoMode\n Wscript.", "Echo \"Video Mode Description: \" & objItem.", "VideoModeDescription\n Wscript.", "Echo \"Video Processor: \" & objItem.", "VideoProcessor\nNext\n\n" ]

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[ "Q:\n\nHow can i get the last lines of string in JAVA\n\n$GPGGA,013810.000,1437.9098,N,12100.2297,E,1,10,1.0,26.4,M,39.1,M,,0000*69\n$GPRMC,013810.000,A,1437.9098,N,12100.2297,E,0.00,122.34,200916,,,A*6A\n$GPGGA,013811.000,1437.9098,N,12100.2297,E,1,10,1.0,26.4,M,39.1,M,,0000*69\n$GPRMC,013811.000,A,1437.9098,N,12100.2297,E,0.00,122.34,200916,,,A*6A\n$GPGGA,013812.000,1437.9098,N,12100.2297,E,1,10,1.0,26.4,M,39.1,M,,0000*69\n$GPRMC,013812.000,A,1437.9098,N,12100.2297,E,0.00,122.34,200916,,,A*6A\n\nEvery Second I'm concatenating String of NMEA to a String Variable. ", "All I want is to get the last $GPGGA and GPRMC because i need it for time and date. ", "Is there a way to do that? ", "Thanks in advance guys.", "\n\nA:\n\nIf you have the following:\nString a = \"$GPGGA,013812.000,1437.9098,N,12100.2297,E,1,10,1.0,26.4,M,39.1,M,,0000*69\";\nString b = \"$GPRMC,013812.000,A,1437.9098,N,12100.2297,E,0.00,122.34,200916,,,A*6A\";\n\nThen split each at the \",\" symbol:\nString[] aAry = a.split(\",\");\nString[] bAry = b.split(\",\");\n\nI think the second element of each array (index 1) contains the time so it can be accessed as aAry[1] which contains the string 013812.000 (as does bAry[1]). ", "I'm not sure where the date is stored in these strings.", "\n\n" ]

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[ "Q:\n\nHow can I get the result?", "\n\nI got a formula\n$$\n- \\frac{ \\frac {\\partial B(\\lambda, \\xi)}{\\partial \\lambda}}{B(\\lambda, \\xi)} = - \\Psi(\\lambda) + \\Psi(\\lambda + \\xi)\n$$\nWhere $B$ is Beta function and $\\Psi$ is digamma function.", "\nHow can I get the result $- \\Psi(\\lambda) + \\Psi(\\lambda + \\xi)$ ?", "\n\nA:\n\n$$B(x,y)=\\frac{\\Gamma(x)\\Gamma(y)}{\\Gamma(x+y)}$$\n$$\\log B(x,y)=\\log \\Gamma(x)+\\log \\Gamma(y)-\\log \\Gamma(x+y)$$\n$$\\frac{\\partial}{\\partial x} \\log B(x,y)= \\psi(x)-\\psi(x+y)$$\nThat follows from the definition of digamma function.", "\nAnd from the chain rule:\n$$\\frac{\\partial}{\\partial x} \\log B(x,y)=\\frac{1}{B(x,y)} \\frac{\\partial}{\\partial x} B(x,y)$$\n\n" ]

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[ "4-Star Enoch Smith, Jr. and Top Recruits to Watch on ESPN Friday Night\n\nDefensive tackle Enoch Smith, Jr. will get his shot to display his skill set on a national platform this Friday. ", "His Mount Carmel (Illinois) High School team will take on St. Rita (Illinois) at 8:30 p.m. EDT on ESPN3.", "\n\nAlthough Smith will be the big name coming into the game, several other players will be looking to showcase their talent. ", "The Caravan have a 4-0 football team that features several other players who are bonafide prospects.", "\n\nSt. Rita will host Mount Carmel in Chicago, and do not feel sorry for the Mustangs. ", "They're also 4-0 and have a pair of recruits who are committed to solid programs.", "\n\nMatt Byrne, OL—St. Rita (2014)\n\nAlthough he is a non-rated offensive lineman, Matt Byrne will be in charge of anchoring a Mustang offensive front versus a talented defensive line unit of Mount Carmel.", "\n\nByrne is 6'4\", 290 pounds and brings his lunchpail and hard-hat to work every night. ", "He has a great motor, knows how to use his size and solid strength at the point of attack and has the ability to be a mauler on running plays.", "\n\nIf St. Rita's offense is to have any success on Friday night, Byrne will have to play a key role in moving Mount Carmel's defensive linemen off their marks.", "\n\nHe has offers from Western Michigan and Central Michigan, per 247Sports.", "\n\nDeontae Brown, S—Mount Carmel (2014)\n\nThe Caravan's secondary will be led by 2-star Deontae Brown. ", "At 6'1\" and 195 pounds, Brown has good size for a defensive back, and also shows impressive range.", "\n\nHe displays good ball-location skills, athleticism and is most comfortable on top of the defense. ", "Brown has a knack for seeing things develop and firing to the ball to make a stop. ", "The Western Michigan commit looks like a potential diamond-in-the-rough prospect.", "\n\nIf he has a big game on Friday, he could see a few BCS schools show him more love.", "\n\nLamar Dawson, CB—St. Rita (2014)\n\nLamar Dawson is a 3-star cornerback for the Mustangs who plays with the mentality of a linebacker. ", "He is tough, physical, smart and instinctive on the field.", "\n\nDawson, who is 6'0\" and 190 pounds, has solid strength to press in man-coverage, but also has the intelligence and anticipation to factor in zone schemes. ", "He shows a willingness to squeeze from the perimeter on running plays, and has adequate straight-line speed.", "\n\nHe is committed to Syracuse, where it wouldn't be shocking to see him develop into a safety. ", "Dawson will have to have a big game for St. Rita to stay unbeaten on Friday night.", "\n\nNathan Oquendo, OL—Mount Carmel (2014)\n\nMount Carmel's offensive line will be led by 2-star blocker Nathan Oquendo. ", "Although he is undersized, as he barely reaches the 6'2\" mark, the 290-pounder has the kind of mentality and physical demeanor that offensive line coaches love.", "\n\nOquendo, who can play center or guard, has good quickness to get out of his stance and plays a little bigger than his listed size at the point of attack. ", "He flashes a powerful punch, can anchor versus massive rushers and has the leg-drive to move his targets out of alleys.", "\n\nKeep an eye on Oquendo during this game, as you will be watching an underrated player. ", "He has an offer from Purdue, according to 247Sports.", "\n\nTommy Mister, RB/S—St. Rita (2014)\n\nA 3-star prospect, Tommy Mister will command respect on the field on Friday night. ", "He will do his damage on offense as a running back, as he is a straight-line runner who has deceptive power.", "\n\nMister, who is 6'2\" and 185 pounds, has a long and lean frame that leads defenses to think he's a receiver or at least a shifty running back. ", "However, he routinely takes hand offs and slams into holes at straight angles with force.", "\n\nHe displays solid speed after a good burst, plus Mister has above-average instincts. ", "He is committed to Iowa State. ", "Do not be shocked to see Mister in the secondary.", "\n\nMatt Domer, RB—Mount Carmel (2014)\n\nMount Carmel's offense will certainly rely heavily on the legs of 3-star running back Matt Domer. ", "The Chicago native is a tough runner who doesn't back down from anyone.", "\n\nAt 6'0\" and 180 pounds, Domer has solid vision, good strength and the lateral quickness to skate to holes and burst upfield. ", "He can doesn't panic when in traffic, can carry a defender for a few extra yards after contact and has above-average speed in the open field.", "\n\nIt would not be surprising to see the Caravan coaches to get Domer involved in the passing game on Friday night, as the Illinois commit flashes adequate hands.", "\n\nSteven Richardson, DT—Mount Carmel (2014)\n\nHalf of an imposing defensive tackle tandem for Mount Carmel, 3-star prospect Steven Richardson will factor into St. Rita's game plan.", "\n\nHe is a stout 6'0\", 285-pounder who has good explosiveness at the snap. ", "Richardson can powerfully fire off the ball, anchor in the trenches and make a mess. ", "He will push pocket as a rusher, as his ability to convert speed into power is above-average.", "\n\nRichardson's toughness infuses energy into the rest of the Caravan's defense, which is just one of the reasons why the coaching staff at Minnesota is likely excited to have him committed.", "\n\nEnoch Smith, Jr., DT—Mount Carmel (2014)\n\nEnoch Smith, Jr. is a 3-star defensive tackle who 247Sports actually rates as a 4-star prospect on its own board. ", "He projects as a solid college player who will be regarded as a consistent performer.", "\n\nSmith, who is 6'2\" and 270 pounds, has a game that is centered around his strength and power. ", "He exhibits adequate quickness at the snap, but has the ability to use his hands to get under an offensive lineman's pads and walk them into the backfield.", "\n\nSt. Rita's offensive line will have some problems with Smith during the course of this game.", "\n\nHe can quickly read plays, anchor when the ball is coming at him or use his solid athleticism to pursue laterally down the line. ", "Smith is the top name playing into this contest, and the Michigan State commit should not disappoint.", "\n\nEdwin Weathersby is the College Football Recruiting Analyst for Bleacher Report. ", "He has worked in scouting/player personnel departments for three professional football teams, including the New York Giants and Cleveland Browns." ]

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0.85, "start": 3953 }, { "analysis_explanation": null, "end": 3976, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 3969 }, { "analysis_explanation": null, "end": 4066, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4061 }, { "analysis_explanation": null, "end": 4370, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4365 }, { "analysis_explanation": null, "end": 4415, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4403 }, { "analysis_explanation": null, "end": 4432, "entity_type": 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"SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4555 }, { "analysis_explanation": null, "end": 4602, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4585 }, { "analysis_explanation": null, "end": 4630, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4620 }, { "analysis_explanation": null, "end": 4724, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4714 }, { "analysis_explanation": null, "end": 4903, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4893 }, { "analysis_explanation": null, "end": 5039, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5030 }, { "analysis_explanation": null, "end": 5092, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5081 }, { "analysis_explanation": null, "end": 5097, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5094 }, { "analysis_explanation": null, "end": 5114, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5102 }, { "analysis_explanation": null, "end": 5120, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5116 }, { "analysis_explanation": null, "end": 5134, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5123 }, { "analysis_explanation": null, "end": 5139, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5136 }, { "analysis_explanation": null, "end": 5328, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5323 }, { "analysis_explanation": null, "end": 5633, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5628 }, { "analysis_explanation": null, "end": 5800, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5795 }, { "analysis_explanation": null, "end": 5913, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 5897 } ]

[ "Q:\n\nPutting Widget above a ListView in Flutter\n\nThe below code is working fine with me for calling and displaying data from firestore:\nreturn ListView(\n padding: const EdgeInsets.only(top: 20.0),\n children: snapshot.map((data) => _buildListItem(context, data)).toList(),\n);\n\nBut If I tried to put it in a column so I add another widget above it, it fails and give stack overflow:\nreturn Column(\n children: <Widget>[\n Text('Hellow'),\n ListView(\n padding: const EdgeInsets.only(top: 20.0),\n children: snapshot.map((data) => _buildListItem(context, data)).toList(),\n)]);\n\nA:\n\nYou need to put your ListView inside an Expanded widget so it knows how much space it can fill.", "\nreturn Column(\n children: <Widget>[\n Text('Hellow'),\n Expanded(\n child: ListView(\n padding: const EdgeInsets.only(top: 20.0),\n children:\n snapshot.map((data) => _buildListItem(context, data)).toList(),\n ),\n ),\n ],\n );\n\n" ]

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[ "Q:\n\nExtending classes and instantiation\n\nLet's suppose we have a RedBlack-Tree implementation which consists of 2 classes:\n\nTree - holds the pointer to the Node *root of the tree and defines all operations over the tree (Insert, Delete, etc)\nNode - a data storage, which holds pointers to Node *parent, Node *left, Node *right nodes and std::string key.", "\n\nThe Tree::Insert() has the following implementation:\nvoid Tree::Insert(const std::string &key)\n{\n Node *z = new Node(key);\n // adding node logic\n}\n\nNow the task: every node has to store the time of its creation.", "\nLimitations: the base tree implementation should be modified as less as possible and should contain details of specific extensions (so it should know nothing about the creation time property).", "\nMy thoughts: extending NodeWithTime : Node and adding unsigned int creation_time property.", "\nWhere I'm in stuck: how would we instantiate the node now?", "\nAny proposals?", "\nPS: it's neither a homework or a job task - I'm just learning c++ and data structures.", "\n\nA:\n\nIt's relatively simple. ", "First, the Node struct:\ntemplate<typename T> struct Node {\n Node(T t) : value(std::move(t)), time(RightNow()) {}\n T value;\n TimeType time;\n std::unique_ptr<Node> left;\n std::unique_ptr<Node> right;\n};\n\nA quick helper make_unique:\ntemplate<typename T, typename... Args> std::unique_ptr<T> make_unique(Args&&... args) {\n return std::unique_ptr<T>(new T(std::forward<Args>(args...)));\n}\ntemplate<typename T> void Tree<T>::Insert(T key) {\n auto z = make_unique<Node<T>>(std::move(key));\n // insert\n}\n\nFirst, I fixed your crappy new and delete and replaced it with smart pointers. ", "Then I also made your tree a template because who needs a tree that can only do one type? ", "Then I swapped out your const T& with a T so that it might live with move-only types.", "\nThen I just added a Time field and called RightNow() in the constructor. ", "The exact TimeType and RightNow() you use depends on your needs and what exactly you mean by \"time of it's creation\". ", "Are we talking about \"6th July, 2013\"? ", "Or a very-high-resolution clock? ", "In any case, these \"creation time\" details do not impact the tree.", "\nEdit: Wait, you want to have one tree type where only some of the nodes know the creation time? ", "Or just to alter the tree so that all the nodes know the creation time? ", "I did #2, but for #1, you could indeed simply inherit from Node. ", "To wit,\ntemplate<typename T> struct Node {\n Node(T t) : value(std::move(t)) {}\n T value;\n std::unique_ptr<Node> left;\n std::unique_ptr<Node> right;\n};\ntemplate<typename T> struct NodeWithTime : Node<T> {\n TimeType time;\n NodeWithTime(T t) : Node(std::move(t)), time(RightNow()) {}\n};\ntemplate<typename T> void Tree<T>::insert(T t) {\n std::unique_ptr<Node> nodeptr;\n if (IWantToStoreCreationTime)\n nodeptr = make_unique<NodeWithTime<T>>(std::move(t));\n else\n nodeptr = make_unique<Node>(std::move(t));\n // insert\n}\n\n" ]

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"recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 362 }, { "analysis_explanation": null, "end": 418, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_139620637004320", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 416 }, { "analysis_explanation": null, "end": 436, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_139620637004320", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 434 }, { "analysis_explanation": null, "end": 1131, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_139620637004320", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 1129 }, { "analysis_explanation": null, "end": 1202, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_139620637004320", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 1200 }, { "analysis_explanation": null, "end": 1234, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_139620637004320", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 1232 }, { "analysis_explanation": null, "end": 1334, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_139620637004320", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 1332 }, { "analysis_explanation": null, "end": 1394, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_139620637004320", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 1392 }, { "analysis_explanation": null, "end": 1419, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": "IpRecognizer_139620637004320", "recognizer_name": "IpRecognizer" }, "score": 0.6, "start": 1417 }, { "analysis_explanation": null, "end": 1537, "entity_type": "IP_ADDRESS", "recognition_metadata": { "recognizer_identifier": 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[ "Q:\n\nI need a figure and image in a fixed width container to span the entire width of browser window\n\nI'd like to solve this with CSS if possible, but if need be I can use a little jQuery. ", "\nIn my pen (link below) I need to get the figure.image-x-large (and image content within) to span the entire full width of the browser window, even though it is within a 1230px container. ", "I cannot modify the structure, but can add/take away classes where needed.", "\nI saw a similar issue here full-width div on a fixed-width page, but with that solution you cannot get the content below the image to flow properly. ", "The content below the full width image in my pen needs to flow properly below it.", "\nMy HTML:\n<article class=\"content\">\n <h3>This is a headline</h3>\n <p>Across the centuries brain is the seed of intelligence, citizens of distant epochs, consciousness Apollonius of Perga billions upon billions Drake Equation network of wormholes another world Sea of Tranquility intelligent beings preserve and cherish\n that pale blue dot citizens of distant epochs globular star cluster network of wormholes another world? ", "Vangelis Euclid hydrogen atoms tendrils of gossamer clouds quasar kindling the energy hidden in matter Cambrian explosion citizens of distant epochs\n dream of the mind's eye, a mote of dust suspended in a sunbeam rings of Uranus Orion's sword made in the interiors of collapsing stars. ", "How far away. ", "Across the centuries intelligent beings.</p>\n <p>Corpus callosum courage of our questions how far away rogue circumnavigated hearts of the stars realm of the galaxies gathered by gravity cosmos, quasar extraplanetary. ", "Of brilliant syntheses Drake Equation network of wormholes dispassionate extraterrestrial\n observer made in the interiors of collapsing stars dispassionate extraterrestrial observer hydrogen atoms culture astonishment another world paroxysm of global death dispassionate extraterrestrial observer prime number hundreds of thousands vanquish\n the impossible ship of the imagination. ", "Descended from astronomers trillion descended from astronomers. ", "Ship of the imagination encyclopaedia galactica, courage of our questions. ", "Are creatures of the cosmos?</p>\n\n <figure class=\"image-x-large\">\n <span class=\"img \">\n <img src=\"http://www.fillmurray.com/1250/750\" class=\"\" alt=\"\" width=\"940\" height=\"705\">\n </span>\n\n <figcaption>\n <div class=\"caption\">Franck Bacquet stands outside Ohm Force's first real office in 2006. ", "The signage advertises French Fries and kebabs.</div>\n <div class=\"credit\">&nbsp;Image: Ohm Force</div>\n </figcaption>\n </figure>\n\n <p>At the edge of forever as a patch of light with pretty stories for which there's little good evidence rings of Uranus tesseract radio telescope of brilliant syntheses, made in the interiors of collapsing stars astonishment Cambrian explosion prime number.", "\n The ash of stellar alchemy take root and flourish bits of moving fluff, citizens of distant epochs consciousness as a patch of light how far away. ", "Sea of Tranquility prime number inconspicuous motes of rock and gas rich in mystery a still more glorious\n dawn awaits galaxies great turbulent clouds citizens of distant epochs. ", "Astonishment vanquish the impossible Hypatia.</p>\n <p>Hundreds of thousands radio telescope, courage of our questions shores of the cosmic ocean dream of the mind's eye, kindling the energy hidden in matter Euclid. ", "The sky calls to us, a still more glorious dawn awaits! ", "Light years. ", "Descended from astronomers\n cosmic fugue, a billion trillion Flatland extraordinary claims require extraordinary evidence gathered by gravity birth Sea of Tranquility, Vangelis two ghostly white figures in coveralls and helmets are soflty dancing, birth tesseract, tingling of\n the spine, ship of the imagination hydrogen atoms, not a sunrise but a galaxyrise cosmic fugue and billions upon billions upon billions upon billions upon billions upon billions upon billions.</p>\n <p>The ash of stellar alchemy take root and flourish bits of moving fluff, citizens of distant epochs consciousness as a patch of light how far away. ", "Sea of Tranquility prime number inconspicuous motes of rock and gas rich in mystery a still more glorious\n dawn awaits galaxies great turbulent clouds citizens of distant epochs. ", "Astonishment vanquish the impossible Hypatia.</p>\n</article>\n\nMy SCSS:\n@import url(http://fonts.googleapis.com/css?family=Source+Sans+Pro:400,900);\n\nbody {\n font-family: \"Source Sans Pro\", sans-serif;\n line-height: 1.5;\n font-size: 18px;\n background-color: snow;\n}\n\n.content {\n width: 1230px;\n margin: 0 auto;\n padding: 0;\n overflow: visible;\n\n .story-content-width {\n padding-left: 200px;\n padding-right: 200px;\n width: 830px;\n position: relative;\n } \n\n h3, p {\n @extend .story-content-width;\n }\n\n h3 {\n font-size: 25px;\n color: SteelBlue;\n }\n\n figure.image-x-large {\n display: table;\n width: 100%;\n margin: 0;\n\n .img {\n img {\n width:100%;\n height: auto;\n }\n }\n\n figcaption {\n text-align: center;\n font-size: 14px;\n border-bottom: 1px solid powderblue;\n padding-bottom: 15px;\n }\n }\n}\n\nMy PEN\nThank you in advance!", "\n\nA:\n\nThe first part is actually pretty simple since there are units that handle the browser window. ", " The second part is a bit more difficult since you'll need to move the image to the edge of the window. ", " Since you have position:relative; on a parent of the image, it won't work with position:absolute;. ", " Instead try this:\nfigure.image-x-large {\n width:100vw;\n margin-left:50%;\n transform:translate(-50%);\n}\n\nThis'll work until the viewport hits the width of your container, then the image will shrink. ", " You'll have to put in a media query to stop that from happening.", "\n@media screen and (max-width:1230px){\n figure.image-x-large{\n margin:0;\n transform:translate(0);\n }\n}\n\n" ]

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[ "Pages\n\n02 November, 2011\n\nBook Review: The Lion Of Mortimer by Juliet Dymoke\n\nPublished in 1979, this short novel about Edward II - it's less than 200 pages long - is out of print, but easily available in online bookshops at a very low price. ", "It's the third volume in Dymoke's The Plantagenets series, after A Pride of Kings and The Royal Griffin (about Edward II's great-aunt Eleanor, who married Simon de Montfort) and before Lady of the Garter (about his niece Joan of Kent). ", "I adore this tacky cover of Lion of Mortimer, and this one of Lady of the Garter, which is the copy I have of the book.", "\n\nThe novel's title is confusing and puzzles me somewhat, as it has little to do with the Mortimers, and features instead Edward II's friend Sir William Montacute (died 1319), his son of the same name who is the future earl of Salisbury, and his wife Elizabeth de Montfort as viewpoint characters. ", "Lion opens in May 1306, just before the mass knighting of nearly 300 men including Edward of Caernarfon and the elder William Montacute, and closes just after Edward III's arrest of Roger Mortimer at Nottingham Castle in October 1330 (as novels about Edward II almost always do).", "\n\nThe Lion of Mortimer is a reasonably good place for a reader keen to learn more about the reign of Edward II to start: it's a fairly basic - hardly surprising, given its lack of length - overview of the era with little in-depth characterisation, and a decent and easy to follow (though dated) narrative of the main events. ", "My favourite scene of the novel is the first one: William Montacute, decked out in all his court finery, walks down to the river Gade near Langley, and spots \"a solitary man rowing a small boat strongly against the current, muscled arms pulling well at the oars, broad shoulders moving smoothly under peasant fustian, the May sunshine glinting on a head of thick curling russet hair.\" ", "This turns out to be the prince of Wales himself, Edward of Caernarfon, who is further described in the scene as a \"tall, healthy-looking young man\" and \"passionately addicted to physical exercise\"; a lovely introduction to his eccentricity and unusual rustic hobbies, and the enormous strength remarked on by chroniclers.", "\n\nEdward and William proceed to a vividly-described feast at his manor of Langley, where many of the important players are introduced to the reader: Roger Mortimer, the young lord of Wigmore, who has \"an air of suppressed intensity\" and is \"not a man to cross\"; Hugh Despenser, very young and insignificant as yet, though already heartily disliked by Mortimer; and of course Piers Gaveston, who \"came from Gascony and knew how to dress, how to carry himself; he had a natural grace but there was an insolent turn to his head, an arrogance in his smile.\" ", "Edward's face glows whenever he looks at Piers. ", "Over the next few pages we also meet, among others, Piers' nemesis the earl of Warwick - whom he mocked as the Black Hound of Arden - who has \"a habitual and uncontrollable dribble of saliva trickling down his chin,\" Edward's cousin and enemy Thomas of Lancaster, loathed by his wife Alice de Lacy, and Edward's queen Isabella, a beautiful but haughty young woman with a habit of writing to her father every time anything annoys her, which is pretty often.", "\n\nUnfortunately, the rest of the novel doesn't entirely live up to the promise of its excellent beginning. ", "It moves at a breakneck speed; the first fifty pages cover the period from May 1306 to Edward's coronation in February 1308, which leaves only 140 pages for Dymoke to write about the period up to October 1330. ", "Piers Gaveston goes into exile and returns with dizzying rapidity, the queen is pregnant and Edward - yawn - abandons her at Tynemouth to save Piers, Piers dies and Edward grieves for half a page, then suddenly it's Bannockburn, then suddenly it's 1318 and the king and queen have three children. ", "And so on. ", "Many of the most interesting and important events are not dramatised: for instance, we see Edward's son the young duke of Aquitaine through the eyes of his friend William Montacute the younger in Hainault in September 1326 just before the invasion of England, and the next scene is Edward II in captivity at Kenilworth Castle months later, grieving for the Despensers, whose executions we never saw. ", "Some pages later at Berkeley, Edward is foully mistreated and then murdered by red-hot poker, scenes I find very hard to read. (", "I console myself with the thought that this mistreatment almost certainly never happened.)", "\n\nThere's little original in Juliet Dymoke's re-telling of Edward II's story, but it does cover the period well, and of course it's not her fault that scholarship has moved on considerably since she wrote it. ", "The portrayal of Edward as a man totally unsuited to his position, unable to change and unable to see what is wrong with the way he behaves, is well-written and plausible, and fits in with what we know of him. ", "I found Isabella irritating more than anything else, but then, I'm not generally given to finding Isabella sympathetic or likeable, so the portrayal of her may well affect other readers entirely differently. ", "There are some lovely vivid scenes in the novel, with Piers Gaveston's jousting tournament at Wallingford in December 1307 and Edward meeting visiting dignitaries while digging a pond at Langley stripped to the waist and muddy being particular favourites of mine. ", "I also enjoyed seeing the story through the eyes of people who rarely appear in fiction about this era. ", "In short, The Lion of Mortimer is a quick easy journey through Edward II's turbulent reign and is well worth a read, especially as you can pick it up for a mere penny on Amazon.", "\n\n5 comments:\n\nI picked it up at amazon for a few pennies just this summer. ", "Not much depth, but a better read than Dogherty. ", "Besides, I wasn't aware of Elizabeth de Montfort as William's wife. ", "I think I'll have to research Montacutes and write a novel about Joan of Kent myself, it looks like a must nowadays)). ", "Everybody does...\n\nI also picked it up last year from Amazon, and haven't got past the beginning. ", "The King's picture on the cover looks more like one of the Stuarts - James 1st - with the clothing in keeping with that period, especially the ruff:>\n\nEdward's titles, 1312\n\nEdward, par la grace de DIEU, Roi d’Engleterre, seignur d’Irlaunde, ducs d’Aquitaine, & conte de Pontif & de Monstroil\n[Edward, by the grace of GOD, King of England, Lord of Ireland, Duke of Aquitaine, and Count of Ponthieu and Montreuil]\n\nEdward II's coronation oath: translation\n\nSire, will you grant and keep and by your oath confirm to the people of England the laws and customs given to them by the previous just and god-fearing kings, your ancestors, and especially the laws, customs, and liberties granted to the clergy and people by the glorious king, the sainted Edward, your predecessor?", "\nI grant and promise them.", "\nSire, will you in all your judgments, so far as in you lies, preserve to God and Holy Church, and to the people and clergy, entire peace and concord before God?", "\nI will preserve them.", "\nSire, will you, so far as in you lies, cause justice to be rendered rightly, impartially, and wisely, in compassion and in truth?", "\nI will do so.", "\nSire, do you grant to be held and observed the just laws and customs that the community of your realm shall determine, and will you, so far as in you lies, defend and strengthen them to the honour of God?", "\nI grant and promise them.", "\n\nPenny of Edward II's reign\n\nTomb of Edward II\n\nAmouncement of the birth of Edward III, November 1312\n\nIsabella, by the grace of God, Queen of England, Lady of Ireland, and Duchess of Aquitaine, to our well-beloved the Mayor and aldermen and the commonalty of London, greeting. ", "Forasmuch as we believe that you would willingly hear good tidings of us, we do make known to you that our Lord, of His grace, has delivered us of a son, on the 13th day of November, with safety to ourselves, and to the child. ", "May our Lord preserve you.", "\n\nBerkeley Castle, scene of Edward II's imprisonment\n\nLetter of Queen Isabella to Edward II, 1314\n\nMy very dear and dread Lord, I commend myself to you as humbly as I can. ", "My dear Lord, you have heard how our seneschal and our controller of Ponthieu have come from Ponthieu concerning our affairs; ...I beg you, my gentle Lord, that by this message it may please you to request your chancellor by letter that he may summon those of your council to him and take steps speedily in this matter, according to what he and your council see what is best to do for your honour and profit....May the Holy Spirit keep you, my very dear and dread Lord.", "\n\nThe Vita Edwardi Secundi on Edward II and Piers Gaveston\n\nI do not remember to have heard that one man so loved another. ", "Jonathan cherished David, Achilles loved Patroclus. ", "But we do not read that they were immoderate. ", "Our King, however, was incapable of moderate favour, and on account of Piers was said to forget himself, and so Piers was accounted a sorcerer." ]

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[ "Choleretic actions of iridoid compounds.", "\nThe intravenous administration of 50 and 100 mg/kg of genipin (GP), gardenogenins (GAR-G), deacetylasperulosidic acid methylester genins (DAM-G), and scandoside methylester genin (SSM-G) exhibited the bile acid-independent choleretic actions. ", "The action of DAM-G was stronger than the actions of other compounds tested. ", "The choleretic action of SSM-G was milder, but longer lasting than those of GAR-G and DAM-G." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Talk:Feuerroter Pfeil und Bogen\n\nAd blocker interference detected!", "\n\nWikia is a free-to-use site that makes money from advertising. ", "We have a modified experience for viewers using ad blockers\n\nWikia is not accessible if you’ve made further modifications. ", "Remove the custom ad blocker rule(s) and the page will load as expected.", "\n\nRules\n\nHello there, welcome to Feuerroter Pfeil und Bogen's talk page! ", "Whilst you are here, we would like you to take a quick look at some rules, failure to follow these rules may result in a block, you have been warned.", "\n\nSign your comments with ~~~~\n\nNo Spamming.", "\n\nProfanity should be kept to a minimum\n\nMake it clear and readable\n\nEnglish only\n\nNo spoilers!", "\n\nPut it under a new heading for a new topic (e.g. \"Titan shifting.\")", "\n\nAlways follow the rules\n\nSing-along English\n\nI would like to know - is the sing-along English also known as English dub? ", "Is it official?", "\n\nA bit of clarification! ", "The Jiyuu e no Shingeki lyrics booklet says that the first line is actually \"Seid ihr das Essen? ", "Nein, wir sind der Jäger!\" (", "which translates to \"Are you the food? ", "No, we are the hunter!\") ", "Technically, 'wir sind *der* Jäger' is grammatically incorrect, but I assume it was chosen to emphasize the groups strong sense of unity.", "\n\nThe text on the scan is stylized and smudged, but I believe you can still read the lines.", "\n\nFunimations \"Sind Sie das Essen? ", "Nein, wir sind der Jäger!\" (\"", "Are you the food? ", "No, we are the hunter!\") ", "is therefore wrong. (", "note that \"Sie\" with a capital S is the formal way to say 'you')\n\n\"Sie sind das Essen und wir sind die Jäger!\" ", "is grammatically correct (and honestly, as a native speaker, that's what I heard when I first listened to the song too), but apparently it's not what's being said in the opening.", "\n\n(I'm new to the wiki, so I'm very sorry if I made any mistakes! ", "Thank you for reading)\n\nHey! ", "I'm sorry, I should've asked you about your edit before undoing it. ", "Thanks for asking to discuss this properly! ", "The lyrics booklet doesn't say anything about this part, as far as I can see. ", "I googled but couldn't find any other trustworthy sources- the one forumpost I could find your version on was fanmade, though. ", "I relistened to the intro, but I couldn't make out anything you added. ", "The sounds seem too short to be \"Panik\" and \"Armut\". ", "The grammar is poor as well: I believe you'd usually say \"Nur Panik, doch wir sind Jäger\"/ \"Nur Armut, doch wir sind Jäger!\", ", "but even that looks off. ", "I found it strange that the rest of the official german lyrics would keep a correct sentence structure except for that bit. ", "That being said, the version I changed this back to wasn't my addition. ", "It made sense to me, so I stuck with it (even if I can hear \"Ha, ha, ha, ha, ha, Attack on Titan..\" as well- but that doesn't fit the end of the song). ", "If you do have any official sources on this, I'd be very grateful if you shared them!", "\n--\nMinyaa (talk) 02:27, July 26, 2013 (UTC)\n\nThere are no official sources for that and that forum post you quoted was actually me as well. ", "But the \"ha ha ha ha\" didn't have any official source and was left there, as well. ", "And if you really only wanted strictly official lyrics, then you would have to remove the \"Angriff auf die Titanen, der Junge von einst...\" part as well, because that is not listed in any official lyrics, as far as I know. ", "Also regarding consistentency of grammar, I have to disagree. ", "Have you seen the lyrics of Jiyuu no Tsubasa? \"", "Mensch, Sie welche sind\" doesn't sound too correct either. ", "And I can hear \"Armut\" and \"Panik\" very clearly (also while the German native singer sings \"Feuerroter Pfeil und Bogen\", you should at least hear that before the two \"wir sind Jäger\" there are two different things spelled), but that is not a matter that can be decided objectively I guess. ", "So, to say the truth, I don't know what to do now. ", "To say the least the part we are discussing is nothing more than a background choir, so in case of doubt, it can always be removed completely. ", "The only thing I will not accept, is that some anon user simply puts in \"ah ah ah ah ah\" there and copy pastes it to the other places, while ignoring that you can clearly hear \"Jäger\" 4 times in the last part, but he simply wrote it as if it was just 2 times. ", "So I at least would like to never see that \"ah ah ah\" part again. ", "Also I feel like there should be more people involved into this discussion to resolve it.", "\n\nGood to know that it was you. ", "I was referring to Guren no Yumiya only, not Jiyuu no Tsubasa, since that's not the topic of our discussion. ", "There definitely is messy german in the latter, but the first one seems fine to me for the most part. ", "It's correct that the german narration is not in the official lyrics booklet, but the words are definitely clear enough. ", "I don't see any reason to remove them. ", "I know that the other anon's version didn't have any official sources either; I said so myself. ", "The only difference between the parts before the two \"wir sind Jäger\" I can hear is a change in pitch; I'm also still of the opinion that the sounds are too short and smooth to contain two syllables each. ", "The pronounciation is simply not clear enough to confirm either version, so I can agree to disagree. ", "I believe it'd be best to remove the choir's lines entirely for now. ", "I have no control over what any other anons decide to do; it unfortunately seems as though people don't check the talk pages too often. ", "I'm afraid it'll be difficult to get more people to discuss this, especially ones who speak German well enough.", "\n\nI have only skimmed through your messages so all I'm going to say now is that you shouldn't count on correct grammar also being correct lyrics. ", "Their knowledge of German aside, they may have altered the words and/or structures to make the lyrics sound better. ", "So, is there any way to figure out which lyrics are the correct one? ", "Like, have they provided them with the soundtrack release, perhaps? ", "Frankly said, it's tiresome seeing the lyrics being edited back and forth every day :x Miskos3Talk 18:02, July 26, 2013 (UTC)\n\nHello! ", "I have scans of the official booklet, but the choir's lines weren't added to the rest of the lyrics. ", "As far as I can see, there are no other official sources that confirm either interpretation for now. ", "I've removed the problematic lines from the wikia, I hope that's okay! ", "I didn't see your response before finishing. ", "--Minyaa (talk) 18:32, July 26, 2013 (UTC)\n\nI agree that that is probably the best solution for now. ", "I doubt we will get anything new regarding the lyrics and I am still convinced of my own interpretation, but I guess it is better to keep it to myself for now and ask others about their opinion first. ", "I still notice a little inconsistency though. ", "Sometimes it is \"wir sind die Jäger\" (we are the hunters) and sometimes it is \"wir sind der Jäger\" (we are the hunter). ", "The former is a little more grammatically correct, as it is the plural form (which fits with \"wir\" which means \"we\"). ", "The latter seems less correct because it doensn't sound like \"der\" at all when listening to it and it also shifts the meaning into a more metaphorical one. ", "In order to be viable, the singular form needs an explanation like, for example, the people (\"we\") are a collective/a group. ", "With that it becomes viable, even though less credible. ", "On the other hand the version that is seen in the booklet is clearly \"Wir sind der Jäger\". [", "I guess \"it is grammatically consistent\" does not apply to this after all]\n\nWhatever we chose at the end, it should at least be consistent. ", "So we either take \"die Jäger\" or \"der Jäger\" from beginning to end. ", "NeoSuperior (talk) 21:24, July 26, 2013 (UTC)\n\nAh, I hadn't noticed that those parts still say \"die\". ", "In my opinion it'd be best to go with \"Wir sind der Jäger\" to stick with the official lyrics all the way through. ", "Minyaa (talk) 21:53, July 26, 2013 (UTC)\n\nSorry, but I have to restart the discussion. ", "I am not so sure if we can use the booklet as a valid source anymore. ", "The reason however is on the right side of the booklet, the Jiyuu no Tsubasa part. ", "So to continue that discussion I would be glad if you could go to the Jiyuu no Tsubasa talk page, thank you!", "\nNeoSuperior (talk) 00:03, July 28, 2013 (UTC)\n\nThe way that it is now, I think, may be conceptually faulty. ", "Why is it referring to \"you\" in the question but then it refers to the collective group (we) in the contradiction? ", "It doesn't make much sense to me, not to mention that even if we assume grammatical incorrectness, the Japanese still have a sense of intonation-- that line as it is in the song sounds like one sentence. ", "No matter how much I replay it, the place where the \"nein\" is supposed to be sounds like an \"und\", and the two words are pretty distinct in sounding. ", "Then again, this is coming from someone with ears untrained in German, and in the song, they pronounce \"sie\" like \"say\" when it's supposed to be prounced like \"see\". ", "Seg162 (talk) 16:56, August 13, 2013 (UTC)\n\nThe anonymus who put the \"Ah ah ah\" part in the lyrics was me, an native german speaker.", "\n\nThere is nothing with \"Armut\" or \"Panik\" in the song.", "\n\nI listen to the song more and more times, friends of me too, and all of them, was the same opinion like me.", "\n\nAnd \"die Jäger\" is right, because \"wir sind Jäger\" is \"we are hunter\" and \"die\" means she and in plural, it's for more persons.", "\n\nSry for my bad english, it isn't really good, but I hope you understand what I mean.", "KiaraKitsune (talk) 10:00, July 29, 2013 (UTC)\n\nI'm a native german speaker as well and I absolutely agree with you! ", "But as we've already established above, it's best to remove it since we can't guarantee that \"Ah ah ah\" is what's being sung. ", "It's also true that \"die Jäger\" would be correct, but the official lyrics say \"der Jäger\". ", "Right now, our best source is the booklet, but if new trustworthy info pops up, we can still edit the article. ", "Minyaa (talk) 14:46, July 29, 2013 (UTC)\n\nRemember that the band is Japanese, therefore it doesn't mean that the German parts are supposed to be grammatically correct. ", "Miskos3Talk 15:07, July 29, 2013 (UTC)\n\nI can confirm (as a native german) that I hear the same \"Sie sind das Essen und wir sind die Jäger\". ", "I also understand that it can be very difficult to hear, for untrained ears. ", "AixonXIV (talk) 12:45, October 30, 2013 (UTC)\n\nEnglish versions still incomplete\n\nI noticed that the english versions are still only the tv-size version. ", "Did anyone find a translation that can be used for the complete version, yet? ", "NeoSuperior (talk) 21:24, July 26, 2013 (UTC)\n\nmarchen-v-friedhof did a complete translation, but I'm hesitant to edit the versions that already exist. ", "I'd suggest adding a new section? ", "I can't tell how accurate the Japanese -> English parts are, but a few words of the German -> English translation could be changed to stay closer to the original lyrics. ", "Minyaa (talk) 22:22, July 26, 2013 (UTC)\n\nIn retrospect, I really should've asked to be given the green light beforehand, I'm sorry. ", "orz I added the English translation I linked above (I only adjusted the german parts a tiny bit) and fixed a few incorrect edits from before. ", "Minyaa (talk) 15:46, July 29, 2013 (UTC)\n\nOfficial name\n\nThe official name of this song (as titled by REVO) is \"Feuerroter Pfeil und Bogen\", therefore the article should be moved to that name (while keeping the redirect page). ", "hfc2X 06:00, August 31, 2013 (UTC)\n\nI know, but that's why the redirect should be kept. ", "The official name of the song is Feuerroter Pfeil und Bogen, not Guren no Yumiya. ", "That's the title the author himself gave it, even though we may not like it. ", "hfc2X 19:58, August 31, 2013 (UTC)\n\nConfirmed: The anime opening credits clearly state the song's name: \"Feuerroter Pfeil und Bogen\". ", "The only reason not to change the name would be due to possible confusion that could arise, but with a redirect that would not be a problem. ", "NeoSuperior (talk) 23:08, September 5, 2013 (UTC)\n\nHelp with Memorization\n\nI am trying to memorize this song (full version) in either japanese or english. ", "I aam having trouble pronouncing the words for the japanese version and the syllables don't fit in the english version. ", "help? - ", "Leonhart322Leonhart322 (talk) 01:07, January 16, 2016 (UTC)\n\nannie laughing like crazy... SO sad they took this out of english dub. :(", "\n\nIdeally, this is not what the talk pages are for, regardless, I'm not sure if there's anything we can do to help you memorize the song. ", "All I can suggest is that you slowly and repeatedly listen to the song until you've got it memorized. ", "Also, the original lyrics are Japanese and a little German, so of course the English translation won't fit lyrically with the beat of the song. ", "The English translation is more for English fans to understand what's being said. ", "If you'd rather sing this song in English I suggest you reword the song with as close a meaning to the original, but still with the same set up as hearing it in the original version.", "\n\nI also moved this to its own section since it was unrelated to where it was placed. ", "EternalLocket (talk) 01:52, January 16, 2016 (UTC)" ]

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[ "Computing at Chaos Manor: Pournelle's on Wi-Fire\n\nJerry Pournelle's Chaos Manor is on fire! ", "Wi-Fire, that is.", "\n\nLaptops like my Lenovo ThinkPad have pretty good built-in wireless capabilities, but the antenna system puts a limit on distance.", "\n\nI solved that problem by getting better range -- and faster connectivity -- with a Wi-Fi receiver/antenna system called Wi-Fire. ", "Made by hField Technologies, Wi-Fire works very well indeed. ", "Here it is connected to my Thinkpad.", "\n\nWi-Fire is an external directional Wi-Fi receiver and antenna that connects through USB. ", "It extends the useful Wi-Fi range considerably. ", "According the materials, it'll work at ranges up to 1,000 feet. ", "I haven’'t tried that, but it definitely added at least a hundred feet to my local Wi-Fi range.", "\n\nAt first, I was a bit concerned about installing it with the ThinkPad. ", "The ThinkPad has its own Wi-Fi management system, which sometimes argues with the Windows 7 Wi-Fi management system. ", "I thought adding yet another system might be a problem. ", "It wasn't, as it turned out, and there's a story I have about that.", "\n\nFirst, I unplugged the Ethernet connector from my ThinkPad and connected to my local Wi-Fi net with the ThinkPad’s wireless. ", "When that was working properly, I turned off ThinkPad Wi-Fi. ", "Then I let the Wi-Fire software disk auto-run to install Wi-Fire. ", "When that was done, I plugged the Wi-Fire antenna in.", "\n\nGetting it to run was tricky: clicking and doubleclicking the Wi-Fire icon did essentially nothing. ", "Eventually, I did a right click on the Wi-Fire icon -- and I saw a menu that included the option to Run as Administrator. ", "That did it.", "\n\nSuddenly, the system showed me an astonishingly large list of potential Wi-Fi sites, most of which I never knew existed. ", "One was my own. ", "Telling Wi-Fire to connect to that resulted in a demand for the password. ", "Seconds later I was connected. ", "I tested it out with Firefox. ", "Everything ran fast and well.", "\n\nJust to be sure, I closed the Wi-Fire software and turned on the ThinkPad’s wireless. ", "That worked as expected, too. ", "It turned out the ThinkPad doesn’t care if there's a Wi-Fire so long as you're not actually running its software.", "\n\nWi-Fire does pretty well at what it's designed to do: it makes good connections to Wi-Fi networks that would otherwise be out of range entirely and improves connection speed with marginal Wi-Fi locations. ", "It works with Windows, the Mac and various forms of Linux.", "\n\nIf you use Wi-Fi out on the road, Wi-Fire is a good tool to have in your road warrior kit. ", "It doesn't cost too much -- under $50 -- and except for my initial installation issues, I think it works great. ", "I recommend it.", "\n\nJerry Pournelle is BYTE's senior technologist. ", "An award-winning novelist and columnist, he's now back at BYTE with Computing at Chaos Manor. ", "Find more of Jerry's stuff at www.jerrypournelle.com. ", "Email him a question or comment at Jerry@BYTE.com." ]

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[ "AP\n\nLAWRENCE, Mass. — Russ Conway, a hockey writer who was a Pulitzer Prize finalist in 1992 for his stories about corruption in the NHL Players Association that helped bring down union head Alan Eagleson, has died. ", "He was 70.", "\n\nHis death was reported by the Eagle-Tribune of Lawrence, Massachusetts, where he had started at the age of 18 and later served as sports editor.", "\n\nA longtime Boston Bruins beat writer, Conway published a series of articles that exposed Eagleson's lucrative conflicts of interest as the union boss, player agent and organizer of international tournaments. ", "Conway's reporting spawned investigations in both the United States and Canada that resulted in Eagleson serving six months in prison and forfeiting his Order of Canada.", "\n\nThe Hockey Hall of Fame kicked Eagleson out and gave Conway its Elmer Ferguson Memorial Award in 1999 for bringing honor to journalism and hockey." ]

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[ "Chyler Leigh: Daughter Suffers From Febrile Seizures\n\nActress Chyler Leigh knows her way around emergency rooms — both real and make-believe.", "\n\nThe Grey’s Anatomy star says her experiences as a mom-of-three have left her well-versed in the medical field, beginning with daughter Taelyn Leigh, 3½, who suffers from febrile seizures.", "\n\n“The first time it happened, I was at home and had no idea what was going on,” Leigh, 28, explains to WebMD Baby. “", "Most seizures end after a few minutes, but hers went on for 25 minutes.”", "\n\nAfter riding in an ambulance to the nearest emergency room, Taelyn was fine.", "\n\n“It was a virus, and the fever just spiked too high too fast, but it’s scary,” Leigh recalls. “", "Any time she’s warm, we watch her.”", "\n\nSon Noah Wilde, 6, has had his share of health scares as well.", "\n\n“He busted his chin on the ground when he decided he wanted to slide like a penguin,” Leigh reveals. “", "He smacked his head on the ground when he was trying to spin and got his pants stuck under his feet. ", "He wound up with a huge goose egg that looked like his brains were coming out.”", "\n\nWith so much going on at work, and at home — Leigh and husband Nathan Westwelcomed daughterAnniston Kae, 1, last May — she admits she often feels like “the oldest 2[8]-year-old on the planet.”", "\n\n“I work, and I’m a full-time mom, and it’s hard for me to sit down and relax because it’s like, ‘Crap, there’s something I’m forgetting,'” she notes.", "\n\nNot her marriage! ", "Leigh says that she and West, an actor, work hard to keep the spark alive.", "\n\n“Even though you’re parents, you’re still a couple,” she says. “", "You need to take time and be together, talk about your dreams and plans, and just be in love.”", "\n\nLOVE her! ", "I wish there was more of her on this site. ", "I can definitely relate to her (well not the whole successful actress thing!)", "\n\nHea\non May 14th, 2010\n\nWe have kids at work who get febrile seizures sometimes. ", "It’s no fun for either them or me but their parents leave paracetamol for them and we try to give it as quick as possible once we notice a fever coming on. ", "It usually works well.", "\n\nAimee\non May 14th, 2010\n\nI also feel like the oldest 28 year old on the planet. ", "I have three little girls 5, 3, and almost 1. ", "We just took my 1 year old to the ER a couple of weeks ago when her fever spiked 105.6. ", "She also had febrile seizures. ", "It is very scary! ", "No one ever said being a mom was going to be boring! ", "LOL There is always something.", "\n\nSarah\non May 14th, 2010\n\nWell if it is any consolation – I feel like the youngest 29 year old with no boyfriend in site even. ", "I think deep down we all want to get married and procreate. ", "Some just do it sooner than others…no worries (yet).", "\n\nhayley\non May 14th, 2010\n\ni got married at 21 and my first baby at 22 and my second at 23 , now 25 i honestly feel like i’m 80 although both babies are healthy we had some horrible horrible scares with them that have aged me by at least 10 years each time, the worse had to be when my daughter was 6 days old we all caught th nora virus, poor thing was so ill and ended up back in hospital, so ill and so tiny she went from 6 pound 1 onz to just 5 pound 2 :( and throwing up for 3 days , 6 days after A C section was no walk in the park either lol\n\nbut still the best job in the world xxxxxxxxxxxxxxxxxxxx\nwe are all in the same tired boat together xxxxxxxxxxx :D x\n\nLuna\non May 14th, 2010\n\nI married at 22, was 24 when I had my first, and 27 when I had my set of twins. ", "By 32, I had 5 kids! ", "I feel like I’m 90! ", "All my friends have like one kid or two kids and it’s like “yeah I’ve got five.” ", "The worst health scare was when my twins were born. ", "They were preemies and had to be in the NICU for almost two weeks, which considering how long it could have been isn’t too bad, but for their mommy, was terrifying. ", "Now they’re healthy. ", "The next scariest was my oldest broke his arm. ", "Motherhood isn’t boring, that’s for sure. ", "I really feel for Chyler. ", "Especially having a child younger than the sick one! ", "Good luck to you Chyler, Nathan, Noah, Taelyn, and Anniston.", "\n\nmolly\non May 16th, 2010\n\nSounds like for 28 she has her head on pretty straight- not to mention all that she seems to juggle and seems to be doing it with gusto and grounded-ness! ", "And agreed- when you become parents it is hard to not remember you were a couple first. ", "While children’s immediate needs need to be met first, parents need to remember that their relationship should be front and center. ", "Because happy parents and happy unions make for happy children. ", "The martyr-dom of taking time for yourself and as a couple should be ignored knowing that when you are taking some time out it is for your children as much as it is for you. ", "Good for Chyler Leigh to do so for her family!", "\n\nmolly\non May 16th, 2010\n\nI just read Sarah’s post. ", "Glad you don’t have worries yet. ", "I am guessing 29 seems old to not have a marriage or kids if you have friends around who are married and/or have children. ", "But enjoy this time now and do the things you want to and utilize the freedoms your life possess’s now! ", "I wouldn’t change my life now being married and having a child, this stage is amazing and so rewarding for me NOW! ", "But I am also glad I waited a bit to travel, meet people, have an education etc and gain perspective and invaluable lessons first. ", "Enjoy what is in your life now and know that if you take advantage of who you are now, the future will be so rewarding to you wherever it leads you!", "\n\nMelody\non May 17th, 2010\n\nI’m 33 now but had 4 kids by the time I was 28 (my 2nd and 3rd were twins) but I don’t feel 80! ", "They keep me young. ", "I still feel like I’m a teenager!", "\n\nEm\non May 17th, 2010\n\nWait, is her son’s name Noah Wilde West? ", "Too funny!! ", "My son has had a couple febrile seizures due to a high spiked fever but has outgrown them (we hope). ", "I’m sure her daugher will be fine although it is pretty scary if you don’t know what’s happening. ", "All the best to her family.", "\n\nAlexandra\non May 17th, 2010\n\nI suffered from a febrile seizure when I was 10 months old. ", "Since then I have suffered from a heart condition and when i get a really bad fever I hallucinate. ", "Whenever a child gets fever of any kind it is best to do anything possible to cool them down. ", "Seizures are painful experiences that no matter what affect your life in ways you don’t expect. ", "I am now a mother myself and because of my past I watch my daughter’s health like a hawk. ", "Remember to watch and pay attention.", "\n\nMegan\non May 17th, 2010\n\nI’m sure it’s very scary any time your child is sick or injured. ", "I would probably freak out if my kid had a cold :)\n\nBrandy\non May 17th, 2010\n\nMy son had 2 febrile seizures in a row when he was 1 year and 9 Months old. ", "I have to say that was the scariest thing I had ever been through. ", "I can’t imagine how he felt. ", "Although the EMT’s weren’t very concerned, I sure was so we took him to the ER where they ran numerous tests on him and I was sure they traumatized him for life (which he is not). ", "I hope and pray that my son and Chyler’s daughter NEVER have another seizure again!" ]

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[ "Metabolic profiling of glucosinolates, anthocyanins, carotenoids, and other secondary metabolites in kohlrabi (Brassica oleracea var. ", "gongylodes).", "\nWe profiled and quantified glucosinolates, anthocyanins, carotenoids, and other secondary metabolites in the skin and flesh of pale green and purple kohlrabis. ", "Analysis of these distinct kohlrabis revealed the presence of 8 glucosinolates, 12 anthocyanins, 2 carotenoids, and 7 phenylpropanoids. ", "Glucosinolate contents varied among the different parts and types of kohlrabi. ", "Glucoerucin contents were 4-fold higher in the flesh of purple kohlrabi than those in the skin. ", "Among the 12 anthocyanins, cyanidin 3-(feruloyl)(sinapoyl) diglucoside-5-glucoside levels were the highest. ", "Carotenoid levels were much higher in the skins than the flesh of both types of kohlrabi. ", "The levels of most phenylpropanoids were higher in purple kohlrabi than in pale green ones. ", "trans-Cinnamic acid content was 12.7-fold higher in the flesh of purple kohlrabi than that in the pale green ones. ", "Thus, the amounts of glucosinolates, anthocyanins, carotenoids, and phenylpropanoids varied widely, and the variations in these compounds between the two types of kohlrabi were significant." ]

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[ "Nebraska Supreme Court Online Library\nwww.nebraska.gov/apps-courts-epub/\n05/04/2018 12:10 AM CDT\n\n\n\n\n - 64 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\n\n\n\n Jayson H. Tilson, appellant, v. Erica M. Tilson,\n appellee, and K imberly L. H ill,\n Intervenor-appellee.", "\n ___ N.W.2d ___\n\n Filed February 16, 2018. ", " No. ", "S-17-468.", "\n\n  1.", "\t Jurisdiction: Appeal and Error. ", "When a jurisdictional question does\n not involve a factual dispute, its determination is a matter of law, which\n requires an appellate court to reach a conclusion independent of the\n decision made by the lower court.", "\n   2.", "\t ____: ____. ", "Before reaching the legal issues presented for review, it is\n the duty of an appellate court to determine whether it has jurisdiction\n over the matter before it.", "\n  3.", "\t Jurisdiction: Final Orders: Time: Appeal and Error. ", "To vest an\n appellate court with jurisdiction, the notice of appeal must be filed\n within 30 days of the entry of the final order.", "\n  4.", "\t Final Orders: Appeal and Error. ", "Under Neb. Rev. Stat. § ", "25-1902\n (Reissue 2016), the three types of final orders which may be reviewed\n on appeal are (1) an order affecting a substantial right in an action, when\n such order in effect determines the action and prevents a judgment;\n (2) an order affecting a substantial right made in a special proceed-\n ing; and (3) an order made upon a summary application in an action\n after judgment.", "\n  5.", "\t Actions: Modification of Decree. ", "Proceedings regarding modification\n of a marital dissolution are special proceedings.", "\n  6.", "\t Actions: Divorce. ", "An application to modify the terms of a divorce\n decree is not the commencement of an action. ", "It constitutes a continua-\n tion of the suit for dissolution of marriage.", "\n  7.", "\t Final Orders: Appeal and Error. ", "An order affects a substantial right\n when the right would be significantly undermined or irrevocably lost by\n postponing appellate review.", "\n  8.", "\t Divorce: Jurisdiction: Final Orders: Appeal and Error. ", "Generally,\n when multiple issues are presented to the district court for simultane-\n ous disposition in the same separate yet connected proceeding within\n\f - 65 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\n the court’s continuing jurisdiction over a dissolution decree, the court’s\n determination of fewer than all the issues presented is not a final order\n for the purpose of an appeal.", "\n 9.", "\t Final Orders. ", "An order merely preserving the status quo pending a\n further order is not final.", "\n\n Appeal from the District Court for Lancaster County: Robert\nR. Otte, Judge. ", "Appeal dismissed.", "\n Matt Catlett, of Law Office of Matt Catlett, for appellant.", "\n David P. Kyker for appellee Kimberly L. Hill.", "\n Heavican, C.J., Miller-Lerman, Cassel, Stacy, K elch, and\nFunke, JJ.", "\n Miller-Lerman, J.\n I. NATURE OF CASE\n In this appeal, Jayson H. Tilson addresses the March 31,\n2017, denial of that portion of his “complaint” and associ-\nated motion asking the district court for Lancaster County\nto declare void a dissolution decree that it had issued more\nthan a year before. ", "He argues that the decree is void because\nprior to the entry of the decree, he had filed a motion to dis-\nmiss the petition for dissolution, which he asserts was self-\nexecuting under Neb. Rev. Stat. § ", "25-602 (Reissue 2016). ", "But\nJayson’s notice of appeal is from an order issued on April 4,\ndenying his requests for various temporary orders and retain-\ning for decision Jayson’s application to modify the custody\nprovisions of the decree. ", "We conclude that the April 4 order\nwas not final. ", "Therefore, we dismiss this appeal for lack\nof jurisdiction.", "\n II. ", "BACKGROUND\n 1. ", "Dissolution\n In September 2014, Jayson filed a complaint for dissolution\nof his marriage to Erica M. Tilson. ", "The record does not reflect\nthat Erica filed an answer, but she made a general appear-\nance before the court. ", "Following a hearing, the court issued\n\f - 66 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\na temporary order awarding custody of the parties’ minor\nchildren to Erica’s mother, Kimberly L. Hill (Kimberly). ", "The\ncourt granted Jayson and Erica supervised parenting time and\nordered them both to pay Kimberly temporary child support.", "\n The court allowed Kimberly to intervene and appointed a\nguardian ad litem for the minor children. ", "Kimberly and her\nhusband filed a complaint, asking for grandparent visitation\nand custody of the children. ", "There is no certificate of service\nattached to the complaint.", "\n Subsequently, on November 16, 2015, at 9 p.m., Jayson\nfiled a motion to dismiss his complaint for dissolution. ", "The\nnext morning, on November 17, Kimberly filed a praecipe\nasking the court to issue summons and deliver to Jayson a\ncopy of the complaint for grandparent visitation, at the hearing\nscheduled at 10 a.m., on November 17. ", "The record contains\ntwo “Process Service Returns” from the sheriff’s office of a\n“Copy of COMPLAINT,” with the service and return charges\npaid by Kimberly’s counsel. ", "The documents reflect that Jayson\nand Erica were personally served copies of the complaint on\nNovember 17.", "\n The hearing was held as scheduled on November 17, 2015,\nwith Jayson in attendance. ", "Referring to the November 17 hear-\ning, the court’s order states “[u]pon motion of [Jayson’s] attor-\nney . . . ", "the Plaintiff’s motion to dismiss is withdrawn.”", "\n The court issued a consent decree of dissolution on December\n8, 2015. ", "The decree ordered the continuation of the children’s\nlegal and physical custody with Kimberly, with set parenting\ntime for Jayson and Erica. ", "Jayson was ordered to pay $200\nper month “toward work-related childcare expenses,” in the\nevent they were not subsidized. ", "Erica was ordered to pay to\nKimberly $100 in monthly child support.", "\n 2. ", "Contempt\n Approximately 10 months later, on October 18, 2016, the\ncourt found Jayson in contempt for failing to comply with\nhis obligation under the decree to contribute to the children’s\nchildcare expenses.", "\n\f - 67 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\n 3. ", "Declaratory R elief,\n Modification, and H abeas\n (a) The “Complaint”\n On February 24, 2017, Jayson filed a “Complaint to Vacate\nor Modify, for Declaratory Judgment, and/or for Writ of Habeas\nCorpus.” ", "The “complaint” was filed under the same case num-\nber as the dissolution decree, and in the same court.", "\n Jayson asserted that the dissolution decree was void by\nvirtue of his November 16, 2015, motion to dismiss. ", "Based\non this assertion, he sought an order of the court declaring\nthe dissolution decree and “all orders flowing therefrom” null\nand void.", "\n Under the rubric of habeas corpus relief, Jayson alleged that\nthe award of temporary custody of the children with Kimberly\nwas unlawful, because it violated the parental preference prin-\nciple. ", "He asked for a writ of habeas corpus placing the custody\nof the children with him.", "\n Alternatively to an order declaring the dissolution void,\nJayson sought an order modifying the decree so as to place\nthe children in his custody. ", "Jayson alleged a change in circum-\nstances. ", "In particular, he alleged that Kimberly was neglect-\ning the children and that Erica was in jail awaiting crimi-\nnal charges.", "\n Kimberly filed an answer generally denying the allegations\nand asking that the matter be dismissed. ", "No ruling on the\nmotion to dismiss is found in the record.", "\n (b) Motion for Declaratory Relief\n and Temporary Orders\n On March 10, 2017, Jayson filed a “Motion for Declaratory\nRelief or Temporary Suspension of Implementation and\nEnforcement of Decree, Temporary Custody, Temporary Child\nSupport, Temporary Restraining Orders.” ", "The district court\nreferred to this motion as “Filing 14.”", "\n Specifically, Jayson moved for a declaration that the decree\nof dissolution and all orders flowing therefrom are void and\nof no effect. ", "In support of this relief, Jayson repeated his\n\f - 68 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\nassertion that his motion to dismiss the complaint for disso-\nlution was self-executing and therefore deprived the court of\njurisdiction to issue the dissolution decree.", "\n “[I]n lieu” of such declaratory relief, Jayson moved for\norders (1) temporarily suspending enforcement of the decree as\nit relates to the care, custody, control, and support of the minor\nchildren; (2) temporarily awarding Jayson exclusive custody\nof the children; (3) temporarily prohibiting Erica from having\nparenting time; (4) temporarily prohibiting Erica from having\naccess to medical and education records; (5) temporarily pro-\nhibiting Kimberly from having visitation with the children; (6)\ntemporarily prohibiting Kimberly from having access to the\nchildren’s medical or education records; and (7) temporarily\nrequiring Erica to pay Jayson child support and share in medi-\ncal and childcare expenses.", "\n In support of this “temporary” relief, Jayson alleged that the\nparental preference principle prohibited the award of custody\nof the children to Kimberly when he had not been found to be\nunfit. ", "He further alleged that Erica was unfit to have custody\nand that it was contrary to the children’s best interests for\nKimberly to have visitation.", "\n (c) March 31, 2017, Order\n On March 31, 2017, the court overruled that part of Jayson’s\n“Filing 14” requesting that the court declare the dissolution\ndecree void. ", "The court’s order, signed and file stamped on\nMarch 31, incorporates its docket entry, stating that “[t]he part\nof the motion requesting declaratory relief (vacating the Decree\nof Dec[.] ", "8, 2015) is overruled.” ", "Also on March 31, the court\ndenied Jayson’s requests for full temporary custody and sus-\npension of child support while the case was pending.", "\n The “custody case” was set for a trial to be held on August\n21, 2017.", "\n (d) April 4, 2017, Order\n On April 4, 2017, the court issued another order. ", "The\nApril 4 order states that “[t]his proceeding came before the\n\f - 69 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\ncourt for consideration of pending matters.” (", "Emphasis sup-\nplied.) ", "And “[u]pon consideration of the issue(s) presented,\nthe court made the docket entry . . .” ", "as follows: “At Filing\n14 is [Jayson’s] Motion for Declaratory Relief Or Temporary\nSuspension Of Implementation And Enforcement Of Decree,\nTemporary Custody, Temporary Child Support, Temporary\nRestraining Orders. ", "The motion was argued and submitted on\n3/31/17. ", "The Motion is overruled. ", "See Order re Docket Entry\nin file.”", "\n\n (e) Notice of Appeal\n On May 3, 2017, Jayson filed a notice of appeal, stating that\nhe was appealing the April 4 order. ", "That is the appeal currently\nbefore us.", "\n\n 4. ", "Orders Subsequent to\n Notice of A ppeal\n The proceedings continued after the May 3, 2017, notice\nof appeal was filed. ", "Kimberly filed an amended answer to\nJayson’s “complaint,” setting forth a cross-complaint for a\nreduction in Jayson’s parenting time, for his visitation to be\nsupervised, and for an award of child support. ", "On May 30,\nthe court issued an order denying a motion by Jayson to con-\ntinue trial and to prohibit Kimberly from serving subpoenas\nupon the Nebraska Department of Health and Human Services\nand “Educare of Lincoln.” ", "The court also granted Kimberly’s\nrequest for a protective order.", "\n After a hearing, on June 20, 2017, the court sustained\nKimberly’s motion to modify parenting time to a “5/2 sched-\nule” “for this temporary order.” ", "But the court explained that\nto “encourage civil collaboration,” Kimberly’s attorney was\nto confer with Jayson’s attorney and the guardian ad litem.", "\n“After doing so, [Kimberly’s attorney] shall submit a proposed\norder as to temporary custody.” ", "The court overruled motions\nby Jayson for sanctions and attorney fees and to reconsider the\ncourt’s appointment of the guardian ad litem.", "\n\f - 70 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\n On June 28, 2017, the court issued an order sustaining\nKimberly’s motion for modification of parenting time. ", "That is\nthe last order in the record.", "\n III. ", "ASSIGNMENT OF ERROR\n Jayson claims that the district court erred when it denied\nhis “February 24, 2017, motion” to declare the dissolution\ndecree void.", "\n IV. ", "STANDARD OF REVIEW\n [1] When a jurisdictional question does not involve a\nfactual dispute, its determination is a matter of law, which\nrequires an appellate court to reach a conclusion independent\nof the decision made by the lower court.1\n V. ANALYSIS\n [2,3] Before reaching the legal issues presented for review,\nit is our duty to determine whether we have jurisdiction over\nthis appeal.2 In this case, it is necessary for us to determine\nwhether the April 4, 2017, order, from which Jayson appeals,\nis final.3 To vest an appellate court with jurisdiction, the notice\nof appeal must be filed within 30 days of the entry of the\nfinal order.4 In contrast, if an order is interlocutory, immediate\nappeal from the order is disallowed so that courts may avoid\npiecemeal review, chaos in trial procedure, and a succession of\nappeals granted in the same case to secure advisory opinions to\ngovern further actions of the trial court.5\n [4] The three types of final orders which may be reviewed\non appeal are (1) an order affecting a substantial right in an\naction, when such order in effect determines the action and\n\n 1\t\n Anderson v. Finkle, 296 Neb. 797, 896 N.W.2d 606 (2017).", "\n 2\t\n See, e.g., Rafert v. Meyer, 298 Neb. 461, 905 N.W.2d 30 (2017).", "\n 3\t\n See Neb. Rev. Stat. §§ ", "25-1911 and 25-1912 (Reissue 2016).", "\n 4\t\n State v. Jacques, 253 Neb. 247, 570 N.W.2d 331 (1997). ", "See, also, Neb.\n Rev. Stat. § ", "25-1931 (Reissue 2016).", "\n 5\t\n State v. Jacques, supra note 4.", "\n\f - 71 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\nprevents a judgment; (2) an order affecting a substantial right\nmade in a special proceeding; and (3) an order made upon a\nsummary application in an action after judgment.6\n [5,6] Proceedings regarding modification of a marital disso-\nlution are special proceedings.7 Jayson’s filings with the same\ndistrict court that issued the dissolution decree, under the same\ncase number, must be construed as motions asking the court\nfor relief pursuant to its continuing jurisdiction over the decree,\nas set forth by the modification statutes.8 An application to\nmodify the terms of a divorce decree is not the commencement\nof an action.9 It constitutes a continuation of the suit for dis-\nsolution of marriage.10\n The jurisdictional question presented is whether the April\n4, 2017, order from which this appeal is taken affected a sub-\nstantial right. ", "A substantial right is an essential legal right,\nnot a mere technical right.11 It is a right of substance.12 It is\nnot enough that the right itself be substantial; the effect of the\norder on that right must also be substantial.13 The duration of\nthe order is therefore relevant to whether it affects a substan-\ntial right.14\n [7,8] Most fundamentally, an order affects a substantial\nright when the right would be significantly undermined or\nirrevocably lost by postponing appellate review.15 Generally,\n\n 6\t\n See Neb. Rev. Stat. § ", "25-1902 (Reissue 2016).", "\n 7\t\n See Steven S. v. Mary S., 277 Neb. 124, 760 N.W.2d 28 (2009).", "\n 8\t\n See Neb. Rev. Stat. §§ ", "42-364(6) and 42-365 (Reissue 2016).", "\n 9\t\n Ruehle v. Ruehle, 161 Neb. 691, 74 N.W.2d 689 (1956).", "\n10\t\n See, Smith-Helstrom v. Yonker, 253 Neb. 189, 569 N.W.2d 243 (1997);\n Nimmer v. Nimmer, 203 Neb. 503, 279 N.W.2d 156 (1979).", "\n11\t\n In re Adoption of Madysen S. et al., ", "293 Neb. 646, 879 N.W.2d 34 (2016).", "\n12\t\n Id.\n13\t\n Id.\n14\t\n See id.\n15\t\n See id.\n\f - 72 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\nwhen multiple issues are presented to the district court for\nsimultaneous disposition in the same “separate yet connected\nproceeding[]”16 within the court’s continuing jurisdiction over\na dissolution decree, the court’s determination of fewer than all\nthe issues presented is not a final order for the purpose of an\nappeal.17 This is because, absent unusual circumstances, post-\nponing appellate review until all the issues presented under the\napplication to modify have been decided will not significantly\nundermine the rights affected by the order.", "\n Huffman v. Huffman18 illustrates the foregoing principles.", "\nIn Huffman, we concluded that an order denying the father’s\nrequest for a change of custody was not final when the\ncourt had not yet decided the father’s alternative request to\nmodify the visitation provisions of the decree. ", "We said that\nwhen the modification application pertains to more than one\nissue involving children affected by the dissolution decree,\na court’s resolution of one issue raised by the application,\nbut retention or reservation of jurisdiction for disposition\nof another issue or issues raised by the application does not\nconstitute a final judgment, order, or decree for the purpose\nof an appeal.19\n In Schepers v. Schepers,20 we likewise held that an order\ndetermining the merits of an application to modify custody\nwas not final when the issue of child support was still pending.", "\n\n16\t\n John P. Lenich, What’s So Special About Special Proceedings? ", "Making\n Sense of Nebraska’s Final Order Statute, 80 Neb. L. Rev. 239, 289 n.227\n (2001).", "\n17\t\n See, Wagner v. Wagner, 275 Neb. 693, 749 N.W.2d 137 (2008); Schepers\n v. Schepers, 236 Neb. 406, 461 N.W.2d 413 (1990); Huffman v. Huffman,\n 236 Neb. 101, 459 N.W.2d 215 (1990); Gerber v. Gerber, 218 Neb. 228,\n 353 N.W.2d 4 (1984); Goldenstein v. Goldenstein, 110 Neb. 788, 195\n N.W. 110 (1923); McCaul v. McCaul, 17 Neb. App. ", "801, 771 N.W.2d 222\n (2009); Paulsen v. Paulsen, 10 Neb. App. ", "269, 634 N.W.2d 12 (2001).", "\n18\t\n Huffman v. Huffman, supra note 17.", "\n19\t\n See id.\n20\t\n Schepers v. Schepers, supra note 17.", "\n\f - 73 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\nThe Nebraska Court of Appeals, in Paulsen v. Paulsen,21 found\nthat a similar order was not final, explaining:\n There are practical reasons why an order in a special\n proceeding which determines less than all of the issues\n submitted to the court is not final. ", "The primary reason\n of course is to prevent piecemeal appeals. ", "There can be\n no doubt that custody and the amount of support for the\n children of a family are closely related issues. . . . ", "There\n is no reason why both issues cannot be decided at the\n same time in an action where both are put [at] issue. . . .", "\n In short, there is no reason not to require a resolution of\n both custody and support to make the order final.", "\n In Johnson v. Johnson,22 the Court of Appeals clarified that\nit does not matter if the issue or issues yet undecided were\nexplicitly requested in the application to modify the decree,\nwhen the issue or issues were “an inherent part of a custody\nmodification action.”", "\n Without commenting on the extent to which Jayson’s\nrequests properly fell under the district court’s continuing\njurisdiction, in his February 24, 2017, “Complaint to Vacate or\nModify, for Declaratory Judgment, and/or for Writ of Habeas\nCorpus,” Jayson presented several issues in the proceedings.", "\nHe asked the court to declare the dissolution decree void and\nto vacate it. ", "He asked the court to issue a writ of habeas corpus\nplacing the children in his custody. ", "Alternatively to vacating\nthe decree or issuing a writ of habeas corpus, Jayson asked\nthe court to modify the dissolution decree to place the children\nin his custody, due to an alleged change in circumstances.", "\nFinally, Jayson moved for several temporary orders, apparently\npending the court’s determination of his underlying requests\nfor relief.", "\n In its order on April 4, 2017, from which this appeal is\ntaken, the court stated that it was overruling “pending matters”\n\n21\t\n Paulsen v. Paulsen, supra note 17, 10 Neb. App. ", "at 275, 634 N.W.2d at 17.", "\n22\t\n Johnson v. Johnson, 15 Neb. App. ", "292, 296, 726 N.W.2d 194, 197 (2006).", "\n\f - 74 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\nunder “Filing 14.” ", "As noted above, “Filing 14” asked for a dec-\nlaration that the dissolution decree was void and, in the alterna-\ntive, for several temporary orders. “", "Filing 14” did not ask for a\nwrit of habeas corpus or for modification of the decree due to\na change of circumstances.", "\n Because in the court’s order issued on March 31, 2017, it\nhad overruled Jayson’s request to declare the dissolution decree\nvoid, the April 4 order’s overruling of the pending matters in\n“Filing 14” necessarily refers to Jayson’s requests for tem-\nporary relief. ", "Specifically, the April 4 order denied Jayson’s\nrequests for (1) temporary suspension of the decree as it relates\nto the care, custody, control, and support of the minor children;\n(2) a temporary award to Jayson of exclusive custody of the\nchildren; (3) a temporary denial of any parenting time for Erica\nand prohibiting Erica from having access to medical and edu-\ncation records; (4) a temporary cessation of grandparent visita-\ntion; and (5) a temporary award of child support.", "\n At the time of the April 4, 2017, order, the court had not\nyet addressed Jayson’s request for a writ of habeas. ", "Likewise,\nthe court had not considered the merits of Jayson’s alternative\nrequest for modification of the decree to place the children per-\nmanently in his custody. ", "On the contrary, it is clear that at the\ntime of the April 4 order, the court had retained the “custody\ncase” for trial. ", "Thus, the court’s April 4 order determined fewer\nthan all the issues submitted and it retained jurisdiction for dis-\nposition of another issue raised by the application.", "\n [9] Furthermore, the April 4, 2017, order pertained only to\nrequests for temporary relief. ", "In several cases, we have held\nthat under the facts presented, orders temporarily affecting\na parent’s custodial, visitation, or educational rights are not\nfinal.23 Despite the importance of the rights affected, such\norders of limited duration failed to have a substantial effect\n\n23\t\n See, In re Interest of Danaisha W. et al., ", "287 Neb. 27, 840 N.W.2d 533\n (2013); Gerber v. Gerber, supra note 17; In re Interest of Angeleah M.\n & Ava M., 23 Neb. App. ", "324, 871 N.W.2d 49 (2015); In re Interest of\n Nathaniel P., 22 Neb. App. ", "46, 846 N.W.2d 681 (2014).", "\n\f - 75 -\n Nebraska Supreme Court A dvance Sheets\n 299 Nebraska R eports\n TILSON v. TILSON\n Cite as 299 Neb. 64\n\non those rights. ", "And here, by denying Jayson’s motion for\ntemporary relief, the April 4 order essentially left unchanged\nthe status quo of the dissolution decree. ", "We have said in other\ncontexts that an order merely preserving the status quo pending\na further order is not final.24\n In his discussion of our jurisdiction in this case, Jayson\nrelies on case law wherein we have held that an order denying\na motion to vacate is a final order.25 We find Jayson’s reli-\nance on this proposition unavailing, because the order before\nus is not the March 31, 2017, order denying that “part of the\nmotion requesting declaratory relief (vacating the Decree of\nDec[.] ", "8, 2015),” but, rather, the April 4 order. ", "Furthermore,\nif the March 31 order is a final order, then Jayson failed to\nperfect an appeal from that order within 30 days as required\nby § 25-1931. ", "If the March 31 order is not a final order, then\nit is appealable once the court has determined all the issues\npending under these current modification proceedings. ", "Either\nway, the finality of the March 31 order does not control the\njurisdictional question in this appeal; that is, whether the April\n4 order is final.", "\n We conclude that the April 4, 2017, ruling was not a final\norder, because it did nothing more than deny requests for\ntemporary relief, preserving the status quo pending the court’s\ndetermination of the other issues raised in the proceedings.", "\nAccordingly, we have no jurisdiction over this appeal.", "\n VI. ", "CONCLUSION\n For the foregoing reasons, we dismiss the appeal.", "\n A ppeal dismissed.", "\n Wright, J., not participating.", "\n\n24\t\n See Shasta Linen Supply v. Applied Underwriters, 290 Neb. 640, 861\n N.W.2d 425 (2015).", "\n25\t\n See, Capitol Construction v. Skinner, 279 Neb. 419, 778 N.W.2d 721\n (2010); State v. Hausmann, 277 Neb. 819, 765 N.W.2d 219 (2009).", "\n\f" ]

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[ "Contact Details\n\nFederation of Holistic Therapy (FHT)\n\nPrices\n\nSee our Special Offers Page for all current Offers\n\nFollow us to get the latest updates.", "\n\nBased in Basildon\n\nBarn Mews Clinic are based in Basildon,\nEssex and are waiting to provide you with the massage services you\nneed. ", "With all services tailored to you specifically, you can get\nexactly what you need with our team.", "\n\nContact Us\n\nFully Qualified\n\nSam is a fully qualified Sports Massage\nTherapist since 2012 and has spent the last three years working on\nher own knowledge and experience for the benefit of her clients." ]

{ "pile_set_name": "Pile-CC" }

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[ "[Constitutional and dermatoglyphic characteristics of children with diabetes mellitus].", "\nA group of Russian children with clinically diagnosed diabetes mellitus were examined using a comprehensive constitutional dermatoglyphic program. ", "Pattern asymmetry was observed in children of both sexes. ", "On the whole the examined population was characterized by reduced incidence of loop patterns and increased incidence of double-delta patterns. ", "In boys the incidence of arches and coils was higher and that of loops lower than in controls, in girls there were no arches and the incidence of radical and ulnar loops was low. ", "Analysis of genetically determined signs, both anthropometric and dermatoglyphic ones, and use of other criteria will help assess the significance of these signs as markers of risk of development of type I diabetes." ]

{ "pile_set_name": "PubMed Abstracts" }

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", "They set off for Sidi Bel\nAbbes.", "\n\nTravelling by camel they call at a cafe on the outskirts to inquire the\nway and meet Zigzig the owner and Sgt Nocker of the Legion. ", "He is\n'shacked-up' very cosily with the voluptuous Zigzig. ", "Nocker is sleeping\noff some form of orgy, but Zigzig directs Bo and Simpson to the barracks.", "\nLife in the Legion under Commandant Burger and his adjutant Capitaine Le\nPice, not to mention the scheming Sgt Nocker and the tough Corporal\nClotski, is full of pitfalls for Bo and the indefatigable Simpson.", "\n\nSheik Abdul Abulbul, leader of the Touaregs, and his henchmen Riff and\nRaff are proving a formidable thorn in the flesh of authority and\nconstantly disrupt the routine of the foreign infidels.", "\n\nMeanwhile, back in England Lady Jane learns of Bo's innocence from Bagshaw\non his deathbed, and sets out to tell Bo that his name has been cleared.", "\n\nFortunately, Bo and Simpson discover that they hold an advantage over Sgt\nNocker, which they exploit to make life easier for themselves. ", "Nocker, Bo\nand Simpson, now friends, visit Zigzigs cafe where they meet and are\nenchanted by the dancer Corktip. ", "Prompted by Abdul she lures Nocker and Bo\nto her house where they are taken captive. ", "Happily the faithful Simpson\nhas followed his master.", "\n\nAfter many adventures on land and sea, Lady Jane arrives at the barracks\nand is surprised to meet an old and valued friend in Burger. ", "The\nCommandant directs her to the cafe, where Abdul is captivated by her\nbeauty and, affected by too much ‘sherbet’; she is enticed to his tent.", "\n\nMeanwhile the captives, Bo and Nocker, arrive at Oasis El Nooki, followed\nat a distance by Simpson. ", "Lady Jane, still under the influence of\n'sherbet', is reunited with Bo who is horrified to learn that she is about\nto become Abduls thirteenth wife. ", "Simpson is captured and the party find\ntemporary sanctuary in the harem tent but are forced to give themselves\nup. ", "Learning of Abduls plans to attack the Legion Fort of Zuassantneuf;\nthe wily Nocker escapes to warn the garrison at Sidi Bel Abbes.", "\n\nSadly Nocker has cried wolf once too often and instead of the heroes\nwelcome he had anticipated, he is placed under arrest. ", "Irrepressible as\never, he eventually persuades the Commandant to organise a relief force.", "\nSo they set out for the oasis where they find Bo and Simpson barely alive.", "\n\nBo confirms that Abdul and his band intend attacking the fort and have\ntaken Lady Jane along with them. ", "Now begins an arduous march across the\nburning sands of the desert, under a cruel sun to the relief of Fort\nZuassantneuf.", "\n\nThe heat and lack of water take their toll, aided by considerable\ndissension in the ranks. ", "So that it is Burger, Nocker, Bo, Simpson,\nClotski and a handful of legionnaires who struggle on, leaving Le Pice to\nreturn for further reinforcements. ", "Against inhuman odds, the Commandant\ndrives his depleted force in the general direction of the fort. ", "Alas! ", "The\ngarrison has been wiped out and the Riffs are celebrating their victory\nnearby.", "\n\nBurger takes over the fort and Bo is distressed to discover that the\nvictory celebrations include the impending marriage of Abdul to Lady Jane.", "\nThey rush to the rescue.", "\n\nAt the Riff encampment, a banquet is in progress and Abdul, while\ncongratulating his warriors on their victory, exhorts them to give gifts\nto the glory of Abdul and his bride-to-be. ", "Lady Jane is sent to his tent\nto receive these tributes and it is there that she is rescued by Bo,\nBurger and Nocker, who leave the hapless Simpson, unconvincingly\ndisguised, in her place.", "\n\nOnce again the fort is under a stage of siege, the irate Abdul pursuing\nSimpson to its very doors. ", "The defiant comrades repel every attack until\ntheir ammunition runs out and it is left to the audacious Sgt Nocker to\neffect their salvation by an ingenious plan.", "\n\nThe story ends where it began, with the surviving characters meeting on\nthe same cricket field. ", "Bo takes his stance at the wicket, ready to\nreceive his first delivery. ", "The bowler turns at the end of his run, and\nbowls an explosive ball. ", "Abduls back!", "\n\nreview\n\nOriginally known as 'Follow that Camel' or the one with Bilko in it, this\nis a historical parody of the Beau Geste films. ", "In the hope of fully\nlaunching the Carry Ons into an international market, Phil Silvers was\ncast as Sgt. ", "Nocker. ", "Primarily known as Sgt. ", "Bilko from the long running\nCBS series, the backers must have thought that they would have a huge\nAmerican hit on their hands. ", "Silvers presence neither helped nor hindered\nthe production and the film did the same sort of business as 'Don't Lose\nYour Head' did several months before. ", "Basically Silvers plays the Nocker\nrole exactly the same way he plays Bilko, although that’s not necessarily\na bad thing. ", "After all that’s why he was chosen for the part.", "\n\nThe whole look of the film is extremely satisfying, mainly thanks to Alan\nHumes excellent lighting work. ", "This is one of the rare times that the\nsouth coast of England (Camber Sands to be precise) looks exactly like a\nbaking hot desert.", "\nAlong with 'Don't Lose Your Head', this was one of the crossover films\nthat explains it rather odd title. ", "Although overseas it was known as Carry\nOn In The Legion. ", "Hmm, not sure which titles better.", "\n\nSo the regulars in the film generally play second fiddle to Phil Silvers,\nwho is on screen 90% of the time. ", "Of them, Kenneth Williams portrays the\nGerman Commandant with suitable aplomb, even going as far to get a brutal\nhaircut. ", "Charles Hawtrey is as ever Charles Hawtrey. ", "Jim Dale and Peter\nButterworth make an excellent double act with suitable understated\nperformances. ", "Bernard Bresslaw gets a dry run for a role he would\nvirtually recreate in Up The Khyber the following year, however the female\nperformers are seriously underwritten for. ", "Joan Sims has a few good lines\nas ZigZig, but Angela Douglas and Anita Harris don't really add anything\nto the plot apart from their looks.", "\n\nTo sum up, Follow That Camel is an average historical Carry On, but\ncertainly not the best. ", "Alas Phil Silvers doesn't fit in well and as a\nresult doesn't really feel like a proper Carry On. ", "Although some of the\ngags are funny, they don't hit the mark as frequently as 1964's Cleo or\n1968's Up The Khyber. ", "The film also suffers from having dark moments e.g.\nA suicide within the first 10 minutes, soldiers dying, the desperate march\nto the Fort. ", "That said, all in all its fairly entertaining, just that the\nteam were capable of producing much better.", "\n\nother information\n\nThe location filming at Camber Sands took three weeks, the longest in\nthe series.", "\n\nWhen The Rank Organisation took over the Carry On series from Anglo\nAmalgamated in 1966, they wanted to remove the famous 'Carry On' prefix,\nfearing that their cinematic output would be tainted with the low brow\nname. ", "The two films that were affected by this were 'Don't Lose Your Head'\nand 'Follow That Camel'. ", "Realising their error, Rank re-released them both\nsoon afterwards and the box office takings soared.", "\n\nNames initially considered for the Phil Silvers role included Woody Allen.", "\n\nPhil Silvers was dramatically losing his site during filming, so has to\nwear both contact lenses and glasses.", "\n\nSheena the Camel was on loan from Chessington Zoo. ", "Unfortunately it had\nnever walked on sand before, so tracks had to be laid down for it.", "\n\nAlthough not involved in the film, three days into shooting Sid James was\nrushed into hospital with a heart attack.", "\n\nWhilst buried in the sand, Jim Dale and Peter Butterworth has to be\nwrapped in blankets and given brandy to keep the cold out." ]

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[ " NOTE: This order is nonprecedential.", "\n\n United States Court of Appeals for the Federal Circuit\n 2009-3075\n\n EARL T. BARNETT\n\n Petitioner,\n\n v.\n\n MERIT SYSTEMS PROTECTION BOARD,\n\n Respondent.", "\n\n Petition for review of the Merit Systems Protection Board in\n PH315H080391-I-1.", "\n\n ON MOTION\n\n ORDER\n\n Earl T. Barnett moves for an extension of time to file his brief. ", "The court\n\nconsiders whether to vacate its March 10, 2009 order dismissing Barnett's petition for\n\nreview for failure to file a brief.", "\n\n Upon consideration thereof,\n\n IT IS ORDERED THAT:\n\n The motion for an extension of time is granted. ", "The March 10 dismissal order\n\nwill be vacated, the mandate will be recalled, and the petition for review will be\n\nreinstated if Barnett files his brief within 30 days of the date of filing of this order.", "\n\n FOR THE COURT\n MAR 2 0 2009 /s/ Jan Horbaly\n Date Jan Horbaly\n FILED\n Clerk U.S. COURT OF APPEALS FOR\n THE FEDERAL CIRCUIT\nCC: Earl T. Bennett\n Bernard E. Doyle, Esq.", "\ns17 MAR 2 0 2009\n\n JAN ii0RtiALY\n CLERK\n\f" ]

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[ "The second-best solution: an apology for democracy.", "\nThe best ways to make group decisions are by consensus or the use of rational rules. ", "Unfortunately, these methods are not general and are limited to various special circumstances. ", "Some poor alternatives include authoritarian rule or chaos. ", "Democracy, essentially one voice and vote for each concerned individual, is the most practical general alternative. ", "A catalogue of democracy's flaws is reviewed, but it is concluded that, faults and all, democracy remains the best choice." ]

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[ "If you are not completely satisfied with your purchase, simply return the items to us in their original condition and packaging within 100 days of receipt of your order for either an exchange of product or a refund. ", "Click here to see our full returns information\n\nDescription\n\nThe Tonik has become one of DC's most popular lines in recent years and that's down to its casual elegance and unassuming nature - As appropriate for squash games, picnics, smart-casual gatherings and fishing holidays as they are for shred-planking with your friends in the raw streets, they are a resilient and versatile vulcanized suede shoe.", "\n\nA sleek classic from DC, the Tonik is up there with the most reliable and sturdy skate shoes on the market. ", "In Charcoal/Black with DC branding on the tongue and sole, with a breathable fabric lining for added luxury.", "\n\nStarting off way back in 1994, DC have gone from just making shoes designed specifically for skateboarding, to being one of the industry leaders, with a wide range of hardware and apparel, covering a huge array of sports. ", "DC are one of the brands that have been really making waves in the action sport world. ", "Pushing boundaries and trying to progress every sport they are involved with, so whether you Skate, BMX, FMX, Rally Drive, Surf or Snowboard, you will realise how big DC shoes has become.", "\n\nhttps://www.routeone.eu/footwear/skate-shoes/dc-tonik-skate-shoes-charcoal-black.htm001044878DC Tonik Skate Shoes - Charcoal/Blackhttps://routeone.images.blucommerce.com/routeone/product/00104/001044878.jpg?auto=format%2Ccompress&w=300&h=382&fit=fillmax&fill=solid&s=3998dce728fd968e22cf76421106caca22.50EUR55.50OutOfStockShoes/Skate ShoesShoesBrands/DCBrandsOffers/Footwear Sale/Skate ShoesOffers/Footwear SaleOffersSale/Footwear/Skate ShoesSale/FootwearSaleThe Tonik has become one of DC's most popular lines in recent years and that's down to its casual elegance and unassuming nature - As appropriate for squash games, picnics, smart-casual gatherings and fishing holidays as they are for shred-planking with your friends in the raw streets, they are a resilient and versatile vulcanized suede shoe. ", "A sleek classic from DC, the Tonik is up there with the most reliable and sturdy skate shoes on the market. ", "In Charcoal/Black with DC branding on...DC" ]

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[ "Piccadilly Loft Apartments, York\n\nConversion of a former Ford garage in the heart of York into prestige, residential apartments attractive to the target market of 50+, second homeowners and downsizers.", "\n\nOur brief was to evaluate the existing space and create an interior specification forming part of the tender package, highlighting selling points for a property of this calibre.", "\n\nWe were also asked to investigate the opportunity for design differentials between apartments, clearly justifying our proposal for each apartment specification.", "\n\nThis building with its strong industrial history lends itself, due to its location, to a residential development of apartments each with its own unique character, whilst remaining faithful to its heritage.", "\n\nThere are two clear facets to the building, the Foss facing apartments, which are more industrial in architectural scale and feel, and the more urban domestic proportions of the Piccadilly facing apartments. ", "The common theme is industrial; the differentiator is the level to which the fixtures and fittings soften the feel.", "\n\nOn the Foss side, obvious architectural cues such as cornice, skirting and four-panelled doors were highlighted and painted structural elements were mixed with industrial style light fittings. ", "Wall lights of more residential domestic type were chosen to provide contrast.", "\n\nKitchens had highly polished flush doors with contrast worktops, whilst the Industrial feel was emphasized using cool calming colours contrasting with elements of rich Walnut to add warmth. ", "Stainless steel highlights give interest and pick up light from the massive windows over looking the river.", "\n\nThe Piccadilly facing apartments are more subservient in proportion & scale than the Foss facing apartments. ", "With lower ceilings the space is more self-contained lending itself to conventional domestic dwelling.", "\n\nOak flooring was used to lighten the feel of the apartments teamed with Oak worktops, with classic simple painted door fronts in the kitchen, whilst the tiles hint at automotive background.", "\n\nBoth Foss and Piccadilly bathrooms and ensuite have crisp clean lines mixed with a unique ceramic floor tile with tonal wall tiles selectively located. ", "Clever use of mirrors increases the perspective of room size.", "\n\nThis development won the Judges Special Award at York Design Awards 2015." ]

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[ "/*\n * Copyright LWJGL. ", "All rights reserved.", "\n * License terms: https://www.lwjgl.org/license\n * MACHINE GENERATED FILE, DO NOT EDIT\n */\npackage org.lwjgl.llvm;\n\nimport javax.annotation.*;", "\n\nimport java.nio.*;", "\n\nimport org.lwjgl.*;", "\nimport org.lwjgl.system.*;", "\n\nimport static org.lwjgl.system.", "MemoryUtil.*;", "\nimport static org.lwjgl.system.", "MemoryStack.*;", "\n\n/**\n * A single result of code completion.", "\n * \n * <h3>Member documentation</h3>\n * \n * <ul>\n * <li>{@code CursorKind} &ndash; \n * the kind of entity that this completion refers to.", "\n * \n * <p>The cursor kind will be a macro, keyword, or a declaration (one of the {@code *Decl} cursor kinds), describing the entity that the completion is\n * referring to.</p></li>\n * <li>{@code CompletionString} &ndash; the code-completion string that describes how to insert this code-completion result into the editing buffer</li>\n * </ul>\n * \n * <h3>Layout</h3>\n * \n * <pre><code>\n * struct CXCompletionResult {\n * enum CXCursorKind CursorKind;\n * CXCompletionString CompletionString;\n * }</code></pre>\n */\npublic class CXCompletionResult extends Struct implements NativeResource {\n\n /** The struct size in bytes. */", "\n public static final int SIZEOF;\n\n /** The struct alignment in bytes. */", "\n public static final int ALIGNOF;\n\n /** The struct member offsets. */", "\n public static final int\n CURSORKIND,\n COMPLETIONSTRING;\n\n static {\n Layout layout = __struct(\n __member(4),\n __member(POINTER_SIZE)\n );\n\n SIZEOF = layout.getSize();\n ALIGNOF = layout.getAlignment();\n\n CURSORKIND = layout.offsetof(0);\n COMPLETIONSTRING = layout.offsetof(1);\n }\n\n /**\n * Creates a {@code CXCompletionResult} instance at the current position of the specified {@link ByteBuffer} container. ", "Changes to the buffer's content will be\n * visible to the struct instance and vice versa.", "\n *\n * <p>The created instance holds a strong reference to the container object.</p>\n */\n public CXCompletionResult(ByteBuffer container) {\n super(memAddress(container), __checkContainer(container, SIZEOF));\n }\n\n @Override\n public int sizeof() { return SIZEOF; }\n\n /** Returns the value of the {@code CursorKind} field. */", "\n @NativeType(\"enum CXCursorKind\")\n public int CursorKind() { return nCursorKind(address()); }\n /** Returns the value of the {@code CompletionString} field. */", "\n @NativeType(\"CXCompletionString\")\n public long CompletionString() { return nCompletionString(address()); }\n\n // -----------------------------------\n\n /** Returns a new {@code CXCompletionResult} instance allocated with {@link MemoryUtil#memAlloc memAlloc}. ", "The instance must be explicitly freed. */", "\n public static CXCompletionResult malloc() {\n return wrap(CXCompletionResult.class, nmemAllocChecked(SIZEOF));\n }\n\n /** Returns a new {@code CXCompletionResult} instance allocated with {@link MemoryUtil#memCalloc memCalloc}. ", "The instance must be explicitly freed. */", "\n public static CXCompletionResult calloc() {\n return wrap(CXCompletionResult.class, nmemCallocChecked(1, SIZEOF));\n }\n\n /** Returns a new {@code CXCompletionResult} instance allocated with {@link BufferUtils}. */", "\n public static CXCompletionResult create() {\n ByteBuffer container = BufferUtils.createByteBuffer(SIZEOF);\n return wrap(CXCompletionResult.class, memAddress(container), container);\n }\n\n /** Returns a new {@code CXCompletionResult} instance for the specified memory address. */", "\n public static CXCompletionResult create(long address) {\n return wrap(CXCompletionResult.class, address);\n }\n\n /** Like {@link #create(long) create}, but returns {@code null} if {@code address} is {@code NULL}. */", "\n @Nullable\n public static CXCompletionResult createSafe(long address) {\n return address == NULL ? ", "null : wrap(CXCompletionResult.class, address);\n }\n\n /**\n * Returns a new {@link CXCompletionResult.", "Buffer} instance allocated with {@link MemoryUtil#memAlloc memAlloc}. ", "The instance must be explicitly freed.", "\n *\n * @param capacity the buffer capacity\n */\n public static CXCompletionResult.", "Buffer malloc(int capacity) {\n return wrap(Buffer.class, nmemAllocChecked(__checkMalloc(capacity, SIZEOF)), capacity);\n }\n\n /**\n * Returns a new {@link CXCompletionResult.", "Buffer} instance allocated with {@link MemoryUtil#memCalloc memCalloc}. ", "The instance must be explicitly freed.", "\n *\n * @param capacity the buffer capacity\n */\n public static CXCompletionResult.", "Buffer calloc(int capacity) {\n return wrap(Buffer.class, nmemCallocChecked(capacity, SIZEOF), capacity);\n }\n\n /**\n * Returns a new {@link CXCompletionResult.", "Buffer} instance allocated with {@link BufferUtils}.", "\n *\n * @param capacity the buffer capacity\n */\n public static CXCompletionResult.", "Buffer create(int capacity) {\n ByteBuffer container = __create(capacity, SIZEOF);\n return wrap(Buffer.class, memAddress(container), capacity, container);\n }\n\n /**\n * Create a {@link CXCompletionResult.", "Buffer} instance at the specified memory.", "\n *\n * @param address the memory address\n * @param capacity the buffer capacity\n */\n public static CXCompletionResult.", "Buffer create(long address, int capacity) {\n return wrap(Buffer.class, address, capacity);\n }\n\n /** Like {@link #create(long, int) create}, but returns {@code null} if {@code address} is {@code NULL}. */", "\n @Nullable\n public static CXCompletionResult.", "Buffer createSafe(long address, int capacity) {\n return address == NULL ? ", "null : wrap(Buffer.class, address, capacity);\n }\n\n // -----------------------------------\n\n /** Returns a new {@code CXCompletionResult} instance allocated on the thread-local {@link MemoryStack}. */", "\n public static CXCompletionResult mallocStack() {\n return mallocStack(stackGet());\n }\n\n /** Returns a new {@code CXCompletionResult} instance allocated on the thread-local {@link MemoryStack} and initializes all its bits to zero. */", "\n public static CXCompletionResult callocStack() {\n return callocStack(stackGet());\n }\n\n /**\n * Returns a new {@code CXCompletionResult} instance allocated on the specified {@link MemoryStack}.", "\n *\n * @param stack the stack from which to allocate\n */\n public static CXCompletionResult mallocStack(MemoryStack stack) {\n return wrap(CXCompletionResult.class, stack.nmalloc(ALIGNOF, SIZEOF));\n }\n\n /**\n * Returns a new {@code CXCompletionResult} instance allocated on the specified {@link MemoryStack} and initializes all its bits to zero.", "\n *\n * @param stack the stack from which to allocate\n */\n public static CXCompletionResult callocStack(MemoryStack stack) {\n return wrap(CXCompletionResult.class, stack.ncalloc(ALIGNOF, 1, SIZEOF));\n }\n\n /**\n * Returns a new {@link CXCompletionResult.", "Buffer} instance allocated on the thread-local {@link MemoryStack}.", "\n *\n * @param capacity the buffer capacity\n */\n public static CXCompletionResult.", "Buffer mallocStack(int capacity) {\n return mallocStack(capacity, stackGet());\n }\n\n /**\n * Returns a new {@link CXCompletionResult.", "Buffer} instance allocated on the thread-local {@link MemoryStack} and initializes all its bits to zero.", "\n *\n * @param capacity the buffer capacity\n */\n public static CXCompletionResult.", "Buffer callocStack(int capacity) {\n return callocStack(capacity, stackGet());\n }\n\n /**\n * Returns a new {@link CXCompletionResult.", "Buffer} instance allocated on the specified {@link MemoryStack}.", "\n *\n * @param stack the stack from which to allocate\n * @param capacity the buffer capacity\n */\n public static CXCompletionResult.", "Buffer mallocStack(int capacity, MemoryStack stack) {\n return wrap(Buffer.class, stack.nmalloc(ALIGNOF, capacity * SIZEOF), capacity);\n }\n\n /**\n * Returns a new {@link CXCompletionResult.", "Buffer} instance allocated on the specified {@link MemoryStack} and initializes all its bits to zero.", "\n *\n * @param stack the stack from which to allocate\n * @param capacity the buffer capacity\n */\n public static CXCompletionResult.", "Buffer callocStack(int capacity, MemoryStack stack) {\n return wrap(Buffer.class, stack.ncalloc(ALIGNOF, capacity, SIZEOF), capacity);\n }\n\n // -----------------------------------\n\n /** Unsafe version of {@link #CursorKind}. */", "\n public static int nCursorKind(long struct) { return UNSAFE.getInt(null, struct + CXCompletionResult.", "CURSORKIND); }\n /** Unsafe version of {@link #CompletionString}. */", "\n public static long nCompletionString(long struct) { return memGetAddress(struct + CXCompletionResult.", "COMPLETIONSTRING); }\n\n // -----------------------------------\n\n /** An array of {@link CXCompletionResult} structs. */", "\n public static class Buffer extends StructBuffer<CXCompletionResult, Buffer> implements NativeResource {\n\n private static final CXCompletionResult ELEMENT_FACTORY = CXCompletionResult.create(-1L);\n\n /**\n * Creates a new {@code CXCompletionResult.", "Buffer} instance backed by the specified container.", "\n *\n * Changes to the container's content will be visible to the struct buffer instance and vice versa. ", "The two buffers' position, limit, and mark values\n * will be independent. ", "The new buffer's position will be zero, its capacity and its limit will be the number of bytes remaining in this buffer divided\n * by {@link CXCompletionResult#SIZEOF}, and its mark will be undefined.", "\n *\n * <p>The created buffer instance holds a strong reference to the container object.</p>\n */\n public Buffer(ByteBuffer container) {\n super(container, container.remaining() / SIZEOF);\n }\n\n public Buffer(long address, int cap) {\n super(address, null, -1, 0, cap, cap);\n }\n\n Buffer(long address, @Nullable ByteBuffer container, int mark, int pos, int lim, int cap) {\n super(address, container, mark, pos, lim, cap);\n }\n\n @Override\n protected Buffer self() {\n return this;\n }\n\n @Override\n protected CXCompletionResult getElementFactory() {\n return ELEMENT_FACTORY;\n }\n\n /** Returns the value of the {@code CursorKind} field. */", "\n @NativeType(\"enum CXCursorKind\")\n public int CursorKind() { return CXCompletionResult.nCursorKind(address()); }\n /** Returns the value of the {@code CompletionString} field. */", "\n @NativeType(\"CXCompletionString\")\n public long CompletionString() { return CXCompletionResult.nCompletionString(address()); }\n\n }\n\n}" ]

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[ "Talk to former NBA coach Eric Musselman and this much becomes clear — he loves basketball. ", "Loves talking about it. ", "Loves coaching it.", "\n\nAnd he’s going to get to do what he loves in the D-League next season with the Reno Bighorns, according to Scott Schroeder of FanHouse. ", "Reno just a short drive from Lake Tahoe, one of the most beautiful places on the planet, so not a bad spot to land.", "\n\nMusselman had conversations with a few teams this summer about an assistant coaching job, but nothing ever rose to the level of serious. ", "So he has decided instead to go the route of former Toronto coach Sam Mitchell and return to the D-League to hone his craft.", "\n\nHowever, this landing spot is a bit interesting because Reno is the D-League team for the Sacramento Kings and the Golden State Warriors — the two teams Musselman coached in the NBA, on his way to a 108-138 record over three seasons.", "\n\nIn Sacramento, Musselman’s credibility was undercut by a DUI before the first practice, and from them on the team seemed to lack a real direction and understanding of what it was trying to do. ", "Brad Miller (a solid veteran) said he didn’t understand his role, and that was 50 games into a season. ", "The Kings let Musselman go after one season (then hired Reggie Theus, which exacerbated their problems, but that’s another story).", "\n\nMusselman was the color commentator on Versus for D-League games last season, so he has some understanding of the league. ", "He also understands that while winning matters, player development is the real reason for the league. ", "Golden State in particular loves to snatch up D-League players and watches the entire league closely.", "\n\nIf he does a good job here, Musselman could find his way back to the NBA (almost certainly as an assistant at first)." ]

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[ "In physics, resonance is the tendency of a system to oscillate with high amplitude when excited by energy at a certain frequency. ", "This frequency is known as the system's natural frequency of vibration or resonant frequency. ", "A resonant object, whether mechanical, acoustic, or electrical, will probably have more than one resonant frequency (especially harmonics of the strongest resonance). ", "It will be easy to vibrate at those frequencies, and more difficult to vibrate at other frequencies. ", "The resonant object will “pick out” its resonant frequency from a complex excitation, such as an impulse or a wideband noise excitation. ", "In effect, it is filtering out all frequencies other than its resonance. ", "Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration (its resonant frequency) than it does at other frequencies.", "\nWhen playing a musical instrument, such as a violoncello (commonly referred to as the cello), the cellist will choose which string or strings to play by depressing the string or strings on a fingerboard while bowing in techniques such as standard bowing, double stops, col legno, spiccato or staccato or by plucking using pizzicato. ", "A difficulty that arises when performing using these various playing techniques on the cello is that during play, mechanical resonance may occur in strings and/or the body of the instrument. ", "Such mechanical resonance causes undesired sound waves hereinafter referred to as wolf tone which may be detrimental to the sound during the performance of the cellist.", "\nIn addition, resonance may be detrimental in other acoustic, mechanical or electrical devices." ]

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[ "---\nabstract: 'In this work, we introduce a novel local pairwise descriptor and then develop a simple, effective iterative method to solve the resulting quadratic assignment through sparsity control for shape correspondence between two approximate isometric surfaces. ", "Our pairwise descriptor is based on the stiffness and mass matrix of finite element approximation of the Laplace-Beltrami differential operator, which is local in space, sparse to represent, and extremely easy to compute while containing global information. ", "It allows us to deal with open surfaces, partial matching, and topological perturbations robustly. ", "To solve the resulting quadratic assignment problem efficiently, the two key ideas of our iterative algorithm are: 1) select pairs with good (approximate) correspondence as anchor points, 2) solve a regularized quadratic assignment problem only in the neighborhood of selected anchor points through sparsity control. ", "These two ingredients can improve and increase the number of anchor points quickly while reducing the computation cost in each quadratic assignment iteration significantly. ", "With enough high-quality anchor points, one may use various pointwise global features with reference to these anchor points to further improve the dense shape correspondence. ", "We use various experiments to show the efficiency, quality, and versatility of our method on large data sets, patches, and point clouds (without global meshes).'", "\nauthor:\n- |\n Rui Xiang\\\n Department of Mathematics\\\n UC Irvine\\\n [xiangr1@uci.edu]{}\n- |\n Rongjie Lai\\\n Department of Mathematics\\\n Rensselaer Polytechnic Institute\\\n [lair@rpi.edu]{}\n- |\n Hongkai Zhao\\\n Department of Mathematics\\\n UC Irvine\\\n [zhao@uci.edu]{}\nbibliography:\n- 'egbib.bib'\ntitle: 'Efficient and Robust Shape Correspondence via Sparsity-Enforced Quadratic Assignment'\n---\n\nIntroduction\n============\n\nGeometric modeling and shape analysis is ubiquitous in computer vision, computer graphics, medical imaging, virtual reality, 3D prototyping and printing, data analysis, etc. ", "Shape correspondence is a basic task in shape registration, comparison, recognition, and retrieval. ", "Unlike images, shapes do not have a canonical representation domain or basis and do not form a linear space. ", "Moreover, their embedding can be highly ambiguous even for intrinsically identical ones. ", "Further complications in practice include noise, topological perturbations (holes), partial shapes, and lack of a good triangulation. ", "These difficulties pose both modeling and computational challenges for shape modeling and analysis.", "\n\nFor dense shape correspondence, the first step is to design desirable descriptors, pointwise, or pairwise. ", "Pointwise descriptors can be extrinsic and local (in space) [@tombari2010unique; @gumhold2001feature; @dubrovina2011approximately; @rodola2012game], or intrinsic (invariant under isometric transformation). ", "Extrinsic pointwise descriptors usually have difficulties in producing accurate dense correspondence, especially if there is non-rigid transformation involved. ", "Many intrinsic pointwise descriptors in the space domain, such as geodesics distance signatures [@van2011survey], heat kernel signatures [@sun2009concise], wave kernel signatures [@aubry2011wave], and in spectrum domain using eigen-functions of the Laplace-Beltrami operator (LBO) have been proposed [@Reuter:06; @Levy:2006IEEECSMA; @Vallet:2008CGF; @Bronstein:2010CVPR; @lai2010metric; @lai2017multiscale]. ", "For example, functional maps [@ovsjanikov2012functional] aims to find proper linear combinations of truncated basis functions, e.g., eigen-functions of the Laplace-Beltrami operator, based on some prior knowledge, e.g., given landmarks and/or region correspondence, as the pointwise descriptor. ", "Then various nearest neighbor searching or linear assignment methods are used in the descriptor space to find the dense point correspondence. ", "These intrinsic pointwise descriptors are typically nonlocal and require to solve certain partial differential equations, e.g., the Laplace-Beltrami equation, on a well-triangulated mesh. ", "Hence they can be sensitive to topological perturbations and boundary conditions. ", "Moreover, pointwise descriptors based on a truncated basis in the spectrum domain lose fine details in the geometry. ", "On the other hand, using good pairwise descriptors, such as pairwise geodesic distance matrix[@vestner2017product] or kernel functions [@vestner2017efficient], to find shape correspondence is usually more robust and accurate since the matching needs to satisfy more and stricter constraints to minimize some kind of distortion. ", "However, a very challenging computational problem, a quadratic assignment problem (QAP) which is NP-hard, needs to be solved [@lawler1963quadratic]. ", "Different kind of methods have been proposed to solve the QAP approximately in a more computational tractable way e.g sub-sampling [@tevs2011intrinsic], coarse-to-fine [@wang2011discrete], geodesic distance sparsity enforcement methods [@gasparetto2017spatial] and various relaxation approaches [@aflalo2015convex; @bronstein2006generalized; @kezurer2015tight; @leordeanu2005spectral; @chen2015robust; @dym2017ds++]. ", "One popular approach is to relax the nonconvex permutation matrix (representing pointwise correspondence) constraint in the QAP to a doubly stochastic matrix (convex) constraint [@aflalo2015convex; @chen2015robust]. ", "However, both the pairwise descriptor and the doubly stochastic matrix are dense matrices, which causes the relaxed QAP still challenging to solve even for a modest size problem.", "\n\nIn this work, we propose a novel approach for dense shape correspondence for two nearly isometric surfaces based on local pairwise descriptor and an efficient iterative algorithm with sparsity control for the doubly stochastic matrix to solve the relaxed QAP. ", "The main novelty and contribution of our proposed method include:\n\n1\\) A local pairwise descriptor using the combination of the stiffness (corresponding to the finite element approximation of the LBO) and the mass matrix (corresponding to local area scaling). ", "It only involves interactions among local neighbors and is extremely simple to compute. ", "Note that all local interactions are coupled like heat diffusion through the whole shape. ", "In other words, global and full spectral information of LBO is embedded implicitly in our pair-wise descriptor. ", "Due to the locality, the descriptor enjoys stability and good performance for open surfaces and with respect to topological perturbations, as shown in Figure \\[patch3\\] and by more examples in Section \\[sec:result\\]. ", "The sparsity of the pairwise descriptor also reduces the computation cost for the relaxed QAP.", "\n\n2\\) An efficient iterative algorithm with sparsity control for the resulting relaxed QAP. ", "We first use a local distortion measurement (see Section \\[sec:faith\\] for details) to select pairs from both shapes with good correspondence as anchor points for the next iteration. ", "Using regularity of the map, we enforce that the neighborhood of anchor points can only map to the neighborhood of the corresponding anchor points which induces a sparsity structure in the doubly stochastic matrix. ", "It results in a significant reduction of variables and hence, the computation cost in each iteration. ", "As we demonstrate in the numerical experiments, the number of high-quality anchor points grow quickly with iterations.", "\n\n![", "Example of partial matching with topological changes. ", "Topological changes are highlighted by red circles. ", "The patch in second column is mapped onto the entire shape in the first column, and non-blue area is the ground truth map. ", "Extra points in the entire shape are colored in blue. ", "The third column is the mapping result using SHOT, and the last column is the mapping result from our method.[]{data-label=\"patch3\"}](figures/centaur_hand.png){width=\"\\linewidth\"}\n\nHere is the outline of our paper. ", "We introduce our quadratic assignment model based on a local pairwise descriptor in Section \\[sec:QAP\\] and then present an efficient iterative algorithm to solve the quadratic assignment problem with sparsity control in Section \\[sec:iterative\\]. ", "In Section \\[sec:dis\\], we extend our method to point cloud data and patch matching. ", "Numerical experiments are demonstrated in Section \\[sec:result\\] and conclusion follows.", "\n\nQuadratic Assignment Model Using Local Pairwise Descriptors {#sec:QAP}\n===========================================================\n\nGiven two manifolds $\\M_1$ and $\\M_2$ sampled by two point clouds $\\mathcal{P}_1=\\{\\x_i\\}_{i=1}^{n}$ and $\\mathcal{P}_2=\\{\\y_i\\}_{i=1}^{n}$ respectively, the typical task of dense shape correspondence is to find a point-to-point map between $\\mathcal{P}_1$ and $\\mathcal{P}_2$. Let $\\bQ_1\\in \\mathbb{R}^{n\\times n}$ and $\\bQ_2\\in \\mathbb{R}^{n\\times n}$ be two given pairwise descriptors, e.g., pairwise geodesic distance, between two points in $\\mathcal{P}_1$ and $\\mathcal{P}_2$ respectively. ", "The shape correspondence problem can be casted as the following QAP: $$\\argminA_{P \\in \\Pi_{n}} \\|P \\bQ_1 - \\bQ_2 P\\|_F^2\n\\label{eq:QAP}$$ where $P\\in \\mathbb{R}^{n\\times n}$ is a permutation matrix with binary $\\{0,1\\}$ elements and each row and column sum is 1, and $\\|\\cdot\\|_F$ is the Frobenius norm of a matrix.", "\n\nSince the QAP problem is NP-hard [@sahni1976p], it is common to relax the permutation matrix in to a doubly stochastic matrix, $D\\in \\mathcal{D}_n = \\{D \\in \\mathbb{R}^{n \\times n}|\\ D \\vec 1=\\vec 1,D^{\\mathsmaller T} \\vec 1=\\vec 1, D_{ij}\\ge 0\\}$, in the shape registration context [@aflalo2015convex; @bronstein2006generalized; @kezurer2015tight; @leordeanu2005spectral]. ", "The doubly stochastic matrix representation not only convexifies the original QAP  but also provides a more general probabilistic interpretation of the map. ", "However, there remain at least two major computational challenges to solve the relaxed QAP for correspondence problems between shapes of relatively large size. ", "First, the usual choice of pairwise descriptors, such as pairwise distance [@vestner2017product], heat kernel [@bronstein2010scale], and wave kernel [@aubry2011wave] are represented as dense matrices and so are the doubly stochastic matrix. ", "It can pose a storage and memory issue when two shapes are of large size even before conducting any computation. ", "In this case, certain approximation has to be used, such as sub-sampling methods [@tevs2011intrinsic], truncation of pairwise descriptors or spectrum approximation [@aflalo2016spectral], though they may lead to accuracy problems due to the approximation error. ", "Computationally, single dense matrix multiplication of the pairwise descriptor matrix and the doubly stochastic matrix requires $O(n^3)$ operations, where $n$ is the number of points. ", "More seriously, the relaxed QAP is usually solved by an iterative method. ", "Due to the coupling of all elements of the doubly stochastic matrix, i.e., every element is affected by all other elements, elements corresponding to good matching can be influenced by those corresponding to the wrong matching initially, which can cause a slow convergence of the optimization process especially when the initial guess is not good enough. ", "Furthermore, for data with noise or distortion, the QAP may propagate the distortion or noise in one region to other regions and cause the solution to the QAP unsatisfactory.", "\n\nTo tackle the aforementioned challenges for the QAP, we propose the following relaxed quadratic assignment using sparse pairwise descriptors and develop an efficient iterative algorithm with sparsity control for the doubly stochastic matrix to find high-quality dense landmarks. ", "These landmarks are then used in the final post-processing step to construct the full correspondence.", "\n\nSparse pairwise descriptors\n---------------------------\n\nLet $(\\M,g)$ be a closed 2-dimensional Riemannian manifold, the LBO is defined as $\\displaystyle \\Delta_{(\\M,g)} \\psi = \\frac{1}{\\sqrt{G}} \\sum_{i=1}^2 \\frac{\\partial}{\\partial x_i}(\\sqrt{G} \\sum_{j=1}^2 g^{ij} \\frac{\\partial \\psi}{\\partial x_j})$ [@chavel1984eigenvalues], here $g^{ij}$ is the inverse of $g_{ij}$ and $G = det(g)$. LBO is an elliptic and self-adjoint operator intrinsically defined on the manifold; thus, it is invariant under isometric transformation. ", "The LBO eigen-system satisfies: $$\\Delta_{(\\M,g)}\\psi_i = -\\lambda_i \\psi_i,\\quad \\int_{\\M}\\psi_i \\psi_j \\mathrm{d} s = \\delta_{ij}\n\\label{lbo}$$ and uniquely determines the underlying manifold up to isometry [@berard1994embedding]. ", "Spectral geometry is widely used in shape analysis  [@Reuter:06; @Levy:2006IEEECSMA; @Vallet:2008CGF; @sun2009concise; @Bronstein:2010CVPR; @lai2010metric; @ovsjanikov2012functional; @lai2017multiscale; @schonsheck2018nonisometric].", "\n\nIn practice, $\\M$ is discretized by a triangular mesh $T = \\{\\tau_\\ell\\}$ with vertices $V = \\{\\x_i\\}_{i=1}^n$ connected by edges $E=\\{e_{ij}\\}$. For each edge $e_{ij}$ connecting points $p_i$ and $p_j$, we define the angles opposite $E_{ij}$ as angles $\\alpha_{ij}$ and $\\beta_{ij}$. Denote the stiffness matrix as $\\bS$, given by [@reddy1993introduction; @reuter2009discrete] $$\\bS_{ij}= \n\\begin{cases}\n-\\frac{1}{2} [cot \\alpha_{ij} + cot \\beta_{ij}]& \\quad i\\sim j\\\\\n\\sum_{k \\sim i} \\bS(i,k)& \\quad i = j\n\\end{cases}$$ where $\\sim$ denotes the connectivity relation by an edge. ", "The mass matrix $\\bM$ is given by $$\\bM_{ij}=\n\\begin{cases}\n\\frac{|\\tau_1|+|\\tau_2|}{12} &i\\sim j\\\\\n\\sum_{k\\sim i} \\bM(i,k)& {i=j}\n\\end{cases}$$ where $|\\tau_1|$ and $|\\tau_2|$ are the areas of the two triangles sharing the same edge $ij$. On the one hand, the eigensystem of LBO can be computed as $\\bS \\psi = \\lambda \\bM \\psi $, which suggests $\\bS$ and $\\bM$ implicitly contain the spectrum information of LBO which can be used to determine a manifold uniquely up to isometry. ", "On the other hand, it has been rigorously shown a global rigidity theorem on the Stiffness matrix, i.e. two polyhedral surfaces share the same Stiffness matrices if on only if their corresponding metrics are the same up to a scaling [@gu2010discrete]. ", "Note that the mass matrix fixes the scaling factor. ", "Furthermore, both of these two matrices are local which are not sensitive to boundary conditions or topological perturbations. ", "Therefore, we expect that $\\bS$ and $\\bM$ together can serve as good sparse pairwise descriptors in a QAP formulation for shape correspondence.", "\n\nRelaxed QAP for shape correspondence\n------------------------------------\n\nGiven two surfaces $\\M_1$ and $\\M_2$ discretized by triangular meshes with vertices $\\{\\x_i\\}_{i=1}^n$ and $\\{\\y_i\\}_{i=1}^n$ respectively. ", "We denote the corresponding stiffness matrices by $\\bS_1, \\bS_2$ and the corresponding mass matrices by $\\bM_1$ and $\\bM_2$. Representing a point-to-point mapping between $\\M_1$ and $\\M_2$ by a permutation matrix $P\\in \\Pi_{n}$, we propose the following QAP problem to construct the point-to-point mapping between these two surfaces: $$\\minimize_{P \\in \\Pi_{n}}\\ \\frac{1}{2} \\|P \\bS_1-\\bS_2 P\\|_F^2 + \\frac{\\mu}{2} \\|P \\bM_1 - \\bM_2 P\\|_F^2,\n\\label{eqn_QAPSM}$$ Where $\\mu$ is a balance parameter. ", "The stiffness matrix captures local geometric information, and the mass matrix captures local area information of the discretized surface. ", "Both matrices have a sparsity structure with the number of nonzero entries linearly scaled with respect to the number of points. ", "This nice sparse property of both matrices already alleviates the memory issue for large data sets significantly. ", "In addition, since both descriptors only capture local geometric information, it potentially allows the proposed model to handle partial matching problem, open surfaces, and topological changes. ", "Since the proposed QPA is NP-hard, we relax the permutation matrix to a doubly stochastic matrix representation of the mapping: $$\\minimize_{D \\in \\mathcal{D}_n}\\ \\frac{1}{2}\\|D \\bS_1-\\bS_2 D\\|_F^2 + \\frac{\\mu}{2} \\| D \\bM_1 - \\bM_2 D \\|_F^2 \n\\label{eqn_QAPSM_relaxed}$$ As an advantage of this relaxation, each row of $D$ can be interpreted as the probability of a point on $\\M_1$ mapping to points on $\\M_2$. Now the relaxed QAP is convex and can be solved by well-known algorithms in convex programming. ", "Here, we use projected gradient descent algorithm with Barzilai-Borwein step size solve this optimization problem (see details in Section \\[subsec:alg\\]).", "\n\nDynamically sparsity-enforced QAP {#sec:iterative}\n=================================\n\nAs we pointed out before, the relaxed QAP problem is still difficult to solve if dense doubly stochastic matrices are used in the optimization process. ", "To overcome those difficulties, we propose an iterative algorithm that 1) selects candidates for well-matched pairs as anchor points, 2) enforces a dynamic sparsity structure of the doubly stochastic matrix by using regularity of the map, i.e., nearby points on the source surface should be mapped to nearby points on the target surface, in the neighborhood of those paired anchor points in each iteration. ", "These two ingredients both reduce the computation cost in each iteration (only sparse matrices are involved) and increase the number of well-matched pairs quickly since only candidates for well-matched points are used to guide the iterations.", "\n\nLocal distortion test {#sec:faith}\n---------------------\n\nTo define a desired sparsity structure for the doubly stochastic matrix $D$ in the relaxed QAP , we first need to detect candidates for well-matched pairs, or equivalently to remove those definitely ill-matched points, dynamically in each iteration. ", "Motivated by the Gromov-Wasserstein distance [@memoli2011gromov] and the unsupervised learning loss in [@halimi2018self], we introduce the following criterion to quantify location distortion of a mapping at a point on the source manifold.", "\n\n\\[def:faithfulness\\] Let $\\phi:\\M_1 \\rightarrow \\M_2$ be a map between two isometric manifolds. ", "For any point $\\x\\in\\M_1$, consider its $\\gamma$-geodesic ball in $\\M_1$ as $\\B_\\gamma(\\x) = \\{\\y\\in\\M_1~|~ d_{\\M_1}(\\x,\\y)\\leq \\gamma\\}$. local distortion of $\\phi$ at $\\x$ is defined as: $$\\F_{\\gamma}(\\phi)(\\x) = \\frac{1}{|\\B_\\gamma(\\x)|} \\int_{\\y\\in \\B_\\gamma(\\x)} DE_\\phi(\\x,\\y)\\mathrm{d} \\y \n\\label{eq:faithfulness}$$ where $\\displaystyle DE_\\phi(\\x,\\y) = \\frac{1}{\\gamma}|d_{\\M_1}(\\x,\\y)-d_{\\M_2}(\\phi(\\x),\\phi(\\y))|$ is the difference between the geodesic distance $d_{\\M_1}, d_{\\M_2}$ on the two corresponding manifolds, and $|\\B_\\gamma|$ is the volume of $\\B_\\gamma$.\n\nWe have the following straightforward properties:\n\n1. ", " If $\\phi$ is an isometric map, $\\F_{\\gamma}(\\phi)(\\x) = 0, \\forall \\x\\in\\M_1, \\gamma>0$.\n\n2. ", " If $\\F_{\\gamma}(\\phi)(\\x) = 0, \\forall \\x\\in\\M_1$ for some $\\gamma>0$, $\\phi$ is isometric.", "\n\nIn discrete setting, $\\M_1$ is represented as $ \\{\\x_i\\}_{i=1}^n$, $\\M_2$ is represented as $ \\{\\y_i\\}_{i=1}^n$and the map $\\phi$ is discretized as a one-to-one map between $ \\{\\x_i\\}_{i=1}^n$ and $ \\{\\y_i\\}_{i=1}^n$. We use the following discrete approximation: $$\\F_{\\gamma}(\\phi)(\\x_i) \\approx \\frac{\\sum_{\\x_j \\in \\B_\\gamma(\\x_i), \\x_j\\ne \\x_i} \\bM_1(j,j) DE_\\phi(\\x_i,\\x_j)}{ \\left(\\sum_{\\x_j \\in \\B_\\gamma(\\x_i), \\x_j\\ne \\x_i } \\bM_1(j,j) \\right)}\n \\label{eq:test}$$ to quantify how much $\\phi$ is distorted locally and use it to prune out those points that have large local distortion in the next iteration for the QAP. ", "In practice, we specify a number $\\epsilon$ and view $x_i$ as a candidate of well-matched anchor point for $\\phi$ if $\\F(\\phi)(\\x_i) < \\epsilon$. Together with $\\phi(\\x_i)$, we extract a collection of anchor pairs $\\{(\\x_i,\\phi(\\x_i))\\}_{i=1}^k$ which are used to define sparsity pattern in the doubly stochastic matrix $D$ dynamically in the relaxed QAP . ", "It is important to note that current anchor pairs will be re-evaluated and updated in later iterations.", "\n\nDynamic sparsity for doubly stochastic matrices\n-----------------------------------------------\n\nSuppose a collection of anchor pairs $\\{(\\x_i,\\phi(\\x_i))\\}_{i=1}^k$ have been selected using the local distortion test. ", "In the next iteration, a sub-QAP only involving points in the neighborhood of selected anchor pairs are solved. ", "We further enforce a sparsity structure on the doubly stochastic matrix for the sub-QAP based on the following two rules.", "\n\n1. ", " Each anchor point is mapped to its corresponding anchor point;\n\n2. ", " Points in the neighborhood of an anchor point on the source surface are mapped to the neighborhood of the corresponding anchor point on the target surface.", "\n\nLet $\\N(\\x)$ denote the neighborhood of a given point on a manifold, e.g., a geodesic ball $\\B_r$ centered at $\\x$ on the manifold, or simply points in the $l$-th ring of $\\x$ on a triangular mesh. ", "Define $\\N(\\{\\x_i\\}_{i=1}^k) = \\bigcup_{i=1}^k \\N(\\x_i)$ and $\\N(\\{\\phi(\\x_i)\\}_{i=1}^k) = \\bigcup_{i=1}^k \\N(\\phi(\\x_i))$. For the doubly stochastic matrix $D$ in the relaxed QAP , we only update variables with indices corresponding to the set $\\N(\\{\\x_i\\}_{i=1}^k)\\times \\N(\\{\\phi(\\x_i)\\}_{i=1}^k)$ together with the following sparsity constraints $$D_{t,s} = \n \\begin{cases}\n \\delta_{\\phi(\\x_s),\\y_t}, & \\text{if}~\\x_s\\in \\{\\x_i\\}_{i=1}^k \\\\\n 0,& \\text{if}~\\x_s\\in \\N(\\x_i) ~ \\text{and}~ \\y_t\\notin \\N(\\phi(\\x_i)) \\\\\n 0, & \\text{if}~\\y_t\\in \\N(\\phi(\\x_i)) ~ \\text{and}~ \\x_s\\notin \\N(\\x_i)\n \\end{cases}.", "\n\\label{eqn_sparsity}$$\n\nBy limiting the optimization region and enforcing the previous two sparsity constraints, the number of variables in the QAP problem after the sparsity enforcement is greatly reduced from $O(n^2)$ to $O(n)$. This can dramatically reduce computation cost. ", "Moreover, since the anchor points are fixed, it will no longer be influenced by other points in the current optimization process; on the contrary, it will enforce a positive influence on the neighboring points.", "\n\nIn practice, we always choose the size of $\\B_\\gamma(\\x)$ in the distortion test smaller than the size of sparsity control neighborhood $\\N(\\x)$ to allow the growth of anchor points in the next iteration. ", "In our experiments, we choose $\\B_\\gamma(\\x_i)$ as points included in the second ring of $\\x_i$ and $\\N(\\x_i)$ as points included in the fourth ring of $\\x_i$. The larger $\\B_\\gamma$ is, the more precise anchor points will be; the larger sparsity neighborhood $\\N(\\x)$ is, the faster the number of anchor points grows. ", "However, computation cost also increases for each QAP iteration when $\\B_\\gamma(\\x)$ and $\\N(\\x)$ become larger since the doubly stochastic matrix is less sparse.", "\n\nOnce the sparsity regularized $D$ is obtained, we update the point-to-point mapping $\\phi$ by choosing the largest element in each row. ", "Then, we find a new collection of anchor pairs by the distortion test based on the updated $\\phi$. Figure \\[fig\\_anchorpairs\\] illustrates an example of this procedure in the first 5 iterations. ", "Ideally, one should grow anchor points until all points are covered. ", "However, because of noise and/or non-isometry, the growth of high-quality anchor points usually slows down after a few iterations. ", "Moreover, even the exact solution of QAP may not produce a desirable result. ", "To balance between efficiency and accuracy, we find that 5 iterations of relaxed QAP  is good enough to find enough high quality anchor points. ", "We then use a post-processing step to construct the correspondence for the remaining points with the help of matched anchor pairs.", "\n\n![", "Growth of anchor pairs. ", "Red points in each column from left to right represent the location of anchor pairs from iteration 1 to 5. []{", "data-label=\"fig_anchorpairs\"}](landmarksgrowing.png){width=\"\\linewidth\"}\n\nPost Processing {#subsec_postprocessing}\n---------------\n\nThe aforementioned sparsity enforced quadratic assignment model based on local features is effective in growing anchor points from initial seed points in the regions where there is no significant non-isometric distortion. ", "However, for regions where there is significant distortion, such as near fingertips or elbow regions of humans in different poses, local features may not be enough to produce satisfactory results. ", "To construct a full correspondence and improve mappings in those regions, one can use global pointwise descriptors with reference to those already well-matched anchor pairs. ", "There are various options for the final post processing step. ", "For example, we use Heat Kernel Signature (HKS) [@sun2009concise] for closed surfaces in our experiments. ", "Let $H_1(\\x,\\x',t)$ and $H_2(\\y,\\y',t)$ denote HKS on $\\M_1$ and $\\M_2$ respectively. ", "Given $\\{\\x_i,\\phi(\\x_i)\\}_{i=1}^\\ell$ as the (sub)set of high quality anchor pairs obtained from solving the QAP , we construct pointwise descriptors of length $\\ell$ for those $\\x\\in \\M_1, \\y\\in \\M_2$ not in the anchor pair set as $\\{H_1(x,\\x_i,t)\\}_{i=1}^\\ell, \\{H_2(y,\\phi(\\x_i),t)\\}_{i=1}^\\ell$. Then we simply perform a nearest neighborhood search in this descriptor space to find the correspondence for non-anchor points. ", "For patches, we use geodesic distance to the chosen anchor pairs on the corresponding surfaces as the pointwise descriptor.", "\n\nNumerical Algorithms {#subsec:alg}\n--------------------\n\nWe use projected gradient descent with Barzilai-Borwein step size [@barzilai1988two], summarized in Algorithm \\[alg1\\], with the dynamic sparsity constraints  in each iteration to solve . ", "The initial doubly stochastic matrix $D_0$ can be a random matrix or using the initial guess provided by SHOT feature [@tombari2010unique] satisfying the sparsity constraint by projection . ", "SHOT feature only need to be computed once at the very beginning to provide the initial doubly stochastic matrix $D_0$ and select anchor points for the first iteration. ", "In later iterations, initial guess can be provided by projecting $D$ from previous iteration according to the new sparsity constraint.", "\n\n1.$Y_{k+1}=D_k - \\alpha_k \\nabla_{D} (\\| D_k \\bS_1-\\bS_2 D_k\\|_F^2+\\mu \\| D_k \\bM_1 - \\bM_2 D_k\\|_F^2)$ 2.$D_{k+1}=\\argminA_{D \\in \\mathcal{D}_n} \\| D - Y_{k+1}\\|^2_F$\\\n\n\\[alg1\\]\n\nNote that we only update entries of $D$ corresponding to those points in the neighborhood of selected anchor pairs $\\N(\\{\\x_i\\}_{i=1}^k)\\times \\N(\\{\\phi(\\x_i)\\}_{i=1}^k)$ and perform the projection on the set of doubly stochastic matrix $D$ satisfying the sparsity constraint . ", "Let $\\C$ be the indicator matrix for the sparsity constraint $$\\C_{t,s} = \n \\begin{cases}\n \\delta_{\\phi(\\x_s),\\y_t}, & \\text{if}~\\x_s\\in \\{\\x_i\\}_{i=1}^k \\\\\n 1,& \\text{if}~\\x_s\\in \\N(\\x_i) ~ \\text{and}~ \\y_t\\in \\N(\\phi(\\x_i)) \\\\\n 0, & \\text{otherwise}\n \\end{cases}.$$ The solution to the projection step in Algorithm \\[alg1\\] $$D_{k+1} = \\argminA_{D \\in \\mathcal{D}_n} \\| D - Y\\|^2_F,\\ \\text{s.t. } ", "\\eqref{eqn_sparsity}$$ is given by $$\\begin{aligned}\n D_{k+1} &= \\Big(Y + \\frac{|Y_{\\C}| - |\\C|}{|\\C|^2} \\vec{1} \\vec{1}^{\\mathsmaller T}\\\\\n &- (Y_{\\C}^{\\mathsmaller T} \\vec{1} - \\vec{1}) \\oslash \\vec{c} \\vec{1}^{\\mathsmaller T} - \\vec{1} ((Y_{\\C} \\vec{1} - \\vec{1} ) \\oslash \\vec{r})^{\\mathsmaller T}\\Big)_{\\C}\n \\end{aligned}\n\\label{eq:projection}$$ where $(\\boldsymbol{\\cdot})_{\\C} = (\\boldsymbol{\\cdot} ) \\odot C$, $|\\boldsymbol{\\cdot} | = \\vec{1}^{\\mathsmaller T} (\\boldsymbol{\\cdot} ) \\vec{1}$, $\\C \\vec{1} = \\vec{r}$, $\\C^{\\mathsmaller T} \\vec{1} = \\vec{c}$ and $\\odot$, $\\oslash$ are Hadamard product and Hadamard division. ", "We further relax our problem by neglecting the nonegative constraint as suggested in [@aflalo2014graph]. ", "This strategy further reduces the computation cost without causing any problem in all of our experiments.", "\n\nOur iterative method for the relaxed QAP  is summarized in Algorithm \\[alg2\\]. ", "Starting from an initial point-to-point map $\\phi^0$ (or converted from an initial doubly stochastic matrix), the three steps in each iteration are: Update the set of anchor pairs using  ; Update the doubly stochastic matrix by Algorithm \\[alg1\\] with sparsity constraint based on updated anchor pairs; Convert the doubly stochastic matrix to an updated point-to-point map by choosing the index of the largest element in each row.", "\n\nNote that all anchor pairs are updated and improved (by decreasing local distortion tolerance $\\epsilon$) during the iterations. ", "Geometrically, our iterative method is like matching by region growing from anchor pairs. ", "The local distortion criterion allows us to efficiently and robustly select a few reasonably good anchor points from a fast process (but not necessarily accurate dense correspondence), such as SHOT. ", "Then anchor pairs will grow as well as improve due to gradually diminishing local distortion tolerance during iterations. ", "In our experiments, we find enough high-quality anchor pairs after 5 iterations by decreasing $\\epsilon$ from 5 to 1. ", "Then we use these anchor pairs to construct the correspondence of remaining points in the final post-processing step as described in Section \\[subsec\\_postprocessing\\].", "\n\n**Input** a point-to-point map $\\phi^0$, iteration steps n, $\\{\\epsilon_i\\}_1^n$ and parameter $\\mu$.\n\n1\\. Find anchor pairs $\\{(\\x_i,\\phi^k(\\x_i)) ~|~ \\F(\\phi^k)(\\x_i)< \\epsilon_k \\}$. Define $\\N^k_1 = \\N(\\{\\x_i\\}_{i=1}^k)$ and $\\N^k_2 = \\N(\\{\\phi^k(\\x_i)\\}_{i=1}^k)$. 2. ", "Compute $D^{k+1}$ by Algorithm \\[alg1\\] with sparsity constraint on $\\N^k_1\\times \\N^k_2$. 3. ", "Update $\\phi^{k+1}(x_s) = y_t$, where $t =\\arg\\max D^{k+1}(s,:)$.\\\n\n\\[alg2\\]\n\nSince we start with a relatively large local distortion tolerance for initial anchor pairs, our method is quite stable with respect to the initialization. ", "Moreover, as we decrease the tolerance with iterations, anchor pairs selected earlier can be updated in later iterations. ", "We remark that the above algorithm can be straightforwardly extended to shape correspondence between two point clouds with different sizes by using a rectangular doubly stochastic matrix with the right dimension.", "\n\nDiscussion {#sec:dis}\n==========\n\n**Point cloud matching**   We can easily extend our method to point clouds, raw data in many applications, without a global triangulation by constructing the stiffness and mass matrices at each point using the local mesh method [@lai2013local] with an adaptive-KNN algorithm.", "\n\nIn [@lai2013local], the local connectivity of a point $p$ on the manifold $M$ is established by constructing a standard Delaunay triangulation in the tangent plane at $p$ of the projections of its K nearest neighbors. ", "However, the classical KNN with fixed $K$ is not adaptive to local geometric feature size or sampling resolution, which may lead to a loss of accuracy. ", "So we introduce the following adaptive-KNN.", "\n\nLet $\\lambda_1^i \\geq \\lambda_2^i \\geq \\lambda_3^i$ be the corresponding eigenvalues the local normalized co-variance matrix. ", "The key idea of our adaptive-KNN is that the local patch should not deviate too much from a planar one for a good linear approximation of the local geometry. ", "Hence we gradually decrease $K$ by removing the $m$ furthest points each time until the ratio $\\lambda_3^i$ by $\\lambda_1^i$ (invariant of local sampling density and patch size) is smaller than a given threshold or a lower bound for $K$ is reached.", "\n\n**Patch matching**   In real applications, well-sampled data for 3D shapes are not easy to obtain. ", "Instead, holes, patches, or partial shapes are more common in real data. ", "Correspondence between shapes with topological perturbations, artificial boundaries, and different sizes are difficult for methods based on global intrinsic descriptors in general. ", "For example, the spectrum of LBO is sensitive to boundary conditions and topological changes.", "\n\nHowever, since our method is based on local features, the effect of boundary conditions and topological perturbations are localized too. ", "Hence our method can be directly applied to those scenarios with good performance. ", "For example, our iterative method for the relaxed QAP using anchor pairs and sparsity control fits the smaller patch into the larger one nicely for partial matching (see Figure \\[patch3\\]). ", "For post processing in patch matching, we switch from HKS to geodesic distance signature since HKS is sensitive to boundary conditions.", "\n\nExperiment Results {#sec:result}\n==================\n\nWe evaluate the performance of our method through various tests on data sets from TOSCA [@bronstein2008numerical] and SCAPE [@anguelov2005correlated] and on patches extracted from TOSCA. ", "All inputs for our tests are raw data without any preprocessing, i.e., no low-resolution model or pre-computed geodesic distance. ", "Experiments are conducted in Matlab on a PC with 16GB RAM and Intel i7-6800k CPU. ", "The result of our method using mesh input is denoted as mesh method, and the result of our method without using mesh is denoted as point cloud method.", "\n\n**Error Metric**   Suppose our constructed correspondence maps $\\x\\in \\M_1$ to $\\y \\in \\M_2$ while the true correspondence is $\\x$ is to $\\y^*$, we measure the quality of our result by computing the geodesic error defined by $e(x) = \\frac{d_{\\M_2}(y,y^*)}{diam(\\M_2)}$, where $diam(\\M_2)$ is the geodesic diameter of $\\M_2$. Local distortion defined in  can also serve as an unsupervised error metric to measure the quality of a map. ", "As shown in Figure \\[faith\\], it’s clear that local distortion decreases as the geodesic error decreases, which indicates that local distortion can serve as a good unsupervised metric to quantify the approximate isometry.", "\n\n![", "Geodesic error and cumulative density function of local distortion for 4 sample pairs from the SCAPE data set (1st row); Original shape and corresponding local distortion heat map for sample 1 to 4 (2nd row). []{", "data-label=\"faith\"}](figures/faithl2_r.png){width=\"0.95\\linewidth\"}\n\n![", "Correspondence accuracy on the TOSCA and SCAPE data sets.[]{data-label=\"TSres\"}](tosca.png \"fig:\"){width=\".9\\linewidth\"}\\\n![", "Correspondence accuracy on the TOSCA and SCAPE data sets.[]{data-label=\"TSres\"}](scape.png \"fig:\"){width=\".9\\linewidth\"}\n\n**TOSCA**   The TOSCA data set contains 76 shapes of 8 different classes, from humans to animals. ", "The number of vertices varies from 4k to 50k. ", "We use 5 iterations to grow the set of anchor pairs. ", "The neighborhood used for local distortion test for selecting anchor points is the second ring, and for sparsity control is the fourth ring. ", "The distortion threshold decreases equally during the iterations from 5 to 1; the gradient descent step size in Algorithm \\[alg1\\] is 75; we approximate the heat kernel by 300 eigen-functions of the LBO with a diffusion time $t = 50$ in the post-processing step. ", "For point clouds without mesh, we use an initial $K=200$, ratio $r=0.05$, and shrink size $m=6$ for our adaptive-KNN; HKS post processing is not used since the spectrum computed directly from the point cloud is not accurate enough. ", "Results of our mesh method with or without post processing, and point cloud method without post processing are presented. ", "We compare our method with the following methods: Blended [@kim2011blended], SGMDS [@aflalo2016spectral], GMDS [@bronstein2006generalized], Kernel Marching [@vestner2017efficient], RSWD [@lai2017multiscale], and HKM 2 corrs [@ovsjanikov2010one]. ", "Figure \\[TSres\\] shows the quantitative result in terms of the geodesic error metric. ", "Our mesh method outperforms most of the state-of-art methods. ", "Our mesh method without post-processing and point cloud method also achieve reasonably good results.", "\n\n**SCAPE**   The SCAPE data set contains 72 shapes of humans in different poses. ", "Each shape has 12,500 vertices. ", "We use the same parameters as those on TOSCA data set except for diffusion time $t = 0.001$ in the post-processing step. ", "Results of our mesh method with or without post processing, and point cloud method are presented. ", "Figure \\[TSres\\] shows the quantitative result. ", "Our method achieves the state-of-art accuracy. ", "Again, our mesh method without post-processing and point cloud method also achieve reasonably good results.", "\n\n![", "Example of matching two patches. ", "The first two images show the location of the patches; the third image is the color map on the first patch; the fourth image is the induced color map based on SHOT feature; the last image is the induced color map from our mesh method. []{", "data-label=\"patch_no_topo\"}](patch0.png){width=\".9\\linewidth\"}\n\n![", "Example of matching patches with topological perturbation and shapes with randomly missing elements. ", "The first and third columns illustrate the patches and shapes to match. ", "The top color map of the first patch/shape is mapped to the second patch/shape using SHOT (middle) and our method (bottom).[]{data-label=\"patch2\"}](figures/cat_wolf.png){width=\"\\linewidth\"}\n\n**Patch Matching**   We present a few test results for patches that have holes, boundaries, and partial matching. ", "We paint the first patch with colors and map the color to the second patch with the correspondence computed using SHOT [@tombari2010unique] as the pointwise descriptor, which also serves as the initial guess for our method, and the correspondence computed from our algorithm to visualize the result. ", "Since HKS is sensitive to boundary conditions and topological changes, we use geodesic distance to those selected anchor pairs as pointwise descriptor in the post processing step.", "\n\nThe first test is matching two patches of a dog with different poses from TOSCA, as shown in Figure \\[patch\\_no\\_topo\\]. ", "The two patches have very irregular boundaries. ", "Using extrinsic pointwise descriptors, such as SHOT, fail to give a good dense correspondence. ", "However, our method performs well since it uses local pairwise descriptors to find high-quality anchor pairs and integrates global pointwise descriptor, the geodesic distance to those anchor pairs, to complete the dense correspondence.", "\n\nThe second test is matching two patches with topological perturbations from TOSCA data, as shown in Figure \\[patch2\\]. ", "The first case is two different poses of a wolf with mesh elements randomly deleted from each surface independently. ", "The second case is body parts of a cat in different poses with topological perturbation, the second patch is not connected at the bottom while the first one is as highlighted in the figure. ", "Since neither local connectivity distortion nor missing elements will significantly influence the stiffness matrix or mass matrix at most points, our method can still produce good results.", "\n\nWe further test our method on a pair of patches with both different sizes (partial matching) and topological changes, as shown in Figure \\[patch3\\]. ", "The example is mapping an arm patch to an entire shape. ", "Extra points are colored as blue. ", "The arm patch has less points than entire shape and the figure tips are cut off, which results in both different size and topological change. ", "Even for this challenging example, our method performs really well.", "\n\n**Time efficiency**   We list the average run time of several examples in TOSCA data set in Table \\[runtime\\]. ", "Most state-of-the-art methods using (dense) pair-wise descriptors and quadratic assignment (QA) require dense matrix multiplication in each step which already has super-quadratic complexity. ", "Although Laplace-Beltrami (LB) eigen-functions can be used to compress the dense matrix by low-rank approximation, it is still less sparse or localized and more time-consuming to compute than our simple, sparse and localized pair-wise descriptor. ", "Combined with our sparsity-enforced method for QA, our method has at most $O(n^2)$ complexity which outperforms methods with super-quadratic complexity when handling data with large size. ", "Experimentally, our method shows complexity even better than $O(n^2)$.\n\nConclusion\n==========\n\nWe develop a simple, effective iterative method to solve a relaxed quadratic assignment model through sparsity control for shape correspondence between two approximate isometric surfaces based on a novel local pairwise descriptor. ", "Two key ideas of our iterative algorithm are: 1) select pairs with good correspondence as anchor points using a local unsupervised distortion test, 2) solve a regularized quadratic assignment problem only in the neighborhood of selected anchor points through sparsity control. ", "With enough high-quality anchor points, various pointwise global features with reference to these anchor points can further improve the dense shape correspondence. ", "Extensive experiments are conducted to show the efficiency, quality, and versatility of our method on large data sets, patches, and purely point cloud data.", "\n\nSimilar to many existing methods, our method will have difficulty in dealing with significant non-isometric distortion and highly non-uniform sampling. ", "These will be further studied in our future research.", "\n\nAcknowledgement {#acknowledgement .unnumbered}\n===============\n\nR. Lai’s research is supported in part by an NSF Career Award DMS–1752934. ", "H. Zhao is partially supported by NSF DMS-1418422. ", "Part of this research was performed while the authors were visiting the Institute for Pure and Applied Mathematics (IPAM), which is supported by the NSF DMS-1440415.", "\n" ]

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[ "A friend of mine once said: ‘You know who is a true friend in comedy? ", "Someone who, after a gig in which you did badly, doesn’t say anything, can’t look you in the eye, and quietly leaves through the back door.", "\n\nHe told me this with his eyes, of course, as he backed out of the fire escape.", "\n\nIf what he said is indeed the case, then in my time I’ve been a social butterfly for many people. ", "I run an open mic night in a small scene, and half the work of promoting is simply apportioning out stage time to the correct people to create a night that is good in quality, lasts an appropriate amount of time for punters but is also constructive to acts. ", "The nature of this scene means demand often outweighs what I can supply.", "\n\nHow does someone choose people to give time to? ", "Quality is one thing, sure, but to ensure the acts are using the stage time constructively I’m currently prioritising effort, which is a hard thing to measure and define. ", "There’s the amount of fine-tuning and new writing an act brings, how dedicated they seem, whether they are coming to watch on nights they are not on, whether they doing gigs that aren’t necessarily going to be easy, things like that.", "\n\nIf they aren’t good yet, you cushion them between good acts until their quality stands by itself. ", "It will come in time, but in this moment their effort is what is important to me. ", "But there is one thing that undermines even that, which makes any amount of effort a complete waste of time. ", "And that is delusion.", "\n\nThere’s a popular term in psychoanalysis: defence mechanisms. ", "It refers to unconscious psychological actions we take to protect ourselves and our acceptable pictures of the world, perhaps from an uncomfortable truth.", "\n\nSome defences are necessary and even healthy (sublimation, or the channelling of pain into higher channels like art, is a good example of this), but many are gateways to mental pain.", "\n\nFor example, a child abused by a parent could believe that they themselves are at fault (‘turning on the self’). ", "And of course, the most classic defence mechanism of all is denial.", "\n\nWhen I said ‘delusion' earlier, I’m aware that it exists on a spectrum. ", "I’m not saying bad open mic comedians are mentally ill. ", "we all use defence mechanisms. ", "We change the subject when the topic is uncomfortable. ", "We avoid people who make us anxious. ", "But unhealthy defence mechanisms are on very public display more often than you think, and dealt with improperly, in the worst possible places: comedy open mic nights and reality television.", "\n\nI never used to watch the X-Factor beyond the auditions. ", "I found myself watching with morbid fascination as terrible, terrible singers subjected themselves to public humiliation and were shocked to find themselves not showered with praise, but criticised by a handful of bored and awkward celebrities.", "\n\nWhy go through such pain? ", "When I watch with other people, they always say ‘nobody has had the guts to tell them they’re a bad singer’, or ‘some idiot has told them they’re brilliant and they’ve swallowed it whole’.", "\n\nThere’s an assumption that this person has lived a life lacking in necessary ‘tough love’. ", "That they have not had their belief that they are a good singer challenged enough.", "\n\nWe see people like this on the open mic scene of course. ", "Even if they do receive the ‘tough love’ from audiences who greet then with total silence or charity chuckles, we all know of six-year vets making no improvement, yet completely lacking in vital self-awareness of the fact. ", "Scribbling down on notepads all the jokes in their dire set that ‘worked’. ", "It’s not necessarily a lack of intelligence, and I don’t think the problem is an absence of tough love. ", "I think that tough love makes things worse.", "\n\nThere’s a famous nonfiction book by Milton Rokeach called The Three Christs of Ypsilanti. ", "It’s really very good. ", "Rokeach, a psychiatrist, decides to conduct a massively unethical experiment.", "\n\nHe gets three separate schizophrenics in his hospital, each one believing that they are the living, breathing second coming of Jesus Christ, and has them work and live together. ", "Living together in an environment where their delusion of identity was constantly challenged simply by the other men’s presence was meant to, in theory, help the men recover. ", "Rokeach also attempted to manipulate other aspects of their delusions by inventing messages from imaginary characters (He wasn’t a nice guy, I don’t think).", "\n\nHe did not, as he had hoped, provoke any lessening of the patients' delusions. ", "In fact in many ways they became worse.", "\n\nWhile initially the three patients quarrelled over who was holier and reached the point of physical altercation, they eventually each explained away the other two as being patients with a mental disability in a hospital, or dead and being operated by machines.", "\n\nUnder constant challenge, many of us simply retreat further and further into our defences and delusions.", "\n\nYou see this in the open mic scene; good gigs invented from a silent crowd or the delusion that the crowd ‘did not get them’. ", "You see this on TV as bad singers get challenged by the biggest names in the music business (questionable as Simon Cowell’s judgement and motives can be) and shrug them off. ", "They’ll see. ", "They’ll all see.", "\n\nI’ve known maybe five acts over my five years as a promoter that I could say with near certainty were never going to get better because of this inability to see themselves honestly. ", "I used to enjoy watching them; I found them fascinating. ", "I bit my lip once as someone told me he wasn’t looking for a job, because comedy was his life. ", "But at the end of The Three Christs, Rokeach says that only one christ was cured of his Godlike delusions. ", "Himself.", "\n\nAs a promoter now I think simply giving these people stage time when I know there is no chance of improvement is as unethical as the experiment. ", "What is the solution? ", "I don’t know if there is one.", "\n\nPerhaps some people should not be given the stage time with which to embarrass themselves or go deeper Into defensiveness, if they’ve had sufficient time to improve and not done so.", "\n\nPsychoanalysts who encounter resistance simply point out to their clients that they are facing resistance and try to interpret it. ", "This can be a bit brazen, but may be helpful in the end.", "\n\nPerson-centred therapists would look at the resistance in an empathic, nonjudgemental way. ", "Maybe as promoters or fellow comics it would help to work on our ability to have difficult conversations with honest, empathic feedback, to be able to slip in the information they need without pushing them deeper into denial.", "\n\nAnd Luke finished writing his article, and saw that it was good. ", "Amen.", "\n\n• Luke Mcgibbon previously wrote A Passive-Aggressive Guide To Running A Gig for Chortle.", "\n\nPublished: 26 Feb 2018" ]

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[ "Audio\n\nA group of protesters plan to gather outside the National Security Agency headquarters tomorrow to challenge the continued use of military drones by U-S agencies.", "\nKBOO’s Jenka Soderberg spoke with one of the protest organizers.", "\n\nPlans for the annual May Day march and rally in Portland are taking form as a broad range of community organizations and labor advocacy groups, including local unions, prepare to celebrate International Workers' Day.", "\nFor more, KBOO’s Susan Cecil spoke with Greg Margolis, who is helping to organize tomorrow’s rally and march for workers in Portland:\nAt tomorrow’s May Day event in Portland, people will begin to gather at the South Park Blocks at 2:00 PM and the rally begins at 3:00 PM with speakers and musicians.", "\nAt 4:00 PM a march will begin through downtown Portland and will end back at the South Park Blocks at about 5:30 PM.", "\nIf you can’t make it downtown, be sure to tune in to the KBOO News tomorrow at 5:00 PM for a special May Day Live report.", "\n\nKBOO’s Jenka Soderberg spoke with Saed Bannoura, Editor-In-Chief of the International Middle East Media Center (IMEMC), about the current state of Palestinian political prisoners held in Israel. ", "The IMEMC has published a document prepared by Palestinian researcher Abdul-Nasser Ferwana.", "\n\nEradicating Offensive Native Mascotry (https://www.facebook.com/mascotry), a group of Native parents and their allies from across the country, are calling on Nike, Inc. to stop selling products that feature the Cleveland Indians' mascot Chief Wahoo. ", "EONM has launched a Facebook event page \"#Dechief Nike Twitterstorm\" to trend the Twitter hashtag #Dechief and demand Nike remove the caricature, Chief Wahoo Nike, from its products. \"", "Dechiefed\" hats, jerseys and jackets of Cleveland fans have been featured on social media where photos of team gear with Chief Wahoo removed are posted accompanied by the hashtag 3dechiefwahoo. ", "The group also plans to protest at Nike's headquarters in Beaverton later this week.", "\nIn this KBOO Evening News story, Paul Roland speaks with the EONM's spokesperson, Jacqueline Keeler about the campaign. ", "Keeler wrote a recent article for Salon.com about the issue:http://www.salon.com/2014/04/13/my_life_as_a_cleveland_indian_the_enduring_disgrace_of_racist_sports_mascots/\n\nThe Federal Communications Commission has proposed changing the rules on how the Internet is regulated.", "\nInternet and free speech activists say the new rules will forever change the free and open Internet to a quote “pay to play” system that is controlled by corporate interests.", "\nKBOO’s Robin Ryan spoke with April Glaser with the Electronic Frontier Foundation, a group which advocates for a free and open Internet.", "\nShe also spoke with Timothy Karr, the senior director of Strategy at Free Press.", "\n\nA report this week by The Oregonian newspaper uncovered a major loophole in the monitoring and regulation of coal and oil transport throughout the state of Oregon.", "\nAccording to The Oregonian’s report, railroad companies are not required to submit full records to the department of transportation.", "\nBut it’s not clear which agency these records SHOULD be submitted to.", "\nSo no one really knows where the oil and coal trains traveling through Oregon are at any given time, or how much fuel is on any given train.", "\nKBOO’s Jenka Soderberg followed up on the Oregonian report by talking to several of the government agencies involved.", "\n\nToday is earth day, a celebration of life on earth and a call to action to save the planet. ", "The day began in 1970, as the first wave of the environmental movement in the U-S was at its height.", "\n\nThis year, cities across the country are planning ten days of action under the theme ‘From Earth Day to May Day’, to try to bring together issues of environmentalism and labor rights. ", "KBOO spoke with Lauren Regan, one of Oregon’s main organizers in the Global Climate Convergence days of action.", "\n\nIn the KBOO studios: Matt Zodrow and Tracy MacDonald the creators of the upcoming documentary project “WHITELANDIA”. ", "The film plans to document Black Oregon and the many turns the state has taken on race relations, and KBOO news in-depth wanted to ask the questions on what the purpose of this docu-film seeks to get across to the residents in Portland and abroad. ", "Whiteland has a Kick-Starter program to raise funds for the film:\n\nIn the KBOO studios: Matt Zodrow and Tracy MacDonald the creators of the upcoming documentary project “WHITELANDIA”. ", "The film plans to document Black Oregon and the many turns the state has taken on race relations, and KBOO news in-depth wanted to ask the questions on what the purpose of this docu-film seeks to get across to the residents in Portland and abroad." ]

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[ "Sally Hansen Air Brush Legs Tan 75ml\n\nwww.wilko.com\n\nlike0%0%dislike\n|\n\nshare |\n\ntweet |\n\ntell a friend\n\nProduct\n\nSally Hansen Air Brush Legs Tan 75ml\n\nOffer from\n\nWilko\n\nPrice\n\n£9.95\n\nDescription\n\nThis lightweight leg makeup enriched with Palmaria Extract enhances coverage of freckles veins and imperfections so legs look and feel silky smooth and sexy. ", "Comes in 4 shades to match any skin tone. ", "For external use only. ", "Keep out of reach of children. ", "Always read instuctions before use.", "\n\nPrice history\n\nPrice compare for Sally Hansen Air Brush Legs Tan 75ml and the best offers and deals in the supermarket and at Wilko\n\nCurrently there is no price history or price compare for the offer Sally Hansen Air Brush Legs Tan 75ml available\n\nThis small Silvine memo book is perfect for note-making on the go. ", "The small lined book...\n\n£0.75\n\nBuy product online\n\nPage content will be loaded...\n\nSally Hansen Air Brush Legs Tan 75ml for £9.95\n\nWhen is Sally Hansen Air Brush Legs Tan 75ml in Wilko available? ", "Sally Hansen Air Brush Legs Tan 75ml ist available from to at Wilko!", "\n\nWhat does Sally Hansen Air Brush Legs Tan 75ml cost at Wilko? ", "You get Sally Hansen Air Brush Legs Tan 75ml at Wilko at the price of £9.95!", "\n\nIf you are looking for the current offer of Sally Hansen Air Brush Legs Tan 75ml at Wilko in ,\nthen you are right with OffersCheck. ", "Here you get the information,\nwhen you can procure Sally Hansen Air Brush Legs Tan 75ml from Wilko!", "\nThe offer for Sally Hansen Air Brush Legs Tan 75ml at Wilko calendar week and many more offers\nYou can view the offer and write a review at OffersCheck.", "\nThe answer to the question Wilko when there is Sally Hansen Air Brush Legs Tan 75ml can also be obtained at OffersCheck.", "\n\nThis offer was indexed on 2016-11-27 from www.wilko.com.", "Please note that this offer might only be available regionally. ", "The detailed informations are available on the homepage of Wilko" ]

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[ "2393\nKoiko's sprite at 1x is only a little shorter than her mother Hanako at 1x.", "\nThe stretchiness aspect refers to the anime Azu Manga Daioh.", "\n\n2394\nTwo jokes going on here: The first refers to the beginning of 2013 where\nYume tries and mostly succeeds at being a professional actor despite the constant interruptions.", "\nHere she does crack up at the second joke referencing a fanfic I wrote many, many, many years ago\nwhere Megaman X tries to speak Spanish to Sutako/Koiko.", "\nBy the way, \"kei\" is how you spell \"what\" in Japanese.", "\n\n2395\nRavy's feet are in what I call the Bloom County Stance.", "\nAs soon as I find that ONE Bloom County comic...\nThe spell checker on my web editor accepts \"stretchiness\" and not \"Ravy?\"", "\n\n2396\nWhen designing Jeseka I used the gym girl outfit as more of a reference for the shape of her body.", "\nI was going to put her in something else and never got around to it. ", "It did set up a rather long running gag\nabout her boyfriend using microscopic spy drones to take pictures of her butt and put them on the big screen.", "\nRavy relents to Koiko's demands because if she goes, he has to take her place.", "\nYep, that means wearing her costume along with the bloomers.", "\n\nRavy Comics, its subcomics,\nand all original material copyright 2014 Joe Pullin.", "\nThe entirety of this website should be considered parody.", "\nIf you're taking any of this seriously, here is what you need to do:\nTake a deep breath and hold it until I can get to you." ]

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[ "Q:\n\nHow does gcc get the alignment for each type on a specific platform?", "\n\nIs it hard coded into gcc's source or fetched somehow programatically?", "\n\nA:\n\nI think it is hardcoded in arch-specific folder, e.g. for sparc\nhttp://www.google.com/codesearch#Yj7Hz1ZInUg/trunk/gcc-4.2.1/gcc/config/sparc/sparc.h\n/* No data type wants to be aligned rounder than this. ", " */\n#define BIGGEST_ALIGNMENT (TARGET_ARCH64 ? ", "128 : 64)\n\n/* The best alignment to use in cases where we have a choice. ", " */\n#define FASTEST_ALIGNMENT 64\n\n...\n/* Make strings word-aligned so strcpy from constants will be faster. ", " */\n#define CONSTANT_ALIGNMENT(EXP, ALIGN) \\\n ((TREE_CODE (EXP) == STRING_CST \\\n && (ALIGN) < FASTEST_ALIGNMENT) \\\n ? ", "FASTEST_ALIGNMENT : (ALIGN))\n\n/* Make arrays of chars word-aligned for the same reasons. ", " */\n#define DATA_ALIGNMENT(TYPE, ALIGN) \\\n (TREE_CODE (TYPE) == ARRAY_TYPE \\\n && TYPE_MODE (TREE_TYPE (TYPE)) == QImode \\\n && (ALIGN) < FASTEST_ALIGNMENT ? ", "FASTEST_ALIGNMENT : (ALIGN))\n\nand sparc.c in the same folder.", "\nSome basic alignment rules are defined in gcc/tree.c e.g. for void:\n /* We are not going to have real types in C with less than byte alignment,\n so we might as well not have any types that claim to have it. ", " */\n TYPE_ALIGN (void_type_node) = BITS_PER_UNIT;\n TYPE_USER_ALIGN (void_type_node) = 0;\n\nIt will be compiled into gcc in the build process.", "\nSo, default aligns are compiled in, but can be changed by manipulating TREE type objects from the gcc code.", "\nUPDATE: x86 config has better comments:\n/* Minimum size in bits of the largest boundary to which any\n and all fundamental data types supported by the hardware\n might need to be aligned. ", "No data type wants to be aligned\n rounder than this.", "\n\n Pentium+ prefers DFmode values to be aligned to 64 bit boundary\n and Pentium Pro XFmode values at 128 bit boundaries. ", " */\n\n#define BIGGEST_ALIGNMENT 128\n\n/* Decide whether a variable of mode MODE should be 128 bit aligned. ", " */\n#define ALIGN_MODE_128(MODE) \\\n ((MODE) == XFmode || SSE_REG_MODE_P (MODE))\n\n/* The published ABIs say that doubles should be aligned on word\n boundaries, so lower the alignment for structure fields unless\n -malign-double is set. ", " */\n\n/* ??? ", "Blah -- this macro is used directly by libobjc. ", " Since it\n supports no vector modes, cut out the complexity and fall back\n on BIGGEST_FIELD_ALIGNMENT. ", " */\n...\n#define BIGGEST_FIELD_ALIGNMENT 32\n...\n/* If defined, a C expression to compute the alignment given to a\n constant that is being placed in memory. ", " EXP is the constant\n and ALIGN is the alignment that the object would ordinarily have.", "\n The value of this macro is used instead of that alignment to align\n the object.", "\n\n If this macro is not defined, then ALIGN is used.", "\n\n The typical use of this macro is to increase alignment for string\n constants to be word aligned so that `strcpy' calls that copy\n constants can be done inline. ", " */\n\n#define CONSTANT_ALIGNMENT(EXP, ALIGN) ix86_constant_alignment ((EXP), (ALIGN))\n\n/* If defined, a C expression to compute the alignment for a static\n variable. ", " TYPE is the data type, and ALIGN is the alignment that\n the object would ordinarily have. ", " The value of this macro is used\n instead of that alignment to align the object.", "\n\n If this macro is not defined, then ALIGN is used.", "\n\n One use of this macro is to increase alignment of medium-size\n data to make it all fit in fewer cache lines. ", " Another is to\n cause character arrays to be word-aligned so that `strcpy' calls\n that copy constants to character arrays can be done inline. ", " */\n\n#define DATA_ALIGNMENT(TYPE, ALIGN) ix86_data_alignment ((TYPE), (ALIGN))\n\n/* If defined, a C expression to compute the alignment for a local\n variable. ", " TYPE is the data type, and ALIGN is the alignment that\n the object would ordinarily have. ", " The value of this macro is used\n instead of that alignment to align the object.", "\n\n If this macro is not defined, then ALIGN is used.", "\n\n One use of this macro is to increase alignment of medium-size\n data to make it all fit in fewer cache lines. ", " */\n\n#define LOCAL_ALIGNMENT(TYPE, ALIGN) ix86_local_alignment ((TYPE), (ALIGN))\n\n ...\n\n/* Set this nonzero if move instructions will actually fail to work\n when given unaligned data. ", " */\n#define STRICT_ALIGNMENT 0\n\nFor arm, mips, sparc, and others archs (which limits unaligned access to memory) the alignment requires of any machine instruction may be recorded in arch.md file (e.g. in sparc.md)\n\n" ]

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[ "---\nabstract: '*This paper studies a periodic-review single-commodity setup-cost inventory model with backorders and holding/backlog costs satisfying quasiconvexity assumptions. ", "We show that the Markov decision process for this inventory model satisfies the assumptions that lead to the validity of optimality equations for discounted and average-cost problems and to the existence of optimal $(s,S)$ policies. ", "In particular, we prove the equicontinuity of the family of discounted value functions and the convergence of optimal discounted lower thresholds to the optimal average-cost one for some sequences of discount factors converging to $1.$ If an arbitrary nonnegative amount of inventory can be ordered, we establish stronger convergence properties: (i) the optimal discounted lower thresholds $s_\\alpha$ converge to optimal average-cost lower threshold $s;$ and (ii) the discounted relative value functions converge to average-cost relative value function. ", "These convergence results previously were known only for subsequences of discount factors even for problems with convex holding/backlog costs. ", "The results of this paper also hold for problems with fixed lead times.*'", "\nauthor:\n- |\n Eugene A. Feinberg, Yan Liang\\\n *Department of Applied Mathematics and Statistics*\\\n *Stony Brook University, Stony Brook, NY 11794*\\\n *eugene.feinberg@stonybrook.edu, yan.liang@stonybrook.edu*\ntitle: '**Stochastic Setup-Cost Inventory Model with Backorders and Quasiconvex Cost Functions** '\n---\n\n***Keywords:** Inventory control, $(s,S)$ policies, average-cost optimality equations, relative value functions.*", "\n\nIntroduction {#sec:introduction}\n============\n\nIn this paper we study a periodic-review single-commodity setup-cost inventory model with backorders and holding/backlog costs satisfying quasiconvexity assumptions. ", "We show that the Markov decision process for this inventory model satisfies the assumptions that lead to the validity of optimality equations for discounted and average-cost problems and to the existence of optimal $(s,S)$ policies. ", "In particular, we prove the equicontinuity of the family of discounted value functions and the convergence of optimal discounted lower thresholds to the optimal average-cost one for some sequences of discount factors converging to $1.$ If an arbitrary nonnegative amount of inventory can be ordered, we establish stronger convergence properties: (i) the optimal discounted lower thresholds $s_\\alpha$ converge to optimal average-cost lower threshold $s;$ and (ii) the discounted relative value functions converge to average-cost relative value function. ", "These convergence results previously were known only for subsequences of discount factors even for problems with convex holding/backlog costs. ", "The results of this paper hold for problems with deterministic positive lead times.", "\n\nFor problems with convex holding/backlog cost functions, Scarf [@Sca60] introduced the concept of $K$-convexity to prove the optimality of $(s,S)$ policies for finite-horizon problems with continuous demand and convex holding/backlog costs. ", "Zabel [@za62] indicated some gaps in Scarf [@Sca60] and corrected them. ", "References [@BCST; @BS99; @CS04a; @CS04b; @Ftut; @FL16; @FLi16a; @FLi16b; @Igl63; @Sca60; @SCB05; @VW65] deal with convex or linear holding/backlog cost functions. ", "Iglehart [@Igl63] extended Scarf’s [@Sca60] results to infinite-horizon problems with continuous demand. ", "Veinott and Wagner [@VW65] proved the optimality of $(s, S)$ policies for both finite-horizon and infinite-horizon problems with discrete demand. ", "Beyer and Sethi [@BS99] completed the missing proofs in Iglehart [@Igl63] and Veinott and Wagner [@VW65]. ", "Chen and Simchi-Levi [@CS04a; @CS04b] studied coordinating inventory control and pricing problems and proved the optimality of $(s,S)$ policies without assuming that the demand is discrete or continuous. ", "Under certain assumptions, their results imply the optimality of $(s,S)$ policies for problems without pricing. ", "Beyer et al.", " [@BCST] and Huh et al.", " [@HJN11] studied problems with parameters depending on exogenous factors modeled by a Markov chain. ", "Additional references can be found in monographs by Porteus [@Por02] and Zipkin [@Zip00].", "\n\nThe analysis of periodic-review inventory models is based on the theory of Markov Decision Processes (MDPs). ", "However, most of inventory control papers use only basic facts from the MDP theory, and the corresponding general results had been unavailable for a long time. ", "Feinberg et al.", " [@FKZ12] developed the results on MDPs with Borel state spaces, possibly noncompact action sets, and possibly unbounded one-step costs. ", "Discrete-time periodic-review inventory control problems are particular examples of such MDPs; see Feinberg [@Ftut] for details. ", "Feinberg and Lewis [@FL16] obtained additional convergence results for convergence of optimal actions for MDPs and established the optimality of $(s,S)$ policies for inventory control problems as well as other results. ", "Feinberg and Liang [@FLi16a] provided descriptions of optimal policies for all possible values of discount factors (for some parameters, optimal $(s,S)$ policies may not exist for discounted and finite-horizon problems). ", "Feinberg and Liang [@FLi16b] proved that discrete-time periodic-review inventory models with backorders and convex holding/backlog costs satisfy the equicontinuity assumption, and this implies several additional properties of optimal average-cost policies including the validity of average-cost optimality equations (ACOEs).", "\n\nVeinott [@Vei66] studied the nonstationary setup-cost inventory model with a fixed lead time, backorders, and holding/backlog costs satisfying quasiconvexity assumptions. ", "Veinott [@Vei66] proved the optimality of $(s,S)$ policies for finite-horizon problems and also provided bounds on the values of the optimal thresholds $s$ and $S.$ Zheng [@Zheng] proved the optimality of $(s,S)$ policies for models with quasiconvex cost functions and discrete demand under both discounted and average cost criteria by constructing a solution to the optimality equations.", "\n\nIn this paper we consider the infinite-horizon stationary inventory model with holding/backlog costs satisfying quasiconvexity assumptions. ", "These quasiconvexity assumptions are introduced by Veinott [@Vei66] for finite-horizon nonstationary models. ", "Zheng [@Zheng] and Chen and Simchi-Levi [@CS04b] considered a slightly stronger quasiconvexity assumption for infinite-horizon stationary models. ", "For inventory model with holding/backlog costs satisfying quasiconvexity assumptions, this paper establishes convergence properties of optimal discounted thresholds for discounted problems to the corresponding thresholds for average-cost problems. ", "Some of the results are new even for problems with convex holding/backlog costs. ", "While convergence of optimal thresholds and relative discounted value functions was known only for subsequences of discount factors (see [@BCST; @FL16; @FLi16b; @HJN11]), here we show that convergence of lower thresholds and discounted value functions takes place for all discount factors tending to 1.", "\n\nThe rest of the paper is organized in the following way. ", "Section \\[sec:inventory control\\] describes the setup-cost inventory model and introduces the assumptions used in this paper. ", "Section \\[sec:mdptotal\\] establishes the optimality of $(\\sa,\\Sa)$ policies for the infinite-horizon problem with the discount factor $\\a.$ Section \\[sec:mdpac\\] verifies average-cost optimality assumptions and the equicontinuity conditions for discounted relative value functions. ", "Section \\[sec:acoe\\] establishes the validity of ACOEs for the inventory model and the optimality of $(s,S)$ policies under the average cost criterion. ", "Section \\[sec:cvg sa\\] establishes the convergence of discounted optimal lower thresholds $\\sa,$ when the discount factor $\\a$ converges to $1,$ to the average-cost optimal lower threshold $s.$ Section \\[sec:cvg ua\\] establishes the convergence of discounted relative value functions, when the discount factor converges to $1.$ Section \\[sec:veinott\\] presents a reduction from the inventory model with constant lead times to the model without lead times using Veinott’s [@Vei66] approach.", "\n\nSetup-Cost Inventory Model with Backorders: Definitions and Assumptions {#sec:inventory control}\n=======================================================================\n\nLet $\\R$ denote the real line, $\\Z$ denote the set of all integers, $\\Rp:=[0,+\\infty)$ and $\\N_0 := \\{0,1,2,\\ldots \\}.$ Consider the stochastic periodic-review setup-cost inventory model with backorders. ", "At times $t=0,1,\\ldots,$ a decision-maker views the current inventory of a single commodity and makes an ordering decision. ", "Assuming zero lead times, the products are immediately available to meet demand. ", "The cost of ordering is incurred at the time of delivery of the order. ", "Demand is then realized, the decision-maker views the remaining inventory, and the process continues. ", "The unmet demand is backlogged. ", "The demand and the order quantity are assumed to be nonnegative. ", "The objective is to minimize the infinite-horizon expected total discounted cost for discount factor $\\a\\in (0,1)$ and long run average cost for $\\a = 1.$ The inventory model is defined by the following parameters:\n\n1. ", " $K > 0$ is a fixed ordering cost;\n\n2. ", " $\\bar{c}>0$ is the per unit ordering cost;\n\n3. ", " $\\{D_t,t=1,2,\\dots\\}$ is a sequence of i.i.d.", " nonnegative finite random variables representing the demand at periods $0,1,\\dots\\ .$ We assume that $\\E [D] < +\\infty$ and $\\PR(D>0)>0,$ where $D$ is a random variable with the same distribution as $D_1;$\n\n4. ", " $h(x)$ is the holding/backlog cost per period if the inventory level is $x.$ Assume that: (i) the function $\\E[h(x-D)]$ is finite and continuous for all $x\\in\\X;$ and (ii) $\\E[h(x-D)]\\to +\\infty$ as $|x|\\to +\\infty.$\n\nWithout loss of generality, assume that the function $\\E[h(x-D)]$ is nonnegative. ", "The assumption $\\PR(D>0)>0$ avoids the trivial case when there is no demand.", "\n\nNow we formulate an MDP for this inventory model. ", "The state and action spaces can be either (i) $\\X=\\R$ and $\\A=\\Rp;$ or (ii) $\\X=\\Z$ and $\\A = \\N_0,$ if the demand $D$ takes only integer values and only integer orders are allowed.", "\n\nThe dynamics of the system are defined by the equation $$\\begin{aligned}\n x_{t+1} = x_t + a_{t} - D_{t+1}, \\qquad t=0,1,2,\\ldots,\n \\label{eqn:dynamic2}\\end{aligned}$$ where $x_t$ and $a_t$ denote the current inventory level and the ordered amount at period $t$ respectively. ", "The transition probability $q(d x_{t+1} | x_t, a_t)$ for the MDP defined by the stochastic equation is $$\\begin{aligned}\n q(B | x_t, a_t) = \\PR (x_t + a_t - D_{t+1} \\in B)\n \\label{eqn:tranp2}\\end{aligned}$$ for each measurable subset $B$ of $\\R.$ The one-step expected cost is $$\\begin{aligned}\n c(x,a) := K \\indF_{\\{ a > 0 \\}} + & {\\bar c}a + \\E[h(x+a-D)], \\qquad (x,a)\\in \\X\\times\\A,\n \\label{eqn:c}\\end{aligned}$$ where $\\indF_B $ is an indicator of the event $B.$\n\nLet $H_t = (\\X\\times\\A)^{t}\\times\\X$ be the set of histories for $t=0,1,\\dots\\ .$ Let $\\PS$ be the set of all policies. ", "A (randomized) decision rule at period $t=0,1,\\dots$ is a regular transition probability $\\pi_t : H_t\\to \\A,$ that is, (i) $\\pi_t(\\cdot|\\bh_t)$ is a probability distribution on $\\A,$ where $\\bh_t=(x_0,a_0,x_1,\\dots,a_{t-1},x_t),$ and (ii) for any measurable subset $B\\subset \\A,$ the function $\\pi_t(B|\\cdot)$ is measurable on $H_t.$ A policy $\\pi$ is a sequence $(\\pi_0,\\pi_1,\\dots)$ of decision rules. ", "Moreover, $\\pi$ is called non-randomized if each probability measure $\\pi_t(\\cdot|\\bh_t)$ is concentrated at one point. ", "A non-randomized policy is called stationary if all decisions depend only on the current state. ", "According to the Ionescu Tulcea theorem (see Hernández-Lerma and Lasserre [@HLL96 p. 178]), given the initial state $x,$ a policy $\\pi$ defines the probability distribution $\\PR_{x}^{\\pi}$ on the set of all trajectories $H_{ +\\infty} = (\\X\\times\\A)^{ +\\infty}$. We denote by $\\E_{x}^{\\pi}$ the expectation with respect to $\\PR_{x}^{\\pi}.$\n\nFor a finite-horizon $N=0,1,\\dots,$ let us define the expected total discounted costs $$\\label{eqn:sec_model def:finite total disc cost}\n v_{N,\\a}^{\\pi} (x) := \\mathbb{E}_{x}^{\\pi} \\Big[ \\sum_{t=0}^{N-1}\n \\alpha^{t} c(x_t,a_t) \\Big] , \\qquad x\\in\\X,$$ where $\\alpha\\in [0,1]$ is the discount factor and $v_{0,\\a}^{\\pi} (x)= 0,$ $x\\in\\X.$ When $N= +\\infty$ and $\\alpha\\in [0,1),$ defines the infinite-horizon expected total discounted cost denoted by $v_{\\a}^{\\pi}(x).$ Let $\\va (x):=\\inf_{\\pi\\in\\PS} \\va^\\pi(x),$ $x\\in\\X.$ A policy $\\pi$ is called optimal for the respective criterion with discount factor $\\a$ if $v_{N,\\a}^{\\pi}(x)=v_{N,\\a}(x)$ or $v^\\pi_\\a(x)=\\va (x)$ for all $x\\in\\X.$\n\nThe *average cost per unit time* is defined as $$\\label{eqn:sec_model def:avg cost}\n w^{\\pi}(x):=\\limsup_{N\\to +\\infty} \\frac{1}{N}v_{N,1}^{\\pi} (x), \\qquad x\\in\\X.$$\n\nDefine the optimal value function $w^{{\\rm ac}}(x):=\\inf_{\\pi\\in\\PS} w^{\\pi} (x),$ $x\\in\\X.$ A policy $\\pi$ is called average-cost optimal if $w^{\\pi}(x)=w^{{\\rm ac}}(x)$ for all $x\\in\\X.$\n\nRecall the definition of quasiconvex functions.", "\n\n\\[def:qc\\] A function $f$ is quasiconvex on a convex set $X\\subset \\R,$ if for all $x,$ $y \\in X$ and $0 \\leq \\lambda \\leq 1$ $$\\begin{aligned}\n f(\\lambda x + (1-\\lambda) y ) \\leq \\max\\{ f(x), f(y) \\}.", "\n \\end{aligned}$$\n\nFor $\\a\\in (0,1],$ let us define $$\\begin{aligned}\n \\h (x) := h (x) + (1-\\a) \\c x + \\c \\E[D], \\qquad x\\in\\X.\n \\label{eqn:def ha}\\end{aligned}$$ Note that since $\\E[h(x-D)]\\to +\\infty$ as $x\\to +\\infty$ and $(1-\\a)\\c\\geq 0$ for all $\\a\\in(0,1],$ the function $\\E[\\h (x-D)] = \\E[h(x-D)] + (1-\\a)\\c x + \\a \\c \\E[D]$ tends to $+\\infty$ as $x\\to +\\infty$ for all $\\a\\in[0,1].$ In addition, for $\\a\\in (0,1]$ the function $\\E[\\h (x-D)]$ is continuous on $\\X$ because the functions $\\E[h (x-D)]$ and $(1-\\a)\\c x$ are continuous on $\\X.$\n\nConsider the following assumptions on the quasiconvexity or convexity of the cost function.", "\n\n\\[assum:qcall\\] There exists $\\a^*\\in[0,1)$ such that for all $\\a\\in (\\a^*,1]:$\n\n(i) \\[assum:qcall1\\] The function $\\E[\\h (x-D)]$ is quasiconvex; and\n\n(ii) \\[assum:qcall2\\] $\\lim_{x\\to -\\infty} \\E[\\h (x-D)] > K + \\inf_{x\\in\\X} \\{ \\E[\\h (x-D)] \\}.$\n\n\\[assum:convex\\] The function $h(\\cdot)$ is convex on $\\X.$\n\nFor the discounted criterion, consider the following assumption, which is weaker than Assumption \\[assum:qcall\\]. ", "Assumption \\[assum:qcall\\] is used for the convergence of discounted-cost problems to average-cost problem.", "\n\n\\[assum:qcalpha\\] For a given $\\a\\in(0,1]$ assume that:\n\n(i) \\[assum:qcalpha:1\\] the function $\\E[\\h (x-D)]$ is quasiconvex; and\n\n(ii) \\[assum:qcalpha:2\\] $\\lim_{x\\to -\\infty} \\E[\\h (x-D)] > K + \\inf_{x\\in\\X} \\{ \\E[\\h (x-D)] \\}.$\n\nWe recall that Veinott [@Vei66] considered quasiconvexity assumptions for finite-horizon nonstationary problems. ", "Being applied to stationary infinite-horizon problems, the corresponding assumption is Assumption \\[assum:qcalpha\\]. ", "For stationary infinite-horizon models and discrete demands, Zheng [@Zheng] used a slightly stronger assumption, which is Assumption \\[assum:qcalpha\\] with replaced with $\\lim_{x\\to -\\infty} \\E[h_{\\a} (x-D)] = +\\infty.$\n\nFor $\\a\\in[0,1],$ if $$\\begin{aligned}\n \\lim_{x\\to -\\infty} \\E[h_\\a (x-D)] > \\inf_{x\\in\\X} \\E[h_\\a (x-D)] ,\n \\label{eqn:raexist}\\end{aligned}$$ then we define $$\\begin{aligned}\n \\ra := \\min \\big\\{ \\underset{x\\in\\X}\\argmin \\{ \\E[\\h (x-D)] \\} \\big\\} .", "\n \\label{eqn:def r alpha r*}\\end{aligned}$$ Since the function $\\E[\\h (x-D)]$ is continuous, $\\E[\\h (x-D)]\\to +\\infty$ as $x\\to +\\infty$ and imply that $|\\ra| < +\\infty.$\n\nThe following assumption is used to establish the convergence of the discounted optimal lower thresholds and relative value functions in Sections \\[sec:cvg sa\\] and \\[sec:cvg ua\\] respectively.", "\n\n\\[assum:decrease\\] For a given $\\a\\in (0,1],$ the function $\\E[h_{\\a} (x-D)]$ is strictly decreasing on $(-\\infty,\\ra],$ where $\\ra$ is defined in .", "\n\nWe state the relationships between these assumptions in the following two lemmas. ", "The proofs of the lemmas presented in this section are available in Appendix \\[sec:inventory control:apx\\].", "\n\n\\[lm:cqc\\] Assumption \\[assum:convex\\] implies the validity of Assumption \\[assum:qcall\\] with $$\\begin{aligned}\n \\a^* \\in [ \\max\\{ 1 + \\lim_{x\\to -\\infty} \\frac{h(x)}{\\c x} ,0\\} , 1)\n \\label{eqn:convexa*}\\end{aligned}$$ and the validity of Assumption \\[assum:decrease\\] for all $\\a\\in(\\a^*,1].$\n\n\\[lm:assumption\\] Assumption \\[assum:qcall\\] implies Assumption \\[assum:qcalpha\\] for $\\a\\in (\\a^*,1].$\n\nSetup-Cost Inventory Model with Discounted Costs {#sec:mdptotal}\n================================================\n\nThis section establishes the existence of optimal $(\\sa,\\Sa)$ polclies for the problems with discounted costs stated in Theorem \\[thm:qcall\\]. ", "We start this section by verifying the weak continuity of the transition probability $q$ defined in and the $\\K$-inf-compactness of the one-step cost function $c$ defined in . ", "These properties, stated in Assumption **W\\***, imply the validity of optimality equations and the convergence of value iterations for problems with discounted costs; see Feinberg et al.", " [@FKZ12 Theorem 4].", "\n\nRecall that a function $f:U\\to \\R\\cup \\{+\\infty\\},$ where $U$ is a subset of a metric space $\\U,$ is called inf-compact, if for every $\\lambda\\in\\R$ the level set $\\{u\\in\\U :f(u)\\leq \\lambda \\}$ is compact.", "\n\n\\[def:k inf compact\\] A function $f:\\X\\times\\A\\to \\bR$ is called $\\K$-inf-compact, if for every nonempty compact subset $K$ of $\\X,$ the function $f:K\\times\\A\\to \\bR$ is inf-compact.", "\n\nIt is known for discounted MDPs that if the one-step cost function $c$ and transition probability $q$ satisfy the Assumption **W\\*** below, then it is possible to write the optimality equations for the finite-horizon and infinite-horizon problems, these equations define the sets of stationary and Markov optimal policies for infinite and finite horizons respectively, $v_{\\a} (x) = \\lim_{N\\to +\\infty} v_{N,\\a} (x)$ for all $x\\in\\X,$ and the functions $v_{N,\\a},$ $N = 1,2,\\ldots,$ and $v_{\\a}$ are lower semicontinuous; see Feinberg et al.", " [@FKZ12 Theorems 3, 4].", "\n\n**Assumption W\\*** ([Feinberg et al.", " [@FKZ12], Feinberg and Lewis [@FL16], or Feinberg [@Ftut]]{})**.**", "\n\n\\(i) The function $c$ is $\\K$-inf-compact and bounded below, and\n\n\\(ii) the transition probability $q(\\cdot|x,a)$ is weakly continuous in $(x,a)\\in \\X\\times\\A,$ that is, for every bounded continuous function $f:\\X\\to\\R,$ the function $\\tilde{f}(x,a):=\\int_\\X f(y)q(dy|x,a)$ is continuous on $\\X\\times\\A.$\n\n\\[thm:W\\*\\] The inventory model satisfies Assumption **W\\***, and the one-step cost function $c$ is inf-compact.", "\n\nSince the function $\\E[h(x-D)]$ is continuous and tends to $ +\\infty$ as $|x|\\to +\\infty,$ Theorem \\[thm:W\\*\\] is proved in Feinberg and Lewis [@FL16 Corollary 5.2] and Feinberg [@Ftut p. 22]\n\nAccording to Feinberg and Lewis [@FL16], since Assumption **W\\*** holds for the MDP corresponding to the described inventory model, the optimality equations for the total discounted costs can be written as $$\\begin{aligned}\n v_{t+1,\\a} (x) &= \\min \\{ \\min_{a\\geq 0}[ K + G_{t,\\alpha}(x+a)], G_{t,\\alpha}(x) \\} - \\bar{c}x, \\quad t=0,1,2,\\ldots,\\ x\\in\\X, \\label{eqn:vna} \\\\\n \\va (x) & = \\min \\{ \\min_{a\\geq 0}[ K + G_{\\alpha}(x+a)], G_{\\alpha}(x) \\} - \\bar{c}x,\\qquad x\\in\\X, \\label{eqn:va}\\end{aligned}$$ where $$\\begin{aligned}\nG_{t, \\alpha}(x) &:= {\\bar c} x + \\E[h(x-D)] + \\alpha \\E [v_{t, \\alpha}(x-D)], \\quad t=0,1,2,\\ldots,\\ x\\in\\X, \\label{eqn:gna} \\\\\nG_{\\alpha}(x) &:= {\\bar c} x + \\E[h(x-D)] + \\alpha \\E [v_{\\alpha}(x-D)],\\qquad x\\in\\X, \\label{eqn:ga}\\end{aligned}$$ and $v_{0,\\a}(x) = 0$ for all $x\\in\\X.$\n\nRecall the definition of $(s,S)$ policies. ", "Suppose $f(x)$ is a lower semicontinuous function such that $\\liminf_{|x|\\to +\\infty}f(x)> K + \\inf_{x\\in\\X} f(x).$ Let $$\\begin{aligned}\n S &\\in \\underset{x\\in\\X}{\\argmin} \\{ f (x) \\} \\label{eqn:def S}, \\\\\n %\\intertext{and}\n s &= \\inf \\{ x\\leq S: f (x) \\leq K + f(S) \\}. ", "\\label{eqn:def s}\\end{aligned}$$\n\n\\[def:sS policy\\] Let $s_t$ and $S_t$ be real numbers such that $s_t\\leq S_t,$ $t=0,1,\\ldots\\ .$ A policy is called an $(s_t,S_t)$ policy at step $t$ if it orders up to the level $S_t,$ if $x_t<s_t,$ and does not order, if $x_t\\geq s_t.$ A Markov policy is called an $(s_t,S_t)$ policy if it is an $(s_t,S_t)$ policy at all steps $t=0,1,\\ldots\\ .$ A policy is called an $(s,S)$ policy if it is stationary and it is an $(s,S)$ policy at all steps $t=0,1,\\ldots\\ .$\n\nIn this section, we consider Assumption \\[assum:qcalpha\\], which guarantees the optimality of $(\\sa,\\Sa)$ policies for infinite-horizon problems with the discount factor $\\a,$ as this is stated in the following theorem.", "\n\n\\[thm:qcall\\] Let Assumption \\[assum:qcalpha\\] hold for $\\a\\in(0,1).$ For the infinite-horizon problem, there exists an optimal $(s_\\alpha, S_\\alpha)$ policy, where $S_{\\a}$ and $s_{\\a}$ are real numbers such that $S_{\\a}$ satisfies and $s_{\\a}$ is defined in with $f(x):=G_{\\a}(x),$ $x\\in\\X.$\n\n\\[rm:sSconvex\\] [Under slightly stronger assumption, this theorem is prove by Zheng [@Zheng] for inventory models with integer demands and integer orders. ", "Under Assumption \\[assum:convex\\] and some other technical assumptions, this conclusion also follows from Chen and Simchi-Levi [@CS04b]. ", "Under Assumption \\[assum:convex\\], Theorem \\[thm:qcall\\] is proved in Feinberg and Liang [@FLi16a Theorem 4.4] with $\\a\\in(\\a^*,1)$ for $\\a^*$ defined in . ", "In addition, a simple structure of optimal polices is described in Feinberg and Liang [@FLi16a Theorem 4.4] for all $\\a\\in[0,1)$. However, under Assumption \\[assum:qcalpha\\] in this paper, if $\\a\\in [0,\\a^*),$ then the structure of optimal policies is currently not clear. ]{}", "\n\nTo prove the optimality of $(\\sa,\\Sa)$ policies, we first consider the same inventory model with a terminal cost $ -\\c x,$ that is, each unit of stock left over can be discarded with the return of $\\c$ and each unit of backlogged demand is satisfied at the cost $\\c.$ For this model with terminal costs, the one step cost function are the same as the original problem and let us denote the expected total discounted cost by $$\\label{eqn:sec_model def:finite total disc cost:t}\n \\tv_{N,\\a}^{\\pi} (x) := \\mathbb{E}_{x}^{\\pi} \\Big[ \\sum_{t=0}^{N-1}\n \\alpha^{t} c(x_t,a_t) -\\a^N \\c x_N \\Big] , \\qquad x\\in\\X .$$ Then we transform the problem into the one with $\\c = 0$ and follow the induction proofs in Veinott [@Vei66] to establish properties for $\\tv_{\\a}$. Then, we shall also show that $\\tv_{\\a} = \\va.$\n\nThe finite-horizon discounted cost optimality equations for the inventory model with terminal costs $-\\c x$ can be written as $$\\begin{aligned}\n \\tv_{t+1,\\a} (x) &= \\min \\{ \\min_{a\\geq 0}[ K + \\tG_{t,\\alpha}(x+a)], \\tG_{t,\\alpha}(x) \\} - \\bar{c}x, \\quad t=0,1,2,\\ldots,\\ x\\in\\X, \\label{eqn:vna:t}\\end{aligned}$$ where $$\\begin{aligned}\n\\tG_{t, \\alpha}(x) &:= {\\bar c} x+\\E[h(x-D)]+\\alpha\\E [\\tv_{t,\\alpha}(x-D)],\\quad t=0,1,2,\\ldots,\\ x\\in\\X \\label{eqn:gna:t}\\end{aligned}$$ and $\\tv_{0,\\a}(x) = -\\c x$ for all $x\\in\\X.$ Then, following Veinott [@Vei66], we transform the model with positive unit ordering cost and terminal costs $-\\c x$ into the model with zero unit and terminal costs and holding/backlog costs $\\h$ defined in . ", "The one-step cost function for the new model is $$\\begin{aligned}\n\\label{eqn:c:trans}\n c_\\a (x,a) = K\\indF_{\\{a>0 \\}} +\\E[\\h (x+a-D)].\\end{aligned}$$ Since the function $\\E[\\h (x-D)]$ is quasiconvex, $\\lim_{x\\to-\\infty}\\E[\\h (x-D)] > K + \\inf_{x\\in\\X} \\E[\\h (x-D)],$ and $\\lim_{x\\to+\\infty} \\E[\\h (x-D)]=+\\infty,$ the function $\\E[\\h (x-D)]$ is bounded below. ", "Therefore, $c_\\a$ is bounded below and the new model satisfies Assumption **W\\***. ", "The optimality equations for the new model are $$\\begin{aligned}\n \\bv_{t+1,\\a} (x) & = \\min \\{ \\min_{a\\geq 0} [K + \\bG_{t,\\a} (x+a)], \\bG_{t,\\a} (x) \\}, \\quad t = 0,1,2,\\ldots, \\ x\\in\\X, \\label{eqn:vna:trans} \\\\\n \\bva (x) &= \\min \\{ \\min_{a\\geq 0} [K + \\bGa (x+a)], \\bGa(x) \\}, \\qquad x\\in\\X, \\label{eqn:va:trans}\\end{aligned}$$ where $$\\begin{aligned}\n \\bG_{t,\\a} (x) & = \\E[\\h (x-D)] + \\a \\E[\\bv_{t,\\a} (x-D)], \\quad t = 0,1,2,\\ldots,\\ x\\in\\X, \\label{eqn:gna:trans} \\\\\n \\bGa (x) & = \\E[\\h (x-D)] + \\a \\E[\\bva (x-D)] , \\qquad x\\in\\X, \\label{eqn:ga:trans}\\end{aligned}$$ and $\\bv_{0,\\a} (x) = \\tv_{0,\\a} (x)+\\c x = 0$ for all $x\\in\\X.$ It is easy to see by induction that $$\\begin{aligned}\n \\bv_{t,\\a} (x) & = \\tv_{t,\\a} (x)+\\c x, \\qquad x\\in\\X, \\label{eqn:trans:f} \\\\\n \\bG_{t,\\a} (x) & = \\tG_{t,\\a} (x), \\qquad t = 0,1,2,\\ldots,\\ x\\in\\X.\n \\label{eqn:bga=tga}\\end{aligned}$$ Since the validity of Assumption **W\\*** for the model with zero unit cost implies that $\\bv_{t,\\a} \\to \\bva$ as $t\\to +\\infty,$ in view of and , we can define $$\\begin{aligned}\n \\tva (x) := \\lim_{t\\to+\\infty} \\tv_{t,\\a} (x) = \\lim_{t\\to+\\infty} \\bv_{t,\\a} (x) - \\c x = \\bva (x) - \\c x . ", "\\qquad x\\in\\X . ", "\\label{eqn:trans}\\end{aligned}$$ In view of , the finite-horizon model with terminal costs $-\\c x$ and the finite-horizon model with zero unit and terminal costs have the same sets of optimal actions for the same state-time pairs. ", "In addition, implies that $$\\begin{aligned}\n \\tva (x) & = \\min \\{ \\min_{a\\geq 0}[ K + \\tG_{\\alpha}(x+a)], \\tG_{\\alpha}(x) \\} - \\bar{c}x , \\label{eqn:va:t}\\end{aligned}$$ where, in view of , $$\\begin{aligned}\n\\tG_{\\alpha}(x)= \\bG_{\\alpha} (x) = {\\bar c} x + \\E[h(x-D)] + \\alpha \\E [\\tv_{\\alpha}(x-D)] , \\qquad x\\in\\X. \\label{eqn:ga:t}\\end{aligned}$$\n\nNow, we extend the properties of finite-horizon value functions $\\bv_{t,\\a}$ and $\\bG_{t,\\a},$ $t = 0,1,2,\\ldots,$ stated in Veinott [@Vei66 Lemmas 1 and 2] to infinite-horizon value functions $\\bva$ and $\\bGa.$ The proofs of the lemmas presented in this section are available in Appendix \\[sec:mdptotal:apx\\].", "\n\n\\[lm:sS1\\] For $x\\leq y$ and $t=1,2,\\ldots$ $$\\begin{aligned}\n \\bv_{t,\\a} (x) & \\leq \\bv_{t,\\a} (y) + K, \\label{eqn:vta1} \\\\\n \\bva (x) & \\leq \\bva (y) + K, \\label{eqn:va1} \\\\\n \\bG_{t,\\a} (y) - \\bG_{t,\\a} (x) & \\geq \\E[\\h(y-D)] - \\E[\\h(x-D)] - \\a K, \\label{eqn:Gta1} \\\\\n \\bG_{\\a} (y) - \\bG_{\\a} (x) & \\geq \\E[\\h(y-D)] - \\E[\\h(x-D)] - \\a K. \\label{eqn:Ga1}\\end{aligned}$$\n\n\\[lm:order\\] Let Assumption \\[assum:qcalpha\\] hold for $\\a\\in(0,1).$ Then for $t =0,1,\\ldots$ and $x\\leq y \\leq \\ra,$ where $\\ra$ is defined in , $$\\begin{aligned}\n \\bG_{t,\\a} (y) - \\bG_{t,\\a} (x) & \\leq 0, \\label{eqn:Gtade1} \\\\\n \\bv_{t,\\a} (y) - \\bv_{t,\\a} (x) & \\leq 0. ", "\\label{eqn:vtade1}\\end{aligned}$$\n\nTo prove the optimality of $(\\sa,\\Sa)$ policies for infinite-horizon problems, we establish the same properties of the infinite-horizon value functions $\\bv_{\\a}$ and $\\bG_{\\a}$ in the following lemma.", "\n\n\\[lm:vaorder\\] Let Assumption \\[assum:qcalpha\\] hold for $\\a\\in(0,1).$ Then for $x\\leq y \\leq \\ra$ $$\\begin{aligned}\n \\bv_{\\a} (y) - \\bv_{\\a} (x) & \\leq 0, \\label{eqn:vade1} \\\\\n \\bG_{\\a} (y) - \\bG_{\\a} (x) & \\leq 0. ", "\\label{eqn:Gade1}\\end{aligned}$$\n\n\\[thm:qcall:t\\] Let Assumption \\[assum:qcalpha\\] hold for $\\a\\in(0,1).$ For the inventory model with zero unit and terminal costs, the following statements hold:\n\n(i) \\[thm:qcall:t:1\\] For $N=1,2,\\ldots$ horizon problem, there exists an optimal $(s_{t,\\a},S_{t,\\a})_{t=0,1,2,\\ldots,N-1}$ policy, where $S_{t,\\a}$ and $s_{t,\\a}$ are real numbers such that $S_{t,\\a}$ satisfies and $s_{t,\\a}$ is defined in with $f(x):=\\bG_{N-t-1,\\a}(x),$ $t=0,1,2,\\ldots,N-1,$ $x\\in\\X;$\n\n(ii) \\[thm:qcall:t:2\\] For infinite-horizon problem, there exists an optimal $(\\sa, \\Sa)$ policy, where $S_{\\a}$ and $s_{\\a}$ are real numbers such that $S_{\\a}$ satisfies and $s_{\\a}$ is defined in with $f(x):=\\bG_{\\a}(x),$ $x\\in\\X;$\n\n(iii) \\[thm:qcall:t:3\\] For all $s_{t,\\a},$ $S_{t,\\a},$ $t=0,1,2,\\ldots,$ and $\\Sa$ defined in (i) and (ii), $$\\begin{aligned}\n s_{t,\\a} \\leq \\ra \\leq S_{t,\\a} \\leq \\barS_\\a \\quad \\text{and} \\quad \\sa \\leq \\ra \\leq \\Sa \\leq \\barS_\\a,\n \\label{eqn:ubdStaSa}\n \\end{aligned}$$ where $$\\begin{aligned}\n \\barS_\\a := \\inf\\{x>\\ra : \\E[\\h (x-D)]\\geq K + \\E[\\h (\\ra -D)] .", "\n \\label{eqn:defbarS}\n \\end{aligned}$$\n\nConsider $N = 1,2,\\ldots$ and $t=0,1,2,\\ldots,N-1.$ Since Assumption **W\\*** holds in view of Theorem \\[thm:W\\*\\], Feinberg et al.", " [@FKZ12 Theorem 2] implies that $\\bv_{N-t-1,\\a} (x)$ and $\\bG_{N-t-1,\\a} (x)$ are lower semicontinuous functions. ", "In view of Lemma \\[lm:order\\], the function $\\bG_{N-t-1,\\a} (x)$ is nonincreasing on $(-\\infty,\\ra],$ where $\\ra$ is defined in . ", "In view of , $\\bG_{N-t-1,\\a} (x) \\geq \\c x\\to +\\infty$ as $x\\to +\\infty.$ Therefore, $\\bG_{N-t-1,\\a} (x)$ is inf-compact; see the definition of inf-compact functions in the paragraph before Definition \\[def:k inf compact\\]. ", "In view of and , $\\bG_{N-t-1,\\a} (x) \\geq \\E[\\h (x-D)] + \\a \\E[\\bv_{N-t-1,\\a} (\\ra - D)]$ for all $x\\leq \\ra.$ Therefore, $$\\begin{aligned}\n\\begin{split}\n \\liminf_{x\\to -\\infty} \\bG_{N-t-1,\\a} (x) & \\geq \\lim_{x\\to -\\infty} \\E[\\h (x-D)] + \\a \\E[\\bv_{N-t-1,\\a} (\\ra - D)] \\\\\n &> K + \\E[\\h (\\ra-D)] + \\a \\E[\\bv_{N-t-1,\\a} (\\ra - D)] \\\\\n &= K + \\bG_{N-t-1,\\a} (\\ra) \\geq K + \\inf_{x\\in\\X} \\bG_{N-t-1,\\a} (x) ,\n\\end{split}\n \\label{eqn:limGa>KinfGa}\\end{aligned}$$ where the first inequality follows from the equation in the previous sentence, the second inequality follows from Assumption \\[assum:qcalpha\\], the equality follows from the definition of the function $\\bG_{N-t-1,\\a}$ in , and the last inequality is straightforward.", "\n\nLet $S_{t,\\a}$ satisfy and $s_{t,\\a}$ be defined in with $f:=\\bG_{N-t-1,\\a}.$ The lower semicontinuity of $\\bG_{N-t-1,\\a} (x)$ implies that $$\\begin{aligned}\n \\bG_{N-t-1,\\a}(s_{t,\\a}) \\leq \\bG_{N-t-1,\\a} (S_{t,\\a}) + K.\n \\label{eqn:Ga(sa)<GK}\\end{aligned}$$ Since $\\bG_{N-t-1,\\a} (x)$ is nonincreasing on $(-\\infty,\\ra],$ $$\\begin{aligned}\n S_{t,\\a} \\geq \\ra.", "\n \\label{eqn:Sara}\\end{aligned}$$\n\nTo prove the optimality of $(s_{t,\\a},S_{t,\\a})$ policies, we consider three cases: (1) $x\\geq \\ra;$ (2) $s_{t,\\a}\\leq x\\leq \\ra;$ and (3) $x<s_{t,\\a}.$\n\n\\(1) In view of Lemma \\[lm:sS1\\], for $\\ra\\leq x<y$ $$\\begin{aligned}\n \\bG_{N-t-1,\\a} (y) + K - \\bG_{N-t-1,\\a} (x) \\geq \\E[\\h(y-D)] - \\E[\\h(x-D)] + K - \\a K > 0,\n \\label{eqn:gantorder1}\\end{aligned}$$ where the first inequality follows from and the second one holds because the function $\\E[\\h(x-D)]$ is nondecreasing on $[\\ra, +\\infty)$ and $K-\\a K >0.$ Therefore, the action $a=0$ is optimal for $x\\geq \\ra.$ In addition, implies that $\\bG_{N-t-1,\\a} (x)<\\bG_{N-t-1,\\a} (S_{t,\\a}) + K$ for all $x\\in[\\ra,S_{t,\\a}],$ which implies that $$\\begin{aligned}\ns_{t,\\a} \\leq \\ra.", "\n\\label{eqn:sara}\\end{aligned}$$\n\n\\(2) For $s_{t,\\a} \\leq x \\leq \\ra$ $$\\begin{aligned}\n \\bG_{N-t-1,\\a} (x) \\leq \\bG_{N-t-1,\\a} (s_{t,\\a}) \\leq K + \\bG_{N-t-1,\\a} (S_{t,\\a}) = K + \\min_{y\\in\\X} \\bG_{N-t-1,\\a} (y),\\end{aligned}$$ where the first inequality follows from and the second one follows from . ", "Therefore, the action $a=0$ is optimal for $s_{t,\\a} \\leq x\\leq \\ra.$\n\n\\(3) For $x<s_{t,\\a}$ $$\\begin{aligned}\n \\bG_{N-t-1,\\a} (x) > K + \\bG_{N-t-1,\\a} (S_{t,\\a}) = K + \\min_{y\\in\\X} \\bG_{N-t-1,\\a} (y),\\end{aligned}$$ where the inequality follows from the definition of $s_{t,\\a}$ in with $f:=\\bG_{N-t-1,\\a}.$ Therefore, the action $a=S_{t,\\a}-x$ is optimal for $x<s_{t,\\a}.$ Thus, for $N$-horizon problem the $(s_{t,\\a},S_{t,\\a})_{t=0,1,2,\\ldots,N-1}$ policy is optimal.", "\n\nIn view of Lemmas \\[lm:sS1\\], \\[lm:order\\], and \\[lm:vaorder\\], $\\bGa$ and $\\bva$ satisfy the same properties as $\\bG_{t,\\a}$ and $\\bv_{t,\\a}.$ Therefore, statement follows from the same arguments in the proof of with $\\bG_{N-t-1,\\a},$ $\\bv_{N-t-1,\\a},$ $s_{t,\\a},$ and $S_{t,\\a}$ replaced with $\\bGa,$ $\\bva,$ $\\sa,$ and $\\Sa$ respectively.", "\n\nIn view of , $\\lim_{x\\to+\\infty} \\E[\\h (x-D)] = +\\infty$ and Assumption \\[assum:qcalpha\\] imply that $|\\barS_\\a| < +\\infty$ and for $x > \\barS_\\a$ $$\\begin{aligned}\n \\E[\\h(x-D)] \\geq \\E[\\h (\\barS_\\a - D)] \\geq K + \\E[\\h (\\ra - D)].", "\n \\label{eqn:x>barS:1}\\end{aligned}$$ Therefore, and imply that for $t=0,1,2,\\ldots$ and $x>\\barS_\\a$ $$\\begin{aligned}\n\\begin{split}\n \\bG_{t,\\a} (x) - \\bG_{t,\\a} (\\ra) &\\geq \\E[\\h(x-D)] - \\E[\\h(\\ra-D)] - \\a K \\\\\n &\\geq K - \\a K > 0,\n\\end{split}\n \\label{eqn:x>barS:2}\\end{aligned}$$ which is equivalent to for $t=0,1,2,\\ldots$ and $x>\\barS_\\a$ $$\\begin{aligned}\n \\bG_{t,\\a} (x) > \\bG_{t,\\a} (\\ra) \\geq \\min_{x\\in\\X} \\bG_{t,\\a} (x).", "\n \\label{eqn:x>barS:3}\\end{aligned}$$ Therefore, if $x\\in \\argmin\\{\\bG_{t,\\a} (x)\\},$ $t=0,1,2,\\ldots,$ then $x \\leq \\barS_\\a.$ Thus, $S_{t,\\a} \\leq \\barS_\\a,$ $t=0,1,2,\\ldots\\ .$ In addition, the same arguments with and $\\bG_{t,\\a}$ replaced with and $\\bGa$ imply that $\\Sa \\leq \\barS_\\a.$\n\nFurthermore, and imply that $s_{t,\\a} \\leq \\ra \\leq S_{t,\\a}$ and the same arguments before and being applied to infinite-horizon problem with $\\bG_{N-t-1,\\a}$ replaced with $\\bGa$ imply that $\\sa \\leq \\ra \\leq \\Sa.$ Hence, holds.", "\n\n\\[lm:samevalues\\] Let Assumption \\[assum:qcalpha\\] hold for $\\a\\in(0,1).$ Then $$\\begin{aligned}\n \\bva (x) - \\c x = \\tva (x) = \\va (x) \\geq 0, \\qquad x\\in\\X.\n \\label{eqn:modeltrans}\n \\end{aligned}$$ In addition, implies that $\\Ga (x) = \\bGa (x),$ $x\\in\\X.$\n\nTheorem \\[thm:qcall\\] follows from Theorem \\[thm:qcall:t\\] and Lemma \\[lm:samevalues\\] because equations and are equivalent, and they define the same optimal $(\\sa,\\Sa)$ policies.", "\n\n\\[rm:sSoptfinite\\] [ Note that $(s_{t,\\a},S_{t,\\a})_{t=0,1,2,\\ldots,N-1}$ policies are optimal for $N=1,2,\\ldots$ horizon inventory models with terminal costs $-\\c x$ (see Theorem \\[thm:qcall:t\\]), they may not be optimal for finite-horizon inventory models without terminal costs (see Example \\[ex:sSnotoptfinite\\]). ", "However, Theorem \\[thm:qcall\\] states that there exists an optimal $(\\sa,\\Sa)$ policy for infinite-horizon discounted cost inventory models without terminal costs. ]{}", "\n\n\\[ex:sSnotoptfinite\\] [Consider the inventory model without terminal costs defined by the following parameters: fixed ordering cost $K = 1,$ per unit ordering cost $\\c = 1,$ deterministic demand $D = 1,$ holding/backlog cost function $h(x) = \\frac{1}{2} | x |,$ and the discount factor $\\a = \\frac{3}{4}.$ Since $\\E[\\h (x-D)] = \\frac{1}{2} |x-1| + \\frac{1}{4} x + \\frac{3}{4},$ the function $\\E[h_\\a (x-D)]$ is convex and hence quasiconvex. ", "In addition, $\\lim_{x\\to -\\infty} \\E[\\h (x-D)] = +\\infty > K+\\inf_{x\\in\\X} \\E[\\h (x-D)].$ Therefore, Assumption \\[assum:qcalpha\\] holds. ", "For the single-period problem the policy that does not order is optimal, because the cost incurred, if nothing is ordered, is $\\frac{1}{2} |x-1|$ and the cost incurred, if $a > 0$ units are ordered, is $1+a+\\frac{1}{2}|x+a-1| = 1 + \\frac{1}{2}(a + |-a| + |x+a-1|) \\geq 1 +\n\\frac{1}{2}(a + |-a + x+a-1|) > \\frac{1}{2}|x-1|.$ ]{}\n\nVerification of Average-Cost Optimality Assumptions for the Setup-Cost Inventory Model {#sec:mdpac}\n======================================================================================\n\nIn this section we show that, in addition to Assumption **W\\***, under Assumption \\[assum:qcall\\], the setup-cost inventory model satisfies Assumption **B** introduced by Schäl [@Sch93]. ", "This implies the validity of average-cost optimality inequalities (ACOIs) and the existence of stationary optimal policies; see Feinberg et al.", " [@FKZ12 Theorem 4]. ", "In addition, we show that, under Assumption \\[assum:qcall\\] the inventory model satisfies the equicontinuity condition from Feinberg and Liang [@FLi16b Theorem 3.2], which implies the validity of the ACOE for the inventory model.", "\n\nAs in Schäl [@Sch93] and Feinberg et al.", " [@FKZ12], define $$\\begin{aligned}\n\\label{defmauaw}\n \\begin{split}\n m_{\\alpha}: = \\underset{x\\in\\X}{\\inf} v_{\\alpha}(x), & \\quad\n u_{\\alpha}(x): = v_{\\alpha}(x) - m_{\\alpha}, \\\\\n \\underline{w}: = \\underset{\\alpha\\uparrow1}{\\liminf}(1-\\alpha)m_{\\alpha}, & \\quad\n \\bar{w}: = \\underset{\\alpha\\uparrow1}{\\limsup}(1-\\alpha)m_{\\alpha} .", "\n \\end{split}\\end{aligned}$$ The function $\\ua$ is called the discounted relative value function. ", "Consider the following assumption in addition to Assumption **W\\***.", "\n\n**Assumption B.** (i) $w^{*} := \\inf_{x\\in\\X} w^{{\\rm ac}}(x)< +\\infty,$ and (ii) $\\underset{\\alpha\\in [0,1)}{\\sup} u_{\\alpha}(x) < +\\infty,$ $x\\in\\X.$\n\nAs follows from Schäl [@Sch93 Lemma 1.2(a)], Assumption **B**(i) implies that $m_\\alpha<+\\infty$ for all $\\alpha\\in [0,1).$ Thus, all the quantities in are defined. ", "According to Feinberg et al.", " [@FKZ12 Theorems 3, 4], if Assumptions **W\\*** and **B** hold, then $\\underline{w} = \\bar{w}$ and therefore, $$\\begin{aligned}\n \\lim_{\\a\\uparrow1} (1-\\a) m_{\\a} = \\underline{w} = \\bar{w}.", "\n\\label{eqn:bar w = underline w}\\end{aligned}$$\n\nDefine the following function on $\\X$ for the sequence $\\{ \\a_n\\uparrow 1 \\}_{n=1,2,\\ldots} :$ $$\\begin{aligned}\n\\label{EQN1}\n \\tu(x) &:=& \\liminf_{n\\to +\\infty,y\\rightarrow x} u_{\\a_n}(y) .\\end{aligned}$$ In words, ${\\tilde u}(x)$ is the largest number such that ${\\tilde u}(x)\\le \\liminf_{n\\to +\\infty}u_{\\alpha_n}(y_n)$ for all sequences $\\{y_n\\to x\\}.$ Since $u_{\\a}(x)$ is nonnegative by definition, $\\tu(x)$ is also nonnegative. ", "The function $\\tilde u,$ defined in for a sequence $\\{ \\a_n\\uparrow 1 \\}_{n=1,2,\\ldots}$ of nonnegative discount factors, is called an average-cost relative value function.", "\n\nIf Assumptions **W\\*** and **B** hold, then Feinberg et al.", " [@FKZ12 Corollary 2] implies the validity of ACOIs and $$\\begin{aligned}\n\\label{eqsfkz}\n w^{\\phi}(x)= \\underline{w} = \\lim_{\\alpha\\uparrow 1}\n (1-\\alpha)v_{\\alpha} (x) = \\bar{w} = w^*, \\qquad x\\in\\X,\\end{aligned}$$ where $w^{\\phi} (x)$ is defined in . ", "Furthermore, let us define $w:=\\underline{w};$ see and for other equalities for $w.$\n\nConsider the renewal counting process $$\\begin{aligned}\n \\textbf{N}(t) := \\sup \\{ n=0,1,\\ldots\\ : \\textbf{S}_n \\leq t \\},\n \\label{renew}\\end{aligned}$$ where $t\\in\\Rp,$ $\\textbf{S}_0 := 0,$ and $$\\begin{aligned}\n \\textbf{S}_n := \\sum_{j=1}^n D_j, \\qquad n=1,2,\\ldots\\ .", "\n \\label{eqn:Sn}\\end{aligned}$$\n\nObserve that since $\\PR(D > 0) > 0,$ $\\E[\\textbf{N}(t)] < +\\infty,$ $t\\in\\Rp;$ see Resnick [@Res92 Theorem 3.3.1]. ", "For $x\\in\\X$ and $y\\ge 0$ define $$\\begin{aligned}\n E_y(x) := \\E[h(x - \\textbf{S}_{\\textbf{N}(y)+1})].", "\n \\label{eqn:Eyx}\\end{aligned}$$ Since $x-y\\leq x-\\textbf{S}_{\\textbf{N}(y)} \\leq x$ and the function $\\E[h(x-D)]$ is quasiconvex, $$\\begin{aligned}\n E_y (x) = \\E[h( x-\\textbf{S}_{\\textbf{N}(y)} - D )] \\leq \\max\\{ \\E[h(x-y-D)],\\E[h(x-D)] \\} < +\\infty.", "\n \\label{eqn:Eyxfinite}\\end{aligned}$$\n\n\\[thm:B\\] Let Assumption \\[assum:qcall\\] hold. ", "The inventory model satisfies Assumption **B**.", "\n\nAssumption **B**(i) follows from the same arguments in the first paragraph of the proof in Feinberg and Lewis [@FL16 Proposition 6.3].", "\n\nThe inf-compactness of the function $c:\\X\\times\\A\\to \\R$ and the validity of Assumption **W\\*** imply that for each $\\a\\in [0,1)$ the function $\\va $ is inf-compact (Feinberg and Lewis [@FL07 Proposition 3.1(iv)]), and therefore the set $$\\begin{aligned}\nX_\\alpha:=\\{x\\in\\X : \\va (x)=m_\\alpha\\},\n\\label{eqn:Xa}\\end{aligned}$$ where $m_\\a$ is defined in , is nonempty and compact. ", "Furthermore, the validity of Assumption **B**(i) implies that there is a compact subset $\\cal K$ of $\\X$ such that $\\X_\\alpha\\subset {\\cal K}$ for all $\\a\\in [0,1);$ see Feinberg et al.", " [@FKZ12 Theorem 6]. ", "Following Feinberg and Lewis [@FL16], consider a bounded interval $[x^*_L,x^*_U]\\subset \\X$ such that $$\\label{eq:boundmaxlul}\nX_\\a\\subset [x^*_L,x^*_U]\\qquad {\\rm for\\ all\\ } \\alpha\\in [0,1).$$ Consider an arbitrary $\\alpha\\in [0,1)$ and a state $x_\\alpha$ such that $\\va (x_\\alpha)=m_\\a,$ where $m_\\a$ is defined in . ", "In view of , the inequalities $x^*_L\\le x_\\a\\le x^*_U$ hold.", "\n\nLet $$\\begin{aligned}\n E(x):=\\E[h(x-D)]+E_{x-x^*_L}(x)< +\\infty,\n \\label{eqn:Ex}\\end{aligned}$$ where the function $E_y(x)$ is defined in and its finiteness is stated in . ", "For $x_t=x-{\\bf S}_t,$ $t=1,\\ldots, {\\bf N}(x-x^*_L)+1,$ $$\\begin{aligned}\n\\E [h(x_t)]\\le \\E[h(x-D)]+\\E [h(x-{\\bf S}_{{\\bf N}(x-x^*_L)+1})]= E(x), \\label{est0sum}\\end{aligned}$$ where the inequality holds because the function $\\E[h(x-D)]$ is quasiconvex and $x-{\\bf S}_{{\\bf N}(x-x^*_L)+1} = x-{\\bf S}_{{\\bf N}(x-x^*_L)} - D\\leq x_t = x_{t-1}-D \\leq x-D$ for $t=1,\\ldots, {\\bf N}(x-x^*_L)+1 .$\n\nBy considering the same policy $\\sigma$ and following the arguments thereafter as in the proof in Feinberg and Lewis [@FL16 Proposition 6.3] with the equation (6.14) there replaced with , we obtain the validity of Assumption [**B**]{}.", "\n\nNow we establish the boundedness and the equicontinuity of the discounted relative value functions $\\ua$ defined in . ", "Consider $$\\begin{aligned}\n U(x) :=\n \\begin{cases} \nK+\\bar{c}(x^*_U - x), & \\text{if } x < x^*_L, \\\\\nK+\\bar{c}(x^*_U - x^*_L) + (E(x) + \\bar{c}\\E[D])(1+\\E[\\textbf{N}(x-x^*_L)]), & \\text{if } x\\ge x^*_L ,\n \\end{cases}\n \\label{eqn:def U(x)}\\end{aligned}$$ where the real numbers $x^*_L$ and $x^*_U$ are defined in and the function $E(x)$ is defined in .", "\n\n\\[lm:U(x) bounded\\] Let Assumption \\[assum:qcall\\] hold. ", "The following inequalities hold for $\\alpha\\in [0,1):$\n\n(i) $\\ua (x)\\le U(x) < +\\infty$ for all $x\\in\\X;$\n\n(ii) If $x_*,x\\in\\X$ and $x_*\\le x,$ then $C(x_*,x):=\\sup_{y\\in [x_*,x]} U(y)< +\\infty;$\n\n(iii) $\\E[U(x-D)] < +\\infty$ for all $x\\in\\X.$\n\nThe proof of this lemma is identical to the proof in Feinberg and Liang [@FLi16b Lemma 4.6].", "\n\nThe following theorem is proved in Feinberg and Lewis [@FL16 Theorem 6.10(iii)] under Assumption \\[assum:convex\\]. ", "Under Assumption \\[assum:qcall\\], since Assumptions **W\\*** and **B** hold and there exist optimal $(\\sa,\\Sa)$ policies for all $\\a\\in (\\a^*,1),$ the proof of the following lemma coincides with the proof in Feinberg and Lewis [@FL16 Theorem 6.10(iii)].", "\n\n\\[thm:fle\\] Let Assumption \\[assum:qcall\\] hold. ", "For each nonnegative discount factor $\\alpha\\in\n (\\alpha^*,1)$, consider an optimal $(s^\\prime_\\alpha, S^\\prime_\\alpha)$ policy for the discounted criterion with the discount factor $\\alpha.$ Let $\\{\\alpha_n\\uparrow 1\\}_{n=1,2,\\ldots}$ be a sequence of negative numbers with $\\alpha_1> \\alpha^*.$ Every sequence $\\{(s^\\prime_{\\alpha_n}, S^\\prime_{\\alpha_n})\\}_{n=1,2,\\ldots}$ is bounded, and each its limit point $(s^*,S^*)$ defines an average-cost optimal $(s^*,S^*)$ policy. ", "Furthermore, this policy satisfies the optimality inequality $$\\begin{aligned}\n w + \\tu (x) \\geq \\min \\{ \\min_{a\\geq 0}[ K + H(x+a)], H(x) \\} - \\bar{c}x,\n \\label{eqn:IC ACOE-1}\\end{aligned}$$ where $$\\begin{aligned}\n H(x) := \\bar{c}x +\\E[h(x-D)] + \\E[\\tu (x-D)],\n \\label{eqn:IC ACOE-2}\\end{aligned}$$ where the function $\\tilde u$ is defined in for an arbitrary subsequence $\\{\\alpha_{n_k}\\}_{k=1,2,\\ldots}$ of $\\{\\alpha_{n}\\}_{n=1,2,\\ldots}$ satisfying $(s^*,S^*)=\\lim_{k\\to +\\infty} (s^\\prime_{\\alpha_{n_k}}, S^\\prime_{\\alpha_{n_k}}).$\n\nRecall the following definition of equicontinuity.", "\n\nA family $\\mathcal{H}$ of real-valued functions on a metric space $X$ is called equicontinuous at the point $x\\in X$ if for each $\\eps > 0$ there exists an open set $G$ containing $x$ such that $$| h(y) - h(x) | < \\eps \\;\\;\\; \\text {for all}\\ y\\in G \\text{ and for all } h\\in\\mathcal{H}.$$ The family of functions $\\mathcal{H}$ is called equicontinuous (on $X$) if it is equicontinuous at all $x \\in X.$ \\[def:equicontinuous\\]\n\nConsider the following assumption on the discounted relative value functions.", "\n\n**Assumption EC** (Feinberg and Liang [@FLi16b])**.** ", "There exists a sequence $\\{ \\a_n\\uparrow1 \\}_{n=1,2,\\ldots}$ of nonnegative discount factors such that\n\n\\(i) the family of functions $\\{u_{\\a_n}\\}_{n=1,2,\\ldots}$ is equicontinuous, and\n\n\\(ii) there exists a nonnegative measurable function $U(x),$ $x\\in\\X,$ such that $U(x)\\geq u_{\\a_n}(x),$ $n=1,2,\\ldots,$ and $\\int_{\\X} U(y)q(dy|x,a) < +\\infty$ for all $x\\in\\X$ and $a\\in \\A.$\n\nThe following theorem provides sufficient conditions under which there exist a stationary policy $\\phi$ and a function $\\tu(\\cdot)$ such that the ACOEs hold for MDPs satisfying Assumptions **W\\*** and **B**.", "\n\nLet Assumptions **W\\*** and **B** hold. ", "Consider a sequence $\\{ \\a_n\\uparrow1 \\}_{n=1,2,\\ldots}$ of nonnegative discount factors. ", "If Assumption **EC** is satisfied for the sequence $\\{ \\a_n\\}_{n=1,2,\\ldots},$ then the following statements hold.", "\n\n(i) There exists a subsequence $\\{ \\a_{n_k} \\}_{k=1,2,\\ldots}$ of $\\{ \\a_n \\}_{n=1,2,\\ldots}$ such that $\\{u_{\\a_{n_k}}(x)\\}$ converges pointwise to $\\tu(x),$ $x\\in\\X,$ where $\\tu (x)$ is defined in for the subsequence $\\{ \\a_{n_k}\\}_{k=1,2,\\ldots},$ and the convergence is uniform on each compact subset of $\\X.$ In addition, the function $\\tu(x)$ is continuous. ", "\\[stat:1\\]\n\n(ii) There exists a stationary policy $\\phi$ satisfying the ACOE with the nonnegative function $\\tilde u$ defined for the sequence $\\{ \\a_{n_k} \\}_{k=1,2,\\ldots}$ mentioned in statement , that is, for all $x\\in\\X,$ $$\\begin{aligned}\n w + \\tu(x) = c(x,\\phi(x)) + \\int_{\\X} \\tu(y)q(dy|x,\\phi(x)) =\n \\min_{a\\in \\A} [ c(x,a) + \\int_{\\X} \\tu(y)q(dy|x,a) ],\n \\label{EQN11}\n \\end{aligned}$$ and every stationary policy satisfying is average-cost optimal.", "\n\n\\[thm:acoe\\]\n\nThe following theorem shows that the equicontinuity conditions stated in Theorem \\[thm:acoe\\] holds for the inventory model with holding/backlog costs satisfying quasiconvexity assumptions.", "\n\n\\[thm:u a equicont\\] Let Assumption \\[assum:qcall\\] hold. ", "Then for each $\\b \\in (\\a^*, 1),$ the family of functions $\\{u_{\\a}\\}_{\\a\\in [\\b,1)}$ is equicontinuous on $\\X.$\n\nWe first follow the same procedure as in the proof in Feinberg and Liang [@FLi16b Theorem 4.9(a)] to prove that, for each $\\b\\in (\\a^*,1),$ the family of functions $\\{u_{\\a}\\}_{\\a\\in[\\b,1)}$ is equicontinuous on $(-\\infty,M]$ for any given $M.$\n\nAccording to Theorem \\[thm:qcall\\], since the $(\\sa,\\Sa)$ policies are optimal, the arguments provided to prove Equation (4.38) in the proof in Feinberg and Liang [@FLi16b Theorem 4.9(a)] imply that there exist constants $b>0$ and $\\delta_0 > 0$ such that, for each $\\b\\in(\\a^*,1),$ $s_{\\a}\\in (-b,b)$ and $$\\begin{aligned}\n -b\\leq s_{\\a} - \\delta_0 < s_{\\a} + \\delta_0\\leq b , \\qquad \\a\\in [\\b,1) .", "\n \\label{eqn:sab} \\end{aligned}$$\n\nFor each $\\b\\in (\\a^*,1),$ let $\\a\\in [\\b,1).$ Consider $M > b,$ $z_1$ and $z_2$ satisfying $M > z_1,z_2\\geq s_{\\a}.$ Without loss of generality, assume that $z_1<z_2.$ With $\\a_n$ replaced with $\\a,$ the arguments provided before Equation (4.20) in the proof in Feinberg and Liang [@FLi16b Lemma 4.7] imply that $$\\begin{aligned}\n\\begin{split}\n & |u_{\\a}(z_1) - u_{\\a}(z_2)| = |v_{\\a}(z_1) - v_{\\a}(z_2)| \\\\\n = & {\\Big |}\\E[\\sum_{j=1}^{\\textbf{N}(z_1-s_{\\a})+1} \\a^{j-1}(\\tilde{h}(z_1-\\textbf{S}_{j-1}) - \\tilde{h}(z_2-\\textbf{S}_{j-1})) \\\\\n & + \\a^{\\textbf{N}(z_1-s_{\\a})+1} (v_{\\a}(z_1-\\textbf{S}_{\\textbf{N}(z_1-s_{\\a})+1}) - v_{\\a}(z_2-\\textbf{S}_{\\textbf{N}(z_1-s_{\\a})+1}) )] {\\Big |} \\\\\n \\leq & \\E[\\sum_{j=1}^{\\textbf{N}(M+b)+1} |\\tilde{h}(z_1-\\textbf{S}_{j-1}) - \\tilde{h}(z_2-\\textbf{S}_{j-1})|] \\\\\n & + \\E[ |u_{\\a}(z_1-\\textbf{S}_{\\textbf{N}(z_1-s_{\\a})+1}) - u_{\\a}(z_2-\\textbf{S}_{\\textbf{N}(z_1-s_{\\a})+1})|] ,\n \\end{split}\n \\label{eqn:ubd2}\\end{aligned}$$ where $\\tilde{h} (x) := \\E[h(x-D)],$ the inequality holds because of $\\a < 1,$ in view of the standard properties of expectations and absolute values, and because $-b < s_{\\a}\\leq z_1 < M.$ Recall that the function $\\tilde{h} (x)$ is continuous and finite. ", "Therefore, the function $\\tilde{h}$ is uniformly continuous on the closed interval $[-(M+2b), M].$ In addition, Assumption \\[assum:qcall\\] implies that the function $\\tilde{h}$ is quasiconvex.", "\n\nSince $-(M+2b) < x-\\textbf{S}_{j-1} < M$ for all $x\\in [-b,M]$ and $j=1,2,\\ldots,\\textbf{N}(M+b)+1,$ the nonnegativity and quasiconvexity of $\\tilde{h}$ imply that for all $x\\in (-b,M)$ $$\\begin{aligned}\n 0\\leq \\tilde{h}(x-\\textbf{S}_{j-1}) \\leq \\max \\{ \\tilde{h}(-(M+2b)),\\tilde{h}(M) \\}.", "\n \\label{eqn:th1}\\end{aligned}$$ Furthermore, for $-b < z_1<z_2 < M,$ $$\\begin{aligned}\n\\begin{split}\n &\\E[\\sum_{j=1}^{\\textbf{N}(M+b)+1} |\\tilde{h}(z_1-\\textbf{S}_{j-1}) - \\tilde{h}(z_2-\\textbf{S}_{j-1}) |]\n \\\\\n \\leq &\\E[\\sum_{j=1}^{\\textbf{N}(M+b)+1} \\max \\{ \\tilde{h}(-(M+2b)),\\tilde{h}(M) \\}]\n \\\\\n \\leq &\\E[\\textbf{N}(M+b)+1]\\max \\{ \\tilde{h}(-(M+2b)),\\tilde{h}(M) \\} < +\\infty,\n \\end{split}\n \\label{eqn:thfinite}\\end{aligned}$$ where the first inequality follows from , the second one follows from Wald’s identity, and the last one follows from the finiteness of the function $\\tilde{h}.$ Therefore, for $-b < z_1<z_2 < M,$ $$\\begin{aligned}\n\\begin{split}\n & \\lim_{z_1\\to z_2} \\E[\\sum_{j=1}^{\\textbf{N}(M+b)+1} |\\tilde{h}(z_1-\\textbf{S}_{j-1}) - \\tilde{h}(z_2-\\textbf{S}_{j-1}) |] \\\\\n = & \\E[\\sum_{j=1}^{\\textbf{N}(M+b)+1} \\lim_{z_1\\to z_2} |\\tilde{h}(z_1-\\textbf{S}_{j-1}) - \\tilde{h}(z_2-\\textbf{S}_{j-1}) |] = 0,\n\\end{split}\n \\label{eqn:thlimit}\\end{aligned}$$ where the first equality follows from and Lebesgue’s dominated convergence theorem, and the second one follows from the continuity of $\\tilde{h}.$\n\nConsider $\\eps > 0.$ In view of , since $-b < z_1<z_2<M,$ there exists $\\delta_1 \\in (0,\\delta_0)$ such that for $s_{\\a}\\leq z_1<z_2$ satisfying $|z_1 - z_2|<\\delta_1$ $$\\begin{aligned}\n \\E[\\sum_{j=1}^{\\textbf{N}(M+b)+1} |\\tilde{h}(z_1-\\textbf{S}_{j-1}) - \\tilde{h}(z_2-\\textbf{S}_{j-1})|] \n \\leq \\frac{\\eps}{2}.", "\n \\label{eqn:ubd2-1}\\end{aligned}$$\n\nAdditional arguments are needed to estimate the last term in . ", "Next we prove that there exists $\\delta_2\\in (0,\\delta_1)$ such that for $x\\in [\\sa,\\sa+\\delta_2],$ $$\\begin{aligned}\n |\\ua (x) - \\ua (\\sa)| < \\frac{\\epsilon}{4}.", "\n \\label{eqn:ubd ux uan}\\end{aligned}$$\n\nLet $x\\ge s_\\a.$ Then $$\\va (x ) =\n \\tilde{h}(x) + \\a \\E[\\va (x-D)] \\label{firstfrom423}$$ and $$\\begin{aligned}\n\\begin{split}\n&\\E[\\va(x-D)] =\n\\PR(D\\geq x - \\sa) \\E[\\bar{c}(\\sa - x + D)|D\\geq x - \\sa] \\\\\n&+ \\PR(0<D< x - \\sa) \\E[\\va (x-D)|0<D< x - \\sa]\n+ \\PR(D = 0) \\va (x)\n\\end{split}\n\\label{secondfrom423}\\end{aligned}$$ Formulas and imply $$\\begin{aligned}\n[1&-\\a \\PR(D=0)] \\va (x) = \\tilde{h}(x) + \\a (\\PR(D\\geq x - \\sa) \\E[\\bar{c}(\\sa - x + D)|D\\geq x - \\sa] \\nonumber \\\\\n& + \\PR(0<D< x - \\sa) \\E[\\va (x-D)|0<D< x - \\sa]).", "\n \\label{eqn: ua-1}\\end{aligned}$$ Therefore, since $\\ua (y_1) - \\ua (y_2) = \\va (y_1) - \\va (y_2) $ for all $y_1,y_2\\in\\X,$ for $x\\in [\\sa,\\sa+\\delta_1]$ $$\\begin{aligned}\n\\begin{split}\n & [1-\\a\\PR(D=0)]|\\ua (x) - \\ua (\\sa)| = [1-\\a\\PR(D=0)]|\\va (x) - \\va (\\sa)| \\\\\n &= \\Big |\\tilde{h}(x)-\\tilde{h}(\\sa) +\\a\\PR(D\\geq x - \\sa)\\bar{c}(\\sa - x) \\\\ & +\\a\\PR(0<D< x - \\sa)\\E[\\ua (x-D)\n -\\ua (\\sa-D)|0<D< x - \\sa] \\Big | \\\\\n &\\leq |\\tilde{h}(x)-\\tilde{h}(\\sa)|+\\bar{c}(x-\\sa)+ 2 \\PR(0<D< x-\\sa) C(-b,b),\n\\end{split}\n\\label{eqn:dif ua ubd}\\end{aligned}$$ where the nonnegative function $C$ is defined in Lemma \\[lm:U(x) bounded\\]. ", "Let us define $Q_1:= (1-\\PR(D=0))^{-1},$ and $Q_2(x,\\sa ):=\\PR(0<D< x-\\sa).$ Recall that $\\PR(D>0)>0, $ which is equivalent to $\\PR(D=0)<1.$ Since $(1-\\a\\PR(D=0))^{-1}\\le Q_1,$ formula implies that $$|\\ua (x) - \\ua (\\sa)|\\le Q_1(|\\tilde{h}(x)-\\tilde{h}(\\sa)|+\\bar{c}(x-\\sa) + 2 Q_2(x,\\sa ) C(-b,b)).$$ Since the function $\\tilde{h}$ is uniform continuous on the interval $[-(M+2b),M],$ all three summands in the right-hand side of the last equations converge uniformly in $\\a$ to 0 as $x\\downarrow \\sa.$ Therefore, there exists $\\delta_2\\in (0,\\delta_1)$ such that holds for all $x\\in [\\sa,\\sa+\\delta_2].$\n\nSince $\\ua (x) = \\bar{c}(\\sa - x) + \\ua (\\sa)$ for all $x\\leq \\sa,$ then for all $x,y\\le \\sa$ $$\\begin{aligned}\n |\\ua (x) - \\ua (y)| =\\bar{c}|x-y|< \\frac{\\epsilon}{4},\n \\label{eqn:ubd u x < san}\\end{aligned}$$ for $|x-y|<\\frac{\\epsilon}{4{\\bar c}}.$ Let $\\delta_3:=\\min\\{\\frac{\\epsilon}{4{\\bar c}},\\delta_2\\}.$ Then holds for $|x-y|<\\delta_3.$\n\nFor $x \\leq \\sa \\leq y$ satisfying $|x-y|< \\delta_3$ $$\\begin{aligned}\n |\\ua (x) - \\ua (y)| \\leq |\\ua (x) - \\ua (\\sa)| + |\\ua (\\sa) - \\ua (y)|\n < \\frac{\\epsilon}{2},\n \\label{eqn:ubd x < san < y}\\end{aligned}$$ where the first inequality is the triangle property and the second one follows from and . ", "Therefore, , and imply that $|\\ua (x) - \\ua (y)| <\\frac{\\epsilon}{2}$ for all $x,y \\leq \\sa + \\delta_3$ satisfying $|x-y|< \\delta_3.$ Then for $|z_1-z_2|< \\delta_3$ with probability $1$ $$|\\ua (z_1-\\textbf{S}_{\\textbf{N}(z_1-\\sa) + 1}) - \\ua (z_2-\\textbf{S}_{\\textbf{N}(z_1-\\sa) + 1})| < \\frac{\\epsilon}{2},$$ and therefore $$\\begin{aligned}\n \\E[|\\ua (z_1-\\textbf{S}_{\\textbf{N}(z_1-\\sa) + 1}) - \\ua (z_2-\\textbf{S}_{\\textbf{N}(z_1-\\sa) + 1})|] < \\frac{\\epsilon}{2},\n \\label{eqn:ubd2-2}\\end{aligned}$$ Formulae , . ", "and imply that for $z_1,$ $z_2\\geq \\sa$ satisfying $|z_1-z_2|< \\delta_3$ $$\\begin{aligned}\n |\\ua (z_1) - \\ua (z_2) | < \\epsilon .", "\n \\label{eqn:ubd x12>san}\\end{aligned}$$\n\nTherefore, , , and imply that for all $x,$ $y \\in (-\\infty, M)$ satisfying $|x-y|<\\delta_3$ $$\\begin{aligned}\n |u_{\\a}(x) - u_{\\a}(y) | < \\eps .\\end{aligned}$$ Since $M$ can be chosen arbitrarily large, for each $\\b\\in (\\a^*,1)$ the family of functions $\\{u_{\\a}\\}_{\\a\\in[\\b,1)}$ is equicontinuous on $\\X.$\n\n\\[thm:Gacont\\] Let Assumption \\[assum:qcall\\] hold. ", "Then for $\\a \\in (\\a^*, 1),$ the functions $\\va$ and $\\Ga$ are continuous on $\\X.$\n\nAccording to Theorem \\[thm:qcall\\], there exists an optimal $(\\sa,\\Sa)$ optimal policy for the infinite-horizon problem. ", "In addition, Theorem \\[thm:u a equicont\\] implies that the function $\\va (x) = \\ua (x) + \\ma$ is continuous on $\\X.$ Therefore, since the function $\\E[h(x-D)]$ is continuous, the same arguments in the proof of Feinberg and Liang [@FLi16a Theorem 5.3] starting from the definition of the function $g_\\a$ there imply that the function $\\Ga$ is continuous on $\\X.$\n\nSetup-Cost Inventory Model: Average Costs per Unit Time {#sec:acoe}\n=======================================================\n\nThe following theorem establishes the convergence of discounted-cost optimality equations to the ACOEs for the described inventory model and the optimality of $(s,S)$ policies under the average cost criterion under Assumption \\[assum:qcall\\]. ", "It is proved in Chen and Simchi-Levi [@CS04b] that there exists an average-cost optimal $(s,S)$ policy if only Assumption \\[assum:qcalpha\\] for $\\a = 1$ is assumed. ", "We are interested in approximating the average-cost optimal $(s,S)$ policy from the discount-cost optimal $(\\sa,\\Sa)$ policies as the discount factor $\\a\\uparrow1.$\n\n\\[thm:inventory:acoe\\] Let Assumption \\[assum:qcall\\] hold. ", "For every sequence $\\{\\alpha_n\\uparrow 1\\}_{n=1,2,\\ldots}$ of nonnegative discount factors with $\\alpha_1 > \\a^*,$ there exist a subsequence $\\{\\alpha_{n_k}\\}_{k=1,2,\\ldots}$ of $\\{\\alpha_n\\}_{n=1,2,\\ldots},$ a stationary policy $\\varphi,$ and a function $\\tu$ defined in for the subsequence $\\{\\alpha_{n_k}\\}_{k=1,2,\\ldots}$ such that for all $x\\in\\X$ $$\\begin{aligned}\n\\label{eqn:IC ACOE}\n\\begin{split}\n w + \\tu(x) &= K \\indF_{\\{\\varphi(x)>0\\}} + H(x+\\varphi(x)) - \\bar{c}x \\\\\n &=\\min \\{ \\min_{a\\geq 0}[ K + H(x+a)], H(x) \\} - \\bar{c}x,\n \\end{split}\\end{aligned}$$ where the function $H$ is defined in . ", "In addition, the functions $\\tilde u$ and $H$ are continuous and inf-compact, and a stationary optimal policy $\\varphi$ satisfying can be selected as an $(s^*,S^*)$ policy described in Theorem \\[thm:fle\\]. ", "It also can be selected as an $(s,S)$ policy with the real numbers $S$ and $s$ satisfying and defined in respectively for $f(x)=H(x),$ $x\\in\\X.$\n\n[The relations between the function $\\tu$ in the ACOE and the solutions to the ACOE constructed by Chen and Simchi-Levi [@CS04b] are currently not clear. ]{}", "\n\nTo prove Theorem \\[thm:inventory:acoe\\], we first establish several properties of the average-cost relative value function. ", "The proofs of the lemma and corollary presented in this section are available in Appendix \\[sec:acoe:apx\\].", "\n\n\\[lm:Horder\\] Let Assumption \\[assum:qcall\\] hold. ", "Consider the function $\\tu$ defined in for a sequence $\\{ \\a_n \\}_{n=1,2,\\ldots}$ such that $\\alpha_n\\uparrow 1$ and $\\a_1>\\a^*.$ Then the following statements hold:\n\n(i) For $x\\leq y$ $$\\begin{aligned}\n \\tu (x) + \\c x & \\leq \\tu (y) + \\c y + K, \\label{eqn:tu1} \\\\\n H(y) - H (x) & \\geq \\E[h(y-D)] - \\E[h(x-D)] - \\a K. \\label{eqn:H1}\\end{aligned}$$\n\n(ii) For $x\\leq y \\leq \\rone$ $$\\begin{aligned}\n \\tu (y) + \\c y - \\tu (x) - \\c x & \\leq 0, \\label{eqn:tude1} \\\\\n H (y) - H (x) & \\leq 0. ", "\\label{eqn:Hde1}\\end{aligned}$$\n\nThe proof of this thoerem is identical to the proof in Feinberg and Liang [@FLi16b Theorem 4.5] with (i) Lemmas 4.6 and 4.7 there replaced with Lemma \\[lm:U(x) bounded\\] and Theorem \\[thm:u a equicont\\] from this paper respectively; and (ii) the proof of the $K$-convexity of the functions $u$ and $H$ and the optimality of $(s,S)$ policies under the average cost criterion replaced with the following arguments. ", "Consider the cases (1)-(3) in the proof of Theorem \\[thm:qcall:t\\] with $G_{N-t-1,\\a},$ $\\h$ and $\\ra$ replaced with $H,$ $h,$ and $\\rone$ respectively. ", "Then Lemma \\[lm:Horder\\] implies that there exists an optimal $(s,S)$ policy, with the real numbers $S$ and $s$ satisfying and defined in for $f:=H.$\n\nFurthermore, the continuity of average-cost relative value functions implies the following corollary.", "\n\n\\[cor:ordering at sa\\] Let Assumption \\[assum:qcall\\] hold, the state space $\\X = \\R,$ and the action space $\\A = \\Rp.$ For the $(s,S)$ policy defined in Theorems \\[thm:inventory:acoe\\], consider the stationary policy $\\varphi$ coinciding with this policy at all $x\\in\\X,$ except $x=s,$ and with $\\varphi(s)=S-s.$ Then the stationary policy $\\varphi$ also satisfies the optimality equation , and is therefore average-cost optimal.", "\n\nConvergence of Optimal Lower Thresholds $\\sa$ {#sec:cvg sa}\n=============================================\n\nThis section establishes for the inventory model with holding/backlog costs satisfying quasiconvexity assumptions the convergence of discounted optimal lower thresholds $\\sa\\to s$ as $\\a\\uparrow1,$ where $s$ the average-cost optimal lower threshold (stated in Theorem \\[thm:inventory:acoe\\]). ", "In this and the following sections, we assume that the state space $\\X=\\R$ and the action sets $\\A = A(x) = \\Rp$ for all $x\\in\\X.$ This means an arbitrary nonnegative amount of inventory can be ordered at any state.", "\n\nThe quasiconvexity of $\\E[h(x-D)]$ assumed in Assumption \\[assum:qcall\\] implies that the function $\\E[h(x-D)]$ is nonincreasing on $(-\\infty,\\rone),$ where $\\rone$ is defined in . ", "The stronger Assumption \\[assum:decrease\\] is used in this section and Section \\[sec:cvg ua\\].", "\n\nThe following theorem establishes the convergence of the discounted optimal lower thresholds $\\sa$ when the discount factor $\\a$ converges to $1.$\n\n\\[thm:limit s alpha\\] Let Assumptions \\[assum:qcall\\] and \\[assum:decrease\\] hold for $\\a = 1.$ Then the limit $$\\begin{aligned}\n s^* := \\lim_{\\a\\uparrow 1} \\sa\n \\label{eqn:def s*}\n \\end{aligned}$$ exists and $s^* \\leq \\rone,$ where $\\rone$ is defined in .", "\n\n\\[rm:s\\] [As shown in Corollary \\[cor:inventory:acoe\\], if Assumptions \\[assum:qcall\\] and \\[assum:decrease\\] hold for $\\a=1,$ then all the sequences $\\{\\a_n\\uparrow1\\}_{n=1,2,\\ldots}$ define the same functions $\\tilde{u}$ and $H$ in , and, according to Theorem \\[thm:uniqueac\\], there exists a unique threshold $s^*,$ for which there is an $(s^*,S^*)$ policy satisfying the ACOE . ]{}", "\n\nBefore the proof of Theorem \\[thm:limit s alpha\\], we first state several auxiliary facts. ", "Consider the infinite-horizon value function $\\bva$ for the model with zero unit and terminal costs. ", "According to Lemma \\[lm:samevalues\\], $\\bva (x) - \\c x = \\va (x),$ $x\\in\\X.$ For $x\\in\\X,$ define $$\\begin{aligned}\n\\bma := \\min_{x\\in\\X} \\{ \\bva (x) \\} \\quad \\text{and} \\quad \\bua (x) := \\bva (x) - \\bma.", "\n\\label{eqn:def bua}\\end{aligned}$$\n\nIf there exists an $\\a$-discount optimal $(\\sa,\\Sa)$ policy, then can be written as $$\\begin{aligned}\n \\bva (x) =\n \\begin{cases}\n \\Ga (x) & \\text{if } x \\geq \\sa , \\\\\n K + \\Ga (\\Sa) & \\text{if } x < \\sa , \\\\\n \\end{cases}\n \\label{eqn:bva sS}\\end{aligned}$$ which implies that $$\\begin{aligned}\n \\bma = \\min_{x\\in\\X} \\{ \\Ga (x) \\} = \\Ga (\\Sa).", "\n \\label{eqn:bma}\\end{aligned}$$\n\nConsider $x_{\\a} \\in X_{\\a},$ where $X_{\\a}$ is defined in . ", "For $\\a\\in[0,1)$ $$\\begin{aligned}\n \\bma \\leq \\bva (x_{\\a}) = \\ma + \\c x_{\\a} \\leq \\ma + \\c x_U^* ,\n \\label{eqn:ubd bma}\\end{aligned}$$ where $x^*_U$ is defined in . ", "In view of , the continuity of $\\bva(x)$ implies that $\\bva(x) = \\bva(\\sa)$ for all $x \\leq \\sa.$ Therefore, $$\\begin{aligned}\n \\bma = \\inf_{x\\geq \\sa} \\bva(x) = \\inf_{x\\geq \\sa} \\{ \\va (x) + \\c x \\} \\geq \\inf_{x\\geq \\sa} \\{ \\va (x) + \\c \\sa \\} \\geq \\ma + \\c \\sa,\n \\label{eqn:lbd bma}\\end{aligned}$$ where the first inequality holds because $x\\geq \\sa$ and the last one follows from $\\ma = \\inf_x \\va (x).$ Then and imply $$\\begin{aligned}\n \\ma + \\c \\sa \\leq \\bma \\leq \\ma + \\c x_U^*.", "\n \\label{eqn:bounds on bma}\\end{aligned}$$\n\nFor $\\a\\in (\\a^*,1)$ define the set of all possible optimal discounted lower thresholds $$\\begin{aligned}\n \\mathcal{G}_\\alpha := \\{ x \\leq \\Sa : \\Ga (y) = K + \\Ga (\\Sa) \\text{ for all } y\\in[\\sa,x] \\},\n \\label{eqn:set of sa}\\end{aligned}$$ where $\\Sa$ satisfies and $\\sa$ is defined in with $f:=\\Ga.$ Note that $\\sa\\in \\mathcal{G}_\\a$ and $y \\geq \\sa$ for all $y\\in\\mathcal{G}_\\a.$\n\n\\[rm:mathcalGa\\] [The set $\\mathcal{G}_\\a$ is not empty if $\\X=\\R$ because the function $\\Ga $ is continuous (see Theorem \\[thm:Gacont\\]) and $\\lim_{x\\to-\\infty} \\Ga (x) > K + \\Ga (\\Sa).$ If $\\X = \\Z,$ as this takes place for problems with discrete commodity, it is possible that $\\mathcal{G}_\\a$ is an empty set. ]{}", "\n\nThe following three lemmas state the relations between parameters defined in this section. ", "The proofs of the lemmas presented in this section are available in Appendix \\[sec:cvg sa:apx\\].", "\n\n\\[lm:sa\\] Let Assumption \\[assum:qcall\\] hold. ", "Then, for all $\\a\\in (\\a^*,1)$ and $y \\in \\mathcal{G}_\\a,$ $$\\begin{aligned}\n (1-\\a)(\\bma + K) = \\E[\\h (y - D)].", "\n \\label{eqn:value and ha}\n \\end{aligned}$$\n\n\\[lm:r alpha &lt;= r\\*\\] Let Assumption \\[assum:qcall\\] hold. ", "Then, for all $\\a\\in (\\a^*,1)$ and $y \\in \\mathcal{G}_\\a,$ $$\\begin{aligned}\n y \\leq \\ra \\leq \\rone.", "\n %\\label{eqn:r alpha <= r_1}\n \\end{aligned}$$\n\n\\[lm:limit m\\*\\] Let Assumption \\[assum:qcall\\] hold. ", "Then $$\\begin{aligned}\n \\lim_{\\a\\uparrow 1} (1-\\a) \\bma = \\lim_{\\a\\uparrow1}\\E[h_{\\a} (s_{\\a} - D)] = w .", "\n \\label{eqn:equality for limit}\n \\end{aligned}$$\n\nThe proof is by contradiction. ", "According to Theorem \\[thm:fle\\], for $\\a_n\\uparrow 1,$ $n=1,2,\\ldots,$ with $\\a_1 > \\a^*,$ every sequence $\\{(s_{\\a_n},S_{\\a_n})\\}_{n=1,2,\\ldots}$ is bounded. ", "Consider two real numbers $s^{(1)} < s^{(2)}$ such that there exist two sequences $\\{\\a_n\\}_{n=1,2,\\ldots}$ and $\\{\\tilde{\\a}_n\\}_{n=1,2,\\ldots}$ satisfying $\\lim_{n\\to +\\infty} s_{\\a_n} = s^{(1)}$ and $\\lim_{n\\to +\\infty} s_{\\tilde{\\a}_n} = s^{(2)}.$\n\nSince the function $\\E[h(x-D)]$ is continuous, $$\\begin{aligned}\n \\lim_{n\\to +\\infty}\\E[h(s_{\\a_n} - D)] = \\E[h(s^{(1)} - D)].", "\n \\label{eqn:limit:part 1}\\end{aligned}$$ Therefore, $$\\begin{aligned}\n \\lim_{n\\to +\\infty} \\E[h_{\\a_n} (s_{\\a_n} - D)] &= \\lim_{n\\to +\\infty} \\big\\{ \\E[h (s_{\\a_n} - D)] + (1-\\a_n)\\c s_{\\a_n} + \\a_n \\c \\E[D] \\big \\} \\nonumber \\\\\n & = \\E[h(s^{(1)} - D)] + \\c \\E[D],\n \\label{eqn:limit ha(sn-D)}\\end{aligned}$$ where the second equality follows from and $s_{\\a_n}\\to s^{(1)}\\in\\R$ as $\\a_n\\uparrow 1.$ According to Lemma \\[lm:limit m\\*\\], $\\E[h(s^{(1)} - D)] = w - \\c\\E[D].$ By the same arguments with $\\a_n$ replaced with $\\tilde{\\a}_n,$ $\\E[h(s^{(2)} - D)] = w - \\c\\E[D].$ Therefore, $$\\begin{aligned}\n \\E[h(s^{(1)} - D)] = \\E[h(s^{(2)} - D)].", "\n \\label{eqn:h(s1)=h(s2)}\\end{aligned}$$\n\nAccording to Lemma \\[lm:r alpha &lt;= r\\*\\], $\\sa \\leq \\ra$ for all $\\a\\in (\\a^*,1).$ Therefore $$\\begin{aligned}\n s^{(2)} = \\lim_{n\\to +\\infty} s_{\\tilde{\\a}_n} \\leq \\liminf_{n\\to +\\infty} \\rtan \\leq \\rone,\n \\label{eqn:s<r*}\\end{aligned}$$ where the last inequality follows from Lemma \\[lm:r alpha &lt;= r\\*\\]. ", "Since $s^{(1)} < s^{(2)} \\leq \\rone,$ Assumption \\[assum:decrease\\] implies that $$\\begin{aligned}\n \\E[h(s^{(1)} - D)] > \\E[h(s^{(2)} - D)],\n \\label{eqn:h(s1)>h(s2)}\\end{aligned}$$ which contradicts . ", "Thus, the limit $\\lim_{\\a\\uparrow 1} \\sa$ exists and implies that $s^* \\leq \\rone.$\n\nThe following theorem establishes the uniqueness of possible optimal lower thresholds for the inventory model with convex cost functions under the discounted criterion.", "\n\n\\[thm:unique\\] Let Assumptions \\[assum:qcall\\] and \\[assum:decrease\\] hold for $\\a\\in(\\a^*,1).$ Then $$\\begin{aligned}\n \\mathcal{G}_\\a = \\{ \\sa \\},\\end{aligned}$$ where $\\mathcal{G}_\\a$ and $\\sa$ are defined in and with $f:=\\Ga$ respectively.", "\n\nRecall that $\\sa\\in\\mathcal{G}_\\a$ and $y\\geq \\sa$ for all $y\\in\\mathcal{G}_\\a.$ The proof is by contradiction. ", "Assume that there exists $y_1\\in \\mathcal{G}_\\a$ such that $y_1 > \\sa.$ According to Lemma \\[lm:sa\\], $$\\begin{aligned}\n \\E[\\h (y_1-D)] = (1-\\a)(\\bma + K) = \\E[\\h (\\sa - D)].\\end{aligned}$$ Since Assumption \\[assum:decrease\\] holds for the discount factor $\\a,$ $\\ra< y_1,$ where $\\ra$ is defined in . ", "However, according to Lemma \\[lm:r alpha &lt;= r\\*\\], $y_1\\leq \\ra ,$ which implies that $y_1\\leq \\ra <y_1.$ Therefore, $\\mathcal{G}_\\a = \\{ \\sa \\}.$\n\nConvergence of Discounted Relative Value Functions {#sec:cvg ua}\n==================================================\n\nThis section establishes the convergence of discounted relative value functions to the average-cost relative value function for the setup-cost inventory model when the discount factor tends to $1.$ This is a stronger result than the convergence for a subsequence that follows from Theorem \\[thm:inventory:acoe\\]. ", "We recall that in this section it is assumed that $\\X = \\R$ and $\\A = A(x) = \\Rp$ for all $x\\in\\X.$ The proofs of the proposition and lemmas presented in this section are available in Appendix \\[sec:cvg ua:apx\\].", "\n\nLet us define $$\\begin{aligned}\n u (x) := \\liminf_{\\a\\uparrow1, y\\to x} u_{\\a} (y).", "\n \\label{eqn:FKZu}\\end{aligned}$$ According to Feinberg et el.", " [@FKZ12 Theorems 3, 4], the ACOI holds for the relative value functions $\\tilde{u}$ and $u$ defined in and respectively.", "\n\nThe following theorem states the convergence of discounted relative value functions, when the discount factor converges to 1, to the average-cost relative value function $u.$\n\n\\[thm:ua converge\\] Let Assumptions \\[assum:qcall\\] and \\[assum:decrease\\] hold for $\\a=1.$ Then, $$\\begin{aligned}\n \\lim_{\\a\\uparrow1} u_{\\a}(x) = u (x), \\qquad x\\in\\X,\n \\label{eqn:ua converge-1}\\end{aligned}$$ and the function $u$ is continuous.", "\n\nIn particular, Theorem \\[thm:ua converge\\] implies that the function $\\tilde{u}$ defined in is the same for every particular sequence $\\{\\a_n\\uparrow1\\}_{n=1,2,\\ldots}.$ The following example demonstrates that this is not true in general under Assumptions **W\\*** and **B**.", "\n\n\\[ex:mdplimit\\]\n\nConsider a MDP with state space $\\X = \\{-2, -1, 0, 1, 2, \\ldots \\}$ and action space $\\A = \\{a^s , a^c\\},$ where the action $a^s$ stands for “stop” and the action $c$ stands for “continue”; see Figure \\[fig:mdplimit\\]. ", "Let $A(-1) = \\A$ and $A(n) = \\{ a^c \\}$ for $n \\in \\X\\setminus \\{ -1 \\}.$ The transition probabilities are $P(-1 | -1, a^s) = 1$ and $P(n + 1 | n, a^c) = 1$ for $n\\in \\X.$ The costs are $c(-2, a^c) = 0,$ $c(-1, a) = 1$ for $a\\in\\A,$ and $c(n, a^c) = \\zone_n $ for $n = 0,1,\\ldots,$ where $\\zone_n$ is defined as $$\\begin{aligned}\n \\zone_n =\n \\begin{cases}\n z_0 + 1, & \\text{if } n = 0, \\\\\n z_n - z_{n-1} + 1, & \\text{if } n = 1,2,\\ldots,\n \\end{cases}\n \\label{eqn:ex1:defzn1}\\end{aligned}$$ where the sequence $z_n$ is taken from Bishop et al.", " [@BFZ14 Equation (11)]: $$\\begin{aligned}\n z_n =\n \\begin{cases}\n 1, & \\text{if } D(2k - 1) \\leq n < D(2k), \\quad k = 1,2,\\ldots, \\\\\n 0, & \\text{otherwise,}\n \\end{cases}\n %\\label{eqn:ex1:defzn}\\end{aligned}$$ where $D(k) := \\sum_{i=1}^k i! ,", "$ $k = 1,2,\\ldots\\ .$ For the sequence $\\{ z_n \\}_{n=0,1,\\ldots},$ define the function $$\\begin{aligned}\n f(\\a) := (1 - \\a) \\sum_{i=0}^{\\infty} z_i \\a^i , \\qquad \\a \\in [0,1) .", "\n \\label{eqn:ex1:deffalpha}\\end{aligned}$$\n\n![", "MDP described in Example \\[ex:mdplimit\\][]{data-label=\"fig:mdplimit\"}](mdpExample1.png)\n\nAs shown in the proof of Proposition \\[prop:ex1:assumption\\] in Appendix \\[sec:cvg ua:apx\\], the relative value function $$\\begin{aligned}\n \\ua (n) =\n \\begin{cases}\n 0, & \\text{if } n = -2, \\\\\n 1, & \\text{if } n = -1, \\\\\n f(\\a) + 1, & \\text{if } n = 0, \\\\\n (1-\\a)\\sum_{i=0}^{\\infty} z_{n+i} \\a^i - z_{n-1} + 1, & \\text{if } n = 1,2,\\ldots\\ .", "\n \\end{cases}\n \\label{eqn:ex1:ua}\\end{aligned}$$ According to Bishop et al.", " [@BFZ14 Proposition 1], $\\liminf_{\\a\\uparrow1}f(\\a)=0$ and $\\limsup_{\\a\\uparrow1} f(\\a) = 1.$ Hence, $\\liminf_{\\a\\uparrow1} \\ua (0) = 1$ and $\\limsup_{\\a\\uparrow1} \\ua (0) = 2,$ that is, in this example there exist multiple relative value functions $\\tu$ defined in .", "\n\n\\[prop:ex1:assumption\\] The MDP described in Example \\[ex:mdplimit\\] satisfies Assumptions **W\\*** and **B**, where the discrete metric $d(x,y) = \\indF_{\\{x = y\\}}$ is considered on $\\X$ and $\\A.$\n\nBefore the proof of Theorem \\[thm:ua converge\\], we first state several properties of the functions $\\bua$ defined in . ", "If there exists an $\\a$-discounted optimal $(\\sa,\\Sa)$ optimal policy, then implies that $$\\begin{aligned}\n \\bua (x) =\n \\begin{cases}\n \\Ga (x) - \\bma & \\text{if } x \\geq \\sa, \\\\\n K & \\text{if } x < \\sa.", "\n \\end{cases}\n \\label{eqn:bua-2}\\end{aligned}$$\n\n\\[lm:bua equicontinuous\\] Let Assumption \\[assum:qcall\\] hold. ", "Then,\n\n(i) for each $\\b\\in (\\a^*,1)$ the family of functions $\\{\\bua\\}_{\\a\\in [\\b, 1)}$ is equicontinuous on $\\X;$ \\[lm:bua-equi\\]\n\n(ii) $\\sup_{\\a\\in (\\a^*,1)} \\bua (x) < +\\infty$ for all $x\\in\\X.$ \\[lm:bua-bd\\]\n\n\\[lm:bua pointwise converge\\] Let Assumptions \\[assum:qcall\\] and \\[assum:decrease\\] hold for $\\a=1.$ Then there exists the limit $$\\begin{aligned}\n \\bu (x) := \\lim_{\\a\\uparrow1} \\bu_{\\a}(x) , \\qquad x\\in\\X,\n \\label{eqn:convergence-1}\\end{aligned}$$ where the function $\\bu$ is continuous on $\\X.$\n\nIn view of , and , $$\\begin{aligned}\n \\ua (x) = \\bua (x) + \\bma - \\ma - \\c x, \\qquad x\\in\\X.\n \\label{eqn:ubu}\\end{aligned}$$\n\nThe theorem follows from the following two statements:\n\n(i) \\[enum:thmua:1\\] there exists the limit $u^* (x):=\\lim_{\\a\\uparrow1} u_{\\a} (x),$ $x\\in\\X,$ and the function $u^*$ is continuous on $\\X;$ and\n\n(ii) \\[enum:thmua:2\\] $u^* (x) = u (x) := \\liminf_{\\a\\uparrow1, y\\to x}u_{\\a} (x)$ for all $x\\in\\X.$\n\nLet us prove statements and . ", "We first prove that there exists the limit $u^* (s^*) := \\lim_{\\a\\uparrow1} u_{\\a}(s^*),$ where $s^*$ is defined in .", "\n\nConsider $x_\\a \\in X_{\\a},$ $\\a\\in[0,1),$ where $X_{\\a}$ is defined in , and any given $\\b\\in (\\a^*,1).$ In view of , since $X_{\\a}\\subset [x_L^*,x_U^*]$ for all $\\a\\in[0,1),$ for every sequence $\\{ \\a_n \\uparrow 1\\}_{n=1,2,\\ldots},$ there exists a subsequence $\\{ \\a_{n_k} \\uparrow 1\\}_{k=1,2,\\ldots}$ of the sequence $\\{ \\a_n \\uparrow 1\\}_{n=1,2,\\ldots}$ such that $\\a_{n_1}\\geq \\b$ and $x_{\\a_{n_k}}\\to x^*$ as $k\\to +\\infty$ for some $x^*\\in[x_L^*,x_U^*].$\n\nConsider $\\eps > 0.$ Since the family of functions $\\{ \\ua \\}_{\\a\\in [\\b,1)}$ is equicontinuous (see Theorem \\[thm:u a equicont\\]), there exists an integer $M(\\eps) > 0$ such that for all $k \\geq M(\\eps)$ $$\\begin{aligned}\n |u_{\\a_{n_k}} (x_{\\a_{n_k}}) - u_{\\a_{n_k}} (x^*)| < \\eps.", "\n \\label{eqn:limit u(x*)}\\end{aligned}$$ Since $u_{\\a_{n_k}} (x_{\\a_{n_k}}) = 0$ for all $k=1,2,\\ldots,$ implies that for $k \\geq M(\\eps)$ $$\\begin{aligned}\n |u_{\\a_{n_k}} (x^*) | < \\eps.", "\n \\label{eqn:uan(x*)<e}\\end{aligned}$$ Therefore, implies that $$\\begin{aligned}\n \\lim_{k\\to +\\infty} u_{\\a_{n_k}} (x^*) = 0 .", "\n \\label{eqn:limit uan(x*)=0}\\end{aligned}$$ Since the function $u_{\\a_{n_k}}$ is nonnegative, implies that for $k \\geq M(\\eps)$ $$\\begin{aligned}\n u_{\\a_{n_k}} (x^*) < u_{\\a_{n_k}} (x) + \\eps, \\qquad x\\in\\X .", "\n \\label{eqn:min value-1}\\end{aligned}$$ Then and imply that for $k \\geq M(\\eps)$ $$\\begin{aligned}\n \\bar{u}_{\\a_{n_k}} (x^*) - \\bar{c}x^* < \\bar{u}_{\\a_{n_k}} (x) - \\bar{c}x + \\eps,\n \\qquad x\\in\\X.\n \\label{eqn:min value-2}\\end{aligned}$$ By taking the limit of both sides of as $k\\to +\\infty,$ Lemma \\[lm:bua pointwise converge\\] implies that $$\\begin{aligned}\n \\bu (x^*) - \\bar{c} x^* \\leq \\bu (x) - \\bar{c}x + \\eps, \\qquad x\\in\\X .", "\n \\label{eqn:min value-3}\\end{aligned}$$ Since $\\eps$ can be chosen arbitrarily, implies that $$\\begin{aligned}\n \\bu (x^*) - \\bar{c} x^* = \\min_{x\\in\\X} \\{ \\bu (x) - \\bar{c}x \\} .", "\n \\label{eqn:minV-4}\\end{aligned}$$ Let $M_{\\bu}:= \\bu (s^*) - \\bar{c}s^* - \\min_{x\\in\\X} \\{ \\bu (x) - \\bar{c}x \\}.$ Then $$\\begin{aligned}\n\\begin{split}\n &\\lim_{k\\to +\\infty} u_{\\a_{n_k}} (s^*) - u_{\\a_{n_k}} (x^*) = \\lim_{k\\to +\\infty} \\bar{u}_{\\a_{n_k}} (s^*) - \\bar{c}s^* - [\\bar{u}_{\\a_{n_k}} (x^*) - \\bar{c}x^*] \\\\\n =& \\bu (s^*) - \\bar{c}s^* -[\\bu (x^*) - \\bar{c}x^*] = \\bu (s^*) - \\bar{c}s^* - \\min_{x\\in\\X} \\{ \\bu (x) - \\bar{c}x \\} = M_{\\bu},\n\\end{split}\n \\label{eqn:LimitOfDiff}\\end{aligned}$$ where the first equality follows from , the second one follows from Lemma \\[lm:bua pointwise converge\\] and the third one follows from . ", "In view of and , $$\\begin{aligned}\n \\lim_{k\\to +\\infty} u_{\\a_{n_k}} (s^*) = M_{\\bu}.", "\n \\label{eqn:limit u(s*)}\\end{aligned}$$ Thus, for every sequence $\\{ \\a_n \\uparrow1 \\}_{n=1,2,\\ldots }$ there exists a subsequence $\\{ \\a_{n_k} \\}_{k=1,2,\\ldots}$ such that holds. ", "Therefore, $\\lim_{n\\to +\\infty} u_{\\a_n} (s^*) = M_{\\bu}$ for every sequence $\\{ \\a_n \\uparrow1 \\}_{n=1,2,\\ldots },$ which is equivalent to $$\\begin{aligned}\n u^* (s^*) := \\lim_{\\a\\uparrow1} u_{\\a} (s^*) = M_{\\bu} .", "\n \\label{eqn:limit u(s*) all}\\end{aligned}$$\n\nNow we prove that there exists the limit $u^* (x):=\\lim_{\\a\\uparrow1} u(x)$ for $x \\in\\X.$ For $x\\in\\X$ $$\\begin{aligned}\n\\begin{split}\n \\lim_{\\a\\uparrow1} \\ua (x) - \\ua (s^*) & =\n \\lim_{\\a\\uparrow1} \\bua (x) - \\c x - [\\bua (s^*) - \\c s^*] \\\\\n & = \\bu (x) - \\c x - [\\bu (s^*) - \\c s^*],\n\\end{split}\n \\label{eqn:limit u(y)}\\end{aligned}$$ where the first equality follows from and the second one follows from Lemma \\[lm:bua pointwise converge\\]. ", "Therefore, and implies that there exists the limit $$\\begin{aligned}\n u^* (x) := \\lim_{\\a\\uparrow1} u_{\\a} (x) = M_{\\bu} + \\bu (x) - \\bar{c} x - [\\bu (s^*) - \\bar{c} s^*], \\qquad x\\in\\X.\n \\label{eqn:limit u(y) all}\\end{aligned}$$\n\nFurthermore, since the family of functions $\\{ \\ua \\}_{ \\a \\in [\\b,1) }$ is equicontinuous and Assumption **B** holds, Arzelà-Ascoli theorem implies that the function $u^*$ is continuous.", "\n\n\\(ii) Consider sequences $\\{ \\a_n\\uparrow1 \\}_{n=1,2,\\ldots}$ and $\\{ y_n\\to x \\}_{n=1,2,\\ldots}$ such that $\\a_1 > \\a^* $ and $\\lim_{n\\to +\\infty} u_{\\a_n}(y_n) = \\liminf_{\\a\\uparrow1, y\\to x} u_{\\a}(y).$ Then, $$\\begin{aligned}\n \\liminf_{\\a\\uparrow1, y\\to x} u_{\\a}(y) \\leq\n \\liminf_{n\\to +\\infty, y\\to x} u_{\\a_n}(y) \\leq \\lim_{n\\to +\\infty} u_{\\a_n}(y_n) = \\liminf_{\\a\\uparrow1, y\\to x} u_{\\a}(x),\\end{aligned}$$ which implies that $$\\begin{aligned}\n \\liminf_{\\a\\uparrow1, y\\to x} u_{\\a}(y) = \\liminf_{n\\to +\\infty, y\\to x} u_{\\a_n}(y).", "\n \\label{eqn:lim=1}\\end{aligned}$$ According to Feinberg and Liang [@FLi16b Lemma 3.3], since $\\lim_{n\\to +\\infty} u_{\\a_n} (x) = u^* (x),$ Theorems \\[thm:B\\] and \\[thm:u a equicont\\] imply that $$\\begin{aligned}\n \\liminf_{n\\to +\\infty, y\\to x} u_{\\a_n}(y) = \\lim_{n\\to +\\infty} u_{\\a_n} (x) = u^* (x) .", "\n \\label{eqn:lim=2}\\end{aligned}$$ Therefore, and imply that $u:=\\liminf_{\\a\\uparrow1, y\\to x} u_{\\a}(y) = u^*.$ This completes the proof.", "\n\nTheorem \\[thm:ua converge\\] implies that can be written as $$\\begin{aligned}\n H(x) := \\bar{c}x + \\E[h (x-D)] + \\E[u (x-D)].", "\n \\label{eqn:def H(x)}\\end{aligned}$$\n\n\\[cor:inventory:acoe\\] Let Assumptions \\[assum:qcall\\] and \\[assum:decrease\\] hold for $\\a=1.$ Then the conclusions of Theorem \\[thm:inventory:acoe\\] hold with $\\tilde{u}=u$ defined in and $s^*$ defined in , that is, the functions $\\tilde{u}$ and the thresholds $s^*$ defined in and Theorem \\[thm:fle\\] respectively, are the same for all sequences $\\{ \\a_n\\uparrow1 \\}_{n=1,2,\\ldots}.$\n\nDefine the set of all possible optimal average-cost lower thresholds $$\\begin{aligned}\n \\mathcal{G} := \\{ x \\leq S : H (y) = K + H (S) \\text{ for all } y\\in[s,x] \\},\n \\label{eqn:set of s}\\end{aligned}$$ where $S=\\min\\big\\{ \\argmin_x\\{ H(x) \\} \\big\\}$ and $s$ is defined in with $f:=H.$ Note that $s\\in \\mathcal{G}$ and $y \\geq s$ for all $y\\in\\mathcal{G}.$\n\nThe following theorem establishes the uniqueness of the optimal lower threshold satisfying the optimality equations for the inventory model with holding/backlog costs satisfying quasiconvexity assumptions under the average cost criterion.", "\n\n\\[thm:uniqueac\\] Let Assumptions \\[assum:qcall\\] and \\[assum:decrease\\] hold for $\\a=1.$ Then, $$\\begin{aligned}\n \\mathcal{G} = \\{ s^* \\},\\end{aligned}$$ where $\\mathcal{G}$ and $s^*$ are defined in and respectively.", "\n\nConsider $\\mathcal{G}$ and $S$ defined in . ", "Recall that $s \\in\\mathcal{G}$ and $y\\geq s,$ where $s$ is defined in with $f:=H.$ According to Theorem \\[thm:inventory:acoe\\] and Corollary \\[cor:inventory:acoe\\], for $y\\in\\mathcal{G}$ $$\\begin{aligned}\n w + u(x) + \\c x =\n \\begin{cases}\n K + H(S) & \\text{if } x \\leq y, \\\\\n H(x) & \\text{if } x \\geq y,\n \\end{cases}\n \\label{eqn:Hy0}\\end{aligned}$$ which implies that for $x \\leq y$ $$\\begin{aligned}\n\\begin{split}\n H (x) &= \\c x + \\E[h(x - D)] + \\E[u (x - D)] \\\\\n &= K + \\E[h(x - D)] + H (S) + \\c\\E[D] - w .", "\n\\end{split}\n \\label{eqn:Hy1}\\end{aligned}$$ Since $H(y) = K + H(S)$ for $y\\in\\mathcal{G},$ in view of , $$\\begin{aligned}\n \\E[h (y - D)] = w - \\c\\E[D], \\qquad y\\in\\mathcal{G} .", "\n \\label{eqn:Hy2}\\end{aligned}$$\n\nThe following proof is by contradiction. ", "Assume that there exists $y_1\\in \\mathcal{G}$ such that $y_1 > s.$ Then implies that $\\E[h (y_1-D)] = \\E[h (s - D)]. ", "$ Therefore, Assumption \\[assum:decrease\\] implies that $\\rone < y_1,$ where $\\rone$ is defined in . ", "Since $S=\\min\\big\\{ \\argmin_x\\{ H(x) \\} \\big\\},$ implies that for $x < S$ $$\\begin{aligned}\n w + u(x) + \\c x > H(S).", "\n \\label{eqn:ry1}\\end{aligned}$$ Therefore, $$\\begin{aligned}\n\\begin{split}\n H (y_1) &= K + H(S) = K + \\c S + \\E[h(S-D)] + \\E[u(x-D)] \\\\\n &> K + \\E[h(\\rone - D)] + H(S) + \\c\\E[D] -w,\n\\end{split}\n \\label{eqn:rycontra}\\end{aligned}$$ where the first equality holds because $y_1\\in\\mathcal{G},$ the second follows from , and the inequality holds because $ \\E[h(S-D)]\\geq \\E[h(\\rone-D)],$ and $\\PR (D>0) > 0.$ Since $y\\in\\mathcal{G}$ and $\\rone < y_1,$ $H(\\rone) \\geq H(y_1).$ In view of , $$\\begin{aligned}\n H(y_1) \\leq H(\\rone)= K + \\E[h (\\rone - D) ] + H(S) + \\c\\E[D] - w ,\\end{aligned}$$ which contradicts . ", "Then, $\\mathcal{G} = \\{ s \\}.$ In addition, Corollary \\[cor:inventory:acoe\\] implies that $s^*\\in \\mathcal{G},$ where $s^*$ is defined in . ", "Therefore, $s=s^*$ and $\\mathcal{G} = \\{ s^* \\}.$\n\nThe following corollary states that all the results of this paper hold for inventory models with convex holding/backlog costs.", "\n\n\\[cor:inventory convex\\] The conclusions of lemmas, theorems, and corollaries in Sections \\[sec:cvg sa\\] and \\[sec:cvg ua\\] hold under Assumption \\[assum:convex\\].", "\n\nVeinott’s Reduction of Problems with Backorders and Positive Lead Times to Problems without Lead Times {#sec:veinott}\n======================================================================================================\n\nIn this section, we explain, by using the technique introduced by Veinott [@Vei66] for finite-horizon problems with continuous demand and without formal proofs, that the infinite-horizon inventory model with positive lead times and backorders can be reduced to the model without lead times. ", "Therefore, the results of this paper, Feinberg and Lewis [@FL16], and Feinberg and Liang [@FLi16a; @FLi16b] also hold for the inventory model with positive lead times. ", "For inventory model with a positive lead times, we also provide a formal formulation of the MDP with transformed state space for future reference.", "\n\nConsider the inventory model defined in Section \\[sec:inventory control\\]. ", "Instead of assuming zero lead times, assume that the fixed lead time is $L\\in \\N := \\{1,2,\\ldots\\},$ that is, an order placed at the beginning of time $t$ will be delivered at the beginning of time $t+L.$ In addition, let $h^L(x)$ be the holding/backlog cost per period if the inventory level is $x.$ We define $$\\begin{aligned}\n h^* (x) : = \\E[h^L (x-\\sum_{i=1}^L D_i)] .", "\n \\label{eqn:h*}\\end{aligned}$$\n\nFor the inventory model, the dynamics of the system are defined by the equation $$\\begin{aligned}\n x_{t+1} = x_t + a_{t-L} - D_{t+1}, \\qquad t=0,1,2,\\ldots ,\n \\label{eqn:dynamic1}\\end{aligned}$$ where $x_t$ and $a_t$ are the current inventory level before replenishment and the ordered amount at period $t.$ In addition, at period $t,$ the one-step cost is $$\\begin{aligned}\n \\tilde{c} (\\bh^L_t,a_t) := K \\indF_{\\{ a_{t-L} > 0 \\}} + \\c a_{t-L} + \\E[h^L (x_t + a_{t-L} - D_{t+1})] ,\n \\qquad t = 0,1,\\ldots,\n \\label{cost1}\\end{aligned}$$ where $ \\bh^L_t = (a_{-L},a_{-L+1},\\ldots,a_{-1},x_0,a_0,\\ldots,a_{t-1},x_t)$ is the history at period $t.$\n\nEquation  means that a decision-maker observes at the end of the period $t$ the history $h_t,$ places an order of amount $a_t,$ which will be delivered in $L$ periods (that is, at the end of the period $t+L$), and the demand occurred during the period $t+1$ is $D_{t+1}.$\n\nAs usual, consider the set of possible trajectories $\\bh^L_{ +\\infty} = (\\bh^L_t,a_t,x_{t+1},a_{t+1},\\ldots) .$ An arbitrary policy is a regular probability distribution $\\pi (d a_{t}|\\bh^L_t),$ $t=0,1,\\ldots,$ on $\\Rp.$ It defines the transition probability for $\\bh^L_t$ to $(\\bh^L_t,a_{t}).$ The transition probability for $(\\bh^L_t,a_{t})$ can be defined by . ", "Therefore, given the initial state $\\bh^L_0 = (a_{-L},a_{-L+1},\\ldots,a_{-1},x_0),$ a policy $\\pi$ defines, in view of the Ionescu Tulcea theorem, the probability distribution $\\PR_{\\bh^L_0}^{\\pi}$ on the set of trajectories. ", "We denote by $\\E_{\\bh^L_0}^{\\pi}$ the expectation with respect to $\\PR_{\\bh^L_0}^{\\pi}.$\n\nFor a finite-horizon $N=1,2,\\dots$ the expected total discounted cost is $$\\begin{aligned}\n\\label{eqn:costs2y}\n \\tilde{v}_{N,\\a}^{\\pi} (\\bh^L_0) := \\E_{\\bh^L_0}^{\\pi} \\Big[ \\sum_{t=0}^{N-1}\n \\alpha^{t} \\tilde{c}(x_t,a_t) \\Big]\n = \\E_{\\bh^L_0}^{\\pi} \\Big[ \\sum_{t=0}^{L-1} \\a^t \\tilde{c}(x_t,a_t) + \\a^L \\sum_{t=0}^{N-1} \\a^t \\tilde{c}(x_{t+L},a_{t+L}) \\Big] ,\\end{aligned}$$ where $\\alpha\\in [0,1]$ is the discount factor and $\\tilde{v}_{0,\\a}^{\\pi} (\\bh^L_0)= 0.$ When $N= +\\infty$ and $\\a\\in [0,1),$ defines the infinite-horizon expected total discounted cost denoted by $\\tilde{v}_{\\a}^{\\pi}(\\bh^L_0).$ The *average cost per unit time* is defined as $\\tilde{w}^{\\pi} (h_0):=\\limsup_{N\\to +\\infty} \\frac{1}{N}\\tilde{v}_{N,1}^{\\pi} (\\bh^L_0).$\n\nLet us define $$\\begin{aligned}\n y_t := x_t + \\sum_{i=1}^{L}a_{t-i} = x_{t+L} + \\sum_{i=1}^L D_{t+i}, \\qquad t=0,1,\\ldots,\n \\label{xy}\\end{aligned}$$ where $y_t$ is the sum of the current inventory level and the outstanding orders at the end of period $t.$ Since the distribution of $x_{t+L}$ is determined by $y_t,$ in view of , we show that it is possible to make the decision $a_t$ only based on the quantity $y_t.$\n\nLet us construct an MDP with state space $\\Y = \\R$ (or $\\Y=\\Z$) with states $y_t$ defined in . ", "The actions are the amount of orders that can be placed at each period $t;$ $A(y) = \\A = \\Rp$ (or $A(y) = \\A=\\N_0$) for all $y\\in\\Y.$ In view of and , the dynamics of the system are defined by the equation $$\\begin{aligned}\n y_{t+1} = y_t + a_{t} - D_{t+1}, \\quad t=0,1,2,\\dots\\ .", "\n \\label{eqn:dynamic2y}\\end{aligned}$$ The transition probabilities for the MDP corresponding to is $$\\begin{aligned}\n q^*(B | y_t, a_t) = \\PR (y_t + a_t - D_{t+1} \\in B) ,\n \\label{eqn:tranp2y}\\end{aligned}$$ for each measurable subset $B$ of $\\Y .$ Let the one-step cost be $$\\begin{aligned}\n c^*(y,a) := K\\indF_{\\{ a > 0 \\}} + & \\c a + \\E[h^*(y + a - D)] .", "\n \\label{eqn:cy}\\end{aligned}$$\n\nAs was noticed by Veinott [@Vei66], the sum of current and ordered inventories forms an MDP whose dynamics and costs are defined by expressions –. ", "So, we have the same MDP as for in the problem without lead time with the only difference that the holding/backlog cost function $h$ is substituted with the function $h^*$. In addition, though the amount of inventory $x_{t+L}$ at time $(t+L)$ is not known at time $t,$ the distribution of $x_{t+L}$ is known because $x_{t+L} \\sim y_t - \\sum_{l=1}^L D^{(l)},$ where $D^{(1)},\\ldots,D^{(L)}$ are i.i.d. ", "random variables with $D^{(l)} \\sim D,$ $l=1,2,\\ldots,L.$ Since the actual amount of inventory level $x_{t+L}$ is unknown at time $t$, when the amount $a_t$ is ordered, this problem can be modeled as a Partially Observable Markov Decision Process (POMDP). ", "According to current available theory (see Hernández-Lerma [@Her89 Chapter 4], Feinberg et al.", " [@FKZ16], and references therein), such models can be reduced to the MDPs whose states are probability distributions of $x_{t+L}$ known at time $t,$ which is the distribution of $y_t - \\sum_{l=1}^L D^{(l)} .$ Therefore, optimal policies for the MDP introduced by Veinott [@Vei66] with state space $\\Y,$ action space $\\A,$ and transition probabilities , and costs define the optimal actions at time $t=0,1,2,\\ldots\\ .$\n\n\\[thm:veinott1\\] Consider the problem with the lead time $L=1,2,\\ldots\\ .$ Then the MDP $\\{ \\Y,\\A,q^*,c^* \\}$ coincides the MDP $\\{ \\X,\\A,q,c \\}$ with the function $h$ substituted with $h^*$ in the latter one. ", "Therefore, the conclusions of theorems in this paper hold for the problems with the lead time $L=1,2,\\ldots,$ if the holding/backlog cost function $h^*$ satisfies the conditions assumed for the function $h$ in the corresponding statements.", "\n\nSince $y_t\\in\\X$ and the actions are the same for these two models, we need to verify only the correspondence for transition probabilities and costs. ", "If $h = h^*,$ then formulae and coincide with $x_t = y_t.$ The transition probabilities $q^*$ defined in also coincides with . ", "Observe that it is easy to show that $$\\begin{aligned}\n \\tilde{v}_{N,\\a}^{\\pi} (\\bh^L_0) = f(\\bh^L_0) + \\a^L v_{N,\\a}^{\\pi} (y_0),\n \\label{eqn:costs2}\\end{aligned}$$ where $f(\\bh^L_0) := \\sum_{t=0}^{L-1} \\a^t \\E[\\tilde{c} (x_0 + \\sum_{i=0}^{t-1} a_{-L+i} - \\sum_{i=0}^{t-1} D_{t+i}, a_t ) ] .$\n\nFor the problems with convex holding/backlog cost function $h^L,$ the function $h^*$ is also convex and $\\E[h^* (x-D)] \\to +\\infty$ as $|x|\\to +\\infty.$ We also need the addition assumption that $\\E[h^* (x-D)] < +\\infty$ for all $x\\in\\X.$ Then the results in this paper formulated under Assumption \\[assum:convex\\] and the results in Feinberg and Lewis [@FL16] and Feinberg and Liang [@FLi16a; @FLi16b] hold for the problems with the lead time $L=1,2,\\ldots\\ .$\n\n\\[rm:finiteh\\] [Note that the assumption on the finiteness of the function $\\E[h^* (x-D)]$ is necessary for the problems with convex holding/backlog costs. ", "Consider the lead time $L=1,$ the holding/backlog cost function $$\\begin{aligned}\n h^L (x) :=\n \\begin{cases}\n x + \\frac{e^{2}}{5}, & \\text{if } x > 0, \\\\\n \\frac{e^{-x+2}}{(x-2)^2 + 1}, & \\text{if } x \\leq 0 ,\n \\end{cases}\n %\\label{eqn:ex:hL}\\end{aligned}$$ and the random variable $D$ follows the exponential distribution with density function $f_D (x) = e^{-x},$ if $x > 0,$ and $f_D (x) = 0,$ otherwise. ", "Then the random variable $\\textbf{S}_2$ follows the Erlang distribution with density function $f_{\\textbf{S}_2} (x) = xe^{-x},$ if $x > 0,$ and $f_{\\textbf{S}_2} (x)= 0,$ otherwise. ", "Observe that the function $h^L$ is continuous and nonnegative. ", "Some calculations show that the function $h^L$ is convex on $\\R$ and $\\E[h^L (x-D)] < +\\infty$ for all $x\\in\\R.$ However, $\\E[h^* (0-D)] = \\E[h^L (0-\\textbf{S}_2)] = +\\infty.$ ]{}\n\n\\[rm:lostsales\\] [ The reduction discussed in this section does not hold for the inventory model with lost-sales. ", "For such model with lead time $L > 0,$ the dynamics of the system are defined by the equation $$\\begin{aligned}\n x_{t+1} = (x_t + a_{t-L} - D_{t+1})^+ :=\\max\\{x_t + a_{t-L} - D_{t+1} ,0\\},\\qquad t = 0,1,2,\\ldots\\ .", "\n %\\label{eqn:ls2}\n \\end{aligned}$$ Consider the transformation similar to the one defined in . ", "Then $x_{t+L} = y_t - \\sum_{i=1}^L \\tilde{D}_{t+i},$ where $\\tilde{D}_{j} :=\\min\\{ D_j,x_{j-1}+a_{j-L-1} \\},$ $j=t+1,t+2,\\ldots,t+L.$ Since the distribution of $x_{t+L}$ does not depend solely on the information available at time $t,$ the reduction does not hold. ", "Indeed, the structure of the optimal policies may depend on the lead times. ", "In particular, if the lead times are large, then the constant-order policy performs nearly optimally; see Goldberg et al.", " [@GKLSS]. ]{}", "\n\n[**Acknowledgement.**]{} ", "This research was partially supported by NSF grants CMMI-1335296 and CMMI-1636193.", "\n\nBishop C. J., Feinberg E. A., & Zhang J. 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[*", "Foundations of inventory management.*]{} ", "McGraw-Hill, New York.", "\n\nProofs to Section \\[sec:inventory control\\] {#sec:inventory control:apx}\n===========================================\n\nSince $\\E[h(x-D)]\\to +\\infty$ as $x\\to -\\infty,$ $$\\begin{aligned}\n\\limsup_{x\\to -\\infty }h(x) = +\\infty.", "\n\\label{eqn:hinfty}\\end{aligned}$$ To see this note if $\\limsup_{x\\to -\\infty} h(x) < +\\infty,$ then there exist real numbers $M_1,$ $M_2 > 0$ such that $ h (x) \\leq M_1$ for $x \\leq -M_2.$ Since $D$ is a nonnegative random variable, $\\E[h(x-D)] \\leq M_1$ for $x\\leq -M_2$ and $\\limsup_{x\\to -\\infty} \\E[h(x-D)] \\leq M_1 < +\\infty.$ This contradicts the assumption that $\\E[h(x-D)]\\to +\\infty$ as $x \\to -\\infty.$\n\nSince the function $h$ is convex, the function $\\E[h(x-D)]$ is convex. ", "Therefore, in view of , the function $\\E[\\h (x-D)]$ is convex for all $\\a\\in[0,1].$ Since every convex function is quasiconvex, the function $\\E[\\h (x-D)]$ is quasiconvex for all $\\a\\in[0,1].$\n\nSince the function $h$ is convex on $\\X,$ it is continuous. ", "Therefore, implies $$\\begin{aligned}\n \\lim_{x\\to -\\infty} h(x) = +\\infty .", "\n \\label{eqn:hinfty1}\\end{aligned}$$ As explained in Feinberg and Liang [@FLi16a Equations (2.3), (4.1)], and the convexity of the function $h$ imply that $1+\\lim_{x\\to -\\infty} \\frac{h(x)}{\\c x} < 1.$\n\nConsider $\\a^* \\in [\\max\\{ 1 + \\lim_{x\\to -\\infty} \\frac{h(x)}{\\c x},0 \\},1).$ For $\\a\\in(\\a^*,1],$ since the function $\\h (x) = \\c x(\\frac{h(x)}{\\c x}+1-\\a)$ tends to $+\\infty$ as $x\\to-\\infty,$ $$\\begin{aligned}\n \\lim_{x\\to -\\infty}\\E[h_{\\a}(x-D)] = +\\infty, \\qquad \\a\\in (\\a^*,1].", "\n \\label{eqn:limitha:1}\\end{aligned}$$ Therefore, the convexity of the function $\\E[h_{\\a} (x-D)]$ implies that $\\lim_{x\\to -\\infty}\\E[\\h (x-D)] > K + \\inf_{x\\in\\X} \\E[\\h (x-D)] $ for all $\\a\\in(\\a^*,1].$ Hence, Assumption \\[assum:qcall\\] holds with $\\a^* \\in [\\max\\{1 + \\lim_{x\\to -\\infty} \\frac{h(x)}{\\c x},0\\},1).$ In view of , the convexity of the function $\\E[h_{\\a} (x-D)]$ implies that Assumption \\[assum:decrease\\] holds for all $\\a\\in(\\a^*,1].$\n\nIt is straightforward that Assumption \\[assum:qcall\\] implies Assumption \\[assum:qcalpha\\] for $\\a\\in (\\a^*,1).$ In addition, since $\\E[\\h (x-D)] \\to \\E[h (x-D)]$ as $\\a\\uparrow1$ for all $x\\in\\X,$ the quasiconvexity of the function $\\E[\\h (x-D)]$ implies that the function $\\E[h(x-D)]$ is quasiconvex. ", "Since $\\inf_{x\\in\\X} \\E[h (x-D)] < +\\infty $ and $\\E[h (x-D)] = \\E[\\h (x-D)] - (1-\\a)\\c x\\to +\\infty$ as $x\\to-\\infty$ for each $\\a\\in (\\a^*,1),$ Assumption \\[assum:qcalpha\\] holds for $\\a = 1.$\n\nProofs to Section \\[sec:mdptotal\\] {#sec:mdptotal:apx}\n==================================\n\nIn view of , for $x\\leq y$ and $t=1,2,\\ldots$ $$\\begin{aligned}\n \\bv_{t,\\a} (x) &=\\min\\{ \\min_{a\\geq 0}\\{ K + \\bG_{t-1,\\a}(x+a) \\},\\bG_{t-1,\\a} (x) \\}\\leq \\min_{a\\geq 0} \\{ K+ \\bG_{t-1,\\a} (x + a) \\} \\\\\n & \\leq K + \\min_{a\\geq y-x} \\bG_{t-1,\\a} (x + a) = K + \\min_{a\\geq 0} \\bG_{t-1,\\a} (y + a) \\\\\n & \\leq K + \\min\\{ \\min_{a\\geq 0}\\{ K + \\bG_{t-1,\\a}(y+a) \\},\\bG_{t-1,\\a} (y) \\} = K + \\bv_{t,\\a} (y) ,\\end{aligned}$$ where the second inequality follows from $y-x \\geq 0.$ Furthermore, and the same arguments imply .", "\n\nIn view of , for $x\\leq y$ and $t=1,2,\\ldots $ $$\\begin{aligned}\n \\bG_{t,\\a} (y) - \\bG_{t,\\a} (x) =& \\E[\\h(y-D)] - \\E[\\h(x-D)] +\\a\\E[\\bv_{t,\\a} (y-D) - \\bv_{t,\\a} (x-D) ] \\\\\n \\leq & \\E[\\h(y-D)] - \\E[\\h(x-D)] + \\a K,\\end{aligned}$$ where the inequality follows from . ", "Furthermore, and the same arguments imply .", "\n\nThe proof is by induction on $t.$ For $t = 0,$ holds because $\\bv_{0,\\a} (x) = 0,$ $x\\in\\X,$ and follows from $\\bG_{0,\\a} (x) = \\E[\\h (x-D)],$ $x\\in\\X,$ and Assumption \\[assum:qcalpha\\]. ", "To complete the induction arguments, assume that holds for $t = k \\in \\{0,1,2,\\ldots\\}.$ Then for $x\\leq y\\leq\\ra$ $$\\begin{aligned}\n & \\bv_{k+1,\\a} (x) = \\min\\big\\{ \\bG_{k,\\a} (x), \\min_{a\\geq 0}\\{ K+\\bG_{k,\\a} (x+a)\\} \\big\\} \\\\\n = & \\min\\big\\{ \\bG_{k,\\a} (x), \\min_{a\\geq 0}\\{ K+\\bG_{k,\\a} (x+a)\\} \\big\\} \\\\\n \\geq & \\min\\big\\{ \\bG_{k,\\a} (y), \\min_{0\\leq a< y-x}\\{ K+\\bG_{k,\\a} (x+a)\\}, \\min_{a\\geq y-x}\\{ K+\\bG_{k,\\a} (x+a) \\} \\big\\} \\\\\n \\geq & \\min\\big\\{ \\bG_{k,\\a} (y), K+\\bG_{k,\\a}(y) , \\min_{a\\geq 0}\\{ K+\\bG_{k,\\a} (y+a)\\} \\big\\} \\\\ \n \\geq & \\min\\big\\{ \\bG_{k,\\a} (y) ,\\min_{a\\geq0}\\{ K+\\bG_{k,\\a}(y+a)\\} \\big\\} = \\bv_{k+1,\\a} (y) ,\\end{aligned}$$ where the first and last equalities follow from , the first two inequalities follow from , and the last inequality follows from $K>0.$ Thus, holds for $t=k+1.$ In addition, for $x\\leq y \\leq \\ra$ $$\\begin{aligned}\n &\\bG_{k+1,\\a}(y) - \\bG_{k+1,\\a} (x) \\\\\n = & \\E[\\h (y-D)] - \\E[\\h (x-D)] +\\a\\E[\\bv_{k+1,\\a}(y-D) - \\bv_{k+1,\\a} (x-D) ] \\leq 0,\\end{aligned}$$ where the equality follows from and the inequality holds because the function $\\E[\\h (x-D)]$ is nonincreasing on $(-\\infty,\\ra]$ and .", "\n\nNote that the equality in the Lemma \\[lm:vaorder\\] follows from . ", "For the model with zero unit and terminal costs, since $\\bv_{t,\\a} \\to \\bva$ as $t\\to+\\infty,$ implies . ", "In addition, for $x\\leq y \\leq \\ra$ $$\\begin{aligned}\n \\bGa (y) -\\bGa (x) = \\E[\\h (y-D)] - \\E[\\h (x-D)] +\\a\\E[\\bva (y-D)- \\bva (x-D) ] \\leq 0,\\end{aligned}$$ where the equality follows from and the inequality holds because the function $\\E[\\h (x-D)]$ is nonincreasing on $(-\\infty,\\ra]$ and .", "\n\nWe first prove that $$\\begin{aligned}\n \\bva (x) - \\c x = \\tva (x) \\geq \\va (x) \\geq 0, \\qquad x\\in\\X.\n \\label{eqn:tva>=0}\n \\end{aligned}$$ Note that $\\va (x) \\geq 0$ for all $x\\in\\X,$ because all costs in the original inventory model are nonnegative. ", "Theorem \\[thm:qcall:t\\], , and imply that for $N = 1,2,\\ldots$ $$\\begin{aligned}\n \\tv_{N,\\a} (x) = \\tv_{N,\\a}^{\\phi^N} (x), \\qquad x\\in\\X,\n \\label{eqn:tvtaval}\\end{aligned}$$ where the policy $\\phi^N$ is the $(s_{t,\\a},S_{t,\\a})_{t = 0,1,2,\\ldots,N-1}$ policy defined in Theorem \\[thm:qcall:t\\]. ", "Therefore, $$\\begin{aligned}\n\\begin{split}\n \\tv_{N,\\a} (x) &= \\tv_{N,\\a}^{\\phi^N} (x) = \\E_x^{\\phi^N} \\big[\\sum_{t=0}^{N-1} c(x_t,a_t) - \\a^N \\c x_N \\big] \\\\\n &= v_{N,\\a}^{\\phi^N} (x) - \\a^N \\c \\E_x^{\\phi^N}[x_N] \\geq v_{N,\\a} (x)- \\a^N \\c \\max\\{x,\\barS_\\a\\}, \\qquad x\\in\\X,\n\\end{split}\n \\label{eqn:tvasS}\\end{aligned}$$ where the last inequality holds because $v_{N,\\a}^{\\phi^N} (x) \\geq v_{N,\\a} (x),$ $x\\in\\X,$ and for all $N = 1,2,\\ldots$ Theorem \\[thm:qcall:t\\] implies that $\\E_x^{\\phi^N} [x_N] \\leq \\max\\{ x, \\barS_\\a \\} .$ Hence, $$\\begin{aligned}\n \\bva (x) - \\c x=\\tva (x) =\\lim_{N\\to+\\infty} \\tv_{N,\\a} (x) \\geq \\lim_{N\\to+\\infty} v_{N,\\a} (x) = \\va (x) \\geq 0 ,\\end{aligned}$$ where the first two equalities follow from , the first inequality follows from and $\\lim_{N\\to+\\infty} \\a^N \\c \\max\\{x,\\barS_\\a\\} = 0$ for each $x\\in\\X.$ Therefore, holds.", "\n\nTo prove Lemma \\[lm:samevalues\\], it remains to prove that $\\va (x) \\geq \\tva (x),$ $x\\in\\X. $ Observe that for $t=0,1,2,\\ldots$ and $\\pi\\in\\PS$ $$\\begin{aligned}\n x_t \\geq x_0 - \\textbf{S}_t \\quad \\text{ and } \\quad \\E_{x_0}^{\\pi}[x_t] \\geq x_0 - t\\E[D] ,\n %\\label{eqn:lbdxt}\\end{aligned}$$ where $\\textbf{S}_t$ is defined in . ", "Then for $N = 1,2,\\ldots$ $$\\begin{aligned}\n\\begin{split}\n \\tv_{N,\\a} (x) &\\leq \\tv^{\\pi}_{N,\\a} (x) = \\E_x^{\\pi} \\big[\\sum_{t=0}^{N-1} c(x_t,a_t) - \\a^N \\c x_N \\big] = v_{N,\\a}^{\\pi} (x) - \\a^N \\c \\E_x^{\\pi}[x_N] \\\\\n & \\leq v^{\\pi}_{N,\\a} (x)- \\a^N \\c (x - N\\E[D]), \\qquad x\\in\\X .", "\n\\end{split}\n \\label{eqn:tvasS:1}\\end{aligned}$$ Observe that $\\lim_{N\\to+\\infty} \\a^N \\c (x - N\\E[D]) = 0$ for each $x\\in\\X.$ Thus, by taking the limits as $N\\to+\\infty$ of both sides of , $\\tv_{\\a} (x) \\leq v^{\\pi}_{\\a} (x)$ for all $\\pi\\in\\PS,$ which implies that $\\tva (x) \\leq \\va (x),$ $x\\in\\X.$ Hence, $\\tva (x) = \\va (x) = \\bva (x) - \\c x,$ $x\\in\\X.$\n\nProofs to Section \\[sec:acoe\\] {#sec:acoe:apx}\n==============================\n\n\\(i) In view of and Lemma \\[lm:samevalues\\], holds because $\\ua (x) - \\ua (y) = \\va (x) - \\va (y) = \\bva (x) -\\c x - (\\bva (y) - \\c y)$ and the function $u_{\\a_n} (x)$ converges pointwise to $\\tu (x)$ as $n\\to +\\infty.$ For $x\\leq y,$ $$\\begin{aligned}\n H (y) - H (x) =& \\E[h(y-D)] +\\a\\E[\\tu (y-D) + \\c (y-D)] \\\\\n & - \\E[h(x-D)]-\\a\\E[\\tu (x-D) + \\c (x-D)] \\\\\n \\leq & \\E[\\h(y-D)] - \\E[\\h(x-D)] + \\a K,\\end{aligned}$$ where the equality follows from and the inequality follows from .", "\n\n\\(ii) We first show that for $1\\geq \\a \\geq \\b > \\a^*$ $$\\begin{aligned}\n \\ra \\geq \\rb .", "\n \\label{eqn:ra<rb}\\end{aligned}$$ To verify this inequality, consider $1\\geq \\a\\geq \\b>\\a^*.$ Then, for $x < \\rb$ $$\\begin{aligned}\n\\begin{split}\n \\E & [\\h (x-D)] - \\E[\\h(\\rb - D)] \\\\\n= \\E & [h(x-D)] + \\E[h(\\rb - D)] + (1-\\a)\\c(x-\\rb) \\\\\n> \\E & [h(x-D)] + \\E[h(\\rb - D)] + (1-\\b)\\c(x-\\rb) \\\\\n= \\E & [h_\\b (x-D)] - \\E[h_\\b(\\rb - D)] > 0,\n\\end{split}\n\\label{eqn:raincrease}\\end{aligned}$$ where the equalities follow from and the inequality holds because $1-\\a < 1-\\b$ and $\\c(x-\\rb) < 0.$ If $\\ra < \\rb,$ then with $x = \\ra$ implies that $$\\begin{aligned}\n \\E[\\h (\\ra -D)] - \\E[\\h (\\rb -D)] > 0 .", "\n \\label{eqn:raincrease:contra}\\end{aligned}$$ However, the definition of $\\ra$ in implies that $\\E[\\h (\\ra -D)] - \\E[\\h (\\rb -D)] \\leq 0 ,$ which contradicts . ", "Therefore, holds.", "\n\nNow, we prove that $\\ra\\uparrow\\rone$ as $\\a\\uparrow 1.$ Consider a fixed discount factor $\\b\\in (\\a^*,1).$ In view of , since $\\rb\\leq \\ra \\leq \\rone$ for all $\\a\\in (\\b,1)$ and $|\\rb|,$ $|\\rone|<+\\infty,$ the monotone convergence theorem implies that there exists $\\ronea\\in[\\rb,\\rone]$ such that $\\ra\\uparrow\\ronea$ as $\\a\\uparrow1. ", "$ In addition, for $\\a\\in (\\b,1)$ $$\\begin{aligned}\n\\begin{split}\n 0 & \\leq \\E [h_1 (\\ra-D)] - \\E[h_1 (\\rone - D)] \\\\\n &= \\E [\\h (\\ra-D)] - (1-\\a)\\c (\\ra - \\E[D])- \\E[h_1 (\\rone - D)] \\\\\n &\\leq \\E [\\h (\\rone-D)] - (1-\\a)\\c (\\ra - \\E[D]) - \\E[h_1(\\rone - D)] \\\\\n&= (1-\\a)\\c (\\rone - \\ra) \\leq (1-\\a)\\c (\\rone - \\rb),\n\\end{split}\n\\label{eqn:raincrease:limit}\\end{aligned}$$ where the first two inequalities follows from the definition of $\\rone$ and $\\ra$ in , the first equality holds because $\\E [h_1 (\\ra-D)] = \\E [\\h (\\ra-D)] - (1-\\a)\\c (\\ra - \\E[D]),$ the second equality holds because $\\E [\\h (\\rone-D)] -\\E [h_1 (\\rone-D)] = (1-\\a)\\c (\\rone - \\E[D]),$ and the last inequality follows from $\\rb\\leq \\ra$ and $(1-\\a)\\c>0$ for $\\a\\in (\\b,1).$ Observe that $(1-\\a)\\c (\\rone - \\rb)\\to 0$ as $\\a\\uparrow1.$ Then implies that $\\lim_{\\a\\uparrow1} \\E [h_1 (\\ra-D)] - \\E[h_1 (\\rone - D)] = 0.$ Therefore, the continuity of the function $\\E[h_1 (x-D)]$ implies that $$\\begin{aligned}\n \\E [h_1 (\\ronea-D)] = \\E[h_1 (\\rone - D)].", "\n \\label{eqn:raincrease:limit:contra}\\end{aligned}$$ Recall that $\\ronea\\in[\\rb,\\rone].$ If $\\ronea < \\rone,$ then Assumption \\[assum:qcall\\] and imply that $\\E [h_1 (\\ronea-D)] > \\E[h_1 (\\rone - D)],$ which contradicts . ", "Therefore, $\\ronea = \\rone$ and $\\ra\\uparrow\\rone$ as $\\a\\uparrow 1.$\n\nIn view of and Lemma \\[lm:samevalues\\], holds because $\\ua (x) - \\ua (y) = \\va (x) - \\va (y)= \\bva (x) -\\c x - (\\bva (y) - \\c y),$ the function $u_{\\a_n} (x)$ converges pointwise to $\\tu (x)$ as $n\\to +\\infty,$ and $\\ra\\uparrow\\rone$ as $\\a\\uparrow 1.$ For $x\\leq y \\leq \\rone,$ $$\\begin{aligned}\n H(y) - H (x) = & \\E[h (y-D)] - \\E[h (x-D)] \\\\\n & + \\a\\E[\\tu(y-D) + \\c (y-D) - \\tu (x-D) - \\c (x-D) ] \\leq 0,\\end{aligned}$$ where the equality follows from and the inequality follows from that the function $\\E[h (x-D)]$ is nonincreasing on $(-\\infty,\\rone]$ and .", "\n\nThe proof of the optimality of $(s,S)$ policies is based on the fact that $K+H(S)<H(x),$ if $x<s,$ and $K+H(S)\\ge H(x),$ if $x\\ge s.$ Since the function $H$ is continuous, we have that $K+H(S)=H(s).$ Thus both actions are optimal at the state $s.$\n\nProofs to Section \\[sec:cvg sa\\] {#sec:cvg sa:apx}\n================================\n\nAccording to , $\\bva (x) = K + \\Ga (\\Sa) = K + \\bma$ for $x \\leq y.$ In view of , , and Lemma \\[lm:samevalues\\], $$\\begin{aligned}\n K + \\bma = \\Ga (y) = \\E[\\h (y - D)] + \\a \\E[\\bva (y - D)] = \\E[\\h (y - D)] + \\a (K+\\bma),\\end{aligned}$$ which implies .", "\n\nObserve that the second inequality in Lemma \\[lm:r alpha &lt;= r\\*\\] follows from . ", "The following proof is by contradiction. ", "Assume that there exist $\\a\\in (\\a^*,1)$ and $y \\in\\mathcal{G}_{\\a}$ such that $y > \\ra.$ According to , $\\bva (x) = K + \\bma$ for $x \\leq y.$ Therefore, and Lemma \\[lm:samevalues\\] imply that for $x\\leq y$ $$\\begin{aligned}\n \\Ga (x) = \\E[\\h (x - D)] + \\a (K + \\bma) .", "\n \\label{eqn:Ga(ra)}\\end{aligned}$$ The definition of $\\ra$ and imply that $\\Ga(\\ra)\\leq \\Ga(y).$ According to the definition of $\\sa$ in , $\\Ga(x) \\geq \\Ga(y)$ for $x\\leq y.$ Therefore, $\\Ga(\\ra) = \\Ga(y),$ which implies that $$\\begin{aligned}\n\\begin{split}\n & \\E[\\h (\\ra - D)] + \\a (K + \\bma) = \\Ga(\\ra) = \\Ga (y) = K + \\Ga(\\Sa) \\\\\n = & K + \\E[\\h (\\Sa - D)] + \\a \\E[\\bva (\\Sa - D)] > \\E[\\h(\\ra - D)] + \\a (K + \\bma),\n\\end{split}\n \\label{eqn:contra y>ra}\\end{aligned}$$ where the first equality follows from , the last equality follows from and Lemma \\[lm:samevalues\\], and the inequality follows from $K > \\a K$ and the definition of $\\ra$ and $\\bma.$ The contradiction in implies that $y \\leq \\ra$ for all $y \\in \\mathcal{G}_\\a.$\n\nAccording to equation , for any given $\\b\\in (\\a^*,1),$ there exists a constant $b>0$ such that $s_{\\a}\\in (-b,b)$ for all $\\a\\in [\\b,1).$ In view of , since $b$ and $x_U^*$ are real numbers, where $x^*_U$ is defined in , $$\\begin{aligned}\n\\lim_{\\a\\uparrow1}(1-\\a)(\\ma - \\c b) = \\lim_{\\a\\uparrow1} (1-\\a) (\\ma + \\c x_U^*) = w.\n\\label{eqn:limit bounds of bma}\\end{aligned}$$ Therefore, since $\\sa > -b$ for all $\\a\\in[\\b,1),$ and imply that $$\\begin{aligned}\n \\lim_{\\a\\uparrow1} (1-\\a) \\bma = w .", "\n \\label{eqn:limit (1-a) bma}\\end{aligned}$$ Therefore, and Lemma \\[lm:sa\\] implies that $\\lim_{\\a\\uparrow1}\\E[h_{\\a} (s_{\\a} - D)] = w .$\n\nProofs to Section \\[sec:cvg ua\\] {#sec:cvg ua:apx}\n================================\n\nWe first verify the validity of Assumption **W\\***. ", "It is obvious the nonnegative cost function $c$ is $\\K$-inf-compact and the transition probabilities are weakly continuous. ", "Thus, Assumption **W\\*** holds.", "\n\nTo verify the validity of Assumption **B**. ", "we calculate the relative value function $\\ua.$\n\nLet us calculate the value functions $\\va$ for $\\a\\in [0,1).$ Since there is only one action at $n = 0, 1,\\ldots,$ the infinite-horizon value function $$\\begin{aligned}\n \\va (n) = \\sum_{i = 0}^{\\infty} \\zone_{n + i} \\a^i, \\qquad n = 0,1,\\ldots\\ .", "\n \\label{eqn:ex1:van>=0}\\end{aligned}$$ Therefore, for $n = 0,$ implies $$\\begin{aligned}\n\\begin{split}\n \\va (0) &= \\sum_{i = 0}^{\\infty} \\zone_{i} \\a^i = z_0 + \\sum_{i = 1}^{\\infty} (z_i - z_{i-1})\\a^i\n + \\sum_{i = 0}^{\\infty} \\a^i \\\\\n &= \\sum_{i = 0}^{\\infty} z_i \\a^i - \\a \\sum_{i = 0}^{\\infty} z_i \\a^{i} + \\frac{1}{1-\\a} = f(\\a) + \\frac{1}{1-\\a} ,\n\\end{split}\n \\label{eqn:ex1:van=0}\\end{aligned}$$ where the second equality follows from , the third equality is straightforward, and the last equality follows from . ", "Furthermore, implies that for $n=1,2,\\ldots$ $$\\begin{aligned}\n\\begin{split}\n \\va (n) &= \\sum_{i=0}^{\\infty} (z_{n+i} - z_{n+i-1} + 1) \\a^i = (1-\\a) \\sum_{i=0}^{\\infty} z_{n+i} \\a^i - z_{n-1} + \\frac{1}{1-\\a} .", "\n\\end{split}\n \\label{eqn:ex1:van>0}\\end{aligned}$$ For the state $-1\\in\\X,$ let $\\varphi^{(k)},$ $k=0,1,\\ldots,$ be the policy that takes action $a^s$ at steps $0,1,\\ldots,k-1$ and $a^c$ at step $k$ and $\\varphi^{(\\infty)}$ be the policy that always takes action $a^s.$ Then for $k = 0,1,\\ldots$ $$\\begin{aligned}\n \\va^{\\varphi^{(\\infty)}} (-1) = \\frac{1}{1-\\a} < \\a^{k+1} [ f(\\a) + \\frac{1}{1-\\a} ] + \\frac{1-\\a^{k+1}}{1-\\a}\n = \\va^{\\varphi^{(k)}} (-1) ,\\end{aligned}$$ where the inequality follows from $f(\\a) > 0.$ Therefore, $$\\begin{aligned}\n \\va (-1) = \\frac{1}{1-\\a}.", "\n \\label{eqn:ex1:van=-1}\\end{aligned}$$ For state $-2 \\in \\X,$ and imply $$\\begin{aligned}\n \\va (-2) = \\a \\va (-1) = \\frac{\\a}{1-\\a} \\leq \\va (-1) \\leq \\va (0) .", "\n \\label{eqn:ex1:van=-2}\\end{aligned}$$ In view of and , for $n=1,2,\\ldots$ $$\\begin{aligned}\n \\va (n) \\geq -1 + \\frac{1}{1-\\a} = \\va (-2),\n \\label{eqn:ex1:van>van=-2}\\end{aligned}$$ where the inequality follows from $z_n \\in \\{ 0,1 \\},$ $n = 0, 1, \\ldots\\ .$ and imply $$\\begin{aligned}\n \\ma = \\va (-2) = \\frac{\\a}{1-\\a},\n \\label{eqn:ex1:ma}\\end{aligned}$$ where $\\ma := \\inf_{x\\in\\X} \\va (x)$ is defined in . ", "Thus, – and imply .", "\n\nNote that $w^* \\leq w^{\\varphi^{(\\infty)}} (-1) = 1 < \\infty.$ Then to complete the proof of the validity of Assumption **B**, we need to prove that $\\sup_{\\a\\in[0,1)} \\ua (n) < \\infty$ for $n\\in\\X.$ According to Feinberg et al.", " [@FKZ12 Lemma 5], since the cost function $c \\geq 0$ and $w^* < \\infty,$ it is equivalent to prove that for $n\\in \\X$ $$\\begin{aligned}\n \\limsup_{\\a\\uparrow1} \\ua (n) < \\infty.", "\n \\label{eqn:ex1:limitua<infty}\\end{aligned}$$ Since $0\\leq z_n \\leq 1,$ $n = 0,1,\\ldots,$ implies that $0 \\leq \\ua (n) \\leq 1 + (1-\\a) \\sum_{i=0}^{\\infty} \\a^i = 2$ for $n\\in\\X$ and $\\a\\in[0,1).$ Hence, holds. ", "This completes the proof.", "\n\nFor all $\\a\\in [0,1)$ $$\\begin{aligned}\n\\begin{split}\n & |\\bua (x) - \\bua (y)| = |\\bva (x) - \\bva (y)| = |\\va (x) - \\va (y) + \\c (x - y)| \\\\\n = & |\\ua (x) - \\ua (y) + \\c (x - y) | \\leq |\\ua (x) - \\ua (y)| + \\c |x - y| ,\n\\end{split}\n \\label{eqn:equicont-1}\\end{aligned}$$ where the first equality follows from , the second one follows from Lemma \\[lm:samevalues\\], and the third one follows from .", "\n\nConsider $\\eps > 0.$ For each $\\b\\in (\\a^*,1),$ since the family of functions $\\{ \\ua \\}_{\\a\\in [\\b,1)}$ is equicontinuous (see Theorem \\[thm:u a equicont\\]), there exists $\\delta > 0$ such that $|\\ua (x) - \\ua (y)| < \\frac{\\eps}{2}$ for all $|x-y|<\\delta$ and $\\a\\in [\\b,1).$ Therefore, for $|x-y| < \\delta_1 := \\min\\{ \\delta, \\frac{\\eps}{2\\c} \\},$ $\\c | x-y|<\\frac{\\eps}{2}$ and implies that for $|x-y|<\\delta_1$ and $\\a\\in [\\b,1)$ $$\\begin{aligned}\n |\\bua (x) - \\bua (y)| \\leq \\eps.\\end{aligned}$$ Thus, the family of functions $\\{\\bua\\}_{\\a\\in [\\b, 1)}$ is equicontinuous.", "\n\nConsider $x\\in\\X.$ For all $\\a\\in (\\a^*,1),$ $$\\begin{aligned}\n\\begin{split}\n & \\bua (x) - \\ua(x) \\leq |\\bua (x) - \\ua (x)| \\\\\n = & |\\bva (x) - \\va (x) - (\\bma - m_\\a) | = |\\c x -(\\bma - m_\\a) | \\\\\n \\leq & \\c |x| + |\\bma - m_\\a| \\leq \\c (|x| + |\\sa| + |x_U^*|) \\leq \\c (|x| + b + |x_U^*|),\n\\end{split}\n \\label{eqn:difbuaua}\\end{aligned}$$ where the last two inequalities follow from and Theorem \\[thm:limit s alpha\\] respectively.", "\n\nAccording to Theorem \\[thm:B\\], since Assumption ${\\bf B}$ holds, $\\sup_{\\a\\in (\\a^*,1)} \\ua (x) < +\\infty.$ Therefore, implies that $$\\begin{aligned}\n\\sup_{\\a\\in (\\a^*,1)} \\bua (x) \\leq \\c (|x| + b + |x_U^*|) + \\sup_{\\a\\in (\\a^*,1)} \\ua (x) < +\\infty,\n\\qquad x\\in\\X.\\end{aligned}$$\n\nConsider any given $\\b\\in (\\a^*,1).$ According to , there exists $b>0$ such that $\\sa\\in [-b,b]$ for all $\\a\\in [\\b,1).$\n\nConsider $s^*$ defined in . ", "We first prove that the limit $\\lim_{\\a\\uparrow1} \\bu_{\\a}(x)$ exists for $x<s^*.$ For $x < s^*,$ according to Theorem \\[thm:limit s alpha\\], there exists $\\hat{\\a} > \\b$ such that $\\sa > x$ for all $\\a \\in [\\hat{\\a},1),$ then implies that $\\bua (x) = K$ for all $\\a \\in [\\hat{\\a},1).$ Therefore, $$\\begin{aligned}\n \\lim_{\\a \\uparrow1} \\bua(x) = K, \\qquad x < s^*.", "\n \\label{eqn:bu x<s*}\\end{aligned}$$\n\nFor $x > s^*,$ according to Theorem \\[thm:limit s alpha\\], there exists $\\hat{\\a} >\\b$ such that $\\sa < x$ for all $\\a \\in [\\hat{\\a},1).$ Therefore, in view of , , , and , for all $\\a \\in [\\hat{\\a},1)$ $$\\begin{aligned}\n \\bua (x) = \\E[h_\\a (x-D)] + \\a \\E[\\bua (x-D)] - (1-\\a) \\bma .", "\n \\label{eqn:bua x>s*-1}\\end{aligned}$$ Then, and imply that $$\\begin{aligned}\n \\bua (x) = \\E[\\sum_{j = 1}^{\\textbf{N}(x - \\sa) + 1} \\a^{j-1} (\\tilde{h}_{\\a} (x - \\textbf{S}_{j-1}) - (1-\\a)\\bma) ]\n + \\E[\\a^{\\textbf{N}(x - \\sa) + 1} K ],\n \\label{eqn:bua x>s*-2}\\end{aligned}$$ where $\\tilde{h}_{\\a} (x) := \\E[h_{\\a} (x-D)],$ $x\\in\\X,$ and $\\textbf{N}(\\cdot)$ is defined in . ", "For $\\a\\in[\\b,1),$ $$\\begin{aligned}\n 1\\geq \\E[\\a^{\\textbf{N}(x - \\sa) + 1}] \\geq \\E[\\a^{\\textbf{N}(x + b) + 1}]\\geq \\a^{\\E[\\textbf{N}(x + b) + 1]},\n \\label{eqn:boundaK1}\\end{aligned}$$ where the first inequality follows from $\\a < 1,$ the second one follows from $\\sa \\geq -b$ and $\\a < 1,$ and the last one follows from Jensen’s inequality. ", "Since $\\PR(D>0)>0,$ $\\E[\\textbf{N}(x + b) + 1]< +\\infty,$ which implies that $$\\begin{aligned}\n \\lim_{\\a\\uparrow1}\\a^{\\E[\\textbf{N}(x + b) + 1]}\\to 1.", "\n \\label{eqn:boundaK2}\\end{aligned}$$ Therefore, and imply that $$\\begin{aligned}\n \\lim_{\\a\\uparrow1} \\E[\\a^{\\textbf{N}(x - \\sa) + 1} K ] = K.\n \\label{eqn:boundaK3}\\end{aligned}$$\n\nThe first term of the right hand side of can be written as $$\\begin{aligned}\n\\begin{split}\n & \\E[\\sum_{j = 1}^{\\textbf{N}(x - \\sa) + 1} \\a^{j-1} (\\tilde{h}_{\\a} (x - \\textbf{S}_{j-1})- (1-\\a)\\bma)] \\\\\n = & \\sum_{i = 0}^{+\\infty} \\sum_{j=1}^{i+1} \\a^{j-1}\\E[\\tilde{h}_{\\a}(x- \\textbf{S}_{j-1})- (1-\\a)\\bma|\\textbf{N}(x - \\sa) =i] \\PR(\\textbf{N}(x-\\sa)=i) \\\\\n = & \\sum_{j = 0}^{+\\infty} \\sum_{i=j}^{+\\infty} \\a^j \\E[\\tilde{h}_{\\a}(x- \\textbf{S}_j)- (1-\\a)\\bma|\\textbf{N}(x - \\sa) =i] \\PR(\\textbf{N}(x-\\sa)=i) \\\\\n = & \\sum_{j = 0}^{+\\infty} \\a^j\\E[\\tilde{h}_{\\a}(x- \\textbf{S}_j)- (1-\\a)\\bma|\\textbf{N}(x - \\sa)\\geq j] \\PR(\\textbf{N}(x-\\sa)\\geq j) \\\\\n = & \\sum_{j = 0}^{+\\infty} \\a^j \\E[\\tilde{h}_{\\a}(x-\\textbf{S}_j)- (1-\\a)\\bma|\\textbf{S}_j \\leq x - \\sa] \\PR(\\textbf{S}_j \\leq x - \\sa),\n\\end{split}\n \\label{eqn:sum of h}\\end{aligned}$$ where the first and third equalities follow from the properties of conditional expectations, the second equality changes the order of summation, and its validity follows from the nonnegativity of $h(\\cdot)$ and the finiteness of $\\bua (x),$ and the last equality follows from the fact that $\\PR(\\textbf{N}(t) \\geq n) = \\PR(\\textbf{S}_n \\leq t).$\n\nNow we prove that, if $\\a\\uparrow1,$ then the limit of the expression in as $\\a\\uparrow1$ exists almost everywhere on $(s^*, +\\infty).$ Consider the sets $\\mathcal{D}_n,$ $n = 0,1,\\ldots,$ on which the distribution function of $\\textbf{S}_n,$ is not continuous. ", "Since every distribution function is right-continuous, $$\\begin{aligned}\n \\mathcal{D}_n := \\{ x\\in\\R : \\lim_{y\\uparrow x} \\PR(\\textbf{S}_n \\leq y) \\neq \\PR(\\textbf{S}_n \\leq x) \\}.\\end{aligned}$$ Therefore, each set $\\mathcal{D}_n,$ $n=0,1,\\ldots,$ is at most countably infinite. ", "Let $$\\begin{aligned}\n \\mathcal{D} = \\{ x > s^*: x = s^* + y, \\quad y\\in \\cup_{n=0}^{+\\infty} \\mathcal{D}_n \\}\n \\qquad \\text{and} \\qquad\n \\mathcal{C} = (s^*,+\\infty) \\setminus \\mathcal{D}.", "\n \\label{eqn:def of discont cont pts}\\end{aligned}$$ Hence, $\\mathcal{D}$ is also at most countably infinite. ", "In addition, $\\PR(\\textbf{S}_n \\leq x -s^*)$ is continuous at $x-s^*$ and $\\lim_{\\a\\uparrow1} \\PR(\\textbf{S}_n \\leq x - \\sa) = \\PR(\\textbf{S}_n \\leq x -s^*)$ for all $x\\in\\mathcal{C}$ and $n=0,1,\\ldots\\ .$\n\nConsider $x\\in\\mathcal{C}.$ Since the function $\\h(x)$ is quasiconvex, $\\a^j \\E[\\tilde{h}_{\\a}(x-\\textbf{S}_j)|\\textbf{S}_j \\leq x - \\sa] \\leq \\E[\\h(x - D)] + \\E[\\h (-b - D)] < +\\infty.$ Since $\\PR(D > 0)>0,$ there exists a real number $\\Delta_D>0$ such that $\\PR(D > \\Delta_D)>0.$ Consider $$\\begin{aligned}\n \\tilde{D} =\n \\begin{cases}\n 0 & \\text{if } D < \\Delta_D, \\\\\n \\Delta_D & \\text{otherwise.}", "\n \\end{cases}\n %\\label{eqn:tD}\\end{aligned}$$ Then $\\E[\\tilde{D}] = \\Delta_D \\PR(D\\geq \\Delta_D) >0$ and $Var(\\tilde{D}) = \\Delta_D^2 \\PR(D\\geq \\Delta_D) (1-\\PR(D \\geq \\Delta_D)) < +\\infty.$ Define $\\tilde{\\textbf{S}}_0 = 0$ and $\\tilde{\\textbf{S}}_n = \\sum_{i=1}^n \\tilde{D},$ $n=1,2,\\ldots\\ .$ Therefore, $\\PR(\\textbf{S}_n \\leq x) \\leq \\PR(\\tilde{\\textbf{S}}_n \\leq x)$ for all $x\\in\\R$ and $n=0,1,\\ldots\\ .$ Since $\\E[\\tilde{D}] > 0,$ there exists $N_1 > 0$ such that $n\\E[\\tilde{D}] > x + b$ for all $n > N_1.$ Let $\\Delta(n) := n\\E[\\tilde{D}] - (x+b) >0.$ Hence, for $n > N_1$ $$\\begin{aligned}\n & \\PR(\\textbf{S}_n \\leq x - \\sa) \\leq \\PR(\\tilde{\\textbf{S}}_n \\leq x - \\sa)\n \\leq \\PR(\\tilde{\\textbf{S}}_n \\leq x + b) \\\\\n = & \\PR(\\tilde{\\textbf{S}}_n-n\\E[\\tilde{D}]\\leq x+b - n\\E[\\tilde{D}]) \\leq \\PR(|\\tilde{\\textbf{S}}_n - n\\E[\\tilde{D}]| \\geq \\Delta(n) ) \\leq \\frac{Var(\\tilde{D})}{\\Delta^2 (n)},\\end{aligned}$$ where the last inequality follows from Chebyshev’s inequality. ", "In addition, according to Lemma \\[lm:limit m\\*\\], there exists $M_1 > 0$ such that $|(1-\\a)\\bma| \\leq M_1$ for all $\\a\\in [\\b,1).$ Therefore, the summation $\\sum_{j = N_1}^{+\\infty} ( \\E[\\h(x - D)] + \\E[\\h (-b - D)] + M_1) \\frac{Var(\\tilde{D})}{\\Delta^2 (j)} < +\\infty.$ By taking the limit of the first and last terms of as $\\a\\uparrow1,$ $$\\begin{aligned}\n\\begin{split}\n &\\lim_{\\a\\uparrow1} \\E[\\sum_{j = 1}^{\\textbf{N}(x - \\sa) + 1} \\a^{j-1} (\\tilde{h}_{\\a} (x - \\textbf{S}_{j-1})- (1-\\a)\\bma) ]\n \\\\\n =& \\sum_{j = 0}^{+\\infty} \\E[\\tilde{h}_{1}(x-\\textbf{S}_j)- w|\\textbf{S}_j \\leq x - s^*] \\PR(\\textbf{S}_j \\leq x - s^*) \\\\\n =& \\E[\\sum_{j = 1}^{\\textbf{N}(x - s^*) + 1} (\\tilde{h}_1 (x - \\textbf{S}_{j-1})- w)],\n\\end{split}\n \\label{eqn:limit of sum-2}\\end{aligned}$$ where the first equality follows from the Lebesgue’s dominated convergence theorem, Theorem \\[thm:limit s alpha\\], and Lemma \\[lm:limit m\\*\\], and the second equality follows from with $\\sa$ replaced with $s^*$ and $\\a^j$ replaced with $1.$ In view of , , and , $$\\begin{aligned}\n \\lim_{\\a\\uparrow 1} \\bua (x) =\n \\E[\\sum_{j = 1}^{\\textbf{N}(x - s^*) + 1} (\\tilde{h}_1 (x - \\textbf{S}_{j-1})- w)] + K, \\qquad x\\in\\mathcal{C} .", "\n \\label{eqn:convegC}\\end{aligned}$$\n\nLet $\\bar{\\mathcal{D}}:= \\mathcal{D}\\cup \\{s^*\\}.$ The complement of $\\bar{\\mathcal{D}}$ is $\\bar{\\mathcal{D}}^c = \\X\\setminus\\bar{\\mathcal{D}} = (-\\infty,s^*)\\cup\\mathcal{C}.$ In view of and , there exists the limit $$\\begin{aligned}\n \\bu (x) := \\lim_{\\a\\uparrow1} \\bua (x), \\qquad x\\in \\bar{\\mathcal{D}}^c.", "\n \\label{eqn:convergDc} \\end{aligned}$$\n\nNow it remains to prove that holds for $x\\in \\bar{\\mathcal{D}}.$ In view of Lemma \\[lm:bua equicontinuous\\] and Arzelà-Ascoli theorem (see Hernández-Lerma and Lasserre [@HLL96 p. 96]), there exist a sequence $\\{ \\a_n\\uparrow1 \\}_{n=1,2,\\ldots}$ with $\\a_1 \\geq \\b$ and a continuous function $\\bar{u}^*$ such that $$\\begin{aligned}\n \\lim_{n\\to +\\infty} \\bu_{\\a_n}(x) = \\bu^* (x) , \\qquad x\\in\\X,\n \\label{eqn:bu*-1}\\end{aligned}$$ In view of and , $$\\begin{aligned}\n \\bu (x) = \\bu^* (x), \\qquad x\\in \\bar{\\mathcal{D}}^c.", "\n \\label{eqn:bu=bu*}\\end{aligned}$$\n\nThe following proof is by contradiction. ", "Consider $z\\in\\bar{\\mathcal{D}}.$ Assume that there exists a sequence $\\{ \\gamma_n\\uparrow1 \\}_{n=1,2,\\ldots}$ with $\\gamma_1 \\geq \\b$ such that $\\lim_{n\\to +\\infty} \\bu_{\\gamma_n} (z) \\neq \\bu^* (z).$ According to Arzelà-Ascoli theorem, there exist a subsequence $\\{ \\gamma_{n_k} \\}_{k=1,2,\\ldots}$ of the sequence $\\{ \\gamma_n\\uparrow1 \\}_{n=1,2,\\ldots}$ and a continuous function $u^\\prime$ such that $$\\begin{aligned}\n \\lim_{k\\to +\\infty} \\bu_{\\gamma_{n_k}}(x) = \\bu^\\prime (x) , \\qquad x\\in\\X .", "\n \\label{eqn:bu*-2}\\end{aligned}$$ Therefore, $\\bu^\\prime (z) \\neq \\bu^* (z).$ However, in view of , , and , $\\bu^* (x) = \\bu^\\prime (x)$ for all $x\\in \\bar{\\mathcal{D}}^c,$ which implies that $$\\begin{aligned}\n\\bu^* (z) = \\lim_{y\\to z, y\\in \\bar{\\mathcal{D}}^c} \\bu^* (y) = \\lim_{y\\to z, y\\in \\bar{\\mathcal{D}}^c} \\bu^\\prime (y) = \\bu^\\prime (z).\\end{aligned}$$ Therefore, there exists the limit $$\\begin{aligned}\n \\bu (x) := \\lim_{\\a\\uparrow1} \\bua (x), \\qquad x\\in \\bar{\\mathcal{D}}.", "\n \\label{eqn:convergDc-1} \\end{aligned}$$ Furthermore, , , and implies that $\\bu = \\bu^*$ and the function $\\bu$ is continuous.", "\n\nThis corollary follows from Theorems \\[thm:inventory:acoe\\], \\[thm:limit s alpha\\] and \\[thm:ua converge\\].", "\n\nThis corollary holds because Assumption \\[assum:convex\\] implies Assumptions \\[assum:qcall\\] and \\[assum:decrease\\]; see Lemma \\[lm:cqc\\]\n" ]

{ "pile_set_name": "ArXiv" }

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[ "Q:\n\nHashSet behavior when changing field value\n\nI just did the following code:\nimport java.util.", "HashSet;\nimport java.util.", "Set;\n\npublic class MyClass {\n\n private static class MyObject {\n private int field;\n\n public int getField() {\n return field;\n }\n\n public void setField(int aField) {\n field = aField;\n }\n\n @Override\n public boolean equals(Object other) {\n boolean result = false;\n if (other !", "= null && other instanceof MyObject) {\n MyObject that = (MyObject) other;\n result = (this.getField() == that.getField());\n }\n return result;\n }\n\n @Override\n public int hashCode() {\n return field;\n }\n }\n\n public static void main(String[] args) {\n Set<MyObject> mySet = new HashSet<MyObject>();\n MyObject object = new MyObject();\n object.setField(3);\n mySet.add(object);\n object.setField(5);\n System.out.println(mySet.contains(object));\n MyObject firstElement = mySet.iterator().next();\n System.out.println(\"The set object: \" + firstElement + \" the object itself: \" + object);\n }\n\n}\n\nIt prints:\nfalse\nThe set object: MyClass$MyObject@5 the object itself: MyClass$MyObject@5\n\nBasically meaning that the object is not considered to be in the set, whiile its instance itself apparantly is in the set. ", "this means that if I insert a object in a set, then change the value of a field that participates in the calculation of the hashCode method, then the HashSet method will seize working as expected. ", "Isn;t this too big source of possible errors? ", "How can someone defend against such cases?", "\n\nA:\n\nBelow is the quote from Set API. ", "It explains everything. ", "\n\nNote: Great care must be exercised if mutable objects are used as set elements. ", "The behavior of a set is not specified if the value of an object is changed in a manner that affects equals comparisons while the object is an element in the set. ", "A special case of this prohibition is that it is not permissible for a set to contain itself as an element.", "\n\nhttp://docs.oracle.com/javase/7/docs/api/java/util/Set.html\n\n" ]

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[ "WASHINGTON (Reuters) - U.S. President Donald Trump is keen to advance talks with Switzerland on a free trade deal, Swiss President Ueli Maurer told reporters in Washington after the first visit by a Swiss president to the Oval Office.", "\n\nMaurer described the meeting with Trump as constructive and said the U.S. president was “positive” about work on a free trade deal, but wanted to get it done “more quickly than with the EU (European Union).” ", "Specific details were not discussed, he said.", "\n\n“He thinks we should accelerate the issue,” Maurer told reporters after the meeting.", "\n\nThe United States and the European Union are working to launch trade negotiations but the process has taken longer than expected.", "\n\nSwitzerland, the seventh largest foreign investor in the United States with $309 billion, is keen to expand economic ties with the United States, said Maurer, who is also finance minister.", "\n\nBilateral Swiss-U.S. trade in goods and services totaled $122 billion in 2017, according to data from the U.S. Trade Representative’s office.", "\n\nMaurer and Trump had been due to meet at the World Economic Forum in Davos, Switzerland in January, but Trump canceled his attendance due to a U.S. government shutdown.", "\n\n“The fact that Switzerland - a Swiss president - was invited to the White House for the first time confirms that we have good relations ... and that there is a desire to deepen them,” Maurer said. “", "That was an important step which I am convinced will be followed by others.”", "\n\nHe said the two leaders also discussed Iran, where Switzerland provides protective and consular services for some 100 U.S. citizens and 12,000 people with both U.S. and Iranian citizenship, but declined to give further details.", "\n\nThe White House earlier said Trump discussed crises in the Middle East and Venezuela in the meeting with Maurer, expressing gratitude for Switzerland’s role in facilitating diplomatic relations on behalf of the United States.", "\n\nSwitzerland is ready to play a similar role in Venezuela, but is waiting for approval by Caracas, Maurer said.", "\n\nAlso on the agenda, Maurer said, were China and Huawei Technologies Co Ltd, which the U.S. Commerce Department on Thursday formally placed on its “Entity List” - a move that bans the Chinese telecom giant from buying components from U.S. companies without U.S. government approval.", "\n\nMaurer, who met with Chinese President Xi Jinping in Beijing in April, said his country had chosen a different path in dealing with China than Washington, preferring to advocate for its values directly with Beijing.", "\n\nHe said Switzerland had banned all foreign companies from providing services or hardware for its critical infrastructure, but Huawei was present in the private commercial market.", "\n\n17-May-2019PIANGO\n\nDespite the failures of the EPA to deliver real development to Pacific countries it looks as though the European Union will once again, through the Post Cotonou Agreement, push for enhanced and undistorted access for European investments to Pacific resources.", "\n\nbilaterals.org is a collaborative space to share information and support movements struggling against bilateral trade and investment deals which serve corporations, not people. ", "Multilingual. ", "Global. ", "No one owns it. ", "Open publishing. ", "Get involved." ]

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[ "Prometheus is one of those awesome open source monitoring services that I simply cannot live without. ", "Prometheus is a Time Series Database that collects metrics from services using it's exporters functionality. ", "Prometheus has its own query language called PromQL and makes graphing epic visualiztions with services such as Grafana a breeze.", "\n\nWhat are we doing today\n\nWe will install the prometheus service and set up node_exporter to consume node related metrics such as cpu, memory, io etc that will be scraped by the exporter configuration on prometheus, which then gets pushed into prometheus's time series database. ", "Which can then be used by services such as Grafana to visualize the data.", "\n\nOther exporters is also available, such as: haproxy_exporter , blackbox_exporter etc, then you also get pushgateway which is used to push data to, and then your exporter configuration scrapes the data from the pushgateway endpoint. ", "In a later tutorial, we will set up push gateway as well.", "\n\nInstall Prometheus\n\nFirst, let's provision our dedicated system users for prometheus and node exporter:\n\n$ useradd --no-create-home --shell /bin/false prometheus $ useradd --no-create-home --shell /bin/false node_exporter\n\nCreate the directories for it's system files:\n\n$ mkdir /etc/prometheus $ mkdir /var/lib/prometheus\n\nApply the permissions:\n\n$ chown prometheus:prometheus /etc/prometheus $ chown prometheus:prometheus /var/lib/prometheus\n\nNext, update your system:\n\n$ apt update && apt upgrade -y\n\nLet's install prometheus, head over to https://prometheus.io/download/ and get the latest version of prometheus:\n\n$ wget https://github.com/prometheus/prometheus/releases/download/v2.8.0/prometheus-2.8.0.linux-amd64.tar.gz $ tar -xf prometheus-2.8.0.linux-amd64.tar.gz $ cp prometheus-2.8.0.linux-amd64/prometheus /usr/local/bin/ $ cp prometheus-2.8.0.linux-amd64/promtool /usr/local/bin/ $ chown prometheus:prometheus /usr/local/bin/prometheus $ chown prometheus:prometheus /usr/local/bin/promtool $ cp -r prometheus-2.8.0.linux-amd64/consoles /etc/prometheus/ $ cp -r prometheus-2.8.0.linux-amd64/console_libraries /etc/prometheus/ $ chown -R prometheus:prometheus /etc/prometheus/consoles $ chown -R prometheus:prometheus /etc/prometheus/console_libraries $ rm -rf prometheus-2.8.0.linux-amd64*\n\nConfigure Prometheus\n\nWe need to tell prometheus to scrape itself in order to get prometheus performance data, edit the prometheus configuration:\n\n$ vim /etc/prometheus/prometheus.yml\n\nAnd add a scrape config: Set the interval on when it needs to scrap, the job name which will be in your metric and the endpoint which it needs to scrape:\n\nglobal: scrape_interval: 15s scrape_configs: - job_name: 'prometheus' scrape_interval: 5s static_configs: - targets: ['localhost:9090']\n\nApply permissions to the configured file:\n\n$ chown prometheus:prometheus /etc/prometheus/prometheus.yml\n\nNext, we need to define a systemd unit file so we can control the daemon using systemd:\n\n$ vim /etc/systemd/system/prometheus.service\n\nThe config:\n\n[Unit] Description=Prometheus Wants=network-online.target After=network-online.target [Service] User=prometheus Group=prometheus Type=simple ExecStart=/usr/local/bin/prometheus \\ --config.file /etc/prometheus/prometheus.yml \\ --storage.tsdb.path /var/lib/prometheus/ \\ --web.console.templates=/etc/prometheus/consoles \\ --web.console.libraries=/etc/prometheus/console_libraries [Install] WantedBy=multi-user.target\n\nSince we created a new systemd unit file, we need to reload the systemd daemon, then start the service:\n\n$ systemctl daemon-reload $ systemctl start prometheus\n\nLet's look at the status to see if everything works as expected:\n\n$ systemctl status prometheus prometheus.service - Prometheus Loaded: loaded (/etc/systemd/system/prometheus.service; disabled; vendor preset: enabled) Active: active (running) since Tue 2019-03-26 11:59:10 UTC; 6s ago Main PID: 16374 (prometheus) Tasks: 9 (limit: 4704) CGroup: /system.slice/prometheus.service └─16374 /usr/local/bin/prometheus --config.file /etc/prometheus/prometheus.yml --storage.tsdb.path /var/lib/prometheus/ --web.console.templates=/etc/prometheus/consoles --web.console.libraries= ... Mar 26 11:59:10 ip-172-31-41-126 prometheus[16374]: level=info ts=2019-03-26T11:59:10.893770598Z caller=main.go:655 msg=\"TSDB started\"\n\nSeems legit! ", "Enable the service on startup:\n\n$ systemctl enable prometheus\n\nInstall Node Exporter\n\nNow since we have prometheus up and running, we can start adding exporters to publish data into our prometheus time series database. ", "As mentioned before, with node exporter, we will allow prometheus to scrape the node exporter endpoint to consume metrics about the node:\n\nYou will find the latest version from their website, which I have added at the top of this post.", "\n\n$ wget https://github.com/prometheus/node_exporter/releases/download/v0.17.0/node_exporter-0.17.0.linux-amd64.tar.gz $ tar -xf node_exporter-0.17.0.linux-amd64.tar.gz $ cp node_exporter-0.17.0.linux-amd64/node_exporter /usr/local/bin $ chown node_exporter:node_exporter /usr/local/bin/node_exporter $ rm -rf node_exporter-0.17.0.linux-amd64*\n\nCreate the systemd unit file:\n\n$ vim /etc/systemd/system/node_exporter.service\n\nApply this configuration:\n\n[Unit] Description=Node Exporter Wants=network-online.target After=network-online.target [Service] User=node_exporter Group=node_exporter Type=simple ExecStart=/usr/local/bin/node_exporter [Install] WantedBy=multi-user.target\n\nReload the systemd daemon and start node exporter:\n\n$ systemctl daemon-reload $ systemctl start node_exporter\n\nLook at the status:\n\n$ node_exporter.service - Node Exporter Loaded: loaded (/etc/systemd/system/node_exporter.service; disabled; vendor preset: enabled) Active: active (running) since Tue 2019-03-26 12:01:39 UTC; 5s ago Main PID: 16474 (node_exporter) Tasks: 4 (limit: 4704) CGroup: /system.slice/node_exporter.service └─16474 /usr/local/bin/node_exporter ... Mar 26 12:01:39 ip-172-31-41-126 node_exporter[16474]: time=\"2019-03-26T12:01:39Z\" level=info msg=\"Listening on :9100\" source=\"node_exporter.go:111\"\n\nIf everything looks good, enable the service on boot:\n\n$ systemctl enable node_exporter\n\nConfigure Node Exporter\n\nNow that we have node exporter running, we need to tell prometheus how to scrape node exporter, so that the node related metrics can end up into prometheus. ", "Edit the prometheus config:\n\n$ vim /etc/prometheus/prometheus.yml\n\nI'm providing the full config, but the config is the last section, where you can see the jobname is node_exporter:\n\nglobal: scrape_interval: 15s scrape_configs: - job_name: 'prometheus' scrape_interval: 5s static_configs: - targets: ['localhost:9090'] - job_name: 'node_exporter' scrape_interval: 5s static_configs: - targets: ['localhost:9100']\n\nOnce the config is saved, restart prometheus and have a look at the status if everything is going as expected:\n\n$ systemctl restart prometheus $ systemctl status prometheus\n\nNginx Reverse Proxy\n\nLet's add a layer of security and front our setup with a nginx reverse proxy, so that we don't have to access prometheus on high ports and we have the option to enable basic http authentication. ", "Install nginx:\n\n$ apt install nginx apache2-utils -y\n\nCreate the authentication file:\n\n$ htpasswd -c /etc/nginx/.htpasswd admin\n\nCreate the nginx site configuration, this will tel nginx to route connections on port 80, to reverse proxy to localhost, port 9090, if authenticated:\n\n$ rm /etc/nginx/sites-enabled/default $ vim /etc/nginx/sites-enabled/prometheus.conf\n\nAnd this is the config:\n\nserver { listen 80 default_server; listen [::]:80 default_server; root /var/www/html; index index.html index.htm index.nginx-debian.html; server_name _; location / { auth_basic \"Prometheus Auth\"; auth_basic_user_file /etc/nginx/.htpasswd; proxy_pass http://localhost:9090; proxy_http_version 1.1; proxy_set_header Upgrade $http_upgrade; proxy_set_header Connection 'upgrade'; proxy_set_header Host $host; proxy_cache_bypass $http_upgrade; } }\n\nReload nginx configuration:\n\n$ systemctl reload nginx\n\nAccess the Beauty of Prometheus Land!", "\n\nOnce you have authenticated, head over to status, here you will see status info such as your targets, this wil be the endpoints that prometheus is scraping:\n\nFrom the main screen, let's dive into some queries using PromQL. ", "Also see my Prometheus Cheatsheet.", "\n\nFor the first query, we want to see the available memory of this node in bytes ( node_memory_MemAvailable_bytes ):\n\nNow since the value is in bytes, let's convert the value to MB, ( node_memory_MemAvailable_bytes/1024/1024 )\n\nLet's say we want to see the average memory available in 5 minute buckets:\n\nThat's a few basic ones, but feel free to checkout my Prometheus Cheatsheet for other examples. ", "I update them as I find more queries.", "\n\nThanks\n\nHope this was informative. ", "I am planning to publish a post on visualizing prometheus data with Grafana (which is EPIC!) ", "and installing Pushgateway for custom integrations." ]

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[ "In looking for a way to create an abbreviated pathway for\nthe Food and Drug Administration (FDA) to approve generic biologic therapies\n(aka biogenerics or follow-on biologics), there are lots of questions about how\nto achieve the proper balance between innovation and competition. ", "The sticking\npoint (in general) has been that the brand name drugmakers and generics can't\nagree on how long a biotech drug should be on the market before a generic\ndrugmaker can market a generic.", "\n\nUnder the proposed law, if FDA approves a biological product\non the grounds that it is interchangeable to a reference product, the\nDepartment of Health and Human Services (HHS) is prohibited from making a\ndetermination that a second or subsequent biological product is interchangeable\nto that same reference product until one year after the first commercial\nmarketing of the first interchangeable product.", "\n\nThe act also authorizes HHS to issue guidance with respect\nto the licensure of biological products under this new pathway, and it includes\nprovisions governing patent infringement concerns such as the exchange of\ninformation, good faith negotiations and initiation infringement actions.", "\n\nThe Biotech Industry Organization (BIO) has called for 14\nyears of market exclusivity, while generic makers want the period limited to no\nmore than five years of protection. ", "Not to be confused with patents, data\nexclusivity is the period after the FDA approves a product during which an\nimitator can't rely on the innovator's clinical data for safety and\neffectiveness. ", "It can run during and longer than the period of patent\nprotection.", "\n\nThe current measure for 12 years passed 16 to 7, despite an\nearlier decree by the Obama administration that a seven-year exclusivity limit\nsounded good. ", "The Obama administration had sent out an earlier warning shot\nthat it considered seven years enough time to protect brand-name biotechnology\nmedicines from generic competitors. ", "In a letter to Rep. Henry Waxman (D-CA),\nthe White House said seven years \"strikes the appropriate balance between\ninnovation and competition by providing for seven years of exclusivity.\"", "\n\nThe posturing by the current administration is not a\nsurprise given that the U.S. government is the largest consumer of medical care\nvia Medicare and Medicaid and the fact that sales of biotech drugs were $40.3\nbillion last year. ", "With creating a governmental health care system at the top\nof its priority list, ways to cut costs are critical to any reform.", "\n\nAfter considering at least four proposals all titled the\n\"Biologics Price Competition and Innovation Act of 2009,\" the HELP committee\ndeclined several other proposals including voting down one by Sen. Sherrod\nBrown (D-OH), which would have provided only seven years of exclusivity for\nbrand name biologics.", "\n\nSen. Barbara Mikulski's (D-MD) proposed a 10-year\nexclusivity period, which could be extendable by one year if a supplemental\napplication was approved for one or more new therapeutic indications. ", "Sen. John\nMcCain's (R-AZ) proposal would have provided a 10-year period of exclusivity\nthat could be extended by two years \"if there has been significant therapeutic\nadvancements with respect to the reference product.\"", "\n\nThe vote was at least a small victory for major biotech\ndrugmakers, which have been lobbying for a period of 12 to 14 years before\ngeneric equivalents could be approved. ", "Biotech companies have been pushing for a longer period of data\nexclusivity, saying that it can take 15 years and a $1 billion to develop and\nmarket a biotech drug, so they need the longer period to make back their\ninvestment. ", "Generic drugmakers, not surprising, would like the exclusivity\nperiod to be as little as possible.", "\n\nThis is just as small step, since the Senate plan could\nchange when the healthcare bill goes to the floor for a vote. ", "It also must be\napproved by the House.", "\n\nSo, what will the final number be for exclusivity? ", "We'll\nhave to wait to see.", "\n\nStephen Albainy-Jenei is a patent attorney at Frost Brown Todd LLC, serving up chat at PatentBaristas.com. ", "Write him with comments or questions at Stephen@patentbaristas.com. ", "Albainy-Jenei doesn't own shares of companies mentioned in this article." ]

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[ "Both sides have point in Reichel situation\n\nMarch 16, 2014\n\nThe former Westwood High School boys basketball coach posted a 430-201 overall record in 28 seasons at WHS before retiring a second time in September of 2007.", "\n\nDieterle led the Patriots to a pair of state semifinal appearances in 1994 in Class B and 2003 in Class C.\n\nArticle Photos\n\nCRAIG?REMSBURG\n\nHe took the Patriots to nine conference, 10 district, four regional and two quarterfinal titles during his tenure.", "\n\nDieterle IS the face of WHS basketball and still attends many Westwood home games as a spectator.", "\n\nRyan Reichel, on the other hand, coached the Patriot boys' team the last three seasons, gong 14-47 overall and 5-14 this past season.", "\n\nA 2003 WHS graduate who played and coached under Dieterle, Reichel officially submitted his resignation March 7 after school officials told him to use Dieterle as a mentor \"however he saw fit.\"", "\n\nReichel, 29, declined, deciding he was \"not the right fit\" to continue coaching the Patriots' team with Dieterle sharing many of the school's varsity boys basketball duties.", "\n\nIt's not that Reichel and Dieterle do not like each other. ", "On the contrary, Reichel cherishes the time he spent playing for - and coaching with - Dieterle years ago and has called the latter for advice.", "\n\nThe legendary coach, meanwhile, considers Reichel \"like a son.\"", "\n\nBut like any young coach who has worked hard and spent countless hours trying to rebuild a team, Reichel wanted the Patriots to be his team, not Dieterle's.", "\n\nHe didn't want to coach the Patriots with Dieterle looming over his shoulder.", "\n\n\"I want to stand on my own two feet,\" Reichel said.", "\n\nBoth WHS officials and Reichel have valid points in this situation.", "\n\nDieterle, with his experience, basketball knowledge and coaching savvy, could help bring the WHS boys' program back to where it once was: one of the premier teams in Marquette County and the Upper Peninsula.", "\n\nBut it's also understandable why Reichel feels the way he does about Dieterle coming back.", "\n\nAfter putting so much time and effort into resurrecting the WHS boys varsity program, Reichel wants control of his team and to be free to make decisions he feels best for the Patriots.", "\n\nHe truly believes his \"five-year plan\" to rebuild the Patriots is beginning to bear fruit after three seasons. ", "To coach with someone else \"mentoring\" him and maybe wanting to do something different that he wants didn't appeal to him.", "\n\nThus, he decided \"I wasn't right for the job at this time\" and resigned.", "\n\nCaught in the middle of all this is Dieterle, who no doubt only has the success of the WHS boys varsity team at heart.", "\n\nFinding a replacement for Reichel might be tough, especially if WHS officials say the new coach would have to be \"mentored\" by Dieterle, as well.", "\n\nThe best scenario would be for WHS officials to hire a coach who's a \"good fit\" for the program and can build on what Reichel has started, and for the latter to find another coaching job that could benefit from his coaching skills." ]

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[ "A new honey-harvesting beekeeping invention has raised some impressive buzz to the tune of $10 million.", "\n\nCedar and Stuart Anderson, a father and son beekeeper duo from Australia spent 10 years perfecting an invention that radically improves the labor-intensive and high-risk art of harvesting honey. ", "They then launched a crowdfunding campaign for their invention.", "\n\nThe family beekeeping team set a goal to raise $70,000 for the Flow Hive. ", "And, judging from the way they structured their campaign, they weren’t even all that sure they would hit it. ", "The crowdfunding campaign was launched as a “flexible” campaign on Indiegogo, an option that allows campaign owners to collect whatever money they raise, even if they don’t hit their target goal. ", "Not reaching one’s goal, however, means paying a higher percentage of earnings to the platform as a fee for the service.", "\n\nThe Andersons’ caution was for naught. ", "They’ve raised more than $10 million from more than 27,000 people, making it the highest-earning campaign in Indiegogo history. ", "The campaign still has six days left and it’s pulled in 14,720 percent of the initial fundraising goal.", "\n\n“It's been a dream for me for many long years, to create a system that allows you to harvest the honey directly from the hive without opening it. ", "After a decade of work, my father and I have achieved our goal and it now works better than I ever dreamt it would,” writes Cedar on Indiegogo about the campaign. “", "It's so exciting to be bringing this to the world.”", "\n\nAs it turns out, Cedar isn’t the only one excited about his new invention. ", "Buzz on, guys!", "\n\nCatherine Clifford\n\nCatherine Clifford is senior entrepreneurship writer at CNBC. ", "She was formerly a senior writer at Entrepreneur.com, the small business reporter at CNNMoney and an assistant in the New York bureau for CNN. ", "Clifford attended Columbi...\n\nThis website uses cookies to allow us to see how our website and related online services are being used. ", "By continuing to use this website, you consent to our cookie collection. ", "More information about how we collect cookies is found here." ]

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[ "Tags\n\nRelated Posts\n\nShare This\n\nChapter 7 Bankruptcy: Pros and Cons\n\nDeclaring bankruptcy is inevitably a difficult choice to make. ", "It means giving up your assets when you can no longer afford to continue making payments on your debts or when you are struggling to support yourself or your business. ", "While this likely frustrating and upsetting, it can also be a saving grace, when you are struggling under significant debt. ", "However, before declaring bankruptcy, you must understand the type of bankruptcy that is right for you and your situation. ", "Each of the different forms of bankruptcy applies to different situations and different income levels. ", "Chapter 7 bankruptcy is one of the most common forms of bankruptcy and it has a variety of requirements that you must follow to be eligible. ", "Fortunately, the legal specialists at FindLaw have provided an overview of the pros and cons of choosing Chapter 7 bankruptcy.", "\n\nFiling for Chapter 7 bankruptcy allows you to cancel any or all of the debts that you are facing. ", "In order to do this, however, you may be forced to liquidate your property and assets in order to repay creditors. ", "This is one of the quickest and simplest forms of bankruptcy available, which is why many people choose this route. ", "In order to qualify for Chapter 7 bankruptcy, you must undergo a means test, which indicates the assets that you have available and if you are capable of repaying any amount of your debt. ", "With the help of a Raleigh bankruptcy lawyer, many of the people who wish to file for Chapter 7 bankruptcy are capable of effectively doing so. ", "Before you decide to move forward with Chapter 7 bankruptcy, however, it is important to understand the pros and cons of this plan of action. ", "Some of the cons include:\n\nThe inclusion of bankruptcy on your credit report for up to 10 years\n\nLoss of property and valuable possessions\n\nLoss of all credit cards\n\nDifficulty acquiring a mortgage\n\nYou cannot file for Chapter 7 bankruptcy more than once\n\nAlthough these negative aspects of bankruptcy may turn many people away, there are also several positives, which can help you and your loved ones, such as:\n\nYou receive financial relief within 3-6 months of filing\n\nLenders cannot take any further collection action\n\nChapter 7 can relieve even extremely high amounts of debt\n\nMany of the things you own are exempt from being sold during bankruptcy\n\nOver time you may be able to obtain new lines of credit and rebuild your financial standing\n\nThis is only a brief overview of the different aspects to consider before filing for bankruptcy. ", "Only an experienced lawyer can truly help you understand your rights and the best course of action to take. ", "Filing for bankruptcy may hurt your pride and your credit, but in the long-term, it can be the right solution to find some relief from serious debt. ", "Your life should not be filled with only financial struggles, and bankruptcy may be able to help." ]

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[ "106 F.3d 413\n97 CJ C.A.R. 148\nNOTICE: Although citation of unpublished opinions remains unfavored, unpublished opinions may now be cited if the opinion has persuasive value on a material issue, and a copy is attached to the citing document or, if cited in oral argument, copies are furnished to the Court and all parties. ", " See General Order of November 29, 1993, suspending 10th Cir. ", "Rule 36.3 until December 31, 1995, or further order.", "\nAlfred L. CAMERON, Petitioner-Appellant,v.R.G. THOMPSON; United States Parole Commission,Respondents-Appellees.", "\nNo. ", "96-6201.", "\nUnited States Court of Appeals, Tenth Circuit.", "\nJan. 24, 1997.", "\n\nBefore ANDERSON, HENRY, and BRISCOE, Circuit Judges.", "\nORDER AND JUDGMENT*\nBRISCOE, Circuit Judge.", "\n\n\n1\nAfter examining the briefs and appellate record, this panel has determined unanimously that oral argument would not materially assist the determination of this appeal. ", " See Fed. ", " R.App. ", "P. 34(a); 10th Cir. ", " R. 34.1.9. ", " Therefore, the case is ordered submitted without oral argument.", "\n\n\n2\nAlfred L. Cameron, a federal inmate appearing pro se, appeals the district court's denial of his petition for writ of habeas corpus pursuant to 28 U.S.C. § 2241. ", " We affirm.", "\n\n\n3\nCameron challenges the decision of the United States Parole Commission (USPC) revoking his parole and requiring him to serve 210 months for his parole violation behavior before reparole. ", " More specifically, he contends the USPC (1) violated his due process rights and acted contrary to its own regulations by imposing a reparole term that is longer than the time remaining to be served on his original sentence, and (2) placed him in double jeopardy by \"imposing a second punishment against [him] for a state offense that has already been served.\" ", " Petition at 7.", "\n\n\n4\nThe district court referred Cameron's petition to a magistrate judge and, on January 19, 1996, the magistrate concluded the USPC had acted properly and had not violated Cameron's constitutional rights. ", " Cameron filed written objections to the magistrate's report and, on May 21, 1996, the district court denied the petition for the reasons stated in the magistrate's report. ", " Cameron filed his notice of appeal with the district court on June 6, 1996. ", " On June 20, 1996, the district court issued an order concluding Cameron had failed to make a substantial showing of the denial of a federal right. ", " Accordingly, the district court purported to deny Cameron a certificate of appealability under 28 U.S.C. § 2253 (as amended on April 24, 1996, by the Antiterrorism and Effective Death Penalty Act of 1996, Pub.", "L. No. ", "104-132, 110 Stat. ", "1214 § 101).", "\n\n\n5\nWe note that it was unnecessary for Cameron to obtain a certificate of appealability. ", " Although the newly-amended § 2253 requires a person to obtain a certificate of appealability in \"a habeas corpus proceeding in which the detention complained of arises out of process issued by a State court,\" or \"in a proceeding under section 2255,\" it does not impose such a requirement on a person seeking to appeal a final order in a proceeding under 28 U.S.C. § 2241. ", " Bradshaw v. Story, 86 F.3d 164, 165-66 (10th Cir.1996). ", " Here, Cameron properly filed his petition under § 2241, see id. at 166 (noting a § 2241 petition attacks the execution of a sentence and must be filed in the district where the prisoner is confined), and seeks to appeal the district court's denial of that petition. ", " No certificate of appealability is necessary.", "\n\n\n6\nWe turn to the merits of Cameron's appeal. ", " Cameron contends the USPC violated 28 C.F.R. § 2.52(c)(2) by imposing a reparole term of 210 months when he only had 162 months left to serve on his original sentence. ", " Cameron has misconstrued the applicable regulations.", "\n\n\n7\nUnder § 2.52, the USPC can revoke parole and impose a new period of confinement (i.e., a violator term). ", " The only restriction is that the violator term, taken together with the time served by the parolee prior to release, cannot exceed the total length of the parolee's original sentence. ", " Here, the USPC complied with this requirement because the violator term imposed and the time Cameron served prior to parole are equal to the original sentence imposed (i.e., 240 months). ", " The 210-month reparole term is an entirely separate determination made by the USPC and the determination is not subject to the same restrictions. ", " In particular, there is no requirement that the reparole term be less than the original sentence. ", " See generally 28 C.F.R. § 2.20, § 2.21 (concerning computation of reparole term). ", " We note in passing that Cameron's presumptive reparole date (May 28, 2001) falls well within the full expiration of his violator term (April 18, 2008), as well as within his new mandatory release date (October 28, 2003). ", " We therefore find no error in the USPC's computations. ", " See Kell v. United States Parole Com'n, 26 F.3d 1016, 1019 (10th Cir.1994) (holding that a decision of the USPC will not be disturbed unless there is a clear showing of arbitrary and capricious action or an abuse of discretion).", "\n\n\n8\nCameron also contends the USPC's determination of a presumptive parole date violates the Double Jeopardy Clause because it punishes him for time already served on an intervening state sentence. ", " Cameron is apparently complaining that the reparole term calculated by the USPC (210 months) takes into account 131 months that he spent serving an Oregon state sentence that was imposed while he was on parole. ", " As noted by the district court, parole determinations are not viewed as criminal punishment subject to the Double Jeopardy Clause. ", " Id. at 1020. ", " Moreover, inclusion of the 131 months in the reparole term did not extend Cameron's sentence beyond the 240 months originally imposed. ", " This issue is without merit.", "\n\n\n9\nAFFIRMED. ", "The mandate shall issue forthwith.", "\n\n\n\n*\n This order and judgment is not binding precedent, except under the doctrines of law of the case, res judicata, and collateral estoppel. ", " The court generally disfavors the citation of orders and judgments; nevertheless, an order and judgment may be cited under the terms and conditions of 10th Cir. ", " R. 36.3\n\n\n" ]

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[ "Q:\n\nCustom widget doesn't show in admin\n\nI am learning Magento (1.5) and am trying to create a custom widget to use in static blocks.", "\nI have created a module:\n<?", "xml version=\"1.0\" encoding=\"UTF-8\"?", ">\n<config>\n <modules>\n <Freedom_Slidingwidget>\n <active>true</active>\n <codePool>local</codePool>\n <depends>\n <Mage_Widget />\n </depends>\n </Freedom_Slidingwidget>\n </modules>\n</config>\n\nand added the following xml files\n\\app\\code\\local\\Freedom\\Slidingwidget\\etc\\config.xml\n<?", "xml version=\"1.0\" encoding=\"UTF-8\"?", ">\n<config>\n <modules>\n <Freedom_Slidingwidget>\n <version>0.1.0</version>\n </Freedom_Slidingwidget>\n </modules>\n <global>\n <helpers>\n <slidingwidget>\n <class>Freedom_Slidingwidget_Helper</class>\n </slidingwidget>\n </helpers>\n <blocks>\n <slidingwidget>\n <class>Freedom_Slidingwidget_Block</class>\n </slidingwidget>\n </blocks>\n </global>\n</config>\n\n\\app\\code\\local\\Freedom\\Slidingwidget\\etc\\widget.xml\n<?", "xml version=\"1.0\" encoding=\"UTF-8\"?", ">\n<widgets>\n <catalog_sliding type=\"slidingwidget/sliding\" translate=\"name description\" module=\"slidingwidget\">\n <name>Catalog Products List</name>\n <description>List of Products in Category</description>\n <parameters>\n <category_id translate=\"label\">\n <visible>1</visible>\n <required>1</required>\n <label>Category</label>\n <type>label</type>\n <helper_block>\n <type>adminhtml/catalog_category_widget_chooser</type>\n <data>\n <button translate=\"open\">\n <open>Select Category...</open>\n </button>\n </data>\n </helper_block>\n <sort_order>10</sort_order>\n </category_id>\n <template translate=\"label\">\n <required>1</required>\n <label>Template</label>\n <visible>1</visible>\n <type>select</type>\n <value>freedom/slidingwidget/widget/sliding_category_products.phtml</value>\n <values>\n <default translate=\"label\">\n <value>freedom/catalogproducts/widget/sliding_category_products.phtml</value>\n <label>Sliding Category Products</label>\n </default>\n </values>\n </template>\n </parameters>\n </catalog_sliding>\n</widgets>\n\nAs soon as I upload the widget.xml file all the widgets in admin dissapear, remove the file and all is ok.", "\nI have been googling this for a couple of days now and judging by all I have read, this should be working.", "\nI am also getting the following warnings in my system.log\nWarning: include(Mage_Slidingwidget_Helper_Data.php): failed to open stream: No such file or directory in /home/freedoms/public_html/magento_1.5.1.0/includes/src/Varien_Autoload.php on line 93\nWarning: include(Mage_Slidingwidget_Helper_Data.php): failed to open stream: No such file or directory in /home/freedoms/public_html/magento_1.5.1.0/includes/src/Varien_Autoload.php on line 93\nWarning: include(): Failed opening 'Mage_Slidingwidget_Helper_Data.php' for inclusion (include_path='/home/freedoms/public_html/magento_1.5.1.0/includes/src:.:/opt/cpanel/ea-php55/root/usr/share/pear') in /home/freedoms/public_html/magento_1.5.1.0/includes/src/Varien_Autoload.php on line 93\n\nDoes anyone have any ideas as to what I am doing wrong?", "\n\nA:\n\nHappy to see that you finally got it working. ", "This answer helps you to resolve the final notice error that you are getting in system.log.", "\nCreate following helper class in your module.", "\nFile: app\\code\\local\\Freedom\\Catalog\\Helper\\Data.php\n<?", "php\nclass Freedom_Catalog_Helper_Data extends Mage_Core_Helper_Abstract\n{\n}\n\nEDIT\nAdd your helper class accordingly. ", "ie,\nFile: app\\code\\local\\Freedom\\Slidingwidget\\Helper\\Data.php\n<?", "php\nclass Freedom_Slidingwidget_Helper_Data extends Mage_Core_Helper_Abstract\n{\n}\n\nNow the actual problem here now is, you are enabled your modules compilation and after the changes that you have made, you didn't recompile it.", "\nSo disable compilation (this is what the best recommendation) and clear all your cache. ", "All errors will be gone.", "\n\n" ]

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[ "1994 NCAA Division I-A football season\n\nThe 1994 NCAA Division I-A football season, play of college football in the United States at the NCAA Division I-A level, began in August 1994 and ended on January 2, 1995. ", "Nebraska, who finished the season undefeated, ended the year ranked No. ", "1 in both the Associated Press and Coaches polls. ", "This was the first national championship of coach Tom Osborne's career at Nebraska, despite coming close in two prior attempts; in 1983, his team lost to Miami after Osborne, with his team trailing 31–30 late in the game, elected to try for the lead instead of the tie and failed. ", "In the previous season, Osborne's team lost to eventual national champion Florida State on a missed field goal as time expired.", "\n\nAlthough Osborne's team finished the season unbeaten, the national championship picture again was engulfed in controversy. ", "For much of the second half of the season, Nebraska and Penn State were regarded as the top two teams in the country. ", "This raised the possibility of a split national championship for the third time since 1990, due in large part to the system in place that had been concocted to avoid a split title.", "\n\nFollowing the 1991 season, where Miami and Washington split the national championship in the AP and Coaches' polls, the Bowl Coalition was founded. ", "The Coalition consisted of six bowls, with the Orange, Fiesta, Cotton, and Sugar bowls were all considered potential hosts for a national championship game. ", "Since three of these bowls already had specific tie-ins with conferences, an agreement was struck where the conferences would agree to release those teams from their contractual obligations in order to achieve a #1 vs #2 matchup. ", "For the first two years of the Coalition, this did occur without incident as the Sugar and Orange Bowls in 1993 and 1994 featured #1 vs. #2 matchups in their respective games.", "\n\nThe problem with this as far as 1994 was concerned was that the Rose Bowl, which featured the Pac-10 and Big Ten champions playing each other, was not included in the Coalition and thus a team that finished #1 or #2 in the polls from those two conferences could not be considered by the Coalition to be its national champion. ", "Nebraska, as a member of the Big Eight Conference, was part of the coalition while Penn State was not. ", "As Nebraska went on to win the conference title, it earned an automatic bid to the Orange Bowl to face off against #3 Miami, who won the Big East title and was #2 in the Coalition pool. ", "Thus Miami, who as recently as two years earlier was in the Coalition championship game, had a chance to stake a claim as the national champion with a win (as they would have been awarded the Coaches' Trophy) and all but ensure a split title with Penn State provided they defeated #13 Oregon in the Rose Bowl.", "\n\nOn January 1, 1995, Nebraska defeated Miami in the Orange Bowl 24-17 and clinched the championship. ", "The next day Penn State defeated Oregon in the Rose Bowl by a count of 38-20 and secured the #2 spot in the polls.", "\n\nIn the offseason that followed, the Bowl Coalition was disbanded and in its place came the Bowl Alliance, which attempted to serve the same purpose by rotating a national championship game between the Sugar, Fiesta, and Orange Bowls. ", "Like the Bowl Coalition before it, the Bowl Alliance did not include the Rose Bowl and two of the three national championship games did not feature a #1 vs. #2 matchup, with the 1997 season seeing another split national championship.", "\n\nConference and program changes\nThe number of teams in Division 1-A grew to 107 as Northeast Louisiana University left Division I-AA's Southland Conference and became an independent.", "\n\nSouthwest Conference announces dissolution\nIn February 1994, before the season began, an announcement was made regarding the future of the Southwest Conference. ", "In 1991, the SWC became an all-Texas conference as Arkansas left the SWC to join the Southeastern Conference. ", "As 1994 began Texas was rumored to be considering joining the Pac-10 with Big Eight member Colorado (rumors that would resurface over a decade later, which eventually resulted in Colorado joining the Pac-10 with Utah to form the Pac-12), while Texas A&M was reported to be looking at joining the SEC (which they would eventually do in 2012). ", "On February 25, 1994, it was announced that Texas, Texas Tech, Texas A&M, and Baylor would be joining with all eight of the teams in the Big Eight to form the Big 12 Conference, in 1996. ", "Following this decision, another decision was made regarding the future of remaining SWC members SMU, Houston, TCU, and Rice; SMU, TCU, and Rice would join the Western Athletic Conference while Houston joined Conference USA. (", "Of the schools that joined the Big 12, as noted, the only one that did not stay in the conference was Texas A&M. TCU, SMU, and Rice all eventually became part of Conference USA as well, with TCU being the first to join while the other three schools joined as part of the 2005 conference realignment. ", "TCU left for the Mountain West Conference in 2005 and eventually joined their former SWC brethren in the Big 12, while SMU and Houston became part of the American Athletic Conference in 2013 with the former Big East football schools that were still in the conference. ", "Rice still plays in C-USA.)", "\n\nHeisman Trophy\nThe 1994 Heisman Trophy presentation ceremony was held on December 10, 1994, at the Downtown Athletic Club in New York City. ", "The five finalists were:\n\nJay Barker, quarterback, Alabama\nKi-Jana Carter, running back, Penn State\nKerry Collins, quarterback, Penn State\nSteve McNair, quarterback, Alcorn State\nRashaan Salaam, running back, Colorado\n\nWarren Sapp from Miami was the 6th finalist and also attended the ceremony.", "\n\nMcNair's nomination as a finalist was a rare feat, as Alcorn State was a member of Division I-AA and I-AA awarded the Walter Payton Award to its most outstanding player (which McNair won).", "\n\nThe Heisman voters awarded the trophy to Salaam, who also won the Walter Camp Award and the Doak Walker Award. ", "Salaam received 400 first place votes and 1743 total points, 842 more than second-place Carter. ", "McNair finished third, sixteen points ahead of Collins, and Barker finished a distant fifth.", "\n\nOther players receiving votes were Miami defensive tackle Warren Sapp, Georgia quarterback Eric Zeier, Nebraska running back Lawrence Phillips and offensive tackle Zach Wiegert, and Washington running back Napoleon Kaufman.", "\n\nNotable games\nThe Miracle at Michigan: in a September 24 matchup between #4 Michigan and #7 Colorado, the visiting Buffaloes trailed the host Wolverines 26-14 with 2:16 remaining in the game. ", "Colorado scored two touchdowns in the final minutes, the last being a 64-yard pass from Kordell Stewart to Michael Westbrook on the last play of the game.", "\nChoke at Doak: In the annual matchup between Florida and Florida State, the visiting Gators led the defending national champion Seminoles 31-3 entering the fourth quarter. ", "Florida State rallied to score four touchdowns in the final period, but ran out of time to potentially score the winning points on their last possession and the game ended in a 31-31 tie.", "\nPenn State-Indiana: Despite beating #21 Ohio State 63-14 in Happy Valley on October 29, Penn State surprisingly dropped to #2 in the subsequent AP poll after #3 Nebraska defeated #2 Colorado 24-7. ", "The Nittany Lions remained #1 in the CNN/USA Today Coaches poll by a small margin. ", "Penn State traveled to Indiana for their next game and took a comfortable 35-14 lead in the fourth quarter. ", "Penn State coach Joe Paterno elected to pull his starters with the lead, which allowed Indiana to score two touchdowns late in the game including a deflected Hail Mary and two-point conversion with no time on the clock. ", "Penn State won 35-29, but fell further behind Nebraska in the AP poll and dropped to #2 in the CNN/USA Today coaches poll as well. ", "The Indiana game is often cited erroneously as the single point at which Nebraska passed Penn State, but the reality is that the Nittany Lions fell to #2 in the AP poll a week prior to that game.", "\n\nOther notes\nAfter being played for the first two years at Legion Field in Birmingham, Alabama, the SEC Championship Game moved to its now-permanent home in Atlanta's Georgia Dome. ", "Meanwhile, in Jacksonville, the demolition and reconstruction of Gator Bowl Stadium that coincided with the Jacksonville Jaguars' entry into the NFL for 1995 forced the Gator Bowl to moved to Ben Hill Griffin Stadium in Gainesville for its 1994 playing. ", "The game would return to Jacksonville in the newly built Jacksonville Municipal Stadium the following year. ", "Also, John Hancock Insurance's deal for naming rights to the Sun Bowl expired and the game reverted to its former name.", "\n\nAlthough Nebraska, Penn State and Alabama were still ranked in the Top 10, many of college football's legendary teams finished the regular season with their lowest rankings in years. ", "Ohio State finished the season ranked #14 in the AP poll while Michigan was #20 and USC #21. ", "Notre Dame, which started the season ranked fourth, finished the season unranked as did preseason #16 Oklahoma.", "\n\nRule changes\nDue to several fighting incidents that occurred during the 1993 season (including one between the Miami Hurricanes and the Colorado Buffaloes that resulted in 12 ejections), the following changes were made:\n Players involved in fighting on the field will draw a 15-yard penalty and an automatic ejection. ", " If the ejection occurs in the first half, the player(s) will be disqualified for the remainder of the game. ", " If the ejection occurs in the second half (or in overtime as of the 1996 season), the player(s) will be disqualified for the remainder of that game plus the first half of his team's next regularly scheduled game.", "\n Players leaving the bench to participate in fights will be ejected for the remainder of the game plus his team's entire next regularly scheduled game.", "\n Repeat offenders will be ejected and suspended for the remainder of the season.", "\n The officials' jurisdiction over games will begin 60 minutes before kickoff. ", " Any pre-game fights or taunting will be penalized the same as if the fight/taunting occurred during the game, with any yardage penalties enforced on the opening kickoff.", "\n The prohibition against \"offset uprights\" is deleted, reversing a 1985 rule. ", "LSU was allowed by the NCAA to place goalposts with offset uprights in Tiger Stadium late in the 1993 season in conjunction with its football centennial, soon Florida State would follow suit and install similar \"offset uprights\" goal posts.", "\n The use of officials from different conferences (\"split crews\") was outlawed, except for game contracts signed before January 1, 1994. ", "The NCAA extended the ban to all games before the 1998 season.", "\n\nConference standings\n\nBowl Coalition #1 and #2\nThe Bowl Coalition did not include the Big 10 and Pacific-10 conferences, whose champions played in the Rose Bowl. ", " Penn State, which was ranked #1 in the Oct 18 and Oct 25 polls, and #2 for the remainder of the season, finished the regular season 11-0-0 and played in the Rose Bowl as the champion of the Big Ten.", "\n\nBowl games\n\nOrange Bowl: #1 Nebraska 24, #3 Miami 17\nRose Bowl: #2 Penn State 38, #12 Oregon 20\n: #7 Florida State 23, #5 Florida 17\n: #21 USC 55, Texas Tech 14\nFiesta Bowl: #4 Colorado 41, Notre Dame 24\n: #23 NC State 28, #16 Mississippi State 24\n: #6 Alabama 24, #13 Ohio State 17\nHall of Fame Bowl: Wisconsin 34, #25 Duke 20\n: South Carolina 24, West Virginia 21\nSun Bowl: Texas 35, #18 North Carolina 31\nGator Bowl: Tennessee 45, #17 Virginia Tech 23\nCopper Bowl: #22 BYU 31, Oklahoma 6\nAlamo Bowl: #24 Washington State 10, Baylor 3\nHoliday Bowl: #20 Michigan 24, #10 Colorado State 14\n: #14 Utah 16, #15 Arizona 13\n: Illinois 30, East Carolina 0\nAloha Bowl: Boston College 12, #11 Kansas State 7\n: #18 Virginia 20, TCU 10\n: 52, Central Michigan 24\n\nFinal AP Poll\n\nNebraska\nPenn State\nColorado\nFlorida State\nAlabama\nMiami (FL)\nFlorida\nTexas A&M\nAuburn\nUtah\nOregon\nMichigan\nUSC\nOhio State\nVirginia\nColorado State\nN.C. State\nBYU\nKansas State\nArizona\nWashington State\nTennessee\nBoston College\nMississippi State\nTexas\n\nFinal Coaches Poll\n Nebraska\n Penn State\n Colorado\n Alabama\n Florida State\n Miami (FL)\n Florida\n Utah\n Ohio St.\n Brigham Young\n Oregon\n Michigan\n Virginia\n Colorado State\n Southern California\n Kansas State\n North Carolina State\n Tennessee\n Washington State\n Arizona\n North Carolina\n Boston College\n Texas\n Virginia Tech\n Mississippi State\n\nHeisman Trophy voting\nThe Heisman Memorial Trophy Award is given to the Most Outstanding Player of the year\n\nWinner:\n\nRashaan Salaam, Colorado, JR. ", "RB (1400 votes)\n2. ", "Ki-Jana Carter, Penn St., Jr. RB (1080 votes)\n3. ", "Steve McNair, Alcorn St., Sr. ", "QB (982 votes)\n4. ", "Kerry Collins, Penn St., Sr. ", "QB (392 votes)\n5. ", "Jay Barker, Alabama, Sr. ", "QB (294 votes)\n\nOther major awards\n\nMaxwell Award (College Player of the Year) – Kerry Collins, Penn State\nWalter Camp Award (Back) – Rashaan Salaam, Colorado\nDavey O'Brien Award (Quarterback) – Kerry Collins, Penn State\nDoak Walker Award (Running Back) – Rashaan Salaam, Colorado\nDick Butkus Award (Linebacker) – Dana Howard, Illinois\nLombardi Award (Lineman or Linebacker) – Warren Sapp, Miami\nOutland Trophy (Interior Lineman) – Zach Wiegert, OT, Nebraska\nJim Thorpe Award (Defensive Back) – Chris Hudson, Colorado\nAFCA Coach of the Year – Tom Osborne, Nebraska\nFWAA Coach of the Year – Joe Paterno, Penn State\nPaul \"Bear\" Bryant Award – Rich Brooks, Oregon\n\nReferences\n\n*" ]

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[ "Exploring regional variation in antipsychotic coprescribing practice: a Danish questionnaire survey.", "\nThe pharmacologic treatment of schizophrenia is characterized by excessive use of antipsychotic polypharmacy, which reflects a gap between evidence and practice. ", "The aim of the present study was to investigate regional differences in treatment setting characteristics and in physician and nurse attitudes toward antipsychotic polypharmacy and clinical guidelines. ", "Cross-sectional postal questionnaire survey directed to physicians and nurses at 2 pairs of treatment settings in Denmark, characterized by low and high prevalence of antipsychotic polypharmacy, respectively. ", "The questionnaire investigation was conducted during November 2007 to February 2008. ", "Satisfactory response rates were obtained (physicians: 93%; nurses: 87%). ", "The treatment settings with low use of antipsychotic polypharmacy were characterized by raised knowledge/awareness of local antipsychotic treatment guidelines (P = .02 for physicians; P = .01 for nurses). ", "Among physicians, these settings were also characterized by an elevated confidence in these guidelines (P = .01), frequent local educational activities (P < .0001), and increased recent involvement in research (P = .01). ", "Among nurses, a perception of an overwhelming work load (P = .01) and time pressure (P = .003) was significantly more prevalent in treatment settings with high rates of antipsychotic coprescribing, as was the belief in the benefit of antipsychotic polypharmacy augmentation (P = .001). ", "Albeit no causal relationships can be inferred from this cross-sectional observational study, we recommend the furtherance of a treatment environment characterized by easily accessible clinical guidelines, frequent academic activities, and an unruffled atmosphere." ]

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[ "Transgenic plants with improved agronomic traits such as yield, environmental stress tolerance, pest resistance, herbicide tolerance, improved seed compositions, and the like are desired by both farmers and consumers. ", "Although considerable efforts in plant breeding have provided significant gains in desired traits, the ability to introduce specific DNA into plant genomes provides further opportunities for generation of plants with improved and/or unique traits. ", "Merely introducing recombinant DNA into a plant genome doesn't always produce a transgenic plant with an enhanced agronomic trait. ", "Methods to select individual transgenic events from a population are required to identify those transgenic events that are characterized by the enhanced agronomic trait." ]

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[ "Cuts would have broad impact on arts\n\nArts education projects and cultural programs aimed at diverse communities would come under the ax through Mecklenburg County's proposed budget. ", "Arts groups already hit by sharp funding cuts from the Arts & Science Council would feel a further squeeze. ", "And the future of uptown's Spirit Square would be in question.", "\n\nThe spending plan presented Monday would affect three programs the county supports through the ASC.", "\n\nFunding for arts projects in Charlotte-Mecklenburg Schools would shrink from the current year's $349,600 to zero.", "\n\nMoney for cultural programs aimed at multicultural audiences would go from $406,600 to zero.", "\n\nBe the first to know.", "\n\nNo one covers what is happening in our community better than we do. ", "And with a digital subscription, you'll never miss a local story.", "\n\nSupport for Spirit Square, which the county owns but Blumenthal Performing Arts Center manages, would fall from this year's $1,051,808 to $750,000 - a 29 percent drop.", "\n\nThe cuts would force the ASC to rein in programs that reach across Mecklenburg, ASC President Scott Provancher said Tuesday. ", "The programs tie in with priorities the county has identified - such as serving the county's cultural diversity.", "\n\nWithout the county's support, Provancher said, the ASC would have to eliminate a program that funds events targeted for African-American, Asian, Latino and Native American culture. ", "The activities have included a showcase of Vietnamese folk tales; performances for American Indian Heritage Month; and an eight-week program on African drumming and dance based in the Hampton Park neighborhood.", "\n\n\"We built that program to meet ... what the county was looking for,\" Provancher said.", "\n\nWhile many of the events have been produced by community groups such as YMCA branches, Provancher said, some of the 26 main groups the ASC supports have also taken part. ", "The loss of the county money would mean a 4 percent reduction in the pool of money available for them.", "\n\n\"In and of itself, a 4 percent reduction is not devastating,\" Provancher said. ", "But the groups already suffered sharp cuts in their ASC support last year after the recession crimped fundraising. ", "The additional cut would intensify their challenges.", "\n\nWithout the county's contribution for arts-education projects, the ASC would have about 40 percent less money to spend on them next year, Provancher said. ", "It would have to eliminate a program that gives each CMS school a few thousand dollars to bring in projects that dovetail with the school's curriculum - such as workshops, demonstrations or hands-on activities for students.", "\n\nBecause these programs serve needs that county leaders have emphasized, the ASC hopes to persuade them to restore at least some of the funding, Provancher said. ", "It may be possible, he added, to leverage county money to draw support from donors - linking in with Charlotte's long tradition of public-private partnerships.", "\n\n\"We understand the challenges the county is going through,\" Provancher said. \"", "We also think the ASC is delivering real value to the community.\"", "\n\nWith Spirit Square, the county intends to revive discussions that began a few years ago about redeveloping the building, county management analyst Faith Leach said.", "\n\nThe $750,000 called for in the spending plan would be enough to operate the center for at least six months. ", "During that time, county leaders will host discussions with the ASC and Blumenthal Center about longer-term plans for the building, which adjoins a 19th-century church sanctuary.", "\n\nIn the meantime, Provancher said, the ASC hopes to find ways to keep Spirit Square \"operating and vibrant with the resources that are there.\"" ]

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[ "After what the automaker called an “online unveiling” last month for its new Revero, a plug-in sedan based on the defunct Fisker Karma, Karma Automotive officially launches the Revero today. ", "For the occasion, the company released all the specs of its plug-in hybrid and it revealed an updated interior.", "\n\nFirst surprise, the Revero actually starts at $130,000 and not $115,000 as previously thought. ", "How does Karma justify the price tag? ", "After all, for the same price you can get a Tesla Model S P100D that can go 0 to 60 mph in 2.5 seconds and has a range of 315 miles.", "\n\nThe company is betting on its new revamped interior featuring a more luxurious look and unique features like reclaimed wood from different sources resulting in interior wood trim “straight from nature”.", "\n\nThe infotainment system also received a complete redesign from the original Fisker and the vehicle now has the capacity to receive over-the-air software updates. ", "It looks like one of the first updates to come will be to support both Apple Car Play and Android Auto coming in 2017, according to the company.", "\n\nKarma released pictures of the interior for the first time:\n\nAs for the powertrain, Karma is predicting an all-electric range of about 50 miles on the 21.4 kWh LiFePO battery pack mounted in the center of the vehicle – like in the original Fisker Karma. ", "The gas engine can bring the range up to about 300 miles.", "\n\nThe Revero can accelerate from 0 to 60 mph in 5.4 seconds and it features a software-limited top speed of 125 mph.", "\n\nA surprise with the official launch, Karma is adding the capability for DC fast-charging up to 40 kW. The automaker says that it bring the State Of Charge to 80% in 24 minutes on 480 V at 110 amps.", "\n\nKarma plans to start production by the end of the year with a slow ramp up – starting with about 900 Reveros during its first year of production.", "\n\nHere’s the brochure with the new spec sheet at the end:\n\nFTC: We use income earning auto affiliate links. ", "More.", "\n\nSubscribe to Electrek on YouTube for exclusive videos and subscribe to the podcast." ]

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[ "Pete Raymond\n\nPeter \"Pete\" Harlow Raymond (born January 21, 1947) is a beekeeper, father of two, and an American former rower who competed in the 1968 Summer Olympics and in the 1972 Summer Olympics. ", " He was born in Princeton, New Jersey and attended South Kent School and Princeton University.", "\n\nIn 1968, he was stroke of the American boat which finished fifth in the coxless four event.", "\nFour years later, he rowed #6 in the silver medal American eight in the 1972 eights competition.", "\nFrom 1974–85 he served as editor of The U. S. Rowing Association's magazineThe Oarsman which became the Rowing U.S.A. He was First Violin with the C.R.A.S.H.-B Marching Chamber Orchestra 1982–86. ", "He is a writer and English teacher at Noble and Greenough school.", "\n\nSee also\n List of Princeton University Olympians\n\nReferences\n\nCategory:1947 births\nCategory:Living people\nCategory:American male rowers\nCategory:Olympic rowers of the United States\nCategory:Olympic silver medalists for the United States in rowing\nCategory:People from Princeton, New Jersey\nCategory:Princeton University alumni\nCategory:Rowers at the 1968 Summer Olympics\nCategory:Rowers at the 1972 Summer Olympics\nCategory:South Kent School alumni\nCategory:Medalists at the 1972 Summer Olympics" ]

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[ "You've probably heard a lot about salmonella in reference to food poisoning, but the latest outbreak isn't about eating cooked animals - it's about touching live ones.", "\n\nThe Centers for Disease Control and Prevention announced that 93 people in a total of 23 states have been infected with strains of salmonella: specifically, strains known as Salmonella Infantis, Salmonella Newport, and Salmonella Lille. ", "Of those affected, 18 patients have been hospitalized and one death may be related to the outbreak under investigation too.", "\n\nA large portion - 37% - of the those infected are 10 years old or younger, according to the CDC.", "\n\nSalmonella infection causes bad diarrhea generally. ", "But in some people - especially young children, elderly persons or those who have weakened immune systems - can have more serious symptoms and even die.", "\n\nThe origin of this outbreak appears to be chicks and ducklings that came from a mail-order hatchery in Ohio, public health officials have determined. ", "The hatchery was also implicated in a 2011 outbreak of salmonella infections. ", "This month, veterinarians inspected the hatchery and made recommendations to improve conditions.", "\n\nMany of the people who got sick in this outbreak were buying poultry for backyard flocks, for eggs and meat, said Dr. Ian Williams, Chief of the Outbreak Response and Prevention Branch at the CDC. ", "Chicken and ducks can appear perfectly healthy but still shed salmonella in their droppings.", "\n\n\"If you don't wash your hands carefully after you're handling your chickens and cleaning up after them, you can bring salmonella into the house and contaminate the foods you eat,\" Williams said.", "\n\nIn the last couple of years, there has been increasing interest in people keeping poultry in their backyard, a trend that may contribute to this outbreak, Williams said. ", "There is also better detection of salmonella throughout the United States through a surveillance network called PulseNet.", "\n\nThe CDC has several tips for keeping safe around live poultry: Wash your hands thoroughly with soap and water after you touch these animals, and don't let children under 5 handle them. ", "That's because they may snuggle with the chicks or kiss them, which can transmit bacteria, says Williams. ", "The CDC also discourages giving small chicks as presents to children. ", "The agency also recommends against keeping live poultry inside your house. ", "It's best for everyone if the birds live outside." ]

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[ "Q:\n\nCannot apply multi background color to material ui snackbar\n\nHow to apply multi background color to material UI snackbar? ", "I tried with linear-gradient as mentioned below but it doesn't work.", "\nimport Snackbar from 'material-ui/Snackbar';\n\nconst bodyStyle = {\n border: `2px solid ${config.actualWhite}`,\n minWidth: '50%',\n maxWidth: '100%',\n height:'55px',\n backgroundColor: 'linear-gradient(to right bottom, #00897B, #FFE082)',\n fontFamily: config.fontFamily,\n fontStyle: config.fontStyle,\n fontWeight: config.fontWeight,\n fontSize: config.fontSize\n}\n\n<Snackbar\n open={this.state.openLogout}\n message=\"You are Successfuly loggedout! ", "Thanks for being part of web Family!\"", "\n autoHideDuration={4000}\n bodyStyle={bodyStyle}\n action=\"Close\"\n onRequestClose={this.handleRequestClose}\n onActionTouchTap={this.handleRequestClose}\n style={myTheme.snackbarfromTop}\n/>\n\nSnackbar screenshot\n\nA:\n\nmaterial-ui v0\nYou've got a slight error in your CSS. ", "Specifically, backgroundColor should be background because the linear-gradient function returns an image, not a color. ", "So, you should have:\nconst bodyStyle = {\n border: `2px solid ${config.actualWhite}`,\n minWidth: '50%',\n maxWidth: '100%',\n height:'55px',\n // Note the change to background here\n background: 'linear-gradient(to right bottom, #00897B, #FFE082)',\n fontFamily: config.fontFamily,\n fontStyle: config.fontStyle,\n fontWeight: config.fontWeight,\n fontSize: config.fontSize\n}\n\nNote that you should consider making the switch to the v1-beta, which should be promoted to the stable version sometime in early 2018. ", "I describe the appropriate solution for that below.", "\nmaterial-ui v1\nChanging the backgroundColor of a Snackbar works but will have no visible effect because the entire Snackbar is filled by one of it's children, SnackbarContent, and that child has it's background hardcoded in the source. ", "By default, that backgroundColor is set to:\nconst backgroundColor = theme.palette.shades[reverseType].background.default;\n\nSo, what's happening is that your desired gradient background is being covered up by the child.", "\nTo fix this, you need to use the SnackbarContentProps described in the Snackbar API to override the backgroundColor in the child:\nconst styles = theme => ({\n myCustomBackground: {\n background: 'linear-gradient(to right bottom, #00897B, #FFE082)',\n },\n});\n\n<Snackbar\n SnackbarContentProps={{\n className: classes.myCustomBackground,\n }}\n/>\n\nThe SnackbarContentProps are spread down to the child (visible on line 252 of the source as of December 2017), so everything you put in that object will become a prop to the SnackbarContent child. ", "Here, you're setting the child's className property to myCustomBackground so that it will display your desired gradient instead of the default.", "\nHere are a couple of other points to note:\n\nI've left off all the other props and styling to keep the example as condensed as possible.", "\nGradient backgrounds must be set with the background CSS attribute instead of the backgroundColor attribute because gradients are images, not colors.", "\n\n" ]

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[ "Tag: Pakistan Idol\n\nThe world biggest singing reality show- “IDOL” . ", "After mesmerizing 460 million viewers in over 150 countries worldwide from many years. ", "It is now comes in Pakistan with Pakistan Idol. ", "Pakistan Idol is here to offer you …" ]

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[ "Q:\n\nCapturing WM_MOUSEMOVE events in parent window\n\nI have a (parent) window in which a child-window is created by a another library (Ogre3d). ", "Window initialization uses the bare Win32 API.", "\nI'd like to capture the mouse input in my parent window, but it seems like I my WM_MOUSEMOVE events are received only by the child-window, which makes sense, since that fills all of my client-area.", "\nIs there a way to capture the WM_MOUSEMOVE messages in the parent window or (unintrusively) redirect those messages from the child-window?", "\n\nA:\n\nIf you can obtain a handle to the window in question you can subclass it. ", " \nIn a nutshell, you get to register a callback function that gets a crack at all of the messages sent to the sub-classed window. ", "\nThe linked article should get you where you need to be.", "\n\n" ]

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[ "The first business inside the new Bluffs at Glade Path development behind the Beaver Valley Mall opened on Monday.", "\n\nCENTER TWP. — ", "The first business inside the new Bluffs at Glade Path development behind the Beaver Valley Mall opened Monday.", "\n\nHeritage Valley Health System announced in October 2017 it was building a new “medical neighborhood” in the development, which is 45 acres and will include a mix of residential and commercial properties.", "\n\nOfficially open for business as of Monday, Heritage Valley’s new facility is the eighth medical neighborhood it operates in the region. ", "The 59,000-square-foot facility is the largest such facility run by Heritage Valley.", "\n\nThe medical neighborhood facility will offer primary and specialty care for patients as well as a walk-in clinic, diagnostic imaging and lab services, and a four-room ambulatory surgery center that will open later this spring.", "\n\nIt also will offer outpatient surgical services in the areas of orthopedics, ophthalmology, otolaryngology, general surgery, gynecology, podiatry and urology.", "\n\nNorm Mitry, the president and chief executive officer of Heritage Valley, said in a news release that the company is proud to bring “high-quality, expanded health care services to Center Township.”", "\n\n“It is the commitment of our board of directors to ensure that the communities we serve have access to the services they need without having to make a trip to the hospital,” he said. “", "Our medical neighborhoods are at the heart of meeting those needs.”", "\n\nHeritage Valley currently operates medical neighborhood facilities in Chippewa Township, Ellwood City, Moon Township, Robinson Township, Edgeworth, West Allegheny and Calcutta, Ohio. ", "The new facility is located at 79 Wagner Road.", "\n\nWhile the Heritage Valley facility was the first business to open in the Bluffs at Glade Path, it won’t be the last. ", "The development is slated to feature hundreds of apartments and condominiums, as well as a $20 million cancer center built by Allegheny Health Network.", "\n\nThe Allegheny Health Network facility is slated to open later this year." ]

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[ "1. ", "Field of the Invention\nThe present invention is directed to a drug delivery system and, in particular, to a closed loop system and method for controlling muscle activity by infusion of drugs, e.g., antispasmodic drugs, via an intrathecal/intraspinal catheter.", "\n2. ", "Description of Related Art\nMuscle disorders can have debilitating effects on an individual's daily life. ", "It is desirable to administer drugs to reduce or control undesirable muscle activity. ", "By way of example, spasticity is an abnormal involuntary muscle activity with increased muscle tone (rigidity) and sustained muscle contractions (spasm) caused by damage to the central nervous system resulting, for example, from a spinal cord or head injury. ", "Often spasticity is but a symptom associated with a disorder such as multiple sclerosis, cerebral palsy, stroke, Parkinson's or Epilepsy.", "\nThere is a widespread degree of spasticity ranging from moderate to severe. ", "Moderate spasticity may have little interference in the patient's normal life and typically is controlled by physical therapy and/or oral muscle relaxants. ", "Patients that suffer from severe spasticity may be treated by way of intrathecal therapy administering the drug directly to the spinal subarachnoid space via an implantable pump. ", "There are two main types of pumps that can be implanted for administration of drug via the intrathecal catheter. ", "A fixed rate pump may be used to control the drug dosage, but this device does not permit dosage adjustment. ", "Alternatively, a pump may be used that is capable of being programmed by a physician via an external battery powered computer to alter the drug dosage. ", "This, however, is still disadvantageous in that it requires a physician or clinician to adjust or control the drug dosage. ", "It would be desirable to adjust the drug dosage automatically without intervention by a physician or clinician.", "\nOther types of undesirable muscle activity may likewise have a negative impact on one' daily activities and life. ", "U.S. Pat. ", "No. ", "6,263,237 discloses a method for the treatment of anxiety disorders by brain stimulation and drug infusion. ", "Specifically, closed-loop feedback infusion of medicine and stimulation directly to the brain is disclosed in response to an electromyograph (EMG) sensor signal. ", "The EMG sensor signal detects anxiety disorder related symptoms, e.g., excessive muscle tension or tremors. ", "Since anxiety is controlled by the neural circuitry of the brain, the drug is delivered directly to the brain. ", "This patented method closed-loop feedback infusion of antianxiety drugs directly to the brain based on the detection of muscle activity is disclosed exclusively for the treatment of anxiety disorders.", "\nIt is therefore desirable to subside, reduce, eliminate or control muscle activity by developing a closed loop feedback drug delivery system for the infusion of a drug directly to the spinal cord the dosage of which is automatically controlled based on detected muscle activity without intervention by a physician or clinician." ]

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[ "Tashbulatovo\n\nTashbulatovo () is a rural locality (a selo) in Abzelilovsky District, Bashkortostan, Russia. ", "The population was 1,277 as of 2010. ", "There are 20 streets.", "\n\nReferences \n\nCategory:Rural localities in Bashkortostan" ]

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[ "Lake Powell Real Estate: Mountain View Subdivision\n\nLast week I had the opportunity to visit Mountain View Subdivision and spend an hour or so with the developer, Dean Slavens.", "\n\nPage is located in the remote, high deserts of Northern Arizona and Mountain View Subdivision does well to capture the “wilderness” feeling. ", "You are five minutes from Walmart, six from Safeway and downtown, but it feels like it could be hours.", "\n\nSet on the edge of Page, south of Ranchette Estates, this is a great place to get an affordable piece of Lake Powell real estate. ", "There are currently 14 lots for sale in the subdivision, between $41,900 and $45,900 and all at 5000 square feet or over. ", "These are perfect for manufactured and modular homes.", "\n\nThe lots all have views of the Vermilion Cliffs and Navajo Mountain as well as beautiful scenery to the south.", "\n\nMountain View Estates Subdivision\n\nClick Photos to Enlarge\n\nNavajo Mountain\n\nLooking Toward Glen Canyon\n\nAll utilities are curbside and ready for your Lake Powell Home. ", "Come to Page and see why Outdoor Magazine rated us in the TOP TEN places to live." ]

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[ "Agustín Codazzi (disambiguation)\n\nAgustín Codazzi may refer to:\nAgostino Codazzi, Italian military, veteran of Napoleonic Wars, scientist, geographer and cartographer\nAgustín Codazzi, Cesar, a Colombian town named after Codazzi, who died there\nGeographic Institute Agustín Codazzi, a Colombian cartographic institute" ]

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[ "For Students\n\nThe Spread of Islam in West Africa: Containment, Mixing, and Reform from the Eighth to the Twentieth Century\n\nAuthors\n\nMargari Hill\n\nThe history of Islam in West Africa can be explained in three stages, containment, mixing, and reform. ", "In the first stage, African kings contained Muslim influence by segregating Muslim communities, in the second stage African rulers blended Islam with local traditions as the population selectively appropriated Islamic practices, and finally in the third stage, African Muslims pressed for reforms in an effort to rid their societies of mixed practices and implement Shariah." ]

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[ "MUSKEGON, Mich. - A man allegedly stole several artifacts from a veterans museum over the weekend.", "\n\nSomeone stole a number of hats, buttons, medals and other items that were on display at the USS LST 393 Veterans Museum in Muskegon. ", "Staff at the museum believes they were taken on Saturday, August 3rd.", "\n\nMuseum manager Ike Villalpando first noticed something was wrong when he came in for work on Monday. ", "He first noticed items missing from the museum's Margaret Tolar exhibit. ", "A hat, multiple medals and a hat were taken from her area.", "\n\n“To the family that donated this, its priceless. ", "Its priceless,\" Villalpando says.", "\n\nOnce staff noticed that a thief had made the rounds, they contacted police. ", "After looking at surveillance video, police identified a person of interest in the case. ", "They want to speak to the man in the images, believing he likely knows something about the missing items.", "\n\nJohn Stephenson, who is on the museum's board of directors, says the theft is disheartening. “", "We put stuff in cases, behind plexiglass but you have to have a certain trust factor that people won’t take artifacts and dishonor the artifacts and veterans.”", "\n\nThe thief is believed to have taken items from multiple areas in the museum- including a purple heart medal that was in a display case.", "\n\nAnyone with information is asked to call the Muskegon Police Department at (231) 724-6750." ]

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[ "Event-related potential correlates of processing alcohol-related pictures in young adult binge drinkers.", "\nAlcohol-dependent individuals exhibit dissociable event-related potential (ERP) responses to alcohol-related cues. ", "Fewer studies have examined if similar effects can be found in non-dependent young adults who binge drink. ", "To delineate the neurocognitive correlates of inhibiting behavioral responses to alcoholic and non-alcoholic beverage cues in social drinkers with differing numbers of binge episodes and instances of intoxication. ", "ERP data were acquired while 50 participants performed a Go/No-go paradigm consisting of shapes and pictures of alcoholic and non-alcoholic beverages. ", "Behavioral and self-report data were also collected. ", "We grouped participants into those with: 0 binge episodes, 1 ≤ 5 binge episodes, and ≥ 8 episodes. ", "Across participants, alcohol images elicited reduced N200 components and a more positive late slow-wave than non-alcoholic images. ", "While the group with the higher number of binge episodes exhibited altered N100 amplitudes and both groups of binge drinkers exhibited minor differences in P300 topography, these effects were not specifically related to processing alcohol images. ", "However, participants with greater instances of intoxication exhibited an enhanced N200 to alcoholic stimuli compared to individuals with fewer instances of intoxication. ", "This effect was correlated with subjective ratings of alcoholic beverage images. ", "These data suggest that binge drinking, particularly more severe binge drinking, is associated with functional modifications of cortical systems related to attentional control. ", "Further, the data suggest that young adult social drinkers with riskier patterns of alcohol use (greater instances of intoxication) require the allocation of increased cortical resources to successfully inhibit responses to alcohol-related cues." ]

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[ "Q:\n\nAre REST API's really RESTful?", "\n\nI'm new to this game so I might be misunderstanding things. ", "Actually, if someone tells me that I'm misunderstanding things, it will be a favor. ", "Maybe this person will be considerate enough to show me the right path. ", "But...\nOne of the \"guidelines\" or \"best practices\" of REST as it applies to Web Services (http://en.wikipedia.org/wiki/Representational_state_transfer#Applied_to_web_services) is that you should use the proper HTTP methods when making calls (did I misunderstand it?) ", "to REST API's.", "\nBut looking at many API implementations on the web, what I see is that 100% of the calls made to them are actually GET calls that, depending on their URI, will be interpreted by the API as being of one of the HTTP verbs or methods. ", "\nSo, for example, looking at the REST API documentation for Twitter (https://dev.twitter.com/rest/public) which, in principle, only defines two verbs/methods (GET and POST), actually have all calls sent as GET and, based on the URI in the GET call, are interpreted by the API and acted upon.", "\nExample:\nGET statuses/lookup: https://api.twitter.com/1.1/statuses/lookup.json\nPOST statuses/update (PUT?): ", "https://api.twitter.com/1.1/statuses/update.json\nIn both cases, the call itself was made using GET and the last part of the URI defined it as a real GET or as a POST.", "\nIn summary, to be truly RESTful, shouldn't client side implementations of REST API's for web services use the proper HTTP verbs/methods?", "\nWhat am I missing?", "\n\nA:\n\nYou're missing a lot, but don't worry about it, most people are.", "\nThe fact is that very few so-called REST APIs publicly available on the internet are really RESTful, mostly because they are not hypertext driven. ", "REST became a buzzword to refer to any HTTP API that isn't SOAP, so don't expect for an API to really be RESTful just because it says it's a REST API. ", "I recommend reading this answer.", "\nFrom my experience, most API developers aren't aware what REST really is and believe any HTTP API that uses HTTP and avoids verbs in URIs is REST.", "\nREST is defined by a set of constraints. ", "Among them is the uniform interface, which in simple terms means that you should not change the expected behavior of the underlying protocol. ", "REST isn't coupled to any particular protocol, but since it's common to be used with HTTP, they get convoluted sometimes.", "\nHTTP has very well defined semantics for the GET, POST, PUT, DELETE, PATCH and HEAD methods, and the POST method has its semantics determined by the server. ", "Ideally, a REST API should respond to the methods other than POST exactly as determined in the RFC 7231, but as you noticed, there are many APIs who call themselves REST but don't do that. ", "This happens for many reasons. ", "Sometimes there's a simple misunderstanding about the correct semantics, or it's done to keep consistency, or because of backwards compatibility with intermediaries that don't support all methods, and many other reasons.", "\nSo, there's a lot more that has to be done to be truly RESTful other than using the HTTP methods correctly. ", "If an API doesn't get even that right, it needs to find another buzzword, because it's definitely not REST.", "\n\n" ]

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[ "Search\n\nI’ve somewhat prided myself on not being one of the “girlie girls.” ", "You know, the “can’t go to the corner store without my face beat for the GAWDS” kind of woman, for whom spending time and money on hair, shoes and makeup is a requisite, and not a nice add-on, for personality. ", "Included in my definition of “girlie girl” is an undying love of all things Carrie Bradshaw, she of “Sex and the City.” ", "Now don’t get me wrong. ", "I was tardy for the party but I have definitely enjoyed just about all six seasons’ worth of episodes of the show. ", "I’m speaking of the women who subscribe to the “Carrie, Charlotte, Samantha or Miranda” character in their lives, using these limited ideas to shape their narratives in love and careers. ", "The idea of forming my reactions to a dynamic, constantly shifting concept like relationship communication based on the static fictional characters was always a laugh.", "\n\nWhich is why when I came across “Mr. Big Syndrome Ruins Lives” from Luvvie Ajayi on Clutch this morning, I gave a huff and a shrug to the idea that seeking any kind of male character type from this show would be in good form. ", "In her post, Luvvie addresses the likelihood that the successful but relationship-challenged Mr. Big types will leave you high, dry and broken-hearted. ", "Personally, any woman past the age of say 24 that believes in a man that clearly has ulterior motives and back-burners you on a consistent basis needs to have her head examined.", "\n\nThe only person who I’ve known who could believe the best in a guy I would write off as a louse is my best friend from college, Chané. ", "She was one of the most ever-cheerful people I’ve known, especially when it came to love. ", "Despite the follies of relationships, and the inevitable disappointment of many of the men we dealt with as undergrad students and then wet-behind-the-ears 20-somethings, she never gave up her belief in that “can’t breathe it hurts so good” kind of love. ", "I’ve never believed in that, being far more pragmatic about human relationships. ", "But in instances like the dissolution of my first serious investment in the male species, she was the positive light in my den of negativity. ", "And it didn’t hurt that she had a squeal/scream (squeam?) ", "just like Sarah Jessica Parker gave her legendary role.", "\n\nWell, since I can’t be a Carrie Bradshaw, nor am I bitter enough for the Miranda, lustful enough for the Samantha or desperate enough for the Charlotte, I will continue to balance the desire for the damn near unattainable kind of passion from shows like Sex and the City and movies like The Notebook with the reality of the facts: sometimes men just don’t do passion. ", "They do pragmatics, they do the tangible. ", "But that concept (see, bringing in some of my research class terminology in this one!) ", "of “soul mate” eludes them. ", "So you must decide your strategy, and for the love of all things Carrie, stick to it!" ]

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[ "The International (play)\n\nThe International is a play by the American playwright John Howard Lawson. ", "It was first produced by the New Playwrights' Theatre in New York, opening on January 12 1928. ", "Lawson directed this production, while John Dos Passos designed the sets, Edward A. Ziman composed its music, Don Oscar Becque choreographed the dances, and Helen Johnson designed the costumes.", "\n\nCharacters\n Simeon Silas Fitch\n Edward Elliott Spunk\n Ethel\n David Fitch\n T. Jerome Henley\n Karneski\n Alise\n Rubeloff (Soviet Commissar)\n The Living Buddha of Lhasa\n Tim\n Madam Miau\n Gussie\n General Fitzmaurice (of the British Army)\n Monsieur Fouchard (of the French Ministry)\n Benjamin Krumb\n Marines\n Native Soldiers\n Gendarmes\n Workmen\n\nSources\n Lawson, John Howard. ", "1927. ", "The International. ", "New York: The Macaulay Company.", "\n\nExternal links\n \n\nCategory:1928 plays\nCategory:Broadway plays\nCategory:Plays by John Howard Lawson\nCategory:Modernist theatre" ]

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[ "In ethylene slurry polymerization processes, diluents such as hexane are used to dissolve the ethylene monomer, comonomers, and hydrogen. ", "The monomer(s) are polymerized with a catalyst.", "\nIn some multi-reactor cascade processes, monomer(s), hydrogen, catalyst and diluent are fed into a first reactor where a slurry forms from the polymer particles contained within the diluent and unreacted monomer. ", "The reactors can be operated in parallel or in series, and the types/amounts of monomer and conditions can be varied in each reactor to produce a variety of polyethylene materials, including unimodal (molecular weight distribution) or multimodal polyethylene material.", "\nZiegler type catalysts have been used in ethylene polymerization processes. ", "These catalysts use aluminum alkyl compounds as co-catalyst activators to activate titanium or vanadium sites on the catalyst. ", "The amount of co-catalyst present in the reactor affects the yields and selectivity of the ethylene slurry polymerization process.", "\nVarious compounds, such as oxygen-containing polar molecules, can poison Ziegler type catalysts, thereby degrading yields and selectivity. ", "These compounds can be contained as impurities in various feeds to the polymerization such as in the monomer(s), in the diluent, or in other feed streams.", "\nA need exists for multi-reactor ethylene slurry polymerization processes in the production of multimodal polyethylenes to (i) minimize the adverse effects of catalyst poisons on reactor yields and selectivity and (ii) ensure that polyethylenes of constant structure and composition are produced in each polymerization reactor." ]

{ "pile_set_name": "USPTO Backgrounds" }

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[ "/*\n * searchtools.js_t\n * ~~~~~~~~~~~~~~~~\n *\n * Sphinx JavaScript utilities for the full-text search.", "\n *\n * :copyright: Copyright 2007-2018 by the Sphinx team, see AUTHORS.", "\n * :license: BSD, see LICENSE for details.", "\n *\n */\n\n\n/* Non-minified version JS is _stemmer.js if file is provided */ \n/**\n * Porter Stemmer\n */\nvar Stemmer = function() {\n\n var step2list = {\n ational: 'ate',\n tional: 'tion',\n enci: 'ence',\n anci: 'ance',\n izer: 'ize',\n bli: 'ble',\n alli: 'al',\n entli: 'ent',\n eli: 'e',\n ousli: 'ous',\n ization: 'ize',\n ation: 'ate',\n ator: 'ate',\n alism: 'al',\n iveness: 'ive',\n fulness: 'ful',\n ousness: 'ous',\n aliti: 'al',\n iviti: 'ive',\n biliti: 'ble',\n logi: 'log'\n };\n\n var step3list = {\n icate: 'ic',\n ative: '',\n alize: 'al',\n iciti: 'ic',\n ical: 'ic',\n ful: '',\n ness: ''\n };\n\n var c = \"[^aeiou]\"; // consonant\n var v = \"[aeiouy]\"; // vowel\n var C = c + \"[^aeiouy]*\"; // consonant sequence\n var V = v + \"[aeiou]*\"; // vowel sequence\n\n var mgr0 = \"^(\" + C + \")?\" ", "+ V + C; // [C]VC... is m>0\n var meq1 = \"^(\" + C + \")?\" ", "+ V + C + \"(\" + V + \")?", "$\"; // [C]VC[V] is m=1\n var mgr1 = \"^(\" + C + \")?\" ", "+ V + C + V + C; // [C]VCVC... is m>1\n var s_v = \"^(\" + C + \")?\" ", "+ v; // vowel in stem\n\n this.stemWord = function (w) {\n var stem;\n var suffix;\n var firstch;\n var origword = w;\n\n if (w.length < 3)\n return w;\n\n var re;\n var re2;\n var re3;\n var re4;\n\n firstch = w.substr(0,1);\n if (firstch == \"y\")\n w = firstch.toUpperCase() + w.substr(1);\n\n // Step 1a\n re = /^(.+?)(ss|i)es$/;\n re2 = /^(.+?)([^s])s$/;\n\n if (re.test(w))\n w = w.replace(re,\"$1$2\");\n else if (re2.test(w))\n w = w.replace(re2,\"$1$2\");\n\n // Step 1b\n re = /^(.+?)eed$/;\n re2 = /^(.+?)(ed|ing)$/;\n if (re.test(w)) {\n var fp = re.exec(w);\n re = new RegExp(mgr0);\n if (re.test(fp[1])) {\n re = /.$/;\n w = w.replace(re,\"\");\n }\n }\n else if (re2.test(w)) {\n var fp = re2.exec(w);\n stem = fp[1];\n re2 = new RegExp(s_v);\n if (re2.test(stem)) {\n w = stem;\n re2 = /(at|bl|iz)$/;\n re3 = new RegExp(\"([^aeiouylsz])\\\\1$\");\n re4 = new RegExp(\"^\" + C + v + \"[^aeiouwxy]$\");\n if (re2.test(w))\n w = w + \"e\";\n else if (re3.test(w)) {\n re = /.$/;\n w = w.replace(re,\"\");\n }\n else if (re4.test(w))\n w = w + \"e\";\n }\n }\n\n // Step 1c\n re = /^(.+?)y$/;\n if (re.test(w)) {\n var fp = re.exec(w);\n stem = fp[1];\n re = new RegExp(s_v);\n if (re.test(stem))\n w = stem + \"i\";\n }\n\n // Step 2\n re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;\n if (re.test(w)) {\n var fp = re.exec(w);\n stem = fp[1];\n suffix = fp[2];\n re = new RegExp(mgr0);\n if (re.test(stem))\n w = stem + step2list[suffix];\n }\n\n // Step 3\n re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;\n if (re.test(w)) {\n var fp = re.exec(w);\n stem = fp[1];\n suffix = fp[2];\n re = new RegExp(mgr0);\n if (re.test(stem))\n w = stem + step3list[suffix];\n }\n\n // Step 4\n re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;\n re2 = /^(.+?)(s|t)(ion)$/;\n if (re.test(w)) {\n var fp = re.exec(w);\n stem = fp[1];\n re = new RegExp(mgr1);\n if (re.test(stem))\n w = stem;\n }\n else if (re2.test(w)) {\n var fp = re2.exec(w);\n stem = fp[1] + fp[2];\n re2 = new RegExp(mgr1);\n if (re2.test(stem))\n w = stem;\n }\n\n // Step 5\n re = /^(.+?)e$/;\n if (re.test(w)) {\n var fp = re.exec(w);\n stem = fp[1];\n re = new RegExp(mgr1);\n re2 = new RegExp(meq1);\n re3 = new RegExp(\"^\" + C + v + \"[^aeiouwxy]$\");\n if (re.test(stem) || (re2.test(stem) && !(", "re3.test(stem))))\n w = stem;\n }\n re = /ll$/;\n re2 = new RegExp(mgr1);\n if (re.test(w) && re2.test(w)) {\n re = /.$/;\n w = w.replace(re,\"\");\n }\n\n // and turn initial Y back to y\n if (firstch == \"y\")\n w = firstch.toLowerCase() + w.substr(1);\n return w;\n }\n}\n\n\n\n/**\n * Simple result scoring code.", "\n */\nvar Scorer = {\n // Implement the following function to further tweak the score for each result\n // The function takes a result array [filename, title, anchor, descr, score]\n // and returns the new score.", "\n /*\n score: function(result) {\n return result[4];\n },\n */\n\n // query matches the full name of an object\n objNameMatch: 11,\n // or matches in the last dotted part of the object name\n objPartialMatch: 6,\n // Additive scores depending on the priority of the object\n objPrio: {0: 15, // used to be importantResults\n 1: 5, // used to be objectResults\n 2: -5}, // used to be unimportantResults\n // Used when the priority is not in the mapping.", "\n objPrioDefault: 0,\n\n // query found in title\n title: 15,\n // query found in terms\n term: 5\n};\n\n\n\n\n\nvar splitChars = (function() {\n var result = {};\n var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,\n 1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,\n 2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,\n 2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,\n 3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,\n 3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,\n 4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,\n 8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,\n 11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,\n 43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];\n var i, j, start, end;\n for (i = 0; i < singles.length; i++) {\n result[singles[i]] = true;\n }\n var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],\n [722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],\n [1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],\n [1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],\n [1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],\n [2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],\n [2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],\n [2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],\n [2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],\n [2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],\n [2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],\n [2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],\n [3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],\n [3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],\n [3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],\n [3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],\n [3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],\n [3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],\n [4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],\n [4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],\n [4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],\n [4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],\n [5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],\n [6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],\n [6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],\n [6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],\n [6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],\n [7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],\n [7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],\n [8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],\n [8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],\n [8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],\n [10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],\n [11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],\n [12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],\n [12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],\n [12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],\n [19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],\n [42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],\n [42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],\n [43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],\n [43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],\n [43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],\n [43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],\n [44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295],\n [57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274],\n [64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007],\n [65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381],\n [65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]];\n for (i = 0; i < ranges.length; i++) {\n start = ranges[i][0];\n end = ranges[i][1];\n for (j = start; j <= end; j++) {\n result[j] = true;\n }\n }\n return result;\n})();\n\nfunction splitQuery(query) {\n var result = [];\n var start = -1;\n for (var i = 0; i < query.length; i++) {\n if (splitChars[query.charCodeAt(i)]) {\n if (start !", "== -1) {\n result.push(query.slice(start, i));\n start = -1;\n }\n } else if (start === -1) {\n start = i;\n }\n }\n if (start !", "== -1) {\n result.push(query.slice(start));\n }\n return result;\n}\n\n\n\n\n/**\n * Search Module\n */\nvar Search = {\n\n _index : null,\n _queued_query : null,\n _pulse_status : -1,\n\n init : function() {\n var params = $.getQueryParameters();\n if (params.q) {\n var query = params.q[0];\n $('input[name=\"q\"]')[0].value = query;\n this.performSearch(query);\n }\n },\n\n loadIndex : function(url) {\n $.ajax({type: \"GET\", url: url, data: null,\n dataType: \"script\", cache: true,\n complete: function(jqxhr, textstatus) {\n if (textstatus !", "= \"success\") {\n document.getElementById(\"searchindexloader\").src = url;\n }\n }});\n },\n\n setIndex : function(index) {\n var q;\n this._index = index;\n if ((q = this._queued_query) !", "== null) {\n this._queued_query = null;\n Search.query(q);\n }\n },\n\n hasIndex : function() {\n return this._index !", "== null;\n },\n\n deferQuery : function(query) {\n this._queued_query = query;\n },\n\n stopPulse : function() {\n this._pulse_status = 0;\n },\n\n startPulse : function() {\n if (this._pulse_status >= 0)\n return;\n function pulse() {\n var i;\n Search._pulse_status = (Search._pulse_status + 1) % 4;\n var dotString = '';\n for (i = 0; i < Search._pulse_status; i++)\n dotString += '.';", "\n Search.dots.text(dotString);\n if (Search._pulse_status > -1)\n window.setTimeout(pulse, 500);\n }\n pulse();\n },\n\n /**\n * perform a search for something (or wait until index is loaded)\n */\n performSearch : function(query) {\n // create the required interface elements\n this.out = $('#search-results');\n this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);\n this.dots = $('<span></span>').appendTo(this.title);\n this.status = $('<p style=\"display: none\"></p>').appendTo(this.out);\n this.output = $('<ul class=\"search\"/>').appendTo(this.out);\n\n $('#search-progress').text(_('Preparing search...'));\n this.startPulse();\n\n // index already loaded, the browser was quick!", "\n if (this.hasIndex())\n this.query(query);\n else\n this.deferQuery(query);\n },\n\n /**\n * execute search (requires search index to be loaded)\n */\n query : function(query) {\n var i;\n var stopwords = [\"a\",\"and\",\"are\",\"as\",\"at\",\"be\",\"but\",\"by\",\"for\",\"if\",\"in\",\"into\",\"is\",\"it\",\"near\",\"no\",\"not\",\"of\",\"on\",\"or\",\"such\",\"that\",\"the\",\"their\",\"then\",\"there\",\"these\",\"they\",\"this\",\"to\",\"was\",\"will\",\"with\"];\n\n // stem the searchterms and add them to the correct list\n var stemmer = new Stemmer();\n var searchterms = [];\n var excluded = [];\n var hlterms = [];\n var tmp = splitQuery(query);\n var objectterms = [];\n for (i = 0; i < tmp.length; i++) {\n if (tmp[i] !", "== \"\") {\n objectterms.push(tmp[i].toLowerCase());\n }\n\n if ($u.indexOf(stopwords, tmp[i].toLowerCase()) !", "= -1 || tmp[i].match(/^\\d+$/) ||\n tmp[i] === \"\") {\n // skip this \"word\"\n continue;\n }\n // stem the word\n var word = stemmer.stemWord(tmp[i].toLowerCase());\n // prevent stemmer from cutting word smaller than two chars\n if(word.length < 3 && tmp[i].length >= 3) {\n word = tmp[i];\n }\n var toAppend;\n // select the correct list\n if (word[0] == '-') {\n toAppend = excluded;\n word = word.substr(1);\n }\n else {\n toAppend = searchterms;\n hlterms.push(tmp[i].toLowerCase());\n }\n // only add if not already in the list\n if (!", "$u.contains(toAppend, word))\n toAppend.push(word);\n }\n var highlightstring = '?", "highlight=' + $.urlencode(hlterms.join(\" \"));\n\n // console.debug('SEARCH: searching for:');\n // console.info('required: ', searchterms);\n // console.info('excluded: ', excluded);\n\n // prepare search\n var terms = this._index.terms;\n var titleterms = this._index.titleterms;\n\n // array of [filename, title, anchor, descr, score]\n var results = [];\n $('#search-progress').empty();\n\n // lookup as object\n for (i = 0; i < objectterms.length; i++) {\n var others = [].concat(objectterms.slice(0, i),\n objectterms.slice(i+1, objectterms.length));\n results = results.concat(this.performObjectSearch(objectterms[i], others));\n }\n\n // lookup as search terms in fulltext\n results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));\n\n // let the scorer override scores with a custom scoring function\n if (Scorer.score) {\n for (i = 0; i < results.length; i++)\n results[i][4] = Scorer.score(results[i]);\n }\n\n // now sort the results by score (in opposite order of appearance, since the\n // display function below uses pop() to retrieve items) and then\n // alphabetically\n results.sort(function(a, b) {\n var left = a[4];\n var right = b[4];\n if (left > right) {\n return 1;\n } else if (left < right) {\n return -1;\n } else {\n // same score: sort alphabetically\n left = a[1].toLowerCase();\n right = b[1].toLowerCase();\n return (left > right) ? ", "-1 : ((left < right) ? ", "1 : 0);\n }\n });\n\n // for debugging\n //Search.lastresults = results.slice(); // a copy\n //console.info('search results:', Search.lastresults);\n\n // print the results\n var resultCount = results.length;\n function displayNextItem() {\n // results left, load the summary and display it\n if (results.length) {\n var item = results.pop();\n var listItem = $('<li style=\"display:none\"></li>');\n if (DOCUMENTATION_OPTIONS.FILE_SUFFIX === '') {\n // dirhtml builder\n var dirname = item[0] + '/';\n if (dirname.match(/\\/index\\/$/)) {\n dirname = dirname.substring(0, dirname.length-6);\n } else if (dirname == 'index/') {\n dirname = '';\n }\n listItem.append($('<a/>').attr('href',\n DOCUMENTATION_OPTIONS.URL_ROOT + dirname +\n highlightstring + item[2]).html(item[1]));\n } else {\n // normal html builders\n listItem.append($('<a/>').attr('href',\n item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX +\n highlightstring + item[2]).html(item[1]));\n }\n if (item[3]) {\n listItem.append($('<span> (' + item[3] + ')</span>'));\n Search.output.append(listItem);\n listItem.slideDown(5, function() {\n displayNextItem();\n });\n } else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {\n var suffix = DOCUMENTATION_OPTIONS.SOURCELINK_SUFFIX;\n if (suffix === undefined) {\n suffix = '.txt';\n }\n $.ajax({url: DOCUMENTATION_OPTIONS.URL_ROOT + '_sources/' + item[5] + (item[5].slice(-suffix.length) === suffix ? '' : ", "suffix),\n dataType: \"text\",\n complete: function(jqxhr, textstatus) {\n var data = jqxhr.responseText;\n if (data !", "== '' && data !", "== undefined) {\n listItem.append(Search.makeSearchSummary(data, searchterms, hlterms));\n }\n Search.output.append(listItem);\n listItem.slideDown(5, function() {\n displayNextItem();\n });\n }});\n } else {\n // no source available, just display title\n Search.output.append(listItem);\n listItem.slideDown(5, function() {\n displayNextItem();\n });\n }\n }\n // search finished, update title and status message\n else {\n Search.stopPulse();\n Search.title.text(_('Search Results'));\n if (!", "resultCount)\n Search.status.text(_('Your search did not match any documents. ", "Please make sure that all words are spelled correctly and that you\\'ve selected enough categories.'));", "\n else\n Search.status.text(_('Search finished, found %s page(s) matching the search query.", "').replace('%s', resultCount));\n Search.status.fadeIn(500);\n }\n }\n displayNextItem();\n },\n\n /**\n * search for object names\n */\n performObjectSearch : function(object, otherterms) {\n var filenames = this._index.filenames;\n var docnames = this._index.docnames;\n var objects = this._index.objects;\n var objnames = this._index.objnames;\n var titles = this._index.titles;\n\n var i;\n var results = [];\n\n for (var prefix in objects) {\n for (var name in objects[prefix]) {\n var fullname = (prefix ? ", "prefix + '.' : '') ", "+ name;\n if (fullname.toLowerCase().indexOf(object) > -1) {\n var score = 0;\n var parts = fullname.split('.');", "\n // check for different match types: exact matches of full name or\n // \"last name\" (i.e. last dotted part)\n if (fullname == object || parts[parts.length - 1] == object) {\n score += Scorer.objNameMatch;\n // matches in last name\n } else if (parts[parts.length - 1].indexOf(object) > -1) {\n score += Scorer.objPartialMatch;\n }\n var match = objects[prefix][name];\n var objname = objnames[match[1]][2];\n var title = titles[match[0]];\n // If more than one term searched for, we require other words to be\n // found in the name/title/description\n if (otherterms.length > 0) {\n var haystack = (prefix + ' ' + name + ' ' +\n objname + ' ' + title).toLowerCase();\n var allfound = true;\n for (i = 0; i < otherterms.length; i++) {\n if (haystack.indexOf(otherterms[i]) == -1) {\n allfound = false;\n break;\n }\n }\n if (!", "allfound) {\n continue;\n }\n }\n var descr = objname + _(', in ') + title;\n\n var anchor = match[3];\n if (anchor === '')\n anchor = fullname;\n else if (anchor == '-')\n anchor = objnames[match[1]][1] + '-' + fullname;\n // add custom score for some objects according to scorer\n if (Scorer.objPrio.hasOwnProperty(match[2])) {\n score += Scorer.objPrio[match[2]];\n } else {\n score += Scorer.objPrioDefault;\n }\n results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]);\n }\n }\n }\n\n return results;\n },\n\n /**\n * search for full-text terms in the index\n */\n performTermsSearch : function(searchterms, excluded, terms, titleterms) {\n var docnames = this._index.docnames;\n var filenames = this._index.filenames;\n var titles = this._index.titles;\n\n var i, j, file;\n var fileMap = {};\n var scoreMap = {};\n var results = [];\n\n // perform the search on the required terms\n for (i = 0; i < searchterms.length; i++) {\n var word = searchterms[i];\n var files = [];\n var _o = [\n {files: terms[word], score: Scorer.term},\n {files: titleterms[word], score: Scorer.title}\n ];\n\n // no match but word was a required one\n if ($u.every(_o, function(o){return o.files === undefined;})) {\n break;\n }\n // found search word in contents\n $u.each(_o, function(o) {\n var _files = o.files;\n if (_files === undefined)\n return\n\n if (_files.length === undefined)\n _files = [_files];\n files = files.concat(_files);\n\n // set score for the word in each file to Scorer.term\n for (j = 0; j < _files.length; j++) {\n file = _files[j];\n if (!(", "file in scoreMap))\n scoreMap[file] = {}\n scoreMap[file][word] = o.score;\n }\n });\n\n // create the mapping\n for (j = 0; j < files.length; j++) {\n file = files[j];\n if (file in fileMap)\n fileMap[file].push(word);\n else\n fileMap[file] = [word];\n }\n }\n\n // now check if the files don't contain excluded terms\n for (file in fileMap) {\n var valid = true;\n\n // check if all requirements are matched\n if (fileMap[file].length !", "= searchterms.length)\n continue;\n\n // ensure that none of the excluded terms is in the search result\n for (i = 0; i < excluded.length; i++) {\n if (terms[excluded[i]] == file ||\n titleterms[excluded[i]] == file ||\n $u.contains(terms[excluded[i]] || [], file) ||\n $u.contains(titleterms[excluded[i]] || [], file)) {\n valid = false;\n break;\n }\n }\n\n // if we have still a valid result we can add it to the result list\n if (valid) {\n // select one (max) score for the file.", "\n // for better ranking, we should calculate ranking by using words statistics like basic tf-idf...\n var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));\n results.push([docnames[file], titles[file], '', null, score, filenames[file]]);\n }\n }\n return results;\n },\n\n /**\n * helper function to return a node containing the\n * search summary for a given text. ", "keywords is a list\n * of stemmed words, hlwords is the list of normal, unstemmed\n * words. ", "the first one is used to find the occurrence, the\n * latter for highlighting it.", "\n */\n makeSearchSummary : function(text, keywords, hlwords) {\n var textLower = text.toLowerCase();\n var start = 0;\n $.each(keywords, function() {\n var i = textLower.indexOf(this.toLowerCase());\n if (i > -1)\n start = i;\n });\n start = Math.max(start - 120, 0);\n var excerpt = ((start > 0) ? '...' : '') ", "+\n $.trim(text.substr(start, 240)) +\n ((start + 240 - text.length) ? '...' : '');", "\n var rv = $('<div class=\"context\"></div>').text(excerpt);\n $.each(hlwords, function() {\n rv = rv.highlightText(this, 'highlighted');\n });\n return rv;\n }\n};\n\n$(document).ready(function() {\n Search.init();\n});" ]

{ "pile_set_name": "Github" }

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[ "Southland Leisure Centre\n\nThe Southland Leisure Centre is an indoor leisure centre situated in the southwest community on Palliser in Calgary, Alberta. ", "The multipurpose recreational facility was built at the same time (although additions and redesigns have been made since) as the surrounding neighbourhood and is one of two leisure centres owned and operated by The City of Calgary.", "\n\nSouthland Leisure Centre provides a wide range of registered programs and drop-in programs and activities, including sports training, gymnastics, day camps, racquet sports, skating, dance, martial arts, so-pitch, hockey and skating lessons. ", "Southland also offers preschool programs including playschool, tot's gym time and more.", "\n\nFacilities\n\n Wave pool begins wide and shallow (much like a beach) progressively deepening into a regular swimming pool halved in width is the box-shaped \"deep end\" with a rope swing. (", "No diving). ", "\n Water park: A water park with a 500-gallon dump bucket, rope bridges, spray guns and other splash stations. ", " \n Water slides: Includes the \"red slide\" and \"blue slide\". ", " There are also 4 smaller slides in the water park area. ", "\n Rope swing: Use of the rope swing is allowed while the wave system is off. ", " \n Deepwater dive tank and diving board\n Hot tub.", "\n Steam room. ", "\n Two ice rinks, named after Joe Kryczka and Ed Whalen.", "\n Climbing Wall\n Weight room\n Multipurpose rooms named after communities in the area, sometimes called birthday rooms. ", "\n Rental Centre for floating aids, tubes, etc. ", "as well as selling pool equipment.", "\n\nAccess \nBy car, Southland Leisure Centre is accessible off of Southland Drive.", "\n\nBy bus, it can be accessed directly by bus route 56 from Southland Station.", "\n\nReferences\n\nExternal links\n The City of Calgary Leisure Centres\n\nCategory: Sports venues in Calgary" ]

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[ "Pilot Grove Township\n\nPilot Grove Township may refer to:\n\n Pilot Grove Township, Hancock County, Illinois\n Pilot Grove Township, Montgomery County, Iowa, in Montgomery County, Iowa\n Pilot Grove Township, Faribault County, Minnesota\n Pilot Grove Township, Cooper County, Missouri\n Pilot Grove Township, Moniteau County, Missouri\n\nCategory:Township name disambiguation pages" ]

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[ "Patient Radiation Exposure During Fluoro-Assisted Direct Anterior Approach Total Hip Arthroplasty.", "\nThis study sought to quantify the total patient radiation exposure during fluoro-assisted direct anterior approach (DAA) total hip arthroplasty (THA). ", "We hypothesized that the patient radiation exposure would fall within acceptable published limits for a 1-time patient exposure. ", "After institutional review board approval, we performed a retrospective chart review of consecutive unilateral primary DAA THAs at 2 institutions (N = 157) between 2012 and 2014 by a single fellowship-trained arthroplasty surgeon assisted by residents and fellows. ", "Incomplete dose reporting information was the sole exclusion criterion. ", "Patient electronic medical records were queried regarding exposure time (seconds), radiation emittance (mGy), and peak kilovoltage (kVp). ", "Descriptive statistics were calculated. ", "Pearson correlation coefficients were used to determine the correlation between variables. ", "Mean radiation dose for patient exposure measured 2.97 ± 1.63 mGy (range: 0.29-9.83). ", "Positive but weak linear relationship with radiation dose and body mass index (BMI; r = 0.34; P < .0002). ", "Average exposure time per procedure was 23.74 s (range: 11.3-61.7). ", "Average kVp per procedure was 75.38 (range: 65-86). ", "Average BMI was 28.32 (range: 16.6-39.8). ", "There was a significantly strong correlation between kVp and BMI (r = 0.75; P < .0001). ", "Total patient radiation exposure was nearly identical with previously published values for a screening mammogram (3 mGy) and 4 times less than that of a standard chest computed tomography (13 mGy). ", "Although it is difficult to ascertain the exact patient-absorbed radiation, our data suggest that a 1-time exposure during DAA THA is likely negligible and provides the surgeon with additional data for counseling patients preoperatively." ]

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[ "Prognostic risk factors for treatment decision in pT1a,b N0M0 HER2-positive breast cancers.", "\nAlthough outcomes for women with breast cancers may vary by biologic subtype, patients with T1a,b N0M0 tumors have an excellent prognosis across all subgroups. ", "HER2 overexpression occurs in 15-20% of primary breast tumors, and is associated with diminished disease-free and overall survival. ", "The anti-HER2 monoclonal antibody trastuzumab in combination with chemotherapy is an effective treatment for all stages of HER2 positive breast cancer (bc). ", "However, the absolute benefit decreases as the risk of recurrence lessens and no available randomized adjuvant trial has evaluated the role of trastuzumab in women with pT1a,b N0M0, HER2-positive breast tumors. ", "These findings may explain the debate about the appropriate indication for adjuvant chemotherapy plus trastuzumab in this setting of patients. ", "The aim of this review was to describe known and novel prognostic risk factors to be used for tailored treatment decision in pT1a,b N0M0 HER2-positive tumors. ", "Whether patients with small HER2-positive bc may be suitable for (chemo)therapy reduction strategies, the current available data cannot exclude the need for a more aggressive treatment in a small subset of these subjects. ", "Novel clinical prognostic factors such as interval cancer (IC) detection may help to address this clinically important controversy. ", "A multicenter population-based cancer registry study is currently evaluating whether IC detection may identify patients with pT1a N0M0 HER2-positive tumors in whom the rate of recurrence justifies consideration for use of conventional, trastuzumab-based chemotherapy regimens." ]

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[ "“Options on ETFs are exceptionally popular in the US market and the appetite for them in Europe is strong. ", "The listing of these contracts further diversifies Liffe’s product range and provides investors with new opportunities,” said Jonathan Seymour, the exchange’s director of equity derivatives.", "\n\nThe new options, which launch on February 18, will have contract sizes and expiry schedules common in other Liffe-listed equity options in both the UK and Europe. ", "Contracts on the iShares FTSE 100 ETF will be listed in London, while contracts referencing the DJ Euro Stoxx 50 fund will trade on Liffe’s Amsterdam market.", "\n\nFlexible versions of both contracts will also be accessible over the bourse’s BClear platform, which permits centralised clearing of similar wholesale over-the-counter equity derivatives trades.", "\n\nThis white paper looks at the Basel Committee's BCBS239 principles, also known as PERDARR (Principles for Effective Risk Data Aggregation and Risk Reporting), which comes into force from 1 January 2016." ]

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[ "/*\n * Copyright (c) Facebook, Inc. and its affiliates.", "\n *\n * This source code is licensed under the MIT license found in the\n * LICENSE file in the root directory of this source tree.", "\n */\n\npackage com.facebook.react.modules.network;\n\nimport okhttp3.OkHttpClient;\n\npublic interface OkHttpClientFactory {\n OkHttpClient createNewNetworkModuleClient();\n};\n" ]

{ "pile_set_name": "Github" }

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[ "Regulation of p27(kip1) mRNA expression by microRNAs.", "\np27(kip1) (p27) is a cell cycle inhibitor and tumor suppressor whose expression is highly regulated in the cell. ", "Low levels of p27 have been associated with poor prognosis in cancer. ", "Recently, several microRNAs have been described to control p27 expression in various tumor types. ", "In this chapter, we will provide an overview on the role of microRNAs in cancer, and will discuss how microRNAs regulate p27 expression and the implications for tumor progression." ]

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[ "When it comes to ice creams, Giani has enough of gyaan. ", "It tries to take the tried and tested route — vanilla, strawberry, pineapple and so on. ", "Their flavours are not out of the ordinary. ", "Punjabi Delight contains dry fruits and is one of their popular picks. ", "Along with traditional treats such as Kulfi Faluda and Royal Faluda, they have introduced many new varieties such as Premium Ice Cream, Italian Gelato (low fat), sundaes, Diet and Lite Desserts, Brownie Mousse, Cold Stone and many more. ..." ]

{ "pile_set_name": "Pile-CC" }

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[ "Irish Citizen, Bernard Doyle, a representative with the UNHCR\n\nIt’s still early days but it appears from the latest Wikileaks document release that an innocent Irish citizen, Bernard Doyle, was targeted by the NSA. ", "Doyle is currently the United Nations High Commissioner for Refugees (UNHCR) “Regional Representative for Central Asia.”", "\n\nLatest Wikileaks Release showing “NSA high priority targets for the UN”\n\nS2C32 is the NSA unit responsible for targeting the UN. ", "The heading “Information_Need” suggests that Doyle was targeted since 2003. ", "Most likely this was because during this time period, Doyle was “Head of UNHCR Sub-Office in Herat, Afghanistan.” ", "before moving on to be the UNHCR Representative in Iran in 2011. ", "The UNHCR does vital work in Afghanistan with over 1.4 million refugees supported through its support programs.", "\n\nUNHCR’s extensive work supporting refugees in Afghanistan and Pakistan\n\nNothing new here…\n\nRegular readers of the various post-Snowden releases will find it no surprise that NGOs, the UN or its various agencies (including the children’s agency UNICEF) have been targeted for digital penetration by the NSA and GCHQ.", "\n\nIndeed, a number of NGO workers in various parts of the world have reported to Security First that they have been targeted by Western governments/businesses for human intelligence penetration attempts — particularly in countries where they have significant interests.", "\n\nWhy do governments want to target NGOs?", "\n\nPrimarily because they have access to physical locations, people and information where government intelligence gathering operations cannot reach. ", "For example, many NGOs are the only organisation’s with reliable data on drone strikes. ", "This would be particularly useful for military planners.", "\n\nSo why does this matter?", "\n\nThis is why it matters.", "\n\nPolio, once nearly eradicated in Afghanistan and Pakistan — has re-emerged.", "\n\nIt re-emerged because US intelligence abused goodwill towards local NGOs in order to launch a fake polio eradication scheme to gather intelligence and DNA during the hunt for Bin Laden. ", "While no one is going to shed many tears over the death of a mass murderer —\n\nshort term tactical policy or intelligence/military objectives risk undermining long-term strategic aims.", "\n\nNGOs are increasingly collecting large amounts of data on the people who they are caring for (which many are struggling to properly collect, manage utilise and secure) and if it becomes increasingly seen by the recipients on the ground that the information is vulnerable to outside digital/human penetration, then the NGO worker on the ground becomes a target, people are killed and important projects with vital long-term strategy impact are damaged. ", "Already most NGO security professionals will recognise that they are being seen less and less as neutral observers and increasingly as targets for crime, arrest, kidnap, murder and terrorism. ", "Also, NGOs are increasingly concerned about sharing sharing sensitive security relevant information with other NGOs (as they don’t know if they can trust them), which means that many people die due to preventable incidents.", "\n\nAttacks on Aid Workers are rising. ", "Source: https://aidworkersecurity.org\n\nGlobally, reported attacks on aid workers (who are just one subset of the NGO community that also includes human rights defenders, environmental defenders etc) are on the increase and it this is happening all over the world.", "\n\nLocation of attacks on aid workers. ", "Source: https://aidworkersecurity.org\n\nWhat happens when local populations no longer think the UN and NGO communities are neutral\n\nEven if we set aside the moral argument about spying on people trying to genuinely do good for humanity and unfortunately just speak about realpolitik, policy-makers authorising intelligence operations against NGO’s need to consider the damage this may cause to their long-term ability to actually achieve their objectives. ", "For example, by abusing the UN or NGOs for intelligence operations in places like Afghanistan, Pakistan, Iran or Iraq, the policy-maker has damaged their neutrality and actually hampered their ability to conduct their work. ", "No matter what the latest Civil Military Cooperation (CIMIC) fad, modern militaries have generally shown themselves incapable of meeting the reconstruction and recovery needs of local populations without the help of the local and international NGO community. ", "The targeting of an innocent Irish citizen and the UNHCR is just another example of this short-term thinking which may potentially have devastating consequences for the millions of innocent refugees who rely on its services." ]

{ "pile_set_name": "OpenWebText2" }

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"recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 175 }, { "analysis_explanation": null, "end": 220, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 215 }, { "analysis_explanation": null, "end": 333, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 321 }, { "analysis_explanation": null, "end": 515, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 510 }, { "analysis_explanation": null, "end": 539, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 535 }, { "analysis_explanation": null, "end": 600, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 595 }, { "analysis_explanation": null, "end": 639, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 634 }, { "analysis_explanation": null, "end": 652, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 641 }, { "analysis_explanation": null, "end": 710, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 706 }, { "analysis_explanation": null, "end": 718, "entity_type": "DATE_TIME", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 714 }, { "analysis_explanation": null, "end": 760, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 749 }, { "analysis_explanation": null, "end": 889, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 878 }, { "analysis_explanation": null, "end": 902, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 894 }, { "analysis_explanation": null, "end": 1281, "entity_type": "NRP", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1274 }, { "analysis_explanation": null, "end": 1840, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1829 }, { "analysis_explanation": null, "end": 1853, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1845 }, { "analysis_explanation": null, "end": 1896, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 1894 }, { "analysis_explanation": null, "end": 2056, "entity_type": "PERSON", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 2047 }, { "analysis_explanation": null, "end": 3993, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 3982 }, { "analysis_explanation": null, "end": 4003, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 3995 }, { "analysis_explanation": null, "end": 4009, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4005 }, { "analysis_explanation": null, "end": 4017, "entity_type": "LOCATION", "recognition_metadata": { "recognizer_identifier": "SpacyRecognizer_139620637004608", "recognizer_name": "SpacyRecognizer" }, "score": 0.85, "start": 4013 }, { "analysis_explanation": null, "end": 4417, 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[ "est to -13 in -0.1, 4, 1, -5?", "\n-5\nWhich is the nearest to -2? ", " (a) 0.022 (b) -0.4 (c) 3\nb\nWhich is the nearest to 64? ", " (a) 0.3 (b) -5 (c) 0.7\nc\nWhich is the nearest to -2? ", " (a) -3/2 (b) -3 (c) 2 (d) 0.024\na\nWhich is the closest to -0.2? ", " (a) 5 (b) -7 (c) 2/9 (d) -2/5\nd\nWhich is the nearest to -2/3? ", " (a) 19 (b) -0.3 (c) -13\nb\nWhat is the closest to 2/7 in -0.42, -5, -3/4, 0?", "\n0\nWhich is the closest to -41? ", " (a) -6/11 (b) 2/7 (c) -0.1 (d) -0.5\na\nWhich is the nearest to -2/3? ", " (a) 1/7 (b) -1 (c) -11.68\nb\nWhich is the nearest to 0? ", " (a) 22 (b) -23 (c) 6 (d) -2\nd\nWhat is the closest to -2/5 in 11, 2, -0.1?", "\n-0.1\nWhich is the nearest to 265? ", " (a) 1 (b) 5 (c) 3 (d) -2/13\nb\nWhat is the closest to 1 in -4, 4, 3/4?", "\n3/4\nWhat is the closest to 4 in -2/7, -4, 2/7?", "\n2/7\nWhich is the closest to 0.1? ", " (a) -5 (b) 59 (c) -1/8\nc\nWhat is the nearest to 1/2 in -0.1, 4, 0.4, 91?", "\n0.4\nWhat is the nearest to 2/9 in 0.2, 0, 292?", "\n0.2\nWhat is the nearest to 1.7 in 1, -3/5, -2, 3?", "\n1\nWhich is the closest to 1? ", " (a) 2/5 (b) -2/7 (c) 2 (d) 2/15\na\nWhat is the nearest to 1 in 5, 0.4, -1/5, -5/4?", "\n0.4\nWhat is the nearest to 12 in 2, 0.02, 0.2, -1/3?", "\n2\nWhat is the closest to -2/5 in 0.5, -4/5, 1, -0.3?", "\n-0.3\nWhat is the closest to 0.1 in 0.1, -2/7, -5, 0.3?", "\n0.1\nWhich is the closest to 1/2? ", " (a) -0.1 (b) -3 (c) 25\na\nWhat is the closest to 1 in 1/8, -2/3, 9?", "\n1/8\nWhich is the closest to -2? ", " (a) 1 (b) -29 (c) -0.1\nc\nWhat is the closest to 1 in -53.4, -0.05, 0.4, -4?", "\n0.4\nWhat is the closest to -0.1 in 25, 0.4, -3, -2/17?", "\n-2/17\nWhich is the nearest to -59/9? ", " (a) -1/5 (b) -4 (c) 5\nb\nWhich is the closest to -2/29? ", " (a) 3 (b) 0 (c) 0.4 (d) 3/4\nb\nWhich is the closest to 0.1? ", " (a) 2 (b) -1/3 (c) 317 (d) -1\nb\nWhich is the nearest to -5? ", " (a) -6/7 (b) -7 (c) 1/6\nb\nWhich is the nearest to 1? ", " (a) 0 (b) -0.4 (c) 1709\na\nWhat is the closest to 12 in -1, 3, -13, 1/2?", "\n3\nWhat is the nearest to 2/5 in 0.4, 1/3, 2.1?", "\n0.4\nWhich is the nearest to 0.2? ", " (a) 4 (b) -39/14 (c) 0.5\nc\nWhat is the closest to -0.3 in 21, 2, 1.7?", "\n1.7\nWhich is the closest to 0? ", " (a) -0.5 (b) -0.39 (c) 2/19\nc\nWhat is the closest to -0.1 in -1, 1, -1/7, -7/4?", "\n-1/7\nWhich is the nearest to 3? ", " (a) -60 (b) -32 (c) -5\nc\nWhich is the closest to 4? ", " (a) 3/5 (b) -5 (c) 4 (d) 3\nc\nWhat is the closest to -3/134 in 0.2, 1, -1/9?", "\n-1/9\nWhich is the closest to -1? ", " (a) -1 (b) -2/9 (c) -2/7\na\nWhich is the closest to 2/3? ", " (a) -2 (b) -1 (c) 0 (d) -48\nc\nWhat is the nearest to -1/4 in 4, -0.3, 2, -33/14?", "\n-0.3\nWhich is the nearest to -644? ", " (a) 0.4 (b) -1/2 (c) -2\nc\nWhich is the nearest to -4? ", " (a) 2/3 (b) -4/3 (c) -0.3 (d) 4\nb\nWhat is the closest to -0.2 in 2, 0, -1/5, -7/34?", "\n-1/5\nWhich is the nearest to -0.06? ", " (a) 3 (b) -0.1 (c) 0.05\nb\nWhat is the nearest to 1 in 2, -10, -1?", "\n2\nWhich is the closest to -2/7? ", " (a) 1/4 (b) -34 (c) 5\na\nWhat is the nearest to 1/6 in -6/5, -97, -0.5?", "\n-0.5\nWhich is the closest to -5? ", " (a) 4 (b) 0.09 (c) -0.03 (d) -4\nd\nWhat is the closest to -0.09 in -2, -3/5, 0.01, -4?", "\n0.01\nWhich is the closest to -0.1? ", " (a) -0.5 (b) -9/2 (c) -4 (d) -2\na\nWhat is the nearest to 0.1 in -10, -1.1, 3?", "\n-1.1\nWhich is the nearest to 0? ", " (a) -49 (b) -0.3 (c) 0.17\nc\nWhat is the nearest to 6 in -6, 5, -1/5, 0?", "\n5\nWhich is the nearest to 2? ", " (a) 8 (b) -2 (c) -2/25 (d) 3\nd\nWhich is the closest to 2? ", " (a) -2 (b) 0.3 (c) 1/5 (d) -5\nb\nWhat is the nearest to 0 in 23, 2, 5, -0.5?", "\n-0.5\nWhich is the closest to 2? ", " (a) 1/4 (b) 2/387 (c) -4/3\na\nWhat is the nearest to -0.1 in -1, -36, 0.1, 5?", "\n0.1\nWhat is the closest to -6 in 1, -9, 0, -0.5?", "\n-9\nWhich is the nearest to -1/2? ", " (a) -1/5 (b) 0.5 (c) 2/13 (d) -62/17\na\nWhat is the closest to 1/2 in -2/3, -8, -2/13, 12?", "\n-2/13\nWhat is the nearest to -0.1 in -0.5, -8, -0.14?", "\n-0.14\nWhat is the closest to 48 in 2/7, 0.5, -7?", "\n0.5\nWhich is the nearest to 3/7? ", " (a) -1 (b) 3/5 (c) 2 (d) -5\nb\nWhat is the nearest to -0.1 in 1/5, 4, -4, 7?", "\n1/5\nWhich is the closest to 7? ", " (a) 0.2 (b) -0.3 (c) -1/4\na\nWhich is the closest to -50? ", " (a) 0.1 (b) -1 (c) 1.4\nb\nWhat is the closest to 0.1 in -1/5, 2, 0.5, -2?", "\n-1/5\nWhich is the closest to -1? ", " (a) -2/3 (b) -1 (c) 2/97\nb\nWhat is the closest to 1 in 9, 0, -2, -5?", "\n0\nWhat is the nearest to -3 in -3.5, 0.1, -5, -1/3?", "\n-3.5\nWhat is the closest to -0.1 in 4, -0.023, -0.2?", "\n-0.023\nWhat is the closest to 0 in 0, -1/6, 1, 100?", "\n0\nWhat is the closest to 11/2 in -1/5, 1, -2/5?", "\n1\nWhich is the nearest to 42? ", " (a) -0.1 (b) 1 (c) 5\nc\nWhich is the nearest to -3/2? ", " (a) -9 (b) -0.2 (c) 0.4 (d) 0.2\nb\nWhat is the closest to -0.141 in 1/5, 1, 5, -4?", "\n1/5\nWhat is the closest to 0 in -25, 2, -0.2, 1?", "\n-0.2\nWhat is the closest to 1 in 1/49, -0.21, 0.1?", "\n0.1\nWhat is the nearest to -1/4 in 0.5, 9, 5, -2?", "\n0.5\nWhat is the nearest to 0 in 0.3, -2/3, 0, 11.3?", "\n0\nWhich is the nearest to -2.8? ", " (a) -0.02 (b) -1/9 (c) -11\nb\nWhat is the closest to -1 in 4, 2/9, 4/3, 2?", "\n2/9\nWhich is the closest to -0.5? ", " (a) 0.4 (b) 1 (c) 0.02\nc\nWhat is the closest to 1 in 1/74, -0.06, -0.03?", "\n1/74\nWhat is the closest to 0 in -1/6, 2.3, 15?", "\n-1/6\nWhich is the closest to -1? ", " (a) -0.2 (b) 31/2 (c) 7\na\nWhat is the nearest to -1/4 in 0.4, 0.34, 2/107?", "\n2/107\nWhich is the closest to 0? ", " (a) -2/9 (b) 1/2 (c) -79\na\nWhat is the nearest to -0.4 in -3, -2, -3/2?", "\n-3/2\nWhat is the nearest to -0.05 in -3/4, -5/6, 3/5?", "\n3/5\nWhat is the nearest to -1/13 in 0.04, -2, -2/9?", "\n0.04\nWhich is the closest to -0.03? ", " (a) -1 (b) 3/5 (c) -35\nb\nWhich is the nearest to -2? ", " (a) -5 (b) 2/3 (c) 0 (d) 0.2\nc\nWhat is the closest to 10/3 in -3/2, 0.1, 3/4?", "\n3/4\nWhat is the nearest to -0.2 in 2/9, 3/2, 7?", "\n2/9\nWhat is the nearest to 1/2 in -0.2, -27, 30/13?", "\n-0.2\nWhat is the nearest to -35 in 3, -3, 0.1, -4?", "\n-4\nWhat is the closest to 1 in -5/6, 4/5, 0.06, -0.3?", "\n4/5\nWhat is the nearest to 0 in 3, 9, -2?", "\n-2\nWhich is the nearest to 5/4? ", " (a) 0.3 (b) -5 (c) -4 (d) -0.5\na\nWhich is the nearest to 0.3? ", " (a) -132 (b) 2 (c) 1/11\nc\nWhich is the closest to 0.01? ", " (a) -0.3 (b) 9 (c) 12 (d) 2/17\nd\nWhich is the nearest to 0.03? ", " (a) -1/9 (b) -9 (c) -4 (d) 2/5\na\nWhich is the closest to 3? ", " (a) -0.5 (b) 3 (c) 12 (d) 4\nb\nWhich is the nearest to -1/42? ", " (a) 2 (b) 0 (c) -2/3 (d) 0.3\nb\nWhat is the closest to -1/3 in 0.3, 6.68, 5?", "\n0.3\nWhich is the nearest to -0.1? ", " (a) -40 (b) -1/6 (c) 1 (d) 1/7\nb\nWhat is the nearest to -32 in -5, -0.02, -1/7?", "\n-5\nWhich is the closest to 2? ", " (a) 1/7 (b) 2 (c) -192/11\nb\nWhat is the nearest to 0.3 in 2/19, -0.3, 2?", "\n2/19\nWhich is the closest to -1? ", " (a) -0.397 (b) 2/7 (c) 2/13\na\nWhich is the nearest to 7/4? ", " (a) -3 (b) 4 (c) -0.1\nc\nWhich is the nearest to 0? ", " (a) 2 (b) -0.5 (c) 0.2 (d) -6/11\nc\nWhat is the nearest to 1 in 0, -0.4, 3, -47/2?", "\n0\nWhat is the nearest to -0.2 in -2/15, -3/10, 5, -2?", "\n-2/15\nWhich is the closest to 0? ", " (a) -8 (b) 1 (c) -0.1\nc\nWhat is the nearest to 2.1 in -3, 4, -2?", "\n4\nWhich is the nearest to -1? ", " (a) -146/3 (b) 1 (c) 4 (d) 0\nd\nWhich is the closest to -2/3? ", " (a) -4 (b) -6/5 (c) -5 (d) 5\nb\nWhich is the closest to 14? ", " (a) 5 (b) -5 (c) 0.5 (d) -1/3\na\nWhich is the nearest to 1/5? ", " (a) -6/5 (b) 0.2 (c) 0.1\nb\nWhat is the nearest to 0.17 in 4/7, -0.3, -0.1, -5?", "\n-0.1\nWhich is the closest to 0.1? ", " (a) -10 (b) -1/2 (c) 2/23 (d) 1\nc\nWhat is the closest to 1 in 3/5, -3/2, -4, -0.12?", "\n3/5\nWhat is the closest to 1 in 2/11, -0.6, 0.5, 0?", "\n0.5\nWhat is the closest to -2/5 in -1.8, -0.5, 1/3?", "\n-0.5\nWhich is the closest to -2/11? ", " (a) 0.1 (b) 1/6 (c) 4 (d) 1\na\nWhich is the nearest to -1/3? ", " (a) 2 (b) -9 (c) -0.5\nc\nWhich is the nearest to 1? ", " (a) 2/15 (b) 31 (c) 4 (d) -4/9\na\nWhich is the closest to 2/7? ", " (a) 621 (b) 2/9 (c) 1/3\nc\nWhat is the nearest to -2 in 6, 4, 1/2?", "\n1/2\nWhich is the nearest to -1/4? ", " (a) 5 (b) -4 (c) -1/12 (d) 0.1\nc\nWhat is the closest to -2/11 in -2, 0.2, 7?", "\n0.2\nWhat is the nearest to 1 in -6, -29, 2/3, 3?", "\n2/3\nWhat is the closest to -1 in 0.1, -1/2, 3?", "\n-1/2\nWhat is the nearest to -5 in 1/3, 0.32, -1/10?", "\n-1/10\nWhich is the nearest to 1? ", " (a) 6 (b) 1/3 (c) 0.3 (d) -28\nb\nWhat is the nearest to -19 in 2, 12, -4, 1?", "\n-4\nWhich is the closest to 1/3? ", " (a) -0.4 (b) 69 (c) 0\nc\nWhich is the closest to -2/9? ", " (a) 0.5 (b) 1 (c) -0.1 (d) -3\nc\nWhich is the closest to 0.4? ", " (a) -2 (b) 0.4 (c) -" ]

{ "pile_set_name": "DM Mathematics" }

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[ "//===- Traits.cpp - Common op traits shared by dialects -------------------===//\n//\n// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.", "\n// See https://llvm.org/LICENSE.txt for license information.", "\n// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception\n//\n//===----------------------------------------------------------------------===//\n\n#include \"mlir/Dialect/Traits.h\"\n#include \"mlir/IR/StandardTypes.h\"\n#include \"mlir/IR/TypeUtilities.h\"\n#include \"llvm/Support/FormatVariadic.h\"\n\nusing namespace mlir;\n\nbool OpTrait::util::staticallyKnownBroadcastable(ArrayRef<int64_t> shape1,\n ArrayRef<int64_t> shape2) {\n // Two dimensions are compatible when\n // 1. ", "they are defined and equal, or\n // 2. ", "one of them is 1\n return llvm::all_of(llvm::zip(llvm::reverse(shape1), llvm::reverse(shape2)),\n [](auto dimensions) {\n auto dim1 = std::get<0>(dimensions);\n auto dim2 = std::get<1>(dimensions);\n if (dim1 == 1 || dim2 == 1)\n return true;\n if (dim1 == dim2 && !", "ShapedType::isDynamic(dim1))\n return true;\n return false;\n });\n}\n\nbool OpTrait::util::getBroadcastedShape(ArrayRef<int64_t> shape1,\n ArrayRef<int64_t> shape2,\n SmallVectorImpl<int64_t> &resultShape) {\n // To compute the result broadcasted shape, we compare operand shapes\n // element-wise: starting with the trailing dimensions, and working the\n // way backward. ", "Two dimensions are compatible when\n // 1. ", "they are equal, or\n // 2. ", "one of them is 1\n // The result shape has the maximum among the two inputs at every\n // dimension index.", "\n\n resultShape.clear();\n if (shape1.size() > shape2.size()) {\n std::copy(shape1.begin(), shape1.end(), std::back_inserter(resultShape));\n } else {\n std::copy(shape2.begin(), shape2.end(), std::back_inserter(resultShape));\n }\n\n auto i1 = shape1.rbegin(), e1 = shape1.rend();\n auto i2 = shape2.rbegin(), e2 = shape2.rend();\n auto iR = resultShape.rbegin();\n\n // Check each dimension is consistent.", "\n for (; i1 !", "= e1 && i2 !", "= e2; ++i1, ++i2, ++iR) {\n if (*i1 == -1 || *i2 == -1) {\n // One or both dimensions is unknown. ", "Follow TensorFlow behavior:\n // - If either dimension is greater than 1, we assume that the program is\n // correct, and the other dimension will be broadcast to match it.", "\n // - If either dimension is 1, the other dimension is the output.", "\n if (*i1 > 1) {\n *iR = *i1;\n } else if (*i2 > 1) {\n *iR = *i2;\n } else if (*i1 == 1) {\n *iR = *i2;\n } else if (*i2 == 1) {\n *iR = *i1;\n } else {\n *iR = -1;\n }\n } else {\n if (*i1 == *i2 || *i2 == 1) {\n *iR = *i1;\n } else if (*i1 == 1) {\n *iR = *i2;\n } else {\n // This dimension of the two operand types is incompatible.", "\n resultShape.clear();\n return false;\n }\n }\n }\n\n return true;\n}\n\n/// Returns the shape of the given type. ", "Scalars will be considered as having a\n/// shape with zero dimensions.", "\nstatic ArrayRef<int64_t> getShape(Type type) {\n if (auto sType = type.dyn_cast<ShapedType>())\n return sType.getShape();\n return {};\n}\n\n/// Returns the result broadcast composition type from the two given types by\n/// following NumPy broadcast semantics. ", "Returned type may have dynamic shape if\n/// either of the input types has dynamic shape. ", "Returns null type if the two\n/// given types are not broadcast-compatible.", "\n///\n/// elementType, if specified, will be used as the element type of the\n/// broadcasted result type. ", "Otherwise it is required that the element type of\n/// type1 and type2 is the same and this element type will be used as the\n/// resultant element type.", "\nType OpTrait::util::getBroadcastedType(Type type1, Type type2,\n Type elementType) {\n // If the elementType is not specified, then the use the common element type\n // of the inputs or fail if there is no common element type.", "\n if (!", "elementType) {\n elementType = getElementTypeOrSelf(type1);\n if (elementType !", "= getElementTypeOrSelf(type2))\n return {};\n }\n\n // If one of the types is unranked tensor, then the other type shouldn't be\n // vector and the result should have unranked tensor type.", "\n if (type1.isa<UnrankedTensorType>() || type2.isa<UnrankedTensorType>()) {\n if (type1.isa<VectorType>() || type2.isa<VectorType>())\n return {};\n return UnrankedTensorType::get(elementType);\n }\n\n // Returns the type kind if the given type is a vector or ranked tensor type.", "\n // Returns llvm::None otherwise.", "\n auto getCompositeTypeKind = [](Type type) -> Optional<TypeID> {\n if (type.isa<VectorType, RankedTensorType>())\n return type.getTypeID();\n return llvm::None;\n };\n\n // Make sure the composite type, if has, is consistent.", "\n Optional<TypeID> compositeKind1 = getCompositeTypeKind(type1);\n Optional<TypeID> compositeKind2 = getCompositeTypeKind(type2);\n Optional<TypeID> resultCompositeKind;\n\n if (compositeKind1 && compositeKind2) {\n // Disallow mixing vector and tensor.", "\n if (compositeKind1 !", "= compositeKind2)\n return {};\n resultCompositeKind = compositeKind1;\n } else if (compositeKind1) {\n resultCompositeKind = compositeKind1;\n } else if (compositeKind2) {\n resultCompositeKind = compositeKind2;\n }\n\n // Get the shape of each type.", "\n SmallVector<int64_t, 4> resultShape;\n if (!", "getBroadcastedShape(getShape(type1), getShape(type2), resultShape))\n return {};\n\n // Compose the final broadcasted type\n if (resultCompositeKind == VectorType::getTypeID())\n return VectorType::get(resultShape, elementType);\n if (resultCompositeKind == RankedTensorType::getTypeID())\n return RankedTensorType::get(resultShape, elementType);\n return elementType;\n}\n\n/// Returns a tuple corresponding to whether range has tensor or vector type.", "\ntemplate <typename iterator_range>\nstatic std::tuple<bool, bool> hasTensorOrVectorType(iterator_range types) {\n return std::make_tuple(\n llvm::any_of(types, [](Type t) { return t.isa<TensorType>(); }),\n llvm::any_of(types, [](Type t) { return t.isa<VectorType>(); }));\n}\n\nstatic bool areCompatibleShapes(ArrayRef<int64_t> shape1,\n ArrayRef<int64_t> shape2) {\n auto isCompatible = [](int64_t dim1, int64_t dim2) {\n return dim1 == dim2 || dim1 == -1 || dim2 == -1;\n };\n if (shape1.size() !", "= shape2.size())\n return false;\n for (auto p : llvm::zip(shape1, shape2))\n if (!", "isCompatible(std::get<0>(p), std::get<1>(p)))\n return false;\n return true;\n}\n\nstatic std::string getShapeString(ArrayRef<int64_t> shape) {\n // TODO: should replace with printing shape more uniformly across here and\n // when in type.", "\n return std::string(\n formatv(\"'{0:$[x]}'\", llvm::make_range(shape.begin(), shape.end())));\n}\n\nLogicalResult OpTrait::impl::verifyCompatibleOperandBroadcast(Operation *op) {\n // Ensure broadcasting only tensor or only vector types.", "\n auto operandsHasTensorVectorType =\n hasTensorOrVectorType(op->getOperandTypes());\n auto resultsHasTensorVectorType = hasTensorOrVectorType(op->getResultTypes());\n if ((std::get<0>(operandsHasTensorVectorType) ||\n std::get<0>(resultsHasTensorVectorType)) &&\n (std::get<1>(operandsHasTensorVectorType) ||\n std::get<1>(resultsHasTensorVectorType)))\n return op->emitError(\"cannot broadcast vector with tensor\");\n\n auto rankedOperands = make_filter_range(\n op->getOperandTypes(), [](Type t) { return t.isa<RankedTensorType>(); });\n\n // If all operands are unranked, then all result shapes are possible.", "\n if (rankedOperands.empty())\n return success();\n\n // Compute broadcasted shape of operands (which requires that operands are\n // broadcast compatible). ", "The results need to be broadcast compatible with\n // this result shape.", "\n SmallVector<int64_t, 4> resultShape;\n (void)util::getBroadcastedShape(getShape(*rankedOperands.begin()), {},\n resultShape);\n for (auto other : make_early_inc_range(rankedOperands)) {\n SmallVector<int64_t, 4> temp = resultShape;\n if (!", "util::getBroadcastedShape(temp, getShape(other), resultShape))\n return op->emitOpError(\"operands don't have broadcast-compatible shapes\");\n }\n\n auto rankedResults = make_filter_range(\n op->getResultTypes(), [](Type t) { return t.isa<RankedTensorType>(); });\n\n // If all of the results are unranked then no further verification.", "\n if (rankedResults.empty())\n return success();\n\n for (auto type : rankedResults) {\n ArrayRef<int64_t> actualSuffix =\n getShape(type).take_back(resultShape.size());\n if (!", "areCompatibleShapes(actualSuffix, resultShape))\n return op->emitOpError()\n << \"result type \" << getShapeString(getShape(type))\n << \" not broadcast compatible with broadcasted operands's shapes \"\n << getShapeString(resultShape);\n }\n return success();\n}\n" ]

{ "pile_set_name": "Github" }

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[ "Q:\n\nAutocorrelation and trends\n\nWhat is the relation between the autocorrelation and the trend? ", "Can a trend exist in a time series of independent variables? ", "And in time series with a non-zero autocorrelation, does a trend always exist?", "\n\nA:\n\nThe autocorrelation(acf) function summarizes the correlation of different lags and is a descriptive statistic. ", "If there is a \"trend\" in the data then the acf will suggest non-stationarity. ", "However a non-stationary acf does not necessarily suggest a \"trend\". ", "If the series is impacted by one or more level/step shifts the the acf will suggest non-stationarity (symptom) but the cause is simple a shift in the mean at one or more points in time. \"", "Trends\" in time series can sometimes be adequately handled by incorporating a deterministic structure. ", "There are a few forms ( the software package needs to help here and/or the skilled analyst ) to determine which form is the most adequate. ", "One form is to incorporate a predictor series(x1) such as 1,2,3,4,..n which would imply one and only one trend. ", "Another might be to incororporate two input series (x1 and x2) where x1=1,2,3,4,,..n and x2=0,0,0,0,0,1,2,3,..n reflecting two trends where the second trend starts at period 6 in this example. ", "Of course there could be multiple \"trends\" or breakpoints in trend.", "\nAn alternative way of incorporating a \"trend\" is to model the data as some variety of a differencing model of the form (1-B)Y(T) = constant + [theta(B)/phi(B)]*A(T) which suggests one and only 1 trend . ", "Good analytics will suggest the \"most correct\" approach to an individual data set. ", "If you have exogenous/causal/supporting/input series then the \"trend\" in Y could well be explained by one or more of these series. ", "The acf is of little or no help in helping you decide which \"trend model\" is appropriate.", "\n\n" ]

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[ "Michael Bolton at 60: Through the Decades\n\nSixty years ago today, Michael Bolton was born in New Haven, Connecticut, into a family of Russian Jewish immigrants. ", "He'd eventually change his name to Michael Bolton and go on to become one of the most successful musicians of the late '80s and early '90s by either reviving the sounds of classic soul and R&B and buffing them to a modern shine, or, in the view of his many critics, by exploiting and defiling the legacies of great black artists like Otis Redding and Percy Sledge.", "\n\nMost Popular\n\nBut like many of pop's great schmaltzmeisters, he's a more interesting individual than surface appearances would suggest. ", "Bolton's written a massive amount of songs for other artists, from Kenny Rogers to Kiss, and like fellow adult contemporary balladeer Billy Joel, his early career includes a little-known detour into hard rock. ", "And as his 2011 collaboration with the Lonely Island proves, he's a chill enough guy to laugh at his own reputation.", "\n\nIn recognition of these qualities, and for his astounding artistic endurance, we're saluting Michael Bolton with these highlights from his six decades on earth.", "\n\n'50s Michael Bolton\n\nAdvertisement - Continue Reading Below\n\nAccording to Bolton, he joined his first band at age seven. ", "While the group didn't leave behind any recordings, he says that he was influenced from a young age by Ray Charles, and if that fact inspires you to imagine a child-sized Michael Bolton trying to replicate \"Mess Around,\" that's probably normal.", "\n\n'60s Michael Bolton\n\nPercy Sledge's \"When a Man Loves a Woman\" is one of the most soulful moments of the '60s. ", "Two-plus decades later, Bolton would record a version that, whether we like it or not, is, for many of us, the first rendition that comes to mind when we read the title.", "\n\n'70s Michael Bolton\n\nAdvertisement - Continue Reading Below\n\nBolton got his first big break in the music industry as the frontman for a hard rock band called Blackjack. ", "At one point, they toured with Ozzy Osbourne, and while they weren't quite the transgressive Satanic metal maniac that Ozzy was, \"Love Me Tonight\" has a respectably Thin Lizzy-ish 'tude.", "\n\n'80s Bolton\n\nMost Popular\n\nBolton would have to wait until 1983 for his first real pop hit, when Laura Branigan's version of \"How Am I Supposed to Live Without You\" (which he co-wrote with Doug James) reached number 12 on the Hot 100 and topped the Adult Contemporary chart. ", "His own recording of it went all the way to number one in 1990. ", "But the song actually debuted in 1981, with a rendition by Lisa Hartman that appeared on the TV show Knots Landing.", "\n\n'90s Bolton\n\nBy the time the '90s rolled around, Bolton had established himself as a pop icon, and his flowing locks and uber-smooth stylings made him an easy target for critics of the period's most overproduced excesses. ", "Those people probably weren't happy when he teamed up with Kenny G, who, like Bolton, had a funky early career that most people don't know about.", "\n\n'00s Bolton\n\nWhen you've sold as ungodly an amount of records as Michael Bolton, even your periods of being out of fashion still involve appearances at major televised events backed by a huge jazz orchestra." ]

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[ "California’s cash crop could become dirt cheap if the state legalizes marijuana.", "\n\nResearchers associated with the Rand Corp.'s Drug Policy Research Center said Wednesday that not much is certain about the potential impact of Proposition 19 except that the price of California’s choicest weed could plunge more than 80%, down from $300 to $450 per ounce to about $38.", "\n\n“That’s a significant drop,” said Beau Kilmer, co-director of the center. “", "We’re very clear about the fact that the price will go down.”", "\n\nThe implications of such a drop would be profound. ", "Kilmer and four other researchers who analyzed marijuana legalization said consumption would rise, but they could not determine with any certainty by how much. “", "We cannot rule out increases of 50% to 100% or perhaps higher, but we just don’t know,” he said.", "\n\nSuch a low price could also affect pot prices across the nation, encourage marijuana tourism in the state, increase the amount of pot shipped out of state, disrupt the smuggling of marijuana from Mexico and stimulate an underground market designed to avoid high taxes that might be imposed.", "\n\nRand, the Santa Monica-based nonpartisan research institute, had five prominent drug policy experts spend about six months examining what might happen to marijuana use and tax revenues if Californians approve the measure on the November ballot or the Legislature passes a bill introduced by Assemblyman Tom Ammiano (D- San Francisco) that would legalize pot and impose a $50-per-ounce tax.", "\n\nThe report called “Altered State?” ", "is the most scholarly examination of the issue so far. ", "It is likely to be scrutinized and cited by both sides in the debate.", "\n\n“The uncertainty and the potential chaotic nature of what could happen here just totally derails this initiative,” said Roger Salazar, the spokesman for Public Safety First, one of four opposition committees that plan to fight the initiative. “", "Outside of the prices going down there is nothing else that is certain here and certainly not worth having the state of California become the first entity in the world to completely legalize production and sales of marijuana.”", "\n\nStephen Gutwillig, the California director of the Drug Policy Alliance, said: “The current system is loaded with the certainty of mass arrest, racist enforcement and boondoggle law enforcement expenses to the tune of hundreds of millions of dollars,” he said.", "\n\nThe report noted that it was impossible to predict tax revenues from the initiative, which leaves that decision to cities and counties, but concluded that revenues from a statewide $50-per-ounce tax could range from $650 million to $1.49 billion.", "\n\nTo calculate the price drop, researchers looked at the cost of growing marijuana in a 1,500-square-foot house. ", "The researchers concluded that the wages paid to employees who tend the crop would slip from as much as $25 per hour to no more than $10, just a little above what nursery laborers earn.", "\n\nThe report is likely to make it even harder for legalization advocates to persuade the state’s growers and suppliers, particularly in the Emerald Triangle, to support the initiative. ", "The triangle area includes Humboldt, Mendocino and Trinity counties.", "\n\nDale Gieringer, director of the state chapter of the National Organization for the Reform of Marijuana Laws, who has also looked at the issue, said the calculated price drop sounded reasonable, but he said it would not occur overnight. “", "It will descend slowly, is the likely scenario,” he said. “", "If you took it out of the statute book and dealt with it like parsley, yes, it would plummet.”", "\n\nHe acknowledged that consumption would probably increase if Proposition 19 passes, but said it is half the level it was in the late 1970s. “", "Fads come and go, drugs come in and out of fashion,” he said. “", "I think we’re in for a short-term increase in marijuana consumption regardless of whether the initiative passes.”", "\n\nResearchers also looked at estimates of the cost of enforcing marijuana laws in California, which range from $200 million to $1.9 billion, and put it at “probably less than $300 million.” ", "They also concluded that it is not possible to determine whether increased use would lead to more drugged driving accidents and to more use of harder drugs, such as cocaine, finding that the research is inconclusive.", "\n\njohn.hoeffel@latimes.com" ]

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[ "OpenData 1.0 should help clarify the data nomenclature\n\nThe IAB Tech Lab is rolling out a set of terms as a way of unifying the data nomenclature used across the industry when reporting the results of digital campaigns. ", "The initiative, called OpenData 1.0, is meant to create uniform guidelines to help analysts cut down on the amount of time spent cleaning up performance-related spreadsheets.", "\n\nThe project announced today could help normalize a complex and convoluted industry with varying definitions and uses for dozens of terms like “flight,” “purchase order” and “anonymized ID.” ", "IAB members have 60 days to submit comments about the list of terms, which was created by a committee of two dozen data service providers, data-management companies, ad agencies and others.", "\n\nDavid L. Smith, CEO of Mediasmith, and co-chair of the IAB Tech Lab OpenData Task Force, said the terms could help “simplify the flow” of both money and data. ", "He said some advertisers are pulling data from more than a dozen sources, causing some data scientists to spend as much as 80 percent of their time organizing data rather than understanding it.", "\n\n“By the IAB taking on the centralization of a standard nomenclature, it gives the industry the ability to either standardize for certain names or to create pointers that says this means this and this means that,” he said.", "\n\nWhile the project has been in the works for more than year, officials say cleaning up data has been a problem for much longer. ", "Smith said that when agencies started using third-party ad services such as DoubleClick, data would flow from a single place. ", "However, as Google and other media companies like Facebook grew in size, so did their complexity.", "\n\nAccording to Dennis Buchheim, svp and gm of IAB Tech Lab, the list of terms could in the future have wider implications for everything from programmatic advertising to epayments. ", "He said uniform terms are needed to make data science more efficient so less time is spent “jockeying spreadsheets around.”", "\n\n“Are these two things apples, or is one an apple and another an orange?” ", "he said." ]

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[ "Soil solid-phase organic matter-mediated microbial reduction of iron minerals increases with land use change sequence from fallow to paddy fields.", "\nThe microbial reduction of Fe(III) minerals (MRF) is an important process in paddy soil because it can affect the biogeochemical cycles of many major and trace elements. ", "Natural organic matter (NOM) that mainly exists in the form of solid phase in soil can mediate MRF through electron shuttling functionality. ", "However, whether a link exists between solid-phase NOM-mediated MRF in soil and the age of paddy field since the reclamation on fallow is unclear. ", "Here, we use microbial reduction method to assess the solid-phase NOM-mediated MRF of paddy soils with different reclamation ages. ", "The results show that solid-phase NOM-mediated MRF exhibits a positive response to land use change sequence from fallow to paddy field, indicating that the long-term natural development of paddy field favors the electron shuttling of NOM between cells and Fe(III) minerals. ", "This increase in the electron shuttling of NOM is not due to the increase in the redox functional groups of NOM, but may be attributed to the formation of NOM-mineral complex through the synergistic increases in NOM content and transformation of soil texture from clay loam to loam. ", "The decrease in the redox potential of Fe(III) minerals in soil caused by decreased pH and the increase in Fe content in the organic matter-complexed form may also partly facilitate electron transfer from NOM to Fe(III) minerals. ", "Our work is useful in predicting the role of soil solid-phase NOM in mediating MRF in the context of long-term reclamation of paddy field and provides guidance for the environmental management of paddy fields." ]

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[ "The Seattle Mariners today announced that Safeco Field will be the first Major League Baseball facility to illuminate the playing field with LED lights.", "\n\nThe Mariners partnered with Planled to replace outdated metal halide fixtures at Safeco Field with state-of-the-art GigaTera LED fixtures from KMW Inc. The conversion was completed this month and will be unveiled to the public at the 17th Annual Seattle Mariners FanFest at Safeco Field on January 24 & 25.", "\n\nLED (light emitting diode) fixtures focus multiple narrow beams of light. ", "They produce brighter, more uniform light, which significantly reduces glare and shadows on the field and creates a better atmosphere for players and fans watching the game at the ballpark.", "\n\nFor fans watching on HDTV, LED lights provide better color rendering by more evenly distributing light across the spectrum. ", "There is also no flicker, which is necessary for the super-slow-motion technology now in use during game telecasts.", "\n\nJoe Garagiola, Jr., Senior Vice President of Standards & On-Field Operations for Major League Baseball, said: \"Thus far, our experience has indicated that the Mariners new LED technology at Safeco Field will be better for our players, fans in the ballpark and viewers watching at home. ", "We applaud the Mariners for an innovative step that promises to improve efficiency and the fan experience in numerous ways, all while serving as a welcome addition to our overall greening efforts.\"", "\n\nIn addition to the improved experience for players and fans, LED fixtures are more efficient and have a longer lifespan than metal halide lamps. ", "Safeco Field's LED conversion will reduce energy consumption for field lighting by 60-70 percent. ", "In addition to energy efficiency, the LED lamps last over 100,000 hours, or more than 30 years. ", "Metal halide lamps must be changed every 3,000 hours or so. ", "And unlike metal halide lights, which need a 20 minute warm-up, LED lights respond instantly when switched on.", "\n\n\"The benefits of converting to LED lighting are across the board from the play on the field to supporting the Mariners long-established sustainability goals,\" said Joe Myhra, Seattle Mariners Vice President Ballpark Operations. \"", "The GigaTera fixtures represent the latest in LED technology. ", "This project was the result of the work of many partners, including Planled and KMW, working together on this new approach to sports lighting.\"", "\n\n\"It's a privilege for us to partner with the Seattle Mariners to light the first MLB stadium with the most advanced sports lighting system in sports history,\" said John Hwang, Planled CEO. \"", "We are also planning to hold workshops and seminars in partnership with Lighting Design Lab, Green Sports Alliance and Human Centric Lighting Society to share our experiences with other venues.\"", "\n\nPlanled is producing a video that documents the project from the beginning to serve as a resource for others who are interested in learning more about the use of LED lighting.", "\n\nNRG Stadium, the home of the Houston Texans, University of Phoenix Stadium in Arizona, which is hosting the 2015 Super Bowl on February 1, and Staples Center in Los Angeles are among the professional sports facilities in the U.S. that have converted to LED lighting." ]

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[ "Evaluation of nitrate effects in the aqueous photodegradability of selected phenolic pollutants.", "\nThe effect of nitrate in the aqueous photodegradation of five phenolic environmental pollutants (ortho-phenylphenol, OPP; methyl paraben, MeP; propyl paraben, PrP; Triclosan, TCS and bisphenol A, BPA) is evaluated. ", "Time-course of precursor compounds and formation of transformation products (TPs) were investigated by liquid chromatography quadrupole time-of-flight mass spectrometry (LC-QTOF-MS). ", "Nitrate showed a positive effect in the removal of selected pollutants. ", "Observed TPs resulted from hydroxylation, aromatic nitration (with or without molecule cleavage) and nitro dehalogenation processes. ", "The above reactions involved the participation of ·OH and ·NO2 radicals arising from photolysis of nitrate. ", "Nitro TPs were produced in a different extent depending on the structure of the precursor pollutant, nitrate concentration, light source (254 nm UV and solar light) and water matrix (ultrapure, surface and urban wastewater). ", "Some of these nitro TPs were also observed during UV irradiation of untreated and unbuffered wastewater, either naturally polluted with parent phenolic compounds or spiked with these species at the sub μg L-1 level. ", "Nitration reactions were particularly favourable for OPP with the generated nitro TPs displaying a higher stability than the precursor molecule and the hydroxylated TPs of the same compound." ]

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[ "Q:\n\nSequence of fractions that converges to $\\sqrt{n}$\n\nBegin with any two positive integers $a,b$. Let\n$$s_1 = \\frac{a}{b}$$\nand recursively we define $s_{i+1}$ from $s_i$ as follows: If ${s_i}$ is the fraction $\\frac{a'}{b'}$, then set\n$$s_{i+1} = \\frac{a'+2b'}{a'+b'}$$\n(Notice that the actual value of the $s_{i+1}$ does not depend on the exact way we choose to represent $s_i$ in fractions)\nHow do we show that $s_i \\to \\sqrt{2}$ as $i\\to \\infty$?", "\nIn general, sending $\\frac{a'}{b'}$ to $\\frac{a'+nb'}{a'+b'}$ supposedly leads to $s_i \\to \\sqrt{n}$. How might we prove this?", "\n\nA:\n\nIn the general case dividing by $b'$ in the nominator and the denominator we have that:\n$$s_{i+1} = \\frac{s_i + n}{s_i + 1}$$\nNow consider two cases, namely $s_i \\le \\sqrt{n}$ and $s_i > \\sqrt{n}$. Now let WLOG $s_i \\le \\sqrt{n}$. Then expressing $s_{i+2}$ by $s_i$ we have that:\n$$s_{i+2} = \\frac{s_{i+1} + n}{s_{i+1} + 1} = \\frac{\\frac{s_i + n}{s_i + 1} + n}{\\frac{s_i + n}{s_i + 1} + 1} = \\frac{(n+1)s_i + 2n}{2s_i + (n+1)}$$\nFrom this we have that $s_{i+2} \\ge s_i \\iff (n+1)s_i + 2n \\ge 2s_i^2 + (n+1)s_i \\iff n \\ge s_i^2$, which is true. ", "Also we have that $s_{i+2} \\le \\sqrt{n} \\iff ((n+1) - 2\\sqrt{n})s_i \\le \\sqrt{n}(n+1) - 2n$, but this is true as: $((n+1) - 2\\sqrt{n})s_i \\le ((n+1) - 2\\sqrt{n})\\sqrt{n} = \\sqrt{n}(n+1) - 2n$. Therefore if $i$ is odd/even we have that the sequence of odd/even indexes is convergent. ", "Let WLOG $i$ be odd, then we can write $\\lim_{n \\to \\infty} s_{2i} = L$. Taking the limit from the previous equation we have:\n$$L = \\frac{(n+1)L + 2n}{2L + (n+1)} \\iff 2L^2 + (n+1)L = (n+1)L + 2n \\iff L = \\sqrt{n}$$\nSimilarly we can prove the case when $s_i > \\sqrt{n}$ and also that the subsequence with indexes of other parity is convergent to $\\sqrt{n}$.\nFinaly as both $s_{2i}$ and $s_{2i+1}$ converge to $\\sqrt{n}$ we can conclude that $s_i$ converges to $\\sqrt{n}$\n\n" ]

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[ "Hungi\n\nHungi is a village development committee in Palpa District in the Lumbini Zone of southern Nepal. ", "At the time of the 1991 Nepal census it had a population of 4355 people living in 830 individual households.", "\n\nReferences\n\nCategory:Populated places in Palpa District" ]

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[ "Hardy hoping he's in 'good' place with O's\n\nShortstop wants another 20-plus homer, 70-plus RBI campaign\n\nBy Brittany Ghiroli / MLB.com\n\nSARASOTA, Fla. -- J.J. Hardy has been the young All-Star infielder -- belting 26 homers in 2007 as part of a budding crop of Brewers' talent -- and less than two years later, the Triple-A player sitting in a hotel room with the news that his free agency clock has been set back another year.", "\n\nHe spent years in the Minor Leagues relearning to swing after blowing out his left shoulder in Triple-A, and the last two seasons in Milwaukee looking over it as fans clamored for the imminent arrival of shortstop Alcides Escobar.", "\n\nHardy has tried to change his mental game, going along with then-Brewers manager Ken Macha's suggestion that he see a sports psychologist, which resulted in an anti-depressant medication that Hardy deems \"his worst decision ever.\" ", "He altered his approach at the plate at the Twins' urging last season, swapping his power stroke for Minnesota's preference for punching singles.", "\n\nSo, when Hardy finished his first round of batting practice last month and saw Orioles hitting coach Jim Presley walking toward him, his first inclination was, what now?", "\n\n\"I thought 'Here we go again,'\" said Hardy, who was traded to Baltimore this winter. \"", "But [Presley] goes, 'What is your approach?' ", "And he just started talking about my approach, and he said basically everything I wanted to hear.\"", "\n\nPresley didn't need to preach philosophy. ", "He just wanted Hardy to quit trying to be someone else.", "\n\n\"I told him you got to get back to what made you successful,\" said Presley, who saw Hardy from the other dugout when he was the Marlins hitting coach and Hardy was a Brewer.", "\n\n\"That [swing] was not the same swing I saw back then. ", "I just wanted to get him in a more aggressive state of mind at the plate ... I said 'I saw you good. ", "Nobody else has seen you good in '07 and '08. ", "Let's try to get back to that.'\"", "\n\nSights & Sounds\n\nSpring Training Info\n\nSo far, so good for Hardy, who is hitting .370 (10-for-27) with a double, a homer and three RBIs in his first nine spring games. ", "While the Orioles' new power bats -- third baseman Mark Reynolds and designated hitter Vladimir Guerrero -- have gotten more attention, Hardy is two seasons removed from back-to-back 20-plus homers and 70-plus RBI campaigns.", "\n\n\"He's been told to just stay the other way, and he said 'I kind of lost my swing, I lost my juice,'\" said Presley, who calls the lean Hardy \"stringy strong.\"", "\n\n\"I told him to get rid of that thought because we are fixing it. ", "He's not a [punching] Judy. ", "This guy doesn't flare the ball the other way. ", "He's got some juice and he can drive some runs in.\"", "\n\nThat is, if he can stay healthy, a nagging question that has followed Hardy his entire Major League career. ", "His shoulder injury in the Minors was his first surgery, and Hardy admits now that he mentally mismanaged it, not realizing just how long it would take to come back. ", "He had season-ending ankle surgery in '06 and didn't want to be shelved again in Minnesota, so he played through a left wrist strain last season, a nagging injury that never went away.", "\n\n\"I felt like every swing hurt,\" said Hardy, who seesawed on-and-off the disabled list.", "\n\nWhen he could tolerate the injury, which was diagnosed as a bone bruise, Hardy didn't do any extra hitting in an attempt to save his \"good swings\" for the game.", "\n\n\"It would help, but I was still dealing with some pain,\" said Hardy who managed six homers and 38 RBIs in 101 games. \"", "That's really all I could have done. ", "I felt like I got some singles, and that was basically what I could do.\"", "\n\nThe Twins' payroll-extended by several long-term contracts -- made the arbitration-eligible Hardy expendable and Minnesota dealt him along with infielder Brendan Harris to Baltimore in exchange for a pair of pitching prospects. ", "The 28-year-old Hardy will make $5.85 million in 2011.", "\n\nNow with his third organization, Hardy has another chance to start fresh and get his career back on track. ", "He's been here before, but this time he's using his past in a good way.", "\n\n\"The fact that I've done it, I've been there, helps me believe I can do it,\" Hardy said of returning to his '07 and '08 form.", "\n\n\"I'm healthy, I feel like I'm back to my old approach. \"[", "I'm] very, very confident that it can happen.\"", "\n\nAdded Presley: \"This kid can hit 15, 17 homers and drive in 65-70 RBIs. ", "That right there would make us a better team as far as winning ballgames.\"" ]

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[ "Before starting work at the toll plaza each night, crews will close the on-ramp from 24th Street Northwest to eastbound SR 16 at 8 p.m.\n\nCrews will then close all of the Good To Go! ", "electronic toll lanes by 10 p.m. All of the Good To Go! ", "lanes and the 24th Street ramp will reopen by 5 a.m. the following morning. ", "During the closures all vehicles will be detoured through the toll booths." ]

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[ "Bijawar-Panna Plateau\n\nThe Bijawar-Panna Plateau covers portions of Chhatarpur and Panna districts in the Indian state of Madhya Pradesh.", "\n\nGeography\nBehind the Bijawar Hills in Sagar Division is the 25-30 km wide Bijawar-Panna Plateau. ", "The Bijawar-Panna Plateau rises from the north to south in three well marked escarpments roughly followed by 300, 375 and 450 m contours, towards the longitudinal valleys of the rivers Mirhasan and Sonar. ", "To the north-east of Panna there are two main branches – the southern is called Panna hills and the northern one Vindhyachal Range. ", "The Panna Range merely forms a table land 15 km broad. ", "Its general slope is from south-west to north-east.", "\n\nIt is part of the Bundelkhand Plateau.", "\n\nA series of plateaux runs along the Kaimur Range. ", "These fluvial plateaux, consists of a series of descending plateaux, starting with the Panna Plateau in the west, followed by Bhander Plateau and Rewa Plateau and ending with Rohtas Plateau in the east.", "\n\nCrossing the Bijawar-Panna hills, the Ken River cuts a 60 km long, and 150-180 m deep gorge. ", "Several streams join the Ken in this gorge making waterfalls.", "\n\nReferences\n\nCategory:Plateaus of Madhya Pradesh" ]

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[ "There’s only really so many ways to verify the age of someone that you’ve never seen (actually, it often isn’t all that much easier in person, but that’s another story).", "\n\nYou can treat them as if they’re of-age if they have a credit card, but that’s inaccurate and a violation of credit-card merchant agreements (symptoms include suddenly having to change payment providers).", "\n\nYou can match identification document information against an identification provider like Aristotle-Integrity, but that’s unreliable and fraught with issues, and doesn’t prove that the information describes the applicant.", "\n\nThere must be a simpler way to verify Second Life accounts as adults! ", "Oh, wait…. ", "here it is!", "\n\nHere’s the latest Second Life age-verification page. ", "It asks you for your date-of-birth (it already has it filled in, if you provided it at any previous time), and asks you to promise that you’re being honest about it.", "\n\nNow, before you jump up and down about the inadequacy of such measures, I’ll make a mention that this meets the US Federal Trade Commission’s best-practices for age-verification for access to online adult content. ", "That is, the US Government feels that this sort of system is fine.", "\n\nWell, actually, no – the US Government doesn’t feel that this is fine, however it is the best and most accurate system that it has so far been possible to build, more to the point – that is, nobody’s so far able to effectively improve on it. ", "Everyone’s got deceptively simple ideas on how to do accurate age-verification, most of which are based on false premises. ", "Really, the whole thing falls down as soon as someone pulls out a fake ID.", "\n\nSo, there you go. ", "If you’ve been holding off getting age-verified because you didn’t want to send sensitive identity information to a private foreign firm, now’s your chance to get it done." ]

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[ "Food the old fashioned way\n\nCategory Archives: Fritters\n\nin Context: Like carrots, parsnips are native to Eurasia and have been eaten there since ancient times. ", "Zohary and Hopf note that the archaeological evidence for the cultivation of the parsnip is “still rather limited”, and that Greek and Roman literary sources are a major source about its early use. ", "They warn that “there are some difficulties in distinguishing between parsnip and carrot (which, in Roman times, were white or purple) in classical writings since both vegetables seem to have been sometimes called pastinaca, yet each vegetable appears to be well under cultivation in Roman times”. ", "The parsnip was much esteemed, and the Emperor Tiberius accepted part of the tribute payable to Rome by Germany in the form of parsnips. ", "In Europe, the vegetable was used as a source of sugar before cane and beet sugars were available. ", "As pastinache comuni, the “common” pastinaca figures in the long list of comestibles enjoyed by the Milanese given by Bonvesin da la Riva in his “Marvels of Milan” (1288).", "\n\nThis plant was introduced to North America simultaneously by the French colonists in Canada and the British in the Thirteen Colonies for use as a root vegetable, but in the mid-19th century, it was replaced as the main source of starch by the potato and consequently was less widely cultivated.", "\n\nIn 1859, a new cultivar called ‘Student’ was developed by James Buckman at the Royal Agricultural College in England. ", "He back-crossed cultivated plants to wild stock, aiming to demonstrate how native plants could be improved by selective breeding. ", "This experiment was so successful, ‘Student’ became the major variety in cultivation in the late 19th century." ]

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[ "Of the year 2014\n\nI did one Mexico trip (also one the fall before) and two Maple trips, spring and fall. ", "Also the Cathedral near St. George. ", "Locally, I spent most of the summer at the Bear Crag, and most of the winter at the Gold Wall.", "\n\nFlamethrower – photo by Vincent, and Anais, my two new French friends.", "\n\nI got to hang with some super nice amazing 5.14 climbers at Maple, who supported my sends way beyond anything I expected. ", "It was really cool to send my trip proj with my new friends making a special hike up to the Minimum to cheer me on, and bringing beer and junk food to the campsite after. ", "Thanks for being my friend, Jeremy and Abby. ", "Even though you used my proj for a warmup 🙂\n\nAmate Amarillo\n\nI had numerous one fall burns on a couple of 12+ at Chonta, though no super sends as on the previous trip. ", "I fell going for it though, and took the long whips, which I am very pleased about. ", "Same at Bear – when I fell, I fell going for it. ", "Falling trying as hard as you can doesn’t feel like failure.", "\n\nMy head was good all year. ", "Thanks, Arno! ", "That class was totally worth it. ", "Best of any year.", "\n\nI tried to send both Eastside Flamethrowers in one weekend but didn’t succeed (one fall burn on the Pine Creek version). ", "I also sent a bunch of GW 12s, and did really well on Mortal Kombat there. ", "I got totally spanked at Jailhouse.", "\n\nClimbing well inspired me to start training, according to the RCTM. ", "I also took Arno Ilgner’s class on falling (and belaying!), ", "which was very helpful. ", "Unfortunately, about halfway through the first periodization cycle, I managed to get injured, so when I get to start up again in the indefinite future, I’ll be starting over from scratch.", "\n\nBeing unable to climb has been an opportunity to see how non-climbers live. ", "What do you people do with all this time? ", "I can kill time with the best of them, but reading books and watching movies no longer fills my days with any sense having done anything. ", "If I’m not exerting maximum effort, it feels like I’m wasting my life. ", "Because of limited mobility, home improvement projects have been out, as have photo sessions (until recently I was unable to hold a camera with my right hand). ", "Long writing sessions were also out. ", "Enforced normal life is coming to an end, but for a while, it was pretty much just reading, whatever I could put on the HDTV, and drinking.", "\n\nNot only climbing injuries. ", "I also managed to pull a hamstring severely enough to turn the back of my thigh all sorts of interesting colors, so that was the end of running for a few months in the fall. ", "And bronchitis, let’s not forget that. ", "One of the best-of-this-year will be inhalers. ", "Magic! ", "Why didn’t we have those when I was a kid?", "\n\nsee the pretty colors\n\nNo poodle dog bush though.", "\n\nFritz photobombing the Golden Gate Bridge\n\nBest museum trip: I didn’t make it anyplace special this year, though I visited SF, Mexico, and Germany (with side trips to Switzerland and Austria). ", "The best exhibit I saw was See The Light at LACMA. ", "An opportunity to see a lot of well-known photos in person, rather than in a book or on the internet. ", "That makes a difference. ", "I also got to sneak in the tail end of a Abellardo Morell guided tour of his own exhibit at the Getty just by happenstance. ", "I love serendipity.", "\n\nThe view from Lake Constance\n\nThe LACMA history-of-expressionism exhibit, From Van Gogh to Kandinsky was very interesting – not being a art history student, it was eye-opening to me to see the more-or-less logical progression of modern art. ", "I’m sure this is old hat to artists, but it was revelatory to me.", "\n\nI took some pictures that I’m really pleased with. ", "You’ve seen them here.", "\n\nMay 15 was a pretty good day for my ego. ‘", "Nuff said.", "\n\nI had one really excellent ski day in the Austrian Alps. ", "And the first time I’ve been able to fly to Europe without getting killed by back pain.", "\n\nI had a great trip hanging with Australian friends in SF, where I drank more than I thought possible anymore. ", "The trick is pacing.", "\n\nThe fun car got rear-ended by a driver who was texting, didn’t have a license, insurance, or even a valid license plate, and tried to drive away. ", "AAA covered it though, and McCurdy did a great job tracking down 30 year old parts and making it look the best it has since it rolled out of Stuttgart. ", "McCurdy fixed all the dents, scratches, and dings, and AAA spotted me the deductible, so there’s that. ", "I did lose use of it for six months though.", "\n\nwhat’s wrong with this picture?", "\n\nGadgets: The new ashcan Mac Pro, though it’s not really much faster than an MBP for most purposes. ", "It is amazing that you can get a supercomputer in something the size of a coffee pot. ", "Sadly Matlab is not optimized to use the screaming dual GPUs. ", "Or Thunderbolt for that matter. ", "Or retina displays. ", "Mathworks seems to live in a world where scientists are going to use worse displays, slower and fewer connections, and less computing power. ", "I wonder how that’s going to work out for them in the long run.", "\n\nDonjoy Iceman, though I’m pretty sure I’ve called that out before. ", "If you’re an athlete, you have to have one of these. ", "This is pro-level icing, or cryotherapy as it says on the rehab sheet.", "\n\nAdapter from my old Makita drill to the new Li-ion batteries. ", "The old NiMH batts were worn out and barely held a charge overnight. ", "Having to charge up every single time is a PITA if you wanted to just do something quickly. ", "$65 for new NiMH, or $85 for the Li-ion equivalent, $50 for reconditioning the old ones. ", "Or $40 for a a little plastic adapter that converts the 18V Li-ion 18V impact wrench batteries to the old NiMH battery. ", "Overpriced for a bit of plastic and metal, but it works a charm. ", "I probably could have bought a new battery-compatible drill for that much. ", "But this is more green. ", "It bugs the shit out of me to throw away a perfectly good drill.", "\n\nAnd just to rave about the impact wrench some more, the batteries stay charged and useful basically forever.", "\n\nSaddleback leather briefcase. ", "I am a sucker for good leather – just look in my closet. ", "I bought myself a real grown-up briefcase for my convalescence, since the worn-out, ahem, well-loved original first generation Chrome bike bag didn’t really work with my injury. ", "Maybe it’ll end up in the closet for a lot of its life, along with the Lost Worlds, Real McCoys, and Aeros that I can’t really wear much in modern-day post-climate-change-super-drought hot California. ", "Someday I’ll pony up full price for a lightweight Goodwear custom jacket that I can wear on a 50 F night. ", "The Saddleback end up in the closet, I mean. ", "The Chrome I expect will see me out, broken fastex buckles and completely worn-out velcro aside. ", "But I really like quality workmanship, and good leather. ", "Horsehide is the best.", "\n\nBut I’d buy a new Chrome replacement if I could find something I liked. ", "The new Chrome is a little too, and the Mission bags just aren’t talking to me either.", "\n\n2014 was the year of the manbag. ", "The man-purse. ", "The murse. ", "If one wants to be kind to one’s self, the satchel. ", "Being from Texas, and somewhat of a manly man (climbing-kneepad-and- bicycling-inspired-leg-shaving aside [1]), I don’t like it. ", "It goes against the grain. ", "But I lost access to half my pockets for three months, and the satchel is eminently practical. ", "Something had to be done, because wallet, keys, and phone is three pockets, and my jeans only have two pockets on each side. ", "Jack Spade’s manliness wasn’t helped by the card they helpfully included:\n\nJack? ", "Spade\n\nInjury pro-tip: put the belt in the pants before you put them on.", "\n\nNot my favorite year. ", "No life-altering films, books, or lovers. ", "No change of career. ", "A lot of time around doctors, and not enough climbing. ", "But the dogs are good, and have lots of friends (they’re off climbing with a buddy now, even if I can’t be), and my injuries should be well on the way to recovery, so things are looking up in the near future. ", "I might even be better (faster, stronger!) ", "with the old joints in for their 50000 mile tuneup. ", "Could be worse…\n\nWell, it could be raining. ", "Right now, in SoCal on a 90 F day in February, and injured, rain would be a pretty okay thing.", "\n\n[1] I don’t care if shaving my legs takes a few seconds off the PR on the ride to work. ", "I do care that when I inevitably lay it down, the leg hairs won’t be pulling on the adhesive. ", "And if you wear kneepads for climbing (more appropriately, thigh pads), you have to shave the bits that the pads sit on. ", "Or you’ll regret it." ]

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[ "Introduction\n============\n\nFew studies have evaluated detection of pancreatic carcinoma in situ (PCIS). ", "The number of patients with pancreatic cancer in Japan is increasing every year. ", "According to vital statistics of the Ministry of Health, Labor, and Welfare, the number of pancreatic cancer-related deaths exceeded 30,000 for the first time in 2013 [@OR1180-1] . ", "Furthermore, pancreatic cancer was reported to be the fourth leading cause of cancer-related deaths after lung, stomach, and colorectal cancer [@OR1180-1] . ", "Rahib et al. [", "@JR1180-2] estimated that by 2030, pancreatic cancer would be the second leading cause of cancer-related deaths in the United States. ", "The actual reason for the increased death rate is difficulty in early diagnosis, and by the time the disease is diagnosed, it is often too late. ", "Early diagnosis is critical for improving survival in these patients. ", "In 2012, the Japan Pancreas Society reported outcomes of the pancreatic cancer registry, in which 5-year survival rates according to tumor size were 80.4 % for 3- to 10-mm and 50 % for 10- to 20-mm tumors. ", "According to staging, the 5-year survival rates based on the Union for International Cancer Control classification were 85.8 % for stage 0 and 68.7 % for stage Ia disease [@JR1180-3] . ", "To improve the prognosis of pancreatic cancer, early diagnosis of stage 0 or of \\< 10-mm tumors is indispensable.", "\n\nThe 2013 Japanese clinical guidelines for pancreatic cancer emphasize detection of indirect findings, such as dilatation of the main pancreatic duct (MPD) and pancreatic cysts, for early diagnosis of pancreatic cancer [@JR1180-4] . ", "Considering that no neoplastic lesions are delineated on abdominal ultrasonography or computed tomography examination, magnetic resonance cholangiopancreatography (MRCP) and endoscopic ultrasound (EUS) are recommended [@JR1180-4] . ", "However, EUS findings of PCIS are not well characterized because very few reports have described PCIS in detail. ", "At the Onomichi General Hospital, since 2007, a concerted effort has been made to diagnose pancreatic cancer early through cooperation between hospitals and clinics [@JR1180-5] . ", "As a result of these efforts, a total of 16 cases of PCIS were detected over a period of 8 years. ", "This study was conducted to evaluate the EUS findings and pathological features of PCIS.", "\n\nPatients and methods\n====================\n\nThe current study was approved by the Institutional Review Board of the Onomichi General Hospital. ", "We retrospectively analyzed 16 patients (mean age, 68.4 ± 9.1 years; range, 52 -- 84 years; male-to-female ratio, 9:7) undergoing pancreatectomy and diagnosed with PCIS at the Onomichi General Hospital between January 2007 and April 2015.", "\n\nPanIN occurs from the pancreatic duct epithelium and is a noninvasive intraepithelial neoplastic lesion with a papillary or flat morphology observed at the microscopic level. ", "PanIN is composed of cylindrical to cubic cells with varying amounts of mucus that exhibiting varying degrees of cellular and structural atypia. ", "PanIN is usually found in pancreatic ducts with diameters less than 5 mm [@JR1180-6] . ", "It is classified as PanIN-1 to 3, and PCIS in this paper is defined pathologically as a lesion with atypia equivalent to PanIN-3.", " PanIN is considered to be an important lesion as a precursor to invasive ductal carcinoma. ", "According to the most recent Baltimore pathology classification, PCIS is defined as a lesion equivalent to high-grade PanIN [@JR1180-7] .", "\n\nAn intraepithelial lesion corresponding to PanIN-3 was found in the MPD or the pancreatic duct branches surrounding the MPD stricture. ", "The maximum diameter of the progress range of six cases of PCIS described in pathological diagnosis was 2 to 20 mm (median 10.5 mm). ", "In 12 of 16 cases, adenocarcinoma was detected by preoperative pancreatic juice cytology, and surgery was performed by diagnosis of pancreatic cancer. ", "Because adenocarcinoma was detected by pancreatic juice cytology, endoscopic ultrasound-guided fine-needle aspiration (EUS-FNA) was not a requirement. ", "In three cases, malignant cells were not recognized by preoperative pancreatic juice cytology, but malignancy could not be ruled out on diagnostic imaging, and surgery was performed for a diagnosis of suspected pancreatic cancer. ", "In two of these three cases, EUS-FNA was not required because hypoechoic areas surrounding the MPD stricture were observed and fibrosis by PCIS was assumed. ", "1 case had a hypoechoic mass and EUS-FNA was also considered, but because of coexisting distal cholangiocarcinoma, EUS-FNA was omitted and surgery was performed. ", "In one case, surgery was performed for diagnosis of distal cholangiocarcinoma, and PCIS was incidentally observed in the pancreatic cut end margin of the resected specimen. ", "Only in that case, MPD stricture and dilatation were not observed. ", "All 16 cases in this paper are PCIS and invasive pancreatic duct carcinoma and intraductal papillary mucinous neoplasms (IPMN) were not included.", "\n\nMPD dilatation on the distal side of the MPD stricture was defined as a diameter of 3 mm or more, and larger than the MPD diameter on the proximal side of the MPD stricture. ", "The key findings that led to early diagnosis were dilatation of the MPD in 10 patients, dilatation of the MPD plus pancreatic cyst in five, and incidental diagnosis in one. ", "The affected sites were the pancreatic head in four patients, pancreatic body in 11, and pancreatic tail in one. ", "The lesions were localized in the MPD plus pancreatic duct branches in 10 patients, MPD in four, and pancreatic duct branches in two. ", "MPD stricture was confirmed on MRCP or endoscopic retrograde cholangiopancreatography (ERCP) in 15 patients (93.8 %). ", "EUS was preoperatively performed in all patients. ", "The study subjects were examined in terms of stricture of the MPD on EUS, presence or absence of hypoechoic areas surrounding the MPD stricture on EUS, the noncancerous part (pancreas of background) on EUS and histopathology, and histological findings adjacent to the area of PCIS.", "\n\nEUS findings for the noncancerous part were evaluated in accordance with the Rosemont classification [@JR1180-8] and the 2009 Japanese Clinical Diagnostic Criteria for Chronic Pancreatitis [@OR1180-9] . ", "In 2009, Catalano et al. [", "@JR1180-8] proposed the new EUS-based diagnostic criteria for chronic pancreatitis (Rosemont classification). ", "In Japan, this proposal was accepted and clinical diagnostic criteria for early chronic pancreatitis were included in the 2009 Japanese clinical diagnostic criteria for chronic pancreatitis [@OR1180-9] as the first in the world. ", "According to the diagnostic criteria, the four markers of pancreatic parenchyma disorder due to pancreatitis or risk factors for pancreatitis are: 1) repeated and inordinate abdominal pain; 2) abnormality (serum or urine) of pancreatic enzyme levels; 3) reduced pancreatic exocrine function; and 4) continuous heavy drinking \\> 80 g/day. ", "Early chronic pancreatitis was defined as a patient who had two or more of the four markers and a slightly abnormal finding of the pancreatic parenchyma or pancreatic duct suggesting early lesions of chronic pancreatitis on EUS or ERCP. ", "For EUS diagnosis, seven findings are relevant: 1) lobularity with honeycombing; 2) lobularity without honeycombing; 3) hyperechoic foci without shadowing; 4) stranding; 50 cysts; 6) dilated side branches; and 7) hyperechoic main pancreatic duct margin. ", "When two or more items including 1 and 4 were recognized, an image was deemed to fulfill the diagnosis of early chronic pancreatitis. ", "In 2016, Whitcomb et al. [", "@JR1180-10] announced a \\\"new mechanistic definition\\\" of chronic pancreatitis, taking into account the onset mechanism of pancreatitis. ", "The proposed definition said, \"Chronic pancreatitis is a pathologic fibro-inflammatory syndrome of the pancreas in individuals with genetic, environmental and/or other risk factors who develop persistent pathologic responses to parenchymal injury or stress.\" ", "In the new definition, a conceptual model of five stages also was proposed, from \\\"at risk\\\" to \\\"AP-RAP, acute pancreatitis and recurrent acute pancreatitis,\\\" \\\"early CP, chronic pancreatitis,\\\" and \\\"established CP,\\\" to \\\"end stage CP\\\". ", "\\\"Early CP\\\" is the preliminary stage of \\\"established CP\\\" and is regarded as a condition that can be brought into remission. ", "\\\"Established CP\\\" is a stage where obvious functional abnormalities are confirmed in two or more systems -- immune, exocrine, and endocrine -- and pathologic pain and metaplasia are present because of persistent parenchymal injury or stress added to \\\"early CP.\\\" \\\"End stage CP\\\" is a stage where dysfunctions are recognized in two or more systems. ", "Pancreatic fatty infiltration was determined by pancreatic parenchymal hyperechoic findings with deep echo attenuation in EUS findings of the noncancerous part. ", "It is a well-known fact that in cases with MPD stricture, obstructive pancreatitis occurs on the distal side of the stricture. ", "Therefore, pathological findings of the noncancerous part were proximally evaluated from the MPD stricture to exclude the effects of obstructive pancreatitis. ", "Pathological findings of chronic pancreatitis were examined according to the characteristic histological findings included in the 2009 Japanese Clinical Diagnostic Criteria for Chronic Pancreatitis [@OR1180-9] . ", "Definitive diagnosis of chronic pancreatitis was based on observation of fibrosis and loss of pancreatic parenchyma. ", "Pancreatic fibrosis was primarily observed interlobularly with a nodular small lobe, which in other words, appears like cirrhosis. ", "Criteria for definitive diagnosis of chronic pancreatitis include loss of pancreatic parenchyma with interlobular fibrosis or interlobular and intralobular fibrosis. ", "The Olympus EU-ME1, EU-ME2, or Hitachi-Aloka Medical ProSound Alpha 10 instrument was used as the measurement device, and the Olympus GF-UE260-AL5 or GF-UM2000 scope was used for endoscopy.", "\n\nResults\n=======\n\nClinicopathological characteristics of the 16 subjects are shown in [Table 1](#TB1180-1){ref-type=\"table\"} , [Table 2](#TB1180-2){ref-type=\"table\"} , and [Table 3](#TB1180-3){ref-type=\"table\"} .", "\n\n###### Study group (n = 16), including the characteristics of pancreatic carcinoma in situ.", "\n\n ------------------------- -----------------------------\n Age, mean ± SD 68.4 ± 9.1 (52 -- 84) years\n Sex ratio (male/female)  9/7\n Opportunity \n MPD dilatation 10\n MPD dilatation + cysts  5\n Other  1\n Region \n Head  4\n Body 11\n Tail  1\n Localization \n MPD + Branch 10\n MPD  4\n Branch  2\n ------------------------- -----------------------------\n\nNumber of cases is indicated unless otherwise indicated. ", "SD, standard deviation; MPD, main pancreatic duct.", "\n\n###### Clinical information on patients included in the study.", "\n\n Case Age Sex Opportunity Region Localization EUS findings MPD stricture/ Hypoechoic (size) Pathological findings Noncancerous part/ Periphery of the lesion\n ------ ----- ----- ------------------------ -------- -------------- ----------------------------------------------- ------------------------------------------------------------------\n  1 73 F MPD dilatation Body Branch  +/ +  CP/Inflammation and fibrosis\n  2 70 M MPD dilatation Body MPD + Branch  +/ +  CP/Inflammation and fibrosis\n  3 78 F MPD dilatation Body MPD  +/ +  CP/Inflammation and fibrosis\n  4 61 M MPD dilatation Body MPD  +/− CP/Inflammation and fibrosis\n  5 82 M MPD dilatation + Cysts Head Branch  +/ +  CP/Inflammation and fibrosis\n  6 84 F MPD dilatation Body MPD + Branch  +/ +  CP/Inflammation and fibrosis\n  7 75 M MPD dilatation + Cysts Body MPD + Branch  +/− CP/Inflammation and fibrosis\n  8 65 F MPD dilatation Body MPD + Branch  +/ + (10 mm) CP/Inflammation and fibrosis\n  9 63 F MPD dilatation + Cysts Body MPD + Branch  +/− normal/Inflammation and fibrosis\n 10 66 M MPD dilatation + Cysts Head MPD + Branch  +/ + (11 mm) CP/Inflammation and fibrosis\n 11 58 M MPD dilatation + Cysts Tail MPD + Branch  +/− CP/Inflammation and fibrosis\n 12 52 F MPD dilatation Body MPD + Branch  +/ + (10 mm) normal/Inflammation and fibrosis\n 13 59 F MPD dilatation Body MPD  +/− normal/Inflammation and fibrosis\n 14 76 M MPD dilatation Head MPD + Branch  +/ +  CP/Inflammation and fibrosis\n 15 69 M Other (accidental) Head MPD −/− CP/Inflammation and fibrosis\n 16 64 M MPD dilatation Body MPD + Branch  +/− CP/Inflammation and fibrosis\n\nMPD, main pancreatic duct; CP, chronic pancreatitis.", "\n\n###### Pathological findings of the patients included in the study.", "\n\n Case Age Sex EUS findings Pathological findings \n ------ ----- ----- --------------- ----------------------- -------- ----------------------- --------------------------- -----------------\n  1 73 F  +/ +  FI CP Inflammation and fibrosis \n  2 70 M  +/ +  CP CP Inflammation and fibrosis \n  3 78 F  +/ +  FI CP Inflammation and fibrosis \n  4 61 M  +/− FI CP FI Inflammation and fibrosis \n  5 82 M  +/ +  CP CP Inflammation and fibrosis \n  6 84 F  +/ +  CP CP Inflammation and fibrosis \n  7 75 M  +/− FI CP FI (severe) Inflammation and fibrosis \n  8 65 F  +/ + (10 mm) FI CP FI Inflammation and fibrosis \n  9 63 F  +/− normal normal Inflammation and fibrosis Mild fibrosis\n 10 66 M  +/ + (11 mm) CP CP Inflammation and fibrosis \n 11 58 M  +/− FI CP FI (severe) Inflammation and fibrosis Mild fibrosis\n 12 52 F  +/ + (10 mm) ECP normal Sporadic fat droplets Inflammation and fibrosis Severe fibrosis\n 13 59 F  +/− ECP normal Sporadic fat droplets Inflammation and fibrosis \n 14 76 M  +/ +  CP CP Inflammation and fibrosis \n 15 69 M −/− CP CP Inflammation and fibrosis \n 16 64 M  +/− FI CP FI Inflammation and fibrosis \n\nMPD, main pancreatic duct; FI, fatty infiltration; CP, chronic pancreatitis; ECP, early chronic pancreatitis.", "\n\nAn MPD stricture was identified on EUS in 15 patients (93.8%). ", "One such patient is shown in [Fig.", " 1](#FI1180-1){ref-type=\"fig\"} . ", "In one patient, the MPD stricture could not be identified on EUS; identification of the same stricture was also difficult on MRCP. ", "PCIS in this patient was incidentally diagnosed on pathological examination of the resected pancreatic specimen.", "\n\n{#FI1180-1}\n\nOn EUS, the hypoechoic areas surrounding the MPD stricture were observed in nine patients (56.3 %), including three (18.8 %) with a hypoechoic mass (10 -- 11 mm). ", "One such patient is shown in [Fig.", " 2](#FI1180-2){ref-type=\"fig\"} .", "\n\n{#FI1180-2}\n\nEUS findings on the noncancerous part indicated chronic pancreatitis in six patients (37.5 %), fatty infiltration in seven (43.8 %), early chronic pancreatitis [@JR1180-7] in two (12.5 %), and normal pancreas in one (6.3 %). ", "Histopathological examination of the noncancerous part (proximal to the MPD stricture) revealed characteristic findings of chronic pancreatitis in 13 patients (81.3 %), including eight with severe inflammation in the pancreatic parenchyma distal to the stricture) and pancreatic fatty infiltration in five (31.3 %). ", "Concurrent IPMN was observed in the resected and residual pancreas in five patients (31.3 %), all of whom had branch duct IPMN. ", "Concurrent pancreatic intraepithelial neoplasia (PanIN) not in continuity with the primary lesion of the resected pancreas was observed in 12 patients (75 %). ", "Two patients who fulfilled the Japanese Clinical Diagnostic Criteria for early chronic pancreatitis [@OR1180-9] (Cases 12 and 13) were relatively young women with no history of regular alcohol intake, and did not show characteristic histological findings of chronic pancreatitis, but only showed mild sporadic fat droplets. ", "Cases of chronic pancreatitis, pancreatic fatty infiltration, and early chronic pancreatitis are shown in [Fig.", " 3](#FI1180-3){ref-type=\"fig\"} as pathological findings of noncancerous part, respectively [Fig.", " 3a](#FI1180-3){ref-type=\"fig\"} shows chronic pancreatitis (Case 8), [Fig.", " 3b](#FI1180-3){ref-type=\"fig\"} shows fatty infiltration (Case 7), and [Fig.", " 3c](#FI1180-3){ref-type=\"fig\"} shows early chronic pancreatitis (Case 13).", "\n\n{#FI1180-3}\n\nPerilesional interstitial inflammatory cell infiltration and fibrosis were observed in all 16 patients. ", "One such patient is shown in [Fig.", " 4](#FI1180-4){ref-type=\"fig\"} .", "\n\n{#FI1180-4}\n\nDiscussion\n==========\n\nIn the 1950 s, a hypothesis was proposed that pancreatic cancer progressively develops from hyperplasia of the pancreatic duct epithelium after development into atypical lesions [@JR1180-11] . ", "In 2000, Hruban et al. [", "@JR1180-12] proposed PanIN, a multistep model of the carcinogenesis of pancreatic cancer. ", "Thereafter, molecular pathological examinations and analysis of genetically modified mice demonstrated the precancerous nature of PanIN. ", "Malignant transformation in the pancreas is caused by accumulation of genetic abnormalities in genes, such as in *KRAS* , *CDKN2A* , *TP53* , and *SMAD4* , with a stepwise transition from PanIN-1A to PanIN-3, corresponding to carcinoma in situ and progressing to invasive cancer. ", "Pancreatic cancer is well-known to be accompanied by severe fibrosis around the tumor cells and desmoplastic reaction (DR). ", "In 2004, pancreatic stellate cells, which contribute to fibrosis in chronic pancreatitis, were demonstrated to produce an extracellular matrix of cancer stroma [@JR1180-13] . ", "Interaction between pancreatic cancer and DR has also been explained at the molecular level, in which partial changes are observed at the stage of PanIN and IPMN without invasive cancer. ", "Furthermore, Yachida et al. [", "@JR1180-14] examined pancreatic cancer using autopsy cases; they estimated a mean of 11.7 ± 3.1 years from initial appearance of the genetic abnormality to development of invasive cancer; 6.8 ± 3.4 years from the stage of invasive cancer to development of metastatic potential, and 2.7 ± 1.2 years from acquiring metastatic potential until actual metastasis. ", "We believe that development of diagnostic interventions for use during the period between carcinoma in situ and development of invasive cancer could help improve the likelihood of early diagnosis of pancreatic cancer. ", "The clinical significance for the reader of Endoscopy International Open is to identify early pancreatic cancer by understanding imaging and pathological findings for PCIS and carrying out appropriate diagnostic imaging.", "\n\nThe regions were the pancreatic head in four patients, pancreatic body in 11, and pancreatic tail in one ( [Table 1](#TB1180-1){ref-type=\"table\"} ). ", "Most cases of PCIS were identified through indirect means, such as dilatation of the MPD and pancreatic cysts. ", "Because it is difficult to make such findings in the pancreatic head and tail on abdominal US, lesions in the body of the pancreas may be overrepresented in this study.", "\n\nDel Chiaro M et al. [", "@JR1180-15] reported that during a median follow-up of approximately 1 year, pancreatic lesions were detected in 40 % of patients, of whom five underwent surgery, and a noninvasive magnetic resonance imaging (MRI)-based screening protocol in individuals at risk seems to be effective. ", "Harinck et al. [", "@JR1180-16] reported that EUS and/or MRI detected clinically relevant pancreatic lesions in 6 % of high-risk individuals, and both imaging techniques were complementary rather than interchangeable. ", "Canto MI et al. [", "@JR1180-17] reported that screening of asymptomatic high-risk individuals frequently detects small pancreatic cysts, including curable, noninvasive high-grade neoplasms. ", "EUS and MRI detect pancreatic lesions better than does CT. ", "Verna EC et al. [", "@JR1180-18] reported that pancreatic cancer screening for high-risk patients with a comprehensive strategy of imaging and genetics is effective and identifies curable neoplasms that can be resected. ", "Yasuda I et al. [", "@JR1180-19] reported that EUS is strongly recommended for early detection of small pancreatic cancer in patients in whom dilation of the main pancreatic duct was detected in previous imaging tests, with or without increase of pancreatic enzymes or tumor markers. ", "Kamata K et al. [", "@JR1180-20] reported that IPMN-concomitant pancreatic ductal adenocarcinomas are quite often found at diagnosis and during follow-up, and EUS examination of the whole pancreas plays an important role in management of IPMNs as it allows early detection of these small, invasive carcinomas. ", "Reports on usefulness of MRCP and EUS for early diagnosis of pancreatic cancer are scattered, but there are very few reports on PCIS imaging diagnosis. ", "In diagnostic imaging, PCIS itself cannot be drawn, so it is necessary to estimate from the MPD stricture and surrounding tissue change by PCIS.", " It is important for image diagnosis to capture localized MPD stricture and a surrounding fibrotic area caused by PCIS.", " Noninvasive MRCP is useful for screening for MPD stricture, and EUS with high resolution is effective for evaluating the surrounding fibrotic area.", "\n\nA localized MPD stricture was frequently observed on the image finding for PCIS.", " Pathologically, several cases in our study exhibited localized inflammation and fibrosis in the interstitial tissue around the pancreatic ducts in which the PCIS was located. ", "In our report concerning 16 patients with PCIS, most patients had a localized MPD stricture (15/16, 93.8 %) ( [Table 2](#TB1180-2){ref-type=\"table\"} ). ", "Evaluation by MRCP revealed dilatation of the MPD distal to the stricture in nine of 16 patients (56.3 %), whereas six (37.5 %) did not show any dilatation. ", "Even in patients with mild MPD stricture and no dilatation at the MPD distal to the stricture, presence of PCIS should be considered. ", "We believe that detailed examination should be performed in such cases. ", "Furthermore, due consideration should be given to the fact that the site of the MPD stricture and cancer as perceived on MRCP and EUS may not necessarily coincide with the pathologically confirmed site [@JR1180-21] . ", "There are some cases wherein the observed stricture range is more extensive than the area occupied by the carcinoma; there exist some cases which are contrary [@JR1180-21] . ", "At the Onomichi General Hospital, surgical plans for patients with localized MPD stricture and positive pancreatic juice cytology are prepared, considering the possibility that the cancer may be more extensive than that inferred from the range of the stricture. ", "We make an incision from the margin of the stricture to a distance of approximately 2 cm distally or proximally, and verify the margin by an intraoperative rapid pathological assessment [@JR1180-21] . ", "Furthermore, concurrent PanIN is commonly found in the resected pancreas. ", "Therefore, from the perspective of multicentric carcinogenesis, rigorous postoperative follow-up observation is recommended in such cases.", "\n\nBased on comparisons with pathological findings, it was suggested that hypoechoic areas surrounding the MPD stricture on EUS might reflect localized inflammation and fibrosis in the vicinity of the lesion. ", "Regarding the hypoechoic areas, we did not measure them because the boundary with the surrounding pancreatic parenchyma was unclear. ", "Regarding the hypoechoic mass observed in three cases, it was measured because the boundary with the surrounding pancreatic parenchyma was clear. ", "The hypoechoic mass may be drawn due to localized inflammation and fibrosis in the interstitial tissue around the pancreatic ducts in which the PCIS was located, and it is necessary to differentiate it from small invasive ductal carcinoma. ", "When the hypoechoic lesion is depicted surrounding the MPD stricture, if the boundary with the surrounding pancreatic parenchyma is unclear, it is necessary to distinguish the fibrotic area associated with PCIS.", " Furthermore, if the boundary with the surrounding pancreatic parenchyma is clear, it is necessary to distinguish small invasive ductal carcinoma in addition to PCIS. ", "We also observed that patients without hypoechoic areas surrounding the MPD stricture tend to have less fibrosis and more extensive fatty infiltration ( [Table 3](#TB1180-3){ref-type=\"table\"} ). ", "Although other causes, such as chronic pancreatitis, can result in findings similar to those of pancreatic duct stricture for patients with pathologically proven malignant cells, hypoechoic areas surrounding the MPD stricture are useful markers indicating the presence of cancer. ", "Moreover, such areas, in some cases, were more extensively delineated beyond the range of stenosis. ", "However, the reliability of using such criteria for cancer diagnosis must be examined in a larger sample of patients.", "\n\nAt the Onomichi General Hospital, when hypoechoic areas are observed surrounding the MPD stricture, we note the possibility of PCIS and proactively perform pancreatic juice cytology multiple times using ERCP and endoscopic nasopancreatic drainage (ENPD). ", "This approach has achieved good diagnostic results [@JR1180-22] . ", "In the event of mass-like delineation, such as that observed in three of our cases, because differentiation between small invasive ductal carcinoma and PCIS is required, performing EUS-FNA is considered initially. ", "However, it is difficult to rule out PCIS even when EUS-FNA results are negative. ", "To differentiate PCIS from invasive ductal carcinoma, careful imaging examination is required. ", "As a diagnostic strategy for MPD stricture, EUS reveals hypoechoic areas with unclear boundary surrounding the MPD stricture, we consider the possibility of PCIS, and perform ERCP (ENPD). ", "When a hypoechoic mass with clear boundary surrounding the MPD stricture is seen on EUS, we consider the possibility of small invasive ductal carcinoma, and perform EUS-FNA. ", "However, even if EUS-FNA results are negative, it does not rule out PCIS, so we also consider ERCP (ENPD). ", "In the future, differential use of ERCP (ENPD) and EUS-FNA must be studied further.", "\n\nWe believe that screening for cases with risk factors for pancreatic cancer is important for early diagnosis of the disease. ", "Chronic pancreatitis, pancreatic fatty infiltration, and IPMN have been reported to be risks factor for pancreatic cancer [@JR1180-23] [@JR1180-24] [@JR1180-25] [@JR1180-26] [@JR1180-27] . ", "In this study, histopathological examination of the noncancerous part (proximal to the MPD stricture) revealed characteristic findings of chronic pancreatitis in 13 patients (81.3 %). ", "Histopathological findings of the noncancerous part demonstrated pancreatic fatty infiltration in five patients (31.3 %). ", "Because pancreatic fatty infiltration is often seen to be scattered in the noncancerous part, its size has not been measured. ", "Based on our examination of the 16 patients with PCIS, it appears that fatty infiltration tends to obviate EUS findings of chronic pancreatitis ( [Table 3](#TB1180-3){ref-type=\"table\"} ). ", "Concurrent IPMN was observed in the resected and residual pancreas in five patients (31.3 %), all of whom had branch duct IPMN. ", "It is necessary to pay attention to occurrence of pancreatic cancer at a site distant from the IPMN. ", "In this study, the two patients who fulfilled the Japanese Clinical Diagnostic Criteria for early chronic pancreatitis [@OR1180-9] were relatively young women who had no history of regular alcohol intake; they did not demonstrate characteristic histological findings of chronic pancreatitis, but only had mild sporadic fat droplets. ", "To clarify the pathological findings and long-term prognosis (progression to chronic pancreatitis and risk of cancer onset) in patients with early chronic pancreatitis, data concerning more cases must be gathered in the future [@JR1180-28] .", "\n\nConclusions\n===========\n\nWe examined the EUS findings from and pathological characteristics of 16 patients with PCIS. ", "PCIS frequently causes localized changes in inflammation and fibrosis around the pancreatic duct. ", "It often accompanies chronic pancreatitis and pancreatic fatty infiltration in the background pancreas. ", "EUS offers sufficient resolution to demonstrate pancreatic changes of PCIS.", "\n\nDr. Izumi would like to express his deepest gratitude to Professor Kazuaki Chayama of the Department of Gastroenterology and Metabolism of Hiroshima University, and to Professor Yutaka Sasaki of the Department of Gastroenterology and Hepatology of Kumamoto University for their cooperation in training at Onomichi General Hospital. ", "A part of this report was presented at the 89th Congress of the Japan Gastroenterological Endoscopy Society (Nagoya city, May, 2015).", "\n\n**Competing interests** None\n" ]

{ "pile_set_name": "PubMed Central" }

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[ "Facebook and Google are at it again, and application developers are getting caught in the crossfire.", "\n\nFacebook created last week an official list of acceptable ad providers that developers can use to make money with their Facebook applications. ", "Notably absent from the list is Google's popular AdSense service, an omission that has developers on various forums up in arms. ", "Also missing: Amazon.com, which offers an advertising API.", "\n\nGoogle and Amazon apparently didn't make the list because they refused to sign on the dotted line of Facebook's new and arguably restrictive terms of service for ad providers. ", "In short, advertising providers are forbidden from receiving, directly or indirectly, any type of Facebook user data, even if a Facebook user consents to sharing it. ", "Should any such data end up in an ad provider's stores, the provider is required to alert Facebook immediately and purge said data.", "\n\nThe list isn't finalized, so it's entirely possibly Google and Amazon will sign on. ", "But given the recent spats between Google and Facebook over sharing user data as they fight to grab the most user eyeballs, it's tough to predict who is going to blink first.", "\n\nAs it stands, developers are expressing outrage that they're no longer permitted to use AdSense and Amazon. \"", "I hope you don't expect us to put our money into small startups from the approved list, simply because they are unable to supply enough inventory or haven't earned their reputation yet,\" wrote developer Anatoly Lubarsky on the Facebook Developers forum. \"", "Regarding larger companies on the list: Most of them have a very bad track record.\"", "\n\nLubarsky and others observed that users and developers could end up suffering if developers move to lesser-known, less reliable providers. \"", "It downgrades the user experience from Amazon and Google AdSense ads to badly designed intrusive ads from 'approved' companies,\" he wrote.", "\n\nOther commentators observed that forcing developers to switch to unreliable ad providers could have undesirable long-term ramifications on the quality of apps that make it to Facebook. \"", "Now that Google has been axed, we have to find an alternative. ", "If the alternatives don't pay as well, then developers will get discouraged from developing on Facebook,\" read a post from username vincenz2004.", "\n\nThere's also a passionate discussion taking place at Hacker News. ", "One of the participants, with the username wheels, says the move is emblematic of \"the changing landscape of ever more tightly controlled 'platforms' [such as Facebook]. ", "It used to be that the way software interacted with a platform was via APIs; now it's increasingly in alignment with the platform owner's business goals as well.\"", "\n\n\"When Microsoft crushed Netscape, it did so by controlling the platform and making the alternative seem unnecessary, but it would have been unthinkably brutish for them to disallow another browser,\" he wrote.\" ", "But what the App Store and Facebook are doing makes Microsoft's actions look positively charitable.\"", "\n\nWhether Google or Amazon will bow to Facebook's terms remains to be seen. ", "Developers are going to struggle in the short term as they're forced to acclimate to a different provider, though the standoff could give other ad providers out there a chance to shine, thus opening up more choices to developers.", "\n\nThis story, \"Developers rage after Facebook blocks Google AdSense,\" was originally published at InfoWorld.com. ", "Get the first word on what the important tech news really means with the InfoWorld Tech Watch blog. ", "For the latest business technology news, follow InfoWorld.com on Twitter." ]

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[ "Holy cow, there’s only three endings left in the book? ", "IT’S ANNOUNCEMENT TIME! ", "Find out what books the brothers could be reading next, and make sure to vote on Twitter for the one you most want to inflict upon them! (", "One of the options is a user suggestion!)", "\n\nAlso, Chris debuts the new segment Cool Days & Philosopher Knights, Matt gets to skip making a quiz so the guys can ANNOUNCE NEW BOOK OPTIONS, predictions are touched on, and did you know dragons might be real after all?", "\n\nTell us what to Read Next on Twitter\n\nT-Shirt Time: Hogmanay All Day!", "\n\nListen on Apple Podcasts\n\nWe’re on Stitcher, Too\n\nCheck Out Songs from the Musical and More on SoundCloud\n\nCatch up on Meanwhile in the Cave of Time, if You So Desire\n\nLook at More Dumb Stuff on Our YouTube\n\nOriginal illustrations by Paul Granger.", "\n\n🏁🤡\n\n\n\n" ]

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[ "Q:\n\nVBScript: Printing all characters in UTF-8\n\nI'm writing a simple script to build a HTML page to check if all the characters in UTF-8 are being rendered properly:\nDim oStream : Set oStream = CreateObject(\"ADODB.Stream\")\noStream.", "Open\noStream.", "CharSet = \"utf-8\"\n\n' Code writing out the top HTML snipped for brevity\n\nDim iChar\nFor iChar = 32 to 255\n oStream.", "WriteText iChar & \" = \" & Chr(iChar) & \"<br/>\" & VbCrLf\nNext\n\n' Code writing out the bottom HTML snipped for brevity\n\noStream.", "SaveToFile \"page.html\", 2\nSet oStream = Nothing\n\nThis works great, until I try and print characters beyond 255 in which case I get the error: Invalid procedure call or argument: 'Chr' (800A0005).", "\nCan someone please explain how I can print all the characters within the UTF-8 character set?", "\nThe test is designed to see how the raw characters renders - so having a file with &#256; in it would not be a correct as it would need to print the actual Latin capital letter A with macron (Ā).", "\n\nA:\n\nYou want the ChrW() variant;\n\nChrW is provided for 32-bit platforms that use Unicode characters.", "\n Its argument is a Unicode (wide) character code, thereby avoiding the\n conversion from ANSI to Unicode.", "\n\n" ]

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[ "It’s been two years since former Hollywood power couple Angelina Jolie and Brad Pitt called it quits, but the custody battle their split precipitated seems no closer to ending. ", "At issue now — according to TMZ — is whether Jolie is allowing Pitt to be a part of their children’s lives, as mandated by the court. ", "If she isn’t, an expert tells Yahoo Lifestyle, she may be in danger of losing custody herself.", "\n\nAfter reports that Angelina Jolie was attempting to block Brad Pitt from seeing their shared children, a judge is taking measures to ensure that the kids can interact freely with their dad. (", "Photo: Getty Images, Anthony Harvey)\n\nThe tug of war over the couple’s six children — Maddox, 17; Pax, 14; Zahara, 13; Shiloh, 12; and Knox and Vivienne, 10 — began almost immediately after Jolie filed for divorce in 2016, citing “irreconcilable differences.” ", "Just 10 days later, Jolie was granted full custody of all six kids with Pitt, whom she accused of having a drug problem. ", "Pitt, as a result, was given therapist-supervised visitation rights with random drug testing required.", "\n\nAt the heart of the early battle were allegations that Pitt had been physically abusive to Maddox — Jolie’s eldest, whom she adopted prior to meeting Pitt on the set of Mr. and Mrs. Smith. ", "Jolie alleged that a drunken Pitt became physically abusive toward Maddox while on a fuel stop aboard their private plane. ", "An investigation was launched by the Los Angeles County Department of Child and Family Services (DCFS), which — in November 2016 — cleared Pitt of any child abuse charges.", "\n\nJolie then released a statement saying she was satisfied that DCFS felt the right “safeguards were in place” and agreed to form a “united front” with Pitt, who was granted full visitation rights. ", "The plan seemed to be running smoothly until this June, when the Blast uncovered court documents showing a judge’s concern about Pitt’s lack of access to the kids. ", "The document says in part, “If the minor children remain closed down to their father … it may result in a reduction of the time they spend with [Jolie] and may result in the Court ordering primary physical custody to [Pitt].”", "\n\nIn a statement to Refinery29, representatives for Jolie called it a “misleading leak” that only serves to hurt the kids. “", "Angelina has been focused only on their health and needs, which is why it was so important that this last court hearing be conducted privately,” the reps said. “", "It’s deplorable that someone, for their own selfish reasons, leaked selective portions of the confidential and sealed court record to create an inaccurate and unfair picture of what is really happening.”", "\n\nSubsequently, Jolie filed a claim against Pitt alleging that he had paid “no meaningful child support since separation” (a claim he vehemently denies). ", "While the monetary disagreements are a battle all their own, Kara M. Bellew, a New York City-based divorce attorney who handles high-profile clients, suggests Jolie may be in danger of losing custody.", "\n\n“The starting point for any custody dispute is the best interest of the children — that’s the standard,” Bellew tells Yahoo Lifestyle. “", "The law takes the view that it’s in the best interest of the children to have meaningful relationships with both parents. ", "The burden is on the custodial parent to foster and facilitate the relationship between the kids and other parent. ", "If the court believes the custodial parent is unwilling or unable to do that, then that can be the basis for the court to change custody.”", "\n\nAlthough Bellew thinks restrictions made sense in the beginning, she says that if Pitt has shown himself to be fit to parent, the law allows him open access. “", "The safety of the kids is going to be at the forefront for the court, but it’s so inauthentic for someone to see a child with a third party present,” she says. “", "So if you have someone who is ostensibly doing the right things — they’re sober, they’re compliant, he’s in therapy — then, well, he’s their dad,” she says. “", "The courts really start to relax supervision, because in that case, he has every right to enjoy a meaningful relationship with them without her interference.”", "\n\nBellew can only speculate as to Jolie and Pitt’s situation, but in others like it that she has dealt with, it’s often the children’s lawyers who can push a judge over the edge. “", "Children are almost routinely assigned attorneys in custody cases. ", "One may say, ‘I hate my dad; I never want to see him,’ and another may say, ‘I want to see him every day,’ and in that case, they need their own attorney,” she said. “", "Their job is to advocate their client positions.”", "\n\nBased on the news that’s come out publicly, Bellew thinks Jolie may need to tread lightly when it comes to Pitt — or else risk losing the custody she already has. “", "Even if Angelina thinks Brad is a dirtbag, she should be able to put that aside and say, ‘My children deserve a father and they deserve this relationship,’” says Bellew. “", "He shouldn’t be relegated to be an afterthought.”" ]

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