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tomekkorbak

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[ "FEDERAL DEFICIT WIDENED IN AUGUST\n\nThe federal government went another $27.8 billion deeper in the red in August, bringing the budget deficit to $203.4 billion with one month left to go in the government's fiscal year.", "\n\nThe latest projection of the Office of Management and Budget is for the 1985 deficit to reach a record $211.3 billion by the Sept. 30 end of the fiscal year.", "\n\nThe existing record is 1983's $195.4 billion.", "\n\nSpending on social programs through the Department of Health and Human Services is up 2 percent from the same October-August period in the last fiscal year, to $290.5 billion.", "\n\nPentagon spending, the second-largest category, is up 10.2 percent, to $223 billion.", "\n\nThe third largest single category of spending is now interest on the national debt, up 17.1 percent from the same 11-month period last year, to $165.7 billion.", "\n\nThe administration projects that in the 1986 fiscal year the interest on the $1.8 trillion national debt will be larger than the annual deficit. ", "Interest alone is expected to be $179.3 billion next year, compared to a deficit the White House says will be only $175.4 billion.", "\n\nWith the economy as slow as it is, however, many analysts say next year's projection for the total deficit is unrealistically low and that, if interest rates go higher, the interest cost could also be more.", "\n\nThe White House expects the government to end this fiscal year having spent $937.3 billion while taking in only $736 billion.", "\n\nIn August the government spent $83.6 billion and collected $55.8 billion.", "\n\nIndividual income taxes, at $296.3 billion for 11 months, are running 12 percent ahead of last year.", "\n\nCorporate taxes, at $50.4 billion, are also 12 percent ahead of the same period in fiscal 1984." ]

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[ "Q:\n\nИнтеграция сортировки по цене в фильтр\n\n$(\".select\").change(function(){\r\n\r\n // список доступных фильтров\r\n var filters = $(\".select\").toArray().map( function(v){\r\n return $(v).data('filter');\r\n });\r\n \r\n // проверяем все элементы списка\r\n $(\"#items li\").each(function(idx, li){\r\n var show = true; // по умолчанию показываем\r\n \r\n // сверяем все data- атрибуты доступных фильтров\r\n $.each(filters, function(fIdx, fname){ \r\n // значение селекта фильтра \r\n var fv = $(\".select-\" + fname + \" :selected\").data('sort');\r\n \r\n if(fv == 'all') return true;\r\n \r\n // сверяям значение селекта с дата-атрбутом\r\n if( $(li).data(fname) !", "= fv){\r\n show = false;\r\n return false;\r\n } \r\n });\r\n \r\n $(this).toggle(show);\r\n });\r\n\r\n});\n<script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js\"></script>\r\n<select class=\"select select-type\" data-filter=\"type\">\r\n <option value=\"all\" data-sort=\"all\">All</option>\r\n <option value=\"2\" data-sort=\"pistol\">Pistol</option>\r\n <option value=\"3\" data-sort=\"riffle\">Riffle</option>\r\n <option value=\"4\" data-sort=\"smg\">SMG</option>\r\n</select>\r\n\r\n<select class=\"select select-class\" data-filter=\"class\">\r\n <option value=\"all\" data-sort=\"all\">Все</option>\r\n <option value=\"2\" data-sort=\"Base Grade\">Base Grade</option>\r\n <option value=\"3\" data-sort=\"Extraordinary\">Extraordinary</option>\r\n <option value=\"4\" data-sort=\"Industrial Grade\">Industrial Grade</option>\r\n</select>\r\n\r\n<select class=\"select2\">\r\n <option value=\"1\">Сначала дорогие</option>\r\n <option value=\"2\">Сначала дешевые</option>\r\n</select>\r\n\r\n<ul id=\"items\">\r\n <li data-type=\"pistol\" data-class=\"Base Grade\" data-price=\"10\" >Item 1 (Pistol,Base Grad, 10)</li>\r\n <li data-type=\"pistol\" data-class=\"Base Grade\" data-price=\"20\">Item 2 (Pistol,Base Grad, 20)</li>\r\n <li data-type=\"smg\" data-class=\"Extraordinary\" data-price=\"15\">Item 3 (smg,Extraordinary, 15)</li>\r\n <li data-type=\"riffle\" data-class=\"Extraordinary\" data-price=\"30\">Item 4 (riffle,Extraordinary, 30)</li>\r\n <li data-type=\"riffle\" data-class=\"Industrial Grade\" data-price=\"5\">Item 5 (riffle,Industrial Grade, 5)</li>\r\n <li data-type=\"riffle\" data-class=\"Industrial Grade\" data-price=\"10\">Item 6 (riffle,Industrial Grade, 10)</li>\r\n <li data-type=\"smg\" data-class=\"Industrial Grade\" data-price=\"50\">Item 7 (smg,Industrial Grade, 50)</li>\r\n <li data-type=\"smg\" data-class=\"Extraordinary\" data-price=\"25\">Item 8 (smg,Extraordinary, 25)</li>\r\n</ul>\n\nСообственно нужна сортировка по цене, по параметру data-price, желательно интегрировать в фильтрацию. ", "Под словом интегрировать я имею ввиду, чтобы при изменении параметров фильтрации - сортировка учитывалась тоже.", "\n\nA:\n\nЕсли не брать в расчет одновременную сортировку по нескольким полям, то будет как то так.", "\n\n$(\".select-filter\").change(function(){\r\n\r\n // список доступных фильтров\r\n var filters = $(\".select-filter\").toArray().map( function(v){\r\n return $(v).data('filter');\r\n });\r\n \r\n // проверяем все элементы списка\r\n $(\"#items li\").each(function(idx, li){\r\n var show = true; // по умолчанию показываем\r\n \r\n // сверяем все data- атрибуты доступных фильтров\r\n $.each(filters, function(fIdx, fname){ \r\n // значение селекта фильтра \r\n var fv = $(\".select-\" + fname + \" :selected\").data('sort');\r\n \r\n if(fv == 'all') return true;\r\n \r\n // сверяям значение селекта с дата-атрбутом\r\n if( $(li).data(fname) !", "= fv){\r\n show = false;\r\n return false;\r\n } \r\n });\r\n \r\n $(this).toggle(show);\r\n });\r\n\r\n});\r\n\r\n$(\".select-sort\").change(function(){\r\n var order = $(this).val();\r\n \r\n var items = $(\"#items li\").sort(function(a,b){\r\n var av = $(a).data('price');\r\n var bv = $(b).data('price');\r\n return order == 'desc' ? ", "av-bv : bv-av;\r\n });\r\n $(items).detach().appendTo(\"#items\");\r\n});\n<script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js\"></script>\r\n<select class=\"select-filter select-type\" data-filter=\"type\">\r\n <option value=\"all\" data-sort=\"all\">All</option>\r\n <option value=\"2\" data-sort=\"pistol\">Pistol</option>\r\n <option value=\"3\" data-sort=\"riffle\">Riffle</option>\r\n <option value=\"4\" data-sort=\"smg\">SMG</option>\r\n</select>\r\n\r\n<select class=\"select-filter select-class\" data-filter=\"class\">\r\n <option value=\"all\" data-sort=\"all\">Все</option>\r\n <option value=\"2\" data-sort=\"Base Grade\">Base Grade</option>\r\n <option value=\"3\" data-sort=\"Extraordinary\">Extraordinary</option>\r\n <option value=\"4\" data-sort=\"Industrial Grade\">Industrial Grade</option>\r\n</select>\r\n\r\n<select class=\"select-sort\" data-sort=\"price\">\r\n <option value=\"asc\">Сначала дорогие</option>\r\n <option value=\"desc\">Сначала дешевые</option>\r\n</select>\r\n\r\n<ul id=\"items\">\r\n <li data-type=\"pistol\" data-class=\"Base Grade\" data-price=\"10\" >Item 1 (Pistol,Base Grad, 10)</li>\r\n <li data-type=\"pistol\" data-class=\"Base Grade\" data-price=\"20\">Item 2 (Pistol,Base Grad, 20)</li>\r\n <li data-type=\"smg\" data-class=\"Extraordinary\" data-price=\"15\">Item 3 (smg,Extraordinary, 15)</li>\r\n <li data-type=\"riffle\" data-class=\"Extraordinary\" data-price=\"30\">Item 4 (riffle,Extraordinary, 30)</li>\r\n <li data-type=\"riffle\" data-class=\"Industrial Grade\" data-price=\"5\">Item 5 (riffle,Industrial Grade, 5)</li>\r\n <li data-type=\"riffle\" data-class=\"Industrial Grade\" data-price=\"10\">Item 6 (riffle,Industrial Grade, 10)</li>\r\n <li data-type=\"smg\" data-class=\"Industrial Grade\" data-price=\"50\">Item 7 (smg,Industrial Grade, 50)</li>\r\n <li data-type=\"smg\" data-class=\"Extraordinary\" data-price=\"25\">Item 8 (smg,Extraordinary, 25)</li>\r\n</ul>\n\n" ]

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[ "1. ", "Introduction\n===============\n\nMultiple myeloma (MM) primarily occurs in the elderly, with the median diagnosis reported at 69 years. ", "As per the National Cancer Institute report, MM comprises of 1.6% of all bone malignancies in the United States and the 5-year survival rate is less than 50%.^\\[[@R1]\\]^ Although often misunderstood as a rare disease, MM is in fact the 2nd most commonly diagnosed hematologic malignancy in the Western world.^\\[[@R2]\\]^ Being a skeletal malignant disease of older adults, this disease is a clinically significant problem, if left unresolved. ", "This is mainly attributed to a substantial increase in life expectancy with medical advancements, resulting in a continually increasing aged population, shifting the bulk of socioeconomic burden onto elderly care services and facilities.^\\[[@R3]\\]^ Vertebral compression fractures (VCFs) are the most common type of fractures in patients with MM.^\\[[@R4]\\]^ VCFs are known to occur at the onset of MM in 34% to 64% of patients.^\\[[@R5]\\]^ The efficacy of current intervention therapies on reducing the risk of mortality remains less well understood.^\\[[@R6]\\]^ Accordingly, early diagnosis and treatment are critical in slowing down the disease progression rate and deterioration of quality of life.^\\[[@R7]\\]^\n\nMost MM patients report back pain at diagnosis.^\\[[@R8]\\]^ Although MM patients are checked for biological symptoms such as anemia, hypercalcemia, or renal insufficiency,^\\[[@R9]\\]^ radiological indications for the presence of MM are diffuse bone loss, focal osteolytic bone lesions and bone marrow edema, and fragility axial fractures. ", "Diffuse bone loss alone is often misdiagnosed as Osteoporosis, a skeletal disease known to result in significant bone loss,^\\[[@R10]\\]^ until more symptoms associated with MM develops. ", "Bone marrow edema is a common finding during magnetic resonance imaging in acute VCFs.^\\[[@R11]\\]^ Majority of MM cases, as high as 80% of patients, are diagnosed during routine radiological scan procedures.^\\[[@R12]\\]^ When focal osteolytic lesions or significant diffuse bone loss are observed, risk for axial fractures in the vertebrae are high.^\\[[@R13]\\]^\n\nBone mineral density (BMD) and its related T-score are the indicators for assessing the risk of fracture. ", "Almost 80% of MM patients are diagnosed with osteoporosis; hence BMD currently has a major impact on survival in MM patients.^\\[[@R14],[@R15]\\]^ It is believed that osteoporosis status could be an indicator of disease progression to MM.^\\[[@R16]\\]^ Osteoporotic patients (20%) presenting with vertebral fractures have either monoclonal gammopathy undetermined significance or MM.^\\[[@R13]\\]^ However, there are 3 problems with the use of BMD as a diagnostic tool of MM. ", "First, decline in BMD as a result of aging and/or osteoporosis has been understood; it declines 0.1% to 0.2% per year due to aging while after menopause and onset of osteoporosis, it peaks to 1% to 2% and then slows back to decline due to aging.^\\[[@R9]\\]^ However, the decline in BMD in MM-induced osteoporosis has been less understood. ", "In a recent study, Borggrefe et al^\\[[@R17]\\]^ found that BMD of fracture cases in MM patients were significantly reduced in men, but not in women. ", "Hence, understanding the decline in BMD due to MM-induced osteoporosis may be unreliable. ", "Second, BMD has been challenged as a limited tool for the diagnosis of osteoporosis itself as it only partially predicts fracture risk,^\\[[@R18]\\]^ which renders its use in the diagnostic evaluation of MM less valid. ", "Also, routine assessment of BMD in MM patients has not been recommended due to methodological difficulties of this technique in these patients and the frequent use of bisphosphonates in all symptomatic MM patients.^\\[[@R19]\\]^ Third, there is no established clinical criterion in differentiating between osteoporotic VCFs and MM-induced osteoporotic VCFs.^\\[[@R20]\\]^\n\nFinite element (FE) analysis, based on computed tomography (CT) imaging, is a noninvasive alternative to assess bone strength. ", "FE analysis is a computational approach, where radiological scan data of patients are translated into three-dimensional (3D) models to predict structural behavior using numerical method.^\\[[@R21]\\]^ These patient-specific anatomical models are provided with appropriate material properties, boundary, and loading conditions that aims to mimic as closely the in vivo fracture conditions as possible, to obtain realistic predictions of the structural strength and other related properties, and to better understand the multifactorial etiology behind fractures for instance. ", "The supremacy of CT-based FE analysis, for example, in predicting bone strength over the use of gold standard BMD, differentiating femoral strength due to various treatment options, and discerning patients with and without osteoporosis have been established in several studies.^\\[[@R22]--[@R27]\\]^\n\nTherefore, this preliminary study aims to first validate FE analysis using experimentally determined failure load values obtained during an in vitro experiment performed on vertebra segments (T9--T12) from 3 fresh frozen human donors. ", "This study also aims to apply the validated FE analysis to vertebra segments (T1--L5) modeled from in vivo multidetector computed tomography (MDCT) imaging scans from 4 MM patients with and without VCFs to assess individual fracture risk as well as correlate the fracture risk with MDCT-derived BMD measurements.", "\n\n2. ", "Materials and methods\n========================\n\n2.1. ", "Specimens and subjects\n---------------------------\n\nFresh human vertebrae (n = 12; anatomical location: T9--T12) from 3 donors (one 74-year-old woman and two 46- and 62-year-old men, respectively) were obtained from the local Institute of pathology and anatomy. ", "These donors were free of any skeletal diseases. ", "The donors had dedicated their bodies for educational and research purposes to the local Institute prior to death, in compliance with local institutional and legislative requirements. ", "Whole-body MDCT images of 4 subjects (one 60-year-old man and three 58-, 68-, and 71-year-old women, respectively) with new diagnosis of MM were retrospectively identified in our institution\\'s digital image archive (PACS). ", "The study was reviewed and approved by the local institutional review board (Ethikkommission der Fakultaet fuer Medizin der Technischen Universitaet Muenchen, Munich, Germany).", "\n\n2.2. ", "MDCT imaging\n-----------------\n\nThe in vitro vertebrae were scanned using a 256-row MDCT scanner (iCT, Philips, Netherlands.). ", "Scan parameters were a tube voltage of 120 kVp, a tube load of 585 mAs, an image matrix of 1024 × 1024 pixels, and a field of view of 150 mm. ", "Transverse sections were reconstructed with a high-resolution bone kernel (YE). ", "The interpolated voxel size was of 146 × 146 × 300 μm^3^, while the real spatial resolution, as determined at q50 of the modulation-transfer-function, was 250 × 250 × 600 μm^3^. A dedicated calibration phantom (Mindways Osteoporosis Phantom, San Francisco, CA) was placed in the scanner mat beneath the vertebrae in all scans. ", "In vivo MDCT imaging of patient with MM were performed with a 64-row MDCT scanner (Somatom Sensation 64, Siemens Healthcare, Erlangen, Germany). ", "Scan parameters were a tube voltage of 120 kVp, an averaged tube current of 78 mA, an image matrix of 512 × 512 pixels, a pixel spacing of 977 × 977 μm^2^, a slice thickness of 670 μm, and a field of view of 150 mm. ", "Transverse sections were reconstructed with a bone kernel (B70f). ", "For calibration purposes, a reference phantom with a bone-like and a water-like phase (Osteo Phantom, Siemens Healthcare) was placed in the scanner mat beneath patients.", "\n\n2.3. ", "Biomechanical testing\n--------------------------\n\nEach vertebra was embedded in resin (Rencast Isocyanat and Polyol, Huntsman Group, Bad Säckingen, Germany) up to 2 mm above respectively below their vertebral endplates for the purpose of mechanical testing. ", "The resin fixation was performed with parallel alignment of the upper and lower endplate of the vertebrae with the outer surface of the resin chock to guarantee strict axial loading conditions of the vertebrae during the uniaxial mechanical test. ", "The resin-embedded vertebrae were fixed in a mechanical testing system (Wolpert Werkstoffprüfmaschinen AG, Schaffhausen, Switzerland). ", "First, 10 preconditioning cycles with uniaxial tension-compression up to a load between 10 and 400 N with a rate of 5 mm/minute were applied. ", "Then, a monotonic, uniaxial compression was performed at the same rate. ", "The load--displacement curve was recorded and vertebral failure load was defined as the 1st peak of the load--displacement curve with a subsequent drop of \\>10%.", "\n\n2.4. ", "Finite element analysis of in vitro and in vivo models\n-----------------------------------------------------------\n\nFE analysis was applied for the 12 in vitro vertebrae samples as well as the in vivo MDCT whole-body scans of 4 MM patients obtained (n = 4). ", "The DICOM images were imported into commercial software, Mimics (Materialise, Harislee, Belgium). ", "3D models of the in vitro vertebrae samples were immediately generated whereas, for each in vivo MDCT scan of MM patients, 3D models of the whole spine was 1st generated and then the thoracic and lumbar vertebrae (T1--L5) were segmented into individual segments (Fig. [", "1](#F1){ref-type=\"fig\"}).", "\n\n{#F1}\n\nFirst, wrapping was applied to all vertebrae segments to reduce surface roughness that can result in meshing difficulties. ", "This was followed by automatic meshing by 3-Matic (Materialise, Harislee, Belgium) using linear tetrahedral C3D4 elements with a constraint of a maximum aspect ratio of 25 (Fig. [", "1](#F1){ref-type=\"fig\"}). ", "Heterogeneous, nonlinear, and anisotropic material properties were assigned by discretizing the model into 10 different sets of materials.^\\[[@R28]\\]^ Cortical bone was simplified and assumed as denser trabecular bone;^\\[[@R29]\\]^ hence, only 1 set of relationships were used to calculate material properties as presented in Table [1](#T1){ref-type=\"table\"}. ", "Negative modulus values resulting from low density regions were set to 0.0001 MPa.^\\[[@R22]\\]^ Material yield and ultimate failure were assumed to coincide, and a nonlinear postyield material behavior was adopted.^\\[[@R30]\\]^\n\n###### \n\nMaterial property relations adapted from literature.", "\n\n![](", "medi-96-e5825-g002)\n\nFE analysis was performed using ABAQUS version 6.10 (Hibbitt, Karlsson, and Sorensen, Inc., Pawtucket, RI). ", "Boundary conditions were applied to emulate axial compression in the vertical direction, as VCFs are the most common type of fractures resulting from compressive loadings. ", "The displacement and rotation of the surface nodes on the inferior endplate was constrained in all directions, while a displacement load in the z-direction was applied incrementally on the surface nodes on the superior endplate (Fig. [", "1](#F1){ref-type=\"fig\"}).^\\[[@R31]\\]^ The predicted fracture load was defined as the peak force of the force--displacement curve over the displacement increments. ", "The predicted fracture load values were then compared with the experimentally measured values.", "\n\n2.5. ", "MDCT-derived BMD assessment\n--------------------------------\n\nElliptical regions of interest (ROIs) were placed on the each axial slice, with a slice thickness of 0.67 mm, for each vertebra (T1--L5) for each patient. ", "The ROIs are placed such that they cover as big a diameter in the vertebra segment as possible, excluding any cortical bone.^\\[[@R32]\\]^ The mean and standard deviation of Hounsfield units (HUs) were calculated in each ROI. ", "In addition, reference ROIs were also placed within 2 regions in the bone density calibration phantom composed of hydroxyapatite (HA), where the water-like part of phantom has HA density of 0 mg/cm^3^ (HA~w~), and the bone-like part of the phantom has HA density of 200 mg/cm^3^ (HA~b~). ", "The HUs of these reference ROI regions were also measured on each slice; HU~w~ and HU~b~ representing the HUs for the water-like and bone-like regions, respectively. ", "By assuming a linear relationship and by interpolating between the water-like and bone-like HUs, BMD was calculated by the following formula: BMD = \\[HA~b~/(HU~b~ − HU~w~)\\]∗(HU − HU~w~).^\\[[@R33]\\]^\n\n2.6. ", "Statistical analysis\n-------------------------\n\nDue to the small number of subjects analyzed in this study, pooled values of BMD, experimental, and FE-predicted vertebral strength values for all vertebra segments (n = 68) were compared and correlated. ", "Unadjusted Spearman rank correlation coefficient values were calculated since it is resistant to outliers.^\\[[@R34]\\]^ The *P* values were considered significant if \\<0.05. ", "All analyses were performed with a spreadsheet application (Microsoft Office Excel 2010, Redmond, WA).", "\n\n3. ", "Results\n==========\n\n3.1. ", "In vitro validation\n------------------------\n\nFailure load values predicted from the FE models (F~FE~) of the in vitro vertebrae samples (n = 12) realistically matched experimentally obtained values (F~exp~), with a significant correlation of *r* = 0.85 (*P* \\< 0.001) (Fig. [", "2](#F2){ref-type=\"fig\"}A). ", "Also, Spearman rank correlation coefficient was also significant with *r* = 0.70 (*P* \\< 0.05) between F~FE~ and BMD (Fig. [", "2](#F2){ref-type=\"fig\"}B), and *r* = 0.75 (*P* \\< 0.05) between F~exp~ and BMD.", "\n\n{#F2}\n\n3.2. ", "In vivo finite-element analysis\n------------------------------------\n\nFE-predicted strength values of each vertebra were studied in each patient (n = 4). ", "There were several key findings obtained in this study. ", "First, this study examined abrupt changes in fracture loads and discovered that subjects with fractures exhibited an erratic behavior in fracture loads between adjacent spinal segments. ", "We characterized this instability by observing peaks in fracture load values highlighted in pink rectangular boxes while the fractured segments were denoted as red columns (Fig. [", "3](#F3){ref-type=\"fig\"}). ", "In subject \\#1, there were peaks associated with T3--T4 (peak 1), T11 (peak 2), and L2--L3 (peak 3) segments and in subject \\#2, there were peaks at T6 (peak 1) and T10 (peak 2). ", "Subject \\#1 had originally attained fractures at the T4, T5, T12, L1, and L4 segments. ", "Consequently, it was indicative that segments adjacent to these peaks seemed to also experience regions of instability. ", "Hence, the 2nd finding was that peaks in fracture load seem to place the peak-associated segments as well as the adjacent segments at risk of fracture. ", "Similarly, for subject \\#2, adjacent segments at risk were T5, T7, T9, and T11. ", "This corresponded to fractured segments attained by subject \\#2, at T6, T10, and T11. ", "Third, subjects without fractures exhibit gradual changes in FE-predicted fracture load values. ", "In subject \\#3 and subject \\#4, no peaks were observed, indicating a low risk of fracture. ", "Third, the existence of peaks were also further quantified by calculating the relative changes of fracture loads of each segment, with respect to its following adjacent segment, for example, T1 with respect to T2, and T2 with respect to T3 (Table [2](#T2){ref-type=\"table\"}). ", "The higher the relative change, the greater the instability locally and for this preliminary study, the relative change was considered to be unstable when it exceeds a value of 1.00. ", "The vertebrae segments highlighted were T4, T11, and T12 in subject \\#1 and T6 and T10 in subject \\#2 (Table [2](#T2){ref-type=\"table\"}). ", "To place this finding into perspective, Table [3](#T3){ref-type=\"table\"} shows the peak-associated segments at risk, adjacent segments at risk, and fractures attained by subject \\#1 and subject \\#2. ", "All fractures attained by subject \\#1 and subject \\#2 were identified as either a peak-associated segment or adjacent segment at risk. ", "Last, it was also observed that geometrically compromised segments exhibited higher maximum principal strain values (denoted by red regions) (Fig. [", "4](#F4){ref-type=\"fig\"}). ", "In subject \\#1 and subject \\#2, T3, T10 and T11, and T5 and T11 showed critical plastic strain regions, respectively, whereas in subject \\#3 and subject \\#4, the segments showed geometric stability and insignificant critical strain regions.", "\n\n{#F3}\n\n###### \n\nRelative changes of fracture loads of each segment with respects to following adjacent segment (values greater than 1.00 denoted in red).", "\n\n![](", "medi-96-e5825-g005)\n\n###### \n\nPeak-associated segments at risk, adjacent segments at risk, segments with critical plastic strain regions, and current fractures attained by subject \\#1 and subject \\#2.", "\n\n![](", "medi-96-e5825-g006)\n\n{#F4}\n\n3.3. ", "MDCT-derived BMD assessment\n--------------------------------\n\nThe Spearman rank correlation coefficient was *r* = 0.79 (*P* \\< 0.001) for the correlation between F~FE~ and BMD for lumbar segments (L1--L5) and *r* = 0.58 (*P* \\< 0.001) for thoracic segments. ", "The pooled coefficient for all the vertebrae segments was *r* = 0.57 (*P* \\< 0.001).", "\n\n4. ", "Discussion\n=============\n\nMM is still not a well-understood skeletal disease, although it poses significant burden to the society, especially being a prevalent condition among the elderly. ", "This study showed that by applying the same universal loading condition to the vertebra segments from T1 to L5, the differences in structural strength could be compared within each patient and between patients. ", "Thus, the assessment of the biomechanical properties of vertebrae segments can be performed with noninvasive CT-based FE modeling. ", "Applying FE methodology in the clinical scenario will enable clinicians to look at all the spine segments concurrently to analyze the structural strength differences and in this case better predict vertebral fracture risk in MM. ", "The accuracy of the FE modeling was validated by performing experimental testing with human cadaveric specimens. ", "Vertebral bone strength was accurately estimated by applying the FE modeling protocol.", "\n\nA novel aspect of this study is the use of MDCT and FE-based structural strength assessment to assess relative vertebral fracture risk within vertebra segments in each subject. ", "Although the correlation between FE-predicted strength and MDCT-derived BMD was moderate (Fig. [", "5](#F5){ref-type=\"fig\"}), the interesting finding was on the erratic nature of fracture load values found in patients who have already attained fractures (ie, subject \\#1 and subject \\#2), placing the peak-associated segments and adjacent segments at high risk to future fractures (Fig. [", "3](#F3){ref-type=\"fig\"}). ", "This could be attributed to the fact that fractured segments have smaller than original geometries, resulting in extremely high bone density within a smaller volume per se, resulting in over-prediction of their fracture loads. ", "Also, they may have altered biomechanical properties that evades away from material relations found in current literature for osteoporosis. ", "This is further exacerbated by influences of MM itself on the bone characteristics, which could also explain the moderate correlation obtained between FE-predicted strength and BMD.", "\n\n{#F5}\n\nNevertheless, with information on fracture load values, relative changes in fracture loads as well as geometric, and critical plastic strain region observations, clinicians could utilize a guiding tool to evaluate patient-specific fracture risk of the spine in MM patients (Fig. [", "6](#F6){ref-type=\"fig\"}). ", "A schematic on how patient-specific risk assessment could be evaluated is illustrated. ", "By first identifying the peak-associated segments at risk, the high relative change segments can be categorized under high risk, while for the segments with moderate/low relative change under low risk. ", "Following that, adjacent segments at risk need to be identified, categorizing them similarly as aforementioned into moderate and low risk categories (Fig. [", "6](#F6){ref-type=\"fig\"}). ", "In the case of subject \\#1, it is evident that regions of severe structural instability were exhibited throughout the individual segments of the spine. ", "This phenomenon suggests that the whole spine of subject \\#1 was at risk of fracture. ", "Evaluation of more MM subjects would enable us to have a more accurate patient-specific risk assessment and treatment strategy.", "\n\n{#F6}\n\nThis study also suggests that absolute value of fracture loads may have little value and it is the relative fracture loads that will provide valuable information on the relative stability between segments. ", "Most studies have presented absolute values in one or more vertebral osteoporotic segments, but this is the first study of its kind to report the fracture load values that can be simultaneously observed across the vertebrae segments in each patient. ", "In early diagnosis, the presence of peaks could indicate regions of low structural stability, providing the clinicians with preemptive treatment options to prevent the occurrence of fractures. ", "This is valuable information to the clinicians as they will be able to prescribe more targeted drug therapy^\\[[@R35]\\]^ as well as exercise regimes that improve the structural stability of the spine at the affected areas.^\\[[@R36]\\]^ Furthermore, fracture load values provide amplified differences between segments, compared to BMD, making it easier to identify segments at high fracture risk.", "\n\nSince MM is a plasma disease, it may result in severe bone loss due to crosstalk between cells responsible for bone cell activity, which explains the significantly low range of fracture loads obtained. ", "A study showed that in osteoporotic patients over the age of 65, the threshold strength in the spine for fragile bone that is highly susceptible to risk of fracture is 4500 N for women and 6500 N for men.^\\[[@R37]\\]^ In this preliminary study of n = 4 subjects, we found that the range of fracture load for subject \\#1 (male) was 310 to 3340 N, whereas for subject \\#2, it was 284 to 1274 N. Studies have shown that women aged over 50 years exhibited high correlation between vertebral strength and load-to-strength ratio to prevalent vertebral fractures.^\\[[@R38]--[@R40]\\]^ These collective literature findings also support the findings in this study that vertebral strength can be used as a diagnostic tool to access the risk of vertebral fractures.^\\[[@R37]\\]^\n\nAlthough the degeneration of the spine due to the onset of MM has not been well understood, osteoporosis of the spine has been sufficiently studied by researchers. ", "Fragility fractures have been understood to be loss in structural strength due to the weakening of the trabecular structure and an under compensation of bone resorption in the bone remodeling process, that leads to lower bone turnover.^\\[[@R41]\\]^ However in MM, the mechanisms are incompletely understood. ", "Due to increased receptor activator of nuclear factor kappa-B ligand production by the bone marrow stromal cells, and an increased degradation of osteoprotegerin, there is increased osteoclast precursor differentiation and consequently, enhanced bone resorption.^\\[[@R42]\\]^ MM-derived mesenchymal stem cells produce osteoblasts that are different from healthy osteoblasts produced by normal mesenchymal stem cells. ", "This may indicate that the progression of MM is independent of osteoporosis, which may be a by-product of the bone carcinoma. ", "It is not clear how osteoporosis influences this bone cancer and vice versa. ", "Also, it is unclear how to explain the nonspecific changes that occur due to underlying biological mechanisms in MM patients, but it seems apparent that MM can result in significant reduction in structural strength, causing certain adjacent segments to have fluctuating strengths.", "\n\nThis study has several limitations. ", "First, this preliminary study only examined 4 MM subjects, 2 with and 2 without fractures. ", "Not only will a bigger sample enable statistical emphasis on the findings, a threshold value for the relative change between vertebra segments could be evaluated too. ", "This threshold value will serve as a better clinical indication on the risk of fracture and consequently aid in predicting the occurrence of fractures. ", "Also, the resolution of scans used for in vitro validation was higher than that of the scans used for in vivo scans of MM subjects, due to the restrictions imposed on radiation exposure. ", "Thirdly, we analyzed one simple compressive loading condition, but there is a combination of loadings occurring in vivo, for example flexion, rotation, and bending. ", "However, axial compressive loading accounts for 90% of fracture cases experienced by clinicians. ", "Nevertheless, future work will entail using combination loading conditions to more accurately predict fractures in MM patients. ", "Only fracture load values were used as an assessment parameter. ", "Future study will also look into using geometric parameters such as buckling ratio, which has been proven to indicate structural stability.", "\n\nIn conclusion, this study found that structural instability between vertebra segments could be the first tell-tale sign of impending fractures. ", "The erratic nature of fracture load values between the segments in patients who have attained fractures is evidence that examining the stability of the vertebrae segments in a patient specific manner could enable early prediction of fractures in MM patients. ", "Further study on establishing a threshold value for the relative change in fracture load values between adjacent segments could be useful for clinicians to identify segments at risk and suggest targeted treatment to the affected segments before the occurrence of fractures. ", "This noninvasive patient-specific examination will serve to provide key information on the relative stability of the vertebra segments in MM patients, reducing the morbidity and mortality of elderly diagnosed with MM in the long run.", "\n\nThe authors thank Deutsche Forschungsgemeinschaft (DFG BA 4085/2-1 \\[to JSK\\] and BA 4906/1-1 \\[to TB\\]) and Singapore University of Technology and Design (SUTD) Startup research Grant (SRG EPD 2015093 \\[KS\\]) for the support.", "\n\nAbbreviations: 3D = three-dimensional, BMD = bone mineral density, CT = computed tomography, FE = finite element, F~FE~ = failure load values predicted from FE models, HA = hydroxyapatite, HU = Hounsfield Unit, MDCT = multidetector computed tomography, MM = multiple myeloma, ROIs = regions of interest, VCF= vertebral compression fracture.", "\n\nFunding/support: This work was supported by grants of the Deutsche Forschungsgemeinschaft (DFG BA 4085/2-1 \\[to JSK\\] and BA 4906/1-1 \\[to TB\\]) and Singapore University of Technology and Design (SUTD) Startup research Grant (SRG EPD 2015093 \\[KS\\]).", "\n\nThe authors have no conflicts of interest to disclose.", "\n" ]

{ "pile_set_name": "PubMed Central" }

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[ "// RUN: %clang_cc1 -fsyntax-only -verify %s\n// RUN: %clang_cc1 -fsyntax-only -verify -std=c++98 %s\n// RUN: %clang_cc1 -fsyntax-only -verify -std=c++11 %s\n\n// PR3990\nnamespace N {\n struct Wibble {\n };\n\n typedef Wibble foo;\n\n int zeppelin; // expected-note{{declared here}}\n}\nusing namespace N;\n\nfoo::bar x; // expected-error{{no type named 'bar' in 'N::Wibble'}}\n\nvoid f() {\n foo::bar = 4; // expected-error{{no member named 'bar' in 'N::Wibble'}}\n}\n\nint f(foo::bar); // expected-error{{no type named 'bar' in 'N::Wibble'}}\n\nint f(doulbe); // expected-error{{did you mean 'double'?}}", "\n\nint fun(zapotron); // expected-error{{unknown type name 'zapotron'}}\nint var(zepelin); // expected-error{{did you mean 'zeppelin'?}}", "\n\ntemplate<typename T>\nstruct A {\n typedef T type;\n\n type f();\n\n type g();\n\n static int n;\n static type m;\n static int h(T::type, int); // expected-error{{missing 'typename'}}\n static int h(T::type x, char); // expected-error{{missing 'typename'}}\n};\n\ntemplate<typename T>\nA<T>::type g(T t) { return t; } // expected-error{{missing 'typename'}}\n\ntemplate<typename T>\nA<T>::type A<T>::f() { return type(); } // expected-error{{missing 'typename'}}\n\ntemplate<typename T>\nvoid f(T::type) { } // expected-error{{missing 'typename'}}\n\ntemplate<typename T>\nvoid g(T::type x) { } // expected-error{{missing 'typename'}}\n\ntemplate<typename T>\nvoid f(T::type, int) { } // expected-error{{missing 'typename'}}\n\ntemplate<typename T>\nvoid f(T::type x, char) { } // expected-error{{missing 'typename'}}\n\ntemplate<typename T>\nvoid f(int, T::type) { } // expected-error{{missing 'typename'}}\n\ntemplate<typename T>\nvoid f(char, T::type x) { } // expected-error{{missing 'typename'}}\n\ntemplate<typename T>\nvoid f(int, T::type, int) { } // expected-error{{missing 'typename'}}\n\ntemplate<typename T>\nvoid f(int, T::type x, char) { } // expected-error{{missing 'typename'}}\n\nint *p;\n\n// FIXME: We should assume that 'undeclared' is a type, not a parameter name\n// here, and produce an 'unknown type name' diagnostic instead.", "\nint f1(undeclared, int); // expected-error{{requires a type specifier}}\n\nint f2(undeclared, 0); // expected-error{{undeclared identifier}}\n\nint f3(undeclared *p, int); // expected-error{{unknown type name 'undeclared'}}\n\nint f4(undeclared *p, 0); // expected-error{{undeclared identifier}}\n\nint *test(UnknownType *fool) { return 0; } // expected-error{{unknown type name 'UnknownType'}}\n\ntemplate<typename T> int A<T>::n(T::value); // ok\ntemplate<typename T>\nA<T>::type // expected-error{{missing 'typename'}}\nA<T>::m(T::value, 0); // ok\n\ntemplate<typename T> int A<T>::h(T::type, int) {} // expected-error{{missing 'typename'}}\ntemplate<typename T> int A<T>::h(T::type x, char) {} // expected-error{{missing 'typename'}}\n\ntemplate<typename T> int h(T::type, int); // expected-error{{missing 'typename'}}\ntemplate<typename T> int h(T::type x, char); // expected-error{{missing 'typename'}}\n\ntemplate<typename T> int junk1(T::junk);\n#if __cplusplus <= 201103L\n// expected-warning@-2 {{variable templates are a C++14 extension}}\n#endif\ntemplate<typename T> int junk2(T::junk) throw(); // expected-error{{missing 'typename'}}\ntemplate<typename T> int junk3(T::junk) = delete; // expected-error{{missing 'typename'}}\n#if __cplusplus <= 199711L\n//expected-warning@-2 {{deleted function definitions are a C++11 extension}}\n#endif\n\ntemplate<typename T> int junk4(T::junk j); // expected-error{{missing 'typename'}}\n\n// FIXME: We can tell this was intended to be a function because it does not\n// have a dependent nested name specifier.", "\ntemplate<typename T> int i(T::type, int());\n#if __cplusplus <= 201103L\n// expected-warning@-2 {{variable templates are a C++14 extension}}\n#endif\n\n\n// FIXME: We know which type specifier should have been specified here. ", "Provide\n// a fix-it to add 'typename A<T>::type'\ntemplate<typename T>\nA<T>::g() { } // expected-error{{requires a type specifier}}\n" ]

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[ "Q:\n\nStore random numbers in an array without adjacent repeats\n\nI want to store random numbers in an array without repeats with in the range 0-9. ", "It is fine if they repeat but not if they are right next to each other like: 1577984 is incorrect(because of the double 7s) but 151515 is theoretically okay.", "\nI've been working at this a day or two now and this is my original base code:\npublic static int[] createRandomNumber(int characters){\n int randomNumberArray[] = new int[characters];\n for(int i =0; i<characters; i++){\n randomNumberArray[i] = (int)(Math.random()*9);\n }\n return randomNumberArray;\n }\n\nAnd this is what I have now but it is doing the exact opposite of what I want it's generating all of the same number:\npublic static int[] createRandomNumber(int characters)\n{\n int randomNumberArray[] = new int[characters];\n int random = (int)(Math.random()*9);\n for(int i = 0; i <characters ; i++)\n {\n randomNumberArray[i] = random;\n if(randomNumberArray[i] == random)\n randomNumberArray[i] = (int)(Math.random()*9);\n else if(randomNumberArray[i] !", "= random)\n randomNumberArray[i] = random;\n }\n return randomNumberArray;\n}\n\nIs there a simple solution that I am just not seeing? ", "I've probably rewritten this method 50 times.", "\nJust so you know the parameter code is\nint characters = in.nextInt();\n\nso just the length of their randomly generated password that they want. ", "Also I know that Math.random is pseudo-random but this isn't for real or anything. ", "Plus there's more methods that generate random letters and such as well. (", "And yes I've done lots of research but no one seems to have my particular problem and believe me asking questions is a last resort for me.)", "\nThanks for any suggestions.", "\n\nA:\n\nIn the for loop, you are assigning random to the number array. ", " But then you are immediately checking if random is equal to that spot you just assigned, which is always true. ", " So it picks another random number, which also may or may not be equal to the previous digit.", "\nI've rewritten the for loop to have a while loop in its body, to keep checking versus the previous digit to see if there is a repeated digit.", "\nfor(int i = 0; i <characters ; i++)\n{\n randomNumberArray[i] = random;\n // If not first, check if it matches the previous digit\n while(i >= 1 && randomNumberArray[i - 1] == random)\n {\n random = (int)(Math.random()*9);\n randomNumberArray[i] = random;\n }\n}\n\n" ]

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[ "After 3PO and R2's destruction in IV, Uncle Owen's plot of land failed, causing domestic turmoil within the Skywalker household, Luke, wanting to rebel his guardians, runs away to Hoth, because he has never seen snow, but this caused his eventual demise" ]

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[ "The Citadel Bulldogs football\n\nThe Citadel Bulldogs football program represents The Citadel, The Military College of South Carolina in the NCAA Division I Football Championship Subdivision (FCS). ", "The Bulldogs play in the Southern Conference, as they have since 1936. ", " The Bulldogs are coached by Brent Thompson, who was hired on January 19, 2016 to replace Mike Houston, who became the head football coach of James Madison University on January 18, 2016.", "\n\nHistory\n\nFacilities\nThe Bulldogs first recorded stadium was College Park, located in the northeast corner of Hampton Park in Charleston, South Carolina. ", "This field predated the current College Park at the same site, which is used as a practice facility for The Citadel Bulldogs baseball. ", "Due to increasing attendance and the poor state of the stadium, the Bulldogs moved to the original Johnson Hagood Stadium in 1927. ", "In 1948, that stadium was replaced by the current Johnson Hagood Stadium, which lies just to the south of The Citadel's gates in Charleston. ", "\n\nJohnson Hagood is a 21,000 seat stadium, in which The Citadel routinely ranks in the top 25 in attendance at the FCS level. ", " In 2001, the Altman Athletic Center opened in the south end zone, complete with new home and visitor's locker rooms, official's locker rooms, and an upstairs hospitality area for donors. ", " In 2008, The Citadel completed a re-construction of the west stands and West Side Tower. ", " The stands contain reserved premium seats and bleacher seats, while the tower, shared with the South Carolina National Guard, contains twelve suites, a club level, and state of the art press box. ", " During preparation for construction, workers discovered the remains of sailors from failed test runs of the H.L. Hunley. ", " These remains were reinterred in Magnolia Cemetery in Charleston.", "\n\nBeginning in 2012, The Citadel implemented a points system for parking and seat selection in Johnson Hagood Stadium, joining many large programs who use similar systems. ", "The program is designed to reward long-time and large donors to The Citadel athletics by giving them preference in selecting seat and parking locations.", "\n\nIn 2016, The Citadel determined that lead paint needed remediation on the east (visitor's) side of the stadium. ", " The work resulted in the entire east side being closed for the first game of the 2016 season and some sections being opened for subsequent games. ", " The capacity was thus 10,500 for the first game and about 15,000 for later games. ", " The Board of Visitors decided to fully renovate the east side of the stadium, announcing that decision on December 2, 2016.", "\n\nPractice and on-campus facilities\nPractices are held at the Maybank Triplets Practice Facility, an artificial turf field at the north edge of campus. ", " The Bulldogs utilize Seignious Hall, located across from McAlister Field House for weightlifting, locker rooms, team meeting and video space, and academic tutoring. ", " The Citadel Sports Medicine Department also utilizes Seignious Hall.", "\n\nCoaches and staff\nCoaches from The Citadel have often been targeted for larger programs. ", "Former head and assistant coaches at The Citadel include Bobby Ross, Charlie Taaffe, Ellis Johnson, Frank Beamer, Al Davis, Ralph Friedgen, and Mike Houston.", "\n\nHead Coaches\n\nCurrent Staff\nThe current coaching staff at the Citadel is:\n\nSeasons and results\n\nConference championships\nThe Citadel has won four conference championships, three outright and one shared.", "\n\n† denotes co–champions\n\nPostseason appearances\n\nBowl games\n\nFCS Playoffs\nThe Citadel has appeared in the FCS Playoffs five times, posting a 2–5 record.", "\n\nRivalries\n\nThe Citadel's primary rivals are the VMI Keydets football and Furman Paladins football. ", " The game with VMI is known as the Military Classic of the South. ", " The Citadel and Furman have been heated, annual rivals since both joined the Southern Conference in 1936. ", " The Citadel is 151-174-9 all-time against in-state opponents.", "\n\nRecord vs. Current SoCon opponents\nExcludes Furman and VMI, listed above.", "\nEast Tennessee State returned to the SoCon in 2016.", "\n\nRecord vs instate opponents\nDivision 1, non-SoCon only\n\nBulldogs in professional football\n\nMany Citadel alumni have played in various professional leagues, including the National Football League, Canadian Football League and Arena Football League. ", " Sixteen players have been drafted in the NFL Draft and AFL Draft, and other players have signed as undrafted free agents. ", " Likely the most famous Citadel alumni in professional football are Running Back Stump Mitchell and broadcaster Paul Maguire. ", " Currently, Andre Roberts is a member of the Atlanta Falcons and Cortez Allen recently played with the Pittsburgh Steelers for 5 seasons; Running Back Travis Jervey played in 2 Super Bowls with the Green Bay Packers and was named an All Pro as a special teams player.", "\n\nNational Football League Draft\n\nAmerican Football League Draft\n\nIndividual honors\n\nAll-Americans\nThis list includes selected First Team All-Americans at The Citadel\n\nRetired Jerseys\n\n14 - Jack Douglas\n15 - Lester Smith\n35 - Stump Mitchell\n51 - Brian Ruff\n59 - Marc Buoniconti\n66 - John Small\n\nFuture schedules\nThis represents the most recent verified future non-conference games as of October 31, 2018. ", "The upcoming season schedule can be found at 2018 The Citadel Bulldogs football team.", "\nNCAA Division I FCS football teams are usually permitted to play 11 games per season. ", " In years when 13 weekends fall between Labor Day and Thanksgiving, they may add a twelfth game. ", " This will be the case in 2019, 2024, and 2025. ", " With nine football playing members, the Southern Conference regular season consists of eight games, leaving 3 non-conference games to be scheduled in most years.", "\n\nReferences\n\n \nCitadel football\nCitadel football" ]

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[ "After matching groups based on the number of missed questions, subjects were\nassigned to either the 12:00 pm control group of symphony music or 12:30 pm treatment\ngroup of rap music time slot to be administered another test the following Thursday\nafternoo\n\nAnother explanation for our findings could be participants were aware of the\ndistractions during the rap music test. ", "This conscious awareness of distractions attributed\nto their attention during the experiment, and caused them to pay greater attention to\n\nNotes Ch 9 and Ch 10\nexternal cost (negative externality)\na cost of an activity that falls on people other than those who pursue the activity\nexternal benefit (or positive externality)\na benefit of an activity received by people other than those who pursu" ]

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[ "Deputy Director of the city’s tourism department Trần Chí Cường said the department in co-operation with the public security force, had completed a report on the case before proposing a strict fine for the violations committed by the Chinese nationals.", "\n\nHe said the Chinese had worked as tourist guides and had done accounting jobs for the company, which handled Chinese tour groups visiting destinations in the city and the central region.", "\n\nIt’s the second such case in which the city’s police and tourism inspection team have found Chinese nationals illegally operating tourist services and violating residency laws.", "\n\nOn July 6, the city fined six Chinese nationals VNĐ125 million (about US$5,500) for illegally operating tourist services and violating residency laws.", "\n\nAccording to the city’s tourism department, at least 60 Chinese guides were working illegally in the city, and most of the Chinese travel agencies handling Chinese tour groups disguised operations with a Vietnamese licence, as directed by Chinese managers.", "\n\nLocal Vietnamese guides had made a video clip and taken a photo of a Chinese guide Xue Chun Zhe, who had presented a distorted view of Vietnamese history and culture during a tour of the Linh Ứng Pagoda and Mỹ Khê Beach.", "\n\nLast month, the city’s tourism department revoked the business licence of a local travel agency for nine months, after one of its Chinese tourists burnt Vietnamese money in a downtown bar in the city.", "\n\nĐà Nẵng’s tourism department distributed 5,000 leaflets in Chinese last week, promoting a code of conduct for Chinese tourists at airports, stations, destinations and hotels, besides resorts and public areas.", "\n\nThe central city hosted 600,000 Chinese tourists in the first half this year, an 83 per cent increase in comparison with last year. ", "Chinese tourists comprised a quarter of all tourists visiting the city.", "\n\nThe city’s Party Secretary Nguyễn Xuân Anh said the city did not discriminate Chinese tourists from other foreign tourists, but the city would fine visitors who violated the law or committed any wrongdoing.", "\n\nThe city plans to establish a tourism police force as a pilot project to boost security for tourists and the tourism sector in the 2016-2020 period. — ", "VNS" ]

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[ "[HMGB1/SREBP-1 mediated IFN-gamma-induced lipid deposition in mouse mesangial cells].", "\nTo explore the possible mechanism of lipid deposition induced by interferon-gamma (IFN-gamma). ", "The mouse mesangial cells (MMC) were randomly divided into control group, stimulation group, stimulation + control vector group (sh-HMGB1) and stimulation+ specific sh-vector group (sh-SREBP-1). ", "RT-PCR was used to detect the expression of HMGB1, SREBP-1 and fatty acid synthetase (FAS) mRNA; the protein expression was determined by Western blot. ", "The Oil Red O staining revealed that the mouse mesangial cells showed significant lipid droplet in IFN-gamma group. ", "IFN-gamma up-regulated the expression of HMGB1, SREBP-1, FAS mRNA and protein time-dependently; Transfection of MMC with HMGB1 siRNA resulted in the suppression of SREBP-1, FAS protein levels induced by IFN-gamma, following with decrease of lipid deposition. ", "Stimulation with HMGB1 markedly induced expression of SREBP-1, FAS expression and peaked at 8 h, decreased at 12 h compared with that at 8 h. Sh-SREBP-1 decreased the lipid deposition induced by HMGB1 in MMC. ", "IFN-gamma might induce lipid deposition in mouse mesangial cells partly by up-regulating the expression of HMGB1/SREBP-1/FAS." ]

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[ "Heat deflection temperature\n\nThe heat deflection temperature or heat distortion temperature (HDT, HDTUL, or DTUL) is the temperature at which a polymer or plastic sample deforms under a specified load. ", " This property of a given plastic material is applied in many aspects of product design, engineering and manufacture of products using thermoplastic components.", "\n\nDetermination \nThe heat distortion temperature is determined by the following test procedure outlined in ASTM D648. ", "The test specimen is loaded in three-point bending in the edgewise direction. ", "The outer fiber stress used for testing is either 0.455 MPa or 1.82 MPa, and the temperature is increased at 2 °C/min until the specimen deflects 0.25 mm. ", "This is similar to the test procedure defined in the ISO 75 standard.", "\n\nLimitations that are associated with the determination of the HDT is that the sample is not thermally isotropic and, in thick samples in particular, will contain a temperature gradient. ", "The HDT of a particular material can also be very sensitive to stress experienced by the component which is dependent on the component’s dimensions. ", "The selected deflection of 0.25 mm (which is 0.2% additional strain) is selected arbitrarily and has no particular physical significance.", "\n\nApplication in injection molding\nAn injection molded plastic part is considered \"safe\" to remove from its mold once it is near or below the HDT. ", "This means that part deformation will be held within acceptable limits after removal. ", " The molding of plastics by necessity occurs at high temperatures (routinely 200 °C or higher) due to the low viscosity of plastics in fluid form (this issue can be addressed to some extent by the addition of plasticizers to the melt, which is a secondary function of a plasticizer). ", "Once plastic is in the mold, it must be cooled to a temperature to which little or no dimensional change will occur after removal. ", " In general, plastics do not conduct heat well and so will take quite a while to cool to room temperature. ", "One way to mitigate this is to use a cold mold (thereby increasing heat loss from the part). ", "Even so, the cooling of the part to room temperature can limit the mass production of parts.", "\n\nChoosing a resin with a higher heat deflection temperature (and therefore closer to melting temperature) can allow manufacturers to achieve a much faster molding process than they would otherwise while maintaining dimensional changes within certain limits.", "\n\nSee also\n Vicat softening point\n\nCategory:Polymer chemistry\nCategory:Threshold temperatures" ]

{ "pile_set_name": "Wikipedia (en)" }

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[ "Q:\n\nProgrammatically generated zip invalid on pc but not on android\n\nSOLVED:\nok so I am basically stupid. ", "I couldn't open the file because I forgot to install winrar or 7zip since this pc is newly formatted... Everything works fine. ", "Sorry to waste anyone's time.", "\nIn my app I programmatically generate a .zip file from photos and .csv files in a directory.", "\nIt creates the zip and then sends the email with the attachment without a hickup. ", "The problem however is that on my pc I can't extract the .zip file because it says it's invalid, but on my device using \"WinZip\" I can check my .zip file and it has everything it is suppose to have. ", "This is confusing me. ", "\nHere is my code:\nHere I check for which checkboxes have been checked then do the zipping\nfor(int i = 0; i < cbStates.size(); ++i)\n {\n if(cbStates.get(i))\n {\n String zipFile = Environment.getExternalStorageDirectory() + \"/ArcFlash/\" + listItems.get(i) + \".zip\";//ex: /storage/sdcard0/ArcFlash/study12.zip\n String srcDir = Environment.getExternalStorageDirectory() + \"/ArcFlash/\" + listItems.get(i);\n\n try\n {\n FileOutputStream fos = new FileOutputStream(zipFile);\n\n ZipOutputStream zos = new ZipOutputStream(fos);\n\n File srcFile = new File(srcDir);\n\n Log.i(\"customException\", \"going to compress\");\n addDirToArchive(zos, srcFile);\n\n // close the ZipOutputStream\n zos.close();\n }\n\n catch (IOException ioe)\n {\n System.out.println(\"Error creating zip file: \" + ioe);\n }\n\n //Send the email\n Intent emailIntent = new Intent(android.content.", "Intent.", "ACTION_SEND);\n emailIntent.setType(\"application/image\");\n emailIntent.putExtra(android.content.", "Intent.", "EXTRA_EMAIL, new String[]{\"jbasson@powercoreeng.com\"});\n emailIntent.putExtra(android.content.", "Intent.", "EXTRA_SUBJECT,\"Test Subject\");\n emailIntent.putExtra(android.content.", "Intent.", "EXTRA_TEXT, \"From My App\");\n\n String folderPath = Environment.getExternalStorageDirectory() + \"/ArcFlash/\" + listItems.get(i) + \".zip\";\n //Uri u = Uri.fromFile(folderPath);\n\n //Log.i(\"customException\", \"uri path: \" + u.getPath());\n emailIntent.putExtra(Intent.", "EXTRA_STREAM, Uri.parse(\"file://\" + folderPath));\n startActivity(Intent.createChooser(emailIntent, \"Send mail...\"));\n\n Toast.makeText(context,\"Case \\\"\" + studyName + \"\\\" has been sent\", Toast.", "LENGTH_LONG).show();\n //adapter.setElement(i, adapter.getStudy(i) + \"(sent)\");\n }\n }\n\nand here is the zip function:\nprivate static void addDirToArchive(ZipOutputStream zos, File srcFile)\n{\n File[] files = srcFile.listFiles();\n\n Log.i(\"customException\", \"Adding directory: \" + srcFile.getName());\n\n for (int i = 0; i < files.length; i++)\n {\n // if the file is directory, use recursion\n if (files[i].isDirectory())\n {\n addDirToArchive(zos, files[i]);\n continue;\n }\n try\n {\n System.out.println(\"tAdding file: \" + files[i].getName());\n\n // create byte buffer\n byte[] buffer = new byte[2048];//1024\n\n FileInputStream fis = new FileInputStream(files[i]);\n\n zos.putNextEntry(new ZipEntry(files[i].getAbsolutePath() + \"/\" + files[i].getName()));//files[i].getName()\n int length;\n while ((length = fis.read(buffer)) > 0)\n {\n zos.write(buffer, 0, length);\n }\n\n zos.closeEntry();\n\n // close the InputStream\n fis.close();\n }\n catch (Exception ex)\n {\n Log.i(\"customException\", \"error zipping: \" + ex.getMessage());\n }\n }\n}\n\nA:\n\nok so I am basically stupid. ", "I couldn't open the file because I forgot to install winrar or 7zip since this pc is newly formatted... \n\n" ]

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{ "pile_set_name": "Github" }

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[ "México fue el único país del G20 en donde el salario real disminuyó en nueve años, al caer 1.7 por ciento, de acuerdo con un informe sobre la evolución de los salarios en el mundo presentado por la Organización Internacional del Trabajo.", "\n\nEl salario real de los mexicanos, que se calcula descontando la inflación para reflejar su verdadero poder adquisitivo, cayó 0.6 por ciento en 2013 y 4.3 en 2014. ", "Para los años 2015 y 2016, aumentó ligeramente a 0.5 y 1.3 por ciento, respectivamente, pero en 2017 volvió a caer hasta un 2 por ciento.", "\n\nCiudad de México, 26 de noviembre (SinEmbargo).– ", "En casi todas las economías de los países del G20 los salarios reales aumentaron de 2008 a 2017, excepto en México, donde disminuyeron 1.7 por ciento, según un informe sobre la evolución de los salarios en el mundo presentado hoy en Ginebra por la Organización Internacional del Trabajo (OIT).", "\n\nEl salario real de los mexicanos, que se calcula descontando la inflación para reflejar su verdadero poder adquisitivo, cayó 0.6 por ciento en 2013 y 4.3 en 2014. ", "Para los años 2015 y 2016, aumentó ligeramente a 0.5 y 1.3 por ciento, respectivamente, pero en 2017 volvió a caer hasta un 2 por ciento.", "\n\nDe acuerdo con el documento, China, India, Arabia Saudita, Indonesia, Turquía, Sudáfrica, Brasil y Rusia presentaron un crecimiento del salario real en nueve años, mientras que en México fue cayendo de 2008 a 2017.", "\n\nEn la región de América Latina y El Caribe, de 2008 a 2017, el salario real en México cayó 1.7 por ciento y se ubica entre los siete países de la región con cifras negativas, junto con Jamaica (4.1 por ciento), Trinidad Tobago (1.9 por ciento), Guatemala (1.8 por ciento), Honduras (0.8 por ciento), Puerto Rico (0.3 por ciento) y El Salvador (0.1 por ciento).", "\n\nLos otros 12 países de la región mostraron un crecimiento de hasta 5 por ciento en el mismo periodo y sus salarios reales se ubicaron por arriba de los de México. ", "A la cabeza está Panamá (5.2 por ciento), seguido de Uruguay (3.5 por ciento), Costa Rica (3.1 por ciento), Chile (2.4 por ciento) y República Dominicana (2.3 por ciento).", "\n\nDe acuerdo con el informe de la OIT, los salarios en América Latina aumentaron de forma marginal el año pasado, un 0.7 por ciento y en la última década, el incremento anual promedio fue del 0.9 por ciento.", "\n\nA nivel mundial, el informe arrojó que el crecimiento de los salarios fue el año pasado el más bajo desde 2008 y muy inferior a los niveles previos a la crisis económica que estalló hace una década.", "\n\nSegún las estadísticas procedentes de 134 países, los analistas de la OIT determinaron que el crecimiento real del salario fue de 1.8 por ciento en 2017, frente a un 2.4 por ciento en 2016.", "\n\nUn informe del Observatorio de Salarios presentado en mayo pasado arrojó que el número de trabajadores a los que no les alcanza su salario para comer y vestir se incrementó a 68 por ciento en el sexenio del Presidente Enrique Peña Nieto, y en los jóvenes pasó a 52 por ciento.", "\n\nEn el análisis “Bienestar y Precariedad laboral en México con énfasis en la población joven”, el Observatorio destacó que en los últimos cinco años se ha registrado un aumento en la incidencia de pobreza monetaria para el trabajador asalariado, tanto aquélla que no alcanza la Línea de Bienestar (LB) como la Línea de Bienestar Mínimo (LBM) del Consejo Nacional de Evaluación de la Política de Desarrollo Social (Coneval).", "\n\nPara el organismo que mide la pobreza en México, la Línea de Bienestar es el valor monetario de una canasta de alimentos, bienes y servicios básicos, mientras que la Línea de Bienestar Mínimo incluye sólo el valor monetario de una canasta alimentaria básica." ]

{ "pile_set_name": "OpenWebText2" }

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[ "The flag of Puerto Rico flies outside the Capitol building in San Juan Thomson Reuters WILMINGTON, Del. (Reuters) - Puerto Rico will begin its bankruptcy proceedings on May 17 in San Juan with a series of requests for managing the case as the commonwealth begins the process of restructuring its $70 billion in debt, according to court filing on Tuesday.", "\n\nPuerto Rico's federally appointed financial oversight board on May 3 filed the debt restructuring petition under Title III of last year's U.S. Congressional rescue law known as PROMESA. ", "While the initial filing was limited to obligations of the central government, it was still the largest-ever U.S. municipal bankruptcy, dwarfing that of Detroit.", "\n\nTwo days later, the oversight board sought bankruptcy protection for debt backed by sales tax revenues, known as COFINA.", "\n\nThe bankruptcy will be overseen by U.S. District Judge Laura Taylor Swain of the Southern District of New York, who was appointed by U.S. Chief Justice John Roberts.", "\n\nThe commonwealth has asked Swain to issue orders for case management, such as notifying its creditors and hiring a firm to manage claims, according to court filings.", "\n\nBankruptcy may not immediately change the day-to-day lives of Puerto Rico's people, 45 percent of whom live in poverty, but it could lead to cuts in pensions and worker benefits and a reduction in health and education services.", "\n\nThe island's economy has been in recession for nearly a decade, and has a current unemployment rate of about 11 percent.", "\n\nThe bankruptcy process will also give Puerto Rico the legal ability to impose drastic discounts on creditor recoveries, but could also spook investors and prolong the island's lack of access to debt markets.", "\n\nPrices for the commonwealth's benchmark general obligation bonds <74514LE86=MSRB> fell to a record low on Tuesday of 58.45.", "\n\n(Reporting by Tom Hals in Wilmington, Delaware; Editing by Meredith Mazzilli)" ]

{ "pile_set_name": "OpenWebText2" }

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[ "Quantitative breast elastography from B-mode images.", "\nElastography images provide information about the mechanical properties of soft tissue in a noninvasive way and can be useful to identify abnormalities and ascertain differential diagnoses of suspicious prior findings obtained through mammography ultrasound. ", "In this work we investigate, from a physics point of view, the feasibility of quantifying the Young's modulus of breast tissue from the autocorrelation of a diffuse acoustic field computed from a sequence of B-mode images acquired through conventional ultrasound scanners. ", "Inspired in the seismological approach of retrieving the Green's function by cross-correlation of diffuse fields, we obtained a quantitative expression that relates the local shear modulus of soft tissue to the autocorrelation of the displacement field generated by the presence of an acoustic diffuse field in the medium. ", "In addition, we designed a mechanical prototype device adaptable to the breast anatomy, in order to create the necessary conditions in terms of diffuse field generation. ", "The device is easy to handle, and its positioning does not interfere with the ultrasonic probe, being friendly to use within the clinical environment. ", "The displacement field was measured from a sequence of B-mode images acquired at standard frame rates (30-50 Hz) with conventional ultrasound equipment. ", "This method was tested in a breast tissue mimicking phantom using two standard ultrasound scanners (Toshiba Nemio NX and SIUI (Shantou Institute of Ultrasonic Instruments) Apogee 3800) and an open source research device (Verasonics V3.07 US). ", "We also performed an in vivo measurement as a preliminary validation. ", "In the reconstructed Young's modulus maps the inclusions were identified and the obtained quantitative results for an inclusion and the background of the phantom were 60.0 ± 4.0 and 20.4 ± 0.5 KPa for the Toshiba equipment, 65.5 ± 6.9 and 22.6 ± 2.7 KPa for the SIUI equipment and 67.2 ± 7.3 KPa and 22.6 ± 2.8 KPa for the Verasonic scanner. ", "These results are in good agreement with the values reported by the phantom's manufacturer of 60 and 20 KPa for the inclusion and the background, respectively. ", "In the case of the in vivo measurement, the obtained images are in accordance with the patient known pathology (BI-RADS 5, Infiltrating Ductal Carcinoma, Score 6). ", "The pathological breast showed a heterogeneous elasticity map with a mean Young's modulus of 98.1 ± 12.9 KPa, while the normal breast displayed a homogeneous map with a mean Young's modulus of 24.7 ± 8.1 KPa. ", "We successfully reconstructed the Young's modulus map of the breast tissue mimicking phantom and of a real breast tumor using B-mode images acquired with conventional ultrasound scanners. ", "The results obtained in this work support that our technique can be developed as a medical tool to obtain quantitative breast tissue elasticity maps." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "#!", "/usr/bin/env python\n#\n# Copyright 2017 Google Inc.\n#\n# Use of this source code is governed by a BSD-style license that can be\n# found in the LICENSE file.", "\n\n\n\"\"\"Common vars used by scripts in this directory.\"\"\"", "\n\n\nimport os\nimport sys\n\nFILE_DIR = os.path.dirname(os.path.abspath(__file__))\nINFRA_BOTS_DIR = os.path.realpath(os.path.join(FILE_DIR, os.pardir, os.pardir))\n\nsys.path.insert(0, INFRA_BOTS_DIR)\nfrom assets import assets\n\nASSET_NAME = os.path.basename(FILE_DIR)\n\n\ndef run(cmd):\n \"\"\"Run a command, eg. \"", "upload\" or \"download\". \"\"\"", "\n assets.main([cmd, ASSET_NAME] + sys.argv[1:])\n" ]

{ "pile_set_name": "Github" }

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[ "package org.geogebra.desktop.euclidian;\r\n\r\nimport java.awt.event.", "FocusEvent;\r\nimport java.awt.event.", "FocusListener;\r\n\r\nimport javax.swing.", "Box;\r\nimport javax.swing.", "SwingUtilities;\r\n\r\nimport org.geogebra.common.awt.", "GColor;\r\nimport org.geogebra.common.awt.", "GGraphics2D;\r\nimport org.geogebra.common.awt.", "GPoint;\r\nimport org.geogebra.common.awt.", "GRectangle;\r\nimport org.geogebra.common.euclidian.", "EuclidianView;\r\nimport org.geogebra.common.euclidian.", "SymbolicEditor;\r\nimport org.geogebra.common.euclidian.draw.", "DrawInputBox;\r\nimport org.geogebra.common.kernel.geos.", "GeoInputBox;\r\nimport org.geogebra.common.main.", "App;\r\nimport org.geogebra.desktop.awt.", "GColorD;\r\nimport org.geogebra.desktop.awt.", "GGraphics2DD;\r\nimport org.geogebra.desktop.awt.", "GRectangleD;\r\n\r\nimport com.himamis.retex.editor.desktop.", "MathFieldD;\r\nimport com.himamis.retex.editor.share.editor.", "MathFieldInternal;\r\nimport com.himamis.retex.renderer.share.", "TeXFont;\r\n\r\npublic class SymbolicEditorD extends SymbolicEditor {\r\n\r\n\tprivate Box box;\r\n\tprivate MathFieldD mathField;\r\n\tprivate double baseline;\r\n\r\n\tprotected SymbolicEditorD(App app, EuclidianView view) {\r\n\t\tsuper(app, view);\r\n\r\n\t\tbox = Box.createHorizontalBox();\r\n\r\n\t\tmathField = new MathFieldD();\r\n\r\n\t\tmathField.getInternal().setFieldListener(this);\r\n\t\tmathField.setVisible(true);\r\n\t\tmathField.getInternal().setType(TeXFont.", "SANSSERIF);\r\n\r\n\t\tmathField.addFocusListener(new FocusListener() {\r\n\t\t\t@Override\r\n\t\t\tpublic void focusGained(FocusEvent focusEvent) {\r\n\t\t\t\t// do nothing\r\n\t\t\t}\r\n\r\n\t\t\t@Override\r\n\t\t\tpublic void focusLost(FocusEvent focusEvent) {\r\n\t\t\t\thide();\r\n\t\t\t}\r\n\t\t});\r\n\r\n\t\tbox.add(mathField);\r\n\t}\r\n\r\n\t@Override\r\n\tpublic void resetChanges() {\r\n\t\tmathField.getInternal().parse(getGeoInputBox().getTextForEditor());\r\n\t}\r\n\r\n\tprotected void showRedefinedBox(final DrawInputBox drawable) {\r\n\t\tSwingUtilities.invokeLater(new Runnable() {\r\n\t\t\t@Override\r\n\t\t\tpublic void run() {\r\n\t\t\t\tdrawable.setWidgetVisible(true);\r\n\t\t\t}\r\n\t\t});\r\n\t}\r\n\r\n\t@Override\r\n\tprotected MathFieldInternal getMathFieldInternal() {\r\n\t\treturn mathField.getInternal();\r\n\t}\r\n\r\n\t@Override\r\n\tpublic void hide() {\r\n\t\tif (getDrawInputBox().isEditing()) {\r\n\t\t\tapplyChanges();\r\n\t\t\tgetDrawInputBox().setEditing(false);\r\n\t\t\tbox.setVisible(false);\r\n\t\t\tview.repaintView();\r\n\t\t}\r\n\t}\r\n\r\n\t@Override\r\n\tpublic boolean isClicked(GPoint point) {\r\n\t\treturn false;\r\n\t}\r\n\r\n\t@Override\r\n\tpublic void attach(GeoInputBox geoInputBox, GRectangle bounds) {\r\n\t\tsetInputBox(geoInputBox);\r\n\t\tgetDrawInputBox().setEditing(true);\r\n\r\n\t\tmathField.getInternal().setType(getGeoInputBox().isSerifContent()\r\n\t\t\t\t? ", "TeXFont.", "SERIF\t: TeXFont.", "SANSSERIF);\r\n\t\tmathField.getInternal().parse(getGeoInputBox().getTextForEditor());\r\n\t\tmathField.setBounds(GRectangleD.getAWTRectangle(bounds));\r\n\t\tmathField.getInternal().setSize(geoInputBox.getFontSizeMultiplier()\r\n\t\t\t\t* (app.getSettings().getFontSettings().getAppFontSize() + 3));\r\n\r\n\t\tbaseline = bounds.getY() + bounds.getHeight() / 2;\r\n\r\n\t\tbox.setBounds(GRectangleD.getAWTRectangle(bounds));\r\n\t\t((EuclidianViewD) view).add(box);\r\n\t\tbox.setVisible(true);\r\n\t\tbox.revalidate();\r\n\r\n\t\tmathField.requestViewFocus();\r\n\t}\r\n\r\n\t@Override\r\n\tpublic void repaintBox(GGraphics2D g) {\r\n\t\tGColor bgColor = getGeoInputBox().getBackgroundColor() !", "= null\r\n\t\t\t\t? ", "getGeoInputBox().getBackgroundColor() : view.getBackgroundCommon();\r\n\r\n\t\tg.saveTransform();\r\n\t\tg.translate(box.getX(), baseline - (double) (box.getHeight()) / 2);\r\n\t\tview.getTextField().drawBounds(g, bgColor, 0, 0, box.getWidth(), box.getHeight());\r\n\r\n\t\tg.translate(DrawInputBox.", "TF_PADDING_HORIZONTAL, 0);\r\n\t\tmathField.setForeground(GColorD.getAwtColor(getGeoInputBox().getObjectColor()));\r\n\t\tbox.paint(GGraphics2DD.getAwtGraphics(g));\r\n\r\n\t\tg.restoreTransform();\r\n\t}\r\n\r\n\t@Override\r\n\tpublic void onKeyTyped(String key) {\r\n\t\tString text = serializer.serialize(getMathFieldInternal().getFormula());\r\n\t\tdouble currentHeight = app.getDrawEquation().measureEquation(app, null, text,\r\n\t\t\t\tgetDrawInputBox().getTextFont(text), false).getHeight() + 2 * DrawInputBox.", "TF_MARGIN_VERTICAL;\r\n\t\tbox.setBounds(box.getX(), box.getY(), box.getWidth(), (int) currentHeight);\r\n\t\tbox.revalidate();\r\n\t\tview.repaintView();\r\n\t}\r\n\r\n\t@Override\r\n\tpublic boolean onEscape() {\r\n\t\treturn false;\r\n\t}\r\n\r\n\t@Override\r\n\tpublic void onTab(boolean shiftDown) {\r\n\t\tapplyChanges();\r\n\t}\r\n}\r\n" ]

{ "pile_set_name": "Github" }

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[ "\n217 F.Supp. ", "705 (1962)\nUNITED STATES of America\nv.\nJohn P. CALISE and Westchester Blood Service, Inc., Defendants.", "\nUnited States District Court S. D. New York.", "\nAugust 14, 1962.", "\n*706 *707 Robert M. Morgenthau, U. S. Atty. ", "for the Southern Dist. ", "of New York, New York City, for the United States of America; Stephen E. Kaufman, Richard A. Givens, Asst. ", "U. S. Attys., ", "of counsel.", "\nLongo & Torrisi, Mt. Vernon, N. Y., for defendants; Joseph F. Longo, Mt. Vernon, of counsel.", "\nCASHIN, District Judge.", "\nThe voluminous eighty count indictment in the above entitled action charges defendants, John P. Calise and Westchester Blood Service, Inc., with several types of violations of the Public Health Service Act and the Federal Food, Drug and Cosmetic Act, and a conspiracy to violate those statutes.", "\nThe defendant John P. Calise moves to dismiss as to himself on the ground that although each count of the indictment sets forth his name as a co-defendant to the alleged unlawful acts, \"the counts and allegations show only acts of alleged wrongdoing committed by Westchester Blood Service, Inc., and attributes no unlawful act to John P. Calise.", "\"[1] This argument is without substance. ", "The counts of the indictment each charge the defendant John P. Calise with offenses in the relevant statutory wording. ", "The fact that the offenses alleged concern blood products sold by the defendant Westchester Blood Service, Inc. does not exculpate Calise from criminal responsibility for the acts charged in the indictment. ", "18 U.S.C. § 2.", "\nDefendants urge that counts 59-75 are vague because they do not show whether the blood number listed is claimed to be the number purporting to identify the pint of blood or the number which in fact identified the pint of blood.[2] The defendants' claim of vagueness is without merit, especially in view of the fact that the government has already voluntarily supplied a bill of particulars specifying that the blood numbers listed are those used by the defendants.", "\nAs for the defendants' general objection that all of the counts of the indictment should be dismissed on the ground that \"* * * the same are vague, ambiguous, indefinite, uncertain and do not apprise the defendants of any alleged offense\",[3] their objection is groundless. ", "The counts substantially follow the terminology of the statutes and they plainly inform the defendants of that which they are accused. ", "The counts of the indictment are sufficiently definite and plain so as to eliminate entirely any possibility that the defendants will be misled as to the offenses with which they stand charged. ", "See United States v. Debrow, 346 U.S. 374, 74 S.Ct. ", "113, 98 L.Ed. ", "92 (1953). ", "The defendants' objections upon the same grounds to Count 80 in particular must likewise fail for the reasons stated above.", "\nThe defendants further assert that counts 31 through 48 inclusive, and counts 55, 56, 57, 58, 59, 60, 62, 65, 66, 67, 70, 72 and 80, alleging violations of the mislabeling provisions of 42 U.S.C. § 262(b), are not within the jurisdiction of this court because the acts complained of occurred entirely within the boundaries of the State of New York.[4] The subsection reads as follows:\n\"(b) No person shall falsely label or mark any package or container of any virus, serum, toxin, antitoxin, or other product aforesaid; nor alter any label or mark on any package or container of any virus, serum, toxin, antitoxin, or other product aforesaid so as to falsify such label or mark.\" *", "708 The language in subsection (b) does not indicate that Congress intended the effect of the statute to be confined merely to products moving in interstate commerce. ", "The restrictive interpretation of subdivision (b) which the defendants urge is not persuasive, in view of the fact that Congress could very easily have expressed such an intention in the Public Health Service Act, as it was cautious to do in 21 U.S.C. § 331(k) where such an intention actually existed. ", "Furthermore, the manner in which Congress separated the mislabeling ban of Section 262(b) from the labeling requirements of Section 262(a) (2) would seem to be indicative of an intention that Section 262(b) was to reach further in its scope from Section 262(a). ", "To restrict Section 262(b) exclusively to products moving in interstate commerce would also be inconsistent with the general purpose of the Public Health Service Act as a whole, because such an interpretation would encourage unscrupulous distributors to sell falsely labeled products on the local market which have been marked so as to apparently meet federal standards, but which do not meet those standards. ", "This would grant such distributors a definite advantage in competing with those who sell interstate products which fulfill the licensing and labeling requirements of 42 U.S.C. § 262(a).", "\nDefendants urge that counts 2, 52 and 53 are specifically defective in that, it is claimed, there is no allegation that the blood labels referred to in the above counts were updated.[5] Counts 2, 52 and 53 contain allegations of \"Days Updated\" of 42plus, 4plus, and 4plus days respectively. ", "Although it is true that the allegations are not as explicit in counts 2, 52 and 53 as the other counts, there can be no question as to their sufficiency. ", "The counts sufficiently inform the defendants of the elements of the crime so that they may prepare their defense and plead the judgment as a bar to any future prosecution. ", "Hagner v. United States, 285 U.S. 427, 431, 52 S.Ct. ", "417, 76 L.Ed. ", "861 (1932).", "\nThe defendants make several objections to the conspiracy Count 80. ", "It is first argued that Count 80 is barred by the statute of limitations because \"more than three years have elapsed since the alleged offense was committed from the date of the indictment.", "\"[6] Since the applicable statute of limitations is five years, the defendants are in error. ", "18 U.S.C. § 3282, as amended 1954. ", "Defendants also assert that although Count 80 alleges that from on or about January 1, 1959 the defendants conspired with other persons to violate certain laws of the United States, the count is invalid because the earliest overt act alleged to have been committed in furtherance of the conspiracy was not committed until substantially later, i. e. May 1960. ", "The point is not well taken. ", "Since the allegation is one of a continuing conspiracy, the Government may prove that the conspiracy was formed at any time during the period referred to in the indictment. ", "Count 80 is sufficient in all respects.", "\nThe indictment further alleges that the defendants falsely labeled and marked and altered a label and mark on a container of whole human blood, \"a product analogous to a therapeutic serum and applicable to the prevention, treatment and cure of diseases and injuries of man.\" ", "The Government maintains that the term \"therapeutic serum\" or \"analogous product\", as used in Section 262 of Title 42, is broad enough to encompass normal human blood. ", "It is the defendants' contention, however, that whole human blood is not a serum, and does not come within the purview of Section 262.[7] The same contention has heretofore been rejected in this district. ", "See United States v. Steinschreiber, (218 F.Supp. ", "426, May 25, 1962). ", "It cannot be said as a matter of law that the statutory terms do not include any serous fluid used for medical purposes. ", "The *709 scientific facts will have to be determined at trial and, of course, such determination will be dependent upon the expert and authoritative scientific evidence adduced at that time. ", "The Government has, however, in its indictment sufficiently charged the defendants with a crime under the statute.", "\nThe defendants further allege that the indictment fails to state an offense against the United States in that 21 U.S.C. § 321(g) is unconstitutional. ", "It is claimed that the definition of \"drugs\" appearing therein is so \"indefinite and uncertain that it contains no ascertainable standard of guilt thereby violating the first essential of due process of law.", "\"[8] Since the Government is relying solely upon Section 321(g) (2), it will be unnecessary to discuss defendants' objections to Section 321(g) (1). ", "Section 321(g) (2) defines drugs as \"articles intended for use in the diagnosis, cure, mitigation, treatment, or prevention of disease in man or other animals.\" ", "There can be no question but that the defendants dealt in blood products for their use in the treatment of human disease. ", "I, therefore, hold that the whole human blood referred to in the indictment would constitute a \"drug\" within the meaning of the statute. ", "The language of Section 321(g) (2) clearly complies with the test of constitutionality. ", "It gives adequate warning to ordinarily intelligent persons as to what manner of conduct is prohibited. ", "It is explicit enough to place defendants on notice that what they were doing might run counter to the law.", "\nCounts 76 through 78 allege that the defendants unlawfully sold in interstate commerce \"* * * a product analogous to a therapeutic serum and applicable to the prevention, treatment and cure of disease and injuries of man, to wit, washed cells from human blood, which had been propagated, manufactured, and prepared at an establishment which did not hold a license issued by the Secretary of Health, Education and Welfare.\" ", "42 U.S.C. § 262(a) provides:\n\"No person shall sell, barter, or exchange, or offer for sale * * * any virus, therapeutic serum, toxin, antitoxin, or analogous product * * *, applicable to the prevention, treatment, or cure of diseases or injuries of man, unless (1) such virus, serum, toxin, antitoxin, or other product has been propagated or manufactured and prepared at an establishment holding an unsuspended and unrevoked license * * *.\"", "\nCount 79 also involves an interpretation of the same statute.", "\nThe defendants claim that blood cannot be \"propagated\" or \"manufactured and prepared\" except in the body of a person, and that therefore blood cannot be one of the products to which Congress intended the licensing statute to apply. ", "Although this argument is truly ingenious, it must be rejected because if it were correct then nothing which is ultimately derived from nature would ever be capable of subsequently being \"manufactured and prepared.\" ", "The word \"manufactured\" as employed in this statute obviously was intended to include \"processing\" within its signification. ", "Unless the correct sanitary precautions were taken by the defendants, any processing of blood products by them could seriously imperil the health of patients. ", "For this reason the establishment is required to be licensed under 42 U.S.C. § 262(a). ", "The construction of the terminology which I have adopted is in accord with the purpose intended by Congress in enacting the statute. ", "See H.R.Rep. ", "No. ", "2713, 57th Cong., ", "1st Sess. (", "1902) on H.R. 15289.", "\nThe defendants next allege that their rights were violated in the Grand Jury proceedings.[9] Their allegation that unauthorized persons may have been present while the Grand Jury was in session has no proof to substantiate it. *", "710 The affidavits of the Foreman of the Grand Jury and of the Assistant United States Attorneys that no such unauthorized persons were ever present are uncontradicted by defendants. ", "The defendants' objections on that ground must therefore be rejected. ", "In like manner must be rejected the request that the indictment be dismissed because newspaper articles published during the Grand Jury session were so slanted that they prejudiced the deliberations. ", "The record is barren of any evidence whatsoever that the Grand Jury did not proceed conscientiously and without prejudice upon independent evidence taken under oath before it.", "\nI reject the defendants' claim that the indictment should be dismissed on the ground that \"there was insufficient evidence before the Grand Jury to warrant an indictment.", "\"[10] The indictment is valid on its face and was returned by an unprejudiced and legally constituted Grand Jury. ", "As such, it is sufficient to call for a trial on the merits without a review by this court of the weight of the evidence before the Grand Jury. ", "See Costello v. United States, 350 U.S. 359, 76 S.Ct. ", "406, 100 L.Ed. ", "397 (1956). ", "The other objections made by defendants to the procedure of the Grand Jury are also rejected.", "\nThe defendants further move for dismissal of the indictment on the ground that evidence presented to the Grand Jury was obtained by illegal search and seizure. ", "The uncontradicted affidavits submitted by the Government in opposition to the defendants' motion show, however, that the evidence referred to was lawfully appropriated by Dr. Tripp, a Public Health Service official. ", "It was trash, in the nature of bona vacantia,[11] which the defendants had abandoned for collection by a trash truck after the lease of the premises in which they formerly did business had expired. ", "And since the permission of the owner of the building was obtained for entering the premises, there is nothing at all to indicate that the appropriation of this abandoned material constituted an illegal search or seizure. ", "In any event, by affidavits which the defendants have failed to contradict, it has been shown that such material was not even submitted to the Grand Jury. ", "The defendants' objections are groundless.", "\nComing to the procedural motions, the defendants' motion for a bill of particulars is denied except to the extent that the Government has supplied the requested information in the bill of particulars voluntarily filed.", "\nThe Government has consented to an order allowing the attorneys for the defendants to inspect or copy or photograph all books, papers, documents and tangible objects obtained from or belonging to the defendants. ", "The defendants' request for a similar order with regard to all such documents and objects obtained from others by seizure or process is denied. ", "United States v. Haug, 21 F.R.D. 22 (N.D.Ohio 1957). ", "The denial is, however, without prejudice to a renewal of the motion in reference to specific documents and objects upon an adequate showing that they are necessary and material to the preparation of the defendants' case.", "\nThe defendants' requests for the return of the matter appropriated by Dr. Tripp, for the suppression of the defendant John P. Calise's testimony at the Grand Jury session, and for inspection of the Grand Jury minutes, are denied.", "\nIn sum, therefore, all defendants' motions are denied, with the exception of the copying, inspection and photographing of items obtained from the defendants, and the bill of particulars voluntarily filed by the Government.", "\nIt is so ordered.", "\nNOTES\n[1] Motion to dismiss, par. ", "1.", "\n[2] Motion to dismiss, par. ", "4.", "\n[3] Motion to dismiss, par. ", "7.", "\n[4] Motion to dismiss, par. ", "3.", "\n[5] See defendants' Memorandum, p. 15.", "\n[6] Motion to dismiss, par. ", "6.", "\n[7] Defendants' Memorandum, p. 11.", "\n[8] Defendants' Memorandum, p. 4.", "\n[9] Motion to dismiss, par. ", "5.", "\n[10] Motion to dismiss, par. ", "5(d).", "\n[11] See United States v. Abel, 362 U.S. 217, 240-241, 80 S.Ct. ", "683, 4 L.Ed.2d 668 (1960).", "\n" ]

{ "pile_set_name": "FreeLaw" }

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[ "Q:\n\nQQuickWindow in shared lib auto close when show in QApplication\n\nI develop a generic interface library with qt. ", "I have trouble with pressed effect on QPushbutton when I click with a touch screen (this effect appears one time on 10 click).", "\nSo I create a basic qml application with one button and pressed effect appear all time. ", "I incude the qml part into my library and load it in QQuickWidget and I have same problem with pressed effect.", "\nSo I want to use only qml. ", "My principal application is a QApplication and I load my library in it in which I load qml file with QQmlApplication Engine. ", "Then I show it by QQuickWindow.", "\nWhen I launch my application I saw the window open but it is automatically close. ", "I think my QApplication don't detect QML and the renderer loop is not start.", "\nI'm on windows with QT5.5.1 (MSVC2013, 32bit)\npro file of main application\nQT += core xml widgets qml quick\n\nTARGET = COM_INT\nCONFIG += console\nCONFIG -= app_bundle\n\nTEMPLATE = app\n\nSOURCES += main.cpp \\\n comint.cpp\nHEADERS += \\\n comint.h \\\n\nINCLUDEPATH += \"$$(My_Workspace)/Modules_Generique/IHM_Soft\"\nRelease{\n LIBS += \"$$(My_Workspace_build)/IHM_Soft/release/IHM_Soft.lib\"\n}\n\nDebug{\n LIBS += \"$$(My_Workspace_build)/IHM_Soft/debug/IHM_Soft.lib\"\n}\n\nMain application (exe) main.cpp\n#include <QApplication>\n#include <QQmlApplicationEngine>\n\n#include \"comint.h\"\n\nint main(int argc, char *argv[])\n{\n QApplication a(argc, argv);\n\n ComInt com;\n com.initialize();\n\n return a.exec();\n}\n\nComInt class:\nSource file comint.cpp\n#include \"comint.h\"\n#include \"ihmsoft.h\"\n\nComInt::ComInt()\n{\n}\n\nvoid ComInt::initialize()\n{\n this->m_pIHMSoft = new IHMSoft();\n}\n\nheader file comint.h\n#ifndef COMINT_H\n#define COMINT_H\n\nclass IHMSoft;\n\nclass ComInt\n{\npublic:\n ComInt();\n void initialize();\nprivate:\n IHMSoft *m_pIHMSoft;\n};\n\n#endif // COMINT_H\n\npro file of shared lib\nQT += xml widgets core qml quick quickwidgets\nCONFIG += c++11\n\nTARGET = IHM_Soft\nTEMPLATE = lib\n\nDEFINES += IHM_SOFT_LIBRARY\n\nSOURCES += ihmsoft.cpp\nHEADERS += ihmsoft.h\\\n ihm_soft_global.h\n\nRESOURCES += \\\n rsc.qrc\n\nShared library: source file ihm_soft.cpp\n#include \"ihmsoft.h\"\n#include <QQmlApplicationEngine>\n#include <QQuickWindow>\n\nIHMSoft::IHMSoft(){\n\n qputenv(\"QT_QUICK_CONTROLS_STYLE\", \"Base\");\n QQmlApplicationEngine engine;\n engine.load(QUrl(QStringLiteral(\"qrc:/IHM_Soft.qml\")));\n QList<QObject*> root = engine.rootObjects();\n QQuickWindow *window = qobject_cast<QQuickWindow*>(root.at(0));\n window->show();\n}\n\nheader file ihm_soft.h\n#ifndef IHM_SOFT_H\n#define IHM_SOFT_H\n\n#include \"ihm_soft_global.h\"\n\nclass IHM_SOFT_SHARED_EXPORT IHM_Soft\n{\n\npublic:\n IHM_Soft();\n};\n\n#endif // IHM_SOFT_H\n\nGlobal file ihm_soft_global.h\n#ifndef IHM_SOFT_GLOBAL_H\n#define IHM_SOFT_GLOBAL_H\n\n#include <QtCore/qglobal.h>\n\n#if defined(IHM_SOFT_LIBRARY)\n# define IHM_SOFT_SHARED_EXPORT Q_DECL_EXPORT\n#else\n# define IHM_SOFT_SHARED_EXPORT Q_DECL_IMPORT\n#endif\n\n#endif // IHM_SOFT_GLOBAL_H\n\nQml file\nimport QtQuick 2.0\nimport QtQuick.", "Controls 1.4\n\nimport QtQuick.", "Window 2.0\n\nApplicationWindow {\n visible: true\n width: 500\n height: 500\n\n Button {\n visible: true\n iconSource: \"resources/t_on_off.png\"\n }\n}\n\nEdit: Sorry the code of the main application was a test application which do not include lib.", "\n\nA:\n\nA variable is deleted when its scope ends, in your case engine is a local variable that is deleted when IHMSoft finishes being built, so you see that the window closes. ", "The solution is to make it a member of the class:\n*.h\n#ifndef IHM_SOFT_H\n#define IHM_SOFT_H\n\n#include \"ihm_soft_global.h\"\n#include <QQmlApplicationEngine>\n\nclass IHM_SOFT_SHARED_EXPORT IHM_Soft\n{\n\npublic:\n IHM_Soft();\nprivate:\n QQmlApplicationEngine engine; // member\n};\n\n#endif // IHM_SOFT_H\n\n*.cpp\n#include \"ihmsoft.h\"\n\nIHMSoft::IHMSoft(){\n qputenv(\"QT_QUICK_CONTROLS_STYLE\", \"Base\");\n engine.load(QUrl(QStringLiteral(\"qrc:/IHM_Soft.qml\")));\n}\n\n" ]

{ "pile_set_name": "StackExchange" }

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[ "The Case of Dr. Oz: Ethics, Evidence, and Does Professional Self-Regulation Work?", "\nDr. Mehmet Oz is widely known not just as a successful media personality donning the title \"America's Doctor®,\" but, we suggest, also as a physician visibly out of step with his profession. ", "A recent, unsuccessful attempt to censure Dr. Oz raises the issue of whether the medical profession can effectively self-regulate at all. ", "It also raises concern that the medical profession's self-regulation might be selectively activated, perhaps only when the subject of professional censure has achieved a level of public visibility. ", "We argue here that the medical profession must look at itself with a healthy dose of self-doubt about whether it has sufficient knowledge of or handle on the less visible Dr. \"Ozes\" quietly operating under the profession's presumptive endorsement." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "---\nabstract: 'We introduce the first analytical model of asymmetric community dynamics to yield Hubbell’s neutral theory in the limit of functional equivalence among all species. ", "Our focus centers on an asymmetric extension of Hubbell’s local community dynamics, while an analogous extension of Hubbell’s metacommunity dynamics is deferred to an appendix. ", "We find that mass-effects may facilitate coexistence in asymmetric local communities and generate unimodal species abundance distributions indistinguishable from those of symmetric communities. ", "Multiple modes, however, only arise from asymmetric processes and provide a strong indication of non-neutral dynamics. ", "Although the exact stationary distributions of fully asymmetric communities must be calculated numerically, we derive approximate sampling distributions for the general case and for nearly neutral communities where symmetry is broken by a single species distinct from all others in ecological fitness and dispersal ability. ", "In the latter case, our approximate distributions are fully normalized, and novel asymptotic expansions of the required hypergeometric functions are provided to make evaluations tractable for large communities. ", "Employing these results in a Bayesian analysis may provide a novel statistical test to assess the consistency of species abundance data with the neutral hypothesis.'", "\naddress:\n- 'Department of Biology, University of Maryland, College Park, MD 20742, USA'\n- 'Center for Mathematics and Computer Science, Science Park 123, 1098 XG Amsterdam, The Netherlands'\n- 'Section of Integrative Biology, University of Texas at Austin, 1 University Station C0930, Austin, TX 78712, USA'\nauthor:\n- 'Andrew E. Noble'\n- 'Nico M. Temme'\n- 'William F. Fagan'\n- 'Timothy H. Keitt'\nbibliography:\n- 'Noble\\_MainText.bib'\ntitle: A sampling theory for asymmetric communities\n---\n\n-10cm\n\nbiodiversity ,neutral theory ,nearly neutral theory ,coexistence ,mass-effects\n\nIntroduction {#intro}\n============\n\nThe ecological symmetry of trophically similar species forms the central assumption in Hubbell’s unified neutral theory of biodiversity and biogeography [@PHubbell:2001p4284]. ", "In the absence of stable coexistence mechanisms, local communities evolve under zero-sum ecological drift – a stochastic process of density-dependent birth, death, and migration that maintains a fixed community size [@PHubbell:2001p4284]. ", "Despite a homogeneous environment, migration inhibits the dominance of any single species and fosters high levels of diversity. ", "The symmetry assumption has allowed for considerable analytical developments that draw on the mathematics of neutral population genetics [@Fisher:1930; @Wright:1931] to derive exact predictions for emergent, macro-ecological patterns [@Chave:2004p1260; @Etienne:2007p3828; @McKane:2000p4318; @Vallade:2003p3851; @Volkov:2003p1299; @Etienne:2004p5302; @McKane:2004p5661; @Pigolotti:2004p5308; @He:2005p7106; @Volkov:2005p6326; @Hu:2007p7107; @Volkov:2007p1300; @Babak:2008p7108; @Babak:2009p7109]. ", "Among the most significant contributions are calculations of multivariate sampling distributions that relate local abundances to those in the regional metacommunity [@Alonso:2004p4321; @Etienne:2005p3829; @Etienne:2005p6998; @Etienne:2007p7111]. ", "Hubbell first emphasized the ultility of sampling theories for testing neutral theory against observed species abundance distributions (SADs) [@PHubbell:2001p4284]. ", "Since then, Etienne and Olff have incorporated sampling distributions as conditional likelihoods in Bayesian analyses [@Etienne:2004p5302; @Etienne:2005p6363; @Etienne:2007p7111; @Etienne:2009p8436]. ", "Recent work has shown that the sampling distributions of neutral theory remain invariant when the restriction of zero-sum dynamics is lifted [@Etienne:2007p5640; @Haegeman:2008p6364; @Conlisk:2010p8340] and when the assumption of strict symmetry is relaxed to a requirement of ecological equivalence [@Etienne:2007p5640; @Haegeman:2008p6364; @Allouche:2009p6354; @Allouche:2009p6355; @Lin:2009p6368].", "\n\nThe success of neutral theory in fitting empirical patterns of biodiversity [@PHubbell:2001p4284; @Volkov:2003p1299; @Volkov:2005p6326; @He:2005p7106; @Chave:2006p6372] has generated a heated debate among ecologists, as there is strong evidence for species asymmetry in the field [@Harper:1977; @Goldberg:1992p6747; @Chase:2003; @Wootton:2005; @Levine:2009p6069]. ", "Echoing previous work on the difficulty of resolving competitive dynamics from the essentially static observations of co-occurence data [@Hastings:1987p8336], recent studies indicate that interspecific tradeoffs may generate unimodal SADs indistinguishable from the expectations of neutral theory [@Chave:2002p6357; @Mouquet:2003p6380; @Chase:2005p6356; @He:2005p7106; @Purves:2005; @Walker:2007p4670; @Doncaster:2009p6361]. ", "These results underscore the compatibility of asymmetries and coexistence. ", "The pioneering work of @Hutchinson:1951p7110, has inspired a large literature on asymmetries in dispersal ability that permit the coexistence of “fugitive species\" with dominant competitors. ", "In particular, @Shmida:1985p7047 extended the work of @Brown:1977p7046 by introducing the paradigm of “mass-effects\", where immigration facilitates the establishment of species in sites where they would otherwise be competitively excluded. ", "Numerous attempts have been made to reconcile such deterministic approaches to the coexistence of asymmetric species with the stochastic model of ecological drift in symmetric neutral theory [@Zhang:1997p6376; @Tilman:2004p4673; @Chase:2005p6356; @Alonso:2006p4856; @Gravel:2006p4668; @Pueyo:2007p1298; @Walker:2007p4670; @Alonso:2008p4724; @Ernest:2008p1316; @Zhou:2008p6377]. ", "Many of these attempts build on insights from the concluding chapter of Hubbell’s book [@PHubbell:2001p4284].", "\n\nNevertheless, the need remains for a fully asymmetric, analytical, sampling theory that contains Hubbell’s model as a limiting case [@Alonso:2006p4856]. ", "In this article, we develop such a theory for local, dispersal-limited communities in the main text and defer an analogous treatment of metacommunities to Appendix A. Hubbell’s assumption of zero-sum dynamics is preserved, but the requirement of per capita ecological equivalence among all species is eliminated. ", "Asymmetries are introduced by allowing for the variations in ecological fitness and dispersal ability that may arise in a heterogeneous environment [@Leibold:2004p1285; @Holyoak:2005]. ", "Our work expands on the numerical simulations of @Zhou:2008p6377, where variations in ecological fitness alone were considered. ", "Coexistence emerges from mass-effects as well as ecological equivalence, and both mechanisms generate unimodal SADs that may be indistinguishable. ", "For local communities and metacommunities, we derive approximate sampling distributions for both the general case and the nearly neutral case, where symmetry is broken by a single species unique in ecological function. ", "These approximations yield the sampling distributions of Hubbell’s neutral model in the limit of functional equivalence among all species.", "\n\nA general sampling theory for local communities {#gen}\n===============================================\n\nFor a local community of $J_L$ individuals and $S$ possible species, we model community dynamics as a stochastic process, $\\vec{N}(\\tau)$, over the labelled community abundance vectors $\\vec{n}=(n_1,\\dots,n_S)$. Consistent with zero-sum dynamics, we require all accessible states to contain $J_L$ total individuals: $\\sum_{i=1}^S n_i=J_L$ and $0\\leq n_i \\leq J_L$ . ", "The number of accessible states is $A=\\sum_{n_1=0}^{J_L} \\dots \\sum_{n_S=0}^{J_L}$ $\\delta(J_L-n_1-\\dots-n_S)$.\n\nAllowed transitions first remove an individual from species $i$ and then add an individual to species $j$. Removals are due to death or emigration and occur with the density-dependent probability $n_i/J_L$. Additions are due either to an immigration event, with probability $m_j$, or a birth event, with probability $1-m_j$. We will refer to the $m_j$ as dispersal abilities. ", "If immigration occurs, we assume that metacommunity relative abundance, $x_j$, determines the proportional representation of species $j$ in the propagule rain and that the probability of establishment is weighted by ecological fitness, $w_j$, where high values correspond to a local competitive advantage or a superior adaptation to the local environment. ", "Therefore, species $j$ recruits with probability , where $x_j\\in(0,1)$, $w_j\\in(0,\\infty)$, and $\\sum_{k=1}^Sx_k=1$. If immigration does not occur, we assume that local relative abundance, $n_j/J_L$, governs propagule rain composition such that species $j$ recruits with probability . ", "In numerical simulations of an asymmetric community, @Zhou:2008p6377 employed a similar probability for recruitment in the absence of immigration. ", "Here, a factor of $w_i$ is subtracted in the denominator because species $i$ loses an individual prior to the birth event for species $j$. An analogous subtraction is absent from Eq.", " \\[othbirthprob\\] because we assume an infinite metacommunity where the $x_j$ are invariant to fluctuations in the finite, local community populations.", "\n\nIn sum, the nonzero transition probabilities are stationary and given by T\\_[ij]{} &=&\\_[0]{}\\\n&=& ((1-m\\_j)+m\\_j), where $\\vec{e}_i$ is an $S$–dimensional unit vector along the $i$th–direction, the $w_k$ must be sufficiently large such that $\\sum_{k=1}^Sw_kn_k-w_i>0$, and the time, $\\tau$, is dimensionless with a scale set by the overall transition rate. ", "The probability of state occupancy, $P_{\\vec{n}}$, evolves according to the master equation =\\_[i=1]{}\\^S\\_[j=1,ji]{}\\^S(T\\_[ij+\\_i-\\_j]{}P\\_[+\\_i-\\_j]{}-T\\_[ji]{}P\\_ ) \\_[ij]{}, where \\_[ij]{}=(J\\_L-(n\\_i+1))(n\\_j-1), and we define the step-function $\\Theta(x)$ to be zero for $x<0$ and one otherwise. ", "Eq.", " \\[evolve1\\] can be recast in terms of a transition probability matrix $W$ =\\_[b=1]{}\\^AP\\_[b]{} W\\_[ba]{}, where $a,b\\in(1, \\dots, A)$ enumerate accessible states with components $(a_1, \\dots,$ $a_S)$, $(b_1, \\dots,$ $b_S)$. The left eigenvector of $W$ with zero eigenvalue yields the stationary distribution for community composition, $P_a^*\\equiv\\lim_{\\tau\\to\\infty}P_a(\\tau)$. Marginal distributions yield the equilibrium abundance probabilities for each species $i$ P\\^[(i)\\*]{}\\_[n]{}=\\_[a=1]{}\\^[A]{} \\_[a\\_i,n]{} P\\_a\\^\\*. ", "From here, we calculate the stationary SAD by following the general treatment of asymmetric communities in @Alonso:2008p4724 S\\^\\*\\_n=\\_[i=1]{}\\^SP\\^[(i)\\*]{}\\_[n]{}. ", "The expected species richness is S\\^\\*=\\_[n=1]{}\\^SS\\_n\\^\\*&lt;S. Given that the local community, with abundances $n_i$, is defined as a sample of the metacommunity, with relative abundances $x_i$, we have established the framework for a general sampling theory of local communities.", "\n\nThis sampling theory incorporates aspects of the mass-effects paradigm [@Brown:1977p7046; @Shmida:1985p7047; @Holt:1993p7063; @Leibold:2004p1285; @Holyoak:2005]. ", "Local asymmetries in ecological fitness imply environmental heterogeneity across the metacommunity such that competitive ability peaks in the local communities where biotic and abiotic factors most closely match niche requirements [@Tilman:1982p7101; @Leibold:1998p7099; @Chase:2003]. ", "Where species experience a competitive disadvantage, the mass-effects of immigration allow for persistence. ", "Indeed, the master equation given by Eq.", " \\[evolve1\\], when applied to open communities where $m_j>0$ for all $j$, admits no absorbing states and ensures that every species has a nonzero probability of being present under equilibrium conditions. ", "By contrast, when Eq.", " \\[evolve1\\] is applied to closed communities where $m_j=0$ for all $j$, the eventual dominance of a single species is guaranteed.", "\n\n-2cm\n\n{width=\".602\\textwidth\"} -0.27cm {width=\".5067\\textwidth\"}\n\n0.0cm\n\n0.03cm {width=\".595\\textwidth\"} -0.13cm {width=\".5000\\textwidth\"}\n\nMass-effects allow for a soft breaking of the symmetry of neutral theory and provide a mechanism for multi-species coexistence. ", "In Fig.", " \\[general\\], we present numerical results for the marginal equilibrium distributions of an asymmetric local community subsidized by a potentially neutral metacommunity, where the five species share a common relative abundance, $x_j$=0.2. ", "Although a single species may dominate due to a locally superior competitive ability (see Fig.", " \\[general\\]a), multi-species coexistence may arise, despite significant competitive asymmetries, due to high levels of immigration that tend to align local relative abundances with those in the metacommunity (see Fig.", " \\[general\\]c). ", "Despite the underlying asymmetric process, coexistence via mass-effects generates unimodal SADs that, given sampling errors in field data, may be indistinguishable from SADs due to neutral dynamics, as shown in Fig.", " \\[general\\]d. ", "This reinforces previous conclusions that the static, aggregate data in unimodal SADs cannot resolve the individual-level rules of engagement governing the origin and maintenance of biodiversity [@Chave:2002p6357; @Mouquet:2003p6380; @Purves:2005; @He:2005p7106; @Chase:2005p6356; @Walker:2007p4670; @Doncaster:2009p6361]. ", "However, SADs with multiple modes are not uncommon in nature [@Dornelas:2008p8337; @Gray:2010p6748] and provide a strong indicator of non-neutral dynamics [@Alonso:2008p4724]. ", "Fig.", " \\[general\\]b presents a bimodal SAD for an asymmetric local community with low levels of immigration.", "\n\nEach plot in Fig.", " \\[general\\] displays results for a relatively small community of $J_L=75$ individuals and $S=5$ possible species. ", "Sparse matrix methods were used to calculate the left eigenvector with zero eigenvalue for transition matrices of rank $\\sim1.5{\\rm M}$. Obtaining stationary distributions for larger, more realistic communities poses a formidable numerical challenge. ", "This motivates a search for analytically tractable approximations to sampling distributions of the general theory.", "\n\nAn approximation to the sampling distribution {#sc00}\n=============================================\n\nThe distribution $P^*_{\\vec{n}}$ is stationary under Eq.", " \\[evolve1\\] if it satisfies the condition of detailed balance T\\_[ij+\\_i-\\_j]{}P\\^\\*\\_[+\\_i-\\_j]{}=T\\_[ji]{}P\\^\\*\\_, for all $i$ and $j$ such that $i\\ne j$ and $\\Theta_{ij}\\ne 0$. For general (g) large–$J_L$ communities where $S,w_k<<\\sum_{l=1}^Sw_ln_l$ for all $k$, we will show that detailed balance is approximately satisfied by P\\^[[g]{}\\*]{}\\_=Z\\_[g]{}\\^[-1]{}\\_[k=1]{}\\^Sw\\_k\\^[n\\_k]{}(1-m\\_k)\\^[n\\_k]{}(\\_[k]{}x\\_k)\\_[n\\_k]{}, where \\_[k]{}=I\\_k, where $(a)_n=\\Gamma(a+n)/\\Gamma(a)$ is the Pochhammer symbol, $Z_{\\rm g}^{-1}$ is a normalization constant, and $I_k=m_k(J_L-1)/(1-m_k)$ is a generalization of the “fundamental dispersal number\" [@Etienne:2005p3829]. ", "From the definition of $T_{ij\\vec{n}}$ in Eq.", " \\[t\\], we have =, and assuming the form of $P^{{\\rm g}*}_{\\vec{n}}$ in Eq.", " \\[gensampdistrib\\], we find =\\_[k=1]{}\\^S\\\n. ", "Now, for large–$J_L$ communities where $w_k<<\\sum_{l=1}^Sw_ln_l$ for all $k$, the ratio $\\epsilon_{ijk}\\equiv (w_i-w_j)/(\\sum_{l=1}^Sw_ln_l-w_k)$ is a small number. ", "Given $(a(1+\\epsilon))_n\\sim(a)_n+{\\cal O}(\\epsilon)$, we expand the right-hand-side of Eq.", " \\[gensamptesta\\] to obtain =+\\_[k=1]{}\\^S[O]{}(\\_[ijk]{}), which validates our assertion that Eq.", " \\[gensampdistrib\\] is an approximate sampling distribution of the general theory when $S<<\\sum_{l=1}^Sw_ln_l$. For communities of species that are symmetric (s) in ecological fitness but asymmetric in dispersal ability, Eq.", " \\[gensampdistrib\\] reduces to an exact sampling distribution P\\^[[s]{}\\*]{}\\_=Z\\_[s]{}\\^[-1]{}\\_[k=1]{}\\^S(1-m\\_k)\\^[n\\_k]{}(I\\_kx\\_k)\\_[n\\_k]{}, that satisfies detailed balance without approximation. ", "Analogous distributions for general and fitness-symmetric metacommunities are provided in Appendix A. However, in all of these results, the normalization constants must be calculated numerically. ", "This limits the utility of our sampling distributions in statistical analyses. ", "Can we find a non-neutral scenario that admits an approximate sampling distribution with an analytical expression for the normalization?", "\n\nSampling nearly neutral communities {#sc1}\n===================================\n\nAs the species abundance vector evolves under Eq.", " \\[evolve1\\], consider the dynamics of marginal abundance probabilities for a single focal species that deviates in ecological function from the surrounding, otherwise symmetric, community. ", "In particular, let the first element of $\\vec{N}(\\tau)$ be the marginal process, $N(\\tau)$, over states $n\\in(0,\\dots,J_L)$, for the abundance of an asymmetric focal species with dispersal ability $m$, ecological fitness $w$, and relative metacommunity abundance $x$. If all other species share a common dispersal ability $m_o$ and ecological fitness $w_o$, then the focal species gains an individual with probability g\\_[n]{}&&\\_[i=2]{}\\^S T\\_[i1(n,n\\_2,…,n\\_S)]{}\\\n&=&((1-m)+m),\\\nand loses an individual with probability r\\_[n]{} && \\_[i=2]{}\\^S T\\_[1i(n,n\\_2,…,n\\_S)]{}\\\n&=&((1-m\\_o)+m\\_o),\\\nwhere we have used $\\sum_{k=1}^Sx_k=1$. These marginal transition probabilities do not depend separately on $w$ and $w_o$, but only on their ratio. ", "Without loss of generality, we redefine $w\\equiv w/w_o$ to be the focal species’ local [*advantage*]{} in ecological fitness. ", "Eqs.", " \\[bn\\] and \\[dn\\], which are independent of the abundances $(n_2,\\dots,n_S)$, suggest a univariate birth-death process for the marginal dynamics of the asymmetric species governed by the master equation &=&g\\_[n-1]{}(n-1)P\\_[n-1]{}+r\\_[n+1]{}(J\\_L-(n+1))P\\_[n+1]{}\\\n&&-(g\\_n(J\\_L-(n+1))+r\\_n(n-1))P\\_n, and we formally derive this result from Eq.", " \\[evolve1\\] in Appendix B. Given the well-known stationary distribution of Eq.", " \\[margprocessasymm\\] P\\_n\\^\\* = P\\_0\\^\\* \\_[i=0]{}\\^[n-1]{}. ", "we find an exact result for the stationary abundance probabilities of the focal species in a nearly neutral (nn) community P\\_n\\^[[nn]{}\\*]{}=Z \\^n , where ${\\rm B}(a,b)=\\Gamma(a)\\Gamma(b)/\\Gamma(a+b)$ is the beta-function Z\\^[-1]{}= \\_2F\\_1(-J\\_L,;1-;), and &=&w,\\\n&=&,\\\n&=& 1+. ", "For the asymmetric focal species, this is an exact result of the general model, Eq.", " \\[evolve1\\], that holds for nearly neutral local communites with any number of additional species. ", "Eq.", " \\[PnNN\\] may be classified broadly as a generalized hypergeometric distribution or more specifically as an exponentially weighted Pólya distribution [@Kemp:1968tSUDDT; @Johnson:1992tUDD].", "\n\nIn the absence of dispersal limitation, Eq.", " \\[PnNN\\] becomes \\_[m,m\\_o1]{}P\\_n\\^[[nn]{}\\*]{}=()\\^[J\\_L]{}(wx)\\^n (1-x)\\^[J\\_L-n]{}, where the identity ${\\rm B}(a,b){\\rm B}(a+b,1-b)=\\pi/(a\\sin(\\pi b))$ has been used. ", "This is a weighted binomial distribution with expected abundance $wxJ_L/(1+x(w-1))$ and variance $wx(1-x)J_L/(1+x(w-1))^2$. In the neutral, or symmetric, limit where $w=1$, Eq.", " \\[PnNNlimit\\] reduces to a binomial sampling of the metacommunity, [*sensu*]{} @Etienne:2005p3829.", "\n\nIn the presence of dispersal limitation, we evaluate $\\Sigma_{n=1}^{J_L} n P_n^{{\\rm nn}*}$ to obtain the expected abundance \\[N\\^\\*\\]&=&Z\\\n&=& , where $N^*\\equiv\\lim_{\\tau\\to\\infty}N(\\tau)$. The variance of the stationary distribution is given by \\[N\\^\\*\\]&=& Z\\\n&=&[E]{}\\[N\\^[\\*2]{}\\]-[E]{}\\[N\\^\\*\\]\\^2, and we evaluate $\\Sigma_{n=1}^{J_L} n^2 P_n^{{\\rm nn}*}$ to obtain \\[N\\^[\\*2]{}\\]= . ", "In Eqs.", " \\[avgn\\] and \\[Var\\], the normalization of Eq.", " \\[NPL\\] generates central moments for the abundance distribution and plays a role analogous to the grand partition function of statistical physics. ", "Recent studies have demonstrated the utility of partition functions in extensions of Hubbell’s neutral theory [@ODwyer:2009p4394; @ODwyer:2009p6371].", "\n\nFor large–$J_L$ communities, evaluation of the hypergeometric functions in Eqs.", " \\[PnNN\\], \\[avgn\\], and \\[avgn2\\] is computationally expensive. ", "To remove this barrier, one of us (N.M.T.) has derived novel asymptotic expansions (see Appendix C). ", "We use these expansions to plot the stationary abundance probabilities for $J_L=1$M. In Fig.", " \\[asymp\\]a, small local advantages in ecological fitness generate substantial increases in expected abundance over the neutral prediction. ", "Hubbell found evidence for these discrepancies in Manu forest data and referred to them as “ecological dominance deviations\" [@PHubbell:2001p4284]. ", "Hubbell also anticipated that dispersal effects would mitigate advantages in ecological fitness [@PHubbell:2001p4284]. ", "The right panel of Fig.", " \\[asymp\\] demonstrates, once again, that enhanced mass-effects due to increased dispersal ability may inhibit the dominance of a locally superior competitor by compelling relative local abundance to align with relative metacommunity abundance.", "\n\n{width=\".58625\\textwidth\"} -0.15cm {width=\".5\\textwidth\"}\n\nAn approximation to the multivariate sampling distribution of nearly neutral local communities is constructed in Appendix B P\\^[[nn]{}\\*]{}\\_=Z\\^[n]{}\\_[i=2]{}\\^S(\\_[on]{} x\\_i)\\_[n\\_i]{}, where \\_[on]{}=I\\_o. ", "A related approximation for the sampling distribution of nearly neutral metacommunities is derived in Appendix A. In the absence of dispersal limitation, Eq.", " \\[PnvecNN\\] becomes \\_[m,m\\_o1]{}P\\^[[nn]{}\\*]{}\\_=()\\^[J\\_L]{}(wx)\\^n\\_[i=2]{}\\^Sx\\_i\\^[n\\_i]{}, where we have used $(a)_n\\sim a^n+{\\cal O}(a^{n-1})$ for large $a$. Finally, in the symmetric limit, Eq.", " \\[PnvecNNlimit\\] reduces to a simple multinomial sampling of the metacommunity, as expected.", "\n\nTo illustrate the impacts of an asymmetric species on the diversity of an otherwise symmetric local community, Fig.", " \\[div\\] plots Shannon’s Index of diversity H=--\\_[i=2]{}\\^S, for various values of the ecological fitness advantage, $w$, and dispersal ability, $m$, in a nearly neutral community of $S=5$ species and $J_L=75$ individuals. ", "All five species share a common relative metacommunity abundance, $x=x_i=0.2$, so given the exact result for ${\\rm E}[N^*]$ in Eq.", " \\[avgn\\], we know immediately that ${\\rm E}[N_i^*]=(J_L-{\\rm E}[N^*])/(S-1)$ for the remaining symmetric species. ", "Note that $H$ is maximized where all abundances are equivalent, such that ${\\rm E}[N^*]/J_L={\\rm E}[N_i^*]/J_L=x_i$. As can be seen from the next section, this relation holds in the neutral limit where $w=1$ and $m=m_o=0.1$, but small asymmetries in dispersal ability have a negligible impact on diversity when all species are symmetric in ecological fitness. ", "Therefore, each curve in Fig.", " \\[div\\] peaks near $w=1$ at approximately the same value of $H$. Away from $w=1$, the declines in diversity are regulated by mass-effects, with more gradual declines at higher values of $m$.\n\n{width=\"80.00000%\"}\n\nRecovering the sampling distribution of neutral theory {#sc2}\n======================================================\n\nIn a perfectly symmetric local community, the stochastic dynamics for each species differ solely due to variations in relative metacommunity abundances, the $x_i$. In particular, if $m_j=m$ and $w_j=1$ for all $j$ in Eq.", " \\[t\\], we recover the multivariate transition probabilities for a neutral sampling theory of local communities, as suggested on p. 287 of Hubbell’s book [@PHubbell:2001p4284]. ", "Similarly, in the symmetric limit of Eq.", " \\[margprocessasymm\\] where $m=m_o$ and $w=1$, we recover the marginal dynamics for neutral (n) local communities with stationary distribution [@McKane:2000p4318] P\\^[[n]{}\\*]{}\\_n=, where $I=m(J_L-1)/(1-m)$. This result follows from the symmetric limit of Eq.", " \\[PnNN\\] after applying the identity $\\Gamma(a)\\Gamma(1-a)=\\pi/\\sin(\\pi a)$. The expected abundance and variance are obtained from the symmetric limits of Eqs.", " \\[avgn\\] and \\[Var\\], respectively, after applying the identities in Eqs.", " C.1.0.1 and C.2.2.2 $$\\begin{aligned}\n{\\rm E}[N^*]&=& xJ_L, \\label{avgnNeutral} \\\\\n{\\rm Var}[N^*]&=&x(1-x)J_L \\frac{J_L+I}{1+I}. ", "\\label{VarNeutral}\\end{aligned}$$ Finally, the symmetric limits of Eqs.", " \\[gensampdistrib\\], \\[gensampdistribfs\\], and \\[PnvecNN\\] all yield the stationary sampling distribution for a neutral local community [@Etienne:2005p3829; @Etienne:2007p5640] P\\^[[n]{}\\*]{}\\_=\\_[i=1]{}\\^S(Ix\\_i)\\_[n\\_i]{}. ", "In the special case of complete neutrality, Eq.", " \\[PnecNeutral\\] is an exact result of the general model, Eq.", " \\[evolve1\\]. ", "This sampling distribution continues to hold when the assumptions of zero-sum dynamics and stationarity are relaxed [@Etienne:2007p5640; @Haegeman:2008p6364].", "\n\nDiscussion {#sc3}\n==========\n\nWe have developed a general sampling theory that extends Hubbell’s neutral theory of local communities and metacommunities to include asymmetries in ecological fitness and dispersal ability. ", "We anticipate that a parameterization of additional biological complexity, such as asymmetries in survivorship probabilities or differences between the establishment probabilities of local reproduction and immigration, may be incorporated without significant changes to the structure of our analytical results. ", "Although the machinery is significantly more complicated for asymmetric theories than their symmetric counterparts, some analytical calculations remain tractable. ", "We find approximate sampling distributions for general and nearly neutral communities that yield Hubbell’s theory in the symmetric limit. ", "Our fully normalized approximation in the nearly neutral case may provide a valuable statistical tool for determining the degree to which an observed SAD is consistent with the assumption of complete neutrality. ", "To facilitate a Bayesian analysis, we have enabled rapid computation of the required hypergeometric functions by deriving previously unknown asymptotic expansions.", "\n\nAcknowledgments {#ack .unnumbered}\n===============\n\nWe gratefully acknowledge the insights of two anonymous reviewers. ", "This work is partially supported by the James S. McDonnell Foundation through their Studying Complex Systems grant (220020138) to W.F.F. N.M.T. acknowledges financial support from Gobierno of Navarra, Res.", " $07/05/2008$ and Ministerio de Ciencia e Innovación, project MTM2009-11686.", "\n\naddtoreset[equation]{}[subsubsection]{}\n\nSampling asymmetric metacommunities {#othapp}\n===================================\n\nThe analytical insights of @Etienne:2007p5640 suggest a clear prescription for translating local community dynamics into metacommunities dynamics in the context of Hubbell’s unified neutral theory of biodiversity and biogeography [@PHubbell:2001p4284]: replace probabilities of immigration, $m_j$, with probabilities of speciation, $\\nu_j$; assume $x_j\\sim 1/S_T+{\\cal O}(1/S_T^2)$ for all $j$, where $S_T$ is the total number of species that could possibly appear through speciation events; and consider asymptotics as $S_T$ becomes large.", "\n\nFollowing this recipe, we translate the transition probabilities for asymmetric local communities, Eq.", " \\[t\\], into the transition probabilities for asymmetric metacommunities ($M$) T\\^M\\_[ij]{} = ((1-\\_j)+\\_j+[O]{}()), where $J_M$ is the number of individuals in the metacommunity, $w_j/\\sum_{k=1}^{S_T}w_k$ is the probability that an individual of species $j$ establishes following a speciation event, and \\_[ij]{}\\^M=(J\\_M-(n\\_i+1))(n\\_j-1). ", "Metacommunity dynamics are governed by the master equation =\\_[i=1]{}\\^[S\\_T]{}\\_[j=1,ji]{}\\^[S\\_T]{}(T\\^M\\_[ij+\\_i-\\_j]{}P\\^M\\_[+\\_i-\\_j]{}-T\\^M\\_[ji]{}P\\^M\\_ ) \\_[ij]{}\\^M. If $\\nu_j>0$ for all $j$, there are no absorbing states, so for large–$S_T$, there is a nonzero probability that any given species $j$ exists. ", "Analogous develops to those in Section \\[sc00\\] show that detailed balance in the general theory is approximated by P\\^[[g,M]{}\\*]{}\\_=Z\\_[g,M]{}\\^[-1]{}\\_[k=1]{}\\^[S\\_T]{}w\\_k\\^[n\\_k]{}(1-\\_k)\\^[n\\_k]{}(\\^[M]{}\\_[k]{})\\_[n\\_k]{}, where \\^[M]{}\\_[k]{}=\\_k, and $\\theta_k=\\nu_k(J_M-1)/(1-\\nu_k)$ is the generalization of Hubbell’s “fundamental biodiversity number\" [@PHubbell:2001p4284]. ", "The fitness-symmetric (s) distribution P\\^[[s,M]{}\\*]{}\\_=Z\\_[s,M]{}\\^[-1]{}\\_[k=1]{}\\^[S\\_T]{}(1-\\_k)\\^[n\\_k]{}(\\_k/S\\_T)\\_[n\\_k]{}, satisfies detailed balance up to ${\\cal O}(1/S_T)$.\n\nFor the special case of nearly neutral metacommunities, we translate the marginal dynamics for an asymmetric species in an otherwise symmetric local community into the marginal dynamics for an asymmetric species in an otherwise symmetric metacommunity. ", "The transition probabilities are g\\^M\\_[n]{}&=&((1-)++[O]{}()),\\\nr\\^M\\_[n]{} &=&((1-\\_o)+\\_o(1-)+[O]{}()),\\\nwhere the asymmetric focal species has speciation probability $\\nu$ and enjoys an ecological fitness advantage, $w$, over all other species, which share a common probability of speciation $\\nu_o$. If $n=0$ is an accessible state, then as $S_T$ becomes large and $w$ remains finite, the equilibrium probability of observing the asymmetric species approaches zero. ", "However, if we assume that the asymmetric species is identified and known to exist at nonzero abundance levels, the stationary distribution is P\\_n\\^[[nn]{},M\\*]{}=Z\\_M \\_M\\^n , with Z\\_M\\^[-1]{}= \\_2F\\_1(-J\\_M,\\_M;1-\\_M;\\_M)-1, and \\_M&=&w+[O]{}(),\\\n\\_M&=&+[O]{}(),\\\n\\_M&=& 1++[O]{}(). ", "where $\\theta=(J_M-1)\\nu/(1-\\nu)$ and $\\theta_o=(J_M-1)\\nu_o/(1-\\nu_o)$ are Hubbell’s “fundamental biodiversity numbers\" for the asymmetric species and all other species, respectively.", "\n\nAn approximate multivariate stationary distribution is obtained in an identical manner to the derivation of Eq.", " \\[PnvecNN\\] P\\^[[nn]{},M\\*]{}\\_&=&Z\\_M\\_M\\^n\\\n&&\\_[i=2]{}\\^[S\\_T]{}(\\_[n,M]{}/S\\_T)\\_[n\\_i]{}, where \\_[n,M]{}=\\_o(1+)+[O]{}().", "\n\nWe now propose a modest extension to the prescription in @Etienne:2007p5640 for converting multivariate distributions over labelled abundance vectors to distributions over unlabelled abundance vectors. ", "Because the asymmetric focal species has been identified and is known to exist with abundance $n>0$, this species must be labelled, while all other species are equivalent and may be unlabelled. ", "Therefore, we aim to transform Eq.", " \\[PnvecNNM\\] into a multivariate distribution over the “mostly unlabelled\" states $\\hat{\\vec{n}}=(n,\\hat{n}_2,\\dots,\\hat{n}_S)$, where $S$ is the number of species observed in a sample and each $(\\hat{n}_2,\\dots,\\hat{n}_S)$ is an integer partition of $J_M-n$. (To provide an example, if $J_M=3$, four distinct states are accessible: $(3)$ with $S=1$, $(2,1)$ with $S=2$, $(1,2)$ with $S=2$, and $(1,1,1)$ with $S=3$.) The conversion is given by P\\^[[nn]{},M\\*]{}\\_=P\\^[[nn]{},M\\*]{}\\_, where $\\hat{\\Phi}_i$ is the number of elements in $(\\hat{n}_2,\\dots,\\hat{n}_S)$ equal to $i$. Note that $\\hat{\\Phi}_0=S_T-1-(S-1)$. Taking the leading behavior for large–$S_T$, we obtain a modification of the @Ewens:1972p4815 sampling distribution appropriate to nearly neutral metacommunities -0.3cm\\_[S\\_T]{}P\\^[[nn]{},M\\*]{}\\_-0.3cm&=&-0.3cm\\_[S\\_T]{}\\\n&&\\\n&&\\_[i=2]{}\\^S\\\n\\\n&=&-0.3cm\\_[S\\_T]{}()\\^[S-1]{}\\\n&&\\_M\\^n(\\_M)\\_[-n]{}\\\n\\\n&=&-0.3cm\\_M\\_M\\^n(\\_M)\\_[-n]{},\\\nwhere $(a)_0=1$ allows us to take a product over the observed species, $S$, rather than the total number of possible species, $S_T$, in the first expression; $(z)_n/(n-1)!\\sim z+{\\cal O}(z^2)$ as $z$ approaches 0 for $n>0$ has been used to obtain the second expression; l’Hôpital’s rule along with $\\lim_{b\\to 0}\\partial {}_2F_1(a,b;c;z)/\\partial b=az{}_3F_2(a+1,1,1;c+1,2;z)/c$ has been used to obtain the third expression; and \\_M\\^[-1]{}=\\_3F\\_2(1-J\\_M,1,1;2-\\_M,2;\\_M), with asymptotics of the hypergeometric function provided in §\\[F21forF32\\] and §\\[F32case\\]. ", "In the neutral limit, we obtain a modification to the Ewens sampling distribution for the scenario where a single species is labelled and guaranteed to exist \\_[S\\_T]{}P\\^[[n]{},M\\*]{}\\_=(\\_[i=1]{}\\^[J\\_M]{}+)\\^[-1]{}. ", "Converting this result to a distribution over the “fully unlabelled\" states $\\hat{\\hat{\\vec{n}}}=\\left(\\hat{\\hat{n}}_1,\\dots,\\hat{\\hat{n}}_S\\right)$, we multiply by (\\_[i=1]{}\\^[J\\_M]{}+), and recover the Ewens sampling distribution [@Ewens:1972p4815], which is also the sampling distribution for Hubbell’s metacommunity theory [@PHubbell:2001p4284].", "\n\naddtoreset[equation]{}[subsubsection]{}\n\nMarginal dynamics for the local community {#app}\n=========================================\n\nWe first demonstrate that the marginal dynamics of the asymmetric species in Eq.", " \\[margprocessasymm\\] can be derived from the multivariate dynamics of Eq.", " \\[evolve1\\]. ", "Let \\^[J\\_L-n]{}\\_[n\\_2=0]{}\\^[J\\_L-n]{} …\\_[n\\_S=0]{}\\^[J\\_L-n]{}(J\\_L-n-n\\_2-…-n\\_S), so that the marginal distribution for the asymmetric species is given by P\\_n=\\^[J\\_L-n]{}P\\_. ", "Applying Eq.", " \\[defsumdeltaasymm\\] to both sides of Eq.", " \\[evolve1\\], we obtain &=&\\^[J\\_L-n]{}\\_[i=1]{}\\^S\\_[j=1,ji]{}\\^S(T\\_[ij+\\_i-\\_j]{}P\\_[+\\_i-\\_j]{}-T\\_[ji]{}P\\_ ) \\_[ij]{}\\\n&=&\\^[J\\_L-n]{}\\_[i=2]{}\\^S\\_[j=2,ji]{}\\^S(T\\_[ij+\\_i-\\_j]{}P\\_[+\\_i-\\_j]{}-T\\_[ji]{}P\\_ ) \\_[ij]{}\\\n&&+\\^[J\\_L-n]{}\\_[j=2]{}\\^S(T\\_[1j+\\_1-\\_j]{}P\\_[+\\_1-\\_j]{}-T\\_[j1]{}P\\_ ) \\_[1j]{}\\\n&&+\\^[J\\_L-n]{}\\_[i=2]{}\\^S(T\\_[i1+\\_i-\\_1]{}P\\_[+\\_i-\\_1]{}-T\\_[1i]{}P\\_ ) \\_[i1]{}. ", "By inspection, the first term is identically zero and the remaining terms generate the right-hand side of Eq.", " \\[margprocessasymm\\], namely \\^[J\\_L-n]{}\\_[j=2]{}\\^S T\\_[1j+\\_1-\\_j]{}P\\_[+\\_1-\\_j]{}\\_[1j]{} &=& r\\_[n+1]{}(J\\_L-(n+1))P\\_[n+1]{},\\\n\\^[J\\_L-n]{}\\_[j=2]{}\\^S T\\_[j1]{}P\\_ \\_[1j]{} &=& g\\_n(J\\_L-(n+1))P\\_n,\\\n\\^[J\\_L-n]{}\\_[i=2]{}\\^S T\\_[i1+\\_i-\\_1]{}P\\_[+\\_i-\\_1]{} \\_[i1]{}&=& g\\_[n-1]{}(n-1)P\\_[n-1]{},\\\n\\^[J\\_L-n]{}\\_[i=2]{}\\^S T\\_[1i]{}P\\_ \\_[i1]{}&=&r\\_n(n-1)P\\_n. ", "To provide an illustration, let $J_L=4$, $S=3$, and $n=1$. Then, &&\\^[J\\_L-n]{}\\_[j=2,ji]{}\\^ST\\_[1j+\\_1-\\_j]{}P\\_[+\\_1-\\_j]{}\\_[1j]{}\\\n&=&(P\\_[(2,0,2)]{}(T\\_[12(2,0,2)]{}+T\\_[13(2,0,2)]{})+P\\_[(2,1,1)]{}(T\\_[12(2,1,1)]{}+T\\_[13(2,1,1)]{}).\\\n&&.+P\\_[(2,2,0)]{}(T\\_[12(2,2,0)]{}+T\\_[13(2,2,0)]{}))(J\\_L-(n+1))\\\n&=&r\\_[n+1]{}(J\\_L-(n+1))(P\\_[(2,0,2)]{}+P\\_[(2,1,1)]{}+P\\_[(2,2,0)]{})\\\n&=&r\\_[n+1]{}(J\\_L-(n+1))P\\_[n+1]{}, where we have used the definitions of $\\Theta_{ij}$ from Eq.", " \\[Theta\\], $r_n$ from Eq.", " \\[dn\\], and $P_n$ from Eq.", " \\[pnexampleasymm\\].", "\n\nWe construct an approximation to the multivariate sampling distribution of a nearly neutral community, $P^{{\\rm nn}*}_{\\vec{n}}$, by following the subsample approach of @Etienne:2005p3829 and @Etienne:2007p5640 that centers on the identity. ", "P\\^[[nn]{}\\*]{}\\_=P\\_n\\^[[nn]{}\\*]{}\\_[f=2]{}\\^[S-1]{}P\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}\\^[[nn]{}\\*]{}. ", "Assuming that $P_n$, $P_{n_2|n}$, $\\dots$, $P_{n_{f-1}|n,n_2,\\dots,n_{f-2}}$ are nonzero and stationary, we argue that conditional marginal dynamics for $P_{n_f|n,n_2,\\dots,n_{f-1}}$ are approximated by the master equation &=&g\\_[n\\_f-1|n,n\\_2,…,n\\_[f-1]{}]{}(n\\_f-1)P\\_[n\\_f-1|n,n\\_2,…,n\\_[f-1]{}]{}\\\n&&+r\\_[n\\_f+1|n,n\\_2,…,n\\_[f-1]{}]{}(J\\_L-(n\\_f+1))P\\_[n\\_f+1|n,n\\_2,…,n\\_[f-1]{}]{}\\\n&&-(g\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}(J\\_L-(n\\_f+1)) .\\\n&&0.26cm .+r\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}(n\\_f-1))P\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}, where g\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}-0.3cm&&-0.3cm\\_[i=f+1]{}\\^S T\\_[if(n,n\\_2,…,n\\_f,…,n\\_S)]{}\\\n&=&-0.3cm((1-m\\_o)+m\\_o)-0.1cm,\\\nr\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}-0.3cm&&-0.3cm\\_[i=f+1]{}\\^S T\\_[fi(n,n\\_2,…,n\\_f,…,n\\_S)]{}\\\n&=&-0.3cm((1-m\\_o)+m\\_o)-0.1cm,\\\nand \\_f&=&n+\\_[k=2]{}\\^fn\\_k,\\\n\\_f&=&x+\\_[k=2]{}\\^fx\\_k. ", "Eq.", " \\[margprocesssymm\\] can be derived from the multivariate dynamics of Eq.", " \\[evolve1\\] under the approximation that stochastic variables $(N(\\tau),\\allowbreak N_2(\\tau),\\allowbreak \\dots,\\allowbreak N_{f-1}(\\tau))=(n,\\allowbreak n_2,\\allowbreak \\dots,\\allowbreak n_{f-1})$ are fixed in time such that $T_{ij\\vec{n}}=0$ for $i,j<f$. In this scenario, the summations on the right-hand side of Eq.", " \\[evolve1\\] may begin at $f$ =\\_[i=f]{}\\^S\\_[j=f,ji]{}\\^S(T\\_[ij+\\_i-\\_j]{}P\\_[+\\_i-\\_j]{}-T\\_[ji]{}P\\_ ) \\_[ij]{}. ", "Given the identity P\\_=P\\_n P\\_[n\\_2|n]{} P\\_[n\\_[f-1]{}|n,n\\_2,…,n\\_[f-2]{}]{} P\\_[n\\_f,…,n\\_S|n,n\\_2,…,n\\_[f-1]{}]{}, the stationary factor $P_n P_{n_2|n} \\cdots P_{n_{f-1}|n,n_2,\\dots,n_{f-2}} $ cancels from both sides of Eq.", " \\[evolve1f\\] to yield &&\\\n&=&\\_[i=f]{}\\^S\\_[j=f,ji]{}\\^S(T\\_[ij+\\_i-\\_j]{}P\\_[\\_f+\\_[fi]{}-\\_[fj]{}|n,n\\_2,…,n\\_[f-1]{}]{}-T\\_[ji]{}P\\_[\\_f|n,n\\_2,…,n\\_[f-1]{}]{} ) \\_[ij]{},\\\nwhere $\\vec{n}_f\\equiv(n_f,\\dots,n_S)$ and $e_{fi}$ is an $(S-f+1)$–dimensional unit vector along the $i$th–direction. ", "Now let \\^[J\\_L--n\\_f]{}\\_[n\\_[f+1]{}=0]{}\\^[J\\_L-n-n\\_2--n\\_f]{} …\\_[n\\_S=0]{}\\^[J\\_L-n-n\\_2--n\\_f]{}(J\\_L-n-n\\_2-…-n\\_S), so that P\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}=\\^[J\\_L--n\\_f]{}P\\_[\\_f|n,n\\_2,…,n\\_[f-1]{}]{}. ", "Applying Eq.", " \\[defsumdeltasymm\\] to both sides of Eq.", " \\[evolve1ff\\], we obtain &&\\\n&=&\\^[J\\_L--n\\_f]{}\\_[i=f+1]{}\\^S\\_[j=f+1,ji]{}\\^S(T\\_[ij+\\_i-\\_j]{}P\\_[\\_f+\\_[fi]{}-\\_[fj]{}|n,n\\_2,…,n\\_[f-1]{}]{}.\\\n&&.-T\\_[ji]{}P\\_[\\_f|n,n\\_2,…,n\\_[f-1]{}]{} ) \\_[ij]{}\\\n&&+\\^[J\\_L--n\\_f]{}\\_[j=f+1]{}\\^S(T\\_[fj+\\_f-\\_j]{}P\\_[\\_f+\\_[ff]{}-\\_[fj]{}|n,n\\_2,…,n\\_[f-1]{}]{}.\\\n&&.-T\\_[jf]{}P\\_[\\_f|n,n\\_2,…,n\\_[f-1]{}]{} ) \\_[fj]{}\\\n&&+\\^[J\\_L--n\\_f]{}\\_[i=f+1]{}\\^S (T\\_[if+\\_i-\\_f]{}P\\_[\\_f+\\_[fi]{}-\\_[ff]{}|n,n\\_2,…,n\\_[f-1]{}]{}.\\\n&&.-T\\_[fi]{}P\\_[\\_f|n,n\\_2,…,n\\_[f-1]{}]{} ) \\_[if]{}.\\\nBy inspection, the first term is identically zero and the remaining terms generate the right-hand side of Eq.", " \\[margprocesssymm\\], namely &&\\^[J\\_L--n\\_f]{}\\_[j=f+1]{}\\^S T\\_[fj+\\_f-\\_j]{}P\\_[\\_f+\\_[ff]{}-\\_[fj]{}|n,n\\_2,…,n\\_[f-1]{}]{} \\_[fj]{}\\\n&&=r\\_[n\\_f+1|n,n\\_2,…,n\\_[f-1]{}]{}(J\\_L-(n\\_f+1))P\\_[n\\_f+1|n,n\\_2,…,n\\_[f-1]{}]{},\\\n&&\\^[J\\_L--n\\_f]{}\\_[j=f+1]{}\\^S T\\_[jf]{}P\\_[\\_f|n,n\\_2,…,n\\_[f-1]{}]{} \\_[fj]{}\\\n&&= g\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}(J\\_L-(n\\_f+1))P\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{},\\\n&&\\^[J\\_L--n\\_f]{}\\_[i=f+1]{}\\^S T\\_[if+\\_i-\\_f]{}P\\_[\\_f+\\_[fi]{}-\\_[ff]{}|n,n\\_2,…,n\\_[f-1]{}]{} \\_[if]{}\\\n&&= g\\_[n\\_f-1|n,n\\_2,…,n\\_[f-1]{}]{}(n\\_f-1)P\\_[n\\_f-1|n,n\\_2,…,n\\_[f-1]{}]{},\\\n&&\\^[J\\_L--n\\_f]{}\\_[i=f+1]{}\\^S T\\_[fi]{}P\\_[\\_f|n,n\\_2,…,n\\_[f-1]{}]{} \\_[if]{}\\\n&&= r\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}(n\\_f-1)P\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}. ", "The stationary distribution of Eq.", " \\[margprocesssymm\\] is a Pólya distribution [@Johnson:1992tUDD] &P\\_[n\\_f|n,n\\_2,…,n\\_[f-1]{}]{}\\^[[nn]{}\\*]{}&\\\n&=&-1.2cm N\\_[Pf]{} ,\\\nwhere N\\_[Pf]{}\\^[-1]{}= , and \\_[on]{}=I\\_o. ", "Plugging Eqs.", " \\[PnNN\\] and \\[Pnf\\] into \\[PnvecNNAppB\\], we obtain the approximate sampling distribution of Eq.", " \\[PnvecNN\\]. ", "To validate Eq.", " \\[PnvecNN\\], we demonstrate approximate detailed balance, as defined by Eq.", " \\[detailedbalance\\], for large–$J_L$ nearly neutral communities where $S,w-1<<\\sum_{l=1}^Sw_ln_l-1=J_L-1+n(w-1)$ such that $\\epsilon\\equiv (w-1)/(J_L-1+n(w-1))$ is a small number. ", "For $i,j\\ge 2$, detailed balance is exact. ", "But for $i=1$ and $j\\ge 2$, we have &=&\\\n&&\\_[k=2]{}\\^S, where \\_[n]{}=I. Given $(a(1+\\epsilon))_n\\sim(a)_n+{\\cal O}(\\epsilon)$, we find =+[O]{}(S). ", "The case of $i\\ge 2$ and $j=1$ is similar.", "\n\naddtoreset[equation]{}[subsubsection]{}\n\nAsymptotic Expansions for Hypergeometric Functions {#app}\n==================================================\n\nCalculating Eqs.", " \\[PnNN\\], \\[avgn\\], \\[avgn2\\], \\[PnvecNN\\], \\[PnNNM\\], \\[PnvecNNM\\], and \\[PnhatvecMlimit\\] for large communities requires computationally intensive evaluations of hypergeometric functions. ", "To address this problem, one of us (N.M.T.) developed previously unknown asymptotic expansions. ", "All required expansions are summarized here. ", "Relevant details can be found in [@Abra65; @Luke:1969:SFA; @Wong:2001:AAI; @Gil:2007:NSF].", "\n\nExpanding ${}_3F_2(1-J_L,1+\\lambda,2;2-\\xi,1;\\eta)$ {#otherform}\n---------------------------------------------------\n\nUsing the reduction formula $$\\label{oth1}\n{}_3F_2(a,b,2;c,1;z)=\\frac{abz}{c}{}_2F_1(a+1,b+1;c+1;z)+{}_2F_1(a,b;c;z),$$ this case can be expanded with the methods of §\\[secondsec\\].", "\n\nExpanding ${}_2F_1(\\alpha-J_L,\\alpha+\\lambda;\\alpha+1-\\xi;\\eta)$ {#secondsec}\n----------------------------------------------------------------\n\n### Notation {#not}\n\nWe write $$\\label{n_1}\na=\\alpha-J_L,\\quad b=\\alpha+\\beta+\\mu J_L,\\quad c=\\alpha+\\gamma+\\rho J_L,$$ with $\\alpha=0,1,2$ and $J_L$ a positive integer. ", "In terms of $w$, $m$, $x$, and $m_o$ we have $$\\label{n_2}\n\\beta=-\\frac{mx}{1-m+x(w-1)},\\quad\\mu=-\\beta,$$ and $$\\label{n_3}\n\\gamma=\\frac{1-xwm_o+x(w-1)}{1-wm_o+x(w-1)},\\quad \\rho =-\\gamma.$$ The asymptotic behaviour will be considered of the Gauss hypergeometric function $$\\label{n_4}\nF={}_2F_1(a,b;c;\\eta),$$ for large–$J_L$, where $$\\label{n_5}\n\\eta=w\\frac{1-m+x(w-1)}{1-wm_o+x(w-1)},$$ and $$\\label{n_6}\nw\\in(0,\\infty),\\quad x,m,m_o\\in(0,1).$$\n\n### The neutral case: $w=1,$ $m=m_o$ {#r1}\n\nIn this case $$\\label{r_}\n\\eta=1,\\quad \\mu=\\frac{mx}{1-m},\\quad \\rho=-\\frac{1-mx}{1-m}.$$ The exact relation $$\\label{r1_2}\n{}_2F_1(-n,b;c;1)=\\frac{(c-b)_n}{(c)_n}=\\frac{\\Gamma(c)\\Gamma(c-b+n)}{\\Gamma(c+n)\\Gamma(c-b)},\\quad n=0,1,2,\\ldots,$$ can be used, together with the asymptotic estimate of the ratio of gamma functions $$\\label{r1_3}\n\\frac{\\Gamma(x+n)}{\\Gamma(y+n)}=n^{x-y}\\left(1+\\bigO(1/n)\\right),\\quad n\\to\\infty.$$\n\n### Critical values {#crit}\n\nConsidered as functions of $w$, $\\mu$ and $\\rho$ become unbounded at $w=w_{c_\\mu}$ and $w=w_{c_\\rho}$, respectively, where $$\\label{cv1}\nw_{c_\\mu}=\\frac{m+x-1}{x},\\quad w_{c_\\rho}=\\frac{1-x}{m_o-x}.$$\n\n### The case $w\\to w_{c_\\mu}$ {#rcmu .unnumbered}\n\nIn this case $\\eta$ becomes small, $b$ becomes unbounded, but the product $b\\eta$ remains finite. ", "The $k$th term of the standard power series of $F$ becomes (see also ) $$\\label{cv2}\n\\frac{(a)_k(b)_k}{k! (", "c)_k}\\eta^k\\sim\n\\frac{(a)_k}{k! (", "c_0)_k}z^k,$$ with $$\\label{cv3}\nz=\\lim_{w\\to w_{c_\\mu}} b\\eta=u+vJ_L,\\quad c_0=\\lim_{w\\to w_{c_\\mu}}c=\\gamma_0+\\rho_0J_L,$$ where $$\\label{cv4}\nu=-\\frac{mx(m+x-1)}{mx-m_o(m+x-1)},\\quad v=-u,$$ and $$\\label{cv5}\n\\gamma_0=\\frac{x(m(1-m_o)+m_o(1-x))}{mx-m_o(m+x-1)},\\quad\n\\rho_0=-\\gamma_0.$$ It follows that $F$ approaches a confluent hypergeometric function: $$\\label{cv6}\n{}_2F_1(a,b;c;\\eta)\\to{}_1F_1(a;c_0;z).$$ Further action is needed to obtain an asymptotic approximation of the ${}_1F_1$–function.", "\n\n### The case $w\\to w_{c_\\rho}$ {#rcnu .unnumbered}\n\nIn this case $\\eta$ and $c$ become unbounded, but the ratio $\\eta/c$ remains finite. ", "The $k$th term of the standard power series of $F$ becomes $$\\label{cv7}\n\\frac{(a)_k(b)_k}{k! (", "c)_k}\\eta^k\\sim\n\\frac{(a)_k(b_0)_k}{k!\\,z^k},$$ with $$\\label{cv8}\nz=\\lim_{w\\to w_{c_\\rho}} c/\\eta=u+vJ_L,\\quad b_0=\\lim_{w\\to w_{c_\\rho}}b=\\beta_0+\\mu_0J_L,$$ where $$\\label{cv9}\nu=\\frac{m_o(m_o-x)(1-x)}{mx-m_o(m+x-1)},\\quad v=-u,$$ and $$\\label{cv10}\n\\beta_0=-\\frac{mx(m_o-x)}{mx-m_o(m+x-1)},\\quad\n\\mu_0=-\\beta_0.$$ It follows that $F$ approaches a ${}_2F_0$ hypergeometric function $$\\label{cv11}\n{}_2F_1(a,b;c;\\eta)\\to{}_2F_0(a,b_0;-;1/z)=\\sum_{k=0}^{-a}\\frac{(a)_k(b_0)_k}{k! ", "\\,z^k},$$ because $a$ is a negative integer. ", "This function can be expressed in terms of the Kummer $U$–function $$\\label{cv12}\n{}_2F_0(a,b_0;-;1/z)=(-z)^aU(a,1+a-b_0,-z).$$ Further action is needed to obtain an asymptotic approximation of the $U$–function.", "\n\n### Expansion A {#simpsad}\n\nAn integral representation is $$\\label{ss1}\n{}_2F_1(a,b;c;\\eta)=\\frac{\\Gamma(c)}{\\Gamma(b)\\Gamma(c-b)}\\int_0^1t^{b-1}(1-t)^{c-b-1}(1-t\\eta)^{-a}\\,dt,$$ valid for $c> b>0, \\eta<1$. This integral can be used when $\\rho>\\mu>0, \\eta<1$.\n\nAs an example, consider $$\\label{ss3}\nr=3, \\quad m=\\tfrac12, \\quad m_o=\\tfrac12, \\quad x=\\tfrac13.$$ This gives $$\\label{ss4}\nb=\\alpha+\\tfrac1{11}(J_L-1), \\quad c=\\alpha+5(J_L-1), \\quad \\mu=\\tfrac1{11},\\quad \\rho= 5,\\quad \\eta=-11.$$\n\nIn this case the integrand becomes small at $t=0$ and $t=1$, and there is a maximum of the integrand at $t=t_1$, with $t_1\\in(0,1)$. This point gives the main contribution.", "\n\nWrite as $$\\label{ss5}\n{}_2F_1(a,b;c;\\eta)=\\frac{\\Gamma(c)}{\\Gamma(b)\\Gamma(c-b)}\n\\int_0^1t^{\\alpha+\\beta-1}(1-t)^{\\gamma-\\beta-1}(1-t\\eta)^{-\\alpha}e^{-J_L\\phi(t)}\\,dt,$$ where $$\\label{ss6}\n\\phi(t)=-\\mu\\ln(t)-(\\rho-\\mu)\\ln(1-t)-\\ln(1-t\\eta).$$ The saddle points $t_0$ and $t_1$ are the zeros of $\\phi^\\prime(t)$. For the example this gives $$\\label{ss7}\nt_0=-0.01169\\cdots,\\quad t_1 =0.1178\\cdots,$$ and $$\\label{ss8}\n\\phi(t_1) =-0.02136\\cdots, \\quad \\phi^{\\prime\\prime}(t_1)=35.83\\cdots\\,.$$\n\nAn asymptotic approximation follows from the substitution $$\\label{ss9}\n\\phi(t)-\\phi(t_1) =\\tfrac12\\phi^{\\prime\\prime}(t_1)s^2,\\quad \\sign(t-t_1)=\\sign(s),$$ which gives $$\\label{ss10}\n{}_2F_1(a,b;c;\\eta)=\\frac{\\Gamma(c)}{\\Gamma(b)\\Gamma(c-b)}\ne^{-J_L\\phi(t_1)}\\int_{-\\infty}^\\infty f(s) e^{-\\tfrac12J_L\\phi^{\\prime\\prime}(t_1)s^2}\\,ds,$$ where $$\\label{ss11}\nf(s)=t^{\\alpha+\\beta-1}(1-t)^{\\gamma-\\beta-1}(1-t\\eta)^{-\\alpha}\\frac{dt}{ds}.$$ Because locally at $t=t_1$ (or $s=0$), $t=t_1+s+\\bigO(s^2)$, we have $dt/ds=1$ at $s=0$, and $$\\label{ss12}\nf(0)=t_1^{\\alpha+\\beta-1}(1-t_1)^{\\gamma-\\beta-1}(1-t_1\\eta)^{-\\alpha}.$$ This gives the first order approximation $$\\label{ss13}\n{}_2F_1(a,b;c;\\eta)\\sim\\frac{\\Gamma(c)}{\\Gamma(b)\\Gamma(c-b)}\ne^{-J_L\\phi(t_1)}f(0)\\int_{-\\infty}^\\infty e^{-\\tfrac12J_L\\phi^{\\prime\\prime}(t_1)s^2}\\,ds,$$ that is $$\\label{ss14}\n{}_2F_1(a,b;c;\\eta)\\sim\\frac{\\Gamma(c)}{\\Gamma(b)\\Gamma(c-b)}\ne^{-J_L\\phi(t_1)}f(0)\\sqrt{\\frac{2\\pi}{J_L\\phi^{\\prime\\prime}(t_1)}},\\quad J_L\\to\\infty.$$\n\n### Expansion B {#othsad}\n\nAnother integral representation is $$\\label{os1}\n{}_2F_1(a,b;c;\\eta)=\\frac{\\Gamma(1+b-c)}{\\Gamma(b)\\Gamma(1-c)}\\int_0^{\\infty}t^{b-1}(t+1)^{c-b-1}(1+t\\eta)^{-a}\\,dt,$$ which is only valid for $a=0,-1,-2,\\ldots$ and $c<a+1$. It can be verified by expanding $(1+t\\eta)^{-a}$ in powers of $\\eta$.\n\nWe have $\\mu>0$ and $\\rho<-1$, and because (see , and ) $$\\label{os2}\n\\eta=-\\frac{mx}{(1-m_ox)}\\,\\frac{\\rho}{\\mu},$$ we see that $\\eta\\ge0$.\n\nAs an example, consider $$\\label{os3}\nr=\\tfrac13, \\quad m=\\tfrac12, \\quad m_o=\\tfrac12, \\quad x=\\tfrac13.$$ This gives $$\\label{os4}\nb=\\alpha+3(J_L-1), \\quad c=\\alpha+\\tfrac{15}{13}(1-J_L), \\quad \\mu=3,\\quad \\rho= -\\tfrac{15}{13},\\quad \\eta=\\tfrac{1}{13}.$$\n\nWrite as $$\\label{os5}\n{}_2F_1(a,b;c;\\eta)=\\frac{\\Gamma(1+b-c)}{\\Gamma(b)\\Gamma(1-c)}\\int_0^{\\infty}\nt^{\\alpha+\\beta-1}(t+1)^{\\gamma-\\beta-1}(1+t\\eta)^{-\\alpha}e^{-J_L\\psi(t)}\\,dt,$$ where $$\\label{os6}\n\\psi(t)=-\\mu\\ln(t)-(\\rho-\\mu)\\ln(t+1)-\\ln(1+t\\eta).$$ The saddle points $t_0$ and $t_1$ are for the example $$\\label{os7}\nt_0=-74.89\\cdots,\\quad t_1 =3.385\\cdots,$$ and $$\\label{os8}\n\\psi(t_1) =2.251\\cdots, \\quad \\psi^{\\prime\\prime}(t_1)=0.04951\\cdots\\,.$$\n\nAn asymptotic approximation follows from the substitution $$\\label{os9}\n\\psi(t)-\\psi(t_1) =\\tfrac12\\psi^{\\prime\\prime}(t_1)s^2,\\quad \\sign(t-t_1)=\\sign(s),$$ which gives $$\\label{os10}\n{}_2F_1(a,b;c;\\eta)=\\frac{\\Gamma(1+b-c)}{\\Gamma(b)\\Gamma(1-c)}\ne^{-J_L\\psi(t_1)}\\int_{-\\infty}^\\infty g(s) e^{-\\tfrac12J_L\\psi^{\\prime\\prime}(t_1)s^2}\\,ds,$$ where $$\\label{os11}\ng(s)=t^{\\alpha+\\beta-1}(1+t)^{\\gamma-\\beta-1}(1+t\\eta)^{-\\alpha}\\frac{dt}{ds}.$$ Because locally at $t=t_1$ (or $s=0$), $t=t_1+s+\\bigO(s^2)$, we have $dt/ds=1$ at $s=0$, and $$\\label{os12}\ng(0)=t_1^{\\alpha+\\beta-1}(1+t_1)^{\\gamma-\\beta-1}(1+t_1\\eta)^{-\\alpha}.$$ This gives the first order approximation $$\\label{os13}\n{}_2F_1(a,b;c;\\eta)\\sim\\frac{\\Gamma(1+b-c)}{\\Gamma(b)\\Gamma(1-c)}\ne^{-J_L\\psi(t_1)}g(0)\\int_{-\\infty}^\\infty e^{-\\tfrac12J_L\\psi^{\\prime\\prime}(t_1)s^2}\\,ds,$$ that is $$\\label{os14}\n{}_2F_1(a,b;c;\\eta)\\sim\\frac{\\Gamma(1+b-c)}{\\Gamma(b)\\Gamma(1-c)}\ne^{-J_L\\psi(t_1)}g(0)\\sqrt{\\frac{2\\pi}{J_L\\psi^{\\prime\\prime}(t_1)}},\\quad J_L\\to\\infty.$$\n\n### Expansion C {#finalsad}\n\nIf $\\mu<\\rho<-1$ and $\\eta<0$, apply the transformation $$\\label{rem2}\n{}_2F_1(a,b;c;\\eta)=(1-\\eta^\\prime)^a{}_2F_1(a,b^\\prime;c;\\eta^\\prime),$$ where $$\\label{rem3}\nb^{\\prime}=c-b=\\beta^\\prime+\\mu^\\prime J_L,\\quad \\beta^\\prime=\\gamma-\\beta,\\quad \\mu^\\prime=\\rho-\\mu, \\quad \\eta^\\prime=\\frac{\\eta}{\\eta-1}.$$ Now, $$\\label{rem4}\n\\mu^\\prime>0,\\quad \\rho<-1,\\quad \\eta^\\prime>0,$$ and it follows that Expansion B, §\\[othsad\\], applies to the Gauss function on the right-hand side of .", "\n\n### General cases for all non-critical values {#remaining}\n\n1. ", " $w_{c_\\mu},w_{c_\\rho}<0$ For all $w>0$, we have $\\mu>0$, $\\rho<-1$, and $\\eta>0$, so use Expansion B, §\\[othsad\\].", "\n\n2. ", " $w_{c_\\mu}>0$, $w_{c_\\rho}<0$ For all $w_{c_\\mu}>w>0$, we have $\\mu<-1$, $\\rho<-1$, and $\\eta<0$, so use Expansion C, §\\[finalsad\\]. ", "For all $w>w_{c_\\mu}$, we have $\\mu>0$, $\\rho<-1$, and $\\eta>0$, so use Expansion B, §\\[othsad\\].", "\n\n3. ", " $w_{c_\\mu}<0$, $w_{c_\\rho}>0$ For all $w_{c_\\rho}>w>0$, we have $\\mu>0$, $\\rho<-1$, and $\\eta>0$, so use Expansion B, §\\[othsad\\]. ", "For all $w>w_{c_\\rho}$, we have $\\rho>\\mu>0$ and $\\eta<0$, so use Expansion A, §\\[simpsad\\].", "\n\n4. ", " $w_{c_\\rho}>w_{c_\\mu}>0$ For all $w_{c_\\mu}>w>0$, we have $\\mu<-1$, $\\rho<-1$, and $\\eta<0$, so use Expansion C, §\\[finalsad\\]. ", "For all $w_{c_\\rho}>w>w_{c_\\mu}$, we have $\\mu>0$, $\\rho<-1$, and $\\eta>0$, so use Expansion B, §\\[simpsad\\]. ", "For all $w>w_{c_\\rho}$, we have $\\rho>\\mu>0$ and $\\eta<0$, so use Expansion A, §\\[simpsad\\].", "\n\nExpanding ${}_2F_1(1-J_M,1;2-\\xi_M;\\eta_M)$ {#F21forF32}\n-------------------------------------------\n\n### Notation {#notation}\n\nWe write $$\\label{othf1}\na=1-J_M,\\quad b=1, \\quad c=\\sigma+\\tau J_M,$$ with $$\\label{othf2}\n\\sigma=1+\\frac{1}{1-w\\nu_o},\\quad \\tau=-\\frac{1}{1-w\\nu_o}.$$ The asymptotic behaviour will be considered of the Gauss hypergeometric function $$\\label{othf3M}\nF={}_2F_1(a,b;c;\\eta_M)$$ for large–$J_M$, where $$\\label{othf4M}\n\\eta_M=\\frac{ w(1-\\nu)}{1 -w\\nu_o},$$ and $$\\label{othf5}\nw\\in(0,\\infty),\\quad \\nu,\\nu_o\\in(0,1).$$\n\n### The neutral case: $w=1$, $\\nu=\\nu_o$ {#othr1}\n\nIn this case $\\eta_M=1$ and can be used to get an exact result in terms of gamma functions.", "\n\n### The critical case $w_{c_{\\nu_o}}=1/\\nu_o$ {#othcrit}\n\nIn this case we have (see also §\\[rcnu\\]) $$\\label{othf6}\n{}_2F_1(a,b;c;\\eta_M)\\to{}_2F_0(a,b;-;1/z)=(-z)^aU(a,1+a-b,-z),$$ where $$\\label{othf7}\nz=-\\frac{(J_M-1)\\nu_o}{1-\\nu}.$$\n\n### The case $0<w<w_{c_{\\nu_o}}$ {#othgenrsmall}\n\nUse the integral representation $$\\label{othf11}\n{}_2F_1(a,b;c;\\eta_M)=\\frac{\\Gamma(1+b-c)}{\\Gamma(b)\\Gamma(1-c)}\\int_0^{\\infty}\nt^{b-1}f(t)e^{-J_M\\phi(t)}\\,dt,$$ where $$\\label{othf12}\nf(t)=(1+t)^{\\sigma-b-1}(1+\\eta_M t)^{-1},\\quad \\phi(t)=-\\tau\\ln(1+t)-\\ln(1+\\eta_M t).$$ The saddle point $t_0$ follows from solving $\\phi^\\prime(t)=0$. This gives $$\\label{othf13}\n\\phi^\\prime(t)=-\\frac{\\tau}{1+t}-\\frac{\\eta_M}{1+\\eta_M t}, \\quad t_0=-\\frac{\\tau+\\eta_M}{\\eta_M(\\tau+1)}.$$ In terms of $w$ and $\\nu$ $$\\label{othf14}\nt_0=-\\frac{(1-w\\nu_o)(1-w+w\\nu)}{\\nu_o(1-\\nu)w^2}.$$\n\n1. ", " If $0<w<1/(1-\\nu)\\equiv w_{c_\\nu}$, then the saddle point is negative, and we can substitute $s=\\phi(t)$, giving $$\\label{othf15}\n {}_2F_1(a,b;c;\\eta_M)=\\frac{\\Gamma(1+b-c)}{\\Gamma(b)\\Gamma(1-c)}\\int_0^{\\infty}\n s^{b-1}g(s) e^{-J_Ms}\\,ds,$$ where $$\\label{othf16}\n g(s)=f(t)\\left(\\frac{t}{s}\\right)^{b-1}\\,\\frac{dt}{ds}=\\left(\\frac{t}{s}\\right)^{b-1}\\,\\frac{f(t)}{\\phi^\\prime(t)}.$$ Apply Watson’s lemma by expanding $g(s)=\\sum_{k=0}^\\infty g_ks^k$ to obtain $$\\label{othf17}\n {}_2F_1(a,b;c;\\eta_M)\\sim\\frac{\\Gamma(1+b-c)}{\\Gamma(b)\\Gamma(1-c)}\\sum_{k=0}^\\infty \\frac{\\Gamma(b+k)\\,g_k}{J_M^{b+k}}.$$ To compute the coefficients $g_k$ we first expand $t=\\sum_{k=1}^\\infty t_ks^k$. The coefficients $t_k$ follow from inverting the expansion $$\\label{othf18}\n s=-\\tau\\ln(1+t)-\\ln(1+\\eta_M t)=\\sum_{k=1}^\\infty s_kt^k,\\quad s_1=-\\tau-\\eta_M.$$ This gives $$\\label{othf19}\n t_1=-\\frac{1}{\\tau+\\eta_M}=\\frac{1-w\\nu_o}{1-w+w\\nu},$$ and for the first coefficient in the expansion $g_0=g(0)=t_1^b$. This gives $$\\label{othf20}\n {}_2F_1(a,b;c;\\eta_M)\\sim\\frac{\\Gamma(1+b-c)}{\\Gamma(1-c)}\\left(\\frac{t_1}{J_M}\\right)^{b}.$$\n\n2. ", " If $w>w_{c_\\nu}$, then $t_0$ is positive, and Laplace’s method can be used, as in §§\\[simpsad\\], \\[othsad\\]. ", "We substitute $$\\label{othf21}\n \\tfrac12\\phi^{\\prime\\prime}(t_0)s^2=\\phi(t)-\\phi(t_0),\\quad \\phi^{\\prime\\prime}(t_0)=\\frac{\\eta_M^2(\\tau+1)^3}{\\tau(\\eta_M-1)^2},$$ and obtain $$\\label{othf22}\n {}_2F_1(a,b;c;\\eta_M)\\sim\\frac{\\Gamma(1+b-c)}{\\Gamma(b)\\Gamma(1-c)}\\sqrt{\\frac{2\\pi}{J_M\\phi^{\\prime\\prime}(t_0)}}e^{-J_M\\phi(t_0)}t_0^{b-1}f(t_0),$$ where $t_0$ is given in .", "\n\n3. ", " If $w=w_{c_\\nu}$, then $t_0=0$ and Laplace’s method on a half-infinite interval can be used.", "\n\n### The case $w>w_{c_{\\nu_o}}$ {#othgenrlarge}\n\nUse the integral representation $$\\label{othf23}\n{}_2F_1(a,b;c;\\eta_M)=\\frac{\\Gamma(c)}{\\Gamma(b)\\Gamma(c-b)}\\int_0^1f(t)e^{-J_M\\phi(t)}\\,dt,$$ where $$\\label{othf24}\nf(t)=t^{b-1}(1-t)^{\\sigma-b-1}(1-\\eta_M t)^{-1},\\quad \\phi(t)=-\\tau\\ln(1-t)-\\ln(1-\\eta_M t).$$ The saddle point $t_0$ follows from solving $\\phi^\\prime(t)=0$. This gives $$\\label{othf25}\n\\phi^\\prime(t)=\\frac{\\tau}{1-t}+\\frac{\\eta_M}{1-\\eta_M t}, \\quad t_0=\\frac{\\tau+\\eta_M}{\\eta_M(\\tau+1)}.$$ In terms of $w$ and $\\nu$ $$\\label{othf26}\nt_0=\\frac{(1-w\\nu_o)(1-w+w\\nu)}{\\nu_o(1-\\nu)w^2}.$$\n\n1. ", " If $w<w_{c_\\nu}$, then $t_0<0$ and Watson’s lemma should be used. ", "The result is $$\\label{othf27}\n {}_2F_1(a,b;c;\\eta_M)\\sim\\frac{\\Gamma(c)}{\\Gamma(c-b)}\\left(\\frac{t_1}{J_M}\\right)^{b},\\quad t_1=\\frac{1}{\\eta_M+\\tau}.$$\n\n2. ", " If $w>w_{c_\\nu}$, then the saddle point $t_0$ is always inside the interval $(0,1)$, with $t_0\\to1$ if $w\\to\\infty$. Laplace’s method should be used. ", "This gives $$\\label{othf28}\n {}_2F_1(a,b;c;\\eta_M)\\sim\\frac{\\Gamma(c)}{\\Gamma(b)\\Gamma(c-b)}\\sqrt{\\frac{2\\pi}{J_M\\phi^{\\prime\\prime}(t_0)}}e^{-J_M\\phi(t_0)}t_0^{b-1}f(t_0),$$ where $f, \\phi$ and $t_0$ are given in – and $$\\label{othf29}\n \\phi^{\\prime\\prime}(t_0)=\\frac{\\eta_M^2(\\tau+1)^3}{\\tau(\\eta_M-1)^2}.$$\n\n3. ", " If $w=w_{c_\\nu}$ then $t_0=0$ and Laplace’s method on a half-infinite interval can be used.", "\n\nExpanding ${}_3F_2(1-J_M,1,1;2,2-\\xi_M;\\eta_M)$ {#F32case}\n-----------------------------------------------\n\n### Notation {#notation-1}\n\nWe write $$\\label{F1}\na=1-J_M, \\quad c=\\sigma+\\tau J_M,$$ with $$\\label{F3}\n\\sigma=1+\\frac{1}{1-w\\nu_o},\\quad \\tau=-\\frac{1}{1-w\\nu_o},$$ The asymptotic behaviour will be considered of the hypergeometric function $$\\label{othf3MM}\nF={}_3F_2(a,1,1;c,2;\\eta_M),$$ for large–$J_M$, where $$\\label{othf4MM}\n\\eta_M=\\frac{ w(1-\\nu)}{1 -w\\nu_o},$$ and $$\\label{F5}\nr\\in(0,\\infty),\\quad \\nu,\\nu_o\\in(0,1).$$ Note that $$\\label{F8}\n{}_3F_2(a,1,1;c,2;\\eta_M)=\\sum_{k=0}^\\infty\\frac{(a)_k(1)_k(1)_k}{k!\\,(c)_k(2)_k}\\eta_M^k=\n\\sum_{k=0}^\\infty\\frac{(a)_k}{(c)_k}\\frac{\\eta_M^k}{k+1},$$ and because $a$ is a negative integer this series terminates at $k=-a$.\n\n### Representation in terms of a Laplace integral {#Lap}\n\nWe substitute $$\\label{F9}\n\\frac{1}{k+1}=\\int_0^\\infty e^{-(k+1)w}\\,dw,$$ and obtain $$\\label{F10}\n{}_3F_2(a,1,1;c,2;\\eta_M)=\\int_0^{\\infty}e^{-w}{}_2F_1(a,1;c,z)\\,dw,\\quad z=\\eta_M e^{-w}.$$ For this representation we use the results of §§\\[othgenrsmall\\], \\[othgenrlarge\\] when, with $\\eta_M$ replaced by $\\eta_M e^{-w}$, the saddle points $t_0$ of and are negative. ", "This gives two cases.", "\n\n1. ", " *The case $w<w_{c_{\\nu_o}}$ and $w<w_{c_\\nu}$.* For this case we use the results in - with $b=1$. We have $$\\label{F11}\n {}_2F_1(a,1;c;z)=\\frac{1-c}{J_M}g_0+\\bigO(1/J_M),$$ where $g_0=t_1$ and $t_1=-1/(\\tau+\\eta_M e^{-w})$. This gives $$\\label{F12}\n {}_3F_2(a,1,1;c,2;\\eta_M)=\\frac{c-1}{J_M}\\int_0^{\\infty}e^{-w}\\,\\frac{dw}{\\tau+\\eta_M e^{-w}}+\\bigO(1/J_M).$$ Evaluating the integral we obtain $$\\label{F13}\n {}_3F_2(a,1,1;c,2;\\eta_M)=\\frac{c-1}{\\tau J_M}\\frac{\\ln(1+\\eta_M/\\tau)}{\\eta_M/\\tau}+\\bigO(1/J_M).$$\n\n2. ", " *The case $w>w_{c_{\\nu_o}}$ and $w<w_{c_\\nu}$.* In this case we use the results in -, again, with $b=1$ and $\\eta_M$ replaced with $\\eta_M e^{-w}$. We use Watson’s lemma for by substituting $s=\\phi(t)$ and obtain $$\\label{F14}\n {}_2F_1(a,1;c;z)=(c-1)\\int_0^\\infty e^{-J_Ms}g(s)\\,ds,\\quad g(s)=\\frac{ (1-t)^{\\sigma-2}}{1-te^{-w}}\\,\\frac{dt}{ds}.$$ Expanding $g$ at $s=0$ we have $g(s)=g_0+\\bigO(s)$, with $g_0=1/(\\tau+\\eta_M e^{-w})$ and, as in the above case, we derive $$\\label{F15}\n {}_3F_2(a,1,1;c,2;\\eta_M)=\\frac{c-1}{\\tau J_M}\\frac{\\ln(1+\\eta_M/\\tau)}{\\eta_M/\\tau}+\\bigO(1/J_M).$$\n\n### Summing the series by integration {#SSI}\n\nWe replace the Pochhammer symbols in by representations in terms of the gamma functions $$\\label{F16}\n(\\alpha)_k=\\frac{\\Gamma(\\alpha+k)}{\\Gamma(\\alpha)}=(-1)^k\\frac{\\Gamma(1-\\alpha)}{\\Gamma(1-\\alpha-k)}.$$ and replace the gamma functions with large positive argument by their asymptotic forms that follow from $$\\label{F17}\n\\Gamma(az+b)\\sim \\sqrt{2\\pi}\\,e^{-az}(az)^{az+b-\\frac12},\\quad z\\to\\infty,\\quad a>0.$$ This gives the remaining two cases.", "\n\n1. ", " *The case $w<w_{c_{\\nu_o}}$ and $w>w_{c_\\nu}$.* In this case $\\tau<-1$ and $ \\eta_M>0$. We replace the Pochhammer symbols in with the second form in . ", "This gives $$\\label{F18}\n {}_3F_2(a,1,1;c,2;\\eta_M)=\\sum_{k=0}^\\infty F(k),$$ where $$\\label{F19}\n F(k)=\\frac{\\Gamma(1-a)}{\\Gamma(1-c)} \\frac{\\eta_M^k}{k+1}\\frac{\\Gamma(1-c-k)}{\\Gamma(1-a-k)},$$ and we replace the summation in by integration, invoking Euler’s summation formula, or the compound trapezoidal rule $$\\label{F20}\n {}_3F_2(a,1,1;c,2;\\eta_M)\\sim\\frac{\\Gamma(1-a)}{\\Gamma(1-c)}\\int_0^{J_M} \\frac{\\eta_M^k}{k+1}\\frac{\\Gamma(1-c-k)}{\\Gamma(1-a-k)}\\,dk.$$ In Euler’s summation formula additional terms occur but in the present case they can be neglected.", "\n\n We replace the gamma functions by their asymptotic estimates following from . ", "This gives $$\\label{F21}\n {}_3F_2(a,1,1;c,2;\\eta_M)\\sim \\frac{\\Gamma(1-a)}{\\Gamma(1-c)}\\int_0^{J_M} \\frac{e^{-\\phi(k)}}{k+1}\\frac{\\sqrt{1-a-k}}{\\sqrt{1-c-k}}\\,dk,$$ where $$\\label{F22}\n \\phi(k)=-k\\ln\\eta_M-(1-c-k)\\ln(1-c-k)+(1-a-k)\\ln(1-a-k).$$ Then, $$\\label{F23}\n \\phi^\\prime(k)=-\\ln \\eta_M+\\ln(1-c-k)-\\ln(1-a-k)),$$ and the derivative vanishes for $k=k_s$, where $$\\label{F24}\n k_s=\\frac{c-1+\\eta_M(1-a)}{1-\\eta_M}=k_0+k_1J_M, \\quad \n k_0=\\frac{\\sigma-1}{\\eta_M-1},\\quad k_1=\\frac{\\tau+\\eta_M}{\\eta_M-1}.$$ and $0<k_1<1$. The dominant point of the integral in is $k=k_s$, and we apply Laplace’s method. ", "We substitute $$\\label{F25}\n \\tfrac12\\phi^{\\prime\\prime}(k_s)s^2=\\phi(k)-\\phi(k_s),\\quad \\phi^{\\prime\\prime}(k_s)=-\\frac{(\\eta_M-1)^2}{J_M\\eta_M(\\tau+1)}+\\bigO(1/J_M^2).$$ This gives $$\\label{F26}\n {}_3F_2(1-J_M,1,1;\\sigma+\\tau J_M,2;\\eta_M)\\, \\sim \\, \n \\sqrt{\\frac{2\\pi}{\\phi^{\\prime\\prime}(k_s)}}\\,F(k_s),$$ where $F(k)$ is given in . ", "After using we obtain $$\\label{F27}\n \\hskip-2cm {}_3F_2(1-J_M,1,1;\\sigma+\\tau J_M,2;\\eta_M) \\nonumber$$ $$\\sim\\sqrt{\\frac{2\\pi}{\\phi^{\\prime\\prime}(k_s)}}\\,\\frac{\\eta_M-1}{(\\eta_M+\\tau)J_M}\\left(-\\frac{\\eta_M}{\\tau}\\right)^{\\frac12-c}\n \\left(\\frac{1+\\tau}{1-\\eta_M}\\right)^{a-c}.$$\n\n2. ", " *The case $w>w_{c_{\\nu_o}}$ and $w>w_{c_\\nu}$.* In this case $\\tau>0$ and $ \\eta_M<0$. We use , replacing the Pochhammer symbol $(a)_k$ by the second form of and $(c)_k$ by the first. ", "This gives $$\\label{F28}\n {}_3F_2(a,1,1;c,2;\\eta_M)=\\sum_{k=0}^\\infty F(k),$$ where $$\\label{F29}\n F(k)=\\frac{\\Gamma(J_M)\\Gamma(c)(-\\eta_M)^k}{(k+1)\\Gamma(J_M-k)\\Gamma(c+k)}.$$ and we replace the summation in by integration,$$\\label{F30}\n {}_3F_2(a,1,1;c,2;\\eta_M)\\sim \\int_0^{J_M} F(k)\\,dk.$$\n\n Applying the asymptotic estimates of gamma functions in , we obtain $$\\label{F31}\n F(k)=\\frac{\\Gamma(J_M)\\Gamma(c)e^{c+J_M}}{2\\pi(k+1)}\\sqrt{(J_M-k)(c+k)} e^{-\\phi(k)},$$ where $$\\label{F32}\n \\phi(k)=(c+k)\\ln(c+k)+(J_M-k)\\ln(J_M-k)-k\\ln(-\\eta_M).$$ We have $$\\label{F33}\n \\phi^\\prime(k)=\\ln(c+k)-\\ln(J_M-k)-\\ln(-\\eta_M),$$ and the saddle point given by $$\\label{F34}\n k_s=\\frac{c+\\eta_M J_M}{\\eta_M-1}=k_0+k_1J_M, \\quad \n k_0=\\frac{\\sigma}{\\eta_M-1},\\quad k_1=\\frac{\\tau+\\eta_M}{\\eta_M-1},$$ where, again, $0<k_1<1$. The dominant point of the integral in is $k=k_s$, and we apply Laplace’s method to this integral. ", "We substitute $$\\label{F35}\n \\tfrac12\\phi^{\\prime\\prime}(k_s)s^2=\\phi(k)-\\phi(k_s),\\quad \\phi^{\\prime\\prime}(k_s)=-\\frac{(\\eta_M-1)^2}{J_M\\eta_M(\\tau+1)}+\\bigO(1/J_M^2),$$ where $\\phi(k)$ is given in . ", "This gives $$\\label{F36}\n {}_3F_2(1-J_M,1,1;\\sigma+\\tau J_M,2;\\eta_M)\\, \\sim \\, \n \\sqrt{\\frac{2\\pi}{\\phi^{\\prime\\prime}(k_s)}}\\,F(k_s),$$ where $F(k)$ is given in . ", "After using we obtain, as in the case above, $$\\label{F37}\n \\hskip-2cm {}_3F_2(1-J_M,1,1;\\sigma+\\tau J_M,2;\\eta_M) \\nonumber$$ $$\\sim\\sqrt{\\frac{2\\pi}{\\phi^{\\prime\\prime}(k_s)}}\\,\\frac{\\eta_M-1}{(\\eta_M+\\tau)J_M}\\left(-\\frac{\\eta_M}{\\tau}\\right)^{\\frac12-c}\n \\left(\\frac{1+\\tau}{1-\\eta_M}\\right)^{a-c}.$$\n" ]

{ "pile_set_name": "ArXiv" }

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[ "“I was honored to deliver a letter from President Donald J. Trump to President Vladimir Putin’s administration,” Rand Paul says. ", "| Bryan Woolston/AP Photo Rand Paul delivers letter from Trump to Putin\n\nSen. Rand Paul on Wednesday delivered a letter from President Donald Trump to Russia President Vladimir Putin that \"emphasized the importance of further engagement\" between the two leaders.", "\n\n“I was honored to deliver a letter from President Donald J. Trump to President Vladimir Putin’s administration,” Paul said in a statement, which also noted that the letter was given to representatives for Putin, who has been out of Moscow all week.", "\n\n\nThe letter highlighted how the U.S. wants to continue to work together with Russia on \"countering terrorism, enhancing legislative dialogue and resuming cultural exchanges,\" Paul said.", "\n\nPaul emerged as one of the few prominent defenders of Trump after his controversial summit with Putin in Helsinki last month, during which Trump publicly sided with the Russian president over U.S. intelligence agencies regarding Russian meddling in the 2016 election.", "\n\nAs an outspoken non-interventionist, Paul praised Trump's willingness to engage with Putin and said at the time that he would travel to Russia in early August to play shuttle diplomacy for Trump.", "\n\nOn Wednesday, White House deputy press secretary Hogan Gidley said in a statement that it was Paul who had requested Trump to provide \"a letter of introduction.\"", "\n\n\"In the letter, the President mentioned topics of interest that Senator Paul wanted to discuss with President Putin,\" Gidley said.", "\n\nSign up here for POLITICO Huddle A daily play-by-play of congressional news in your inbox. ", "Email Sign Up By signing up you agree to receive email newsletters or alerts from POLITICO. ", "You can unsubscribe at any time. ", "This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.", "\n\nPaul has been visiting Moscow this week where he met with Russian officials, in addition to visiting the U.S. embassy in the city. ", "On Monday, Paul announced that Russian lawmakers have agreed to visit the U.S. Capitol, which would be the first time in almost three years that an official Russian delegation has visited the U.S. Capitol.", "\n\nPaul was the latest lawmaker to travel to Russia, as a group seven GOP senators and one House member visited Russia over the July 4 holiday week, just two weeks before Trump and Putin's meeting.", "\n\nThe letter also comes after Putin publicly announced late last month that he invited Trump to Russia for another face-to-face meeting.", "\n\nTrump had initially invited Putin to Washington D.C. this fall, but the White House later announced it was delaying a second meeting between the two leaders." ]

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[ "'use strict';\n\nvar $StringValueOf = require('../helpers/callBound')('String.prototype.valueOf');\n\nvar Type = require('./Type');\n\n// https://ecma-international.org/ecma-262/6.0/#sec-properties-of-the-string-prototype-object\n\nmodule.exports = function thisStringValue(value) {\n\tif (Type(value) === 'String') {\n\t\treturn value;\n\t}\n\n\treturn $StringValueOf(value);\n};\n" ]

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[ "Recurrent retinal artery obstruction as a presenting symptom of ophthalmic artery aneurysm: a case report.", "\nRetinal artery obstruction is an ophthalmic emergency requiring immediate treatment. ", "Recurrent episodes are the result of thromboembolic seeding and necessitate diagnostic efforts to find a possible source for this seeding. ", "The most common sources of such seeding are the valves of the heart and the carotid arteries. ", "We describe a case of a 25-year-old man who had recurrent episodes of retinal artery obstruction due to embolic spread. ", "We suggest the origin of the embolic spread to be a post-traumatic ophthalmic artery aneurysm. ", "The immediate and long-term treatment given to the patient are described, the present case is compared to earlier reports, and the unusual clinical picture and suggested treatment are discussed." ]

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[ "Two years ago, Swedish communications technology giant Ericsson found itself looking for a way to explain the value it saw in the Internet of Things. ", "Rather than publish another whitepaper on the topic, the company struck on a different communication tool: Legos. ", "More specifically, Lego robots.", "\n\nEricsson used Lego Mindstorm robots in a demonstration at the 2012 Mobile World Congress to bring to life its vision of how connected machines might change the way we live. ", "A laundry-robot sorted socks by color and placed them in different baskets while it chatted with the washing machine. ", "A gardening-robot watered the plants when the plants said they were thirsty. ", "A cleaner-robot collapsed and trashed empty cardboard coffee cups that it collected from the table, and a dog-like robot fetched the newspaper when the alarm clock rang.", "\n\nLego’s Mindstorm robots (or education and innovation kits as they are sometimes known) were developed in collaboration with MIT Media Lab as a solution for education and training in the mid to late 90’s. ", "The work was an outcome of research by Professor Seymour Papert, who was co-founder of the MIT Artificial Intelligence Lab with Marvin Minsky. ", "Papert later co-founded the Epistemology and Learning Group within the MIT Media Lab. ", "Papert’s work has had a major impact on how people develop knowledge, and is especially relevant for building twenty-first century skills.", "\n\nPapert and his collaborators’ research indicates that training programs using robotics influences participants’ ability to learn numerous essential skills, especially creativity, critical thinking, and learning to learn or “metacognition”. ", "They also emphasize important approaches to modern work, like collaboration and communication.", "\n\nThis form of learning is called constructionism, and it is premised on the idea that people learn by actively constructing new knowledge, not by having information “poured” into their heads. ", "Moreover, constructionism asserts that people learn with particular effectiveness when they are engaged in “constructing” personally meaningful artifacts. ", "People don’t get ideas; they make them.", "\n\nPapert’s influential book Mindstorms: Children, Computers and Powerful Ideas as well as extensive scientific research into fields such as cognition, psychology, evolutionary psychology, and epistemology illustrate how this pedagogy can be combined with robotics to yield a powerful, hands-on method of training.", "\n\nIn training courses that use robotics, the program leader sets problems to be solved. ", "Teams are presented with a box of pieces and simple programs that can run on iPads, iPhones, or Android tablets and phones. ", "They are given basic training in the simple programming skills required and then set free to solve the problem presented.", "\n\nProblems can be as ‘simple’ as building a robot to pass through a maze in a certain time frame, which requires trial and error and lots of critical thinking. ", "What size wheels to use for speed and maneuverability, what drain on battery power, which sensors to use for guidance around walls. ", "One team may decide to build a small drone to view and map out the terrain of the maze, this would require theorizing on the weight of the robotic drone and relaying data filmed to a mapping system which the on-ground robot could use to negotiate through the maze.", "\n\nIt is an entirely goal-driven process.", "\n\nParticipants get to design, program, and fully control functional robotic models. ", "They use software to plan, test, and modify sequences of instructions for a variety of robotic behaviors. ", "And they learn to collect and analyze data from sensors, using data logging functionalities embedded in the software. ", "They gain the confidence to author algorithms, which taps critical thinking skills, and to creatively configure the robot to pursue goals.", "\n\nParticipants from all backgrounds gain key team building skills through collaborating closely at every stage of ideation, innovation, deployment, evaluation and scaling. ", "At the end of the training teams are required to present their ideas and results, building effective communication skills.", "\n\nIt is quite astonishing to see how teams have developed robots to achieve tasks such as solving Rubik’s cubes in seconds, playing Sudoku and drawing portraits, creating braille printers, taking part in soccer and basketball games. ", "These robots have even been used for improving ATM security.", "\n\nUsing robots in training programs to overcome challenges pushes participants out of their comfort zone. ", "It deepens their awareness of complexity and builds ownership and responsibility.", "\n\nThe array of skills and work techniques that this kind of training offers is more in need today than ever, as technology is rapidly changing the skills demanded in the workplace.", "\n\nInstead of programming people to act like robots, why not teach them to become programmers, creative thinkers, architects, and engineers? ", "For companies seeking to develop these skills in their employees, hands-on goal-focused training using robots can help." ]

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[ "PGHS\n\nPGHS may refer to:\n Pacific Grove High School, Pacific Grove, California, United States\n Palmers Green High School, Palmers Green, London, United States\n Penns Grove High School, Carneys Point, New Jersey, United States\n Palmers Green High School, Pinetown, KwaZulu-Natal, South Africa\n Pleasant Grove High School (California), Elk Grove, California, United States\n Pleasant Grove High School (Utah), Pleasant Grove, Utah, United States\n Pottsgrove High School, Pottsgrove, Pennsylvania, United States\n Prairie Grove High School, Prairie Grove, Arkansas, United States\n Prince George High School, Prince George, Virginia, United States\nProvidence Grove High School, North Carolina, United States" ]

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[ "Q:\n\nrealurl prevar language and get parameter\n\nI have a strange problem:\nTYPO3 7.6 with realul 2.2.1\nI got a page with a form. ", "One field of the form gets prefilled via get-parameter (sysid=xxxxx). ", "\nThe site is multilanguage: german->0, english->1, mapped via prevars '' and en.", "\nWhen I call the page via www.domain.tld/form-page/?sysid=xxxxx I can fetch the get parameter and fill the field.", "\nWhen I call the page via www.domain.tld/en/form-page/?sysid=xxxxx I get a 404. ", "That's weired because www.domain.tld/en/form-page/ works without any problems.", "\nI tried several settings (e.g. exclude sysid from chash generation) but nothing worked. ", "\nAny hints what I could do?", "\nOne additional note: the getvar links are not generated in TYPO3, the are called via barcodes. ", " \n\nA:\n\nNevermind. ", "Error occured because I didn't adjust the realurl-setting for the domain after moving to live. ", "Therefore automatic configuration took place and that didn't work. ", "With manual conf it works.", "\n\n" ]

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[ "Vehicles can incorporate various types of ducts that convey air, for example. ", "Design requirements may necessitate that the ducts be somewhat compliant. ", "The ducts could need to, for example, flex away from a design position in response to a load applied in a particular direction, and then return to the design position after the load is removed. ", "The load could be a load associated with pedestrian protection, or a load resulting from the vehicle bumping into an object.", "\nOne example duct is used to convey air from outside the vehicle to an engine compartment of the vehicle. ", "Such a duct could be used in connection with an active grille shutter system at a front of the vehicle." ]

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[ "<?", "php\n/**\n * Copyright 2010-2013 Amazon.com, Inc. or its affiliates. ", "All Rights Reserved.", "\n *\n * Licensed under the Apache License, Version 2.0 (the \"License\").", "\n * You may not use this file except in compliance with the License.", "\n * A copy of the License is located at\n *\n * http://aws.amazon.com/apache2.0\n *\n * or in the \"license\" file accompanying this file. ", "This file is distributed\n * on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either\n * express or implied. ", "See the License for the specific language governing\n * permissions and limitations under the License.", "\n */\n\nnamespace Aws\\Route53\\Enum;\n\nuse Aws\\Common\\Enum;\n\n/**\n * Contains enumerable Action values\n */\nclass Action extends Enum\n{\n const CREATE = 'CREATE';\n const DELETE = 'DELETE';\n const UPSERT = 'UPSERT';\n}\n" ]

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[ "The effect of leukemic lymphoblasts on normal granulopoiesis.", "\nAcute lymphoblastic leukemia (ALL) in children is often characterized by defective granulopoiesis during initial and relapse stages of the disease, resulting in absolute neutropenia in vivo and in low or absent production of granulocyte-macrophage colonies in vitro. ", "The purpose of this study was to determine if leukemic lymphoblasts from untreated ALL patients could inhibit normal granulopoiesis. ", "Several concentrations of leukemic bone marrow cells from nine patients were mixed with either normal bone marrow cells or with autologous (HLA-identical) remission bone marrow cells, incubated for 1 hour, and co-cultured by the double layer agar technique. ", "The cells were also cultured separately as controls. ", "No statistically significant differences occurred between observed and expected colony counts in the majority of experiments. ", "With three patients, slight inhibition occurred at some but not all leukemic cell concentrations tested; this inhibition was not correlated with the leukemic cell concentration. ", "These results indicate that leukemic cells from untreated ALL patients do not significantly inhibit normal in vitro granulopoiesis at the committed stem cell level or at later levels of differentiation; therefore, such inhibition does not appear to be responsible for ALL-associated neutropenia." ]

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[ "Glenn Beck's Toxic Legacy Will Live On After His Fox News Exit\n\nThe radio host, who appeared to suggest on his show Tuesday that only “hookers” depend on Planned Parenthood, may be departing Fox News. ", "But the polarised media culture he’s thrived in—one that rewards politicians and TV types for inflammatory talk that draws an audience—lives on. ", "Howard Kurtz on the lucrative lure of going too far.", "\n\nAnd yet he was doing exactly what the network wanted—not with the content of his chalkboard rants, but with the incendiary nature of his commentary.", "\n\nThe name of the game in talk television and talk radio today is to register high on the outrage meter, because that’s how you build an audience, and Beck drew a huge one by cable standards. ", "Half the country hates you, half the country loves you, but everyone in the echo chamber is talking about you. ", "And it’s a formula that extends well beyond the media. ", "Our society, not to put too fine a point on it, rewards inflammatory talk.", "\n\nBeck was at it again on his radio show this week, saying that Planned Parenthood is patronized by hookers–thus announcing he has no intention of toning down his scorched-earth, factually challenged approach.", "\n\nHow many people had heard of Republican Joe Wilson before the South Carolina congressman shouted “you lie” during a speech by President Obama? ", "It turned into a fundraising opportunity for him. ", "Democrat Alan Grayson became an MSNBC fixture after he raged that the GOP health plan for sick people was “die quickly”—though it didn’t help him save his House seat. ", "Maybe it’s contagious: During the government-shutdown theatrics, Democrat Louise Slaughter said the Republicans want to “kill women.” ", "I’m all for vigorous debate, but doesn’t that sound a tad overdramatic?", "\n\nThe 535 members of Congress compete in the same static-heavy environment as everyone else, a media culture that rewards finger-in-the-eye rhetoric. ", "They want to get their sound bite on the chat shows, or better yet get invited to make the rounds, and nuanced budget commentary won’t do the trick.", "\n\nIf you’re on Twitter, you want to stand out enough to amass plenty of followers, and caustic tweets are more likely to be picked up and retweeted. ", "Going too far in 140 characters is also a way to get fired, as some journalists have learned, not to mention Gilbert Gottfriend, who was dumped as the Aflac duck after tweeting jokes about the disaster in Japan.", "\n\nHow did we reach this point? ", "The cable-news culture certainly plays a key role. ", "Keith Olbermann, whose style included naming a mock-serious Worst Person in the World and who occasionally regretted bursts of over-the-top rhetoric, left MSNBC after a bitter falling out with management. ", "CNN fired Rick Sanchez after he called Jon Stewart a bigot and suggested that the networks are run by Jews. ", "A world in which Bill O’Reilly regularly anoints pinheads and patriots is one that thrives on polarization—and audiences that cheer for their side’s partisans.", "\n\nIn such a market, Beck was a natural fit. ", "When he was still with Headline News, Beck told the nation’s first Muslim congressman, Keith Ellison, that he felt like saying “Sir, prove to me that you are not working with our enemies.”", "\n\nDuring his 2 1/2-year run at Fox, Beck went from describing the president of the United States as having a “deep-seated hatred of white people” to likening reform Judaism to radical Islam to assailing a shadowy Middle East caliphate with ties to left-wing American groups. ", "And he did this for most of his tenure to striking silence on the right. ", "Only more recently did Bill Kristol and other conservative writers join the likes of David Frum in pronouncing such talk unacceptable. ", "Too many in the opinion world have a disinclination to call out their own side.", "\n\nIt’s a short distance between Beck’s nuttier theories and Donald Trump, celebrity businessman and alleged White House aspirant, jumping on the birther bandwagon. ", "Not long ago, anyone who spouted the nonsense that Barack Obama wasn’t born in Hawaii was dismissed as a fringe figure. ", "But the networks keep giving Trump a platform to make these unfounded charges, with varying degrees of pushback from the anchors. ", "The Donald is colourful and some Republicans believe the born-in-Kenya garbage, so the shows clearly hope to grab some Celebrity Apprentice-style ratings.", "\n\nFox will do just fine without Beck, and the radio host will have no trouble making a living, either. ", "The larger problem is a toxic culture that encourages pundits and politicians alike to do whatever it takes to get noticed. ", "And sometimes that means cranking it up to ultra-high decibels.", "\n\nThere’s no use whining about an environment that favours attacks and exaggeration over analysis and accuracy; it is here to stay. ", "But too many of us play a small role as enablers. ", "If the hosts and bloggers who indulge in the worst excesses didn’t put up the numbers, they wouldn’t get the most prominent perches. ", "Maybe they’re providing what the audience wants. ", "But even in this anything-goes atmosphere, as Beck eventually learned, there is such a thing as going too far.", "\n\nHoward Kurtz is The Daily Beast’s Washington bureau chief. ", "He also hosts CNN’s weekly media program Reliable Sources on Sundays at 11 a.m. ET. ", "The longtime media reporter and columnist for The Washington Post, Kurtz is the author of five books." ]

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