prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the problem encountered when building the fuselage sides?

Read the following text and answer briefly.

Context 1: Probably one of the most frustrating things about building experimental aircraft, especially when starting with a minimum of pre-fabricated parts, is to start building and ending up with an unexpected result  Every builder starts a new project by wanting it to go "perfectly " So when things aren't going well, especially at the beginning, the frustration can lead to an unfinished airplane 
This is the first article in a series dedicated to helping builders of the Rand Robinson KR series planes build a straight and true fuselage -- the first part of the construction process  Borrowing from modern boatbuliding techniques, focus will be on the KR-2S, but the principles apply to the entire lineup of KR-1 & KR-2 series planes 
While building the KR-2(s) a common surprise is encountered by builders when the completed fuselage sides are laid into position to form the fuselage box section  With many hours spent building the sides flat, finding the once straight longerons that now bow up from the building surface, form a most dissatisfying "banana" shape  Especially when using the preformed fiberglass parts, this curve in the top longeron is not acceptable  The builder is left wondering what went wrong and no amount of clamping or brute force forming will solve the problem to any degree of satisfaction  The problem is not the builder's fault  The solution starts by understanding the three dimensional relationship of the assembled parts being built 
First understand that the plans show the finished form of the plane  They show the "projected" form as you would expect to see it if viewing an actual plane from the top, ends and from the side  Since the sides are sloped (flared) outward, looking from the side, the distances given by measuring the profile drawing are "foreshortened" and don't give the proper shape for building the fuselage with a flat top longeron  What needs to be done is to "develop" the "true" distances and shape of the flat panel so that when it is curved into position, the longerons lay flat 
Second, understand that the dimensions called for in the plans put a twist in the sides that tends to work the panel in two directions of curvature  This twist makes the panel "undevelopable" meaning that that shape cannot be unrolled into an equivalent flat shape  This is important when laying out the side and bottom panels onto flat plywood  To illustrate this, try forming a piece of paper around a soda can  The paper can be formed flat around the can either straight or at a diagonal to it's length  It has only one direction of curvature and is by definition "developable"  Now try to form the same piece of paper around a baseball  It won't lie flat on the surface without some deformation (folding, wrinkling or tearing) of the paper  The ball has curvature in more that one direction and is a "compounded" shape  Paper (or plywood) can only be readily formed in developable shapes as opposed to aluminum or other metal which can accept in plane deformation  A developable surface is needed to lay out a curved surface when the materials used can't be deformed with any degree of in-plane strain 
Initially, the fuselage sides are laid out flat with reference to the top longeron measured to a straight chalk line  The bowing problem starts when the side panels are bent and sloped to form the fuselage box section  If the sides were not sloped (tumbled home), the section formed would be cylindrical and the longerons would lie flat  Since the sides are tumbled home, the section formed is now conical  When a conical shape is cut with a plane (building surface) not perpendicular to it's axis, the shape formed is elliptical -- exactly what happens with the top longeron  When it's built flat, bent to form a cylindrical section, and sloped to form a conical section, it takes on an elliptical shape firewall to tailstock 
This method borrows heavily from proven techniques used in the marine trades  It should be stressed at this point that although the layout procedure is not complicated, it is important to take your time  If the layout is not going well initially, start over! Better to erase layout errors now than to have them built it and cause surprises later 
Layout to ensure a fair and true fuselage starts by drawing a reference line (baseline) on the building surface  Refer to figures 2 & 3 and use a wire guide to draw a very straight baseline  About 500 lbs  Of tension should be adequate  One could use a chalk line, but we're talking airplanes here, not house framing 
The main layout difference is that the baseline isn't used as a reference for the top longeron  The baseline references the mid point of the firewall for the developed (and true dimensioned) side panel  Although the baseline will still be the reference, the top and bottom longerons will be laid separately 
Layout differences don't end there  Each of the stations (vertical members) will be laid out with a calculated separation so that when the panels are formed into position, they land on the spacing called for in the plans  Another major difference is that the bottom & side panels are applied after forming the fuselage box section  This is mainly to obtain the ability to "fair" the side and bottom surfaces and insure a straight and true shape 
Refer to figure 1 for the layout of the new developed side panel  The firewall (station a) is layed out perpendicular to the baseline  Longitudinal (station) measurements are given along the length of the baseline from the firewall  Vertical dimensions are given to reference the angle and breadths of the station at the baseline 
Notice that the top longeron is bowed outward and that the stations are spaced slightly greater than called out in the plans  When the panels are formed into the box frame section ,they will work into the dimensions specified in the plans 
Strike a centerline, longer than is needed on the building surface using a wire guide  Draw off the firewall line perpendicular to the centerline at one end 
Using the distances listed in the balloons, mark them off on the centerline  Distances are measured to the nearest sixteenth of an inch  Take time to mark them off carefully  Don't mark off the distances in a cumulative fashion  Use the firewall as a common reference 
Using the angles listed at each station, mark off a station line longer than is needed  The angles are measured to the nearest hundredth of a degree  Take time to mark them off carefully 
At each station, start by marking off each short (bottom longeron) line distance from the centerline  Use your set of trammels or beam compass for doing this  Mark the intersection of the short line with the station line 
At each station, mark off each long (top longeron) line distance from the intersection of the short line distance and the station line  Again the trammels or beam compass is best for completing this step  Mark the intersection of the long line distance with the station line 
Using the longeron as a batten, trace out the inside and outside curves of the longeron  After the batten is secure, in between each station, fasten a keeper block inside and outside to preserve the shape of the longeron taking care to avoid potential future interference with the diagonal members to be installed later  The fairing blocks can be removed or left in place if they won't interfere with building  The vertical station members and their diagonals can now be measured and positioned  Remember to refer to the plans for the material thickness direction 
After vertical and diagonal members are cut and fitted, take time to draw their outlines on the building surface to cut down on time and confusion when laying out the opposite side 
Finishing the side panel is accomplished in a manner similar to that called for in the handbook with the exception that the side and bottom skin panels will be attached later 
The next article in the series will discuss jigging and building techniques to ensure alignment and straightness of the flat built side panels  Also covered will be building a "strongback" jig to assure alignment of the side panels when they are formed into their final shape 
Part 3 in the series will cover assembly of the side panels using the jigs  Some joint details will be discussed that will ensure a stronger and more fair fuselage assembly  Also covered will be the layout & attachment of the side and bottom ply skins 
U S  Mail: Densmore Associates, inc 
ANSI "D" size, computer generated plots of all the layout drawings in this series are available from the author for $30 plus postage & handling  Full (true size) scale plots may be made available depending on demand 
"Scarfing" is the practice of splicing plywood so that short pieces of plywood can be used to span long distances  On the KR, it is required on both the fuselage skins and spar webs  The angle of the splice should be 10 to 12 degrees to maintain strength across the joint  Also, joints should coincide with structural members, such as spar webs or fuselage truss members 
This scarfer is made by mating a regular plunge router (this one costs about $50) to a table saw  Obviously, you really only need a table saw to cut the chamfer, but it does make a nice heavy table for scarfing  You could just as easily use a large work table as the base First, set the table saw for a 5 5 degree cut (for a 1:12 joint, or 6 5 degree cut for a 10:1 joint), and run a 1 x 6 through on edge to chamfer a corner on the board  Then drill the board for three router mounting holes (two are countersunk) and connect the assembly to the table saw with two 1/4 inch bolts  Use a long (2-3 inch) straight cutting bit to do the cutting  Adjust the bit so it doesn't interfere with your table top, and go to town  Keep pressure on the plywood to ensure contact with the table while you're scarfing  Make sure you feed your material from the same end as you would if you were sawing, or the router will take your plywood away from you and put a big dent in your garage door 
In the late 60's Ken Rand and Stuart Robinson were working as flight system engineers for Douglas Avionics  Ken was working as an electrical engineer, having previously worked for Sperry as an autopilots project engineer, while Stu's degree was in aeronautical engineering from Northrop University  They were two of the guys at the end of the DC-8,9, and 10 assembly lines responsible for correcting some of the nits and picks in various systems before delivery to the customer 
They both wanted to build a fast, inexpensive airplane which was also economical to maintain  Several designs were considered, and plans were bought first for the Jeanie's Teenie and then the Taylor Monoplane  The Monoplane was more to their liking, but would require some modification to fit their needs  A cooperative redesign effort ensued, with virtually no dimensions left untouched  Only the basic fuselage structure, airfoil, and powerplant were retained  The tail shape was Stu's, and came directly from the big DC-8s parked on the ramp outside his office window  The landing gear was designed by Ken, after seeing the gear on a Dewey Bird at Santa Paula airport 
Ken was killed in his KR2 a short time later while flying over Cajon Pass in what was apparently a bad weather / low fuel accident  Ken's wife Jeanette became owner of RR overnight, and stepped up to keep the plans and parts coming  Much of the engineering needs are handled by Bill Marcy of Denver, who's been helping out since early '79 
To date, almost 6000 KR1, 9200 KR2, and 760 KR2S plan sets have been sold  1200 KR2s are estimated to be flying, with 5 KR2Ss now in the air  Much of the development work done on KR's is now done by the builders themselves  KR builders tend to be innovative, which leads to some interesting modifications  Some of the mods that work eventually creep into the plans  The KR2S is a case in point  Many builders who'd heard of the pitch sensitivity and tight cabin of the KR2 began to build an enlarged version, with the length determined by the most commonly available longeron material  The result is a KR2 that is stretched 2" between firewall and main spar, and 14" behind the main spar  Higher gross weights dictated more wing area, with the new standard becoming the Diehl wing skin  Those who plan to carry passengers commonly stretch the cabin width a few inches, although 1 5 inches is the limit if you still want to use RR's premolded parts 
Mike Stearns addresses the KR Forum crowd 
This year's KR Forum featured guest speakers Mike Stearns, Steve Trentman, and Bill Marcey  Mike Stearns spoke on several topics, including the many sources for KR and homebuilding information available on the Internet  He also mentioned KRNet, the list server devoted entirely to KR aircraft, as well as several notable World Wide Web home pages  He also brought a sample of the new Rand Robinson wing skins with him, and discussed their high temperature core prepreg construction  His KR2S will receive the first set, which is currently being installed at Hinson Composites 
Steve Trentman spoke on his turbine installation  It uses a turbine engine which saw duty as an A7 attack jet starter engine  Total weight is about 85 pounds, while putting out around 90 horsepower  There is a small stockpile of these engines available from government surplus  sources  This engine can only be throttled back to 52% power, which leads to some pretty interesting landings  One inflight failure has been logged so far, with very little damage to the aircraft  More on this exciting development in next month's issue of KROnline 
Les Palmer's KR2 N202LP won Best KR2, Best Engine Installation, and People's Choice awards at the 1995 KR Gathering at Columbia, TN  After researching the KR series, and reading Neil Bingham's "A Critical Analysis of the KR2" (Jan 88 Sport Aviation), Les decided to build his as a single seater, stretched 24" in the tail, while maintaining a stock width firewall  His fuselage is made from Douglas fir, which weighs in at 4 lbs heavier than if constructed from spruce  It is skinned with 1/8" birch plywood  Spars are covered with plywoood on both fore and aft sides, ala KR2S  Diehl wing skins provide the lift  Horizontal stabilizer and elevator were stretched 7" longer on each side, while the vertical stabilizer and rudder were stretched 8" taller    The fuselage to cowling junction was made more graceful by adding 1 5 inches to the height of the firewall end of the fuselage sides 
Les's canopy is a Dragonfly, using a four linkage system to swing forward when opening  The canopy frame fits snugly into a recess in the foward deck, providing an excellent wind and water seal  The fiberglass work is exemplary 
Seating is luxurious for one 
The cowling is also a work of art, and uses NACA ducts for efficiency  Female molds were made for all the fiberglass parts on Les's plane, so he could proabably be persuaded to make more, if demand dictates  Les also machines a multitude of KR aluminum and steel parts which he now offers for sale 
The firewall was reinforced with aluminum brackets and angles bolted between the longerons in anticipation of the 200 lb Subaru EA-81 engine installation  His 100 HP Asian version is outfitted with an American Holley 5200 caburetor and manifold  It uses a PSRU of Les's own design, featuring two spur gears with a 1 69:1 reduction ratio and a toothed belt  Other than tapping the crank for larger bolts to mount the redrive, no other engine modifications were required  Also, this is probably the only air conditioned KR2 on the planet  The prop is a 60/63 Hegy 
Originally built as a taildragger, the fixed gear is made from 4130 steel tubing  Custom cast 6 00x6 aluminum wheels and steel rotors are mated with 6" Cleveland calipers for braking  An early taxi test accident damaged the main gear, and prompted Les to change to tricycle gear  Again, he designed his own fiberglass main gear, and uses a Diehl nose wheel fork with a 4130 strut and 6" wheel up front 
Early tests revealed cooling problems, which prompted a radiator move from the firewall to a lower cowling location 
The first flight was almost a disaster, as test pilot Randy Smith lost power right after takeoff  He managed a 180 with a safe downwind landing with only minor nosewheel pant damage  The culprit proved to be a spark plug with too much reach, which was quickly remedied  Subsequent flights have shown water temp to be about 210 degrees, oil temp is 220-230, and airspeed is about 180 mph 
Shopping for the Partially Built KR 
This story starts about twenty years ago when I first started looking at the KR-2 as the plane I'd like to build  The only problem at that time was a lack of money, lack of knowledge, and a lack of job stability  I liked the design, except for the low ground clearance of the retractable gear and that a KR was going to be a tight fit for me to fly 
Over the past twenty years I've owned a number of planes, but still always wanted to build my own  I needed one that would fit me, my budget requirements, and have the speed and performance that I wanted  When "KITPLANES" published the article featuring Roy Marsh's new KR-2S, it was the first I had heard of any major modifications or improvements to the same old KR design  I believe that article and Roy Marsh's workmanship have probably been the greatest boon to Rand Robinson (RR) in the last twenty years  It certainly caught my eye! Here was the same design I had decided I wanted to build twenty years ago, with all of the improvements I wanted  It was sitting on fixed gear with some reasonable ground clearance  It had the capability to be built large enough to accommodate me  It has enough prefab parts available that it didn't have to be 100% scratch built if I decided to hurry the project along  And it had the speed I wanted  I knew that Roy's published speeds were probably not realistic expectations for the average KR, but after knocking around for the last three years in my Champ, anything over 90 mph seems pretty fast to me 
After purchasing the info kit and the sales video from Rand Robinson, the next step after deciding for sure to build this plane was to order the KR-2 plans and the KR-2S addendum  I finally got my plans and was putting together my first order to start the plane, when my partner in the Champ pointed out that there was a partially completed KR-2S for sale in Trade-a-plane  My initial answer was "No, I don't even want to look at it  I want to build my own from scratch " My partner insisted that for the advertised price and the fact that it wasn't too far away, I ought to at least give the guy a call and investigate it  "No, I don't think I want to buy someone else's problems," I persisted  That night I went home and crunched up some numbers on the calculator and finally came to the conclusion that for the sake of my budget for the next several years, I really should give this guy a call 
Three days later, I flew to his place about 400 miles away to take a look at his project  At this point I should probably mention that I consider myself to be fairly knowledgeable about airplane construction, although the vast majority of my experience is with tube and fabric  The rest of this article deals with what I looked for and more importantly what I missed and have had to repair in the last year since I purchased the project 
When we went to the seller's house, I found that the left wing was built using the Dan Diehl wing skins and the right wing skins were leaning against the wall inside the house  Also the canopy was in the house with the canopy covered with paper and tape  I wanted to inspect the fuselage first, so off we went to the shop 
There I found a fuselage sitting on it's gear painted in primer gray  The first step was to inspect the quality of workmanship of what could be seen as it sat  The interior of the fuselage looked as if it had been built with a great deal of care  The fit and finish of all of the interior wood was very nice  Even the gussets looked like they had been painstakingly perfectly fitted  The glass work on the turtle back also looked very precise and clean  It was evenly faired into the vertical and horizontal stabs  The tail also appeared to be well built with the exception of a depression directly over the front and rear spars in the horizontal stabs  He explained that when he moved recently, that he had shot the plane with gray primer to protect it from the weather since he wouldn't have ready access to a shop to put it in right away  It ended up sitting out in the hot south Texas summer sun for a few weeks before he got a shop rented to work in  That caused the glass (or possibly the foam inside the horizontal stab) to swell, except that it held onto the spar, so it was slightly ballooned in front of and behind the spars  His recommendation was to fill it back smooth with micro 
I also found a small linear crack in the lower left wing spar cap on the left wing stub  It appeared to be from over tightening the rear spar wing attach fitting bolts  His explanation was that the crack wasn't important because the rear spars only job is to keep the wings from folding back  I also noticed that the holes for attaching the outer wing to the wing stub were badly rounded out on the rear spar  He explained that the Diehl wing skins require the rear spar to be swept slightly more forward than the stock wings  This won't allow you to use the rear spar attach fittings from RR and that I would need to fabricate a new set of rear spar attach fittings 
I also found that the aileron bellcranks were not built or installed as per plans, but found that they looked professional  I couldn't check for function since the right bellcrank and sheeve wasn't installed, the left wing also wasn't installed, and the right wing didn't exist yet 
Next we pulled the inspection panels off of the fuselage and tail and looked at everything I could see with a good flashlight  I didn't find anything else that might be questionable about the fuselage except for a cracked elevator trim tab that was damaged when it fell off it's hanging place on the wall 
Next we spent some time going over his builders log and builders photo album  I still hadn't seen anything that would dissuade me from buying this project 
At this point it was starting to get late and my ride down needed to get airborne for the flight home  I needed to make a decision about whether I wanted this project or not, but I hadn't inspected the wings and canopy yet  I took a cursory look at the left wing and saw lots on micro built up on it and some bubbles in the leading edge, but nothing that looked seriously wrong to my amateur eye  The right wing was only a set of spars in the shop and the Diehl wing skins in the house, so there wasn't much to look at there  The canopy was wrapped in paper and tape, so there wasn't much to look at there either  I decided that even if there were serious problems in the wing that was built, I would be money ahead to go ahead and buy the project  For the advertised price, I could build a new set of wings and still be way ahead financially  We negotiated a final price, shook hands, took my ride to the airport, and started off in search of a U-haul to haul the project home 
Now, at this point, some of you are thinking about what I surely must have forgotten to inspect and why didn't I take a local A & P or EAA member along for the ride  First of all, I don't know any mechanics locally that have any experience with glass and our EAA chapter of which I am VP is woefully lacking in fiberglass knowledge  Secondly, as you will see, I missed plenty  Some by ignorance, some by just not looking close enough 
Now for a list of the problems that I found over the last year and a few of the fixes that I came up with 
I found that the lower set of rear spar attach fittings on the left rear spar were installed backwards with the longer spaced hole towards the fuselage  Since this is the same place that also had the cracked spar cap, it required a major change  Also in the same area he had drilled through the rear spar with a hole saw to create a place for the aileron cable to pass through and managed to cut out the second from the outside vertical brace in the spar  Then he chose to install the aileron bellcranks in front of the rear spar, and cut another hole through the rear spar for the aileron push rod  He also managed to cut out the outside vertical brace in the spar  Since the holes were already drilled through the spar, the choices were to either cut out that section of spar cap and scarf a new piece in, cut the whole rear spar carrythrough out of the fuselage including ruining the left lower wing skin, or do something else creative to reinforce the spar cap and install a custom built set of attach fittings 
I also found that after I built and installed the right side wing stub ribs and skin that the aileron bellcrank setup would not work as installed  The cable that crosses between the two bellcranks had a sharp uphill from the sheeve to the bellcrank in the last 12 inches on either side  This combined with the radius that the bellcranks turn caused the cross cable to pull up tight when the ailerons were pushed to either end of their travel, but allowed the cables to go very slack when the ailerons were centered  Also the Aileron pushrods needed to pass directly through the lower set of rear wing attach fittings to attach to the aileron  This whole rear spar and aileron bellcrank setup was going to either have to be redesigned or cut out and built to plans  The bottom line is that the problems I observed when I inspected this part were much more serious than expected when I had to fix it 
I decided that I had to remove the rear fittings from the left wing to be replaced with the new set that my neighborhood machinist was cutting out for me  When I put the wing on the work bench to start removing the rear fittings, I thought I had better take a closer look at the bubbles in the leading edge  I found that as I pushed on the leading edge, it delaminated between the glass lay-up on top and the upper and lower wing skin edges that were floxed together underneath  I concluded that that area had to come apart and took a belt sander to the leading edge  What I found was that the leading edge had been floxed together and glassed over, but the mold release had never been scrubbed off the leading edge of the wing  It peeled apart for rebuild quite easily 
When I got back to removing the rear spar attach fittings, I noticed that the woodwork inside the wing looked awfully dull  The reason was that the wing had been closed up without varnishing any of the woodwork  This was rectified with a small hole saw, a number of extensions and a modified undercoating sprayer 
I also found that the aluminum drain fitting in the bottom of the left wing tank had been glassed into place upside down  The tapered pipe threads were tapered the wrong way to install the draincock into the tank  Retapping the fitting the right direction seemed to be a good fix for that problem 
When I finally got around to attaching the wing to the fuselage, I found that the front spar attach fittings were badly misaligned  Although they could be forced into alignment, I didn't think I needed that kind of preload on the main spar fittings  This problem was fixed by calling on my local neighborhood machinist to build me an aligning fixture and reaming the attach holes to the next larger size and ordering the new sized bolts 
On the fuselage I found that although it had new Cleveland wheels and brakes on it, one of the brakes had a severe wobble to it  I must complement the manufacturers for taking care of that problem  One call to the Cleveland factory and they shipped me a new set of wheels and brakes even though the receipt for this set was over four years old and in the original builders name  Their only concern was that this set had never been placed in service yet 
I chose to sand the load of micro off the left wing to see what it was covering  When I got down to the glass, I found that there was no glass for the aft inch and a half of the underside of the wing in front of the aileron hinge  With the Diehl wing skins, you build the wings, then cut the ailerons out of trailing edge of the wing  He had mismeasured and cut too much material off the bottom side of the trailing edge in front of the aileron  It was filled by floxing a piece of spruce into the gap to fill the space between the back edge of the fiberglass and the aileron mount  I chose to wrap the trailing edge of that wing, and the other wing to match with a couple of lay-ups of glass 
When I sanded the primer off the aforementioned damaged trim tab, I found that the hinge was floxed to the leading edge of the foam insides of the tab, but not the glass  I also chose to wrap the front of the trim tab with a lay-up of glass 
I decided to pull the paper off the canopy and take a look at it before I'm ready to bolt it on and fly  The original builder had blown his own canopy and after some of the previous problems, I was beginning to have some concerns about not having looked it over closely enough  The canopy turned out to have been blow a little too large  It ended up with a little larger bubble for headroom, which I didn't object to  However, it had more headroom on the right side than the left  Yes, it was just a little bit lopsided  The main problem was that the canopy is stretched thin enough that it can be easily pushed in with one hand when the weather is warm   My fear was that this is just thin enough that it may decide to lay on my head or in my lap when flying on a warm day  It will have to be replaced 
I'm sure that many that are reading this could see several of the potential problems before I mentioned them, but some others may not have and I'm sure that there could have been many other problems that didn't but could have existed on this project  This is also not intended to be critical of the gentleman that started this project as many parts of it, especially the wood work are better than I could have done and much of his work is outstanding  I prefer to think that I'll end up with a better plane with his woodwork combined with my glasswork  This article is intended to feature some of the problems that you may run into in buying someone else's project 
The final question is, knowing what I have found over the past year, would I have still purchased this project  The answer is yes, but primarily because the price was right in that I am still money and work ahead of where I would be if I had started the project from scratch  There are a few things that I would have done differently, but nothing that I can't live with  Although I won't be able to say that I built it all from scratch, I have built and rebuild enough of the plane that I should have no problem qualifying under the 51% rule 
You can send comments directly to the author via e-mail at "jscott@LANL GOV" 
Here is an brief explanation of how I built my turtledecks  The jig was constructed from scrap plywood and a few 1x4s that I ripped into stringers  I made two temporary bulkheads from the plywood, one for each end  Remember the forward bulkhead needs to be shaped in a way that will closely match the aft end of your canopy frame  Make an aft bulkhead by placing a straight edge at the top of your forward bulkhead and the trailing edge of your horizontal stabilizer  This will give you an idea of how tall your aft bulkhead needs to be  As far as location, I placed my aft bulkhead just forward of the lower/front of my vertical fin  I constructed the jig on the fuselage, it is glued together with automotive bondo 
After the bulkheads were bondoed to the fuselage I used the stringers that I ripped from the 1x4s and bondoed them to the bulkheads  This gave me a male form to cover with thin plastic or posterboard  I stapled two layers of posterboard to the jig(thin plastic would work better)  The posterboard wraps down two inches onto the fuselage  After I was satisfied with the way it looked, I then covered the entire thing with duct tape (fiberglass will not stick to duct tape) On top of this I wetout one layer of tri-ply cloth (22oz) that I had left over from an earlier project, and one layer of 8oz  bid  Remember to mask off your fuselage so you don't get epoxy on it  If you are not familiar with composite lay-ups, you should plan on razor cutting your lay-ups 4 to 6 hours after wetout while the lay-up is still soft enough to cut with a razorblade 
After the lay-up cured (2 or 3 days) it was removed from the jig, and the jig was removed from the fuselage and discarded  (be careful, the bondo sticks very well to the spruce, you could splinter your wood during removal) I now have a fiberglass skin that tends to hold the shape of the jig but is still flexible enough to work with  I made two bulkheads out of 1/4 last-a-foam (AS&S) using the plywood formers from the jig as a guide  I covered these foam bulkheads with one 8oz layer of glass on each side, with a glass to glass edge on the bottom  After cure these bulkheads were bondoed into place (to the fuselage)and the fiberglass skin was pulled down tight and floxed to the bulkheads  When the flox cured the bondo joints were broken, again being careful not to harm the wood  The turtledeck was removed from the fuselage and 2 inch tapes added to the bulkheads inside and out 
At this point the turtledeck looked great and only weighed about 5lbs  but I noticed you could deform the skin by pushing hard on the outside  So I flipped the turtledeck over and from 1/4 inch last-a-foam, I cut two inch wide strips that would run the entire length, forward and aft inside the turtledeck  In effect these would act as composite stringers, I made enough of these two inch wide strips to make up three stringers  One down the center (sort of a backbone) and one on each side of the "backbone" half the distance to the edge of the turtledeck  I sanded the edge of the foam so that when covered with a layer of bid @ 45degrees there would be a nice transition from the turtledeck skin up onto the foam and then back onto the turtledeck I scuff sanded and glued the foam stringers in with micro  I covered the foam stringers with one layer of 8oz bid @ 45degrees 
Context 2: \section{Introduction}
Given a data set and a model with some unknown parameters, the inverse problem aims to find the values of the model parameters that best fit the data   
In this work, in which we focus on systems of interacting elements,
 the inverse problem concerns  the statistical inference
 of the underling interaction network and of its coupling coefficients from observed data on the dynamics  of the system  
 Versions of this problem are encountered in physics, biology (e g , \cite{Balakrishnan11,Ekeberg13,Christoph14}), social sciences and finance (e g ,\cite{Mastromatteo12,yamanaka_15}), neuroscience (e g , \cite{Schneidman06,Roudi09a,tyrcha_13}), just to cite a few, and are becoming more and more important due to the increase in the amount of data available from these fields \\
 \indent 
 A standard approach used in statistical inference is to predict the interaction couplings by maximizing the likelihood function 
 This technique, however, requires the evaluation of the  
 
   partition function that, in the most general case, concerns a number of computations scaling exponentially with the system size 
  
  
    Boltzmann machine learning uses Monte Carlo sampling to compute the gradients of the Log-likelihood looking for stationary points \cite{Murphy12} but this method is computationally manageable only for small systems  A series of faster approximations, such as naive mean-field, independent-pair approximation \cite{Roudi09a, Roudi09b}, inversion of TAP equations \cite{Kappen98,Tanaka98}, small correlations expansion \cite{Sessak09}, adaptive TAP \cite{Opper01}, adaptive  cluster expansion \cite{Cocco12} or Bethe approximations \cite{Ricci-Tersenghi12, Nguyen12}  have, then, been developed  These techniques take as input means and correlations of observed variables and most of them assume a fully connected graph as underlying connectivity network, or expand  around it by perturbative dilution   In most cases, network reconstruction turns out to  be not accurate for small data sizes and/or when couplings are  strong or, else, if the original interaction network is sparse \\
\indent
 A further method, substantially improving performances for small data, is the so-called Pseudo-Likelyhood Method (PLM) \cite{Ravikumar10}  In Ref  \cite{Aurell12} Aurell and Ekeberg performed a comparison between PLM and some of the just mentioned mean-field-based algorithms on the pairwise interacting Ising-spin  ($\sigma = \pm 1$) model, showing how PLM performs sensitively better, especially on sparse graphs and in the high-coupling limit, i e , for low temperature 
 
 In this work, we aim at performing statistical inference  on a model whose interacting variables are continuous $XY$ spins, i e , $\sigma \equiv \left(\cos \phi,\sin \phi\right)$ with $\phi \in [0, 2\pi )$  The developed tools can, actually, be also straightforward applied  to the $p$-clock model  \cite{Potts52} where the phase $\phi$ takes discretely equispaced $p$ values  in the $2 \pi$ interval, $\phi_a =  a 2 \pi/p$, with $a= 0,1,\dots,p-1$  The $p$-clock model, else called vector Potts model, gives a hierarchy of discretization of the $XY$ model as $p$ increases  For $p=2$, one recovers the Ising model, for $p=4$ the Ashkin-Teller model \cite{Ashkin43}, for $p=6$ the ice-type model \cite{Pauling35,Baxter82} and the eight-vertex model \cite{Sutherland70,Fan70,Baxter71} for $p=8$   
It turns out to be very useful also for numerical implementations of the continuous $XY$ model  
Recent analysis on the multi-body $XY$ model has shown that for a limited number of discrete phase values ($p\sim 16, 32$) the thermodynamic critical properties of the $p\to\infty$ $XY$ limit are promptly recovered \cite{Marruzzo15, Marruzzo16}   
Our main motivation to study statistical inference is that these kind of models have recently turned out to be rather useful in describing the behavior of optical systems, 
including standard mode-locking lasers \cite{Gordon02,Gat04,Angelani07,Marruzzo15} and random lasers \cite{Angelani06a,Leuzzi09a,Antenucci15a,Antenucci15b,Marruzzo16}  
In particular, the inverse problem on the pairwise XY model analyzed here might be of help in recovering images from light propagated through random media  


      This paper is organized as follows: in Sec  \ref{sec:model} we introduce the general model  and we discuss its  derivation also  as a model for light transmission through random scattering media  
    In Sec  \ref{sec:plm} we introduce the PLM with $l_2$ regularization  and with decimation, two variants of the PLM respectively introduced in Ref  \cite{Wainwright06} and \cite{Aurell12} for the inverse Ising problem  
    Here, we analyze these techniques for continuous $XY$ spins and we test them on thermalized data generated by Exchange Monte Carlo numerical simulations of the original model dynamics  In Sec  \ref{sec:res_reg} we  present the results related to the PLM-$l_2$  In Sec  \ref{sec:res_dec} the results related to the PLM with decimation are reported and its performances are compared to the PLM-$l_2$ and to a variational mean-field method analyzed in Ref  \cite{Tyagi15}  In Sec  \ref{sec:conc}, we outline conclusive remarks and perspectives 

        \section{The leading $XY$ model}
      \label{sec:model}
 The leading model we are considering is defined, for a system of $N$ angular $XY$ variables, by the Hamiltonian 
 \begin{equation}
  \mathcal{H} = - \sum_{ik}^{1,N} J_{ik} \cos{\left(\phi_i-\phi_k\right)} 
  \label{eq:HXY}
 
  \end{equation} 
  
  The $XY$ model is well known in statistical mechanics, displaying important physical
  insights, starting from the Berezinskii-Kosterlitz-Thouless
  transition in two dimensions\cite{Berezinskii70,Berezinskii71,Kosterlitz72} and moving to, e g , the
  transition of liquid helium to its superfluid state \cite{Brezin82}, the roughening transition of the interface of a crystal in equilibrium with its vapor \cite{Cardy96}  In presence of disorder and frustration \cite{Villain77,Fradkin78} the model has been adopted to describe synchronization problems as the Kuramoto model \cite{Kuramoto75} and in the theoretical modeling of Josephson junction arrays \cite{Teitel83a,Teitel83b} and arrays of coupled lasers \cite{Nixon13} 
  Besides several derivations and implementations of the model in quantum and classical physics, equilibrium or out of equilibrium, ordered or fully frustrated systems, Eq  (\ref{eq:HXY}), in its generic form,
  has found applications also in other fields  A rather fascinating example being the behavior of starlings flocks  \cite{Reynolds87,Deneubourg89,Huth90,Vicsek95, Cavagna13} 
  Our interest on the $XY$ model resides, though, in optics  Phasor and phase models with pairwise and  multi-body interaction terms can, indeed, describe the behavior of electromagnetic modes in both linear and nonlinear optical systems in the analysis of problems such as light propagation and lasing \cite{Gordon02, Antenucci15c, Antenucci15d}  As couplings are strongly frustrated, these models turn out to be especially useful to the study of optical properties in random media \cite{Antenucci15a,Antenucci15b}, as in the noticeable case of random lasers \cite{Wiersma08,Andreasen11,Antenucci15e}  and they might as well be applied to linear scattering problems, e g , propagation of waves in opaque systems or disordered fibers  
  
  
  \subsection{A propagating wave model}
  We briefly mention a derivation of the model as a proxy for the propagation of light through random linear media  
 Scattering of light is held responsible to obstruct our view and make objects opaque  Light rays, once that they enter the material, only exit  after getting scattered multiple times within the material  In such a disordered medium, both the direction and the phase of the propagating waves are random  Transmitted light 
 yields a disordered interference pattern typically  having low intensity, random phase and almost no resolution, called a speckle  Nevertheless, in recent years it has been realized that disorder is rather a blessing in disguise \cite{Vellekoop07,Vellekoop08a,Vellekoop08b}  Several experiments have made it possible to control the behavior of light and other optical processes in a given random disordered medium,  
 by exploiting, e g ,  the tools developed for wavefront shaping to control the propagation of light and to engineer the confinement of light \cite{Yilmaz13,Riboli14} 
 \\
 \indent
 In a linear dielectric medium, light propagation can be described through a part of the scattering matrix, the transmission matrix $\mathbb{T}$, linking the outgoing to the incoming fields  
 Consider the case in which there are $N_I$ incoming channels and $N_O$ outgoing ones; we can indicate with $E^{\rm in,out}_k$ the input/output electromagnetic field phasors of channel $k$  In the most general case, i e , without making any particular assumptions on the field polarizations, each light mode and its polarization polarization state can be represented by means of the $4$-dimensional Stokes vector  Each $ t_{ki}$ element of $\mathbb{T}$, thus, is a $4 \times 4$ M{\"u}ller matrix  If, on the other hand, we know that the source is polarized and the observation is made on the same polarization, one can use a scalar model and adopt Jones calculus \cite{Goodman85,Popoff10a,Akbulut11}:
   \begin{eqnarray}
 E^{\rm out}_k = \sum_{i=1}^{N_I}  t_{ki} E^{\rm in}_i \qquad \forall~ k=1,\ldots,N_O
 \label{eq:transm}
 \end{eqnarray}
  We recall that the elements of the transmission matrix are random complex coefficients\cite{Popoff10a}  For the case of completely unpolarized modes, we can also use a scalar model similar to Eq  \eqref{eq:transm}, but whose variables are  the intensities of the outgoing/incoming fields, rather than the fields themselves \\ 
In the following, for simplicity, we will consider Eq  (\ref{eq:transm}) as our starting point,
where $E^{\rm out}_k$, $E^{\rm in}_i$ and $t_{ki}$ are all complex scalars  
If Eq  \eqref{eq:transm} holds for any $k$, we can write:
  \begin{eqnarray}
  \int \prod_{k=1}^{N_O} dE^{\rm out}_k \prod_{k=1}^{N_O}\delta\left(E^{\rm out}_k - \sum_{j=1}^{N_I}  t_{kj} E^{\rm in}_j \right) = 1
  \nonumber
  \\
  \label{eq:deltas}
  \end{eqnarray}

 Observed data are a noisy representation of the true values of the fields  Therefore, in inference problems it is statistically more meaningful to take that noise into account in a probabilistic way, 
 rather than looking  at the precise solutions of the exact equations (whose parameters are unknown)  
 To this aim we can introduce Gaussian distributions whose limit for zero variance are the Dirac deltas in Eq  (\ref{eq:deltas}) 
 Moreover, we move to consider the ensemble of all possible solutions of Eq  (\ref{eq:transm}) at given $\mathbb{T}$, looking at  all configurations of input fields  We, thus, define the function:
 
   \begin{eqnarray}
  Z &\equiv &\int_{{\cal S}_{\rm in}} \prod_{j=1}^{N_I}  dE^{\rm in}_j \int_{{\cal S}_{\rm out}}\prod_{k=1}^{N_O} dE^{\rm out}_k 
  \label{def:Z}
\\
    \times
  &&\prod_{k=1}^{N_O}
   \frac{1}{\sqrt{2\pi \Delta^2}}  \exp\left\{-\frac{1}{2 \Delta^2}\left|
  E^{\rm out}_k -\sum_{j=1}^{N_I}  t_{kj} E^{\rm in}_j\right|^2
\right\} 
\nonumber
 \end{eqnarray}
   We stress that the integral of Eq  \eqref{def:Z} is not exactly a Gaussian integral  Indeed, starting from Eq  \eqref{eq:deltas}, two constraints on the electromagnetic field intensities must be taken into account  

  The space of solutions is  delimited by the total power ${\cal P}$ received by system, i e , 
  ${\cal S}_{\rm in}: \{E^{\rm in} |\sum_k I^{\rm in}_k = \mathcal{P}\}$, also implying  a constraint on the total amount of energy that is transmitted through the medium, i  e , 
  ${\cal S}_{\rm out}:\{E^{\rm out} |\sum_k I^{\rm out}_k=c\mathcal{P}\}$, where the attenuation factor  $c<1$ accounts for total losses 
  As we will see more in details in the following, being interested in inferring the transmission matrix through the PLM, we can omit to explicitly include these terms in Eq  \eqref{eq:H_J} since they do not depend on $\mathbb{T}$ not adding any information on the gradients with respect to the elements of $\mathbb{T}$ 
  
 Taking the same number of incoming and outcoming channels, $N_I=N_O=N/2$, and  ordering the input fields in the first $N/2$ mode indices and the output fields in the last $N/2$ indices, we can drop the ``in'' and ``out'' superscripts and formally write $Z$  as a partition function
    \begin{eqnarray}
        \label{eq:z}
 && Z =\int_{\mathcal S} \prod_{j=1}^{N} dE_j \left(   \frac{1}{\sqrt{2\pi \Delta^2}} \right)^{N/2} 
 \hspace*{- 4cm} \exp\left\{
  -\frac{ {\cal H} [\{E\};\mathbb{T}] }{2\Delta^2}
  \right\}
  \\
&&{\cal H} [\{E\};\mathbb{T}] =
-  \sum_{k=1}^{N/2}\sum_{j=N/2+1}^{N} \left[E^*_j t_{jk} E_k + E_j t^*_{kj} E_k^* 
\right]
 \nonumber
\\
&&\qquad\qquad \qquad + \sum_{j=N/2+1}^{N} |E_j|^2+ \sum_{k,l}^{1,N/2}E_k
U_{kl} E_l^*
 \nonumber
 \\
 \label{eq:H_J}
 &&\hspace*{1 88cm } = - \sum_{nm}^{1,N} E_n J_{nm} E_m^*
 \end{eqnarray}
 where ${\cal H}$ is a real-valued function by construction, we have introduced the effective input-input coupling matrix
\begin{equation}
U_{kl} \equiv \sum_{j=N/2+1}^{N}t^*_{lj} t_{jk} 
 \label{def:U}
 \end{equation}
 and the whole interaction matrix reads (here $\mathbb{T} \equiv \{ t_{jk} \}$)
 \begin{equation}
 \label{def:J}
 \mathbb J\equiv \left(\begin{array}{ccc|ccc}
 \phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}\\
 \phantom{()}&-\mathbb{U} \phantom{()}&\phantom{()}&\phantom{()}&{\mathbb{T}}&\phantom{()}\\
\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}\\
 \hline
\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}\\
 \phantom{()}& \mathbb   T^\dagger&\phantom{()}&\phantom{()}& - \mathbb{I} &\phantom{()}\\
\phantom{a}&\phantom{a}&\phantom{a}&\phantom{a}&\phantom{a}&\phantom{a}\\
 \end{array}\right)
 \end{equation}
 
 Determining the electromagnetic complex amplitude configurations that minimize the {\em cost function} ${\cal H}$, Eq   (\ref{eq:H_J}),  means to maximize the overall distribution peaked around the solutions of the transmission Eqs  (\ref{eq:transm})  As the variance $\Delta^2\to 0$, eventually, the initial set of Eqs  (\ref{eq:transm}) are recovered  The ${\cal H}$ function, thus, plays the role of an Hamiltonian and  $\Delta^2$ the role of a noise-inducing temperature  The exact numerical problem corresponds to the zero temperature limit of the statistical mechanical problem  Working with real data, though, which are noisy, a finite ``temperature''
  allows for a better representation of the ensemble of solutions to the sets of equations of continuous variables  
  

  
  
  Now, we can express every phasor in Eq  \eqref{eq:z}  as $E_k = A_k e^{\imath \phi_k}$  As a working hypothesis we will consider the intensities $A_k^2$ as either homogeneous or as \textit{quenched} with respect to phases 
The first condition occurs, for instance, to the input intensities $|E^{\rm in}_k|$ produced by a phase-only spatial light modulator (SLM) with homogeneous illumination \cite{Popoff11} 
With \textit{quenched} here we mean, instead, that the intensity of each mode is the same for every solution of Eq  \eqref{eq:transm} at fixed $\mathbb T$ 
We stress that, including intensities in the model does not preclude the inference analysis but it is out of the focus of the present work and will be considered elsewhere  

If all intensities are uniform in input and in output, this amount to a constant rescaling for each one of the four sectors of matrix $\mathbb J$ in Eq  (\ref{def:J}) that will not change the properties of the matrices 
For instance, if the original transmission matrix is unitary, so it will be the rescaled one and the matrix $\mathbb U$ will be  diagonal 
Otherwise, if intensities are \textit{quenched}, i e , they can be considered as constants in Eq  (\ref{eq:transm}),
they are inhomogeneous with respect to phases  The generic Hamiltonian element will, therefore, rescale as 
  \begin{eqnarray}
  E^*_n J_{nm} E_m = J_{nm} A_n A_m e^{\imath (\phi_n-\phi_m)} \to J_{nm} e^{\imath (\phi_n-\phi_m)}
  \nonumber
  \end{eqnarray}
  and the properties of the original  $J_{nm}$ components are not conserved  in the rescaled one  In particular, we have no argument, anymore, to possibly set the rescaled $U_{nm}\propto \delta_{nm}$ 
  Eventually, we end up with the complex couplings $XY$ model, whose real-valued Hamiltonian is written as
 \begin{eqnarray}
  \mathcal{H}& = &  - \frac{1}{2} \sum_{nm} J_{nm} e^{-\imath (\phi_n - \phi_m)}  + \mbox{c c } 
    \label{eq:h_im}
\\    &=&  - \frac{1}{2} \sum_{nm} \left[J^R_{nm} \cos(\phi_n - \phi_m)+
  J^I_{nm}\sin (\phi_n - \phi_m)\right] 
  \nonumber
 \end{eqnarray}
where $J_{nm}^R$ and $J_{nm}^I$ are the real and imaginary parts of $J_{nm}$  Being $\mathbb J$  Hermitian, $J^R_{nm}=J^R_{mn}$ is symmetric and $J_{nm}^I=-J_{mn}^I$ is skew-symmetric 

\begin{comment}
\textcolor{red}{
F: comment about quenched:
I think that to obtain the XY model, it is not necessary that the intensities are strictly quenched (that is also a quite unfeasible situation, I guess) 
Indeed eq (2) does not deal with the dynamics of the modes, but just connect the in and out ones 
For this, what it is necessary to have the XY model, it is that the intensities are always the same on the different samples
(so that the matrix $t_{ij}$ is the same for different phase data)  If the intensities are fixed, then they can be incorporated in $t_{ij}$ and eq (2) can be written just for phases as described  \\
}
\end{comment}


  \section{Pseudolikelihood Maximization}
  \label{sec:plm}
The inverse problem consists in the reconstruction of the parameters $J_{nm}$ of the Hamiltonian, Eq  (\ref{eq:h_im})   
Given a set of $M$ data configurations of $N$ spins
 $\bm\sigma = \{ \cos \phi_i^{(\mu)},\sin \phi_i^{(\mu)} \}$, $i = 1,\dots,N$ and $\mu=1,\dots,M$, we want to \emph{infer} the couplings:
 \begin{eqnarray}
\bm \sigma  \rightarrow  \mathbb{J} 
\nonumber
 \end{eqnarray}
 With this purpose in mind,
 in the rest of this section we implement the working equations for the techniques used  
 In order to test our methods, we generate the input data, i e , the configurations, by Monte-Carlo simulations of the model 
 The joint probability distribution of the $N$ variables $\bm{\phi}\equiv\{\phi_1,\dots,\phi_N\}$, follows the Gibbs-Boltzmann distribution:
 \begin{equation}\label{eq:p_xy}
 P(\bm{\phi}) = \frac{1}{Z} e^{-\beta \mathcal{H\left(\bm{\phi}\right)}} \quad \mbox{ where } \quad Z = \int \prod_{k=1}^N d\phi_k  e^{-\beta \mathcal{H\left(\bm{\phi}\right)}}  
 \end{equation}
 and where we denote $\beta=\left( 2\Delta^2 \right)^{-1}$ with respect to Eq  (\ref{def:Z}) formalism 
 In order to stick to usual statistical inference notation, in the following we will rescale the couplings by a factor $\beta / 2$: $\beta J_{ij}/2 \rightarrow J_{ij}$  
 The main idea of the PLM is to work with the conditional probability distribution of one variable $\phi_i$ given all other variables, 
 $\bm{\phi}_{\backslash i}$:
 
  \begin{eqnarray}
	\nonumber
   P(\phi_i | \bm{\phi}_{\backslash i}) &=& \frac{1}{Z_i} \exp \left \{ {H_i^x (\bm{\phi}_{\backslash i})
  	\cos \phi_i + H_i^y (\bm{\phi}_{\backslash i}) \sin \phi_i } \right \}
	\\
 \label{eq:marginal_xy}
	&=&\frac{e^{H_i(\bm{\phi}_{\backslash i}) \cos{\left(\phi_i-\alpha_i(\bm{\phi}_{\backslash i})\right)}}}{2 \pi I_0(H_i)}
  \end{eqnarray}
  where $H_i^x$ and $H_i^y$ are defined as
   \begin{eqnarray}
   H_i^x (\bm{\phi}_{\backslash i})  &=& \sum_{j (\neq i)} J^R_{ij} \cos \phi_j  - \sum_{j  (\neq i) } J_{ij}^{I} \sin \phi_j \phantom{+  h^R_i} \label{eq:26} \\
   H_i^y  (\bm{\phi}_{\backslash i})  &=&  \sum_{j  (\neq i)} J^R_{ij}  \sin \phi_j  + \sum_{j  (\neq i) } J_{ij}^{I}   \cos \phi_j \phantom{ + h_i^{I} }\label{eq:27}
   \end{eqnarray}
and $H_i= \sqrt{(H_i^x)^2 + (H_i^y)^2}$, $\alpha_i = \arctan H_i^y/H_i^x$   and we introduced the modified Bessel function of the first kind:
  \begin{equation}
  \nonumber
   I_k(x) = \frac{1}{2 \pi}\int_{0}^{2 \pi} d \phi e^{x \cos{ \phi}}\cos{k \phi}
  \end{equation}
  
   Given $M$ observation samples $\bm{\phi}^{(\mu)}=\{\phi^\mu_1,\ldots,\phi^\mu_N\}$, $\mu = 1,\dots, M$, the
   pseudo-loglikelihood for the variable $i$ is given by the logarithm of Eq  (\ref{eq:marginal_xy}),
   \begin{eqnarray}
   \label{eq:L_i}
   L_i &=& \frac{1}{M}  \sum_{\mu = 1}^M  \ln P(\phi_i^{(\mu)}|\bm{\phi}^{(\mu)}_{\backslash i})
   \\
   \nonumber
   & =&  \frac{1}{M}  \sum_{\mu = 1}^M  \left[ H_i^{(\mu)} \cos( \phi_i^{(\mu)} - \alpha_i^{(\mu)}) - \ln  2 \pi I_0\left(H_i^{(\mu)}\right)\right] \,  
    \end{eqnarray}
The underlying idea of PLM is that an approximation of the true parameters of the model is obtained for values that maximize the functions $L_i$ 
The specific maximization scheme differentiates the different techniques 


   
   
   \subsection{PLM with $l_2$ regularization}
   Especially for the case of sparse graphs, it is useful to add a regularizer, which prevents the maximization routine to move towards high values of 
   $J_{ij}$ and $h_i$ without converging  We will adopt an $l_2$ regularization so that the Pseudolikelihood function (PLF) at site $i$  reads:
   \begin{equation}\label{eq:plf_i}
  {\cal L}_i = L_i
  - \lambda \sum_{i \neq j} \left(J_{ij}^R\right)^2 - \lambda \sum_{i \neq j} \left(J_{ij}^I\right)^2  
   \end{equation}
   with $\lambda>0$ 
   Note that the values of $\lambda$ have to be chosen arbitrarily, but not too large, in order not to overcome $L_i$ 
   The standard implementation of the PLM consists in maximizing each ${\cal L}_i$, for $i=1\dots N$, separately  The expected values of the couplings are then:
   \begin{equation}
   \{ J_{i j}^*\}_{j\in \partial i} :=  \mbox{arg max}_{ \{ J_{ij} \}}
    \left[{\cal L}_i\right]
   \end{equation}
   In this way, we obtain two estimates for the coupling $J_{ij}$, one from maximization of ${\cal L}_i$, $J_{ij}^{(i)}$, and another one from ${\cal L}_j$, say $J_{ij}^{(j)}$ 
    Since the original Hamiltonian of the $XY$ model is Hermitian, we know that the real part of the couplings is symmetric while the imaginary part is skew-symmetric  
   
     The final estimate for $J_{ij}$ can then be obtained  averaging the two results:
  
  
  
   \begin{equation}\label{eq:symm}
   J_{ij}^{\rm inferred} = \frac{J_{ij}^{(i)} + \bar{J}_{ij}^{(j)}}{2} 
   \end{equation}
   where with $\bar{J}$ we indicate the complex conjugate 
   It is worth noting that the pseudolikelihood $L_i$, Eq  \eqref{eq:L_i}, is characterized by the
   following properties: (i) the normalization term of Eq \eqref{eq:marginal_xy} can be
   computed analytically at odd with the {\em full} likelihood case that
   in general require a computational time which scales exponentially
   with the size of the systems; (ii) the $\ell_2$-regularized pseudolikelihood
   defined in Eq \eqref{eq:plf_i} is strictly concave (i e  it has a single
   maximizer)\cite{Ravikumar10}; (iii) it is consistent, i e  if $M$ samples are
   generated by a model $P(\phi | J*)$ the maximizer tends to $J*$
   for $M\rightarrow\infty$\cite{besag1975}  Note also that (iii) guarantees that  
   $|J^{(i)}_{ij}-J^{(j)}_{ij}| \rightarrow 0$ for $M\rightarrow \infty$ 
   In Secs  \ref{sec:res_reg}, \ref{sec:res_dec} 
   we report the results obtained and we analyze the performances of the PLM having taken the configurations from Monte-Carlo simulations of models whose details are known 
   

   
   \subsection{PLM with decimation}
   Even though the PLM with $l_2$-regularization allows to dwell the inference towards the low temperature region and in the low sampling case with better performances that mean-field methods, in some situations some couplings are overestimated and not at all symmetric  Moreover, in the technique there is the bias of the $l_2$ regularizer 
   Trying to overcome these problems, Decelle and Ricci-Tersenghi introduced a new method \cite{Decelle14}, known as PLM + decimation: the algorithm maximizes the sum of the $L_i$,
   \begin{eqnarray}
    {\cal L}\equiv \frac{1}{N}\sum_{i=1}^N \mbox{L}_i
    \end{eqnarray}  
    and, then, it recursively set to zero couplings which are estimated very small  We expect that as long as we are setting to zero couplings that are unnecessary to fit the data, there should be not much changing on ${\cal L}$  Keeping on with decimation, a point is reached where ${\cal L}$ decreases abruptly indicating  that relevant couplings are being decimated and under-fitting is taking place 
   Let us define  by $x$  the fraction of non-decimated couplings  To have a quantitative measure for the halt criterion of the decimation process, a tilted ${\cal L}$ is defined as,
   \begin{eqnarray}
  \mathcal{L}_t &\equiv& \mathcal{L}  - x \mathcal{L}_{\textup{max}} - (1-x) \mathcal{L}_{\textup{min}} \label{$t$PLF} 
   \end{eqnarray}
   where 
   \begin{itemize}
   \item $\mathcal{L}_{\textup{min}}$ is the pseudolikelyhood of a model with independent variables  In the XY case: $\mathcal{L}_{\textup{min}}=-\ln{2 \pi}$ 
   \item
   $\mathcal{L}_{\textup{max}}$ is the pseudolikelyhood in the fully-connected model and it is maximized over all the $N(N-1)/2$ possible couplings  
   \end{itemize}
   At the first step, when $x=1$, $\mathcal{L}$ takes value $\mathcal{L}_{\rm max}$ and  $\mathcal{L}_t=0$  On the last step, for an empty graph, i e , $x=0$, $\mathcal{L}$ takes the value $\mathcal{L}_{\rm min}$ and, hence, again $\mathcal{L}_t =0$  
   In the intermediate steps, during the decimation procedure, as $x$ is decreasing from $1$ to $0$, one observes firstly that $\mathcal{L}_t$ increases linearly and, then, it displays an abrupt decrease indicating that from this point on relevant couplings are being decimated\cite{Decelle14}  In Fig  \ref{Jor1-$t$PLF} we give an instance of this behavior for the 2D short-range XY model with ordered couplings  We notice that the maximum point of $\mathcal{L}_t$ coincides with the minimum point of the reconstruction error, the latter defined as 
   \begin{eqnarray}\label{eq:errj}
   \mbox{err}_J \equiv \sqrt{\frac{\sum_{i<j} (J^{\rm inferred}_{ij} -J^{\rm true}_{ij})^2}{N(N-1)/2}} \label{err}
   \end{eqnarray}
  We stress that the ${\cal L}_t$ maximum is obtained ignoring the underlying graph, while the err$_J$ minimum can be evaluated once the true graph has been reconstructed  
   
     \begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_tPLF_new eps}
   	\caption{The tilted likelyhood ${\cal L}_t$ curve and the reconstruction error vs the number of decimated couplings  for an ordered, real-valued J on 2D XY model with $N=64$ spins  The peak of ${\cal L}_t$ coincides with the dip of the error }  
   	\label{Jor1-$t$PLF}
   \end{figure} 
       
   
   In the next sections we will show the results obtained on the  $XY$ model analyzing the performances of the two methods and comparing them also with a mean-field method \cite{Tyagi15} 
   
  
    
   \section{Inferred couplings with PLM-$l_2$}
    \label{sec:res_reg}
    \subsection{$XY$ model with real-valued couplings}
    
    In order to obtain the vector of couplings, $J_{ij}^{\rm inferred}$ the function $-\mathcal{L}_i$ is minimized through the vector of derivatives ${\partial \mathcal{L}_i}/\partial J_{ij}$
Context 3: How Oxycontin, Florida and the Sackler Family Created the Opioid Crisis In America
Why are the Sacklers worth $13 billion today? Answer: “The Oxy Express Explained”
(MASS TORT NEXUS MEDIA)
A COMPARISON OF OXYCODONE PRESCRIBING
In the first six months of 2010, Ohio doctors and health care practitioners bought the second-largest number of oxycodone doses in the country at just under 1 million pills 
Florida doctors bought 40 8 million in the same period, the comparison is astounding, yet it flew under the DEA, Opioid Big Pharma and everyone elses radar for years and years 
Of the country’s top 50 oxycodone-dispensing clinics, 49 were in Florida  From August 2008 to November 2009, a new pain clinic opened in Broward and Palm Beach counties on average of every three days 
Pharmacies and distributors are at fault as well, pharmacies ordered jaw-dropping numbers of pills from opioid drug distributors, the middlemen between manufacturers and pharmacies 
90 of 100 of the nation’s top 100 oxy-buying doctors in 2010, were in Florida  49 of 50 of the country’s top oxy-dispensing clinics were in Florida  For some reason this didn’t raise an alarm or cause anyone to look further at the time 
Purdue Pharma New What Was Happening In Florida
Purdue and the Sacklers chose to ignore Florida, because apparently nobody there sued them or complained  In 2007, in other states, the infamous drug maker and three of its executives pled guilty in federal court and paid out $634 5 million in fines for purposefully misleading regulators, doctors, and patients about the addictiveness of their opioid painkiller  Around the same time, Purdue was also sued by several states, including Washington, over similar allegations  Purdue agreed to a $19 5 million multi-state settlement  And in 2015, Purdue settled a case with Kentucky, agreeing to pay $24 million 
As part of the state settlements, Purdue was supposed to set up monitoring programs to make sure that its opioid drug didn’t wind up in the wrong hands  It was supposed to watch out for shady pharmacies, unusually large orders, or suspiciously frequent orders  But on this front, Everett alleges that Purdue once again put profits over people 
Obviously, this was ignored as the Florida based “Oxy Expres”; rolled on for years and years with np input, comment or oversight by Purdue Pharma and the Sackler family other than “show me the money” and enjoying a life of luxury on the misery created and managed in the Purdue Pharma boardroom  But, the Purdue boardroom isn’t the only guilty “Opioid Big Pharma” industry player who designed and supported the opioid prescribing crisis 
For the current status of efforts to make Opioid Big Pharma accept responsibility in litigation filed in federal and state courts across the country, see: https://www masstortnexus com/Briefcases/254/OPIOID-CRISIS-BRIEFCASE-INCLUDING-MDL-2804-OPIATE-PRESCRIPTION-LITIGATION
Why Distributors Are Liable
Cardinal Health, one of the nation’s biggest distributors, sold two CVS pharmacies in Sanford a combined 3 million doses of oxycodone, flooding the town of 54,000 with an average of 250,000 oxycodone pills every month 
West of Jupiter, a Walgreens drug distribution center sold 2 2 million tablets to a single Walgreens’ pharmacy in tiny Hudson, a roughly six-month supply for each of its 12,000 residents  It shipped more than 1 1 million pills to each of two Fort Pierce Walgreens pharmacies 
For 40 days starting in late 2010, the distribution center shipped 3,271 bottles of oxycodone — 327,100 doses of the drug — to a Port Richey Walgreens pharmacy, prompting a distribution manager to ask: “How can they even house this many bottles?”
There were 53 million oxycodone prescriptions filled in 2013 by US pharmacies, according to NIDA  This translates to approximately one bottle of this addictive drug for every 6 people in the country  How was this not noticed by those responsible for monitoring narcotics prescribing in the United States?
Charts and Data On Florida’s Oxycontin Gold Mine
https://www documentcloud org/documents/3936665-Purdue-Pharma-1-in-48-Study html
https://www documentcloud org/documents/3534759-uS-Atty-on-Purdue-Settle html#document/p2/a384323
A Boardroom Contrived Opioid Epidemic
This is the pain chart created by the “Opioid Big Pharma Industry” to support massive over-prescribing of opioids across the country to everyone who walked in to a medical treatment facility, this was an effort to increase narcotic prescribing practices in mainstream medical care–and it worked very very well! This chart became a standard treatment assessment protocol tool across the country 
https://www documentcloud org/documents/3936646-DEA-NATL-DRUG-ASSESSMENT-2010 html#document/p51/a383739
HOW WEST VIRGINIA WAS TARGETED
It-Was-Raining-Opiates-How-drug-companies-submerged-West-Virginia-in-opioids-for-years
Reliably red on the political map, Huntington is a West Virginia town with a 182-year-old university, a storied football team and more than 100 churches 
It’s where Will Lockwood graduated from high school  It’s where he enrolled at Marshall University  It’s where he first tried OxyContin  By the time Lockwood entered Marshall, Detroit dealers were trickling into Huntington, selling OxyContin and pills with OxyContin’s active ingredient, oxycodone 
Even though Lockwood could step out his front door and get the drug, Detroit street dealers weren’t the preferred supplier, they were in Florida 
It may have been 1,000 miles away, but to Lockwood, getting OxyContin and oxycodone from Florida’s loosely regulated pain clinics “was legal, in a sense ”
Twice a month, different “crews” from Huntington crowded into vans and headed south to Palm Beach and Broward counties, home to more than 200 pill mills, the pain clinics where anyone with a fake ache and hard cash could walk out with pills and prescriptions 
After hitting a string of clinics, the Huntington crews drove back with “around 500 to 600 pills per person,” said Lockwood 
But it wasn’t just a few hundred pills  It was tens of thousands 
And it wasn’t just Huntington, The West Virginia vans were part of a nationwide caravan heading to South Florida  Cars bearing tags from Kentucky, Tennessee, the Carolinas, Virginia and Ohio crowded into one clinic parking lot after another, loading up on pills and prescriptions 
News stories and law enforcement focused on those “parking lot” states in Appalachia, where dealers and addicts with a tank of gas or a cheap plane ticket traveled the “Oxy Express” to Palm Beach and Broward 
But Florida’s pill pipeline reached far beyond those roadways 
By 2010, Florida was the oxycodone drug dealer of choice for drug users and dealers in the Great Lakes, Northeast and Mid-Atlantic regions as well as the Southeast, DEA records show, an area spanning virtually every state east of the Mississippi  It wasn’t just that Florida guaranteed a flow of cheap oxycodone  For 10 years, key lawmakers and agency heads repeatedly looked the other way as crooked doctors and bogus clinics flooded almost half the nation with the highly addictive drug 
In failing to crack down, Florida extended by years the amount of time highly addictive oxycodone would be available to both first-time experimenters and addicts  It gave criminals the raw materials for trafficking  It gave Will Lockwood the OxyContin needed to feed his growing habit, It paved the way for his eventual jump to heroin 
Jumping state lines
Teenage high-school wrestling buddies in New Port Richey ran oxycodone into Tennessee; they were paid with cash hidden in teddy bears  A Hillsborough County man mailed 17,000 pills to Glen Fork, W Va , a month’s supply for every man woman and child in the tiny town 
A Boston Chinatown crime boss trafficked pills from Sunrise into Massachusetts, New York, Rhode Island and South Carolina  Wellington twins and pill mill kingpins Paul and Phil George, brothers who oversaw one of the largest operations in the country from their five Palm Beach and Broward clinics, pushing oxycodone into Kentucky, Tennessee, Ohio and South Carolina 
A husband and wife team operating out of a Forest Hill Boulevard clinic funneled pills to Delaware  At Palm Beach International Airport, two federal security agents accepted $500 a pop each time they waved through thousands of pillsbound for Connecticut and New York 
A Palm Bay man’s Puerto Rican family bought local pills destined for the working class town of Holyoke, Mass  In Rhode Island, police pulled over a Lauderhill man caught speeding through Providence  They found 903 oxycodone tablets and 56 morphine pills in the car 
Senior citizen and Tulane business graduate Joel Shumrak funneled more than 1 million pills into eastern Kentucky from his South Florida and Georgia clinics, much of it headed for street sales — an estimated 20 percent of the illicit oxycodone in the entire state 
Van loads of pill-seekers organized by “VIP buyers” traveled from Columbus, Ohio, to three Jacksonville clinics, where armed guards handled crowd control (federal indictment) and doctors generated prescriptions totaling 3 2 million pills in six months  In Miami, Vinny Colangelo created 1,500 internet website names to entice drug users throughout the nation to one of his six South Florida pain clinics or pharmacies 
Even the Mafia got in on the Florida oxy express action: A Bonanno crime family associate oversaw a local crew stocking up on Palm Beach and Broward pain clinic oxycodone, upstreaming profits to the New York family 
At times, it seemed almost no section of the country was free of Florida-supplied pills: When Olubenga Badamosi was arrested driving his Bentley Continental in Miami in 2011, the Oregon man was one of two traffickers overseeing a crew smuggling South Florida oxycodone to sell in Salt Lake City, Seattle and Denver as well as Oregon, Nevada, Texas and even Alaska 
Pharmacy delivers oxy ‘pot of gold’
It would be hard to overstate Florida’s role in feeding the country’s voracious appetite for oxycodone  Oxycodone 30-milligram tablets were favored by addicts  And in 2009 and 2010, roughly four of every 10 of those pills were sold in Florida  Small wonder: Of the nation’s top 100 oxycodone-buying doctors, 90 were in Florida 
Pharmacies, too, ordered jaw-dropping numbers of pills from drug distributors, the middlemen between manufacturers and pharmacies 
West of Jupiter, a Walgreens drug distribution center sold 2 2 million tablets to a single Walgreens’ pharmacy in tiny Hudson, a roughly six-month supply for each of its 12,000 residents  It shipped more than 1 1 million pills to each of two Fort Pierce Walgreens pharmacies  By contrast, a single Walgreens pharmacy in the Central Florida townOviedo bought 169,700 doses of oxycodone in 30 days 
People on both sides of the counter knew what was going on: In a letter to the chief executive of Walgreens, Oviedo’s police chief warned that people were walking out of the town’s two Walgreens stores and selling their drugs on the spot, crushing and snorting them, or — still in the pharmacy’s parking lot — injecting them 
Why Pharmacies are LIABLE
In Fort Pierce, a Walgreens pharmacist accidentally provided an extra 120 oxycodone pills to a customer  When the druggist called to ask that the man return the pills, the customer’s girlfriend bluntly responded that he was an addict, that he sold oxycodone and the 120 pills were “a pot of gold,” DEA records show 
That was in September  The same man came back to the same Walgreens in December and January with a prescription in hand, and the pharmacy filled his prescriptions every time 
‘Wild West of Oxycodone Prescribing’
Cincinnati-based Masters Pharmaceuticals Inc  was a middling-sized drug distributor selling oxycodone to Florida pharmacies 
It sold to other customers in other states  But mostly, it sold to Florida: Oxycodone made up more than 60 percent of its drug sales in 2009 and 2010, according to federal records  Of its top 55 oxycodone customers, 44 were in Florida 
Company CEO Dennis Smith worried that the Florida-bound oxycodone was getting in the wrong hands  A trip to Broward did nothing to ease his mind  “It was,” he later testified, “the Wild West of oxycodone prescribing ”
Bus and park benches touted pain clinics  When Smith picked up and thumbed through City Beat, a free magazine, he found pages of ads for pain clinics  “It would show young people sitting around a pool and it named the pain clinic and say (sic) ‘we dispense on site,’ and that really hit home hard ”
Smith stopped selling to pain clinics  But the company continued to shovel millions of oxycodone pills to Florida pharmacies  Masters executives figured the pharmacies would keep an eye out for excessive prescriptions written by pill mill doctors  But not all pharmacies were worrying about doctors at pain clinics, many pharmacies were courting the pill mills prescribers 
A Lake Worth Family Pharmacy
In 2009, the small pharmacy off Lucerne Avenue in Lake Worth had a history  It had been in business for 43 years  The owner and head pharmacist had been there for 32  It had shaded parking and a downtown location, a stone’s throw from the City Hall Annex 
When a Masters inspector visited, he was alarmed to find Tru-Valu Drugs bustling with a long line of young, thin, tattooed customers arriving in groups of 10 to pick up pills  There were signs in the pharmacy warning of limits on the number of oxycodone pills handed out  Even Mallinckrodt Pharmaceuticals, an oxycodone manufacturer, was worried about the volume of its pill sales there 
Of the 300,000 doses of all drugs the small pharmacy dispensed in December 2008, 192,000 were for oxycodone 30 mg, the dosage preferred by traffickers and users alike 
The huge oxycodone volume was no accident  The owner and head pharmacist, unidentified in DEA records, told a Masters inspector that the pharmacy “has pushed for this (narcotic) business with many of the area pain doctors ”
And, despite the torrent of oxycodone going out the door, the pharmacy owner expressed frustration that drug distributors were limiting the amount of narcotics they would sell to his now-closed pharmacy 
Ohio to Florida and Back
Pharmacy after pharmacy benefited from the combination of Masters’ Ohio oxycodone business and Florida’s unregulated pill mills 
In Englewood, north of Fort Myers, the pharmacy owner filled prescriptions for six pain clinics — including clinics an hour’s drive away  A Masters inspector found cars from Tennessee and Kentucky in the parking lot and young men leaving the pharmacy carrying large trash bags 
Superior Pharmacy not only filled oxycodone prescriptions for pain clinics, it shared waiting room space with a pain clinic in a Temple Terrace strip mall outside Tampa  Neither Masters nor Superior had so much as Googled the background of pain clinic doctors writing those prescriptions, the DEA later said 
Had they done so, the DEA dryly noted, they “would likely have come across a press release” announcing one of the doctors had been arrested and charged with trafficking in prescription drugs 
Hundreds of thousands of oxycodone pills were sent from Ohio distributors to Florida pharmacies  Unknown thousands of pills headed right back up to Ohio 
When Ohio police burst into Christopher Thompson’s home outside Columbus, they found an assault rifle, $80,000 in cash and oxycodone from his Florida deals  A construction worker whose own pill habit started at age 14, Thompson oversaw a ring of 15 Ohio buyers who traveled to Florida to pick up oxycodone to resell in Central Ohio 
Two hours to the west in Martin’s Ferry, David L  Kidd orchestrated a ring of buyers traveling to West Palm Beach and Central Florida to pick up oxycodone for resale on the streets of eastern Ohio and West Virginia 
Doctors and pharmacies from Florida were complicit with Kidd’s ring in fueling Ohio’s opioid epidemic, wrote the U S  attorney for West Virginia after Kidd’s 2011 arrest: “The steady flow of pain pills into the Ohio Valley from Florida must stop ”
Driving To Pick Up Death By Rx
With more drugs came more deaths, in January 2010, say police, Fort Lauderdale pathologist Dr  Lynn Averill started a seven-month oxycodone shopping spree, buying 437,880 oxycodone pills from drug distributors 
The same month, Matthew Koutouzis drove from Toms River, N J , to see Averill in her Broward County pain clinic  The 26-year-old collected prescriptions for 390 pills and overdosed two days later  Brian Moore traveled 13 hours from his Laurel County, Ky , home to see Averill  He left with prescriptions for 600 pills and also overdosed within 48 hours 
Kenneth Hammond didn’t make it back to his Knoxville, Tenn , home  He had a seizure after picking up prescriptions for 540 pills and died in an Ocala gas station parking lot 
Keith Konkol didn’t make it back to Tennessee, either  His body was dumped on the side of a remote South Carolina road after he overdosed in the back seat of a car the same day of his clinic visit  He had collected eight prescriptions totaling 720 doses of oxycodone, methadone, Soma and Xanax  Konkol had every reason to believe he would get those prescriptions: In three previous visits to the Plantation clinic, he had picked up prescriptions for 1,890 pills 
An estimated 60 percent of her patients were from out of state, a former medical assistant told the DEA  In 2015, Averill pleaded not guilty to eight manslaughter charges  She is awaiting trial in Broward County  Averill was just one doctor at just one clinic  In 2010, the year Averill’s patients overdosed, Florida received applications to open 1,026 more pain clinics 
An online message board advising drug users summed it up: “Just go anywhere in South Florida and look for a ‘pain management clinic ’ It shouldn’t be too hard; you can’t swing a dead cat without hitting one ” Complain about anything from a back injury to a hangnail, it advised, “and they’ll set you right up ”
By this time, Kentucky had reined in its pill mills  It didn’t matter, Ohio, Delaware, North Carolina, Connecticut acted as well, but other state’s efforts didn’t matter either, Florida continued ignoring the pill mills and rogue doctors feeding the nation’s oxycodone habit, the pills flowed 
“There were folks down there, where if I had an opportunity to, get my hands around their throat, I would have wrung their neck,” said Huntington Mayor Steve Williams  On Florida’s inaction he stated, “There was total evidence as to what was happening  It lays at the foot, in my opinion, of the public officials there that allowed it to continue on ”
Governor Jeb Bush Backed A Solution
One of the first dinners Florida Gov  Jeb Bush hosted after moving into the governor’s mansion in 1999 was a small one  Among those sitting at the table with Bush were Lt  Gov  Toni Jennings, state Sen  Locke Burt and James McDonough, who would become the state’s hard-nosed drug czar  There was an urgent topic on the agenda that night: the explosion of prescription painkillers  For the state’s first family, it may have been personal  Bush had talked publicly about one of his children’s struggle with addiction 
By the time the meal ended, all had agreed on the need for establishing a prescription drug monitoring program that would collect information and track prescriptions written for controlled substances, such as oxycodone 
Absent a prescription drug monitoring database, there was no way to know whether someone was “doctor shopping,” going from doctor to doctor, getting more and more prescriptions to feed their habit 
And there was no way to know whether a doctor was overprescribing, key to pinpointing whether a pill mill was operating, and where  Similar databases had been adopted by more than a dozen states  It was being described as a “silver bullet” to curb overprescribing  Soon enough, $2 million to get the database up and running would be on the table — but it came with a catch 
Florida Attorney General Misfires Against Purdue
In 2001, OxyContin-maker Purdue Pharma was fending off early criticism of its blockbuster painkiller  At issue was whether Purdue’s aggressive marketing campaign had misled doctors and patients alike  Purdue and three top executives later pleaded guilty to federal charges of illegally marketing the drug



ground_truth: The longerons bow up from the building surface, forming a "banana" shape.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does the performance of the PLM with decimation compare to other methods?

Read the following text and answer briefly.

Context 2:  The process is repeated for all the couplings obtaining then a fully connected adjacency matrix  The results here presented are obtained with $\lambda = 0 01$ 
   For the minimization we have used the MATLAB routine \emph{minFunc\_2012}\cite{min_func}  
      
      \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor11_2D_l2_JR_soJR_TPJR}
    	\caption{Top panels: instances of single site coupling reconstruction for the case of $N=64$ XY spins on a 2D lattice with ordered $J$ (left column) and bimodal distributed $J$ (right column)  
    	
    	Bottom panels: sorted couplings }
    	\label{PL-Jor1}
    \end{figure}

   
To produce the data by means of numerical Monte Carlo simulations a system with $N=64$  spin variables  is considered on a deterministic 2D lattice with periodic boundary conditions  
Each spin has then connectivity $4$, i e , we expect to infer an adjacency matrix with $N c = 256$ couplings different from zero  
The dynamics of the simulated model is based on the Metropolis algorithm and parallel tempering\cite{earl05} is used to speed up the thermalization of the system 
The thermalization is tested looking at the average energy over logarithmic time windows and
the acquisition of independent configurations
starts only after the system is well thermalized 

   For the values of the couplings we considered two cases: an ordered case, indicated in the figure as  $J$ ordered (e g , left column of Fig  \ref{PL-Jor1}) where the couplings can take values $J_{ij}=0,J$, with $J=1$, 
   and a quenched disordered case, indicated in the figures as  $J$ disordered (e g , right column of Fig  \ref{PL-Jor1})
   where the couplings can take also  negative values, i e , 
    $J_{ij}=0,J,-J$, with a certain probability   The results here presented were obtained with bimodal distributed $J$s: 
   
    $P(J_{ij}=J)=P(J_{ij}=-J)=1/2$   The performances of the PLM have shown not to depend on $P(J)$  
   
    We recall that in Sec  \ref{sec:plm} we used the temperature-rescaled notation, i e , $J_{ij}$ stands for $J_{ij}/T$  
   
    To analyze the performances of the PLM, in Fig  \ref{PL-Jor1} the inferred couplings, $\mathbb{J}^R_{\rm inf}$, are shown on top of the original couplings,  $\mathbb{J}^R_{\rm true}$ 
     The first figure (from top) in the left column shows  the $\mathbb{J}^R_{\rm inf}$ (black) and the $\mathbb{J}^R_{\rm tru}$ (green) for a given spin
     at temperature $T/J=0 7$ and number of samples  $M=1024$  PLM appears to reconstruct the correct couplings, though zero couplings are always given a small inferred non-zero value  
     In the left column of Fig   \ref{PL-Jor1},  both the $\mathbb{J}^R_{\rm{inf}}$ and the $\mathbb{J}^R_{\rm{tru}}$ are sorted in decreasing order and plotted on top of each other  
     We can clearly see that $\mathbb{J}^R_{\rm inf}$ reproduces the expected step function  Even though the jump is smeared, the difference between inferred couplings corresponding to the set of non-zero couplings 
     and to the set of zero couplings can be clearly appreciated 
     Similarly, the plots in the right column of Fig  \ref{PL-Jor1} show the results obtained for the case with  bimodal disordered couplings, for the same working temperature and number of samples  
     In particular, note that the algorithm infers half positive and half negative couplings, as expected 
     
     
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{Jor11_2D_l2_errJ_varT_varM}
\caption{Reconstruction error $\mbox{err}_J$, cf  Eq  (\ref{eq:errj}), plotted as a function of temperature (left) for three values of the number of samples $M$ and  as a function $M$ (right) for three values of temperature in the ordered system, i e , $J_{ij}=0,1$  
The system size is $N=64$ }
\label{PL-err-Jor1}
\end{figure}

In order to analyze the effects of the number of samples and of the temperature regimes, we plot in Fig  \ref{PL-err-Jor1} the reconstruction error, Eq  (\ref{err}), as a function of temperature for three different sample sizes $M=64,128$ and $512$  
The error is seen to sharply rise al low temperature, incidentally, in the ordered case, for  $T<T_c \sim 0 893$, which is the Kosterlitz-Thouless transition temperature of the 2XY model\cite{Olsson92}  
 However, we can see that if only $M=64$ samples are considered, $\mbox{err}_J$ remains high independently on the working temperature  
 In the right plot of Fig  \ref{PL-err-Jor1},  $\mbox{err}_J$ is plotted as a function of $M$ for three different working temperatures $T/J=0 4,0 7$ and $1 3$  As we expect, 
 $\mbox{err}_J$  decreases as $M$ increases  This effect was observed also with mean-field inference techniques on the same model\cite{Tyagi15} 

To better understand the performances of the algorithms, in Fig  \ref{PL-varTP-Jor1} we show several True Positive (TP) curves obtained for various values of $M$ at three different temperatures $T$  As $M$ is large and/or temperature is not too small,  we are able to reconstruct correctly all the couplings present in the system (see bottom plots) 
The True Positive curve displays how many times the inference method finds a true link of the original network  as a function of the index of the vector of sorted absolute value of reconstructed couplings $J_{ij}^{\rm inf}$  
The index $n_{(ij)}$ represents the related spin couples $(ij)$  The TP curve is obtained as follows: 
first  the values $|J^{\rm inf}_{ij}|$ are sorted in descending order and  the spin pairs $(ij)$ are ordered according to the sorting position of $|J^{\rm inf}_{ij}|$  Then,
     	a cycle over the ordered set of pairs $(ij)$, indexed by $n_{(ij)}$, is performed, comparing with the original network coupling $J^{\rm true}_{ij}$ and verifying whether it is zero or not  The true positive curve is computed as
\begin{equation}
\mbox{TP}[n_{(ij)}]= \frac{\mbox{TP}\left[n_{(ij)}-1\right] (n_{ij}-1)+ 1 -\delta_{J^{\rm true}_{ij},0}}{n_{(ij)}}
\end{equation}
As far as $J^{\rm true}_{ij} \neq 0$, TP$=1$  As soon as the true coupling of a given $(ij)$ couple in the sorted list is zero, the TP curve departs from one  
In our case, where the connectivity per spin of the original system is  $c=4$ and there are $N=64$ spins, we know that we will have  $256$ non-zero couplings   
     	If the inverse problem is successful, hence, we expect a steep decrease of the TP curve when  $n_{ij}=256$ is overcome 

In Fig  \ref{PL-varTP-Jor1}
it is  shown that,  almost independently of $T/J$, the TP score improves as $M$ increases  Results are plotted for three different temperatures, $T=0 4,1$ and $2 2$, with increasing number of samples $M = 64, 128,512$ and $1024$ (clockwise)  
We can clearly appreciate the improvement in temperature if the size of the data-set is not very large: for small $M$, $T=0 4$ performs better  
When $M$ is high enough (e g , $M=1024$), instead, the TP curves do not appear to be strongly influenced by the temperature 

\begin{figure}[t!]
	\centering
	\includegraphics[width=1\linewidth]{Jor11_2D_l2_TPJR_varT_varM}
	\caption{TP  curves  for 2D short-range ordered $XY$ model with $N=64$ spins at three different values of $T/J$ with increasing - clockwise from top - $M$ }
	\label{PL-varTP-Jor1} 
\end{figure} 

\subsection{$XY$ model with complex-valued couplings}
For the complex $XY$ we have to contemporary  infer $2$ apart coupling matrices,  $J^R_{i j}$ and $J^I_{i j}$   As before, a system of $N=64$ spins is considered on a 2D lattice 
For the couplings we have considered both ordered and bimodal disordered cases 
In Fig  \ref{PL-Jor3}, a single row of the matrix $J$ (top) and the whole sorted couplings (bottom) are displayed for the ordered model (same legend as in Fig  \ref{PL-Jor1}) for the real, $J^R$ (left column), and the imaginary part, $J^I$   

\begin{figure}[t!]
	\centering
\includegraphics[width=1\linewidth]{Jor3_l2_JRJI_soJRJI_TPJRJI}
	\caption{Results related to the ordered complex XY model with $N=64$ spins on a  2D lattice  Top: instances of  single site reconstruction for the real, JR (left column), and
		the imaginary, JI (right column), part of $J_{ij}$  Bottom: sorted values of JR (left) and JI (right) }
		
	\label{PL-Jor3}
\end{figure}
 
 
  \section{PLM with Decimation}
 \label{sec:res_dec}
 

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_tPLF_varT_varM}
    	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted as a function of decimated couplings  Top: Different ${\cal L}_t$ curves obtained for different values of $M$ plotted on top of each other  Here $T=1 3$  The black line indicates the expected number of decimated couplings, $x^*=(N (N-1) - N c)/2=1888$  As we can see, as $M$ increases, the maximum point of ${\cal L}_t$ approaches $x^*$  Bottom: Different ${\cal L}_t$ curves obtained for different values of T with $M=2048$  We can see that, with this value of $M$, no differences can be appreciated on the maximum points of the different  ${\cal L}_t$ curves }
   	\label{var-$t$PLF}
   \end{figure}

\begin{figure}[t!]
    \centering
    \includegraphics[width=1\linewidth]{Jor1_dec_tPLF_peak_statistics_varM_prob eps}
    	\caption{Number of most likely decimated couplings, estimated by the maximum point of $\mathcal{L}_t$, as a function of the number of samples $M$  We can clearly see that the maximum point of $\mathcal{L}_t$ tends toward $x^*$, which is the right expected number of zero couplings in the system }  
    	\label{PLF_peak_statistics}
    \end{figure}
      
      For the ordered real-valued XY model we show in Fig  \ref{var-$t$PLF}, top panel, the outcome on the tilted pseudolikelyhood, $\mathcal{L}_t$ Eq  \eqref{$t$PLF}, of the progressive decimation: from a fully connected lattice  down to an empty lattice  The figure shows the behaviour of $\mathcal{L}_t$ for three different data sizes $M$  A clear data size dependence of the maximum point of  $\mathcal{L}_t$, signalling the most likely value for decimation, is shown  For small $M$ the most likely number of  couplings is overestimated and for increasing $M$ it tends to the true value, as displayed in Fig  \ref{PLF_peak_statistics}   In the bottom panel of Fig  \ref{var-$t$PLF} we display instead different 
 $\mathcal{L}_t$ curves obtained for three different values of $T$ 
  Even though the values of $\mathcal{L}_t$ decrease with increasing temperature, the value of the most likely number of decimated couplings appears to be quite independent on $T$ with $M=2048$ number of samples 
In Fig  \ref{fig:Lt_complex} we eventually display the tilted pseudolikelyhood for a 2D network with complex valued ordered couplings, where the decimation of the real and imaginary coupling matrices proceeds in parallel, that is, 
when a real coupling is small enough to be decimated its imaginary part is also decimated, and vice versa 
One can see that though the apart errors for the real and imaginary parts are different in absolute values, they display the same dip, to be compared with the maximum point of $\mathcal{L}_t$ 
     
       \begin{figure}[t!]
    	\centering
      	\includegraphics[width=1\linewidth]{Jor3_dec_tPLF_new}
      	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted with the reconstruction errors for the XY model with $N=64$ spins on a 2D lattice  These results refer to the case of  ordered and complex valued couplings  The full (red) line indicates ${\cal L}_t$  The dashed (green) 
      		and the dotted (blue) lines show the reconstruction errors (Eq  \eqref{eq:errj}) obtained for the real and the imaginary couplings respectively  We can see that both ${\rm err_{JR}}$ and ${\rm err_{JI}}$ have a minimum at $x^*$ }
          	\label{fig:Lt_complex}
    \end{figure}

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_JR_soJR_TPJR}
   	\caption{XY model on a 2D lattice with $N=64$ sites and real valued couplings  The graphs show the inferred (dashed black lines) and true couplings (full green lines) plotted on top of each other  The left and right columns refer to the
   		 cases of ordered and bimodal disordered couplings, respectively  Top figures: single site reconstruction, i e , one row of the matrix $J$  Bottom figures: couplings are plotted sorted in descending order }  
   	\label{Jor1_dec}
   \end{figure}
   
\begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor3_dec_JRJI_soJRJI_TPJRJI}
    	\caption{XY model on a 2D lattice with $N=64$ sites and ordered complex-valued couplings 
    		The inferred and true couplings are plotted on top of each other  The left and right columns show the real and imaginary parts, respectively, of the couplings  Top figures refer to a single site reconstruction, i e , one row of the matrix $J$  Bottom figures report the couplings sorted in descending order }
    	\label{Jor3_dec}
    \end{figure}
    
       







       \begin{figure}[t!]
     	\centering
     	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_TPJR_varT}
     	\caption{True Positive curves obtained with the three techniques: PLM with decimation, (blue) dotted line,  PLM with $l_2$ regularization, (greed) dashed line, and mean-field, (red) full line   These results refer to real valued ordered couplings with $N=64$ spins on a 2D lattice  The temperature is here $T=0 7$ while the four graphs refer to different sample sizes: $M$ increases clockwise }
     	\label{MF_PL_TP}
     \end{figure}
    
    \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_errJ_varT_varM}
    	\caption{Variation of reconstruction error, ${\rm err_J}$, with respect to temperature as obtained with the three different techniques, see Fig  \ref{MF_PL_TP}, for four different sample size:  clockwise from top   $M=512,1024, 2048$ and $4096$ } 
    	\label{MF_PL_err}
    \end{figure}
    
     Once the most likely network has been identified through the decimation procedure, we perform the same analysis displayed in Fig  \ref{Jor1_dec}  for ordered and then quenched disordered real-valued couplings
and in Fig  \ref{Jor3_dec} for  complex-valued ordered couplings   In comparison to the results shown in Sec  \ref{sec:res_reg},
  the PLM with decimation leads to rather cleaner results  In Figs  \ref{MF_PL_err} and \ref{MF_PL_TP} we compare the performances of the PLM with decimation in respect to ones of the PLM with $l_2$-regularization  These two techniques are also analysed in respect to a mean-field technique previously implemented on the same XY systems\cite{Tyagi15} 
  
    For what concerns the network of connecting links, in Fig  \ref{MF_PL_TP} we compare the TP curves obtained with the three techniques  The results refer to the case of ordered and real valued couplings, but similar behaviours were obtained for the other cases analysed  
  The four graphs are related to different sample sizes, with $M$ increasing clockwise  When $M$ is high enough, all techniques reproduce the true network  
  However, for lower values of $M$ the performances of the PLM with $l_2$ regularization and with decimation drastically overcome those ones of the previous mean field technique  
  In particular, for $M=256$ the PLM techniques still reproduce the original network while the mean-field method fails to find more than half of the couplings  
  When $M=128$, the network is clearly reconstructed only through the PLM with decimation while the PLM with $l_2$ regularization underestimates the couplings  
  Furthermore, we notice that the PLM method with decimation is able to clearly infer the network of interaction even when $M=N$ signalling that it could be considered also in the under-sampling regime $M<N$   
 
 
In Fig  \ref{MF_PL_err} we compare the temperature behaviour of the reconstruction error 
In can be observed that for all temperatures and for all sample sizes  the reconstruction error, ${\rm err_J}$, (plotted here in log-scale) obtained with the PLM+decimation is always smaller than 
that one obtained with the other techniques  The temperature behaviour of ${\rm err_J}$ agrees with the one already observed for Ising spins in \cite{Nguyen12b} and for XY spins  in \cite{Tyagi15} with a mean-field approach:  ${\rm err_J}$ displays a minimum around $T\simeq 1$ and then it increases for very lower $T$; however,
 the error obtained with the PLM with decimation is several times smaller  than the error estimated by the other methods 



 
 

     
     \section{Conclusions}
     \label{sec:conc}


Different statistical inference methods have been applied to the inverse problem of the XY model 
After a short review of techniques based on pseudo-likelihood and their formal generalization to the model we have tested their performances against data generated by means of Monte Carlo numerical simulations of known instances
with diluted, sparse, interactions 

The main outcome is that the best performances are obtained by means of the  pseudo-likelihood method combined with decimation  Putting to zero (i e , decimating) very weak bonds, this technique turns out to be very precise for  problems whose real underlying interaction network is sparse, i e , the number of couplings per variable does not scale with number of variables 
The PLM + decimation method is compared to the PLM + regularization method, with $\ell_2$ regularization and to a mean-field-based method  The behavior of the quality of the network reconstruction is analyzed by looking at the overall sorted couplings and at the single site couplings, comparing them with the real network, and at the true positive curves in all three approaches  In the PLM +decimation method, moreover, the identification of the number of decimated bonds at which the tilted pseudo-likelihood is maximum allows for a precise estimate of the total number of bonds  Concerning this technique, it is also shown that the network with the most likely number of bonds is also the one of least reconstruction error, where not only the prediction of the presence of a bond is estimated but also its value 

The behavior of the inference quality in temperature and in the size of data samples is also investigated, basically confirming the low $T$ behavior hinted by Nguyen and Berg \cite{Nguyen12b} for the Ising model  In temperature, in particular, the reconstruction error curve displays a minimum at a low temperature, close to the critical point in those cases in which a critical behavior occurs, and a sharp increase as temperature goes to zero  The decimation method, once again, appears to enhance this minimum of the reconstruction error of almost an order of magnitude with respect to other methods 
 
The techniques displayed and the results obtained in this work can be of use in any of the many systems whose theoretical representation is given by Eq  \eqref{eq:HXY} or Eq  \eqref{eq:h_im}, some of which are recalled in Sec  \ref{sec:model}  In particular, a possible application can be the field of light waves propagation through random media and the corresponding problem of the  reconstruction of an object seen through an opaque medium or a disordered optical fiber \cite{Vellekoop07,Vellekoop08a,Vellekoop08b, Popoff10a,Akbulut11,Popoff11,Yilmaz13,Riboli14} 

 	
Context 3:  Far from being safe and non-addictive, OxyContin carried the same addiction risk as morphine, and was every bit as potent 
But that was six years away  In 2001, towns in Maine reported an alarming uptick in crime tied to OxyContin  The first of several congressional hearings was ramping up  Critics and parents who lost children were piling on  Reporters were starting to write stories 
In November, Florida Attorney General Bob Butterworth appeared poised to take on the company  Calling OxyContin street sales “a major threat to public health,” Butterworth told a state Board of Medicine committee that Purdue should consider temporarily taking the drug off the market  It wasn’t only traffickers concerning Butterworth  It was the sales pitch 
In late 2001, Butterworth called a young assistant attorney general into his office and gave him a magazine article on OxyContin and an assignment: Look into Purdue marketing  Former Florida Attorney General Bob Butterworth and Palm Beach County State Attorney Dave Aronberg  The young lawyer, now-Palm Beach County State Attorney Dave Aronberg, said he knew nothing about OxyContin  But he didn’t like what he read 
During the yearlong inquiry, 589 Floridians died after taking oxycodone  Nothing criminal was found, Aronberg later said  Instead, Butterworth and Purdue struck a settlement  As part of a $2 million deal, Purdue would pay to establish a prescription monitoring database, the same silver bullet sought by Bush  After Florida’s computerized system was up and running, the same system would be free to any other state  The entire country, not just Florida, would benefit 
It could have been a groundbreaking deal  There was one catch  State lawmakers had to vote to create the prescription monitoring program by 2004, or Purdue would keep its money 
Marco Rubio Kills The Anti-Oxy Rx Bill
A political gight killed the program  “And there was one person who was responsible,” said former state Sen  Burt, now an Ormond Beach insurance executive  “And it was Marco Rubio ”
A rising state lawmaker in 2002, now-U S  Sen  Marco Rubio had the clout to make or break the legislation  He had been one of two state House majority whips and was on the fast track to becoming House speaker 
Rubio didn’t kill the 2002 bill out of opposition to prescription monitoring—it was politics “as usual” yet nobody blamed Rubio for the resulting opioid crisis that seems to have started in his political backyard and flourished beyond belief  
U S  Sen  Marco Rubio, R-Fla , was a leader in the Florida House in 2002 when he blocked a vote on prescription monitoring  That year, Rubio favored a bill changing the Miami-Dade County charter, which failed to pass because of a single “no” vote in the Senate  Burt cast the vote 
Angered by what he saw as Burt’s betrayal, Rubio killed the prescription drug monitoring bill  “When I found out he broke his word, it made the choice easy,” Rubio told The Miami Herald 
It’s not certain that the full Legislature would have passed the bill had it made it to a floor vote  Rubio was the first, not the last, in a line of state legislative leaders over years who would refuse to seriously consider the bill  Most cited privacy concerns 
But prescription monitoring databases in Florida and other states free to use Florida’s model would have pinpointed rogue doctors, would-be pill mills and doctor-shoppers across the country, just as all three were beginning to converge  In doing so, it could have curbed a national opioid epidemic when it was just an emerging problem, not the monster it would become 
Only weeks after the 2002 bill was killed, Bush suppressed a sob as he discussed his daughter’s arrest for forging a prescription  Court-ordered to drug treatment and then briefly to jail, Noelle Bush survived her pill addiction  The 2004 deadline for greenlighting a monitoring system passed  So did Purdue’s million-dollar obligation to pay for it 
Between 2002, the year Rubio killed the database that could have identified doctor-shoppers, and late 2011, when the database finally came online, more than 20,800 Floridians died after taking prescription opioids, including OxyContin, annual Florida Medical Examiners’ reports show  “Not getting that bill through the Legislature resulted in Florida becoming the pill mill capital of the United States,” said Burt 
“There was heartache for thousands of families beyond measure and it didn’t have to happen ”
Florida Officials Were Told Of The Oxy Express
The East Kentucky hills and valleys of Greenup County suit Keith Cooper, a long-haired undercover cop-turned-sheriff: “It’s a backwater  I tell people all the time I am a hick sheriff from a hick location, and by 2011, the rural county and its sheriff had big city problems 
Greenup is near the stretch of interstate highways that provided drug traffickers and users with a straight shot to Palm Beach and Broward pill mills  It’s less than an hour’s ride to Huntington Tri-State Airport, where a $27 flight to Fort Lauderdale was a popular draw for dealers hoping to stock up 
Arrests for Florida pills soon eclipsed local arrests for pot 
“When we locked ’em up, we take all their pill bottles and all their paperwork, and we found maps to the doctors offices and everything,” recalled Cooper 
“I called the (Florida) medical board and gave them a big list of doctors,” Cooper said  He called the state pharmacy board, too  He got no response 
“So then I called the Attorney General’s Office and the Governor’s Office  I was calling them all, the whole state  Of course, I was talking to the state police the entire time  “I told them, all of the profits were down there  And all of the pain’s up here ” Nothing happened  Florida’s oxycodone pipeline continued to flow 
On the other side of the law in Greenup, Mikey Frazier was banking on it 
The Oxy Express
Frazier was on a scholarship to play baseball at his junior college in Chicago when he suffered a torn rotator cuff  Doctors prescribed Percocet, a pill containing oxycodone, in 2002  When doctors cut him off, he bought it on the street  In 2006, he moved to OxyContin, nearly pure oxycodone  In 2007, he gave his friends money to go to Florida and bring him back pills 
“My buddy had a minivan and he would actually go down one week and take two to three people with him, and then the following week I’d go,” said Frazier  He still remembers the route: “I’d take 64 East to 77 South to 95 South  And it’s just a straight shot ”
Others followed suit  “What got everyone started was because the doctors around here won’t write a strong enough prescription,” he recalled  OxyContin and generic oxycodone still could be had — just not in Kentucky, which had a prescription drug monitoring database 
In Florida, “there was none of that … stuff that they check and find out what doctor you’ve been to,” said Frazier 
“And one person does it, and then they tell a friend, and then they go do it, and that’s how it all really got started here ”
MEDICAID-MEDICAIRE PAID MILLIONS FOR OXY
Tallahassee wasn’t just ignoring the epidemic, It was financing it 
Before her office was raided by law enforcement in December 2001, Asuncion M  Luyao’s patients would wait in a line in the rain to get prescriptions from the Port St  Lucie internist and acupuncturist  She was one of the most prolific prescribers of OxyContin in the state 
And hundreds of thousands of those pills were being paid for by Medicaid, Florida’s taxpayer-financed health program for the state’s poorest and sickest citizens  Between 1999 and 2001, Medicaid shelled out $935,634 for OxyContin prescriptions written by Luyao  That was just OxyContin  Luyao was prescribing an array of addictive drugs  In the 12 months leading up to the clinic raid, Medicaid paid roughly $1 million for 7,000 prescriptions, only about 17 percent of them for OxyContin 
Nor did the raid slow her down  Between the raid and her arrest on trafficking charges four months later, Luyao wrote another 282 OxyContin prescriptions billed to Medicaid  She was not an outlier  In 24 months, taxpayers footed the bill for more than 49 million doses of pills containing oxycodone, even though there were only 1 36 million Medicaid patients  Half were children 
The sheer volume of pills might have been a tipoff that the drugs were not all intended for legitimate use  So were arrest reports dating to 2001  One man had used his 7-year-old son’s Medicaid number to doctor-shop for OxyContin  A Miramar pharmacist who billed Medicaid $3 7 million for OxyContin pills was charged with paying Medicaid patients $150 each to use their IDs 
Medicaid paid for more than $300,000 to fill Dr  James Graves’ OxyContin prescriptions  The Florida Panhandle physician was the first doctor in the nation convicted of killing patients by overprescribing OxyContin 
Addiction risk for people taking high doses of oxycodone begins climbing after just three days, a recent study concluded  And most people on Florida Medicaid getting oxycodone prescriptions in 2011 were getting much more than a few days worth  They were getting an average of nine months worth of pills, state officials said 
Pill mill doctors prescribed 1 million of those pills:
Doctors working for the George twins’ trafficking empire prescribed at least 102,081 oxycodone pills billed to Medicaid before the ring collapsed in 2010 
Working out of a Delray Beach pain clinic founded by a convicted drug smuggler, Zvi Harry Perper, son of the Broward County medical examiner, was arrested on trafficking charges, but not before he wrote prescriptions to Medicaid patients for 115,977 doses of oxycodone in 90 days 
In Lake Worth, Cesar Deleon was arrestedas part of a DEA pill mill sweep and charged with 55 counts of illegally distributing drugs  Deleon wrote orders for 20,302 oxycodone pills for Medicaid patients 
Miami internist Dr  Selwyn Carrington authorized 32,411 doses of oxycodone for Medicaid patients in just two years  He was busted for signing his name to hundreds of prescriptions 
Further, Florida wasn’t in any hurry to stop doctors linked to pill mills 
Carrington was arrested for overprescribing in March 2011  The state’s emergency order to suspend his license was signed months after he had pleaded guilty in 2012 
Perper was busted at a Delray Beach pill mill operated by a former felon in 2011  The state did not act against his license until 2014 
Joseph M  Hernandez was writing prescriptions from his car, a veritable pill mill on wheels, when he was busted in February 2010 on one count of trafficking in oxycodone 
 Florida’s Department of Health didn’t file paperwork to restrict his license for almost 18 months 
During that time, Hernandez wrote oxycodone prescriptions for Medicaid patients totaling 258,940 doses representing a taxpayer-footed bill of $130,165 
Purdue Pharma’s Profits Before Patients Creed
Kelly Skidmore is exactly the type of person Purdue Pharma’s OxyContin marketing was intended to reach: Diagnosed with juvenile arthritis, the former state legislator’s struggle with chronic pain began at age 4 
Skidmore was wary of opioid painkillers, though, one reason her willingness in 2009 to work with Purdue was surprising  But she did it to get Florida’s dormant drug monitoring database up and running 
Then a state representative in a district straddling Palm Beach and Broward counties, Skidmore recalled that, “They came to me and said, ‘Could you help get it across the finish line?’ ”
OxyContin and prescription opioids, a serious problem in 2002, had evolved into a full-blown crisis in the ensuing seven years  Broward alone had more pain clinics than it had McDonald’s  Deaths tied to oxycodone had exploded, up by 263 percent since the prescription monitoring database had first been proposed and killed  Overdoses from prescription opioids were claiming more than seven lives a day 
“By God, if we had had seven dolphins a day dying and washing up on Florida beaches, we would have been appropriating money and solving it,” Skidmore said 
Skidmore believed a database wasn’t going to resolve the underlying addiction crisis  Still, it was a start  Not a silver bullet, but “maybe silver buckshot,” she said  The database law passed with gaping loopholes  No health care professional would have to report opioid prescriptions or check the database before prescribing more, and the state refused to pay for it 
“Just to get that one little piece … took nine years of filing bills and then it had no teeth,” Skidmore said  “And it should have been the easiest piece ”
Where Was The DEA and Everyone Else?
The DEA all but wrung its hands over Florida’s lethal inaction  The agency ticked off a devil’s brew of regulatory loopholes: Florida’s Health Department regulated health care professionals but not pain clinics  The state’s Agency for Health Care Administration regulated pain clinics that accepted insurance, but pill mills were most often on a cash-only basis  And the prescription monitoring database, mired in a vendor dispute, remained stalled 
In early 2011, when Gov  Rick Scott took office, just one drug — oxycodone — was tied to six fatal overdoses a day  Deaths tied to all drugs claimed 25 a day  In the handful of Appalachian states where traffickers were bringing back South Florida pills, it was worse 
Ohio’s death rate for oxycodone and similar opioids had doubled in 24 months, federal records show  Kentucky’s was up by more than 50 percent  And in West Virginia, home to hard-hit Huntington, death rates tied to pill mill drugs such as oxycodone and Opana had climbed by 341 percent 
The DEA formally pinpointed Palm Beach, Broward and Miami-Dade counties as the nation’s single biggest hub for trafficking pills across state lines  Within weeks of being sworn in, Scott abolished Florida’s Office of Drug Control, eliminating the state drug czar position, announced plans to drive a final stake in the heart of the database and rebuffed Purdue Pharma’s renewed offer to help pay for it 
Scott, a tea party conservative, cited privacy concerns, expressed skepticism the monitoring program would work and raised the possibility taxpayers would be left with a $500,000-a-year bill to operate it 
Attorney General Pam Bondi had also ridden the tea party wave to her position  She shared many of Scott’s conservative convictions  Unlike Scott, the former prosecutor relentlessly lobbied to keep the database alive  Florida’s failure to adopt the drug monitoring database was so out of step with the rest of the country that it began spawning conspiracy theories on both sides of the law 
Everyone knew prescription monitoring was going to kill the pill smuggling business, said a corrupt Florida Highway Patrol trooper as he drove a load of pills out of Florida, according to a federal lawsuit  Talking to the confidential informant in the seat next to him, the trooper speculated someone in Tallahassee must have a piece of the action, “because (Scott) was so adamant about not putting that system in place  Right?”
In Greenup, an infuriated Cooper told a reporter, “In my opinion, (Scott’s) getting money from somewhere  He has to be ” A few days later, recalled Cooper, “A lieutenant with the state police I’d been talking to down there called me, said, ‘Man, just a head’s up: I wouldn’t come to Florida ’” In states on the receiving end of the Florida pill pipeline and among federal officials, Scott’s resistance triggered outrage 
In Kentucky, where as much as 60 percent of the illicit oxycodone in that state flowed from Florida, Lt  Gov  Daniel Mongiardo proposed erecting billboards at the Florida line: “Welcome to the Oxy Tourism Capital of the World ”
U S  House Appropriations Chairman Hal Rogers, also from Kentucky, twice wrote Scott  “Canceling Florida’s prescription drug monitoring program is equal to firing firefighters while your house is ablaze,” he wrote 
Gil Kerlikowske, director of the White House Office of National Drug Control Policy, asked to meet with Scott  So did DEA Administrator Michele Leonhart 
Three U S  senators — New York’s Chuck Schumer, West Virginia’s Joe Manchin and Rhode Island’s Sheldon Whitehouse — joined Florida’s Bill Nelson in pointing out that the pills weren’t just a Florida problem: There were “serious ramifications for the rest of the country,” wrote Nelson of Scott’s reluctance to crack down  This is a perfect example of how political rhetoric, in-fighting and contrived agendas prevented an early stop to the emerging opioid crisis many years ago 
WHY DIDN’T THE DEA, DRUG DISTRIBUTORS AND PHARMACIES TAKE NOTICE BEFORE THE OPIOID CRISIS SPREAD ACROSS THE COUNTRY LIKE WILDFIRE? WAS IT BECAUSE OF THE BILLIONS IN PROFITS, QUARTERLY BONUSES AND DIVIDENDS? STOCK OPTIONS CASHED IN BY BOARDROOMS AT EVERY OPIOID BIG PHARMA COMPANY? STAY TUNED FOR HOW “PROFITS BEFORE PATIENTS” BECAME THE NORM
(article excerpts and quotes have been taken from publicly available media sources and court records)



ground_truth: It outperforms mean-field methods and the PLM with $l_2$ regularization in terms of reconstruction error and true positive rate.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What was the reason given by Governor Rick Scott for not implementing a prescription drug monitoring database in Florida?

Read the following text and answer briefly.

Context 4:  The problem was to tailor it to the rig  The subsea wellheads had to be reinforced to meet the demands posed by the North Sea, and a buoy loading system needed to be developed for waters where this technology had never been used before 
To gain time, it was decided that the three appraisal wells drilled by Ocean Viking to map the extent of the field – in addition to the discovery well – would be completed for production 
Første testflamme tent på Ekofisk  På Gulftide
1973, Teddy Broadhurst, gulftide,
arbeidsliv, hjelpearbeider
Gulftide, separator – på bildet kan man se at det er fire brønner 
arbeidsliv, gulftide, pionerkultur, arbeid, dekk, Norges første havbunnsbrønner, historie, 1971,
The producers would be topped with hydraulically controlled wellheads  Such equipment had been tried out on the seabed earlier, but on a limited scale and not in the deep and rough waters found on Ekofisk  This challenge was overcome by having the wellheads manufactured and then reinforced at the Phillips base in Dusavik outside Stavanger  Flowlines and control cables would also be laid from each well to Gulftide, with production comingled in a single riser to the topsides 
Weather conditions also represented a major problem when designing the loading buoys  Phillips itself had experience with such facilities, but the concept had only been used before in harbour-like conditions and waters no deeper than 27 metres  They were now to stand in 70 metres in the middle of the North Sea 
Gulftide was converted in the Åmøy Fjord outside Stavanger to cope with conditions on Ekofisk  The processing facilities were installed and reinforcements made to the derrick, helideck, hangar and leg structures 
Gulftide, Ekofisk 2/4 A, boretårn, flare, 1971, utbygging,
Gulftide with Ekofisk 2/4 A in the background  Photo: Aker Mek  Verksted/Norwegian Petroleum Museum
Planning began in late 1970, when Phillips received approval to begin laying the flowlines between wellheads and rig  Brown & Root won this contract, with the first oil pipelines on the Norwegian continental shelf laid by the Hugh W Gordon laybarge 
The production principle on Gulftide was relatively simple  Output flowed from the subsea wellheads to the rig, where it passed through two separation levels to be split into oil and gas while the huge pressure was reduced 
Gas was flared off and the oil was piped to one of the loading buoys where a shuttle tanker was moored  Production could only take place when a ship was present 
Offisiell åpning av norsk oljeproduksjon,
The Greek tanker, Theogennitor, unloads crude oil from loading buoys on the Ekofisk field  Gulftide in the background  Photo: ConocoPhillips/Norwegian Petroleum Museum
As soon as one tanker had become fully laden, the oil flow was switched to the other buoy where another ship was waiting to take on cargo 
The problem with this approach arose when weather conditions meant the tankers had to cast off from the buoys because of strong winds or high waves  The rig then had to shut down production from the wellheads immediately 
Given the weather conditions found on Ekofisk, output regularly had to cease  Production was suspended for 20 per cent of the first year for this reason 
Output began cautiously on 8 July 1971 from a single well  The second producer came on stream that September, the third was ready the following month and all four were producing by February 1972  They each flowed 10 000 barrels of oil per day 
Source: Kvendseth, Stig, Giant discovery, 1988 
Published 9  April 2019 • Updated 25  October 2019
Norpipe H-7
This platform served as a pumping/compressor station to maintain pressure in the 443-kilometre Norpipe gas pipeline from Ekofisk to Emden in Germany, which became operational in September 1977 
Kjappe fakta::
Compressor platform on Ekofisk-Emden gas pipeline
Installed 1976
Operational 1977
Shut down 29 October 2007
Removed 2013
— Norpipe GNSC-H7  Photo: Husmo Foto/Norwegian Petroleum Museum
Gas received initial compression to 132 bar at the Ekofisk Complex  The pipeline was divided into three equal lengths, with Norpipe GNSC B11 positioned at the end of the first third to maintain pressure as and when required 
From there, the gas then travelled the next third of the distance to the second and virtually identical compressor platform, H7 
This was also responsible for maintaining pressure, but additional compression was seldom required on this final leg of the journey to Emden 
Both platforms stood on the German continental shelf, but 48 kilometres of the pipeline also ran across the Danish North Sea sector 
The pipeline is trenched or covered with sand  On its final approach to the coast of East Friesland, it passes beneath the island of Juist before making landfall north of Emden 
Capacity in Norpipe is about 60 million standard cubic metres (scm) or 2 1 billion cubic feet per day  In addition to output from the Ekofisk-area fields, it carries gas from Valhall, Ula and the Statpipe system – primarily Statfjord and Gullfaks  Gas was also transported for a time from Hod and Gyda, but that has ceased 
fritid, Norpipe GNSC-H7,
Magnus Refsland and Werner Hein have pulled the crab trap (full of starfish) on the Norpipe H-7 platform  Photo: Husmo Foto/Norwegian Petroleum Museum
Built in 1976, the B11 platform had six decks  Its permanent staffing totalled 14 people, but various service personnel were also often on board  The regular crew included three in catering 
The 11 Phillips employees comprised the offshore installation manager, the nurse/radio operator, eight operators and a roustabout 
In addition to their direct function, the operators covered various other trades which meant the crew was self-sufficient in most circumstances 
Both platforms obtained a satellite antenna in 1986 which allowed them to received Norwegian TV, while the 24-bed accommodation were redecorated in 1981 and upgraded in the summer of 1990 
Work on the upgrading largely comprised converting all cabins to doubles with shower and WC  The galley and changing rooms were renewed and changing facilities for women provided 
A new module with a lounge for non-smokers, a smoking room, gym and pool room was also installed  During this work, the West Gamma accommodation rig was positioned alongside 
Upgrading equipment on the platform was also initiated in 1990  While the pipeline’s original daily capacity had been estimated at 2 100 million standard cubic feet, this was found to have declined after a number of years to 1 975 million 
To return to the original capacity, the compressors needed to be upgraded and power supply from the turbines increased  This was done both on the Ekofisk tank and on the H7 and B11 platforms  Gas coolers on the tank were replaced as well 
Norpipe GNSC-H7, yrker, radiooperatør,
Radio operator Torleif Førland on the platform Norpipe H-7, with his amateur radio  Photo: Husmo Foto/Norwegian Petroleum Museum
The control systems were also upgraded in parallel  Control panels on turbines and compressors were replaced and metering instruments installed to conduct measurements in this equipment 
While the nearest neighbour to B11 was a Danish oil field, H7 stood in the middle of the shipping channel  M/S Hero broke down 15 nautical miles west of the latter platform at around 13 00 on 12 November 1977 
By 21 00, the ship was still adrift and heading directly for H7, and all 14 crew on the platform made ready to evacuate by helicopter – the waves were too high for the lifeboats  The wreck passed at 21 40 with a clearance of 400 metres 
German cargo carrier Reint collided with H7 on 30 September 1995, despite efforts by the standby ship to avert the threat  Production was halted as a safety measure, but the platform luckily suffered only minor damage  The collision was caused by inadequate watchkeeping on the ship’s bridge 
Operator responsibility for B11 and H7 was transferred at the beginning of 2003 to Norway’s state-owned Gassco company, which runs the Norwegian gas transport network 
This change had little significance for operation of the platforms, since the actual work was still carried out by ConocoPhillips as a technical service provider to Gassco 
H7 was shut down in 2007, and removal had been completed in 2013  In connection with preparations to remove the structure, operator responsibility was transferred to Statoil as the company in charge of the project on Gassco’s behalf 
Published 24  August 2016 • Updated 22  October 2019
Phillips inundates Sola with oil revenues
person by Kristin Øye Gjerde
Stavanger and neighbouring Sola were the first Norwegian local authorities to experience fantastic oil-related growth after the award of the first exploration licences in 1965 
— Phillips er i ferd med å etablere seg på Norscobasen nederst til høyre Ca 1972 Foto: Norsk fly og flyfoto/Norsk Oljemuseum
The Shell refinery at Risavika in Sola was completed two years later, while the Norsco base in Tananger became operational as early as 1966 
But things really took off once the Ekofisk field had been discovered in the autumn of 1969 and started trial production on 14 July 1971 
Operator Phillips Petroleum Company moved its offices from the Dusavik base outside Stavanger to Tananger in Sola, and Shell could finally start refining Norwegian rather than imported crude 
Sola’s population now rose steadily from 8 400 in 1965 to 15 000 two decades later, and jobs grew even faster – from about 2 000 in 1970 to almost 8 000 in 1985  That averages 10 per cent annually 
Phillips and Shell became cornerstone companies  A large part of their workforce, particularly in Phillips, worked offshore  In addition came newly established oil supply firms 
More jobs were also created in retail, public administration, education, health and social care, personal services and so forth 
Although traditional agriculture remained important for the local authority, the number of farmers gradually declined as a result of mechanisation [REMOVE]Fotnote: This article is based on the chapter “Elverket i Oljealderen” in I det regionale spenningsfelt  Sola Energi 1913-1999, Kristin Øye Gjerde 
Boreskipet Drillship ligger ved kai på Norscobasen i Tananger (1968)  Foto: NOM/Norsk Fly og Flyfoto
Boreskipet Drillship ligger ved kai på Norscobasen i Tananger (1968)  Foto: Norsk Fly og Flyfoto/Norsk Oljemuseum
The “agio tax”
The sharp rise in Sola’s revenues was attributable entirely to the oil industry, and it found itself in an enviable position during this period  Tax revenues rose even faster than population and jobs 
To give an indication, the local authority’s overall income from wealth and income taxes rose from NOK 9 3 million in 1966 to NOK 198 million in 1990  The biggest growth came in 1978-82, when it averaged 39 per cent a year [REMOVE]Fotnote: Sola local authority, plans 
The secret behind this sharp increase was the tax paid by the oil companies – primarily Phillips – on agio, or the percentage fee charged when exchanging one currency for another 
Under Norwegian law at the time, the companies paid tax on their interest income to the local authority where they had their head office  In making this rule, however, the government had failed to take account of the considerable sums involved 
As operator of the Greater Ekofisk Area, Phillips had placed capital to be used for new investment in banks around the world – particularly the UK 
These deposits yielded substantial interest payments, and tax was payable on converting this income into Norwegian kroner [REMOVE]Fotnote: Toralv Torstenbø, former chief executive officer in Sola local authority, interviewed by Kristin Øye Gjerde, 22 February 2001 
Sola council is said to have almost gone into shock the first time Phillips paid this agio tax  It suddenly had more money than it could spend 
During the 1970s and early 1980s, Sola’s municipal income always exceeded the budgeted amount  Large sums could be transferred every year to a capital fund 
Since the local authority was in a growth phase, additional funding was needed for the big developments it faced  While the rest of Norway experienced a slump in the late 1970s, Sola continued in top gear without a sign of unemployment 
Net income tax revenues came to NOK 55 5 million in 1978, while net spending was NOK 31 9 million  And these fantastic results went on improving 
By 1982, wealth and income taxes yielded NOK 203 4 million – compared with a budget of NOK 146 million, which was upgraded to NOK 190 million during the year 
According to Toralv Torstensbø, the financial controller, agio tax accounted for almost half this amount – in other words, as much as the tax paid by all other enterprises, private individuals and industry in Sola 
Its chief executive officer became a little overweening  In his comments on the 1982 budget, he declared that it would be “natural for Sola local authority to feel a strong regional responsibility and not to be too strict about the traditional division of costs between state, county and local authority ”
In line with this open-handed policy, Sola paid for both road projects and an upper secondary modern school which the county council was supposed to fund [REMOVE]Fotnote: Chief executive officer’s budget proposal for Sola local authority covering 1974-85 
Tightening up petroleum tax
This unexpected prosperity undoubtedly created some jealously in the neighbouring local authorities, and the media began to show an interest in the issue 
Local daily Stavanger Aftenblad interviewed Sola’s chief executive and controller in 1981, when its photographer took a shot which illustrated the boundless wealth – Torstensbø stood showering hundred-krone notes over his colleague 
This story was not only read by the paper’s regular subscribers  The following day, 150 copies were distributed to members of the Storting (parliament) 
That in turn prompted Centre Party representative Lars Velsand to make a passionate speech in which he described the position as a misuse of tax revenues 
He called on the government to intervene so that individual local authorities were unable to benefit in this way  Nor was he alone in finding it unreasonable that a small community like Sola should get so much money 
The result was an amendment to the Petroleum Tax Act on 11 June 1982, which specified that the proceeds from the agio tax should be transferred in future to central government 
Løfteskipet Uglen i aksjon ved Norscobasen i juli 1980  Foto: NOM/Norsk Fly og Flyfoto
Løfteskipet Uglen i aksjon ved Norscobasen i juli 1980  Foto: Norsk Fly og Flyfoto/Norsk Oljemuseum
Unfortunately, however, Sola had got used to consuming these revenues  It is easy to learn expensive habits, but not so straightforward to shrug them off again 
Matters had become a little unusual when the council’s executive board adopted the style of the oil company chiefs and took a helicopter outing during an ordinary budget meeting [REMOVE]Fotnote: Oskar Goa, former chief technical officer in Sola local authority, interviewed by Kristin Øye Gjerde, 23 October 2000 
However, most of the tax money benefitted the general public  Paying for Sola upper secondary school and new national and county highways is an example of this 
The council also invested on local authority school buildings and community facilities such as the big sports complex at Åsen, with an outdoor athletics ground and two modern indoor arenas  Dysjaland and Tananger also acquired new sports arenas 
A new cultural centre built in central Sola has a distinctive architecture in brick and glass, with a grassed roof to blend with the surrounding Jæren landscape  With two stages and a public library, this became the community’s main venue for events and so forth 
The local authority thereby built up a very good infrastructure  Power cables were laid in the same trenches as water and sewage pipes, a network of cycle lanes was built and street lighting installed 
On the downside, virtually all these investments boosted operating expenses  The council’s running costs rose by an annual average of 30 per cent in 1978-84, with the biggest growth in the last three years of the period 
So the calls by Storting representatives to transfer agio tax receipts from councils to central government represented a real threat to local politicians 
Sola joined forces with other local authorities in the same position, including Stavanger, Oslo and Bærum as well as Rogaland county council 
A delegation met the Storting’s standing committee on finance to present their case, and secured a commitment to accept a phased reduction in revenues over four years 
The local authorities would receive 80 per cent of agio tax receipts during the first year, then 60 per cent, 40 per cent and finally 20 per cent [REMOVE]Fotnote: Amendment to the Petroleum Tax Act adopted on 14 May 1982 
In reality, however, the run-down percentages were adjusted to extend over five years in annual steps of 80, 60, 20, 20 and 20 per cent  The total amount going to the local authorities was the same 
The arrangement was controversial to the last, and also uncertain because it had to be approved in each annual government budget 
Living within its means
After the tax change, Sola’s chief executive officer saw the writing on the wall  It seemed “to be unquestionable that [Sola] has seen its best days in purely financial terms and must return to setting tougher priorities for various assignments,” he asserted in connection with the budget process for 1983 [REMOVE]Fotnote: Chief executive officer’s budget proposal for Sola local authority, 1983 
It took the politicians a little longer to accept this reality, but they were forced to reduce investment and operating expenditures in the years which followed 
Cutting back on the new sports arenas and cultural centre was not very desirable  Nor was it pleasant to have to slow down  But savings had to be made, and long-terms spending plans were removed from the budget for possible reintroduction later 
A raft of measures were stripped from the budget in 1985, such as extensions to and modernisation of schools, sports arenas and swimming pools, a new somatic nursing home, housing for the intellectually disabled and sheltered housing  Grants for national and county roads were reduced [REMOVE]Fotnote: Chief executive officer’s budget proposal for Sola local authority, 1985 
Once the government’s compensation scheme had ended, Torstensbø – now chief executive officer – told Stavanger Aftenblad that he did not want to paint too gloomy a picture 
“But it’s clear that we must set much more moderate financial priorities than we’ve been used to  To sum up the position, we were previously flush with cash and poor in facilities  We’re now flush with facilities and poor in cash ”[REMOVE]Fotnote: Stavanger Aftenblad, ”Alt blir dyrere i det rike Sola”, 19 May 1987 
Sola kulturhus fotografert vinteren 2004
Rogaland county council also raised the question of whether it would be possible to establish a permanent arrangement which allowed local authorities and counties to benefit from some of the tax revenues paid by local oil companies 
The council pointed out that it was otherwise normal practice for Norwegian companies to pay taxes to the local communities they were based in 
This request was turned by Labour finance minister Gunnar Berge because the councils concerned still benefitted from bigger tax payments by oil company employees and on property [REMOVE]Fotnote: Stavanger Aftenblad, “Rogaland reiser skattekrav på ny”, 16 January 1988 
According to Torstensbø, this was only partly true  The big oil companies were not so significant for Sola’s income once the agio tax was excluded 
About NOK 2 million was received annually from Phillips, primarily in property tax  The most important taxpayers in the local authority were the roughly 90 companies at Aker Base  These were service providers such as Halliburton, Schlumberger and Baker Hughes 
At the same time, Sola acquired a steadily growing number of affluent residents and a growing share of its revenue came from income tax  Despite the cut-backs, it remained prosperous 
Published 29  July 2019 • Updated 29  July 2019
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