Were the Warriors just unlucky? Their opponents, the Cleveland Cavaliers, were not a particularly good defensive team during the regular season, either overall or against perimeter shooters, although they may be better with Iman Shumpert and Matthew Dellavedova and Tristan Thompson getting more minutes because of injuries. The Cavs forced the Warriors into some bad possessions, but the Dubs also missed on some good looks, shooting just 2-for-11 on corner threes.But there’s also the old adage: Live by the three, die by the three. If your shooters are going to get crazy hot on some nights, isn’t it inevitable that they’ll shoot a bunch of bricks on another, rendering a team’s offense more inconsistent and making it more upset-prone?Let’s look at some data from the 2014-15 regular season. In the chart below, I’ve sorted teams by the percentage of their field goals that were taken from 3-point range. Then I’ve looked at their game-by-game scoring, calculating their scoring range (as I’ll describe it throughout this article) as the span including the middle 80 percent of their games (that is, throwing out their top 10 percent and bottom 10 percent of performances).The Warriors, for instance, averaged 110 points per game in the regular season, while their scoring range ran from 98 points (at the 10th percentile) to 126 points (at the 90th percentile), a 28-point difference. That seems like a wide range … but it’s perfectly normal. The average NBA team this season had a 27-point scoring range. The average range since 1979-80 (when the 3-point shot was introduced) is 28 points.The Warriors weren’t the league’s most three-happy team, however. They were just seventh — behind the Houston Rockets, Cleveland Cavaliers, Los Angeles Clippers, Atlanta Hawks, Philadelphia 76ers and Portland Trail Blazers. So maybe the Dubs were pretty steady, but were those other teams inconsistent?The Cavaliers were inconsistent: Their scoring range spanned 33 points, tied for the second-highest total in the league after Oklahoma City.2Like the Thunder, who dealt with injuries to Kevin Durant and Russell Westbrook, the Cavs went through numerous lineup changes and new “looks” over the course of the regular season. So that may reflect personnel changes more than inconsistency per se. But Houston, which took 39 percent of its attempts from long range (easily an NBA record), had a scoring range of just 25 points, below the NBA average. The three-happy Atlanta Hawks had a scoring range of just 24 points.What’s going on here? Are teams that shoot a lot of threes actually more consistent than others? (Maybe they’re more resilient when facing different types of defenses or benefit from having better floor spacing?)Actually, it’s mostly just because this data is pretty noisy. I ran a regression on all NBA teams since 1979-80 to predict their scoring range based on (i) the percentage of their field goal attempts that came from behind the arc and (ii) their per-game scoring average. Both variables have a positive and highly statistically significant relationship with a team’s scoring range. Teams that score more points have a wider scoring range, and, once you control for that, teams that shoot more threes do also.But statistical significance is not the same thing as practical significance. In the context of an actual basketball team, this result will make very little difference.Suppose, for instance, that a team scores 100 points per game and that 40 percent of its field-goal attempts are 3-pointers — higher, even, than this year’s record-setting Rockets. Its scoring range, according to the regression analysis, projects to be 29.7 points.What about a team that scores 100 points but does so with only 10 percent of its shots being threes? No team has shot such a low percentage of 3-pointers since the 1999-2000 Philadelphia 76ers, but we’ll run the numbers just for fun. That team, according to the regression, would have a scoring range of 28.0 points. So it’s more consistent, but only barely so; its scoring range is only 6 percent narrower. This just really doesn’t matter much.What matters a lot more, of course, is how effective a team is at scoring overall. The Oklahoma City Thunder, as I mentioned, had the most inconsistent offense in the regular season. But their 10th percentile score, 88 points, was still better than two-thirds of the league because they had a high per game scoring average.And Golden State’s 10th percentile score, 98 points, was better than what almost a third of NBA teams scored on average per game. The Warriors will have better shooting nights than they did Sunday, but their bad nights aren’t indicative of a fundamental problem — they’re just bad nights.CORRECTION (June 9, 11:45 a.m.): An earlier version of this article incorrectly said that if the Golden State Warriors had made 3-pointers at their regular-season accuracy rate, they would have won Sunday’s NBA Finals game 117-95. They would have won 111-95. “You’ll shoot your eye out,” I kept thinking while watching Game 2 of the NBA Finals on Sunday. The Warriors hoisted 35 3-point attempts and made only eight of them en route to scoring just 93 points. It was a maddening, sloppy game full of what-ifs. So … what if the Warriors had sunk threes at their normal accuracy rate?1The Warriors shot .398 on 3-pointers during the regular season, which would equate to making 14 of 35 shots. They would have won 111-95.
Jim Tressel (99-21) will be going for his 100th win as head football coach at Ohio State as the No. 2 Buckeyes (5-0, 1-0) take on Indiana (3-1, 0-1) Saturday in Ohio Stadium. What does the potential accomplishment mean to Tressel? “I guess I’m getting old,” Tressel said. “If you stick around long enough, you’re going to get some of those milestones.” Despite Tressel’s downplay, the win would be historic. Tressel would join Woody Hayes (205) and John Cooper (111) as the only coaches to top the 100 mark in wins as OSU head coaches. More noteworthy is how quickly Tressel might reach the plateau. “Woody got it his 144th game, Cooper his 138th game, and if Jim gets it Saturday, it will be his 121st game. That’s really something,” OSU football historian Jack Park said. Tressel has a chance of achieving another record. “If Ohio State wins every game the rest of the year and wins its postseason game, (Tressel) will have the highest winning percentage of any coach in the history of the Big Ten Conference that has coached in the conference at least 10 years,” Park said. Tressel’s success at OSU should come as no surprise considering what he accomplished at Youngstown State from 1986-2000. Tressel compiled a 135-57-2 record and won four national titles. “A lot of the things they are doing at Ohio State now are things they were doing at Youngstown State,” said Steve Helwagen, Bucknuts.com managing editor. “It’s just the Tressel form. It’s been amazing the success he’s had.”
The Ohio State men’s hockey team couldn’t have been more inconsistent last season. OSU returns 20 letter winners from last year’s squad that went 15-15-5, tying for eighth in the Central Collegiate Hockey Association and losing in the first round of the conference tournament. The team has six newcomers, all freshmen. The Buckeyes’ combination of youth and experience has OSU coach Mark Osiecki optimistic for the upcoming season. “I think after last year and the experience we gained, I think that the youth that we have, there’s a lot of enthusiasm and excitement,” Osiecki said. The team’s growth, along with a number of other topics, including leadership, the CCHA, and the NHL lockout, were discussed heavily at OSU’s media day Oct. 1. Learning from 2011-12 OSU was one of the most inconsistent teams in the country last season. The Buckeyes were predicted to be a conference cellar dweller prior to the 2011-12 season but climbed to the top of the college hockey world by January, winning 14 of their first 19 games. OSU then fell off the face of the collegiate hockey earth, winning only one game in the final two-and-a-half months of the season. As disappointing as that was for OSU, it has them motivated to be better this year. “This year, having another year under our belt, we went through some of those highs and lows (last season) and we know what it takes to be consistent through the whole season,” said sophomore forward Max McCormick. What went wrong last season, according to junior forward Chris Crane, was a little bit of everything. One thing stood out though: poll watching. “I think we looked at (the rankings) a little bit too much, but I think the best thing we can take is it is something we can learn from,” Crane said. Osiecki has made sure that will not occur with this year’s squad. “At one of our preseason meetings, coach (Osiecki) talked about how to handle winning, and how to handle being successful. I think it’s something that we have to learn. There’s a process to it,” said senior defenseman Devon Krogh. Who’s going to wear the ‘C?’ For now, the Scarlet and Gray ‘C’s stitched to the sweaters of the OSU captains don’t have permanent homes. OSU had two captains all last season: former defenseman Sean Duddy and former forward Cory Schneider. This season, captains have yet to be named. “It’ll be interesting to see in terms of leadership. I think that’s one area where it’s going to be a team effort,” Osiecki said. “We’ve told them since day one … we’re going to continue evaluating it.” The Buckeyes have only four seniors, and Osieckisaid even the sophomores could be players that step up and lead. Rah-rah, in-your-face type leadership isn’t OSU’s style this season, though. “I think I’m a big believer in leading by example. They’re pretty big guys already – like grown up. So it’s little things like giving them advice before games,” Krogh said. Getting offensive Along with returning 20 letter winners, the Buckeyes also bring back five of their seven top scorers from the 2011-12 team. Crane and sophomore forward Ryan Dzingel led OSU last season with 24 points, and Osiecki wants his team to be more aggressive inside the blue line this year. “We want them to be more offensive and really put the pressure – I don’t want to say pressure, because pressure’s a bad word – but hold them accountable. We need Dzingel, Crane, McCormick, (sophomore forward Tanner) Fritz – they need to be offensive and they need to get looks at the net,” Osiecki said. Team speed should be an improvement this season as well, with freshman forward Anthony Greco – the team’s quickest player, Osiecki said – leading the bunch. “I think we’re a better skating team now than we were last year. We’re going to try to be a more pressure team, a more transition (team),” Osiecki said. On the road again OSU opens the season with six straight contests on the road: two at Minnesota Duluth, two at Quinnipiac and two at Bowling Green. Ten of the Buckeyes’ first 14 games are away from the Schottenstein Center. As young as OSU is though, with 17 freshmen and sophomores, going on the road early could be a benefit. “I think with a young team, it’s good to get on the road. It certainly brings you closer together,” Osiecki said. OSU concludes its regular season with eight of 12 games at home. The end of the season is when you want to be at home, in front of a raucous crowd gaining momentum for the postseason, Krogh said. “That’s when you really want to play well, going into the playoffs. So I think that’ll help,” he said. Goodbye CCHA, hello Big Ten The CCHA is disbanding after this season. Starting in 2013-14, OSU, along with Michigan, Michigan State, Minnesota, Penn State and Wisconsin, will form the first-ever Big Ten men’s hockey conference. Osiecki said OSU is already starting to reap the benefits of being a Big Ten hockey school, most notably in recruiting. “Especially if you’re in the state of Minnesota, or if you use recruiting differently in certain areas, but in Minnesota, it helps us get in the door of a household,” Osiecki said. “Does it help us land a kid? Maybe not yet, but it certainly opens the door now.” NHL lockout Columbus is home to another major hockey team: the NHL’s Columbus Blue Jackets. For the time being, though, OSU is the only squad that Ohioans will be able to watch play. The NHL lockout has delayed the start of the Blue Jackets’ season, which means OSU could be featured more prominently in Columbus’ hockey spotlight. “Are we going to have a few more fans come in? I’m not sure. It’s a different style, a different brand. It’s obviously a little bit more affordable for families (than the NHL),” Osiecki said. One thing NHL fans that stop by the Schottenstein Center to watch OSU play can expect, Osiecki said, is an effort unlike that in the NHL. “College guys give it every single game. There’s two games a weekend. That’s it. They’re not playing 82 games. It’s such a different brand of hockey,” Osieck said. Building a program Osiecki, a Minnesota native and former NHL defender, is entering his third season at the helm of the OSU men’s hockey program. Despite the Buckeyes’ struggles at the end of last season, OSU’s coach and his staff are pleased with the way their program is developing. This season’s team, more than the previous two squads Osiecki has led at OSU, truly displays what college hockey should be about, the coach said. “When they step on the ice, or stepping in the locker room, they’re ready to go. The mentality of being a hockey player has really changed. It’s been fun to see that growth,” Osiecki said. OSU players have been itching to get on the ice as much as possible since last season ended, Osiecki said, and it’s something the coach loves to see. “You’ve got guys coming in this year – for the first time in the three years we’ve been here – you’ve got guys asking, ‘There’s open ice, can we go out and skate? Can we just go out and shoot pucks?’ No one ever asked that question before,” Osiecki said. OSU, with a storied football program and elite men’s basketball team, likely will never be a typical “hockey school.” It’s getting closer to being one, though. “My first year coaching at North Dakota, it was a great experience for me. The ice was there all day and kids came in periodically throughout the day and skated. They wanted to be a hockey player. I think we’re getting closer to that when kids are coming here, wanting to be a hockey player,” Osiecki said. OSU opens its season with an exhibition game Sunday against Waterloo at 2 p.m. at the Schottenstein Center. The Buckeyes open the regular season Oct. 12 at 7 p.m. against Minnesota Duluth in Duluth, Minn.
Real Madrid defender Sergio Ramos maintains there are no cracks in the Spain camp after the shocking sack of their manager Julen Lopetegui eve of the World Cup tournament and urged his team-mates to move on quickly.The 2010 winners open their World Cup against Portugal in Sochi on Friday as new coach Fernando Hierro takes over. Ramos insists they will not change their plan for the tournament simply because “there is no time”.“We need to move on as soon as possible. These have not been pleasant times at all,” he said, according to Sky Sports.“For me, personally, it was a more delicate moment but I can assure you that these problems provide an opportunity to grow.Zidane reveals Sergio Ramos injury concern for Real Madrid Andrew Smyth – September 14, 2019 Zinedine Zidane has put Sergio Ramos’ availability for Real Madrid’s trip to Sevilla next weekend in doubt after withdrawing him against Levante.“Julen has been part of all the preparations for this World Cup. (But) Spain needs to come before any individual. As soon as possible, let’s move on from this and focus on the World Cup. That is better for everyone.“There are no cracks. We are all individuals and we all think differently, but the collective idea is the same. We are here to go for the World Cup.“The reality is that we will change little, we don’t have time. We have clear ideas and we are not going to change our concept of how to play football one jot.”Spain are one of the favourites despite the change and some controversial omissions from the squad by Lopetegui, including the likes of Cesc Fabregas and Marcos Alonso. They also face Iran and Morocco in Group B.
The Dominican Republic striker spend one year in the French Ligue 1 team and now goes back to Real Madrid in La LigaAfter spending playing for one year in French Ligue 1 side Lyon, Mariano Sanchez has said goodbye and will now join Real Madrid.The 25-year-old feels very grateful to the French team, where he played for 37 matches, scoring 18 goals.But he was not leaving without saying goodbye, and he published on Twitter a heartful letter to the club and fans.“With every effort, every action, every controlled pass, every goal, I have defended with my life the Olympique Lyonnais jersey,” he said on Twitter as reported by Marca.“Today is the day where I say goodbye to a club that helped me to progress as a player and as a person.”Zidane reveals Sergio Ramos injury concern for Real Madrid Andrew Smyth – September 14, 2019 Zinedine Zidane has put Sergio Ramos’ availability for Real Madrid’s trip to Sevilla next weekend in doubt after withdrawing him against Levante.“I can only be thankful to my teammates, to the member of the technical staff, the club’s employees and especially to the fans who are there every day.”The player will be presented in the Santiago Bernabeu stadium tomorrow.À bientôt et merci @OL pic.twitter.com/mbkNwFsViI— Mariano Diaz Mejia (@marianodiaz9) August 30, 2018
Real Madrid captain Sergio Ramos refuses to take Al Ain lightly ahead of this evening’s Club World Cup finalFollowing Wednesday’s 3-1 win against Japanese side Kashima Antlers, Real will now take on local team Al Ain.The European champions are gunning for a third World Cup in a row and are considered the strong favourites.But Ramos knows all too well that in football anything can happen and, therefore, intends to stay on guard as Real attempt to make more history today.“We’ve got another chance to retain the Club World Cup,” said Ramos on the club website.Mourinho: “Lionel Messi made me a better coach” Andrew Smyth – September 14, 2019 Jose Mourinho believes the experience of going up against Barcelona superstar Lionel Messi at Real Madrid made him a greater coach.“No club has won it three years in a row and we’re really looking forward to the final and are hoping to take the trophy home before going on holiday”“We’re really looking forward to the game and we have the utmost respect for the opponent, River were favourites, but we saw that the badge alone doesn’t win you anything.“Physicality and intensity prevail in football. We know that they have the swede up top, the Brazilian on the left or the Egyptian in the midfield.“Football is much more even these days and we’ll go out knowing that it will be a very difficult match”.The World Cup final between Real and Al Ain will take place at the Zayed Sports City Stadium with kick-off set for 17:30 (CET).
Facebook0TwitterEmailPrintFriendly分享Homer Electric Association, Inc. (HEA) members will see an increase in their monthly bills beginning January 1, 2018. According to a press release, HEA proposes an increase to the Cost of Power Adjustment (COPA) rate from $0.06805 to $0.07077 per kilowatt hour, which is an increase of 4.0%. The COPA is adjusted on a quarterly basis and primarily reflects the cost of natural gas used to generate power for HEA members. The average residential member who uses 550 kWh/month will see a $1.49 increase in their bill.
Changes in optimized traffic in the central London subway network after the removal of the station “Bank” (black node). The corresponding costs are γ= 2 (A) and γ= 0.5 (B). Nodes and edges that show an increase (decrease) in traffic appear in red (blue), where their size and thickness correspond to the magnitude of increase (decrease). Nodes and edges with no traffic changes appear in white and black, respectively. Passenger source–destination pairs are identical to those of Fig. 3 [cf. paper], except for the removal of pairs starting or ending destinations in Bank. Copyright © PNAS, doi:10.1073/pnas.1301111110 Finding a single optimal route is easy, but optimizing the combination of multiple routes is a challenge found in a wide range of applications including Internet instant messaging, peer-to-peer networks, subway traffic, airport flight management, water distribution systems, sensor deployment, military convoy logistics, and trip planning. Historically, due to the computational complexity of deriving a global path optimization (that is, one that simultaneously considers all path possibilities), existing routing algorithms typically optimize each paths in isolation. As a consequence, the resulting solutions are less than optimal. Recently, however, scientists at Aston University, United Kingdom and The Hong Kong University of Science and Technology used the physics of interacting polymers (large molecule composed of many repeated subunits, known as monomers) and disordered systems to analyze macroscopic properties of generic path optimization problems. By so doing, they derived a simple yet global, routing algorithm capable of simultaneously considering all individual path alternatives. The researchers then demonstrated the algorithm utility by applying it to Internet-like random graphs, travel on the London Underground, and the global airport network. Moreover, their analysis revealed phase transitions, scaling laws, non-monotonic growth (that is, not always stable or increasing), and other new routing phenomena related to physics. Explore further © 2013 Phys.org. All rights reserved. Removing ‘black sheep’ could make Internet run more efficiently Research Fellow Chi Ho Yeung discussed the research he and his colleagues, Profs. David Saad and K. Y. Michael Wong, conducted – and the challenges they face – with Phys.org. “While, employing tools in physics to solve the system analytically was indeed our most difficult task,” Yeung tells Phys.org, “the analogy between polymers and paths is actually easy to understand. A polymer is a long molecule chain likes a string with two ends,” he illustrates, “Suppose I represent my travel path by a polymer: the two ends will be fixed representations of my starting point and destination, and the polymer body will be flexible depending on my path choice. If every traveler represents their path this way, we’d have a system of polymers on a transportation network – meaning that to suppress congestion, we’d introduce a repulsive force between polymers to discourage users using the same route. On the other hand, to encourage passengers share their path we’d introduce an attraction.”Turning now to their analytic work, Yeung points out that polymer paths are non-local variables, which are more difficult to analyze compared to local variables and interactions in conventional physics models. In addition, he notes that all polymers share the same network infrastructure and any two of them may have overlapping paths. “In our transportation network, when polymers overlap they either interact through an attraction or repulsion. It is thus equivalent to say that any two polymers may interact,” Yeung continues, “and the extent of that interaction depends on the extent of overlap, which is again a non-local consideration regarding all polymers. With all these complications, we had to select the best paths out of all possible individual choices as well as their mutual overlapping.” Compared to ordinary polymer systems (which do not allow overlap), they researchers had a much larger pool of possible states, and thereby a much more difficult question to solve. “After deriving our theoretical results,” Yeung adds, “we obtained the algorithm directly – and testing it on several datasets, found very good results. Once the system was analytically solved, it was straightforward to find its macroscopic properties, such as average path length and energy, by ordinary physics techniques in our area.” One key insight the scientists had, says Yeung, was that while some may think that the shortest path is always the best choice, this is not the case – and in fact, usual choice of going through the shortest path is a bad one when everyone takes the same route. “This isn’t difficult to understand, as some observers may have already noticed. For example,” Yeung illustrates, “during peak hours, some popular routes which lie on the shortest path may be overloaded, causing delays and making this path slower than a slightly longer one.” Yeung points out that their simulations with the London metro data show that – compared to when all passengers travel through the shortest path – if they introduce a repulsive force between passenger paths, and if passengers follow the suggested path, 20% of the assumed cost can be saved at a price of only 6% increase in average path length. “On the other hand,” Yeung continues, “although congestion does not occur in off-peak hours, the shortest path is still a bad choice, because the whole network has to remain active even for reduced usage on the less popular routes. Suppose we encourage off-peak commuters to travel on some common routes and share a large part of their journeys; then, the less popular bus routes or train lines can be discontinued which saves a lot of energy.” Yeung adds that their results show that they can obtain such optimized shared path configurations through the analogy to an attractive polymer system.Other than these results, the scientists also found that when they gradually change the polymer interaction from slightly repulsive to slightly attractive, there is a sharp increase in the number of idle nodes. “This is similar to a discontinuous phase transition observed in other physical systems,” Yeung says. “Surprisingly, while the average path length does not change much, it does have an important implication on transportation or communication networks – that is, one can greatly increase the number of idle nodes without significantly lengthening the average path length, by introducing a slight attractive force between passenger paths. This may save a lot of resources in sparse traffic scenarios.”A key aspect of the researchers’ results was demonstrating the algorithm’s efficacy by applying it to random graphs resembling Internet overlay networks – that is, computer networks built on top of another network, in which nodes can be thought of as being connected by virtual or logical links, each of which corresponds to a path, perhaps through many physical links, in the underlying network. “Networks representing websites interconnected by hyperlinks, or friends linked by instant messengers, are usually not bounded by physical location,” Yeung notes, “and are well described by some specific random structures. We show in a simple random network how we can find the best choice of communication paths according to the attractive or repulsive strength we introduced.”In the case of repulsion, Yeung explains, individual communication paths avoid each other and at last almost everyone has its own path not overlapping with the others. In the case of attraction, the communications go through a small common region of the network, sharing their paths and leaving a lot of other nodes and links idle. “If we consider the idle nodes as routers,” he points out, “a lot of energy can be saved by switching them off.”The researchers also applied their findings to travel on the London Underground network based on Oyster card data. “If we compare to the case where everyone takes their shortest path,” says Yeung, “our simulations show substantial improvement on the London Metro network. Again, at a price of only 6% increase in average path length, 20% and 4% of the assumed cost are saved on the London metro network when one aims to balance or consolidate traffic, respectively. Of course, in practice,” he acknowledges, “some experienced users would adopt a smarter route than the shortest path and the benefit from our algorithm would be less. However, I believe that in many transportation or communication networks there is still a large room of improvement in terms of energy saving if individual paths are well coordinated.” Yeung adds that they did a very similar experiment, and obtain a similar result, in the global airport network.Regarding other innovations that the scientists might develop and apply to the current experimental design, Yeung says that since physicists usually start with a generic model of physical systems, they’ve also assumed a model of interacting polymers which accommodates different type of interaction. “It turns out that we obtain a single algorithm which achieves various goals by tuning a single parameter controlling the attractive and repulsive strength between polymers,” he explains. “Indeed, our approach can take into account interactions other than attraction and repulsion, and which may have other interesting applications. We welcome networking experts to suggest other specific routing problems which our algorithm may be able to tackle.On the practical side, Yeung continues, one idea may be to develop a real-time application, based on their algorithm, to globally coordinate paths for individuals who start their journey at roughly the same time. “It’s not the same as the usual route-finder applications that simply identify the shortest path for individuals without their interactions with others,” he explains. “Rather, the envisioned application would coordinate routes for many individuals who travel at the same time in order to achieve goals like balancing highway or tunnel usage, or to encourage train or plane sharing in off-peak hours or seasons.”Yeung also describes the planned next steps in their research. “Our path solution is static.” He notes. “In other words, it provides an optimized path configuration given a set of destination pairs, and so suits many applications – but not those where the amount of traffic between individual destination pairs is rapidly changing. The next step is, perhaps, to develop routing algorithms based on our framework which address a dynamical routing task.”Yeung notes that other areas of research that might benefit from their study. “Our generic routing algorithm is applicable to any application that involves the path selection and coordination of individual paths,” he tells Phys.org. “I hope our work can contribute to routing problems in transportation and communication networks, as well as sustainability research where the fixed infrastructure of existing transportation or communication systems is better utilized, thereby reducing the needs for further construction. In a more general respect,” Yeung concludes, “I hope that our work demonstrates the power of rigorous physical tools when applied to interdisciplinary areas outside the realm of physics.” More information: From the physics of interacting polymers to optimizing routes on the London Underground, PNAS Published online before print July 29, 2013, doi:10.1073/pnas.1301111110 Optimized traffic on the London subway network. A total of 218 real passenger source–destination pairs are optimized, corresponding to 5% of the data recorded by the Oyster card system between 8:30 AM and 8:31 AM on one Wednesday in November 2009 [cf. citation (35) in paper]. The network consists of 275 stations. (B). Red nodes correspond to stations with nonzero traffic. The size of each node and the thickness of each edge are proportional to traffic through them. (Insets) Zoomed-in views of the central region. Nodes are drawn according to their geographic position. Copyright © PNAS, doi:10.1073/pnas.1301111110 Journal information: Proceedings of the National Academy of Sciences Citation: Planes, trains and molecules: Deriving a generic routing algorithm from the physics of interacting polymers (2013, August 20) retrieved 18 August 2019 from https://phys.org/news/2013-08-planes-molecules-deriving-routing-algorithm.html This document is subject to copyright. Apart from any fair dealing for the purpose of private study or research, no part may be reproduced without the written permission. The content is provided for information purposes only.