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Envelope theorems provide a differential framework for determining how much a rational decision maker (DM) is willing to pay to alter the parameters of a strategic scenario. We generalize this framework to the case of a boundedly rational DM and arbitrary solution concepts. We focus on comparing and contrasting the case where DM&rsquo, s decision to pay to change the parameters is observed by all other players against the case where DM&rsquo, s decision is private information. We decompose DM&rsquo, s willingness to pay a given amount into a sum of three factors: (1) the direct effect a parameter change would have on DM&rsquo, s payoffs in the future strategic scenario, holding strategies of all players constant, (2) the effect due to DM changing its strategy as they react to a change in the game parameters, with the strategies of the other players in that scenario held constant, and (3) the effect there would be due to other players reacting to a the change in the game parameters (could they observe them), with the strategy of DM held constant. We illustrate these results with the quantal response equilibrium and the matching pennies game and discuss how the willingness to pay captures DM&rsquo, s anticipation of their future irrationality.

The IBM Z processor continues to improve over previous System Z processors, but for the first time it does so without a technology improvement as the baseline enabler. The IBM z15 was designed in the same 14-nm High-Performance GLOBALFOUNDRIES technology as the IBM z14 and yet still added 20% more cores, doubled the L3 cache, and increased the L2 cache by a third while also adding a third peripheral component interconnect express (PCIe) port to the chip and an elliptic curve cryptography engine into each core. This article discusses the design, tool, and methodology enhancements required to increase the design content so significantly while maintaining the chip size and power limits from the previous z14 design. This article also discusses other design and methodology improvements that were made possible via the deeper understanding of the technology and how to more fully leverage it in a second generation.

Digital computers implement computations using circuits, as do many naturally occurring systems (e.g., gene regulatory networks). The topology of any such circuit restricts which variables may be physically coupled during the operation of a system implementing a circuit. We investigate how such restrictions on the physical coupling affects the thermodynamic costs of the circuit. To do this we first calculate the minimal additional entropy production that arises when we run a given gate in a circuit, if the physical process implementing that gate can only be coupled to variables in the rest of the circuit that feed in or out of that gate. We then build on this calculation, to analyze how the thermodynamic costs of implementing a computation with a full circuit, comprising multiple connected gates, depends on the topology of that circuit. This analysis provides a rich new set of optimization problems that must be addressed by any designer of a circuit, if they wish to minimize thermodynamic costs.

Shannon information theory provides various measures of so-called syntactic information, which reflect the amount of statistical correlation between systems. By contrast, the concept of ‘semantic information’ refers to those correlations which carry significance or ‘meaning’ for a given system. Semantic information plays an important role in many fields, including biology, cognitive science and philosophy, and there has been a long-standing interest in formulating a broadly applicable and formal theory of semantic information. In this paper, we introduce such a theory. We define semantic information as the syntactic information that a physical system has about its environment which is causally necessary for the system to maintain its own existence. ‘Causal necessity’ is defined in terms of counter-factual interventions which scramble correlations between the system and its environment, while ‘maintaining existence’ is defined in terms of the system's ability to keep itself in a low entropy state. We also use recent results in non-equilibrium statistical physics to analyse semantic information from a thermodynamic point of view. Our framework is grounded in the intrinsic dynamics of a system coupled to an environment, and is applicable to any physical system, living or otherwise. It leads to formal definitions of several concepts that have been intuitively understood to be related to semantic information, including ‘value of information’, ‘semantic content’ and ‘agency’.

Background Hyperglycemia leading to increased oxidative stress is implicated in the increased risk for the development of macrovascular and microvascular complications in patients with type 1 diabetes mellitus. Methods and Results A random subcohort of 349 participants was selected from the DCCT / EDIC (Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications) cohort. This included 320 controls and 29 cardiovascular disease cases that were augmented with 98 additional known cases to yield a case cohort of 447 participants (320 controls, 127 cases). Biosamples from DCCT baseline, year 1, and closeout of DCCT , and 1 to 2 years post‐ DCCT ( EDIC years 1 and 2) were measured for markers of oxidative stress, including plasma myeloperoxidase, paraoxonase activity, urinary F 2α isoprostanes, and its metabolite, 2,3 dinor‐8 iso prostaglandin F 2α . Following adjustment for glycated hemoblobin and weighting the observations inversely proportional to the sampling selection probabilities, higher paraoxonase activity, reflective of antioxidant activity, and 2,3 dinor‐8 iso prostaglandin F 2α , an oxidative marker, were significantly associated with lower risk of cardiovascular disease (−4.5% risk for 10% higher paraoxonase, P iso prostaglandin F 2α , P =0.0092). In contrast, the oxidative markers myeloperoxidase and F 2α isoprostanes were not significantly associated with cardiovascular disease after adjustment for glycated hemoblobin. There were no significant differences between DCCT intensive and conventional treatment groups in the change in all biomarkers across time segments. Conclusions Heightened antioxidant activity (rather than diminished oxidative stress markers) is associated with lower cardiovascular disease risk in type 1 diabetes mellitus, but these biomarkers did not change over time with intensification of glycemic control. Clinical Trial Registration URL : https://www.clinicaltrials.gov . Unique identifiers: NCT 00360815 and NCT 00360893.

This volume grew out of a workshop designed to bring together researchers from different fields and includes contributions from workers in Bayesian analysis, machine learning, neural nets, PAC and VC theory, classical sampling theory statistics and the statistical physics of learning. The contributions present a bird's-eye view of the subject.

There are four types of information an agent can have concerning the state of the universe: information acquired via observation, via control, via prediction, or via retrodiction, i.e., memory. Each of these four types of information appear to rely on a different kind of physical device (e.g., an observation device, a control device, etc.). However it turns out that there is some mathematical structure that is common to those four types of devices. Any device that possesses that structure is known as an “inference device” (ID). Here I review some of the properties of IDs, including their relation with Turing machines, and (more loosely) quantum mechanics. I also review the bounds on the joint information about the physical universe that can be held by any set of IDs. These bounds constrain the possible mathematical structure of any universe that contains agents with information concerning that universe in which they are embedded.

When the strict rationality underlying the Nash equilibria in game theory is relaxed, one arrives at the quantal response equilibria introduced by McKelvey and Palfrey. Here, the players are assigned parameters measuring their degree of rationality, and the resulting equilibria are Gibbs type distribution. This brings us into the realm of the exponential families studied in information geometry, with an additional structure arising from the relations between the players. Tuning these rationality parameters leads to a simple geometric proof of the Nash existence theorem that only employs intersection properties of submanifolds of Euclidean spaces and dispenses with the Brouwer fixed point theorem on which the classical proofs depend. Also, in this geometric framework, we can develop very efficient computational tools for studying examples. The method can also be applied when additional parameters are involved, like the capacity of an information channel.

Gaussian process priors are commonly used in aerospace design for performing Bayesian optimization. Nonetheless, Gaussian processes suffer two significant drawbacks: outliers are a priori assumed unlikely, and the posterior variance conditioned on observed data depends only on the locations of those data, not the associated sample values. Student's-T processes are a generalization of Gaussian processes, founded on the Student's-T distribution instead of the Gaussian distribution. Student's-T processes maintain the primary advantages of Gaussian processes (kernel function, analytic update rule) with additional benefits beyond Gaussian processes. The Student's-T distribution has higher Kurtosis than a Gaussian distribution and so outliers are much more likely, and the posterior variance increases or decreases depending on the variance of observed data sample values. Here, we describe Student's-T processes, and discuss their advantages in the context of aerospace optimization. We show how to construct a Student's-T process using a kernel function and how to update the process given new samples. We provide a clear derivation of optimization-relevant quantities such as expected improvement, and contrast with the related computations for Gaussian processes. Finally, we compare the performance of Student's-T processes against Gaussian process on canonical test problems in Bayesian optimization, and apply the Student's-T process to the optimization of an aerostructural design problem., Comment: 2018 AIAA Non-Deterministic Approaches Conference

Gintis and Helbing discuss some of the major holes in the set of phenomena that are addressed in modern theory of social systems, and argue for a unified approach to fill those holes. Their paper is a major contribution. However it overlooks some of the holes in modern theory that are arguably are at least as important as the ones that Gintis and Helbing consider. In this short commentary I present and discuss two such holes in modern theory of social systems, holes that greatly handicap our theoretical understanding of social systems.

Master equations are commonly used to model the dynamics of physical systems, including systems that implement single-valued functions like a computer's update step. However, many such functions cannot be implemented by any master equation, even approximately, which raises the question of how they can occur in the real world. Here we show how any function over some "visible" states can be implemented with master equation dynamics--if the dynamics exploits additional, "hidden" states at intermediate times. We also show that any master equation implementing a function can be decomposed into a sequence of "hidden" timesteps, demarcated by changes in what state-to-state transitions have nonzero probability. In many real-world situations there is a cost both for more hidden states and for more hidden timesteps. Accordingly, we derive a "space-time" tradeoff between the number of hidden states and the number of hidden timesteps needed to implement any given function., 17 pages, 2 figures

Hemoglobin levels (Hgb) of infants with a single ventricle (SV) are traditionally maintained high to maximize oxygen-carrying capacity during stage 1 palliation (S1P), stage 2 palliation (S2P), and between stages (IS). A single-center observational cohort study was performed to determine if red blood cell transfusion during the convalescent phase of the S1P (late S1P transfusion) to achieve higher Hgb is associated with benefits during the IS including improved growth and decreased acute medical events. 137 infants

Microbes maintain themselves through a variety of processes. Several of these processes can be reduced or shut down entirely when resource availability declines. In pure culture conditions with ample substrate supply, a relationship between the maximum growth rate and the energy invested in maintenance has been reported widely. However, at the other end of the resources spectrum, bacteria are so extremely limited by energy that no growth occurs and metabolism is constrained to the most essential functions only. These minimum energy requirements have been called the basal power requirement. While seemingly different from each other, both aspects are likely components of a continuum of regulated maintenance processes. Here, we analyze cross species tradeoffs in cellular physiology over the range of bacterial size and energy expenditure and determine the contributions to maintenance metabolism at each point along the size-energy spectrum. Furthermore, by exploring the simplest bacteria within this framework-- which are most affected by maintenance constraints-- we uncover which processes become most limiting. For the smallest species, maintenance metabolism converges on total metabolism, where we predict that maintenance is dominated by the repair of proteins. For larger species the relative costs of protein repair decrease and maintenance metabolism is predicted to be dominated by the repair of RNA components. These results provide new insights into which processes are likely to be regulated in environments that are extremely limited by energy.

The original version of the Supplementary Information associated with this Article contained an error throughout in which all inline references to Theorems, Definitions and Lemmas given in the main Article were incorrectly given as ‘??’. The HTML has been updated to include a corrected version of the Supplementary Information.

We consider the problem of how to construct a physical process over a finite state space $X$ that applies some desired conditional distribution $P$ to initial states to produce final states. This problem arises often in the thermodynamics of computation and nonequilibrium statistical physics more generally (e.g., when designing processes to implement some desired computation, feedback controller, or Maxwell demon). It was previously known that some conditional distributions cannot be implemented using any master equation that involves just the states in $X$. However, here we show that any conditional distribution $P$ can in fact be implemented---if additional "hidden" states not in $X$ are available. Moreover, we show that it is always possible to implement $P$ in a thermodynamically reversible manner. We then investigate a novel cost of the physical resources needed to implement a given distribution $P$: the minimal number of hidden states needed to do so. We calculate this cost exactly for the special case where $P$ represents a single-valued function, and provide an upper bound for the general case, in terms of the nonnegative rank of $P$. These results show that having access to one extra binary degree of freedom, thus doubling the total number of states, is sufficient to implement any $P$ with a master equation in a thermodynamically reversible way, if there are no constraints on the allowed form of the master equation. (Such constraints can greatly increase the minimal needed number of hidden states.) Our results also imply that for certain $P$ that can be implemented without hidden states, having hidden states permits an implementation that generates less heat., Comment: 16 pages, 2 figures

Recent years have seen increased interest in the design and deployment of smart grid devices and control algorithms. Each of these smart communicating devices represents a potential access point for an intruder spurring research into intruder prevention and detection. However, no security measures are complete, and intruding attackers will compromise smart grid devices leading to the attacker and the system operator interacting via the grid and its control systems. The outcome of these machine-mediated human-human interactions will depend on the design of the physical and control systems mediating the interactions. If these outcomes can be predicted via simulation, they can be used as a tool for designing attack-resilient grids and control systems. However, accurate predictions require good models of not just the physical and control systems, but also of the human decision making. In this manuscript, we present an approach to develop such tools, i.e. models of the decisions of the cyber-physical intruder who is attacking the systems and the system operator who is defending it, and demonstrate its usefulness for design., Comment: 8 pages, 7 figures, IEEE Transactions on Smart Grids pending

In experimental tests of human behavior in unstructured bargaining games, typically many joint utility outcomes are found to occur, not just one. This suggests we predict the outcome of such a game as a probability distribution. This is in contrast to what is conventionally done (e.g, in the Nash bargaining solution), which is predict a single outcome. We show how to translate Nash's bargaining axioms to provide a distribution over outcomes rather than a single outcome. We then prove that a subset of those axioms forces the distribution over utility outcomes to be a power-law distribution. Unlike Nash's original result, our result holds even if the feasible set is finite. When the feasible set is convex and comprehensive, the mode of the power law distribution is the Harsanyi bargaining solution, and if we require symmetry it is the Nash bargaining solution. However, in general these modes of the joint utility distribution are not the experimentalist's Bayes-optimal predictions for the joint utility. Nor are the bargains corresponding to the modes of those joint utility distributions the modes of the distribution over bargains in general, since more than one bargain may result in the same joint utility. After introducing distributional bargaining solution concepts, we show how an external regulator can use them to optimally design an unstructured bargaining scenario. Throughout we demonstrate our analysis in computational experiments involving flight rerouting negotiations in the National Airspace System. We emphasize that while our results are formulated for unstructured bargaining, they can also be used to make predictions for noncooperative games where the modeler knows the utility functions of the players over possible outcomes of the game, but does not know the move spaces the players use to determine those outcomes.

Introduction Frequent blood testing increases risk of iatrogenic anemia, infection, and blood transfusion. This study describes 3 years of sustained blood testing reduction from a quality improvement (QI) initiative which began in 2011. Methods The cohort consisted of postop children whose surgery had a Risk Adjustment for Congenital Heart Surgery (RACHS) classification consecutively admitted to a tertiary Cardiac Intensive Care Unit. Data were collected for a 2010 preintervention, 2011 intervention, and 2012-13 postintervention periods, tabulating common laboratory studies per patient (labs/pt) and adjusted for length of stay (labs/pt/d). The QI initiative eliminated standing laboratory orders and changed to testing based on individualized patient condition. Adverse outcomes data were collected including reintubation, central line-associated bloodstream infections and hospital mortality. Safety was measured by the number of abnormal laboratory studies, electrolyte replacements, code blue events, and arrhythmias. Results A total of 1169 patients were enrolled (303 preintervention, 315 intervention, and 551 postintervention periods). The number of labs/pt after the QI intervention was sustained (38 vs. 23 vs. 23) and labs/pt/d (15 vs. 11 vs. 10). The postintervention group had greater surgical complexity (P = 0.002), were significantly younger (P = 0.002) and smaller (P = 0.008). Children with RACHS 3-4 classification in the postintervention phase had significant increased risk of reintubation and arrhythmias. Conclusions After the implementation of a QI initiative, blood testing was reduced and sustained in young, complex children after heart surgery. This may or may not have contributed to greater reintubation and arrhythmias among patients with RACHS 3-4 category procedures.

OBJECTIVE To determine whether judicious blood testing impacts timing or amount of packed RBC transfusions in infants after heart surgery. DESIGN A retrospective study comparing before and after initiation of a quality improvement process. SETTING A university-affiliated cardiac ICU at a tertiary care children's hospital. PATIENTS Infants less than 1 year old with Risk Adjustment for Congenital Heart Surgery category 4, 5, 6, or d-transposition of great arteries (Risk Adjustment for Congenital Heart Surgery 3) consecutively treated during 2010 through 2013. INTERVENTION A quality improvement process implemented in 2011 to decrease routine laboratory testing after surgery. MEASUREMENTS AND MAIN RESULTS Fifty-two infants preintervention and 214 postintervention had similar age, weight, proportion of cyanotic lesions, and surgical complexity. Infants with single versus biventricular physiology were compared separately. The number of laboratory tests per patient adjusted for cardiac ICU length of stay (laboratory tests/patient/day) was significantly lower in postintervention populations for single and biventricular groups (9 vs 15 and 10 vs 15, respectively; p < 0.001). The proportion of single ventricle patients transfused post- and preintervention was not statistically different (72% vs 90%; p = 0.130). Transfusion in the biventricular groups was the same over time (65% vs 65%). Time to first transfusion was significantly longer in the postintervention single ventricle group (4 vs 1 d; p < 0.001), and was not statistically different in the biventricular patients (4 vs 7 d; p = 0.058). The median hematocrit level at first transfusion was significantly lower (37% vs 40%; p = 0.004) postintervention in the cyanotic population, but did not differ in the biventricular group (31% vs 31%; p = 0.840). CONCLUSION In infants after heart surgery, blood testing targeted to individual needs significantly decreased the number of blood tests, but did not significantly decrease postoperative blood transfusion.

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field approximation to the target distribution, and update the proposal distribution to be that approximatio. We employ our algorithm to sample the energy distribution for several spin-glasses and we demonstrate the superiority of our algorithm to the conventional MH algorithm in sampling and in annealing optimization., To appear in Europhysics Letters

We analyze how the amount of work dissipated by a fixed nonequilibrium process depends on the initial distribution over states. Specifically, we compare the amount of dissipation when the process is used with some specified initial distribution to the minimal amount of dissipation possible for any initial distribution. We show that the difference between those two amounts of dissipation is given by a simple information-theoretic function that depends only on the initial and final state distributions. Crucially, this difference is independent of the details of the process relating those distributions. We then consider how dissipation depends on the initial distribution for a 'computer', i.e., a nonequilibrium process whose dynamics over coarse-grained macrostates implement some desired input-output map. We show that our results still apply when stated in terms of distributions over the computer's coarse-grained macrostates. This can be viewed as a novel thermodynamic cost of computation, reflecting changes in the distribution over inputs rather than the logical dynamics of the computation.

In Newcomb’s paradox you can choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose though, an antagonist uses a prediction algorithm to accurately deduce your choice, and uses that deduction to fill the two boxes. The way they do this guarantees that you made the wrong choice. Newcomb’s paradox is that game theory’s expected utility and dominance principles appear to provide conflicting recommendations for what you should choose. Here we show that the conflicting recommendations assume different probabilistic structures relating your choice and the algorithm’s prediction. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the probabilistic structure relating the problem’s random variables is open to two, conflicting interpretations. We then show that the accuracy of the prediction algorithm in Newcomb’s paradox, the focus of much previous work, is irrelevant. We end by showing that Newcomb’s paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its ‘prediction’ after you make your choice rather than before.

The IBM z14 design was built with the 14-nm high-performance silicon-on-insulator (SOI) technology of GLOBALFOUNDRIES. This was the first technology node after IBM transitioned from its integrated fabrication facility to operating in a fabless environment, driving significant changes to design processes and methodology. In addition to this partnership, the 14-nm technology introduced significant changes relative to previous technology nodes, including the introduction of fin-shaped field-effect transistors, the use of double patterning for the lowest back-end-of-line layers, and the introduction of middle-of-line layers to exploit contact layers for local interconnects. This combination of technical and business challenges required numerous large-scale innovations for our design, design team, and design methodologies. In this paper, we provide a survey of these innovations, including the fin-based standard cell image, deeply scaled SOI self-heating/electromigration verification, routing strategies to handle double-patterning with interlayer via awareness, fill automation to enable simultaneous design of multiple layers of hierarchy, and high-performance array design with the voltage and noise limitations of the 14-nm technology node.

For many systems characterized as “complex” the patterns exhibited on different scales differ markedly from one another. For example, the biomass distribution in a human body “looks very different” depending on the scale at which one examines it. Conversely, the patterns at different scales in “simple” systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self-dissimilarity between the patterns of a system at various scales constitute a complexity “signature” of that system. Here we present a novel quantification of self-dissimilarity. This signature can, if desired, incorporate a novel information-theoretic measure of the distance between probability distributions that we derive here. Whatever distance measure is chosen, our quantification of self-dissimilarity can be measured for many kinds of real-world data. This allows comparisons of the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. species densities in a rain forest vs. capital density in an economy, etc.). Moreover, in contrast to many other suggested complexity measures, evaluating the self-dissimilarity of a system does not require one to already have a model of the system. These facts may allow self-dissimilarity signatures to be used as the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self-dissimilarity, we present several numerical experiments. In particular, we show that the underlying structure of the logistic map is picked out by the self-dissimilarity signature of time series produced by that map. © 2007 Wiley Periodicals, Inc. Complexity 12: 77–85, 2007

This volume focuses on uncovering the fundamental forces underlying dynamic decision making among multiple interacting, imperfect and selsh decision makers. The chapters are written by leading experts from different disciplines, all considering the many sources of imperfection in decision making, and always with an eye to decreasing the myriad discrepancies between theory and real world human decision making. Topics addressed include uncertainty, deliberation cost and the complexity arising from the inherent large computational scale of decision making in these systems. In particular, analyses and experiments are presented which concern: task allocation to maximize the wisdom of the crowd; design of a society of edutainment robots who account for one anothers emotional states; recognizing and counteracting seemingly non-rational human decision making; coping with extreme scale when learning causality in networks; efciently incorporating expert knowledge in personalized medicine; the effects of personality on risky decision making. The volume is a valuable source for researchers, graduate students and practitioners in machine learning, stochastic control, robotics, and economics, among other elds.

Novel assembly processes for nanocircuits could present compelling alternatives to the detailed design and placement currently used for computers. The resulting architectures however may not be programmable by standard means. In this paper, nanocomputers with unconventional architectures are programmed using adaptive methods. The internals of the device are treated as a "black box" and programming is achieved by manipulating "control voltages." Learning algorithms are used to set the controls. As examples, logic gates and simple arithmetic circuits are implemented. Additionally, similar methods allow for reconfiguration of the devices, and makes them resistant to certain kinds of faults.

Recent work has shown how information theory extends conventional full-rationality game theory to allow bounded rational agents. The associated mathematical framework can be used to solve distributed optimization and control problems. This is done by translating the distributed problem into an iterated game, where each agent's mixed strategy (i.e. its stochastically determined move) sets a different variable of the problem. So the expected value of the objective function of the distributed problem is determined by the joint probability distribution across the moves of the agents. The mixed strategies of the agents are updated from one game iteration to the next so as to converge on a joint distribution that optimizes that expected value of the objective function. Here, a set of new techniques for this updating is presented. These and older techniques are then extended to apply to uncountable move spaces. We also present an extension of the approach to include (in)equality constraints over the underlying variables. Another contribution is that we show how to extend the Monte Carlo version of the approach to cases where some agents have no Monte Carlo samples for some of their moves, and derive an "automatic annealing schedule".

It is well known that a player in a non-cooperative game can benefit by publicly restricting his possible moves before play begins. We show that, more generally, a player may benefit by publicly committing to pay an external party an amount that is contingent on the game’s outcome. We explore what happens when external parties – who we call “game miners” – discover this fact and seek to profit from it by entering an outcome-contingent contract with the players. We analyze various structured bargaining games among such miner(s) and players that determine such an outcome-contingent contract before the start of the original game. These bargaining games include playing the players against one another as in the original game, as well as allowing the players to pay the miner(s) for exclusivity and first-mover advantage. We establish restrictions on the strategic settings in which a game miner can profit and bounds on the game miner’s profit. We also find that game miners can lead to both efficient and inefficient equilibria.

Refractive error (RE) is a complex, multifactorial disorder characterized by a mismatch between the optical power of the eye and its axial length that causes object images to be focused off the retina. The two major subtypes of RE are myopia (nearsightedness) and hyperopia (farsightedness), which represent opposite ends of the distribution of the quantitative measure of spherical refraction. We performed a fixed effects meta-analysis of genome-wide association results of myopia and hyperopia from 9 studies of European-derived populations: AREDS, KORA, FES, OGP-Talana, MESA, RSI, RSII, RSIII and ERF. One genome-wide significant region was observed for myopia, corresponding to a previously identified myopia locus on 8q12 (p = 1.25×10-8), which has been reported by Kiefer et al. as significantly associated with myopia age at onset and Verhoeven et al. as significantly associated to mean spherical-equivalent (MSE) refractive error. We observed two genome-wide significant associations with hyperopia. These regions overlapped with loci on 15q14 (minimum p value = 9.11×10-11) and 8q12 (minimum p value 1.82×10-11) previously reported for MSE and myopia age at onset. We also used an intermarker linkage- disequilibrium-based method for calculating the effective number of tests in targeted regional replication analyses. We analyzed myopia (which represents the closest phenotype in our data to the one used by Kiefer et al.) and showed replication of 10 additional loci associated with myopia previously reported by Kiefer et al. This is the first replication of these loci using myopia as the trait under analysis. "Replication-level" association was also seen between hyperopia and 12 of Kiefer et al.'s published loci. For the loci that show evidence of association to both myopia and hyperopia, the estimated effect of the risk alleles were in opposite directions for the two traits. This suggests that these loci are important contributors to variation of refractive error across the distribution.

We examine the potential for a simple auction to allocate arrival slots during Ground Delay Programs (GDPs) more efficiently than the currently used system. We find that the second-price slot auction has the potential to lower social costs but further analysis is needed to determine which pre-GDP schedules are best suited for an auction. The analysis of these auctions uses Predictive Game Theory (PGT) Wolpert and Bono (2013, 2010), a new approach that produces a probability distribution over strategies instead of an equilibrium set. Furthermore, the slot auction game of this paper represents the first application of PGT to a game of imperfect information and to a pure strategy space.

Consider a given random variable F and a random variable that we can modify, F^. We wish to use asample of F^ as an estimate of a sample of F. The mean squared error between such a pair of samples is asum of four terms. The rst term reects the statistical coupling between Fand F^ and is conventionallyignored in bias-variance analysis. The second term reects the inherent noise in F and is independentof the estimator F^. Accordingly, we cannot a ect this term. In contrast, the third and fourth termsdepend on F^. The third term, called the bias, is independent of the precise samples of both F andF^, and reects the di erence between the means of F and F^. The fourth term, called the variance, isindependent of the precise sample of F, and reects the inherent noise in the estimator as one samplesit. These last two terms can be modi ed by changing the choice of the estimator. In particular, onsmall sample sets, we can often decrease our mean squared error by, for instance, introducing a smallbias that causes a large reduction the variance. While most commonly used in machine learning, thisarticle shows that such bias-variance trade-o s are applicable in a much broader context and in a varietyof situations. We also show, using experiments, how existing bias-variance trade-o s can be applied innovel circumstances to improve the performance of a class of optimization algorithms.

We consider the El Farol bar problem, also known as the minority game (W. B. Arthur, ``The American Economic Review'', 84(2): 406--411 (1994), D. Challet and Y.C. Zhang, ``Physica A'', 256:514 (1998)). We view it as an instance of the general problem of how to configure the nodal elements of a distributed dynamical system so that they do not ``work at cross purposes'', in that their collective dynamics avoids frustration and thereby achieves a provided global goal. We summarize a mathematical theory for such configuration applicable when (as in the bar problem) the global goal can be expressed as minimizing a global energy function and the nodes can be expressed as minimizers of local free energy functions. We show that a system designed with that theory performs nearly optimally for the bar problem., 8 pages

Bagging (Breiman, 1994a) is a technique that tries to improve a learning algorithm‘s performance by using bootstrap replicates of the training set (Efron & Tibshirani, 1993, Efron, 1979). The computational requirements for estimating the resultant generalization error on a test set by means of cross-validation are often prohibitive, for leave-one-out cross-validation one needs to train the underlying algorithm on the order of mν times, where m is the size of the training set and ν is the number of replicates. This paper presents several techniques for estimating the generalization error of a bagged learning algorithm without invoking yet more training of the underlying learning algorithm (beyond that of the bagging itself), as is required by cross-validation-based estimation. These techniques all exploit the bias-variance decomposition (Geman, Bienenstock & Doursat, 1992, Wolpert, 1996). The best of our estimators also exploits stacking (Wolpert, 1992). In a set of experiments reported here, it was found to be more accurate than both the alternative cross-validation-based estimator of the bagged algorithm‘s error and the cross-validation-based estimator of the underlying algorithm‘s error. This improvement was particularly pronounced for small test sets. This suggests a novel justification for using bagging—more accurate estimation of the generalization error than is possible without bagging.