Principal Trade-off Analysis

How are the advantage relations between a set of agents playing a game organized and how do they reflect the structure of the game? In this paper, we illustrate "Principal Trade-off Analysis" (PTA), a decomposition method that embeds games into a low-dimensional feature space. We argue that the embeddings are more revealing than previously demonstrated by developing an analogy to Principal Component Analysis (PCA). PTA represents an arbitrary two-player zero-sum game as the weighted sum of pairs of orthogonal 2D feature planes. We show that the feature planes represent unique strategic trade-offs and truncation of the sequence provides insightful model reduction. We demonstrate the validity of PTA on a quartet of games (Kuhn poker, RPS+2, Blotto, and Pokemon). In Kuhn poker, PTA clearly identifies the trade-off between bluffing and calling. In Blotto, PTA identifies game symmetries, and specifies strategic trade-offs associated with distinct win conditions. These symmetries reveal limitations of PTA unaddressed in previous work. For Pokemon, PTA recovers clusters that naturally correspond to Pokemon types, correctly identifies the designed trade-off between those types, and discovers a rock-paper-scissor (RPS) cycle in the Pokemon generation type - all absent any specific information except game outcomes.Comment: 17 pages, 8 figure

Machine learning in and out of equilibrium

The algorithms used to train neural networks, like stochastic gradient descent (SGD), have close parallels to natural processes that navigate a high-dimensional parameter space -- for example protein folding or evolution. Our study uses a Fokker-Planck approach, adapted from statistical physics, to explore these parallels in a single, unified framework. We focus in particular on the stationary state of the system in the long-time limit, which in conventional SGD is out of equilibrium, exhibiting persistent currents in the space of network parameters. As in its physical analogues, the current is associated with an entropy production rate for any given training trajectory. The stationary distribution of these rates obeys the integral and detailed fluctuation theorems -- nonequilibrium generalizations of the second law of thermodynamics. We validate these relations in two numerical examples, a nonlinear regression network and MNIST digit classification. While the fluctuation theorems are universal, there are other aspects of the stationary state that are highly sensitive to the training details. Surprisingly, the effective loss landscape and diffusion matrix that determine the shape of the stationary distribution vary depending on the simple choice of minibatching done with or without replacement. We can take advantage of this nonequilibrium sensitivity to engineer an equilibrium stationary state for a particular application: sampling from a posterior distribution of network weights in Bayesian machine learning. We propose a new variation of stochastic gradient Langevin dynamics (SGLD) that harnesses without replacement minibatching. In an example system where the posterior is exactly known, this SGWORLD algorithm outperforms SGLD, converging to the posterior orders of magnitude faster as a function of the learning rate.Comment: 24 pages, 6 figure

Be nice if you have to — the neurobiological roots of strategic fairness

Social norms, such as treating others fairly regardless of kin relations, are essential for the functioning of human societies. Their existence may explain why humans, among all species, show unique patterns of prosocial behaviour. The maintenance of social norms often depends on external enforcement, as in the absence of credible sanctioning mechanisms prosocial behaviour deteriorates quickly. This sanction-dependent prosocial behaviour suggests that humans strategically adapt their behaviour and act selfishly if possible but control selfish impulses if necessary. Recent studies point at the role of the dorsolateral prefrontal cortex (DLPFC) in controlling selfish impulses. We test whether the DLPFC is indeed involved in the control of selfish impulses as well as the strategic acquisition of this control mechanism. Using repetitive transcranial magnetic stimulation, we provide evidence for the causal role of the right DLPFC in strategic fairness. Because the DLPFC is phylogenetically one of the latest developed neocortical regions, this could explain why complex norm systems exist in humans but not in other social animals

Daubechies wavelets as a basis set for density functional pseudopotential calculations

Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances and an excellent efficiency for parallel calculations.Comment: 15 pages, 11 figure

Determination of Inter-Phase Line Tension in Langmuir Films

A Langmuir film is a molecularly thin film on the surface of a fluid; we study the evolution of a Langmuir film with two co-existing fluid phases driven by an inter-phase line tension and damped by the viscous drag of the underlying subfluid. Experimentally, we study an 8CB Langmuir film via digitally-imaged Brewster Angle Microscopy (BAM) in a four-roll mill setup which applies a transient strain and images the response. When a compact domain is stretched by the imposed strain, it first assumes a bola shape with two tear-drop shaped reservoirs connected by a thin tether which then slowly relaxes to a circular domain which minimizes the interfacial energy of the system. We process the digital images of the experiment to extract the domain shapes. We then use one of these shapes as an initial condition for the numerical solution of a boundary-integral model of the underlying hydrodynamics and compare the subsequent images of the experiment to the numerical simulation. The numerical evolutions first verify that our hydrodynamical model can reproduce the observed dynamics. They also allow us to deduce the magnitude of the line tension in the system, often to within 1%. We find line tensions in the range of 200-600 pN; we hypothesize that this variation is due to differences in the layer depths of the 8CB fluid phases.Comment: See (http://www.math.hmc.edu/~ajb/bola/) for related movie

TbGT8 is a bifunctional glycosyltransferase that elaborates<em> N</em>-linked glycans on a protein phosphatase AcP115 and a GPI-anchor modifying glycan in <em>Trypanosoma brucei</em>

AbstractThe procyclic form of Trypanosoma brucei expresses procyclin surface glycoproteins with unusual glycosylphosphatidylinositol-anchor side chain structures that contain branched N-acetyllactosamine and lacto-N-biose units. The glycosyltransferase TbGT8 is involved in the synthesis of the branched side chain through its UDP-GlcNAc: βGal β1-3N-acetylglucosaminyltransferase activity. Here, we explored the role of TbGT8 in the mammalian bloodstream form of the parasite with a tetracycline-inducible conditional null T. brucei mutant for TbGT8. Under non-permissive conditions, the mutant showed significantly reduced binding to tomato lectin, which recognizes poly-N-acetyllactosamine-containing glycans. Lectin pull-down assays revealed differences between the wild type and TbGT8 null-mutant T. brucei, notably the absence of a broad protein band with an approximate molecular weight of 110kDa in the mutant lysate. Proteomic analysis revealed that the band contained several glycoproteins, including the acidic ecto-protein phosphatase AcP115, a stage-specific glycoprotein in the bloodstream form of T. brucei. Western blotting with an anti-AcP115 antibody revealed that AcP115 was approximately 10kDa smaller in the mutant. Enzymatic de-N-glycosylation demonstrated that the underlying protein cores were the same, suggesting that the 10-kDa difference was due to differences in N-linked glycans. Immunofluorescence microscopy revealed the colocalization of hemagglutinin epitope-tagged TbGT8 and the Golgi-associated protein GRASP. These data suggest that TbGT8 is involved in the construction of complex poly-N-acetyllactosamine-containing type N-linked and GPI-linked glycans in the Golgi of the bloodstream and procyclic parasite forms, respectively

Longitudinal flow evolution and turbulence structure of dynamically similar, sustained, saline density and turbidity currents

Experimental results are presented concerning flow evolution and turbulence structure of sustained saline and turbidity flows generated on 0°, 3°, 6°, and 9° sloping ramps that terminate abruptly onto a horizontal floor. Two-component velocity and current density were measured with an ultrasonic Doppler velocity profiler and siphon sampler on the slope, just beyond the slope break and downstream on the horizontal floor. Three main factors influence longitudinal flow evolution and turbulence structure: sediment transport and sedimentation, slope angle, and the presence of a slope break. These controls interact differently depending on flow type. Sediment transport is accompanied by an inertial fluid reaction that enhances Reynolds stresses in turbidity flows. Thus turbidity flows mix more vigorously than equivalent saline density flows. For saline flows, turbulent kinetic energy is dependent on slope, and rapid deceleration occurs on the horizontal floor. For turbidity flows, normalized turbulent kinetic energy increases downstream, and mean streamwise deceleration is reduced compared with saline flows. The slope break causes mean bed-normal velocity of turbidity flows to become negative and have a gentler gradient compared with other locations. A reduction of peak Reynolds normal stress in the bed-normal direction is accompanied by an increase in turbulent accelerations across the rest of the flow thickness. Thus the presence of particles acts to increase Reynolds normal stresses independently of gradients of mean velocity, and sediment transport increases across the break in slope. The experiments illustrate that saline density currents may not be good dynamic analogues for natural turbidity currents