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Product Distribution Field TheoryJul 25 2003This paper presents a novel way to approximate a distribution governing a system of coupled particles with a product of independent distributions. The approach is an extension of mean field theory that allows the independent distributions to live in a ... More

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical PhysicsFeb 19 2004A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all real-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with ... More

Overview of Information Theory, Computer Science Theory, and Stochastic Thermodynamics for Thermodynamics of ComputationDec 31 2018Jan 24 2019I give a quick overview of some of the theoretical background necessary for using modern nonequilibrium statistical physics to investigate the thermodynamics of computation. I first present some of the necessary concepts from information theory, and then ... More

The free energy requirements of biological organisms; implications for evolutionMar 30 2016Jun 30 2016Recent advances in nonequilibrium statistical physics have provided unprecedented insight into the thermodynamics of dynamic processes. The author recently used these advances to extend Landauer's semi-formal reasoning concerning the thermodynamics of ... More

Metrics for more than two points at onceApr 16 2004The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the triangle inequality, ... More

On the computational capabilities of physical systems part I: the impossibility of infallible computationMay 23 2000In this first of two papers, strong limits on the accuracy of physical computation are established. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical universe. Next ... More

Stochastic thermodynamics of computationMay 14 2019One of the major resource requirements of computers - ranging from biological cells to human brains to high-performance (engineered) computers - is the energy used to run them. Those costs of performing a computation have long been a focus of research ... More

Physical limits of inferenceAug 10 2007Oct 23 2008I show that physical devices that perform observation, prediction, or recollection share an underlying mathematical structure. I call devices with that structure "inference devices". I present a set of existence and impossibility results concerning inference ... More

Extending Landauer's Bound from Bit Erasure to Arbitrary ComputationAug 21 2015Nov 24 2015Recent analyses have calculated the minimal thermodynamic work required to perform a computation pi when two conditions hold: the output of pi is independent of its input (e.g., as in bit erasure); we use a physical computer C to implement pi that is ... More

A Predictive Theory of GamesDec 08 2005Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium concept is "correct". ... More

On the computational capabilities of physical systems part II: relationship with conventional computer scienceMay 23 2000In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of computation, ``physical ... More

Overview of Information Theory, Computer Science Theory, and Stochastic Thermodynamics for Thermodynamics of ComputationDec 31 2018Jun 19 2019I give a quick overview of some of the theoretical background necessary for using modern non-equilibrium statistical physics to investigate the thermodynamics of computation. I first present some of the necessary concepts from information theory, and ... More

What does Newcomb's paradox teach us?Mar 06 2010In Newcomb's paradox you 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, a prediction algorithm deduces your choice, and fills the two boxes based on that deduction. ... More

An Introduction to Collective IntelligenceAug 17 1999This paper surveys the emerging science of how to design a ``COllective INtelligence'' (COIN). A COIN is a large multi-agent system where: (i) There is little to no centralized communication or control; and (ii) There is a provided world utility function ... More

Estimating Functions of Distributions Defined over Spaces of Unknown SizeNov 18 2013We consider Bayesian estimation of information-theoretic quantities from data, using a Dirichlet prior. Acknowledging the uncertainty of the event space size $m$ and the Dirichlet prior's concentration parameter $c$, we treat both as random variables ... More

Avoiding Braess' Paradox through Collective IntelligenceDec 20 1999In an Ideal Shortest Path Algorithm (ISPA), at each moment each router in a network sends all of its traffic down the path that will incur the lowest cost to that traffic. In the limit of an infinitesimally small amount of traffic for a particular router, ... More

Distributed Control by Lagrangian Steepest DescentMar 10 2004Often adaptive, distributed control can be viewed as an iterated game between independent players. The coupling between the players' mixed strategies, arising as the system evolves from one instant to the next, is determined by the system designer. Information ... More

Semantic information, autonomous agency, and nonequilibrium statistical physicsJun 21 2018Nov 07 2018Shannon information theory provides various measures of so-called "syntactic information", which reflect the amount of statistical correlation between systems. In contrast, the concept of "semantic information" refers to those correlations which carry ... More

Thermodynamic cost due to changing the initial distribution over statesJul 04 2016We consider nonequilibrium systems that obey local detailed balance and are driven by an external system such that no work is dissipated for some initial distribution over states $x \in X$, $q(X)$. We show that in general work is dissipated under that ... More

Dependence of dissipation on the initial distribution over statesJul 04 2016Aug 22 2017We 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 ... More

Dependence of dissipation on the initial distribution over statesJul 04 2016Oct 26 2016We consider the amount of dissipated work occurring in a given nonequilibrium process as a function of the initial distribution over microstates. We show that the extra dissipated work for any distribution, above the minimum achievable, has a simple information-theoretic ... More

What does Newcomb's paradox teach us?Apr 16 2009Sep 30 2010In Newcomb's paradox you 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 deduce your choice, and fills the ... More

Game theoretic modeling of pilot behavior during mid-air encountersMar 26 2011Apr 11 2011We show how to combine Bayes nets and game theory to predict the behavior of hybrid systems involving both humans and automated components. We call this novel framework "Semi Network-Form Games," and illustrate it by predicting aircraft pilot behavior ... More

Estimating Functions of Distributions from A Finite Set of Samples, Part 2: Bayes Estimators for Mutual Information, Chi-Squared, Covariance and other StatisticsMar 08 1994We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint distribution, ... More

Estimating Functions of Probability Distributions from a Finite Set of Samples, Part 1: Bayes Estimators and the Shannon EntropyMar 08 1994We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint distribution, ... More

Constraints on physical reality arising from a formalization of knowledgeNov 09 2017Jun 28 2018There are (at least) four ways that an agent can acquire information concerning the state of the universe: via observation, control, prediction, or via retrodiction, i.e., memory. Each of these four ways of acquiring information seems to rely on a different ... More

Reducing the error of Monte Carlo Algorithms by Learning Control VariatesJun 07 2016Monte Carlo (MC) sampling algorithms are an extremely widely-used technique to estimate expectations of functions f(x), especially in high dimensions. Control variates are a very powerful technique to reduce the error of such estimates, but in their conventional ... More

Adaptive Programming of Unconventional Nano-ArchitecturesSep 19 2006Novel 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 ... More

Using Collective Intelligence to Route Internet TrafficMay 10 1999A COllective INtelligence (COIN) is a set of interacting reinforcement learning (RL) algorithms designed in an automated fashion so that their collective behavior optimizes a global utility function. We summarize the theory of COINs, then present experiments ... More

Parametric Learning and Monte Carlo OptimizationApr 10 2007This paper uncovers and explores the close relationship between Monte Carlo Optimization of a parametrized integral (MCO), Parametric machine-Learning (PL), and `blackbox' or `oracle'-based optimization (BO). We make four contributions. First, we prove ... More

An adaptive Metropolis-Hastings scheme: sampling and optimizationApr 07 2005We 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 ... More

Upgrading from Gaussian Processes to Student's-T ProcessesJan 18 2018Gaussian 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 ... More

The minimal hidden computer needed to implement a visible computationAug 28 2017Jun 06 2018Master equations are commonly used to model the dynamics of physical systems. Surprisingly, many deterministic maps $x \rightarrow f(x)$ cannot be implemented by any master equation, even approximately. This raises the question of how they arise in real-world ... More

General Principles of Learning-Based Multi-Agent SystemsMay 10 1999We consider the problem of how to design large decentralized multi-agent systems (MAS's) in an automated fashion, with little or no hand-tuning. Our approach has each agent run a reinforcement learning algorithm. This converts the problem into one of ... More

Number of hidden states needed to physically implement a given conditional distributionSep 03 2017Aug 22 2018We consider the problem of how to construct a physical process over a state space $X$ that applies some desired conditional distribution $P$ to initial states to produce final states. This problem arises in various scenarios in thermodynamics of computation ... More

Adaptivity in Agent-Based Routing for Data NetworksDec 20 1999Adaptivity, both of the individual agents and of the interaction structure among the agents, seems indispensable for scaling up multi-agent systems (MAS's) in noisy environments. One important consideration in designing adaptive agents is choosing their ... More

Nonlinear Information BottleneckMay 06 2017Sep 04 2018Information bottleneck [IB] is a technique for extracting information in some `input' random variable that is relevant for predicting some different 'output' random variable. IB works by encoding the input in a compressed 'bottleneck variable' from which ... More

Collective Intelligence for Control of Distributed Dynamical SystemsAug 17 1999We 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 ... More

Value of information in noncooperative gamesDec 27 2013Jan 30 2015In some games, additional information hurts a player, e.g., in games with first-mover advantage, the second-mover is hurt by seeing the first-mover's move. What properties of a game determine whether it has such negative "value of information" for a particular ... More

Number of hidden states needed to physically implement a given conditional distributionSep 03 2017Apr 21 2019We 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 ... More

A space-time tradeoff for implementing a function with master equation dynamicsAug 28 2017Apr 21 2019Master 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, ... More

Collectives for the Optimal Combination of Imperfect ObjectsJan 23 2003In this letter we summarize some recent theoretical work on the design of collectives, i.e., of systems containing many agents, each of which can be viewed as trying to maximize an associated private utility, where there is also a world utility rating ... More

Bias-Variance Techniques for Monte Carlo Optimization: Cross-validation for the CE MethodOct 06 2008In this paper, we examine the CE method in the broad context of Monte Carlo Optimization (MCO) and Parametric Learning (PL), a type of machine learning. A well-known overarching principle used to improve the performance of many PL algorithms is the bias-variance ... More

Bias-Variance Tradeoffs: Novel ApplicationsOct 06 2008We present several applications of the bias-variance decomposition, beginning with straightforward Monte Carlo estimation of integrals, but progressing to the more complex problem of Monte Carlo Optimization (MCO), which involves finding a set of parameters ... More

Optimal high-level descriptions of dynamical systemsSep 25 2014Jun 03 2015To analyze high-dimensional systems, many fields in science and engineering rely on high-level descriptions, sometimes called "macrostates," "coarse-grainings," or "effective theories". Examples of such descriptions include the thermodynamic properties ... More

Distributed Constrained Optimization with Semicoordinate TransformationsNov 05 2008Recent 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 constrained optimization problems. This is done by translating ... More

Exact, complete expressions for the thermodynamic costs of circuitsJun 11 2018Dec 31 2018The generalized Landauer's bound gives the minimal amount of heat generated by any physical process that implements a given computation, when there are no constraints on the process. However, common engineered systems implement computations using circuits, ... More

The thermodynamic costs of circuitsJun 11 2018Aug 06 2019Real-world 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 degrees of freedom may be physically coupled during the operation ... More

Counter-Factual Reinforcement Learning: How to Model Decision-Makers That Anticipate The FutureJul 03 2012This paper introduces a novel framework for modeling interacting humans in a multi-stage game. This "iterated semi network-form game" framework has the following desirable characteristics: (1) Bounded rational players, (2) strategic players (i.e., players ... More

Hysteresis effects of changing parameters of noncooperative gamesOct 27 2010We adapt the method used by Jaynes to derive the equilibria of statistical physics to instead derive equilibria of bounded rational game theory. We analyze the dependence of these equilibria on the parameters of the underlying game, focusing on hysteresis ... More

Predicting the behavior of interacting humans by fusing data from multiple sourcesAug 09 2014Multi-fidelity methods combine inexpensive low-fidelity simulations with costly but highfidelity simulations to produce an accurate model of a system of interest at minimal cost. They have proven useful in modeling physical systems and have been applied ... More

Predicting the behavior of interacting humans by fusing data from multiple sourcesJun 26 2012Multi-fidelity methods combine inexpensive low-fidelity simulations with costly but high-fidelity simulations to produce an accurate model of a system of interest at minimal cost. They have proven useful in modeling physical systems and have been applied ... More

Collective Intelligence, Data Routing and Braess' ParadoxJun 09 2011We consider the problem of designing the the utility functions of the utility-maximizing agents in a multi-agent system so that they work synergistically to maximize a global utility. The particular problem domain we explore is the control of network ... More

Using Supervised Learning to Improve Monte Carlo Integral EstimationAug 24 2011Monte Carlo (MC) techniques are often used to estimate integrals of a multivariate function using randomly generated samples of the function. In light of the increasing interest in uncertainty quantification and robust design applications in aerospace ... More

Improving Search Algorithms by Using Intelligent CoordinatesJan 23 2003We consider the problem of designing a set of computational agents so that as they all pursue their self-interests a global function G of the collective system is optimized. Three factors govern the quality of such design. The first relates to conventional ... More

One cannot hear the shape of a drumJul 01 1992We use an extension of Sunada's theorem to construct a nonisometric pair of isospectral simply connected domains in the Euclidean plane, thus answering negatively Kac's question, ``can one hear the shape of a drum?'' In order to construct simply connected ... More

The thermodynamic efficiency of computations made in cells across the range of lifeJun 15 2017Biological organisms must perform computation as they grow, reproduce, and evolve. Moreover, ever since Landauer's bound was proposed it has been known that all computation has some thermodynamic cost -- and that the same computation can be achieved with ... More

Modeling Social Organizations as Communication NetworksFeb 15 2017We identify the "organization" of a human social group as the communication network(s) within that group. We then introduce three theoretical approaches to analyzing what determines the structures of human organizations. All three approaches adopt a group-selection ... More

A quantitative definition of organismality and its application to lichenNov 30 2016The organism is a fundamental concept in biology. However there is no universally accepted, formal, and yet broadly applicable definition of what an organism is. Here we introduce a candidate definition. We adopt the view that the "organism" is a functional ... More

Coarse-graining and the Blackwell orderJan 26 2017Nov 10 2017Suppose we have a pair of information channels, $\kappa_{1},\kappa_{2}$, with a common input. The Blackwell order is a partial order over channels that compares $\kappa_{1}$ and $\kappa_{2}$ by the maximal expected utility an agent can obtain when decisions ... More

Cyber-Physical Security: A Game Theory Model of Humans Interacting over Control SystemsApr 15 2013Recent 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 ... More

A Likelihood Ratio Detector for Identifying Within-Perimeter Computer Network AttacksSep 01 2016The rapid detection of attackers within firewalls of enterprise computer net- works is of paramount importance. Anomaly detectors address this problem by quantifying deviations from baseline statistical models of normal network behav- ior and signaling ... More

Improving Exoplanet Detection Power: Multivariate Gaussian Process Models for Stellar ActivityNov 03 2017Dec 02 2017The radial velocity method is one of the most successful techniques for detecting exoplanets. It works by detecting the velocity of a host star induced by the gravitational effect of an orbiting planet, specifically the velocity along our line of sight, ... More

Maximizing free energy gainApr 28 2017Free energy is energy that is available to do work. Maximizing the free energy gain and the gain in work that can be extracted from a system is important for a wide variety of physical and technological processes, from energy harvesting processes such ... More

Deep Reinforcement Learning for Event-Driven Multi-Agent Decision ProcessesSep 19 2017The incorporation of macro-actions (temporally extended actions) into multi-agent decision problems has the potential to address the curse of dimensionality associated with such decision problems. Since macro-actions last for stochastic durations, multiple ... More

Deep Reinforcement Learning for Event-Driven Multi-Agent Decision ProcessesSep 19 2017May 29 2019The incorporation of macro-actions (temporally extended actions) into multi-agent decision problems has the potential to address the curse of dimensionality associated with such decision problems. Since macro-actions last for stochastic durations, multiple ... More

On families of holomorphic differentials on degenerating annuliAug 16 2011Nov 23 2011We consider the local analytic behavior for a family of holomorphic differentials on a family of degenerating annuli. Three results and discussion are presented. The first is the normal families Lemma 1. The second is an isomorphism of sheaves, formula ... More

Weil-Petersson perspectivesFeb 24 2005Mar 06 2005We highlight recent progresses in the study of the Weil-Petersson (WP) geometry of finite dimensional Teichm\"{u}ller spaces. For recent progress on and the understanding of infinite dimensional Teichm\"{u}ller spaces the reader is directed to the recent ... More

Behavior of geodesic-length functions on Teichmueller spaceJan 19 2007Jan 01 2008Let $\mathcal T$ be the Teichm\"{u}ller space of marked genus $g$, $n$ punctured Riemann surfaces with its bordification $\Tbar$ the {\em augmented Teichm\"{u}ller space} of marked Riemann surfaces with nodes, \cite{Abdegn, Bersdeg}. Provided with the ... More

Families of Riemann surfaces and Weil-Petersson geometryFeb 18 2012A 2008 general overview on Weil-Petersson geometry is offered. A preliminary plan for the subsequent CBMS lectures at Central Connecticut State University is included. Mirzakhani's solution of Witten-Kontsevich is not included - this work essentially ... More

The Weil-Petersson metric geometryDec 31 2007A summary introduction of the Weil-Petersson metric space geometry is presented. Teichmueller space and its augmentation are described in terms of Fenchel-Nielsen coordinates. Formulas for the gradients and Hessians of geodesic-length functions are presented. ... More

Convexity of geodesic-length functions: a repriseFeb 24 2005New results on the convexity of geodesic-length functions on Teichm\"{u}ller space are presented. A formula for the Hessian of geodesic-length is presented. New bounds for the gradient and Hessian of geodesic-length are described. A relationship of geodesic-length ... More

Geodesic-length functions and the Weil-Petersson curvature tensorAug 13 2010Oct 04 2011An expansion is developed for the Weil-Petersson Riemann curvature tensor in the thin region of the Teichm\"{u}ller and moduli spaces. The tensor is evaluated on the gradients of geodesic-lengths for disjoint geodesics. A precise lower bound for sectional ... More

Products of twists, geodesic-lengths and Thurston shearsMar 01 2013Thurston introduced shear deformations (cataclysms) on geodesic laminations - deformations including left and right displacements along geodesics. For hyperbolic surfaces with cusps, we consider shear deformations on disjoint unions of ideal geodesics. ... More

Infinitesimal deformations of nodal stable curvesApr 17 2012An analytic approach and description are presented for the moduli cotangent sheaf for suitable stable curve families including noded fibers. For sections of the square of the relative dualizing sheaf, the residue map at a node gives rise to an exact sequence. ... More

Schiffer variations and Abelian differentialsAug 05 2015Sep 14 2015Deformations of compact Riemann surfaces are considered using a \v{C}ech cohomology sliding overlaps approach. Cocycles are calculated for conformal cutting and regluing deformations at zeros of Abelian differentials. A second order deformation expansion ... More

Extension of the Weil-Petersson connectionSep 16 2007Convexity properties of Weil-Petersson geodesics on the Teichm\"{u}ller space of punctured Riemann surfaces are investigated. A normal form is presented for the Weil-Petersson Levi-Civita connection for pinched hyperbolic metrics. The normal form is used ... More

Weil-Petersson Metric Geometry Quick OverviewMay 08 2007Jul 03 2007A quick overview is provided on the current development of the WP metric geometry.

When is a bit worth much more than kT ln2?May 26 2017Physical processes thatobtain, process, and erase information involve tradeoffs between information and energy. The fundamental energetic value of a bit of information exchanged with a reservoir at temperature T is kT ln2. This paper investigates the ... More

Cusps and the family hyperbolic metricAug 24 2005Mar 13 2007The hyperbolic metric for the punctured unit disc in the Euclidean plane is singular at the origin. A renormalization of the metric at the origin is provided by the Euclidean metric. For Riemann surfaces there is a unique germ for the isometry class of ... More

Geometry of the Weil-Petersson completion of Teichmüller spaceFeb 24 2005We present a view of the current understanding of the geometry of Weil-Petersson (WP) geodesics on the completion of the Teichm\"uller space. We sketch a collection of results by other authors and then proceed to develop the properties of the WP CAT(0) ... More

Understanding Weil-Petersson curvatureSep 22 2008A brief history of the investigation of the Weil-Petersson curvature and a summary of Teichm\"{u}ller theory are provided. A report is presented on the program to describe an intrinsic geometry with the Weil-Petersson metric and geodesic-length functions. ... More

Lectures and notes: Mirzakhani's volume recursion and approach for the Witten-Kontsevich theorem on moduli tautological intersection numbersJul 31 2011The materials accompany a lecture short course presented at the 2011 Park City Mathematics Institute, Graduate Summer School on Moduli Spaces of Riemann Surfaces. The lectures were part of/coordinated with an overall program, including lectures by Ursula ... More

Equiboundedness of the Weil-Petersson metricMar 02 2015May 26 2016Uniform bounds are developed for derivatives of solutions of the $2$-dimensional constant negative curvature equation and the Weil-Petersson metric for the Teichm\"{u}ller and moduli spaces. The dependence of the bounds on the geometry of the underlying ... More

Hybrid Local-Order Mechanism for Inversion Symmetry BreakingDec 16 2017Using classical Monte Carlo simulations, we study a simple statistical mechanical model of relevance to the emergence of polarisation from local displacements on the square and cubic lattices. Our model contains two key ingredients: a Kitaev-like orientation-dependent ... More

Time-resolved observation of coherent excitonic nonlinear response with a table-top narrowband THz pulse waveDec 03 2015By combining a tilted-pulse-intensity-front scheme using a LiNbO3 crystal and a chirped-pulse-beating method, we generated a narrowband intense terahertz (THz) pulse, which had a maximum electric field of more than 10 kV/cm at around 2 THz, a bandwidth ... More

Grafting hyperbolic metrics and Eisenstein seriesApr 24 2007Feb 02 2008The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non holomorphic Eisenstein series $E(\zeta;2)$ are combined to provide an explicit expansion for the hyperbolic metrics for degenerating families of Riemann surfaces. Applications ... More

A cofinite universal space for proper actions for mapping class groupsNov 24 2008Jan 05 2009We prove that the mapping class group $\Gamma_{g,n}$ for surfaces of negative Euler characteristic has a cofinite universal space $\E$ for proper actions (the resulting quotient is a finite $CW$-complex). The approach is to construct a truncated Teichmueller ... More

Topological dynamics of the Weil-Petersson geodesic flowNov 20 2007Oct 05 2009We prove topological transitivity for the Weil Petersson geodesic flow for two-dimensional moduli spaces of hyperbolic structures. Our proof follows a new approach that exploits the density of singular unit tangent vectors, the geometry of cusps and convexity ... More

Tail waiting times and the extremes of stochastic processesDec 24 2015Jul 28 2016In applications where extreme dependence at different spatial locations is of interest, data are almost always time-indexed. When extremes do not occur contemporaneously, existing methods for inference and modeling in this setting often choose window ... More

Model-free inference on extreme dependence via waiting timesDec 24 2015May 21 2018A variety of methods have been proposed for inference about extreme dependence for multivariate or spatially-indexed stochastic processes and time series. Most of these proceed by first transforming data to some specific extreme value marginal distribution, ... More

Classicality of the primordial perturbationsJul 28 2006Apr 21 2008We show that during inflation, a quantum fluctuation becomes classical at all orders if it becomes classical at first order. Implications are discussed.

The CDM isocurvature perturbation in the curvaton scenarioJun 24 2003We discuss the residual isocurvature perturbations, fully-correlated with the curvature perturbation, that are automatic in the curvaton scenario if curvaton decay is sufficiently late. We contrast these residual isocurvature perturbations with the generally ... More

Cosmological consequences of particle creation during inflationSep 23 1996Particle creation during inflation is considered. It could be important for species whose interaction is of gravitational strength or weaker. A complete but economical formalism is given for spin-zero and spin-half particles, and the particle abundance ... More

Conserved cosmological perturbationsJun 24 2003A conserved cosmological perturbation is associated with each quantity whose local evolution is determined entirely by the local expansion of the Universe. It may be defined as the appropriately normalised perturbation of the quantity, defined using a ... More

Generating the curvature perturbation without an inflatonSep 28 2001Mar 06 2002We present a mechanism for the origin of the large-scale curvature perturbation in our Universe by the late decay of a massive scalar field, the curvaton. The curvaton is light during a period of cosmological inflation, when it acquires a perturbation ... More

On the Supremum of Certain Families of Stochastic ProcessesDec 21 2008Nov 14 2009We consider a family of stochastic processes $\{X_t^\epsilon, t \in T\}$ on a metric space $T$, with a parameter $\epsilon \downarrow 0$. We study the conditions under which \lim_{\e \to 0} \P \Big(\sup_{t \in T} |X_t^\e| < \delta \Big) =1 when one has ... More

The curvature perturbation in a boxJul 03 2007Feb 15 2008The stochastic properties of cosmological perturbations are best defined through the Fourier expansion in a finite box. I discuss the reasons for that with reference the curvature perturbation, and explore some issues arising from it.

The gravitino abundance in supersymmetric `new' inflation modelsNov 05 1999Dec 12 1999We consider the abundance of gravitinos created from the vacuum fluctuation, in a class of `new' inflation models for which global supersymmetry is a good approximation. Immediately after inflation, gravitinos are produced, with number density determined ... More

Models of inflation and their predictionsFeb 22 1999Taking field theory seriously, inflation model-building is difficult but not impossible. The observed value of the spectral index of the adiabatic density perturbation is starting to discriminate between models, and may well pick out a unique one in the ... More