Let k be an algebraically closed field of characteristic exponent p ≥ 1. Let G be a connected reductive algebraic group over k and let g be the Lie algebra of G. Note that G acts on G and on g by the adjoint action and on g by the coadjoint action. (For any k-vector space V we denote by V ∗ the dual vector space.) Let GC be the reductive group over C of the same type as G. Let UG be the variety...

Model choice plays an increasingly important role in Statistics. From a Bayesian perspective a crucial goal is to compute the marginal likelihood of the data for a given model. This however is typically a difficult task since it amounts to integrating over all model parameters. The aim of this paper is to illustrate how this may be achieved using ideas from thermodynamic integration or path sam...

We analyse secure computation as a physical process and connect it to recent advances in security, namely Quantitative Information Flow. Using a classic thermodynamic argument involving the second principle and reversibility we show that any deterministic computation, where the final state of the system is observable, must dissipate at least WkBT ln 2. Here W is the information theoretic notion...

First principles computation can be used to investigate an design materials in ways that can not be achieved with experimental means. We show how computations can be used to rapidly capture the essential physics that determines the useful properties in different applications. Some applications for predicting crystal structure, thermodynamic and kinetic properties, and phase stability are discus...

The deep connection between thermodynamics, computation, and information is now well established both theoretically and experimentally. Here, we extend these ideas to show that thermodynamics also places fundamental constraints on statistical estimation and learning. To do so, we investigate the constraints placed by (nonequilibrium) thermodynamics on the ability of biochemical signaling networ...

We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to convention...

The application of stochastic context-free grammars to the determination of RNA foldings allows a simple description of the sub-class of sought secondary structures, but it needs eecient parsing algorithms. The more classic thermodynamic model of folding, popularized by Zuker under the framework of dynamic programming algorithms, allows an easy computation of foldings but its use is delicate wh...

We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to deal with standard optimization methods, such as simulated and quantum annealing, on an equal basis. Consequently, we extend the quantum annealing ...