The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the process state is infinite dimensional. In this paper we show how such approximations can be avoided for a variety of infinite dimensional models driven by some form of Brownian noise. The approach is based on a variational representation for functionals of Brownian motion. Proofs of large deviations properties are reduced to demonstrating basic qualitative properties (existence, uniqueness and tightness) of certain perturbations of the original process.Comment: Published in at http://dx.doi.org/10.1214/07-AOP362 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

No abstract

Machine learning and high-throughput computational screening have been valuable tools in accelerated first-principles screening for the discovery of the next generation of functionalized molecules and materials. The application of machine learning for chemical applications requires the conversion of molecular structures to a machine-readable format known as a molecular representation. The choice of such representations impacts the performance and outcomes of chemical machine learning methods. Herein, we present a new concise molecular representation derived from persistent homology, an applied branch of mathematics. We have demonstrated its applicability in a high-throughput computational screening of a large molecular database (GDB-9) with more than 133,000 organic molecules. Our target is to identify novel molecules that selectively interact with CO 2. The methodology and performance of the novel molecular fingerprinting method is presented and the new chemicallydriven persistence image representation is used to screen the GDB-9 database to suggest molecules and/or functional groups with enhanced properties.

Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains absent. This paper, relying on the theory of point processes, presents a Bayesian framework for inference with persistence diagrams relying on a substitution likelihood argument.In essence, we model persistence diagrams as Poisson point processes with prior intensities and compute posterior intensities by adopting techniques from the theory of marked point processes. We then propose a family of conjugate prior intensities via Gaussian mixtures to obtain a closed form of the posterior intensity. Finally we demonstrate the utility of this Bayesian framework with a classification problem in materials science using Bayes factors.

A large deviation principle is established for a general class of stochastic flows in the small noise limit. This result is then applied to a Bayesian formulation of an image matching problem, and an approximate maximum likelihood property is shown for the solution of an optimization problem involving the large deviations rate function.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ203 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

An understanding of the nanoscale structure and energetics of carbon composites is critical for their applications in electric energy storage. Here, we study the properties of carbon anodes synthesized from low-cost renewable lignin biopolymers for use in energy storage applications such as Li-ion batteries. The anodes possess both nanoscale and mesoscale order, consisting of carbon nanocrystallites distributed within an amorphous carbon matrix. Molecular dynamics simulations of an experimentally validated model of the anode is used to elucidate the nature of Li-ion storage. We report the discovery of a novel mechanism of Li-ion storage, one in which Li + is not intercalated between layers of carbon (as is the case in graphitic anodes), but rather is localized at the interface of crystalline carbon domains. In particular, the effects of Liion binding energy on the Li-Li, Li-H, and Li-C pair distribution functions are revealed, along with the effect on charge distribution. Lastly, the atomic environments surrounding the Li-ions

No abstract

No abstract