The supervised hierarchical Dirichlet process

We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. We compare the sHDP with another leading method for regression on grouped data, the supervised latent Dirichlet allocation (sLDA) model. We evaluate our method on two real-world classification problems and two real-world regression problems. Bayesian nonparametric regression models based on the Dirichlet process, such as the Dirichlet process-generalised linear models (DP-GLM) have previously been explored; these models allow flexibility in modelling nonlinear relationships. However, until now, Hierarchical Dirichlet Process (HDP) mixtures have not seen significant use in supervised problems with grouped data since a straightforward application of the HDP on the grouped data results in learnt clusters that are not predictive of the responses. The sHDP solves this problem by allowing for clusters to be learnt jointly from the group structure and from the label assigned to each group.Comment: 14 page

Entropy production for coarse-grained dynamics

Systems out of equilibrium exhibit a net production of entropy. We study the dynamics of a stochastic system represented by a Master Equation that can be modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic description. We show that the corresponding coarse-grained entropy production contains information on microscopic currents that are not captured by the Fokker-Planck equation and thus cannot be deduced from it. We study a discrete-state and a continuous-state system, deriving in both the cases an analytical expression for the coarse-graining corrections to the entropy production. This result elucidates the limits in which there is no loss of information in passing from a Master Equation to a Fokker-Planck equation describing the same system. Our results are amenable of experimental verification, which could help to infer some information about the underlying microscopic processes

Flory theory for Polymers

We review various simple analytical theories for homopolymers within a unified framework. The common guideline of our approach is the Flory theory, and its various avatars, with the attempt of being reasonably self-contained. We expect this review to be useful as an introduction to the topic at the graduate students level.Comment: Topical review appeared J. Phys.: Condens. Matter, 46 pages, 8 Figures. Sec. VIF added. Typos fixed. Few references adde

A Simplified Mathematical Model for the Formation of Null Singularities Inside Black Holes I - Basic Formulation and a Conjecture

Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial data. We present a simple hyperbolic system of two semi-linear equations inspired by the Einstein equations. We explore a class of solutions to this system which are analogous to static black-hole models. These solutions exhibit a black-hole structure with a finite-time blowup on a characteristic line mimicking the null inner horizon of spinning or charged black holes. We conjecture that this behavior - namely black-hole formation with blow-up on a characteristic line - is a generic feature of our semi-linear system. Our simple system may provide insight into the formation of null singularities inside spinning or charged black holes in the full system of Einstein equations.Comment: 39 pages, 3 figures, extended versio

Zenithal bistable device: comparison of modeling and experiment

A comparative modeling and experimental study of the zenithal bistable liquid crystal device is presented. A dynamic Landau de Gennes theory of nematic liquid crystals is solved numerically to model the electric field induced latching of the device and the results are compared with experimental measurements and theoretical approximations. The study gives a clear insight into the latching mechanism dynamics and enables the dependence of the device latching on both material parameters and surface shape to be determined. Analytical approximation highlights a route to optimize material selection in terms of latching voltages and the numerical model, which includes an accurate surface representation, recovers the complex surface shape effects. Predictions of device performance are presented as a function of both surface anchoring strength and surface shape and grating pitch. A measurement of the homeotropic anchoring energy has been undertaken by comparing the voltage response as a function of cell gap; we find the homeotropic anchoring energies can be varied in the range 0.5 to 4 (10-44 J m-2)