From Entropic Dynamics to Quantum Theory

Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles: positions constitute a configuration space and the corresponding probability distributions constitute a statistical manifold. The dynamics follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. A welcome feature is that the entropic dynamics notion of time incorporates a natural distinction between past and future. The statistical manifold is assumed to be a dynamical entity: its curved and evolving geometry determines the evolution of the particles which, in their turn, react back and determine the evolution of the geometry. Imposing that the dynamics conserve energy leads to the Schroedinger equation and to a natural explanation of its linearity, its unitarity, and of the role of complex numbers. The phase of the wave function is explained as a feature of purely statistical origin. There is a quantum analogue to the gravitational equivalence principle.Comment: Extended and corrected version of a paper presented at MaxEnt 2009, the 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 5-10, 2009, Oxford, Mississippi, USA). In version v3 I corrected a mistake and considerably simplified the argument. The overall conclusions remain unchange

Jaynes' MaxEnt, Steady State Flow Systems and the Maximum Entropy Production Principle

Jaynes' maximum entropy (MaxEnt) principle was recently used to give a conditional, local derivation of the ``maximum entropy production'' (MEP) principle, which states that a flow system with fixed flow(s) or gradient(s) will converge to a steady state of maximum production of thermodynamic entropy (R.K. Niven, Phys. Rev. E, in press). The analysis provides a steady state analog of the MaxEnt formulation of equilibrium thermodynamics, applicable to many complex flow systems at steady state. The present study examines the classification of physical systems, with emphasis on the choice of constraints in MaxEnt. The discussion clarifies the distinction between equilibrium, fluid flow, source/sink, flow/reactive and other systems, leading into an appraisal of the application of MaxEnt to steady state flow and reactive systems.Comment: 6 pages; paper for MaxEnt0

Computational methods for Bayesian model choice

In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and nested sampling from a unified perspective.Comment: 12 pages, 4 figures, submitted to the proceedings of MaxEnt 2009, July 05-10, 2009, to be published by the American Institute of Physic

Entropic Priors and Bayesian Model Selection

We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured, weakening the usual Bayesian "Occam's Razor". This is illustrated with a simple example involving what Jaynes called a "sure thing" hypothesis. Jaynes' resolution of the situation involved introducing a large number of alternative "sure thing" hypotheses that were possible before we observed the data. However, in more complex situations, it may not be possible to explicitly enumerate large numbers of alternatives. The entropic priors formalism produces the desired result without modifying the hypothesis space or requiring explicit enumeration of alternatives; all that is required is a good model for the prior predictive distribution for the data. This idea is illustrated with a simple rigged-lottery example, and we outline how this idea may help to resolve a recent debate amongst cosmologists: is dark energy a cosmological constant, or has it evolved with time in some way? And how shall we decide, when the data are in?Comment: Presented at MaxEnt 2009, the 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 5-10, 2009, Oxford, Mississippi, USA

Measuring on Lattices

Previous derivations of the sum and product rules of probability theory relied on the algebraic properties of Boolean logic. Here they are derived within a more general framework based on lattice theory. The result is a new foundation of probability theory that encompasses and generalizes both the Cox and Kolmogorov formulations. In this picture probability is a bi-valuation defined on a lattice of statements that quantifies the degree to which one statement implies another. The sum rule is a constraint equation that ensures that valuations are assigned so as to not violate associativity of the lattice join and meet. The product rule is much more interesting in that there are actually two product rules: one is a constraint equation arises from associativity of the direct products of lattices, and the other a constraint equation derived from associativity of changes of context. The generality of this formalism enables one to derive the traditionally assumed condition of additivity in measure theory, as well introduce a general notion of product. To illustrate the generic utility of this novel lattice-theoretic foundation of measure, the sum and product rules are applied to number theory. Further application of these concepts to understand the foundation of quantum mechanics is described in a joint paper in this proceedings.Comment: 13 pages, 7 figures, Presented at the 29th International Workshop on Bayesian and Maximum Entropy Methods in Science and Engineering: MaxEnt 200

Anti-proliferative effects of raw and steamed extracts of Panax notoginseng and its ginsenoside constituents on human liver cancer cells

10.1186/1749-8546-6-4Chinese Medicine6

Mechanical properties of polyurethane/montmorillonite nanocomposite prepared by melt mixing

Nanocomposites from polyurethane (PU) and montmorillonite (MMT) were prepared under melt-mixing condition, by a twin screw extruder along with a compatibilizer to enhance dispersion of MMT. MMT used in this study was Cloisite 25A (modified with dimethyl hydrogenated tallow 2-ethylhexyl ammonium) or Cloisite 30B (modified with methyl tallow bis-2-hydroxyethyl ammonium). Maleic anhydride grafted polypropylene (MAPP) was used as the compatibilizer. XRD and TEM analysis demonstrated that melt mixing by a twin-screw extruder was effective in dispersing MMT through the PU matrix. The PU/Cloisite 30B composite exhibited better interlayer separation than the PU/Cloiste 25A composite. Nanoparticle dispersion was the best at 1 wt % of MMT and improved with compatibilizer content for both composites. Properties of the composites such as complex viscosity and storage modulus were higher than that of a pure PU matrix and increased with the increase in MMT content, but decreased with the increase in compatibilizer content. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/56114/1/26721_ftp.pd

An International Collaborative Consensus Statement on En Bloc Resection of Bladder Tumour Incorporating Two Systematic Reviews, a Two-round Delphi Survey and a Consensus Meeting

Funding/Support and role of the sponsor: This study was supported by the General Research Fund/Early Career Scheme of the Research Grants Council, Hong Kong, China (reference no. 24116518).Peer reviewedPostprin