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

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

Discriminating between a Stochastic Gravitational Wave Background and Instrument Noise

The detection of a stochastic background of gravitational waves could significantly impact our understanding of the physical processes that shaped the early Universe. The challenge lies in separating the cosmological signal from other stochastic processes such as instrument noise and astrophysical foregrounds. One approach is to build two or more detectors and cross correlate their output, thereby enhancing the common gravitational wave signal relative to the uncorrelated instrument noise. When only one detector is available, as will likely be the case with the Laser Interferometer Space Antenna (LISA), alternative analysis techniques must be developed. Here we show that models of the noise and signal transfer functions can be used to tease apart the gravitational and instrument noise contributions. We discuss the role of gravitational wave insensitive "null channels" formed from particular combinations of the time delay interferometry, and derive a new combination that maintains this insensitivity for unequal arm length detectors. We show that, in the absence of astrophysical foregrounds, LISA could detect signals with energy densities as low as $\Omega_{\rm gw} = 6 \times 10^{-13}$ with just one month of data. We describe an end-to-end Bayesian analysis pipeline that is able to search for, characterize and assign confidence levels for the detection of a stochastic gravitational wave background, and demonstrate the effectiveness of this approach using simulated data from the third round of Mock LISA Data Challenges.Comment: 10 Pages, 10 Figure

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

A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy

The analysis of data from gravitational wave detectors can be divided into three phases: search, characterization, and evaluation. The evaluation of the detection - determining whether a candidate event is astrophysical in origin or some artifact created by instrument noise - is a crucial step in the analysis. The on-going analyses of data from ground based detectors employ a frequentist approach to the detection problem. A detection statistic is chosen, for which background levels and detection efficiencies are estimated from Monte Carlo studies. This approach frames the detection problem in terms of an infinite collection of trials, with the actual measurement corresponding to some realization of this hypothetical set. Here we explore an alternative, Bayesian approach to the detection problem, that considers prior information and the actual data in hand. Our particular focus is on the computational techniques used to implement the Bayesian analysis. We find that the Parallel Tempered Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases of the anaylsis in a coherent framework. The signals are found by locating the posterior modes, the model parameters are characterized by mapping out the joint posterior distribution, and finally, the model evidence is computed by thermodynamic integration. As a demonstration, we consider the detection problem of selecting between models describing the data as instrument noise, or instrument noise plus the signal from a single compact galactic binary. The evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found to be in close agreement with those computed using a Reversible Jump Markov Chain Monte Carlo algorithm.Comment: 19 pages, 12 figures, revised to address referee's comment

The (Non)Tragic Passing of Rena Walden: Black Female Agency in Charles Chesnutt\u27s The House Behind the Cedars

This project analyzes Charles W. Chesnutt’s The House Behind the Cedars in an attempt to accredit Chesnutt as a forerunner of Critical Race Theory (CRT). Secondly, this project argues that Rena gains agency solely through her black ancestry in her ability to read and write both cultural and written texts. I will also argue in that creating a metanarrative form for his novel, Chesnutt is able to provide a radically feminist text through his representation of the power of Rena’s literacy, and furthermore, that Chesnutt is able to critique the laws and customs of normative white society. Lastly, this project concludes that Rena Walden becomes a representative for the notion of empowered black womanhood, and that although her story ends tragically, she becomes the antithesis of the tragic mulatta character. Chesnutt’s blending of genres promotes this notion of empowerment by using realist tropes such as self-development, social constraints such as miscegenation laws and the one-drop rule, objective narration, the sentimental tropes of letter writing, and the reproduction of the tournament scene from Sir Walter Scott’s Ivanhoe in order to nuance the distinctions between real-world environmental constraints and the ideologies and actions of Rena. After analyzing the effects of the social mechanisms (i.e. law, economics, politics) which usually oppress the black, female characters in postbellum fiction, this study makes the claim that Rena Walden both understands, exists within, and acts against the social constructions of her oppression. In portraying Rena’s autonomy through literacy, Chesnutt presents a character who defies the arbitrary category of race in her movement across the color line from perceived whiteness to accepted black ancestry

Characterizing the Role of Tissue-Specific Retinol Dehydrogenases

The bioactive form of vitamin A, retinoic acid is essential for development, cellular differentiation, epigenetic modifications, the immune system, and a variety of other processes due to its ability to regulate over 500 genes through activation of nuclear receptors. While many studies have focused on characterizing the biosynthesis and signaling of retinoic acid in embryogenesis, few have focused on adult tissues. Recent research has identified a novel retinol dehydrogenase, retinol dehydrogenase epidermal 2 (RDHE2), and shown RDHE2 is a potent, physiologically relevant retinol dehydrogenase in Xenopus. The work in this dissertation characterizes RDHE2 in mammalian models. We identify a paralog of RDHE2, RDHE2-similar (RDHE2S; collectively, RDHEs), and demonstrate both enzymes are physiologically relevant in mice. Furthermore, we demonstrate that RDHEs are tissue-specific retinol dehydrogenases that contribute to both developmental processes and maintenance of adult tissues. RDHEs are most highly expressed in skin, and the absence of RDHEs affects hair follicle development and alters the progression of the hair cycle in adult mice. However, transcripts of RDHEs are expressed in a variety of other tissues, and their absence alters whole body composition with aging. Interestingly, absence of RDHEs does not phenocopy systemic vitamin A deficiency, despite lowering retinoic acid levels in skin. Overall, this dissertation characterizes RDHEs in mammals and demonstrates their capacity to regulate retinoic iv acid biosynthesis in a tissue-specific manner, the disruption of which causes novel and diverse effects

Effects of lithium on electrical activity and potassium ion distribution in the vertebrate central nervous system

Three different regions of the vertebrate central nervous system maintained in vitro (frog spinal cord, guinea pig olfactory cortex and hippocampus) have been used to investigate how Li+ influences membrane potential, membrane resistance, action potentials, synaptic potentials and the transmembrane K+-distribution of neurons and glial cells. In view of the therapeutic action of Li+ in manicdepressive disease, a special effort was made to determine the threshold concentration for the actions of Li+ on the parameters described above. It was observed that Li+ induced a membrane depolarization of both neurons and glial cells, a decrease of action potential amplitudes, a facilitation of monosynaptic excitatory postsynaptic potentials and a depression of polysynaptic reflexes. The membrane resistance of neurons was not altered. Li+ also induced an elevation of the free extracellular potassium concentration and a decrease of the free intracellular potassium concentration. Furthermore, in the presence of Li+ a slowing of the recovery of the membrane potential of neurons and glial cells, and of the extracellular potassium concentration after repetitive synaptic stimulation was observed. The threshold concentrations for the effects of Li+ were below 5 mmol/l in the frog spinal cord and below 2 mmol/l in the guinea pig olfactory cortex and hippocampus. The basic mechanism underlying the action of Li+ may be an interaction with the transport-function of the Na+/K+ pump