Open or Closed? Information Flow Decided by Transfer Operators and Forecastability Quality Metric

A basic systems question concerns the concept of closure, meaning autonomomy (closed) in the sense of describing the (sub)system as fully consistent within itself. Alternatively, the system may be nonautonomous (open) meaning it receives influence from an outside coupling subsystem. Information flow, and related causation inference, are tenant on this simple concept. We take the perspective of Weiner-Granger causality, descriptive of a subsystem forecast quality dependence on considering states of another subsystem. Here we develop a new direct analytic discussion, rather than a data oriented approach. That is, we refer to the underlying Frobenius-Perron transfer operator that moderates evolution of densities of ensembles of orbits, and two alternative forms of the restricted Frobenius-Perron (FP) operator, interpreted as if either closed (determinstic FP) or not closed (the unaccounted outside influence seems stochastic and correspondingly the stochastic FP operator). From this follows contrasting the kernels of the variants of the operators, as if densities in their own rights. However, the corresponding differential entropy to compare by Kulback-Leibler divergence, as one would when leading to transfer entropy, becomes ill-defined. Instead we build our Forecastability Quality Metric (FQM) upon the "symmetrized" variant known as Jensen-Shanon divergence, and also we are able to point out several useful resulting properties that result. We illustrate the FQM by a simple coupled chaotic system. For now, this analysis is a new theoretical direction, but we describe data oriented directions for the future.Comment: 16 pages 2 figure

Ultramicro Black Holes and Finiteness of the Electromagnetic Contribution to the Electron Mass

It is argued that the nonintegrably singular energy density of the electron's electromagnetic field (in both the classical point-charge model and quantum electrodynamics) must entail very strong self-gravitational effects, which, via black hole phenomena at finite radii, could well cut off the otherwise infinite electromagnetic contribution to the electron's mass. The general- relativistic equations for static, spherically symmetric stellar structure are specialized to treat the self-gravitational effects of static, spheri- cally symmetric, nonnegative, localized energy densities which may exhibit nonintegrable singularities at zero radius. It is demonstrated that in many situations, including the electromagnetic ones of interest here, such a system has a black hole whose Schwarzschild radius is that where the original energy per radial distance (the spherical shell area times the original energy density) reaches the inverse of (2G). The total mass of the system is that of this black hole (which follows in the usual way from its Schwarz- schild radius) plus the integrated original energy density outside this black hole. These results produce, for the classical point-charge model of the electron, an electrostatic contribution to its mass which is many orders of magnitude larger than its measured mass. For quantum electrodynamics, how- ever, the result is an electromagnetic mass contribution which is approxi- mately equal to its bare mass -- thus about half of its measured mass.Comment: 21 page

Metric-first & entropy-first surprises

Established idea-sets don't update seamlessly. The tension between new and old views of nature is e.g. documented in Galileo's dialogs and now present in many fields. However the science of Bayesian model-selection has made recent strides in both life & physical sciences, in effect suggesting that we look to models which are quantitatively {\em surprised least} by present-day observations. We illustrate the relevance of this to physics-education with a qualitative look at two paradigm-shifts, namely from {\bf Lorentz-transform to metric-equation} descriptions of motion in space-time, and from {\bf classical to statistical thermodynamics} with help from Boltzmann's choice-multiplicity & Shannon's uncertainty. Connections of the latter to {\bf correlation measures} behind available-work, evolving complexity, and model-selection relevant to physics undergrads are also explored. New strategies are exemplified with Appendices {\em for teachers} on: anyspeed traffic-laws & 3-vector velocity-addition, the energy-momentum half-plane lost to finite lightspeed, the modern distinction between proper & geometric accelerations, metric-first kinematics with acceleration & differential-aging, quantifying risk with a handful of coins, effective number of choices, available work in bits, reversible-thermalization of life's power-stream, and choice-multiplicity measures of layered complex-system health.Comment: 17 pages (12 figs, 4 tables, 68 refs) RevTeX, cf. http://www.umsl.edu/~fraundorfp/ifzx/MinimizingSurprisal.htm

Invariant Feature Mappings for Generalizing Affordance Understanding Using Regularized Metric Learning

This paper presents an approach for learning invariant features for object affordance understanding. One of the major problems for a robotic agent acquiring a deeper understanding of affordances is finding sensory-grounded semantics. Being able to understand what in the representation of an object makes the object afford an action opens up for more efficient manipulation, interchange of objects that visually might not be similar, transfer learning, and robot to human communication. Our approach uses a metric learning algorithm that learns a feature transform that encourages objects that affords the same action to be close in the feature space. We regularize the learning, such that we penalize irrelevant features, allowing the agent to link what in the sensory input caused the object to afford the action. From this, we show how the agent can abstract the affordance and reason about the similarity between different affordances

Unsupervised Assignment Flow: Label Learning on Feature Manifolds by Spatially Regularized Geometric Assignment

This paper introduces the unsupervised assignment flow that couples the assignment flow for supervised image labeling with Riemannian gradient flows for label evolution on feature manifolds. The latter component of the approach encompasses extensions of state-of-the-art clustering approaches to manifold-valued data. Coupling label evolution with the spatially regularized assignment flow induces a sparsifying effect that enables to learn compact label dictionaries in an unsupervised manner. Our approach alleviates the requirement for supervised labeling to have proper labels at hand, because an initial set of labels can evolve and adapt to better values while being assigned to given data. The separation between feature and assignment manifolds enables the flexible application which is demonstrated for three scenarios with manifold-valued features. Experiments demonstrate a beneficial effect in both directions: adaptivity of labels improves image labeling, and steering label evolution by spatially regularized assignments leads to proper labels, because the assignment flow for supervised labeling is exactly used without any approximation for label learning.Comment: 34 pages, 13 figures, published in Journal of Mathematical Imaging and Vision (JMIV

Network Gravity

We introduce the construction of a new framework for probing discrete emergent geometry and boundary-boundary observables based on a fundamentally a-dimensional underlying network structure. Using a gravitationally motivated action with Forman weighted combinatorial curvatures and simplicial volumes relying on a decomposition of an abstract simplicial complex into realized embeddings of proper skeletons, we demonstrate properties such as a minimal volume-scale cutoff, the necessity of a positive-definite cosmological constant-like term as a regulator for non-degenerate geometries, and naturally emergent simplicial structures from Metropolis network evolution simulations with no restrictions on attachment rules or regular building blocks. We see emergent properties which echo results from both the spinfoam formalism and causal dynamical triangulations in quantum gravity, and provide analytical and numerical results to support the analogy. We conclude with a summary of open questions and intent for future work in developing the program.Comment: Preprint: [19 pages, 19 figures]; Submitted to Phys. Rev. D for Publication; Changes: Updated formatting, explicitly defined projection map, updated commentary on IR divergenc

How Generative Adversarial Networks and Their Variants Work: An Overview

Generative Adversarial Networks (GAN) have received wide attention in the machine learning field for their potential to learn high-dimensional, complex real data distribution. Specifically, they do not rely on any assumptions about the distribution and can generate real-like samples from latent space in a simple manner. This powerful property leads GAN to be applied to various applications such as image synthesis, image attribute editing, image translation, domain adaptation and other academic fields. In this paper, we aim to discuss the details of GAN for those readers who are familiar with, but do not comprehend GAN deeply or who wish to view GAN from various perspectives. In addition, we explain how GAN operates and the fundamental meaning of various objective functions that have been suggested recently. We then focus on how the GAN can be combined with an autoencoder framework. Finally, we enumerate the GAN variants that are applied to various tasks and other fields for those who are interested in exploiting GAN for their research.Comment: 41 pages, 16 figures, Published in ACM Computing Surveys (CSUR

CSL Wave Function Collapse Model as a Mechanism for the Emergence of Cosmological Asymmetries in Inflation

As previously discussed in (D. Sudarsky, Int.J.Mod.Phys.D20:509-552, (2011); [arXiv:0906.0315]), the inflationary account for the emergence of the seeds of cosmic structure falls short of actually explaining the generation of primordial anisotropies and inhomogeneities. This description starts from a symmetric background, and invokes symmetric dynamics, so it cannot explain asymmetries. To generate asymmetries, we present an application of the Continuous Spontaneous Localization (CSL) model of wave function collapse (P. Pearle, Phys. Rev. A 39, 2277, (1989); G. C. Ghirardi, P. Pearle and A. Rimini, Phys. Rev. A42, 78 (1990)) in the context of inflation. This modification of quantum dynamics introduces a stochastic non-unitary component to the evolution of the inflaton field perturbations. This leads to passage from a homogeneous and isotropic stage to another, where the quantum uncertainties in the initial state of inflation transmute into the primordial inhomogeneities and anisotropies. We examine requirements for, and show how to achieve, compatibility with the precise observations of the cosmic microwave background (CMB) radiation.Comment: 28 pages, no figures, In press in PR

Holographic Signatures of Cosmological Singularities

To gain insight in the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge/gravity duality. The dual description of the bulk evolution towards the singularity involves N = 4 super Yang-Mills on the expanding branch of deformed de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlators show a strong signature of the singularity around horizon scales and decay at large boundary separation at different rates in different directions. More generally, the boundary evolution exhibits a process of particle creation similar to that in inflation. This leads us to conjecture that information on the quantum nature of cosmological singularities is encoded in long-wavelength features of the boundary wave function.Comment: 5 pages, 3 figures; v3: journal version, minor typos corrected, new figure adde

Entanglement Entropy Near Cosmological Singularities

We investigate the behavior of the entanglement entropy of a confining gauge theory near cosmological singularities using gauge/gravity duality. As expected, the coefficients of the UV divergent terms are given by simple geometric properties of the entangling surface in the time-dependent background. The finite (universal) part of the entanglement entropy either grows without bound or remains bounded depending on the nature of the singularity and entangling region. We also discuss a confinement/deconfinement phase transition as signaled by the entanglement entropy.Comment: 16 pages, 5 figures, v2: typo correcte