Statistical physics of irregular low-density parity-check codes

Low-density parity-check codes with irregular constructions have recently been shown to outperform the most advanced error-correcting codes to date. In this paper we apply methods of statistical physics to study the typical properties of simple irregular codes. We use the replica method to find a phase transition which coincides with Shannon's coding bound when appropriate parameters are chosen. The decoding by belief propagation is also studied using statistical physics arguments; the theoretical solutions obtained are in good agreement with simulation results. We compare the performance of irregular codes with that of regular codes and discuss the factors that contribute to the improvement in performance.

Low density parity check codes: a statistical physics perspective

The modem digital communication systems are made transmission reliable by employing error correction technique for the redundancies. Codes in the low-density parity-check work along the principles of Hamming code, and the parity-check matrix is very sparse, and multiple errors can be corrected. The sparseness of the matrix allows for the decoding process to be carried out by probability propagation methods similar to those employed in Turbo codes. The relation between spin systems in statistical physics and digital error correcting codes is based on the existence of a simple isomorphism between the additive Boolean group and the multiplicative binary group. Shannon proved general results on the natural limits of compression and error-correction by setting up the framework known as information theory. Error-correction codes are based on mapping the original space of words onto a higher dimensional space in such a way that the typical distance between encoded words increases.

Random graph coloring:Statistical physics approach

The problem of vertex coloring in random graphs is studied using methods of statistical physics and probability. Our analytical results are compared to those obtained by exact enumeration and Monte Carlo simulations. We critically discuss the merits and shortcomings of the various methods, and interpret the results obtained. We present an exact analytical expression for the two-coloring problem as well as general replica symmetric approximated solutions for the thermodynamics of the graph coloring problem with p colors and K-body edges. ©2002 The American Physical Society.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Inference and optimization of real edges on sparse graphs:A statistical physics perspective

Inference and optimization of real-value edge variables in sparse graphs are studied using the Bethe approximation and replica method of statistical physics. Equilibrium states of general energy functions involving a large set of real edge variables that interact at the network nodes are obtained in various cases. When applied to the representative problem of network resource allocation, efficient distributed algorithms are also devised. Scaling properties with respect to the network connectivity and the resource availability are found, and links to probabilistic Bayesian approximation methods are established. Different cost measures are considered and algorithmic solutions in the various cases are devised and examined numerically. Simulation results are in full agreement with the theory. © 2007 The American Physical Society.

Network optimisation - A statistical physics perspective

Inference and optimisation of real-value edge variables in sparse graphs are studied using the tree based Bethe approximation optimisation algorithms. Equilibrium states of general energy functions involving a large set of real edge-variables that interact at the network nodes are obtained for networks in various cases. These include different cost functions, connectivity values, constraints on the edge bandwidth and the case of multiclass optimisation.

A Q-Methodology approach to investigating the relationship between level of reflection and typologies among prospective teachers in the physics learning assistant program at Florida International University

The purpose of this mixed methods study was to understand physics Learning Assistants' (LAs) views on reflective teaching, expertise in teaching, and LA program teaching experience and to determine if views predicted level of reflection evident in writing. Interviews were conducted in Phase One, Q methodology was used in Phase Two, and level of reflection in participants' writing was assessed using a rubric based on Hatton and Smith's (1995) "Criteria for the Recognition of Evidence for Different Types of Reflective Writing" in Phase Three. Interview analysis revealed varying perspectives on content knowledge, pedagogical knowledge, and experience in relation to expertise in teaching. Participants revealed that they engaged in reflection on their teaching, believed reflection helps teachers improve, and found peer reflection beneficial. Participants believed teaching experience in the LA program provided preparation for teaching, but that more preparation was needed to teach. Three typologies emerged in Phase Two. Type One LAs found participation in the LA program rewarding and believed expertise in teaching does not require expertise in content or pedagogy, but it develops over time from reflection. Type Two LAs valued reflection, but not writing reflections, felt the LA program teaching experience helped them decide on non-teaching careers and helped them confront gaps in their physics knowledge. Type Three LAs valued reflection, believed expertise in content and pedagogy are necessary for expert teaching, and felt LA program teaching experience increased their likelihood of becoming teachers, but did not prepare them for teaching. Writing assignments submitted in Phase Three were categorized as 19% descriptive writing, 60% descriptive reflections, and 21% dialogic reflections. No assignments were categorized as critical reflection. Using ordinal logistic regression, typologies that emerged in Phase Two were not found to be predictors for the level of reflection evident in the writing assignments. In conclusion, viewpoints of physics LAs were revealed, typologies among them were discovered, and their writing gave evidence of their ability to reflect on teaching. These findings may benefit faculty and staff in the LA program by helping them better understand the views of physics LAs and how to assess their various forms of reflection.

Data Science Seminar: The data science revolution in Physics and Astronomy

Abstract Heading into the 2020s, Physics and Astronomy are undergoing experimental revolutions that will reshape our picture of the fabric of the Universe. The Large Hadron Collider (LHC), the largest particle physics project in the world, produces 30 petabytes of data annually that need to be sifted through, analysed, and modelled. In astrophysics, the Large Synoptic Survey Telescope (LSST) will be taking a high-resolution image of the full sky every 3 days, leading to data rates of 30 terabytes per night over ten years. These experiments endeavour to answer the question why 96% of the content of the universe currently elude our physical understanding. Both the LHC and LSST share the 5-dimensional nature of their data, with position, energy and time being the fundamental axes. This talk will present an overview of the experiments and data that is gathered, and outlines the challenges in extracting information. Common strategies employed are very similar to industrial data! Science problems (e.g., data filtering, machine learning, statistical interpretation) and provide a seed for exchange of knowledge between academia and industry. Speaker Biography Professor Mark Sullivan Mark Sullivan is a Professor of Astrophysics in the Department of Physics and Astronomy. Mark completed his PhD at Cambridge, and following postdoctoral study in Durham, Toronto and Oxford, now leads a research group at Southampton studying dark energy using exploding stars called "type Ia supernovae". Mark has many years' experience of research that involves repeatedly imaging the night sky to track the arrival of transient objects, involving significant challenges in data handling, processing, classification and analysis.

The Usability of a Commercial Game Physics Engine to Develop Physics Educational Materials: an Investigation

Commercial computer games contain “physics engine” components, responsible for providing realistic interactions among game objects. The question naturally arises of whether these engines can be used to develop educational materials for high school and university physics education. To answer this question, the author's group recently conducted a detailed scientific investigation of the physics engine of Unreal Tournament 2004 (UT2004). This article presents their motivation, methodology, and results. The author presents the findings of experiments that probed the accessibility and fidelity of UT2004's physics engine, examples of educational materials developed, and an evaluation of their use in high school classes. The associated pedagogical implications of this approach are discussed, and the author suggests guidelines for educators on how to deploy the approach. Key resources are presented on an associated Web site.

Learning Physics with the Unreal Tournament Engine

Computer games such as Unreal Tournament (UT2004 and UT3) contain a 'physics engine' responsible for producing believable dynamic interactions between players and objects in the three-dimensional (3D) virtual world of a game. Through a series of probing experiments we have evaluated the fidelity and internal consistency of the UT2004 physics engine. These experiments have then led to the production of resources which may be used by learners and teachers of secondary-school physics. We also suggest an approach to learning, where both teachers and pupils may produce learning materials using the Unreal Tournament editor 'UnrealEd'.

The role of nuclear physics in supernovae and the evolution of neutron stars, Neutrino Opacities, Equation of State, Transport Coefficients, and Dark Matter Production

Thesis (Ph.D.)--University of Washington, 2016-08

Superconducting Transition-Edge Sensor Physics

Despite record-setting performance demonstrated by superconducting Transition Edge Sensors (TESs) and growing utilization of the technology, a theoretical model of the physics governing TES devices superconducting phase transition has proven elusive. Earlier attempts to describe TESs assumed them to be uniform superconductors. Sadleir et al. 2010 shows that TESs are weak links and that the superconducting order parameter strength has significant spatial variation. Measurements are presented of the temperature T and magnetic field B dependence of the critical current Ic measured over 7 orders of magnitude on square Mo/Au bilayers ranging in length from 8 to 290 microns. We find our measurements have a natural explanation in terms of a spatially varying order parameter that is enhanced in proximity to the higher transition temperature superconducting leads (the longitudinal proximity effect) and suppressed in proximity to the added normal metal structures (the lateral inverse proximity effect). These in-plane proximity effects and scaling relations are observed over unprecedentedly long lengths (in excess of 1000 times the mean free path) and explained in terms of a Ginzburg-Landau model. Our low temperature Ic(B) measurements are found to agree with a general derivation of a superconducting strip with an edge or geometric barrier to vortex entry and we also derive two conditions that lead to Ic rectification. At high temperatures the Ic(B) exhibits distinct Josephson effect behavior over long length scales and following functional dependences not previously reported. We also investigate how film stress changes the transition, explain some transition features in terms of a nonequilibrium superconductivity effect, and show that our measurements of the resistive transition are not consistent with a percolating resistor network model.