Thouless-Anderson-Palmer Approach for Lossy Compression

We study an ill-posed linear inverse problem, where a binary sequence will be reproduced using a sparce matrix. According to the previous study, this model can theoretically provide an optimal compression scheme for an arbitrary distortion level, though the encoding procedure remains an NP-complete problem. In this paper, we focus on the consistency condition for a dynamics model of Markov-type to derive an iterative algorithm, following the steps of Thouless-Anderson-Palmer's. Numerical results show that the algorithm can empirically saturate the theoretical limit for the sparse construction of our codes, which also is very close to the rate-distortion function.Comment: 10 pages, 3 figure

Modeling reciprocal effects in medical research: critical discussion on the current practices and potential alternative models

Longitudinal designs provide a strong inferential basis for uncovering reciprocal effects or causality between variables. For this analytic purpose, a cross-lagged panel model (CLPM) has been widely used in medical research, but the use of the CLPM has recently been criticized in methodological literature because parameter estimates in the CLPM conflate between-person and within-person processes. The aim of this study is to present some alternative models of the CLPM that can be used to examine reciprocal effects, and to illustrate potential consequences of ignoring the issue. A literature search, case studies, and simulation studies are used for this purpose. We examined more than 300 medical papers published since 2009 that applied cross-lagged longitudinal models, finding that in all studies only a single model (typically the CLPM) was performed and potential alternative models were not considered to test reciprocal effects. In 49% of the studies, only two time points were used, which makes it impossible to test alternative models. Case studies and simulation studies showed that the CLPM and alternative models often produce different (or even inconsistent) parameter estimates for reciprocal effects, suggesting that research that relies only on the CLPM may draw erroneous conclusions about the presence, predominance, and sign of reciprocal effects. Simulation studies also showed that alternative models are sometimes susceptible to improper solutions, even when reseachers do not misspecify the model

Discriminating spin through quantum interference

Many of the proposed solutions to the hierarchy and naturalness problems postulate new `partner' fields to the standard model particles. Determining the spins of these new particles will be critical in distinguishing among the various possible SM extensions, yet proposed methods rely on the underlying models. We propose a new model-independent method for spin measurements which takes advantage of quantum interference among helicity states. We demonstrate that this method will be able to discriminate scalar particles from higher spin states at the ILC, and discuss application to higher spins and possible uses at the LHC.Comment: 11 pages, 11 figure

Statistical mechanical analysis of a hierarchical random code ensemble in signal processing

We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by using the replica method in two situations: lossy data compression and channel coding. For both the situations, the exponents of large deviation analysis characterizing the performance of the ensemble, the distortion rate of lossy data compression and the error exponent of channel coding in Gallager's formalism, are accessible by a generating function of the generalized random energy model. We discuss that the transitions of those exponents observed in the preceding work can be interpreted as phase transitions with respect to the replica number. We also show that the replica symmetry breaking plays an essential role in these transitions.Comment: 24 pages, 4 figure

Inverted Hierarchical Model of Neutrino Masses Revisited

In this letter we highlight the inherent problems associted with the inverted hierarchical model of neutrinos with only three generations and suggest possible solutions within the MSSM. we discuss the new parametrisation of the solar mixing angle which can identify the light side and dark side of the data. We then argue whether the inverted hierarchical neutrino mass matrix can explain the large mixing angle(LMA) MSW solution of the solar neutrino anomaly in the presence of an appropriate texture of charged lepton mass matrix. In model independent way we explore such specific form of the charged lepton mass matrix having special structure in 1-2 block. The contribution to the solar mass splitting arising out of radiative corrections in MSSM, is calculated, thus making the model stable under radiative corrections.Comment: 4pages (To appear in Physics Letters

Susceptibility of the 2D S=1/2 Heisenberg antiferromagnet with an impurity

We use a quantum Monte Carlo method (stochastic series expansion) to study the effects of a magnetic or nonmagnetic impurity on the magnetic susceptibility of the two-dimensional Heisenberg antiferromagnet. At low temperatures, we find a log-divergent contribution to the transverse susceptibility. We also introduce an effective few-spin model that can quantitatively capture the differences between magnetic and nonmagnetic impurities at high and intermediate temperatures.Comment: 5 pages, 4 figures, v2: Updated data in figures, minor changes in text, v3: Final version, cosmetic change

Symplectic SUSY Gauge Theories with Antisymmetric Matter

We investigate the confining phase vacua of supersymmetric Sp(2\NC) gauge theories that contain matter in both fundamental and antisymmetric representations. The moduli spaces of such models with \NF=3 quark flavors and \NA=1 antisymmetric field are analogous to that of SUSY QCD with \NF=\NC+1 flavors. In particular, the forms of their quantum superpotentials are fixed by classical constraints. When mass terms are coupled to W_{(\NF=3,\NA=1)} and heavy fields are integrated out, complete towers of dynamically generated superpotentials for low energy theories with fewer numbers of matter fields can be derived. Following this approach, we deduce exact superpotentials in $Sp(4)$ and $Sp(6)$ theories which cannot be determined by symmetry considerations or integrating in techniques. Building upon these simple symplectic group results, we also examine the ground state structures of several $Sp(4) \times Sp(4)$ and $Sp(6) \times Sp(2)$ models. We emphasize that the top-down approach may be used to methodically find dynamical superpotentials in many other confining supersymmetric gauge theories.Comment: 21 pages, Revte