On the cavity method for decimated random constraint satisfaction problems and the analysis of belief propagation guided decimation algorithms

We introduce a version of the cavity method for diluted mean-field spin models that allows the computation of thermodynamic quantities similar to the Franz-Parisi quenched potential in sparse random graph models. This method is developed in the particular case of partially decimated random constraint satisfaction problems. This allows to develop a theoretical understanding of a class of algorithms for solving constraint satisfaction problems, in which elementary degrees of freedom are sequentially assigned according to the results of a message passing procedure (belief-propagation). We confront this theoretical analysis to the results of extensive numerical simulations.Comment: 32 pages, 24 figure

Antiferromagnetic Heisenberg chains with bond alternation and quenched disorder

We consider S=1/2 antiferromagnetic Heisenberg chains with alternating bonds and quenched disorder, which represents a theoretical model of the compound CuCl_{2x}Br_{2(1-x)}(\gamma-{pic})_2. Using a numerical implementation of the strong disorder renormalization group method we study the low-energy properties of the system as a function of the concentration, x, and the type of correlations in the disorder. For perfect correlation of disorder the system is in the random dimer (Griffiths) phase having a concentration dependent dynamical exponent. For weak or vanishing disorder correlations the system is in the random singlet phase, in which the dynamical exponent is formally infinity. We discuss consequences of our results for the experimentally measured low-temperature susceptibility of CuCl_{2x}Br_{2(1-x)}(\gamma-{pic})_2

Known source detection predictions for higher order correlators

The problem addressed in this paper is whether higher order correlation detectors can perform better in white noise than the cross correlation detector for the detection of a known transient source signal, if additional receiver information is included in the higher order correlations. While the cross correlation is the optimal linear detector for white noise, additional receiver information in the higher order correlations makes them nonlinear. In this paper, formulas that predict the performance of higher order correlation detectors of energy signals are derived for a known source signal. Given the first through fourth order signal moments and the noise variance, the formulas predict the SNR for which the detectors achieve a probability of detection of 0.5 for any level of false alarm, when noise at each receiver is independent and identically distributed. Results show that the performance of the cross correlation, bicorrelation, and tricorrelation detectors are proportional to the second, fourth, and sixth roots of the sampling interval, respectively, but do not depend on the observation time. Also, the SNR gains of the higher order correlation detectors relative to the cross correlation detector improve with decreasing probability of false alarm. The source signal may be repeated in higher order correlations, and gain formulas are derived for these cases as well. Computer simulations with several test signals are compared to the performance predictions of the formulas. The breakdown of the assumptions for signals with too few sample points is discussed, as are limitations on the design of signals for improved higher order gain. Results indicate that in white noise it is difficult for the higher order correlation detectors in a straightforward application to achieve better performance than the cross correlation. © 1998 Acoustical Society of America

Known source detection predictions for higher order correlators

The problem addressed in this paper is whether higher order correlation detectors can perform better in white noise than the cross correlation detector for the detection of a known transient source signal, if additional receiver information is included in the higher order correlations. While the cross correlation is the optimal linear detector for white noise, additional receiver information in the higher order correlations makes them nonlinear. In this paper, formulas that predict the performance of higher order correlation detectors of energy signals are derived for a known source signal. Given the first through fourth order signal moments and the noise variance, the formulas predict the SNR for which the detectors achieve a probability of detection of 0.5 for any level of false alarm, when noise at each receiver is independent and identically distributed. Results show that the performance of the cross correlation, bicorrelation, and tricorrelation detectors are proportional to the second, fourth, and sixth roots of the sampling interval, respectively, but do not depend on the observation time. Also, the SNR gains of the higher order correlation detectors relative to the cross correlation detector improve with decreasing probability of false alarm. The source signal may be repeated in higher order correlations, and gain formulas are derived for these cases as well. Computer simulations with several test signals are compared to the performance predictions of the formulas. The breakdown of the assumptions for signals with too few sample points is discussed, as are limitations on the design of signals for improved higher order gain. Results indicate that in white noise it is difficult for the higher order correlation detectors in a straightforward application to achieve better performance than the cross correlation. © 1998 Acoustical Society of America

Highly-symmetric random one-dimensional spin models

The interplay of disorder and interactions is a challenging topic of condensed matter physics, where correlations are crucial and exotic phases develop. In one spatial dimension, a particularly successful method to analyze such problems is the strong-disorder renormalization group (SDRG). This method, which is asymptotically exact in the limit of large disorder, has been successfully employed in the study of several phases of random magnetic chains. Here we develop an SDRG scheme capable to provide in-depth information on a large class of strongly disordered one-dimensional magnetic chains with a global invariance under a generic continuous group. Our methodology can be applied to any Lie-algebra valued spin Hamiltonian, in any representation. As examples, we focus on the physically relevant cases of SO(N) and Sp(N) magnetism, showing the existence of different randomness-dominated phases. These phases display emergent SU(N) symmetry at low energies and fall in two distinct classes, with meson-like or baryon-like characteristics. Our methodology is here explained in detail and helps to shed light on a general mechanism for symmetry emergence in disordered systems.Comment: 26 pages, 12 figure

Maturation trajectories of cortical resting-state networks depend on the mediating frequency band

The functional significance of resting state networks and their abnormal manifestations in psychiatric disorders are firmly established, as is the importance of the cortical rhythms in mediating these networks. Resting state networks are known to undergo substantial reorganization from childhood to adulthood, but whether distinct cortical rhythms, which are generated by separable neural mechanisms and are often manifested abnormally in psychiatric conditions, mediate maturation differentially, remains unknown. Using magnetoencephalography (MEG) to map frequency band specific maturation of resting state networks from age 7 to 29 in 162 participants (31 independent), we found significant changes with age in networks mediated by the beta (13–30 Hz) and gamma (31–80 Hz) bands. More specifically, gamma band mediated networks followed an expected asymptotic trajectory, but beta band mediated networks followed a linear trajectory. Network integration increased with age in gamma band mediated networks, while local segregation increased with age in beta band mediated networks. Spatially, the hubs that changed in importance with age in the beta band mediated networks had relatively little overlap with those that showed the greatest changes in the gamma band mediated networks. These findings are relevant for our understanding of the neural mechanisms of cortical maturation, in both typical and atypical development.This work was supported by grants from the Nancy Lurie Marks Family Foundation (TK, SK, MGK), Autism Speaks (TK), The Simons Foundation (SFARI 239395, TK), The National Institute of Child Health and Development (R01HD073254, TK), National Institute for Biomedical Imaging and Bioengineering (P41EB015896, 5R01EB009048, MSH), and the Cognitive Rhythms Collaborative: A Discovery Network (NFS 1042134, MSH). (Nancy Lurie Marks Family Foundation; Autism Speaks; SFARI 239395 - Simons Foundation; R01HD073254 - National Institute of Child Health and Development; P41EB015896 - National Institute for Biomedical Imaging and Bioengineering; 5R01EB009048 - National Institute for Biomedical Imaging and Bioengineering; NFS 1042134 - Cognitive Rhythms Collaborative: A Discovery Network

Bark beetle population dynamics in the Anthropocene: Challenges and solutions

Tree-killing bark beetles are the most economically important insects in conifer forests worldwide. However, despite N200 years of research, the drivers of population eruptions and crashes are still not fully understood and the existing knowledge is thus insufficient to face the challenges posed by the Anthropocene. We critically analyze potential biotic and abiotic drivers of population dynamics of an exemplary species, the European spruce bark beetle (ESBB) (Ips typographus) and present a multivariate approach that integrates the many drivers governing this bark beetle system. We call for hypothesis-driven, large-scale collaborative research efforts to improve our understanding of the population dynamics of this and other bark beetle pests. Our approach can serve as a blueprint for tackling other eruptive forest insects

Multibeam Sonar Backscatter Lineaments and Anthropogenic Organic Components in Lacustrine Silty Clay, Evidence of Shipping in Western Lake Ontario

A multibeam sonar survey (95 kHz) covering more than 500 km2 of western Lake Ontario revealed anomalous lineaments of relatively high backscatter. The lineaments did not align with or parallel the most prominent structural zones beneath the lake as expected. Instead, the principal lineaments lay on lines between ports on opposite sides of the lake, especially between Toronto and Welland Canal, and Toronto and Niagara River mouth. As the lineaments underlie current and historical shipping routes used during the steamship era, they are interpreted as an acoustic response to shipping debris cumulated in the near-surface bottom sediment. An exploratory study of the organic components in the silty clay surface sediment, using geochemical and petrological techniques, shows that the upper 10 cm commonly contains silt-sized particles of anthropogenic origin, especially combustion residues. Combustion residues are more abundant on or near the lineaments, consistent with an origin related to shipping. Enhanced acoustic backscatter is evident where silt-sized combustion particles are hosted in dominantly clay-sized sediment. The coarser- grained anthropogenic particles increase the acoustic impedance of the lakebed relative to the bottom water as well as the roughness and volume scattering contributions to lakebed backscatter

A New Generation of Brain-Computer Interface Based on Riemannian Geometry

Based on the cumulated experience over the past 25 years in the field of Brain-Computer Interface (BCI) we can now envision a new generation of BCI. Such BCIs will not require training; instead they will be smartly initialized using remote massive databases and will adapt to the user fast and effectively in the first minute of use. They will be reliable, robust and will maintain good performances within and across sessions. A general classification framework based on recent advances in Riemannian geometry and possessing these characteristics is presented. It applies equally well to BCI based on event-related potentials (ERP), sensorimotor (mu) rhythms and steady-state evoked potential (SSEP). The framework is very simple, both algorithmically and computationally. Due to its simplicity, its ability to learn rapidly (with little training data) and its good across-subject and across-session generalization, this strategy a very good candidate for building a new generation of BCIs, thus we hereby propose it as a benchmark method for the field.Comment: 33 pages, 9 Figures, 17 equations/algorithm