A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice

Starting from a Cluster Variational Method, and inspired by the correctness of the paramagnetic Ansatz (at high temperatures in general, and at any temperature in the 2D Edwards-Anderson model) we propose a novel message passing algorithm --- the Dual algorithm --- to estimate the marginal probabilities of spin glasses on finite dimensional lattices. We show that in a wide range of temperatures our algorithm compares very well with Monte Carlo simulations, with the Double Loop algorithm and with exact calculation of the ground state of 2D systems with bimodal and Gaussian interactions. Moreover it is usually 100 times faster than other provably convergent methods, as the Double Loop algorithm.Comment: 23 pages, 12 figures. v2: improved introductio

Rheology of acid suspensions containing cassava bagasse: Effect of biomass loading, acid content and temperature

[EN] Understanding the characterization and rheological behavior of acid suspensions of cassava bagasse provides essential information for the design of conversion processes. Samples with different cassava bagasse concentrations (0-10% w.w-1), phosphoric acid (0-10% w.w(-1)) at temperatures between 278.13 and 318.13 K were submitted to steady-state flow over a wide range of shear rates (1-265 s(-1)). The biomass particles had considerable residual starch (similar to 50% db), low lignin content and adequate particle size (<200 mu m) for the conversion process. Flow curves were well-fitted to the Herschel-Bulkley model, presenting a Newtonian domain at low solids and acid content and a non-Newtonian behavior with noticeable yield stress and shear-thinning characteristic (n < 1) at above 6% of cassava bagasse. Resistance to flow increased as the solids loading and acid content increased. Temperature dependence could be expressed as a function of an Arrhenius-type equation with good accuracy of fit. (C) 2019 Elsevier B.V. All rights reserved.The authors would like to thank Prof. Rosiane Lopes Cunha and Prof. Ana Carla Kawazoe Sato from University of Campinas (UNICAMP) for their support with particle size analyses. The authors also acknowledge the Sao Paulo Research Foundation - FAPESP (Grant number 2017/06518-2) and the Coordination for the Improvement of Higher Education Personnel -CAPES (Grant number 88881.132626/2016-01) for their financial support.Carregari-Polachini, T.; Mulet Pons, A.; Carcel, JA.; Telis Romero, J. (2019). Rheology of acid suspensions containing cassava bagasse: Effect of biomass loading, acid content and temperature. Powder Technology. 354:271-280. https://doi.org/10.1016/j.powtec.2019.05.086S27128035

Key hydraulic drivers and patterns of fine sediment accumulation in gravel streambeds: A conceptual framework illustrated with a case study from the Kiewa River, Australia

Fine sediment processes in gravel beds may have significant impacts to overall river ecosystem function. In addition to gravitational deposition, horizontal intragravel transport has been recognized to influence fine sediment accumulation. However, the specific hydraulic mechanisms and origin of fine sediment movement are not clearly identified. The purpose of this study was to investigate key hydraulic drivers and patterns of fine sediment accumulation. Using a conceptual framework to set the scene, we implemented an experimental setup in a gravel lateral bar subject to irregular flow fluctuations in the Kiewa River (Australia). We installed nine sets of sediment collector pairs and piezometers into the gravel. Each pair included one horizontally and one horizontally-vertically perforated collector. Mid-range, rather than peak flows, covering the site in water drove fine sediment deposited in the collectors. We estimated horizontal contribution to final deposition as 59%. Such contribution resulted from shear stresses > 3 N m− 2 promoting streamwise near-bed turbulence at the water-sediment interface during flooded conditions. Despite high subsurface hydraulic gradients, intragravel transport in the lower sediment layers via Darcy flow did not show any influence to fine sediment deposition. Our findings contribute to an improved understanding of fine sediment accumulation processes, key for overall river ecosystem functioning, particularly in regulated rivers

Coloring random graphs

We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on $q$, we find the precise value of the critical average connectivity $c_q$. Moreover, we show that below $c_q$ there exist a clustering phase $c\in [c_d,c_q]$ in which ground states spontaneously divide into an exponential number of clusters and where the proliferation of metastable states is responsible for the onset of complexity in local search algorithms.Comment: 4 pages, 1 figure, version to app. in PR

Zero temperature solutions of the Edwards-Anderson model in random Husimi Lattices

We solve the Edwards-Anderson model (EA) in different Husimi lattices. We show that, at T=0, the structure of the solution space depends on the parity of the loop sizes. Husimi lattices with odd loop sizes have always a trivial paramagnetic solution stable under 1RSB perturbations while, in Husimi lattices with even loop sizes, this solution is absent. The range of stability under 1RSB perturbations of this and other RS solutions is computed analytically (when possible) or numerically. We compute the free-energy, the complexity and the ground state energy of different Husimi lattices at the level of the 1RSB approximation. We also show, when the fraction of ferromagnetic couplings increases, the existence, first, of a discontinuous transition from a paramagnetic to a spin glass phase and latter of a continuous transition from a spin glass to a ferromagnetic phase.Comment: 20 pages, 10 figures (v3: Corrected analysis of transitions. Appendix proof fixed

Replicated Bethe Free Energy: A Variational Principle behind Survey Propagation

A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of replicas. In the scheme, survey propagation (SP), which is an efficient algorithm developed recently for analyzing the microscopic properties of glassy states for a fixed sample of disordered systems, can be reproduced by assuming the simplest replica symmetry on stationary points of the replicated Bethe free energy. Belief propagation and generalized SP can also be offered in the identical framework under assumptions of the highest and broken replica symmetries, respectively.Comment: appeared in Journal of the Physical Society of Japan 74, 2133-2136 (2005

Polynomial iterative algorithms for coloring and analyzing random graphs

We study the graph coloring problem over random graphs of finite average connectivity $c$. Given a number $q$ of available colors, we find that graphs with low connectivity admit almost always a proper coloring whereas graphs with high connectivity are uncolorable. Depending on $q$, we find the precise value of the critical average connectivity $c_q$. Moreover, we show that below $c_q$ there exist a clustering phase $c\in [c_d,c_q]$ in which ground states spontaneously divide into an exponential number of clusters. Furthermore, we extended our considerations to the case of single instances showing consistent results. This lead us to propose a new algorithm able to color in polynomial time random graphs in the hard but colorable region, i.e when $c\in [c_d,c_q]$.Comment: 23 pages, 10 eps figure

Against Chaos in Temperature in Mean-Field Spin-Glass Models

We study the problem of chaos in temperature in some mean-field spin-glass models by means of a replica computation over a model of coupled systems. We propose a set of solutions of the saddle point equations which are intrinsically non-chaotic and solve a general problem regarding the consistency of their structure. These solutions are relevant in the case of uncoupled systems too, therefore they imply a non-trivial overlap distribution $P(q_{T1T2})$ between systems at different temperatures. The existence of such solutions is checked to fifth order in an expansion near the critical temperature through highly non-trivial cancellations, while it is proved that a dangerous set of such cancellations holds exactly at all orders in the Sherrington-Kirkpatrick (SK) model. The SK model with soft-spin distribution is also considered obtaining analogous results. Previous analytical results are discussed.Comment: 20 pages, submitted to J.Phys.

Replica Cluster Variational Method: the Replica Symmetric solution for the 2D random bond Ising model

We present and solve the Replica Symmetric equations in the context of the Replica Cluster Variational Method for the 2D random bond Ising model (including the 2D Edwards-Anderson spin glass model). First we solve a linearized version of these equations to obtain the phase diagrams of the model on the square and triangular lattices. In both cases the spin-glass transition temperatures and the tricritical point estimations improve largely over the Bethe predictions. Moreover, we show that this phase diagram is consistent with the behavior of inference algorithms on single instances of the problem. Finally, we present a method to consistently find approximate solutions to the equations in the glassy phase. The method is applied to the triangular lattice down to T=0, also in the presence of an external field.Comment: 22 pages, 11 figure

DNS of the kappa-mechanism. I. Radial modes in the purely radiative case

Context: Hydrodynamical model of the kappa-mechanism in a purely radiative case. Aims: First, to determine the physical conditions propitious to kappa-mechanism in a layer with a configurable conductivity hollow and second, to perform the (nonlinear) direct numerical simulations (DNS) from the most favourable setups. Methods: A linear stability analysis applied to radial modes using a spectral solver and DNS thanks to a high-order finite difference code are compared. Results: Changing the hollow properties (location and shape) lead to well-defined instability strips. For a given position in the layer, the amplitude and width of the hollow appear to be the key parameters to get unstable modes driven by kappa-mechanism. The DNS achieved from these more auspicious configurations confirm the growth rates as well as structures of linearly unstable modes. The nonlinear saturation follows through intricate couplings between the excited fundamental mode and higher damped overtones.Comment: 15 pages, 15 figures, 1 table, accepted for publication in A&