Evaluating zero error noise thresholds by replica method for Gallager code ensembles

The replica method, developed in statistical physics, is employed in conjunction with Gallager's methodology to accurately evaluate zero error noise thresholds for Gallager code ensembles. Our approach generally provides more optimistic evaluations than those reported in the information theory literature for sparse matrices; the difference vanishes as the parity check matrix becomes dense.

Fabrication of Mg foams for biomedical applications by means of a replica method based upon spherical carbon particles

Interest in Mg foams is increasing due to their potential use as biomaterials. Fabrication methods determine to a great extent their structure and, in some cases, may pollute the foam. In this work Mg foams are fabricated by a replica method that uses as skeleton packed spheres of active carbon, a material widely utilized in medicine. After Mg infiltration, carbon particles are eliminated by an oxidizing heat treatment. The latter covers Mg with MgO which improves performance. In particular, oxidation retards degradation of the foam, as the polarization curves of the Mg foam with and without oxide indicate. The sphericity and regularity of C particles allows control of the structure of the produced open-cell foams.

Nanostructured mesoporous bioglass coated zirconia scaffolds for bone tissue engineering

For the filling and reconstruction of non-healing bone defects, the application of porous ceramic scaffold as bone substitutes is considered to be a reasonable choice. In bone tissue engineering, an ideal scaffold must satisfy several criterias such as open porosity, having high compressive strength (it depends where in body, and if external fixatures are used) and the practicability for cell migration. Many researchers have focused on enhancing the mechanical properties of hydroxyapatite scaffolds by combining it with other biomaterials, such as bioglass and polymers. Nevertheless, there is still a lack of suitable scaffolds based on porous biomaterials. In this study, zirconia scaffolds from two different templates (polyurethane (PU) and Acrylonitrile Butadiene Styrene (ABS) templates) were successfully fabricated with dissimilar fabrication techniques. The scaffold surfaces were further modified with mesoporous bioglass for the purpose of bone tissue engineering. In the study of PU template scaffold, high porosity (~88%) sol-gel derived yttria-stabilized zirconia (YSZ) scaffold was prepared by a polyurethane (PU) foam replica method using sol-gel derived zirconia for the first time, and double coated with Mesoporous Bioglass (MBGs) coating. For the ABS template scaffold, two types of templates (cube and cylinder) with different strut spacings were used and fabricated by a 3D Rapid Prototyper. Subsequently, zirconia scaffolds with low porosity (63±2.8% to 68±2.5%) were fabricated by embedding the zirconia powder slurry into the ABS templates and burning out the ABS to produce a uniform porous structure. The zirconia scaffolds were double coated with mesoporous bioglass by dip coating for the first time. The porosities of the scaffolds were calculated before and after coating. The microstructures were then examined using scanning electron microscopy and the mechanical properties were evaluated using compressive test. Accordingly, relationships between microstructure, processing and mechanical behaviour of the porous zirconia was discussed. Scaffold biocompatibility and bioactivity was also evaluated using a bone marrow stromal cell (BMSC) proliferation test and a simulated body fluid test.

Compressible Sherrington-Kirkpatrick spin-glass model

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressure-temperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The second-order para-ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperature-concentration phase diagrams of mixtures of hydrogen-bonded crystals.

Antiferromagnetic spherical spin-glass model

We study the thermodynamic properties and the phase diagrams of a multi-spin antiferromagnetic spherical spin-glass model using the replica method. It is a two-sublattice version of the ferromagnetic spherical p-spin glass model. We consider both the replica-symmetric and the one-step replica-symmetry-breaking solutions, the latter being the most general solution for this model. We find paramagnetic, spin-glass, antiferromagnetic and mixed or glassy antiferromagnetic phases. The phase transitions are always of second order in the thermodynamic sense, but the spin-glass order parameter may undergo a discontinuous change.

Desenvolvimento e caracterização de filtros cerâmicos para aplicações a altas temperaturas

Ceramic filters are cellular structures that can be produced by various techniques, among which we highlight the replication method, or method of polymeric sponge. This method consists of impregnating polymeric foam with ceramic slurry, followed by heat treatment, where will occur decomposition of organic material and the sinter of the ceramic material, resulting in a ceramic whose structure is a replica of the impregnated sponge. Ceramic filters have specific properties that make this type of material very versatile, used in various technological applications such as filters for molten metals and burners, make these materials attractive candidates for high temperature applications. In this work we studied the systems Al2O3-LZSA ceramic filters processed in the laboratory, and commercial Al2O3-SiC ceramics filters, both obtained by the replica method, this work proposes the thermal and mechanical characterization. The sponge used in the processing of filters made in the laboratory was characterized by thermogravimetric analysis. The ceramic filters were characterized by compressive strength, flexural strength at high temperatures, thermal shock, permeability and physical characterization (density and porosity) and microstructural (MEV and X-rays). From the results obtained, the analysis was made of the mechanical behavior of these materials, comparing the model proposed by Gibson and Ashby model and modified the effective area and the tension adjusted, where the modified model adapted itself better to the experimental results, representing better the mechanical behavior of ceramic filters obtained by the replica method

Análise do comportamento mecânico de espumas cerâmicas a base de alumina obtidas pelo método da réplica

Ceramics with porous cellular structure, called ceramic foams, have a potential use in several applications, such as: thermal insulation, catalyst supports, filters, and others. Among these techniques to obtain porous ceramics the replication method is an important process. This method consists of impregnation of a sponge (usually polymer) with ceramic slurry, followed by a heat treatment, which will happen the decomposition of organic material and sintering the ceramic material, resulting in a ceramic structure which is a replica of impregnated sponge. Knowledge of the mechanical properties of these ceramics is important for these materials can be used commercially. Gibson and Ashby developed a mathematical model to describe the mechanical behavior of cellular solids. This model wasn´t for describing the ceramics behavior produced by the replica method, because it doesn´t consider the defects from this type of processing. In this study were researched mechanical behavior of porous alumina ceramics obtained by the replica method and proposed modifications to the model of Gibson and Ashby to accommodate this material. The polymer sponge used in processing was characterized by thermogravimetric analysis and scanning electron microscopy. The materials obtained after sintering were characterized by mechanical strength tests on 4-point bending and compression, density and porosity and by scanning electron microscopy. From these results it was evaluated the mechanical strength behavior compared to Gibson and Ashby model for solid cellular structure and was proposed a correction of this model through a factor related to struts integrity degree, which consider fissures present in the structure of these materials besides defects geometry within the struts

Efeitos de campos aleatórios e de anisotropias em vidros de spins

Ising and m-vector spin-glass models are studied, in the limit of infinite-range in-teractions, through the replica method. First, the m-vector spin glass, in the presence of an external uniform magnetic field, as well as of uniaxial anisotropy fields, is consi-dered. The effects of the anisotropics on the phase diagrams, and in particular, on the Gabay-Toulouse line, which signals the transverse spin-glass ordering, are investigated. The changes in the Gabay-Toulouse line, due to the presence of anisotropy fields which favor spin orientations along the Cartesian axes (m = 2: planar anisotropy; m = 3: cubic anisotropy), are also studied. The antiferromagnetic Ising spin glass, in the presence of uniform and Gaussian random magnetic fields, is investigated through a two-sublattice generalization of the Sherrington-Kirpaktrick model. The effects of the magnetic-field randomness on the phase diagrams of the model are analysed. Some confrontations of the present results with experimental observations available in the literature are discussed

Efeitos de acoplamentos biquadráticos e campos aleatórios em vidros de spins

In this work we have studied the effects of random biquadratic and random fields in spin-glass models using the replica method. The effect of a random biquadratic coupling was studied in two spin-1 spin-glass models: in one case the interactions occur between pairs of spins, whereas in the second one the interactions occur between p spins and the limit p > oo is considered. Both couplings (spin glass and biquadratic) have zero-mean Gaussian probability distributions. In the first model, the replica-symmetric assumption reveals that the system presents two pha¬ses, namely, paramagnetic and spin-glass, separated by a continuous transition line. The stability analysis of the replica-symmetric solution yields, besides the usual instability associated with the spin-glass ordering, a new phase due to the random biquadratic cou¬plings between the spins. For the case p oo, the replica-symmetric assumption yields again only two phases, namely, paramagnetic and quadrupolar. In both these phases the spin-glass parameter is zero. Besides, it is shown that they are stable under the Almeida-Thouless stability analysis. One of them presents negative entropy at low temperatures. We developed one step of replica simmetry breaking and noticed that a new phase, the biquadratic glass phase, emerge. In this way we have obtained the correct phase diagram, with.three first-order transition lines. These lines merges in a common triple point. The effects of random fields were studied in the Sherrington-Kirkpatrick model consi¬dered in the presence of an external random magnetic field following a trimodal distribu¬tion {P{hi) = p+S(hi - h0) +Po${hi) +pS(hi + h0))- It is shown that the border of the ferromagnetic phase may present, for conveniently chosen values of p0 and hQ, first-order phase transitions, as well as tricritical points at finite temperatures. It is verified that the first-order phase transitions are directly related to the dilution in the fields: the extensions of these transitions are reduced for increasing values of po- In fact, the threshold value pg, above which all phase transitions are continuous, is calculated analytically. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified

Sintering of porous alumina obtained by biotemplate fibers for low thermal conductivity applications

In this research report, a sintering process of porous ceramic materials based on Al2O3 was employed using a method where a cation precursor solution is embedded in an organic fibrous cotton matrix. For porous green bodies, the precursor solution and cotton were annealed at temperatures in the range of 100-1600°C using scanning electron microscopy (SEM) and thermogravimetric (TG) analysis to obtain a porous body formation and disposal process containing organic fibers and precursor solution. In a structure consisting of open pores and interconnected nanometric grains, despite the low porosity of around 40% (calculated geometrically), nitrogen physisorption determined a specific surface area of 14m2/g, which shows much sintering of porous bodies. Energy dispersive X-ray (EDX) and X-ray diffraction (XRD) analytical methods revealed a predominant amount of α-Al2O3 in the sintered samples. Thermal properties of the sintered Al2O3 fibers were obtained by using the Laser Flash which resulted in the lower thermal conductivity obtained by α-Al2O3 and therefore improved its potential use as an insulating material. © 2012 Elsevier Ltd.

Obtenção e caracterização de suporte de regeneração óssea de dióxido de titânio

Due to complications caused by metallic implants in the replacement of bone tissue, the biological application of ceramics raised and became a viable alternative. The titania has the ability to promote bone tissue regeneration based on its structure, mechanical and biologically properties compatibility. The present work aims at obtaining and characterization of Titania (TiO2) porous ceramics produced by the polymeric sponge method (replica method). Polyurethane sponge with 10 ppi and 15 ppi (pores per linear inch) were used. The process differentiation is the air blower used to remove excess slurry. The ceramics sponges were dried in an oven, then pre-sintered at 1000 o C and sintered at 1450 o C. The effect of direct sintering at 1450 o C was also assessed. The percentage of solids used to prepare the slurry was 40 to 45% by weight. To increase the surface porosity of the sponge, 20% of starch was added. There was difficulty on controlling the thickness of the slurry layers on the sponge which resulted in the variation of samples mechanical resistance. Despite this, the results obtained are quite promising for the proposed use, indicating that it is possible to obtain titania sponges with an apparent porosity of around 60%, a bulk density ranging from 40 to 47% and a compressive strength resistance – that with better control of layers depositions – can vary from 1 to 4 MPa

Spin-glass behaviour on random lattices

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction w of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that w = 1/2, corresponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase (w < 1/2) from a region with spin-glass, ferromagnetic, mixed and paramagnetic phases (w > 1/2).

Finite connectivity systems as error-correcting codes

We investigate the performance of parity check codes using the mapping onto spin glasses proposed by Sourlas. We study codes where each parity check comprises products of K bits selected from the original digital message with exactly C parity checks per message bit. We show, using the replica method, that these codes saturate Shannon's coding bound for K?8 when the code rate K/C is finite. We then examine the finite temperature case to asses the use of simulated annealing methods for decoding, study the performance of the finite K case and extend the analysis to accommodate different types of noisy channels. The analogy between statistical physics methods and decoding by belief propagation is also discussed.

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.

Noise, regularizers, and unrealizable scenarios in online learning from restricted training sets

We study the dynamics of on-line learning in multilayer neural networks where training examples are sampled with repetition and where the number of examples scales with the number of network weights. The analysis is carried out using the dynamical replica method aimed at obtaining a closed set of coupled equations for a set of macroscopic variables from which both training and generalization errors can be calculated. We focus on scenarios whereby training examples are corrupted by additive Gaussian output noise and regularizers are introduced to improve the network performance. The dependence of the dynamics on the noise level, with and without regularizers, is examined, as well as that of the asymptotic values obtained for both training and generalization errors. We also demonstrate the ability of the method to approximate the learning dynamics in structurally unrealizable scenarios. The theoretical results show good agreement with those obtained by computer simulations.