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.

Error-correcting code on a cactus:A solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica-symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.

Error-correcting codes on a Bethe-like lattice

We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.

Efficient Bayesian inference for learning in the Ising linear perceptron and signal detection in CDMA

Efficient new Bayesian inference technique is employed for studying critical properties of the Ising linear perceptron and for signal detection in code division multiple access (CDMA). The approach is based on a recently introduced message passing technique for densely connected systems. Here we study both critical and non-critical regimes. Results obtained in the non-critical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also studied. © 2006 Elsevier B.V. All rights reserved.

Mössbauer spectroscopic study of the thermal spin crossover in [Fe(II)(isoxazole)6](ClO4)2

The Fe Mössbauer spectroscopy of mononuclear [Fe(II)(isoxazole)](ClO) has been studied to reveal the thermal spin crossover of Fe(II) between low-spin (S = 0) and high-spin (S = 2) states. Temperaturedependent spin transition curves have been constructed with the least-square fitted data obtained from the Mössbauer spectra measured at various temperatures between 84 and 270 K during a cooling and heating cycle. This compound exhibits an unusual temperature-dependent spin transition behaviour with T(?) = 223 and T(?) = 213 K occurring in the reverse order in comparison to those observed in SQUID observation and many other spin transition compounds. The compound has three high-spin Fe(II) sites at the highest temperature of study of which two undergo spin transitions. The compound seems to undergo a structural phase transition around the spin transition temperature, which plays a significant role in the spin crossover behaviour as well as the magnetic properties of the compound at temperatures below T. The present study reveals an increase in high-spin fraction upon heating in the temperature range below T, and an explanation is provided.

Inference by replication in densely connected systems

An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica-symmetric- (RS)-like structure to include a more complex one-step replica-symmetry-breaking-like (1RSB-like) ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in code division multiple access (CDMA) under different noise models. Results obtained under the RS assumption in the noncritical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first-order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behavior, resulting in an improvement in performance. © 2007 The American Physical Society.

Dielectric and electro-optical properties of some cyanobiphenyl liquid-crystals

A variety of methods have been reviewed for obtaining parallel or perpendicular alignment in liquid-crystal cells. Some of these methods have been selected and developed and were used in polarised spectroscopy, dielectric and electro-optic studies. Also, novel dielectric and electro-optic cells were constructed for use over a range of temperature. Dielectric response of thin layers of E7 and E8 (eutectic mixture liquid-crystals) have been measured in the frequency range (12 Hz-100 kHz) and over a range of temperature (183-337K). Dielectric spectra were also obtained for supercooled E7 and E8 in the Hz and kHz range. When the measuring electric field was parallel to the nematic director, one loss peak (low-frequency relaxation process) was observed for E7 and for E8, that exhibits a Debye-type behaviour in the supercooled systems. When the measuring electric field was perpendicular to the nematic director, two resolved dielectric processes have been observed. The phase transitions, effective molecular polarisabilities, anisotropy of polarisabilities and order parameters of three liquid crystal homologs (5CB, 6CB, and 7CB), 60CB and three eutectic nematic mixtures E7, E8, and E607 were calculated using optical and density data measured at several temperatures. The order parameters calculated using the different methods of Vuks, Neugebauer, Saupe-Maier, and Palffy-Muhoray are nearly the same for the liquid crystals considered in the present study. Also, the interrelationship between density and refractive index and the molecular structure of these liquid crystals were established. Accurate dielectric and dipole results of a range of liquid-crystal forming molecules at several temperatures have reported. The role of the cyano-end group, biphenyl core, and flexible tail in molecular association, were investigated using the dielectric method for some molecules which have a structural relationship to the nematogens. Analysis of the dielectric data for solution of the liquid-crystals indicated a high molecular association, comparable to that observed in the nematic or isotropic phases. Electro-optic Kerr effect were investigated for some alkyl cyanobiphenyls, their nematic mixtures and the eutectic mixture liquid-crystals E7 and E8 in the isotropic phase and solution. The Kerr constant of these liquid crystals found to be very high at the nematic-isotropic transition temperatures as the molecules are expected to be highly ordered close to phase transition temperatures. Dynamic Kerr effect behaviour and transient molecular reorientation were also observed in thin layers of some alkyl cyanobiphenyls. Dichroic ratio R and order parameters of solutions containing some azo and anthraquinone dyes in the nematic solvent (E7 and E8), were investigated by the measurement of the intensity of the absorption bands in the visible region of parallel aligned samples. The effective factors on the dichroic ratio of the dyes dissolved in the nematic solvents were determined and discussed.

Statistical physics of error-correcting codes

In this thesis we use statistical physics techniques to study the typical performance of four families of error-correcting codes based on very sparse linear transformations: Sourlas codes, Gallager codes, MacKay-Neal codes and Kanter-Saad codes. We map the decoding problem onto an Ising spin system with many-spins interactions. We then employ the replica method to calculate averages over the quenched disorder represented by the code constructions, the arbitrary messages and the random noise vectors. We find, as the noise level increases, a phase transition between successful decoding and failure phases. This phase transition coincides with upper bounds derived in the information theory literature in most of the cases. We connect the practical decoding algorithm known as probability propagation with the task of finding local minima of the related Bethe free-energy. We show that the practical decoding thresholds correspond to noise levels where suboptimal minima of the free-energy emerge. Simulations of practical decoding scenarios using probability propagation agree with theoretical predictions of the replica symmetric theory. The typical performance predicted by the thermodynamic phase transitions is shown to be attainable in computation times that grow exponentially with the system size. We use the insights obtained to design a method to calculate the performance and optimise parameters of the high performance codes proposed by Kanter and Saad.

Statistical mechanics of distribution networks

This thesis presents an analysis of the stability of complex distribution networks. We present a stability analysis against cascading failures. We propose a spin [binary] model, based on concepts of statistical mechanics. We test macroscopic properties of distribution networks with respect to various topological structures and distributions of microparameters. The equilibrium properties of the systems are obtained in a statistical mechanics framework by application of the replica method. We demonstrate the validity of our approach by comparing it with Monte Carlo simulations. We analyse the network properties in terms of phase diagrams and found both qualitative and quantitative dependence of the network properties on the network structure and macroparameters. The structure of the phase diagrams points at the existence of phase transition and the presence of stable and metastable states in the system. We also present an analysis of robustness against overloading in the distribution networks. We propose a model that describes a distribution process in a network. The model incorporates the currents between any connected hubs in the network, local constraints in the form of Kirchoff's law and a global optimizational criterion. The flow of currents in the system is driven by the consumption. We study two principal types of model: infinite and finite link capacity. The key properties are the distributions of currents in the system. We again use a statistical mechanics framework to describe the currents in the system in terms of macroscopic parameters. In order to obtain observable properties we apply the replica method. We are able to assess the criticality of the level of demand with respect to the available resources and the architecture of the network. Furthermore, the parts of the system, where critical currents may emerge, can be identified. This, in turn, provides us with the characteristic description of the spread of the overloading in the systems.

Formulation and the characterisation of cationic liposomal adjuvants for the delivery of a promising subunit tuberculosis vaccine

Cationic liposomes of dimethyldioctadecylammonium bromide (DDA) incorporating the glycolipid trehalose 6,6-dibehenate (TDB) forms a promising liposomal vaccine adjuvant. To be exploited as effective subunit vaccine delivery systems, the physicochemical characteristics of liposomes were studied in detail and correlated with their effectiveness in vivo, in an attempt to elucidate key aspects controlling their efficacy. This research took the previously optimised DDA-TDB system as a foundation for a range of formulations incorporating additional lipids of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) or 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC), by incrementally replacing the cationic content within DDA-TDB or reducing the total DDA-TDB dose upon its substitution, to ascertain the role of DDA and the effect of DDA-TDB concentration in influencing the resultant immunological performance upon delivery of the novel subunit TB vaccine, Ag85B–ESAT-6-Rv2660c (H56 vaccine). With the aim of using the DPPC based systems for pulmonary vaccine delivery and the DSPC systems for application via the intramuscular route, initial work focused on physicochemical characterisation of the systems with incorporation of DPPC or DSPC displaying comparable physical stability, morphological structure and levels of antigen retention to that of DDA-TDB. Thermodynamic analysis was also conducted to detect main phase transition temperatures and subsequent in vitro cell culture studies demonstrated a favourable reduction in cytotoxicity, stimulation of phagocytic activity and macrophage activation in response to the proposed liposomal immunoadjuvants. Immunisation of mice with H56 vaccine via the proposed liposomal adjuvants showed that DDA was an important factor in mediating resultant immune responses, with partial replacement or substitution of DDA-TDB stimulating Th1 type cellular immunity characterised by elevated levels of IgG2b antibodies and IFN-? and IL-2 cytokines, essential for providing protective efficacy against TB. Upon increased DSPC content within the formulation, either by DDA replacement or reduction of DDA and TDB, responses were skewed towards Th2 type immunity with reduced IgG2b antibody levels and elevated IL-5 and IL-10 cytokine production, as resultant immunological responses were independent of liposomal zeta potential. The role of the cationic DDA lipid and the effect of DDA-TDB concentration were appreciated as the proposed liposomal formulations elicited antigen specific antibody and cellular immune responses, demonstrating the potential of cationic liposomes to be utilised as adjuvants for subunit vaccine delivery. Furthermore, the promising capability of the novel H56 vaccine candidate in eliciting protection against TB was apparent in a mouse model.

Palette-colouring: a belief propagation approach

We consider a variation of the prototype combinatorial optimization problem known as graph colouring. Our optimization goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximize the number of different colours present in the set of nearest neighbours of each given vertex. This problem, which we pictorially call palette-colouring, has been recently addressed as a basic example of a problem arising in the context of distributed data storage. Even though it has not been proved to be NP-complete, random search algorithms find the problem hard to solve. Heuristics based on a naive belief propagation algorithm are observed to work quite well in certain conditions. In this paper, we build upon the mentioned result, working out the correct belief propagation algorithm, which needs to take into account the many-body nature of the constraints present in this problem. This method improves the naive belief propagation approach at the cost of increased computational effort. We also investigate the emergence of a satisfiable-to-unsatisfiable 'phase transition' as a function of the vertex mean degree, for different ensembles of sparse random graphs in the large size ('thermodynamic') limit.

Fluctuation-induced traffic congestion in heterogeneous networks

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analyzing network failures caused by hardware faults or overload, where the network reaction was modeled as rerouting of traffic away from failed or congested elements. Here we model another type of the network reaction to congestion - a sharp reduction of the input traffic rate through congested routes which occurs on much shorter time scales. We consider the onset of congestion in the Internet where local mismatch between demand and capacity results in traffic losses and show that it can be described as a phase transition characterized by strong non-Gaussian loss fluctuations at a mesoscopic time scale. The fluctuations, caused by noise in input traffic, are exacerbated by the heterogeneous nature of the network manifested in a scale-free load distribution. They result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible. © Copyright EPLA, 2012.

Preparation and characterization of gas-filled liposomes:Can they improve oil recovery?

Although well known for delivering various pharmaceutical agents, liposomes can be prepared to entrap gas rather than aqueous media and have the potential to be used as pressure probes in magnetic resonance imaging (MRI). Using these gas-filled liposomes (GFL) as tracers, MRI imaging of pressure regions of a fluid flowing through a porous medium could be established. This knowledge can be exploited to enhance recovery of oil from the porous rock regions within oil fields. In the preliminary studies, we have optimized the lipid composition of GFL prepared using a simple homogenization technique and investigated key physico-chemical characteristics (size and the physical stability) and their efficacy as pressure probes. In contrast to the liposomes possessing an aqueous core which are prepared at temperatures above their phase transition temperature (Tc), homogenization of the phospholipids such as 1,2-dipalmitoyl-sn-glycero-3- phosphocholine (DPPC) or 1,2-distearoyl-sn-glycero-3-phosphocoline (DSPC) in aqueous medium below their Tc was found to be crucial in formation of stable GFL. DSPC based preparations yielded a GFL volume of more than five times compared to their DPPC counter part. Although the initial vesicle sizes of both DSPC and DPPC based GFL were about 10 μm, after 7 days storage at 25°C, the vesicle sizes of both formulations significantly (p < 0.05) increased to 28.3 ± 0.3 μm and 12.3 ± 1.0 μm, respectively. When the DPPC preparation was supplemented with cholesterol at a 1:0.5 or 1:1 molar ratio, significantly (p < 0.05) larger vesicles were formed (12-13 μm), however, compared to DPPC only vesicles, both cholesterol supplemented formulations displayed enhanced stability on storage indicating a stabilizing effect of cholesterol on these gas-filled vesicles. In order to induce surface charge on the GFL, DPPC and cholesterol (1: 0.5 molar ratio) liposomes were supplemented with a cationic surfactant, stearylamine, at a molar ratio of 0.25 or 0.125. Interestingly, the ζ potential values remained around neutrality at both stearylamine ratios suggesting the cationic surfactant was not incorporated within the bilayers of the GFL. Microscopic analysis of GFL confirmed the presence of spherical structures with a size distribution between 1-8 μm. This study has identified that DSPC based GFL in aqueous medium dispersed in 2% w/v methyl cellulose although yielded higher vesicle sizes over time were most stable under high pressures exerted in MRI. Copyright © Informa Healthcare USA, Inc.

A comparative study of cationic liposome and niosome-based adjuvant systems for protein subunit vaccines:characterisation, environmental scanning electron microscopy and immunisation studies in mice

Vesicular adjuvant systems composing dimethyldioctadecylammonium (DDA) can promote both cell-mediated and humoral immune responses to the tuberculosis vaccine fusion protein in mice. However, these DDA preparations were found to be physically unstable, forming aggregates under ambient storage conditions. Therefore there is a need to improve the stability of such systems without undermining their potent adjuvanticity. To this end, the effect of incorporating non-ionic surfactants, such as 1-monopalmitoyl glycerol (MP), in addition to cholesterol (Chol) and trehalose 6,6′-dibehenate (TDB), on the stability and efficacy of these vaccine delivery systems was investigated. Differential scanning calorimetry revealed a reduction in the phase transition temperature (T c) of DDA-based vesicles by ∼12°C when MP and cholesterol (1:1 molar ratio) were incorporated into the DDA system. Transmission electron microscopy (TEM) revealed the addition of MP to DDA vesicles resulted in the formation of multi-lamellar vesicles. Environmental scanning electron microscopy (ESEM) of MP-Chol-DDA-TDB (16:16:4:0.5 μmol) indicated that incorporation of antigen led to increased stability of the vesicles, perhaps as a result of the antigen embedding within the vesicle bilayers. At 4°C DDA liposomes showed significant vesicle aggregation after 28 days, although addition of MP-Chol or TDB was shown to inhibit this instability. Alternatively, at 25°C only the MP-based systems retained their original size. The presence of MP within the vesicle formulation was also shown to promote a sustained release of antigen in-vitro. The adjuvant activity of various systems was tested in mice against three subunit antigens, including mycobacterial fusion protein Ag85b-ESAT-6, and two malarial antigens (Merozoite surface protein 1, MSP1, and the glutamate rich protein, GLURP). The MP- and DDA-based systems induced antibody responses at comparable levels whereas the DDA-based systems induced more powerful cell-mediated immune responses. © 2006 The Authors.

Characterization of cationic liposomes based on dimethyldioctadecylammonium and synthetic cord factor from M. tuberculosis (trehalose 6,6′- dibehenate) - A novel adjuvant inducing both strong CMI and antibody responses:a novel adjuvant inducing both strong CMI and antibody responses

Incorporation of the glycolipid trehalose 6,6′-dibehenate (TDB) into cationic liposomes composed of the quaternary ammonium compound dimethyldioctadecylammonium (DDA) produce an adjuvant system which induces a powerful cell-mediated immune response and a strong antibody response, desirable for a high number of disease targets. We have used differential scanning calorimetry (DSC) to investigate the effect of TDB on the gel-fluid phase transition of DDA liposomes and to demonstrate that TDB is incorporated into DDA liposome bilayers. Transmission Electron Microscopy (TEM) and cryo-TEM confirmed that liposomes were formed when a lipid film of DDA containing small amounts of TDB was hydrated in an aqueous buffer solution at physiological pH. Furthermore, time development of particle size and zeta potential of DDA liposomes incorporating TDB during storage at 4°C and 25°C, indicates that TDB effectively stabilizes the DDA liposomes. Immunization of mice with the mycobacterial fusion protein Ag85B-ESAT-6 in DDA-TDB liposomes induced a strong, specific Th1 type immune response characterized by substantial production of the interferon-γ cytokine and high levels of IgG2b isotype antibodies. The lymphocyte subset releasing the interferon-γ was identified as CD4 T cells.