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.

Bulk and surface switching in Mn-Fe-based Prussian blue analogues

Many Prussian Blue Analogues are known to show a thermally induced phase transition close to room temperature and a reversible, photo-induced phase transition at low temperatures. This work reports on magnetic measurements, X-ray photoemission and Raman spectroscopy on a particular class of these molecular heterobimetallic systems, specifically on Rb0.81Mn[Fe(CN)6]0.95_1.24H2O, Rb0.97Mn[Fe(CN)6]0.98_1.03H2O and Rb0.70Cu0.22Mn0.78[Fe(CN)6]0.86_2.05H2O, to investigate these transition phenomena both in the bulk of the material and at the sample surface. Results indicate a high degree of charge transfer in the bulk, while a substantially reduced conversion is found at the sample surface, even in case of a near perfect (Rb:Mn:Fe=1:1:1) stoichiometry. Thus, the intrinsic incompleteness of the charge transfer transition in these materials is found to be primarily due to surface reconstruction. Substitution of a large fraction of charge transfer active Mn ions by charge transfer inactive Cu ions leads to a proportional conversion reduction with respect to the maximum conversion that is still stoichiometrically possible and shows the charge transfer capability of metal centers to be quite robust upon inclusion of a neighboring impurity. Additionally, a 532 nm photo-induced metastable state, reminiscent of the high temperature Fe(III)Mn(II) ground state, is found at temperatures 50-100 K. The efficiency of photo-excitation to the metastable state is found to be maximized around 90 K. The photo-induced state is observed to relax to the low temperature Fe(II)Mn(III) ground state at a temperature of approximately 123 K.

Interacting nonequilibrium systems with two temperatures

We investigate a simplified model of two fully connected magnetic systems maintained at different temperatures by virtue of being connected to two independent thermal baths while simultaneously being interconnected with each other. Using generating functional analysis, commonly used in statistical mechanics, we find exactly soluble expressions for their individual magnetization that define a two-dimensional nonlinear map, the equations of which have the same form as those obtained for densely connected equilibrium systems. Steady states correspond to the fixed points of this map, separating the parameter space into a rich set of nonequilibrium phases that we analyze in asymptotically high and low (nonequilibrium) temperature limits. The theoretical formalism is shown to revert to the classical nonequilibrium steady state problem for two interacting systems with a nonzero heat transfer between them that catalyzes a phase transition between ambient nonequilibrium states. © 2013 American Physical Society.

Self-sustained clusters and ergodicity breaking in spin models

Self-sustained spin clusters are analytically linked to ergodicity breaking in fully connected Ising and Sherrington-Kirkpatick (SK) models, relating the less understood spin space to the well understood state space. This correspondence is established through the absence of clusters in the paramagnetic phase, the presence of one dominant cluster in the Ising ferromagnet, and the formation of nontrivial clusters in SK spin glass. Yet unobserved phenomena are also revealed such as a first order phase transition in cluster sizes in the SK ferromagnet. The method could be adapted to investigate other spin models. © 2013 American Physical Society.

Effect of incorporating cholesterol into DDA:TDB liposomal adjuvants on Bilayer properties, biodistribution, and immune responses

Cholesterol is an abundant component of mammalian cell membranes and has been extensively studied as an artificial membrane stabilizer in a wide range of phospholipid liposome systems. In this study, the aim was to investigate the role of cholesterol in cationic liposomal adjuvant system based on dimethyldioctadecylammonium (DDA) and trehalose 6,6'-dibehenate (TDB) which has been shown as a strong adjuvant system for vaccines against a wide range of diseases. Packaging of cholesterol within DDA:TDB liposomes was investigated using differential scanning calorimetery and surface pressure-area isotherms of lipid monolayers; incorporation of cholesterol into liposomal membranes promoted the formation of a liquid-condensed monolayer and removed the main phase transition temperature of the system, resulting in an increased bilayer fluidity and reduced antigen retention in vitro. In vivo biodistribution studies found that this increase in membrane fluidity did not alter deposition of liposomes and antigen at the site of injection. In terms of immune responses, early (12 days after immunization) IgG responses were reduced by inclusion of cholesterol; thereafter there were no differences in antibody (IgG, IgG1, IgG2b) responses promoted by DDA:TDB liposomes with and without cholesterol. However, significantly higher levels of IFN-gamma were induced by DDA:TDB liposomes, and liposome uptake by macrophages in vitro was also shown to be higher for DDA:TDB liposomes compared to their cholesterol-containing counterparts, suggesting that small changes in bilayer mechanics can impact both cellular interactions and immune responses. © 2013 American Chemical Society.

Anomalies in stiffness and damping of a 2D discrete viscoelastic system due to negative stiffness components

The recent development of using negative stiffness inclusions to achieve extreme overall stiffness and mechanical damping of composite materials reveals a new avenue for constructing high performance materials. One of the negative stiffness sources can be obtained from phase transforming materials in the vicinity of their phase transition, as suggested by the Landau theory. To understand the underlying mechanism from a microscopic viewpoint, we theoretically analyze a 2D, nested triangular lattice cell with pre-chosen elements containing negative stiffness to demonstrate anomalies in overall stiffness and damping. Combining with current knowledge from continuum models, based on the composite theory, such as the Voigt, Reuss, and Hashin-Shtrikman model, we further explore the stability of the system with Lyapunov's indirect stability theorem. The evolution of the microstructure in terms of the discrete system is discussed. A potential application of the results presented here is to develop special thin films with unusual in-plane mechanical properties. © 2006 Elsevier B.V. All rights reserved.

One- and two-step spin-crossover behavior of [Fe(II)(isoxazole)6]2+ and the structure and magnetic properties of triangular [Fe(III)3O(OAc)6(isoxazole)3][ClO4)]

The structure and spin-crossover magnetic behavior of [FeII16][BF4]2 (1 = isoxazole) and [FeII16][ClO4]2 have been studied. [FeII16][BF4]2 undergoes two reversible spin-crossover transitions at 91 and 192 K, and is the first two-step spin transition to undergo a simultaneous crystallographic phase transition, but does not exhibit thermal hysteresis. The single-crystal structure determinations at 260 [space group P3̄, a = 17.4387(4) Å, c = 7.6847(2) Å] and at 130 K [space group P1̄, a = 17.0901(2) Å, b = 16.7481(2) Å, c = 7.5413(1) Å, α = 90.5309(6)°, β = 91.5231(6)°, γ = 117.8195(8)°] reveal two different iron sites, Fe1 and Fe2, in a 1:2 ratio. The room-temperature magnetic moment of 5.0 μB is consistent with high-spin Fe(II). A plateau in μ(T) having a moment of 3.3 μB centered at 130 K suggests a mixed spin system of some high-spin and some low-spin Fe(II) molecules. On the basis of the Fe−N bond distances at the two temperatures, and the molar fraction of high-spin molecules at the transition plateau, Fe1 and Fe2 can be assigned to the 91 and 192 K transitions, respectively. [FeII16][ClO4]2 [space group P3̄, a = 17.5829(3) Å, c = 7.8043(2) Å, β = 109.820 (3)°, T = 295 K] also possesses Fe1:Fe2 in a 1:2 ratio, and magnetic measurements show a single spin transition at 213 K, indicating that both Fe1 and Fe2 undergo a simultaneous spin transition. [FeII16][ClO4]2 slowly decomposes in solutions containing acetic anhydride to form [FeIII3O(OAc)613][ClO4] [space group I2, a = 10.1547(7) Å, b = 16.5497(11) Å, c = 10.3205(9) Å, β = 109.820 (3)°, T = 200 K]. The isosceles Fe3 unit contains two Fe···Fe distances of 3.2844(1) Å and a third Fe···Fe distance of 3.2857(1) Å. The magnetic data can be fit to a trinuclear model with ℋ = −2J(S1·S2 + S2·S3) − 2J13(S1·S3), where J = −27.1 and J13 = −32.5 cm-1.

Effect of incorporating cholesterol into DDA:TDB liposomal adjuvants on Bilayer properties, biodistribution, and immune responses

Cholesterol is an abundant component of mammalian cell membranes and has been extensively studied as an artificial membrane stabilizer in a wide range of phospholipid liposome systems. In this study, the aim was to investigate the role of cholesterol in cationic liposomal adjuvant system based on dimethyldioctadecylammonium (DDA) and trehalose 6,6'-dibehenate (TDB) which has been shown as a strong adjuvant system for vaccines against a wide range of diseases. Packaging of cholesterol within DDA:TDB liposomes was investigated using differential scanning calorimetery and surface pressure-area isotherms of lipid monolayers; incorporation of cholesterol into liposomal membranes promoted the formation of a liquid-condensed monolayer and removed the main phase transition temperature of the system, resulting in an increased bilayer fluidity and reduced antigen retention in vitro. In vivo biodistribution studies found that this increase in membrane fluidity did not alter deposition of liposomes and antigen at the site of injection. In terms of immune responses, early (12 days after immunization) IgG responses were reduced by inclusion of cholesterol; thereafter there were no differences in antibody (IgG, IgG1, IgG2b) responses promoted by DDA:TDB liposomes with and without cholesterol. However, significantly higher levels of IFN-gamma were induced by DDA:TDB liposomes, and liposome uptake by macrophages in vitro was also shown to be higher for DDA:TDB liposomes compared to their cholesterol-containing counterparts, suggesting that small changes in bilayer mechanics can impact both cellular interactions and immune responses. © 2013 American Chemical Society.