Threshold-induced phase transitions in perceptrons

Error rates of a Boolean perceptron with threshold and either spherical or Ising constraint on the weight vector are calculated for storing patterns from biased input and output distributions derived within a one-step replica symmetry breaking (RSB) treatment. For unbiased output distribution and non-zero stability of the patterns, we find a critical load, α p, above which two solutions to the saddlepoint equations appear; one with higher free energy and zero threshold and a dominant solution with non-zero threshold. We examine this second-order phase transition and the dependence of α p on the required pattern stability, κ, for both one-step RSB and replica symmetry (RS) in the spherical case and for one-step RSB in the Ising case.

Interplay between the charge transport phenomena and the charge-transfer phase transition in RbxMn[Fe(CN)6]y.zH2O

Charge transport and dielectric measurements were carried out on compacted powder and single-crystal samples of bistable RbxMn[Fe(CN)6]y·zH2O in the two valence-tautomeric forms (MnIIFeIII and MnIIIFeII) as a function of temperature (120-350 K) and frequency (10-2-106 Hz). The complex conductivity data reveal universal conductivity behavior and obey the Barton-Nakajima-Namikawa relationship. The charge transport is accompanied by dielectric relaxation that displays the same thermal activation energy as the conductivity. Surprisingly, the activation energy of the conductivity was found very similar in the two valence-tautomeric forms (0.55 eV), and the conductivity change between the two phases is governed mainly by the variation of the preexponential factor in each sample. The phase transition is accompanied by a large thermal hysteresis of the conductivity and the dielectric constant. In the hysteresis region, however, a crossover occurs in the charge transport mechanism at T < 220 K from an Arrhenius-type to a varying activation energy behavior, conferring an unusual “double-loop” shape to the hysteresis.

Spectroscopic studies of field-induced electron emission from isolated microstructures

A detailed investigation has been undertaken into the field induced electron emission (FIEE) mechanism that occurs at microscopically localised `sites' on uncoated and dielectric coated metallic electrodes. These processes have been investigated using two dedicated experimental systems that were developed for this study. The first is a novel combined photo/field emission microscope, which employs a UV source to stimulate photo-electrons from the sample surface in order to generate a topographical image. This system utilises an electrostatic lens column to provide identical optical properties under the different operating conditions required for purely topographical and combined photo/field imaging. The system has been demonstrated to have a resolution approaching 1m. Emission images have been obtained from carbon emission sites using this system to reveal that emission may occur from the edge triple junction or from the bulk of the carbon particle. An existing UHV electron spectrometer has been extensively rebuilt to incorporate a computer control and data acquisition system, improved sample handling and manipulation and a specimen heating stage. Details are given of a comprehensive study into the effects of sample heating on the emission process under conditions of both bulk and transient heating. Similar studies were also performed under conditions of both zero and high applied field. These show that the properties of emission sites are strongly temperature and field dependent thus indicating that the emission process is `non-metallic' in nature. The results have been shown to be consistent with an existing hot electron emission model.

Unveiling temporal correlations characteristic of a phase transition in the output intensity of a fiber laser

We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fiber laser. Ordinal analysis and the horizontal visibility graph applied to the experimentally measured laser output intensity reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods unveil coherent structures with well-defined time scales and strong correlations both, in the timing of the laser pulses and in their peak intensities. Our approach is generic and may be used in other complex systems that undergo similar transitions involving the generation of extreme fluctuations.

Investigating optical complexity of the phase transition in the intensity of a fibre laser radiation

Fibre lasers have been shown to manifest a laminar-to-turbulent transition when increasing its pump power. In order to study the dynamical complexity of this transition we use advanced statistical tools of time-series analysis. We apply ordinal analysis and the horizontal visibility graph to the experimentally measured laser output intensity. This reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods allow us to unveil coherent structures with well defined time-scales and strong correlations both, in the timing of the laser pulses and in their peak intensities.

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.

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.

Dynamics of cholesteric liquid crystals in the presence of a random magnetic field:stochastic dynamics of cholesteric liquid crystal

Based on dynamic renormalization group techniques, this letter analyzes the effects of external stochastic perturbations on the dynamical properties of cholesteric liquid crystals, studied in presence of a random magnetic field. Our analysis quantifies the nature of the temperature dependence of the dynamics; the results also highlight a hitherto unexplored regime in cholesteric liquid crystal dynamics. We show that stochastic fluctuations drive the system to a second-ordered Kosterlitz-Thouless phase transition point, eventually leading to a Kardar-Parisi-Zhang (KPZ) universality class. The results go beyond quasi-first order mean-field theories, and provides the first theoretical understanding of a KPZ phase in distorted nematic liquid crystal dynamics.

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.

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.

Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

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.

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.