Large Deviations of the Free-Energy in Diluted Mean-Field Spin-Glass

Sample-to-sample free energy fluctuations in spin-glasses display a markedly different behaviour in finite-dimensional and fully-connected models, namely Gaussian vs. non-Gaussian. Spin-glass models defined on various types of random graphs are in an intermediate situation between these two classes of models and we investigate whether the nature of their free-energy fluctuations is Gaussian or not. It has been argued that Gaussian behaviour is present whenever the interactions are locally non-homogeneous, i.e. in most cases with the notable exception of models with fixed connectivity and random couplings $J_{ij}=\pm \tilde{J}$. We confirm these expectation by means of various analytical results. In particular we unveil the connection between the spatial fluctuations of the populations of populations of fields defined at different sites of the lattice and the Gaussian nature of the free-energy fluctuations. On the contrary on locally homogeneous lattices the populations do not fluctuate over the sites and as a consequence the small-deviations of the free energy are non-Gaussian and scales as in the Sherrington-Kirkpatrick model

Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model

In this work we analyse the Parisi's infinity-replica symmetry breaking solution of the Sherrington - Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from the numerical solution of the infinity-replica symmetry breaking equations which are solved using a new pseudo-spectral code which allows for very accurate results. With this methods we are able to get more insight into the analytical properties of the solutions. We are also able to determine numerically the end-point x_{max} of the plateau of q(x) and find that lim_{T --> 0} x_{max}(T) > 0.5.Comment: 15 pages, 11 figures, RevTeX 4.

Spin glass transition in a magnetic field: a renormalization group study

We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n to 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order epsilon = 6-d. In the general theory we find a stable fixed-point associated to the spin glass transition in zero field. This fixed-point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed-point to describe the AT transition, in agreement with previous results of other authors.Comment: 36 pages with 4 tables. To be published in Phys. Rev.

Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks

Random input patterns induce a partition of the coupling space of feed-forward neural networks into different cells according to the generated output sequence. For the perceptron this partition forms a random multifractal for which the spectrum $f(\alpha)$ can be calculated analytically using the replica trick. Phase transition in the multifractal spectrum correspond to the crossover from percolating to non-percolating cell sizes. Instabilities of negative moments are related to the VC-dimension.Comment: 10 pages, Latex, submitted to PR

On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance

The frequency-dependent scaling of the dispersive and dissipative parts of the alternating susceptibility is studied for spin glasses at criticality. An extension of the usual $\omega t$-scaling is proposed. Simulational data from the three-dimensional Ising spin glass agree with this new scaling form and moreover reproduce well the scaling functions explicitly calculated for systems satisfying local scale-invariance. There is also a qualitative agreement with existing experimental data.Comment: 19 pages, 2 figures, to appear in special issue of J. Phys. Cond. Matt. dedicated to Lothar Schaefer on the occasion of his 60th birthday, final form with IOP macro

The Phase Diagram of an Anisotropic Potts Model

A study is made of an anisotropic Potts model in three dimensions where the coupling depends on both the Potts state on each site but also the direction of the bond between them using both analytical and numerical methods. The phase diagram is mapped out for all values of the exchange interactions. Six distinct phases are identified. Monte Carlo simulations have been used to obtain the order parameter and the values for the energy and entropy in the ground state and also the transition temperatures. Excellent agreement is found between the simulated and analytic results. We find one region where there are two phase transitions with the lines meeting in a triple point. The orbital ordering that occurs in $LaMnO_3$ occurs as one of the ordered phases.Comment: 30 pages, 19 figures, one tabl

Static chaos and scaling behaviour in the spin-glass phase

We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field and their free energy cost is determined by the finite-temperature fixed point exponents. In this framework, numerical results suggest that mean-field chaos exponents are probably exact in finite dimensions. If we use the droplet approach, numerical results suggest that the zero-temperature fixed point exponent $\theta$ is very close to $\frac{d-3}{2}$. In both approaches $d=3$ is the lower critical dimension in agreement with recent numerical simulations.Comment: 28 pages + 6 figures, LateX, figures uuencoded at the end of fil

Field Theory of Fluctuations in Glasses

We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium arguments we eliminate time from the description and we completely characterize fluctuations in the beta regime. We identify different sources of fluctuations and show that the most relevant ones are associated to variations of "self-induced disorder" in the initial condition of the dynamics. It follows that heterogeneites can be describes through a cubic field theory with an effective random field term. The phenomenon of perturbative dimensional reduction ensues, well known in random field problems, which implies an upper critical dimension of the theory equal to 8. We apply our theory to finite size scaling for mean-field systems and we test its prediction against numerical simulations

Functional Characterization of the Plasmodium falciparum Chloroquine-Resistance Transporter (PfCRT) in Transformed Dictyostelium discoideum Vesicles

Chloroquine (CQ)-resistant Plasmodium falciparum malaria has been a global health catastrophe, yet much about the CQ resistance (CQR) mechanism remains unclear. Hallmarks of the CQR phenotype include reduced accumulation of protonated CQ as a weak base in the digestive vacuole of the erythrocyte-stage parasite, and chemosensitization of CQ-resistant (but not CQ-sensitive) P. falciparum by agents such as verapamil. Mutations in the P. falciparum CQR transporter (PfCRT) confer CQR; particularly important among these mutations is the charge-loss substitution K→T at position 76. Dictyostelium discoideum transformed with mutant PfCRT expresses key features of CQR including reduced drug accumulation and verapamil chemosensitization.We describe the isolation and characterization of PfCRT-transformed, hematin-free vesicles from D. discoideum cells. These vesicles permit assessments of drug accumulation, pH, and membrane potential that are difficult or impossible with hematin-containing digestive vacuoles from P. falciparum-infected erythrocytes. Mutant PfCRT-transformed D. discoideum vesicles show features of the CQR phenotype, and manipulations of vesicle membrane potential by agents including ionophores produce large changes of CQ accumulation that are dissociated from vesicular pH. PfCRT in its native or mutant form blunts the ability of valinomycin to reduce CQ accumulation in transformed vesicles and decreases the ability of K(+) to reverse membrane potential hyperpolarization caused by valinomycin treatment.Isolated vesicles from mutant-PfCRT-transformed D. discoideum exhibit features of the CQR phenotype, consistent with evidence that the drug resistance mechanism operates at the P. falciparum digestive vacuole membrane in malaria. Membrane potential apart from pH has a major effect on the PfCRT-mediated CQR phenotype of D. discoideum vesicles. These results support a model of PfCRT as an electrochemical potential-driven transporter in the drug/metabolite superfamily that (appropriately mutated) acts as a saturable simple carrier for the facilitated diffusion of protonated CQ

Influence of socioeconomic factors on pregnancy outcome in women with structural heart disease

OBJECTIVE: Cardiac disease is the leading cause of indirect maternal mortality. The aim of this study was to analyse to what extent socioeconomic factors influence the outcome of pregnancy in women with heart disease.  METHODS: The Registry of Pregnancy and Cardiac disease is a global prospective registry. For this analysis, countries that enrolled ≥10 patients were included. A combined cardiac endpoint included maternal cardiac death, arrhythmia requiring treatment, heart failure, thromboembolic event, aortic dissection, endocarditis, acute coronary syndrome, hospitalisation for cardiac reason or intervention. Associations between patient characteristics, country characteristics (income inequality expressed as Gini coefficient, health expenditure, schooling, gross domestic product, birth rate and hospital beds) and cardiac endpoints were checked in a three-level model (patient-centre-country).  RESULTS: A total of 30 countries enrolled 2924 patients from 89 centres. At least one endpoint occurred in 645 women (22.1%). Maternal age, New York Heart Association classification and modified WHO risk classification were associated with the combined endpoint and explained 37% of variance in outcome. Gini coefficient and country-specific birth rate explained an additional 4%. There were large differences between the individual countries, but the need for multilevel modelling to account for these differences disappeared after adjustment for patient characteristics, Gini and country-specific birth rate.  CONCLUSION: While there are definite interregional differences in pregnancy outcome in women with cardiac disease, these differences seem to be mainly driven by individual patient characteristics. Adjustment for country characteristics refined the results to a limited extent, but maternal condition seems to be the main determinant of outcome