Multifractality and percolation in the coupling space of perceptrons

The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated analytically using the replica formalism. The storage capacity and the generalization behaviour of the perceptron are shown to be related to properties of $f(\alpha)$ which are correctly described within the replica symmetric ansatz. Replica symmetry breaking is interpreted geometrically as a transition from percolating to non-percolating cells. The existence of empty cells gives rise to singularities in the multifractal spectrum. The analytical results for binary couplings are corroborated by numerical studies.Comment: 13 pages, revtex, 4 eps figures, version accepted for publication in Phys. Rev.

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

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

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

A Genomewide Overexpression Screen Identifies Genes Involved in the Phosphatidylinositol 3-Kinase Pathway in the Human Protozoan Parasite Entamoeba histolytica

Entamoeba histolytica is a protozoan parasite that causes amoebic dysentery and liver abscess. E. histolytica relies on motility, phagocytosis, host cell adhesion, and proteolysis of extracellular matrix for virulence. In eukaryotic cells, these processes are mediated in part by phosphatidylinositol 3-kinase (PI3K) signaling. Thus, PI3K may be critical for virulence. We utilized a functional genomics approach to identify genes whose products may operate in the PI3K pathway in E. histolytica. We treated a population of trophozoites that were overexpressing genes from a cDNA library with a near-lethal dose of the PI3K inhibitor wortmannin. This screen was based on the rationale that survivors would be overexpressing gene products that directly or indirectly function in the PI3K pathway. We sequenced the overexpressed genes in survivors and identified a cDNA encoding a Rap GTPase, a protein previously shown to participate in the PI3K pathway. This supports the validity of our approach. Genes encoding a coactosin-like protein, EhCoactosin, and a serine-rich E. histolytica protein (SREHP) were also identified. Cells overexpressing EhCoactosin or SREHP were also less sensitive to a second PI3K inhibitor, LY294002. This corroborates the link between these proteins and PI3K. Finally, a mutant cell line with an increased level of phosphatidylinositol (3,4,5)-triphosphate, the product of PI3K activity, exhibited increased expression of SREHP and EhCoactosin. This further supports the functional connection between these proteins and PI3K in E. histolytica. To our knowledge, this is the first forward-genetics screen adapted to reveal genes participating in a signal transduction pathway in this pathogen

The WASp-like protein Scar regulates macropinocytosis, phagocytosis and endosomal membrane flow in Dictyostelium

Scar, a member of the WASp protein family, was discovered in Dictyostelium discoideum during a genetic screen for second-site mutations that suppressed a developmental defect. Disruption of the scar gene reduced the levels of cellular F-actin by 50%. To investigate the role of Scar in endocytosis, phagocytosis and endocytic membrane trafficking, processes that depend on actin polymerization, we have analyzed a Dictyostelium cell line that is genetically null for Scar. Rates of fluid phase macropinocytosis and phagocytosis are significantly reduced in the scar- cell-line. In addition, exocytosis of fluid phase is delayed in these cells and movement of fluid phase from lysosomes to post-lysosomes is also delayed. Inhibition of actin polymerization with cytochalasin A resulted in similar phenotypes, suggesting that Scar-mediated polymerization of the actin cytoskeleton was important in the regulation of these processes. Supporting this conclusion, fluorescence microscopy revealed that some endo-lysosomes were ringed with F-actin in control cells but no F-actin was detected associated with endo-lysosomes in Scar null cells. Disruption of the two genes encoding the actin monomer sequestering protein profilin in wild-type cells causes defects in the rate of pinocytosis and fluid phase efflux. Consistent with a predicted physical interaction between Scar and profilin, disrupting the scar gene in the profilin null background results in greater decreases in the rate of fluid phase internalization and fluid phase release compared to either mutant alone. Taken together, these data support a model in which Scar and profilin functionally interact to regulate internalization of fluid and particles and later steps in the endosomal pathway, probably through regulation of actin cytoskeleton polymerization

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

Entamoeba histolytica Dmc1 Catalyzes Homologous DNA Pairing and Strand Exchange That Is Stimulated by Calcium and Hop2-Mnd1

Meiosis depends on homologous recombination (HR) in most sexually reproducing organisms. Efficient meiotic HR requires the activity of the meiosis-specific recombinase, Dmc1. Previous work shows Dmc1 is expressed in Entamoeba histolytica, a eukaryotic parasite responsible for amoebiasis throughout the world, suggesting this organism undergoes meiosis. Here, we demonstrate Dmc1 protein is expressed in E. histolytica. We show that purified ehDmc1 forms presynaptic filaments and catalyzes ATP-dependent homologous DNA pairing and DNA strand exchange over at least several thousand base pairs. The DNA pairing and strand exchange activities are enhanced by the presence of calcium and the meiosis-specific recombination accessory factor, Hop2-Mnd1. In combination, calcium and Hop2-Mnd1 dramatically increase the rate of DNA strand exchange activity of ehDmc1. The biochemical system described herein provides a basis on which to better understand the role of ehDmc1 and other HR proteins in E. histolytica

Stability of the Parisi Solution for the Sherrington-Kirkpatrick model near T=0

To test the stability of the Parisi solution near T=0, we study the spectrum of the Hessian of the Sherrington-Kirkpatrick model near T=0, whose eigenvalues are the masses of the bare propagators in the expansion around the mean-field solution. In the limit $T\ll 1$ two regions can be identified. In the first region, for $x$ close to 0, where $x$ is the Parisi replica symmetry breaking scheme parameter, the spectrum of the Hessian is not trivial and maintains the structure of the full replica symmetry breaking state found at higher temperatures. In the second region $T\ll x \leq 1$ as $T\to 0$, the components of the Hessian become insensitive to changes of the overlaps and the bands typical of the full replica symmetry breaking state collapse. In this region only two eigenvalues are found: a null one and a positive one, ensuring stability for $T\ll 1$. In the limit $T\to 0$ the width of the first region shrinks to zero and only the positive and null eigenvalues survive. As byproduct we enlighten the close analogy between the static Parisi replica symmetry breaking scheme and the multiple time-scales approach of dynamics, and compute the static susceptibility showing that it equals the static limit of the dynamic susceptibility computed via the modified fluctuation dissipation theorem.Comment: 24 pages, 6 figures, J. Phys. A (in press

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