Stability of the Mezard-Parisi solution for random manifolds

The eigenvalues of the Hessian associated with random manifolds are constructed for the general case of $R$ steps of replica symmetry breaking. For the Parisi limit $R\to\infty$ (continuum replica symmetry breaking) which is relevant for the manifold dimension $D<2$, they are shown to be non negative.Comment: LaTeX, 15 page

Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices $M^{\alpha \beta ; \gamma \delta}$, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work.Comment: Latex file, 14 page

Exposure to Host Ligands Correlates with Colocalization of Gal/GalNAc Lectin Subunits in Lipid Rafts and Phosphatidylinositol (4,5)-Bisphosphate Signaling in Entamoeba histolytica

Entamoeba histolytica is an intestinal parasite that causes dysentery and liver abscess. Parasite cell surface receptors, such as the Gal/GalNAc lectin, facilitate attachment to host cells and extracellular matrix. The Gal/GalNAc lectin binds to galactose or N-acetylgalactosamine residues on host components and is composed of heavy (Hgl), intermediate (Igl), and light (Lgl) subunits. Although Igl is constitutively localized to lipid rafts (cholesterol-rich membrane domains), Hgl and Lgl transiently associate with this compartment in a cholesterol-dependent fashion. In this study, trophozoites were exposed to biologically relevant ligands to determine if ligand binding influences the submembrane distribution of the subunits. Exposure to human red blood cells (hRBCs) or collagen, which are bona fide Gal/GalNAc lectin ligands, was correlated with enrichment of Hgl and Lgl in rafts. This enrichment was abrogated in the presence of galactose, suggesting that direct lectin-ligand interactions are necessary to influence subunit location. Using a cell line that is able to attach to, but not phagocytose, hRBCs, it was shown that physical attachment to ligands was not sufficient to induce the enrichment of lectin subunits in rafts. Additionally, the mutant had lower levels of phosphatidylinositol (4,5)-bisphosphate (PIP2); PIP2 loading restored the ability of this mutant to respond to ligands with enrichment of subunits in rafts. Finally, intracellular calcium levels increased upon attachment to collagen; this increase was essential for the enrichment of lectin subunits in rafts. Together, these data provide evidence that ligand-induced enrichment of lectin subunits in rafts may be the first step in a signaling pathway that involves both PIP2 and calcium signaling

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

Involvement of the vacuolar proton-translocating ATPase in multiple steps of the endo-lysosomal system and in the contractile vacuole system of Dictyostelium discoideum

We have investigated the effects of Concanamycin A (CMA), a specific inhibitor of vacuolar type H(+)-ATPases, on acidification and function of the endo-lysosomal and contractile vacuole (CV) systems of D. discoideum. This drug inhibited acidification and increased the pH of endo-lysosomal vesicles both in vivo and in vitro in a dose dependent manner. Treatment also inhibited endocytosis and exocytosis of fluid phase, and phagocytosis of latex beads. This report also confirms our previous conclusions (Cardelli et al. (1989) J. Biol. Chem. 264, 3454–3463) that maintenance of acidic pH in lumenal compartments is required for efficient processing and targeting of a lysosomal enzyme, alpha-mannosidase. CMA treatment compromised the function of the contractile vacuole complex as amoebae exposed to a hypo-osmotic environment in the presence of CMA, swelled rapidly and ruptured. Fluorescence microscopy revealed that CMA treatment induced gross morphological changes in D. discoideum cells, characterized by the formation of large intracellular vacuoles containing fluid phase. The reticular membranes of the CV system were also no longer as apparent in drug treated cells. Finally, this is the first report describing cells that can adapt in the presence of CMA; in nutrient medium, D. discoideum overcame the effects of CMA after one hour of drug treatment even in the absence of protein synthesis. Upon adaptation to CMA, normal sized endo-lysosomal vesicles reappeared, endo-lysosomal pH decreased, and the rate of endocytosis, exocytosis and phagocytosis returned to normal. This study demonstrates that the V-H(+)-ATPase plays an important role in maintaining the integrity and function of the endo-lysosomal and CV systems and that D. discoideum can compensate for the loss of a functional V-H(+)-ATPase

On infrared divergences in spin glasses

By studying the structure of infrared divergences in a toy propagator in the replica approach to the Ising spin glass below $T_c$, we suggest a possible cancellation mechanism which could decrease the degree of singularity in the loop expansion.Comment: 13 pages, Latex , revised versio

Examination of the endosomal and lysosomal pathways in Dictyostelium discoideum myosin I mutants

The role of myosin Is in endosomal trafficking and the lysosomal system was investigated in a Dictyostelium discoideum myosin I double mutant myoB-/C-, that has been previously shown to exhibit defects in fluid-phase endocytosis during growth in suspension culture (Novak et al., 1995). Various properties of the endosomal pathway in the myoB-/C- double mutant as well as in the myoB- and myoC- single mutants, including intravesicular pH, and intracellular retention time and exocytosis of a fluid phase marker, were found to be indistinguishable from wild-type parental cells. The intimate connection between the contractile vacuole complex and the endocytic pathway in Dictyostelium, and the localization of a myosin I to the contractile vacuole in Acanthamoeba, led us to also examine the structure and function of this organelle in the three myosin I mutants. No alteration in contractile vacuole structure or function was observed in the myoB-, myoC- or myoB-/C- cell lines. The transport, processing, and localization of a lysosomal enzyme, alpha-mannosidase, were also unaltered in all three mutants. However, the myoB- and myoB-/C- cell lines, but not the myoC- cell line, were found to oversecrete the lysosomal enzymes alpha-mannosidase and acid phosphatase, during growth and starvation. None of the mutants oversecreted proteins following the constitutive secretory pathway. Two additional myosin I mutants, myoA- and myoA-/B-, were also found to oversecrete the lysosomally localized enzymes alpha-mannosidase and acid phosphatase. Taken together, these results suggest that these myosins do not play a role in the intracellular movement of vesicles, but that they may participate in controlling events that occur at the actin-rich cortical region of the cell. While no direct evidence has been found for the association of myosin Is with lysosomes, we predict that the integrity of the lysosomal system is tied to the fidelity of the actin cortex, and changes in cortical organization could influence lysosomal-related membrane events such as internalization or transit of vesicles to the cell surface

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.

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.

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