Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics

This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Z^n which are discrete analogs of the Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of so-called pseudodifference operators (i.e., pseudodifferential operators on the group Z^n) with analytic symbols and on the limit operators method. We obtain a description of the location of the essential spectra and estimates of the eigenfunctions of the discrete spectra of the main lattice operators of quantum mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on Z^3, and square root Klein-Gordon operators on Z^n

“Galectin-1 Induces Central and Peripheral Cell Death: Implications in T-Cell Physiopathology”

The immune system has a remarkable capacity to maintain a state of equilibrium even as it responds to a diverse array of foreign proteins and despite its contact exposure to self-antigens. Apoptosis is one of the mechanisms aimed at preserving the homeostasis after the completion of an immune response, thus returning the immune system to a basal state and warranting the elimination of autoagressive cells in both central and peripheral lymphoid organs. Targeted deletions in critical genes involved in the apoptotic death machinery together with natural spontaneous mutations have clearly shown the importance of apoptosis in the regulation of the immune response. This complex scenario of stimulatory and inhibitory genes has been enriched with the finding that galectin-1, a 14.5 kDa β-galactoside-binding protein, is able to induce apoptosis of immature cortical thymocytes and mature T cells by cross-linking cell surface glycoconjugates. Galectin-1 is present not only in central and peripheral lymphoid organs, but also at sites of immune privilege. In the present article we will discuss the implications of galectin-1-induced apoptosis in T-cell physiopathology in an attempt to validate its therapeutic potential in autoimmune and inflammatory diseases

Dynamical Encoding by Networks of Competing Neuron Groups: Winnerless Competition

Following studies of olfactory processing in insects and fish, we investigate neural networks whose dynamics in phase space is represented by orbits near the heteroclinic connections between saddle regions (fixed points or limit cycles). These networks encode input information as trajectories along the heteroclinic connections. If there are N neurons in the network, the capacity is approximately e(N-1)!, i.e., much larger than that of most traditional network structures. We show that a small winnerless competition network composed of FitzHugh-Nagumo spiking neurons efficiently transforms input information into a spatiotemporal output

Regulation of eosinophilia and allergic airway inflammation by the glycan-binding protein galectin-1

Galectin-1 (Gal-1), a glycan-binding protein with broad antiinflammatory activities, functions as a proresolving mediator in autoimmune and chronic inflammatory disorders. However, its role in allergic airway inflammation has not yet been elucidated. We evaluated the effects of Gal-1 on eosinophil function and its role in a mouse model of allergic asthma. Allergen exposure resulted in airway recruitment of Gal-1-expressing inflammatory cells, including eosinophils, as well as increased Gal-1 in extracellular spaces in the lungs. In vitro, extracellular Gal-1 exerted divergent effects on eosinophils that were N-glycan- And dose-dependent. At concentrations ≤0.25 μM, Gal-1 increased eosinophil adhesion to vascular cell adhesion molecule-1, caused redistribution of integrin CD49d to the periphery and cell clustering, but inhibited ERK(1/2) activation and eotaxin-1-induced migration. Exposure to concentrations ≥1 μM resulted in ERK(1/2)- dependent apoptosis and disruption of the F- Actin cytoskeleton. At lower concentrations, Gal-1 did not alter expression of adhesion molecules (CD49d, CD18, CD11a, CD11b, L-selectin) or of the chemokine receptor CCR3, but decreased CD49d and CCR3 was observed in eosinophils treated with higher concentrations of this lectin. In vivo, allergen-challenged Gal-1-deficient mice exhibited increased recruitment of eosinophils and CD3+ T lymphocytes in the airways as well as elevated peripheral blood and bone marrow eosinophils relative to corresponding WT mice. Further, these mice had an increased propensity to develop airway hyperresponsiveness and displayed significantly elevated levels of TNF-α in lung tissue. This study suggests that Gal-1 can limit eosinophil recruitment to allergic airways and suppresses airway inflammation by inhibiting cell migration and promoting eosinophil apoptosis.Fil: Ge, Xiao Na. University of Minnesota; Estados UnidosFil: Ha, Sung Gil. University of Minnesota; Estados UnidosFil: Greenberg, Yana G.. University of Minnesota; Estados UnidosFil: Rao, Amrita. University of Minnesota; Estados UnidosFil: Bastan, Idil. University of Minnesota; Estados UnidosFil: Blidner, Ada Gabriela. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Rao, Savita P.. University of Minnesota; Estados UnidosFil: Rabinovich, Gabriel Adrián. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Biología y Medicina Experimental. Fundación de Instituto de Biología y Medicina Experimental. Instituto de Biología y Medicina Experimental; ArgentinaFil: Sriramarao, P.. University of Minnesota; Estados Unido

Nonlinear properties of left-handed metamaterials

We analyze nonlinear properties of microstructured materials with negative refraction, the so-called left-handed metamaterials. We consider a two-dimensional periodic structure created by arrays of wires and split-ring resonators embedded into a nonlinear dielectric, and calculate the effective nonlinear electric permittivity and magnetic permeability. We demonstrate that the hysteresis-type dependence of the magnetic permeability on the field intensity allows changing the material from left- to right-handed and back. These effects can be treated as the second-order phase transitions in the transmission properties induced by the variation of an external field.Comment: 4 pages, 3 figure

Cyclic Statistics In Three Dimensions

While 2-dimensional quantum systems are known to exhibit non-permutation, braid group statistics, it is widely expected that quantum statistics in 3-dimensions is solely determined by representations of the permutation group. This expectation is false for certain 3-dimensional systems, as was shown by the authors of ref. [1,2,3]. In this work we demonstrate the existence of ``cyclic'', or $Z_n$, {\it non-permutation group} statistics for a system of n > 2 identical, unknotted rings embedded in $R^3$. We make crucial use of a theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch relations for the automorphisms of the free product group on n elements.Comment: 13 pages, 1 figure, LaTex, minor page reformattin

Essential spectra of difference operators on \sZ^n-periodic graphs

Let (\cX, \rho) be a discrete metric space. We suppose that the group \sZ^n acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a \sZ^n-periodic discrete metric space. We examine the Fredholm property and essential spectra of band-dominated operators on $l^p(X)$ where $X$ is a \sZ^n-periodic discrete metric space. Our approach is based on the theory of band-dominated operators on \sZ^n and their limit operators. In case $X$ is the set of vertices of a combinatorial graph, the graph structure defines a Schr\"{o}dinger operator on $l^p(X)$ in a natural way. We illustrate our approach by determining the essential spectra of Schr\"{o}dinger operators with slowly oscillating potential both on zig-zag and on hexagonal graphs, the latter being related to nano-structures

Sound and complete axiomatizations of coalgebraic language equivalence

Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are sound and complete with respect to behavioral equivalence can be extended to a coarser coalgebraic language equivalence, which arises from a generalised powerset construction that determinises coalgebras. We show that soundness and completeness are established by proving that expressions modulo axioms of a calculus form the rational fixpoint of the given type functor. Our main result is that the rational fixpoint of the functor $FT$, where $T$ is a monad describing the branching of the systems (e.g. non-determinism, weights, probability etc.), has as a quotient the rational fixpoint of the "determinised" type functor $\bar F$, a lifting of $F$ to the category of $T$-algebras. We apply our framework to the concrete example of weighted automata, for which we present a new sound and complete calculus for weighted language equivalence. As a special case, we obtain non-deterministic automata, where we recover Rabinovich's sound and complete calculus for language equivalence.Comment: Corrected version of published journal articl

Neuronal synchrony: peculiarity and generality

Synchronization in neuronal systems is a new and intriguing application of dynamical systems theory. Why are neuronal systems different as a subject for synchronization? (1) Neurons in themselves are multidimensional nonlinear systems that are able to exhibit a wide variety of different activity patterns. Their “dynamical repertoire” includes regular or chaotic spiking, regular or chaotic bursting, multistability, and complex transient regimes. (2) Usually, neuronal oscillations are the result of the cooperative activity of many synaptically connected neurons (a neuronal circuit). Thus, it is necessary to consider synchronization between different neuronal circuits as well. (3) The synapses that implement the coupling between neurons are also dynamical elements and their intrinsic dynamics influences the process of synchronization or entrainment significantly. In this review we will focus on four new problems: (i) the synchronization in minimal neuronal networks with plastic synapses (synchronization with activity dependent coupling), (ii) synchronization of bursts that are generated by a group of nonsymmetrically coupled inhibitory neurons (heteroclinic synchronization), (iii) the coordination of activities of two coupled neuronal networks (partial synchronization of small composite structures), and (iv) coarse grained synchronization in larger systems (synchronization on a mesoscopic scale