THE EFFECT OF CORTICO-THALAMIC CONNECTIONS ON THE DIVERSITY OF CORTICAL ACTIVATIONS AS MODELED BY THE ISING MODEL

The influence of the thalamus on the diversity of cortical activations is investigated in terms of the Ising model with respect to progressive levels of cortico-thalamic connectivity. The results show that better diversity is achieved at lower modulation levels, being higher than those obtained with counterpart network models.

Density-Profile Processes Describing Biological Signaling Networks: Almost Sure Convergence to Deterministic Trajectories

We introduce jump processes in R(k), called density-profile processes, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with k types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present a simple example of spin-flip stochastic model, associated to a synthetic biology model known as repressilator, which leads to a dynamical system with Hopf and pitchfork bifurcations. Depending on the parameter values, the magnetization random path can either converge to a unique stable fixed point, converge to one of a pair of stable fixed points, or asymptotically evolve close to a deterministic orbit in Rk. We also discuss a simple signaling pathway related to cancer research, called p53 module.

On the motion under focal attraction in a rotating medium

New results are established here on the phase portraits and bifurcations of the kinematic model in system (1), first presented by H.K. Wilson in [3], and by him attributed to L. Markus (unpublished). A new, self-sufficient, study which extends that of [3] and allows an essential conclusion for the applicability of the model is reported here.

EQUIVARIANT PATH FIELDS ON TOPOLOGICAL MANIFOLDS

A classical theorem of H. Hopf asserts that a closed connected smooth manifold admits a nowhere vanishing vector field if and only if its Euler characteristic is zero. R. Brown generalized Hopf`s result to topological manifolds, replacing vector fields with path fields. In this note, we give an equivariant analog of Brown`s theorem for locally smooth G-manifolds where G is a finite group.

Genericity of Nondegenerate Critical Points and Morse Geodesic Functionals

We consider a family of variational problems on a Hilbert manifold parameterized by an open subset of a Banach manifold, and we discuss the genericity of the nondegeneracy condition for the critical points. Using classical techniques, we prove an abstract genericity result that employs the infinite dimensional Sard-Smale theorem, along the lines of an analogous result of B. White [29]. Applications are given by proving the genericity of metrics without degenerate geodesics between fixed endpoints in general (non compact) semi-Riemannian manifolds, in orthogonally split semi-Riemannian manifolds and in globally hyperbolic Lorentzian manifolds. We discuss the genericity property also in stationary Lorentzian manifolds.

ENERGY OF GLOBAL FRAMES

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics.

Finite-dimensional non-associative algebras and codimension growth

Let A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded. Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One of the main tools of independent interest is the construction in the free non-associative algebra of multialternating polynomials satisfying special properties. (C) 2010 Elsevier Inc. All rights reserved.

GENERICITY OF NONDEGENERATE GEODESICS WITH GENERAL BOUNDARY CONDITIONS

Let M be a possibly noncompact manifold. We prove, generically in the C(k)-topology (2 <= k <= infinity), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of L. Biliotti, M. A. Javaloyes and P. Piccione [6] for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P subset of M x M that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal Delta subset of M x M. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C(k)-generic are given.

PILZ Protein Structure and Interactions with PILB and the FIMX EAL Domain: Implications for Control of Type IV Pilus Biogenesis

The PilZ protein was originally identified as necessary for type IV pilus (T4P) biogenesis. Since then, a large and diverse family of bacterial PilZ homology domains have been identified, some of which have been implicated in signaling pathways that control important processes, including motility, virulence and biofilm formation. Furthermore, many PilZ homology domains, though not PilZ itself, have been shown to bind the important bacterial second messenger bis(3`-> 5`)cyclic diGMP (c-diGMP). The crystal structures of the PilZ orthologs from Xanthomonas axonopodis pv Citri (PilZ(XAC1133), this work) and from Xanthomonas campestris pv campestris (XC1028) present significant structural differences to other PilZ homologs that explain its failure to bind c-diGMP. NMR analysis of PilZ(XAC1133) shows that these structural differences are maintained in solution. In spite of their emerging importance in bacterial signaling, the means by which NZ proteins regulate specific processes is not clear. In this study, we show that PilZ(XAC1133) binds to PilB, an ATPase required for TV polymerization, and to the EAL domain of FiMX(XAC2398), which regulates TV biogenesis and localization in other bacterial species. These interactions were confirmed in NMR, two-hybrid and far-Western blot assays and are the first interactions observed between any PilZ domain and a target protein. While we were unable to detect phosphodiesterase activity for FimXX(AC2398) in vitro, we show that it binds c-diGMP both in the presence and in the absence of PilZ(XAC1133). Site-directed mutagenesis studies for conserved and exposed residues suggest that PilZ(XAC1133) interactions with FimX(XAC2398) and PilB(XAC3239) are mediated through a hydrophobic surface and an unstructured C-terminal extension conserved only in PilZ orthologs. The FimX-PilZ-PilB interactions involve a full set of ""degenerate"" GGDEF, EAL and PilZ domains and provide the first evidence of the means by which PilZ orthologs and FimX interact directly with the TP4 machinery. (C) 2009 Elsevier Ltd. All rights reserved.

Optical and electrical characterization of samaria-doped ceria

Ce(0.8)SM(0.2)O(1.9) and CeO(2) nanomaterials were prepared by a solution technique to produce an ultrafine particulate material with high sinterability. In this work, the structural characteristics, the photoluminescent behavior and the ionic conductivity of the synthesized materials are focused. The thermally decomposed material consists of less than 10 nm in diameter nanoparticles. The Raman spectrum of pure CeO(2) consists of a single triple degenerate F(2g) model characteristic of the fluorite-like structure. The full width at half maximum of this band decreases linearly with increasing calcination temperature. The photoluminescence spectra show a broadened emission band assigned to the ligand-to-metal charge-transfer states O -> Ce(4+). The emission spectra of the Ce(0.8)Sm(0.2)O(1.9) specimens present narrow bands arising from the 4G(5/2) -> (6)H(J) transitions (J = 5/2, 7/2, 9/2 and 11/2) of Sm(3+) ion due to the efficient energy transfer from the O -> Ce(4+) transitions to the emitter 4G(5/2) level. The ionic conductivity of sintered specimens shows a significant dependence on density. (C) 2009 Elsevier B.V. All rights reserved.

Electronic structure and chemical bonding in the ground states of Tc(2) and Re(2)

Multiconfiguration second-order perturbation theory, including relativistic effects and spin-orbit coupling, has been employed to investigate the nature of the chemical bonding in the ground state of Tc(2) and Re(2). The Tc(2) ground state is found to be a 0(g)(+) state, with an effective bond order (EBO) of 4.4, and a dissociation energy of 3.25 eV. The Re(2) ground state is a 1(g) state, with EBO = 4.3. Almost degenerate to it, is a 0(g)(+) state (T(e) = 77 cm(-1)), with EBO = 4.1. Experimental evidence also indicates that the ground state is of 1(g) nature. The dissociation energy is computed to be 5.0 eV in agreement with an experimental estimate of 4 +/- 1 eV.

Evidences for charge-transfer complex formation in the benzene adsorption on sulfated TiO2-a resonance Raman spectroscopy investigation

Benzene adsorbed on highly acidic sulfated TiO2 (S-TiO2) shows an intriguing resonance Raman (RR) effect, with excitation in the blue-violet region. There are very interesting spectral features: the preferential enhancement of the e(2g) mode (1595 cm(-1)) in relation to the a(1g) mode (ring-breathing mode at 995 cm(-1)) and the appearance of bands at 1565 and 1514 cm(-1). The band at 1565 cm(-1) is probably one of the components of the e(2g) split band, originally a doubly degenerate mode (8a, 8b) in neat benzene, and the band at 1514 cm(-1) is assigned to the 19a mode, an inactive mode in neat benzene. These facts indicate a lowering of symmetry in adsorbed benzene, which may be caused by a strong interaction between S-TiO2 and the benzene molecule with formation of a benzene to Ti (IV) charge transfer (CT) complex or by the formation of a benzene radical cation species. However, the RR spectra of the adsorbed benzene cannot be assigned to the benzene radical cation because the observed wavenumber of the ring-breathing mode does not have the value expected for this species. Moreover, it was found by ESR measurements that the amount of radicals was very low, and so it was concluded that a CT complex is the species that originates the RR spectra. The most favorable intensification of the band at 1595 cm(-1) in the RR spectra of benzene/S-TiO2 at higher excitation energy corroborates this hypothesis, as an absorption band in this energy range, assigned to a CT transition, is observed. Copyright (C) 2008 John Wiley & Sons, Ltd.