On Switched Regulator Design of Uncertain Nonlinear Systems Using Takagi-Sugeno Fuzzy Models

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Classificação de cônicas e quádricas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análise da influência de variantes do método de solução de escoamentos utilizando os métodos de elementos finitos com compressibilidade artificial e pseudo-características

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stabilization for an ensemble of half-spin systems

Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H-1 topology. This local convergence is shown to be a weak asymptotic convergence for the H-1 topology and thus a strong convergence for the C topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium. (C) 2011 Elsevier Ltd. All rights reserved.

Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

Septin C-Terminal Domain Interactions: Implications for Filament Stability and Assembly

Septins form a conserved family of filament forming GTP binding proteins found in a wide range of eukaryotic cells. They share a common structural architecture consisting of an N-terminal domain, a central GTP binding domain and a C-terminal domain, which is often predicted to adopt a coiled-coil conformation, at least in part. The crystal structure of the human SEPT2/SEPT6/SEPT7 heterocomplex has revealed the importance of the GTP binding domain in filament formation, but surprisingly no electron density was observed for the C-terminal domains and their function remains obscure. The dearth of structural information concerning the C-terminal region has motivated the present study in which the putative C-terminal domains of human SEPT2, SEPT6 and SEPT7 were expressed in E. coli and purified to homogeneity. The thermal stability and secondary structure content of the domains were studied by circular dichroism spectroscopy, and homo- and hetero-interactions were investigated by size exclusion chromatography, chemical cross-linking, analytical ultracentrifugation and surface plasmon resonance. Our results show that SEPT6-C and SEPT7-C are able to form both homo- and heterodimers with a high alpha-helical content in solution. The heterodimer is elongated and considerably more stable than the homodimers, with a K (D) of 15.8 nM. On the other hand, the homodimer SEPT2-C has a much lower affinity, with a K (D) of 4 mu M, and a moderate alpha-helical content. Our findings present the first direct experimental evidence toward better understanding the biophysical properties and coiled-coil pairings of such domains and their potential role in filament assembly and stability.

Entropy Production in Nonequilibrium Systems at Stationary States

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.

Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schrodinger flow

In a previous work El et al. (2006) [1] exact stable oblique soliton solutions were revealed in two-dimensional nonlinear Schrodinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt to build two-soliton solutions shows that the system is "close" to integrability provided that the angle between the solitons is small and/or we are in the hypersonic limit. (C) 2012 Elsevier B.V. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Investigations on DNA methylation by Dnmt2 and impact of tRNA modifications on TLR7 stimulation

The incorporation of modified nucleotides into ribonucleic acids (RNAs) is important for their structure and proper function. These modifications are inserted by distinct catalytic macromolecules one of them being Dnmt2. It methylates the Cytidine (C) at position 38 in tRNA to 5-methylcytidine (m5C). Dnmt2 has been a paradigm in this respect, because all of its nearest neighbors in evolution are DNA-cytosine C5-methyltransferases and methylate DNA, while its (own) DNA methyltransferase activity is the subject of controversial reports with rates varying between zero and very weak. This work determines whether the biochemical potential for DNA methylation is present in the enzyme. It was discovered that DNA fragments, when presented as covalent RNA:DNA hybrids in the structural context of a tRNA, can be more efficiently methylated than the corresponding natural tRNA substrate. Additional minor deviations from a native tRNA structure that were seen to be tolerated by Dnmt2 were used for a stepwise development of a composite system of guide RNAs that enable the enzyme to perform cytidine methylation on single stranded DNA in vitro. Furthermore, a proof-of-principle is presented for utilizing the S-adenosyl methionine-analog cofactor SeAdoYn with Dnmt2 to search for new possible substrates in a SELEX-like approach.rnIn innate immunity, nucleic acids can function as pathogen associated molecular patterns (PAMPs) recognized by pattern recognition receptors (PRRs). The modification pattern of RNA is the discriminating factor for toll-like receptor 7 (TLR7) to distinguish between self and non-self RNA of invading pathogens. It was found that a 2'-O-methylated guanosine (Gm) at position18, naturally occurring at this position in some tRNAs, antagonizes recognition by TLR7. In the second part of this work it is pointed out, that recognition extends to the next downstream nucleotide and the effectively recognized molecular detail is actually a methylated dinucleotide. The immune silencing effect of the ribose methylation is most pronounced if the dinucleotide motif is composed of purin nucleobases whereas pyrimidines diminish the effect. Similar results were obtained when the Gm modification was transposed into other tRNA domains. Point mutations abolishing base pairings important for a proper tertiary structure had no effect on the immune stimulatory potential of a Gm modified tRNA. Taken together these results suggest a processive type of RNA inspection by TLR7.rn

The MSSM with a softly broken U(2)^3 flavor symmetry

In this article we review the phenomenological consequences of radiative flavor-violation (RFV) in the MSSM. In the model under consideration the U(3)^3 flavor symmetry of the gauge sector is broken in a first step to U(2)^3 by the top and bottom Yukawa couplings of the superpotential (and possibly also by the bilinear SUSY-breaking terms). In a second step the remaining U(2)^3 flavor symmetry is softly broken by the trilinear A-terms in order to obtain the measured quark masses and the CKM matrix of the Standard Model (SM) at low energies. The phenomenological implications of this model depend on the actual choice of the SUSY breaking A-terms. If the CKM matrix is generated in the down sector (by A^d), Bs->mu^+mu^- receives non-decoupling contributions from Higgs penguins which become important already for moderate values of tan(beta). Also the Bs mixing amplitude can be significantly modified compared to the SM prediction including a potential induction of a new CP-violating phase (which is not possible in the MSSM with MFV).

Cellular mechanisms of burst firing-mediated long-term depression in rat neocortical pyramidal cells

During wakefulness and sleep, neurons in the neocortex emit action potentials tonically or in rhythmic bursts, respectively. However, the role of synchronized discharge patterns is largely unknown. We have recently shown that pairings of excitatory postsynaptic potentials (EPSPs) and action potential bursts or single spikes lead to long-term depression (burst-LTD) or long-term potentiation, respectively. In this study, we elucidate the cellular mechanisms of burst-LTD and characterize its functional properties. Whole-cell patch-clamp recordings were obtained from layer V pyramidal cells in somatosensory cortex of juvenile rats in vitro and composite EPSPs and EPSCs were evoked extracellularly in layers II/III. Repetitive burst-pairings led to a long-lasting depression of EPSPs and EPSCs that was blocked by inhibitors of metabotropic glutamate group 1 receptors, phospholipase C, protein kinase C (PKC) and calcium release from the endoplasmic reticulum, and that required an intact machinery for endocytosis. Thus, burst-LTD is induced via a Ca2+- and phosphatidylinositol-dependent activation of PKC and expressed through phosphorylation-triggered endocytosis of AMPA receptors. Functionally, burst-LTD is inversely related to EPSP size and bursts dominate single spikes in determining the sign of synaptic plasticity. Thus burst-firing constitutes a signal by which coincident synaptic inputs are proportionally downsized. Overall, our data thus suggest a mechanism by which synaptic weights can be reconfigured during non-rapid eye movement sleep.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

Integration of computational models and experimental characterization to study internal frost damage in cementitious materials

The objective of this doctoral research is to investigate the internal frost damage due to crystallization pore pressure in porous cement-based materials by developing computational and experimental characterization tools. As an essential component of the U.S. infrastructure system, the durability of concrete has significant impact on maintenance costs. In cold climates, freeze-thaw damage is a major issue affecting the durability of concrete. The deleterious effects of the freeze-thaw cycle depend on the microscale characteristics of concrete such as the pore sizes and the pore distribution, as well as the environmental conditions. Recent theories attribute internal frost damage of concrete is caused by crystallization pore pressure in the cold environment. The pore structures have significant impact on freeze-thaw durability of cement/concrete samples. The scanning electron microscope (SEM) and transmission X-ray microscopy (TXM) techniques were applied to characterize freeze-thaw damage within pore structure. In the microscale pore system, the crystallization pressures at sub-cooling temperatures were calculated using interface energy balance with thermodynamic analysis. The multi-phase Extended Finite Element Modeling (XFEM) and bilinear Cohesive Zone Modeling (CZM) were developed to simulate the internal frost damage of heterogeneous cement-based material samples. The fracture simulation with these two techniques were validated by comparing the predicted fracture behavior with the captured damage from compact tension (CT) and single-edge notched beam (SEB) bending tests. The study applied the developed computational tools to simulate the internal frost damage caused by ice crystallization with the two dimensional (2-D) SEM and three dimensional (3-D) reconstructed SEM and TXM digital samples. The pore pressure calculated from thermodynamic analysis was input for model simulation. The 2-D and 3-D bilinear CZM predicted the crack initiation and propagation within cement paste microstructure. The favorably predicted crack paths in concrete/cement samples indicate the developed bilinear CZM techniques have the ability to capture crack nucleation and propagation in cement-based material samples with multiphase and associated interface. By comparing the computational prediction with the actual damaged samples, it also indicates that the ice crystallization pressure is the main mechanism for the internal frost damage in cementitious materials.