Generalized Fractional Evolution Equation

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20

Quantum stochastic calculus associated with quadratic quantum noises

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie dagger-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Ito formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculus extends the Hudson-Parthasarathy quantum stochastic calculus. (C) 2016 AIP Publishing LLC.

Self-trapping of a Fermi superfluid in a double-well potential in the Bose-Einstein-condensate-unitarity crossover

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

Generalized Laplacian Eigenmaps for Modeling and Tracking Human Motions

This paper presents generalized Laplacian eigenmaps, a novel dimensionality reduction approach designed to address stylistic variations in time series. It generates compact and coherent continuous spaces whose geometry is data-driven. This paper also introduces graph-based particle filter, a novel methodology conceived for efficient tracking in low dimensional space derived from a spectral dimensionality reduction method. Its strengths are a propagation scheme, which facilitates the prediction in time and style, and a noise model coherent with the manifold, which prevents divergence, and increases robustness. Experiments show that a combination of both techniques achieves state-of-the-art performance for human pose tracking in underconstrained scenarios.

A class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.

Gross anatomy and positional homology of gills, gonopores, and nephridiopores in “basal” living chitons (Polyplacophora: Lepidopleurina)

Traditional shell characters are insufficient to differentiate taxa within the polyplacophoran order Lepidopleurida. Additional morphological character sets from soft anatomy (e.g., gamete morphology, gill arrangement, and locations of gonopores and nephidiopores) have previously been described from only a small number of taxa. This study reports for the first time, positions of the gonopores and nephridiopores for 17 species in the Lepidopleurina. The position of both types of pores on the longitudinal body axis varies within a generalized range of the posterior third of the body; however, the separation between the pores as a proportion of the specimen’s foot length varies from 3.7% to 17% in different species. Positions of pores relative to the serial gills are also variable within species, and future studies may require a new descriptive basis in order to resolve positional homology. The order Lepidopleurida occupies a critical position with respect to understanding larger-scale patterns in polyplacophoran (and molluscan) evolution.

Improved description of chemical barriers with generalized gradient approximations (GGAs) and meta-GGAs

The performance of exchange and correlation (xc) functionals of the generalized gradient approximation (GGA) type and of the meta-GGA type in the calculation of chemical reactions is related to topological features of the electron density which, in turn, are connected to the orbital structure of chemical bonds within the Kohn-Sham (KS) theory. Seventeen GGA and meta-GGA xc functionals are assessed for 15 hydrogen abstraction reactions and 3 symmetrical S(N)2 reactions. Systems that are problematic for standard GGAs characteristically have enhanced values of the dimensionless gradient argument s(sigma)(2) with local maxima in the bonding region. The origin of this topological feature is the occupation of valence KS orbitals with an antibonding or essentially nonbonding character. The local enhancement of s(sigma)(2) yields too negative exchange-correlation energies with standard GGAs for the transition state of the S(N)2 reaction, which leads to the reduced calculated reaction barriers. The unwarranted localization of the effective xc hole of the standard GGAs, i.e., the nondynamical correlation that is built into them but is spurious in this case, wields its effect by their s(sigma)(2) dependence. Barriers are improved for xc functionals with the exchange functional OPTX as x component, which has a modified dependence on s(sigma)(2). Standard GGAs also underestimate the barriers for the hydrogen abstraction reactions. In this case the barriers are improved by correlation functionals, such as the Laplacian-dependent (LAP3) functional, which has a modified dependence on the Coulomb correlation of the opposite- and like-spin electrons. The best overall performance is established for the combination OLAP3 of OPTX and LAP3.

Generalized systemic cryptococcosis in a dog after immunosuppressive corticotherapy

Um cão da raça Boxer, macho, com 2 anos e 11 meses de idade foi encaminhado ao hospital veterinário com histórico de distúrbio gastroentérico de dois meses de duração, apatia, hiporexia, emagrecimento progressivo e deficiência visual. Ataxia e vocalização foram observadas posteriormente. O animal estava sendo tratado em outra clínica veterinária com antibióticos e doses imunossupressoras de corticóides, direcionados ao controle de provável enterite alimentar. A morte ocorreu após cinco dias. As observações macro e microscópica revelaram tratar-se de criptococose sistêmica, atingindo trato digestório, olhos, SNC, rins, pâncreas e linfonodos. O presente relato enfatiza a infecção fúngica criptocócica quanto aos seus aspectos grastrointestinais iniciais a serem considerados no diagnóstico clínico, ressaltando a imunossupressão induzida pela corticoterapia.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.