Functions and vector fields on C(CPn)-singular manifolds

Let M2n+1 be a C(CPn) -singular manifold. We study functions and vector fields with isolated singularities on M2n+1. A C(CPn) -singular manifold is obtained from a smooth manifold M2n+1 with boundary in the form of a disjoint union of complex projective spaces CPn boolean OR CPn boolean OR ... boolean OR CPn with subsequent capture of a cone over each component of the boundary. Let M2n+1 be a compact C(CPn) -singular manifold with k singular points. The Euler characteristic of M2n+1 is equal to chi(M2n+1) = k(1 - n)/2. Let M2n+1 be a C(CPn)-singular manifold with singular points m(1), ..., m(k). Suppose that, on M2n+1, there exists an almost smooth vector field V (x) with finite number of zeros m(1), ..., m(k), x(1), ..., x(1). Then chi(M2n+1) = Sigma(l)(i=1) ind(x(i)) + Sigma(k)(i=1) ind(m(i)).

Schur-Szegö composition of entire functions

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

Teaching general concepts about sensors and transfer functions with a voltage divider

This work proposes the use of a simple voltage divider circuit composed by one potentiometer and one resistor to simulate the behavior of the electrical output signal of linear and nonlinear sensors. It is a low cost way to implement practical experiments in classroom and it also enables the analysis of interesting topics of electricity. This work induces naturally to a class guide where students can build and characterize a voltage divider to explore several concepts about sensors output signal. As the result of this teaching activity it is expected that students understand fundamentals of voltage divider, potentiometer operation, fundamental sensor characteristics, transfer function, and, besides, associate directly concepts of physics and mathematics with a practical approach.

Class Notes for Math 921/922: Real Analysis, Instructor Mikil Foss

Topics include: Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon- Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration, Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon-Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration.

Class Notes for Math 871: General Topology, Instructor Jamie Radcliffe

Topics include: Topological space and continuous functions (bases, the product topology, the box topology, the subspace topology, the quotient topology, the metric topology), connectedness (path connected, locally connected), compactness, completeness, countability, filters, and the fundamental group.

Solvability in the large for a class of complex vector fields on the cylinder

This work deals with global solvability of a class of complex vector fields of the form L = partial derivative/partial derivative t + (a(x, t)+ ib(x, t))partial derivative/partial derivative x, where a and b are real-valued C-infinity functions, defined on the cylinder Omega = R x S-1. Relatively compact (Sussmann) orbits are allowed. The connection with Malgrange's notion of L-convexity for supports is investigated. (C) 2011 Elsevier Masson SAS. All rights reserved.

Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented. (C) 2011 Elsevier B.V. All rights reserved.

The massless two-loop two-point function and zeta functions in counterterms of Feynman diagrams

The main part of this thesis describes a method of calculating the massless two-loop two-point function which allows expanding the integral up to an arbitrary order in the dimensional regularization parameter epsilon by rewriting it as a double Mellin-Barnes integral. Closing the contour and collecting the residues then transforms this integral into a form that enables us to utilize S. Weinzierl's computer library nestedsums. We could show that multiple zeta values and rational numbers are sufficient for expanding the massless two-loop two-point function to all orders in epsilon. We then use the Hopf algebra of Feynman diagrams and its antipode, to investigate the appearance of Riemann's zeta function in counterterms of Feynman diagrams in massless Yukawa theory and massless QED. The class of Feynman diagrams we consider consists of graphs built from primitive one-loop diagrams and the non-planar vertex correction, where the vertex corrections only depend on one external momentum. We showed the absence of powers of pi in the counterterms of the non-planar vertex correction and diagrams built by shuffling it with the one-loop vertex correction. We also found the invariance of some coefficients of zeta functions under a change of momentum flow through these vertex corrections.

HLA class II mismatch alleles as targets of the alloreactive CD4 T-cell response

In allogeneic hematopoietic stem cell transplantation (allo-HSCT), alloreactive T lymphocytes of donor origin mediate the beneficial graft-versus-leukemia effect but also induce graft-versus-host disease (GvHD). Since human leukocyte antigens (HLA) mismatch alleles represent major targets of alloreactive T lymphocytes, patient and donor are usually matched for the class I molecules A, B, C, and for the class II molecules DRB1 and DQB1, in order do reduce the risk of GvHD. The HLA-DPB1 locus, however, is still ignored in donor selection. Interestingly, clinical studies have demonstrated that disparities at HLA-DQB1 alleles as well as distinct HLA DPB1 mismatch constellations do not adversely affect the outcome of allo-HSCT. It has also been shown that HLA class II is predominantly expressed on hematopoietic cells under non-inflammatory conditions. Therefore, this PhD thesis focused on the application of CD4 T cells in adoptive immunotherapy of leukemias.rnIn the first part of this thesis we developed a rapid screening approach to detect T-cell reactivity of donors to single HLA class II mismatch alleles. Allo-HLA reactivity was measured in naive, memory, and entire CD4 T cells isolated from PBMC of healthy donors by flow cytometric cell sorting according to expression of the differentiation markers CD45RA, CD45RO, CD62L, and CCR7. T-cell populations were defined by a single marker to facilitate translation into a clinical-grade allo-depletion procedure. Alloreactivity to single HLA-DR/-DQ mismatch alleles was analyzed in short-term mixed lymphocyte reactions (MLR) in vitro. As standard antigen-presenting cells, we used the HLA-deficient cell line K562 upon electroporation with single HLA-DR/-DQ allele mRNA. We observed in IFN-γ ELISpot assays that allo-HLA-reactivity preferentially derived from subsets enriched for naive compared to memory T cells in healthy donors, irrespective of the HLA mismatch allele. This separation was most efficient if CD62L (P=0.008) or CD45RA (P=0.011) were used as marker. Median numbers of allo-HLA-reactive effector cells were 3.5-fold and 16.6-fold lower in CD62Lneg and CD45RAneg memory CD4 T cells than in entire CD4 T cells, respectively. In allele-specific analysis, alloreactivity to single HLA-DR alleles clearly exceeded that to HLA-DQ alleles. In terms of alloproliferation no significant difference could be observed between individual CD4 T-cell subsets. rnThe second part of this thesis dealed with the generation of allo-HLA-DQ/-DP specific CD4 T cells. Naive CD45RApos CD4 T cells isolated from healthy donor PBMC by flow cytometric cell sorting were stimulated in MLR against single allo-HLA-DQ/-DP alleles transfected into autologous mature monocyte-derived dendritic cells by mRNA electroporation. Rapidly expanding HLA-DQ/-DP mismatch reactive T cells significantly recognized and cytolysed primary acute myeloid leukemia (AML) blasts, fibroblasts (FB) and keratinocytes (KC) in IFN-γ ELISpot and 51chromium release assays if the targets carried the HLA DQ/ DP allele used for T cell priming. While AML blasts were recognized independent of pre-incubating them with IFN-γ, recognition of FB and KC required IFN-γ pre treatment. We further investigated HLA class II expression on hematopoietic and non-hematopoietic cells by flow cytometry. HLA class II was not detected on primary FB, KC, and non-malignant kidney cells, but was expressed at significant levels on primary AML blasts and B-LCL. Up-regulation of HLA class II expression was observed on all cell types after pre-incubation with IFN-γ.rnIn summary, the novel K562-HLA based MLR approach revealed that naive-depleted CD4 T-cell subsets of healthy individuals contain decreased allo-HLA reactivity in vitro. We propose the application of CD45RAneg naive-depleted CD4 T cells as memory T cell therapy, which might be beneficial for HLA-mismatched patients at high-risk of GvHD and low-risk of leukemia relapse. Memory T cells might also provide important post-transplant immune functions against infectious agents. Additionally, the screening approach could be employed as test system to detect donors which have low risks for the emergence of GvHD after allo-HSCT. In the second part of this thesis we developed a protocol for the generation of allo-HLA-DQ/-DP specific CD4 T cell lines, which could be applied in situations in which patient and donor are matched in all HLA alleles but one HLA-DQ/-DP allele with low GvHD potential. These T cells showed lytic activity to leukemia cells while presumably sparing non-hematopoietic tissues under non-inflammatory conditions. Therefore, they might be advantageous for allo-HSCT patients with advanced stage AML after reduced-intensity conditioning and T-cell depletion for the replenishment of anti-leukemic reactivity if the risk for disease relapse is high. rn

Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

Class-switzched B cells display response to therapeutic B-cell depletion in rheumatoid arthritis

Introduction Reconstitution of peripheral blood (PB) B cells after therapeutic depletion with the chimeric anti-CD20 antibody rituximab (RTX) mimics lymphatic ontogeny. In this situation, the repletion kinetics and migratory properties of distinct developmental B-cell stages and their correlation to disease activity might facilitate our understanding of innate and adaptive B-cell functions in rheumatoid arthritis (RA). Methods Thirty-five 'RTX-naïve' RA patients with active arthritis were treated after failure of tumour necrosis factor blockade in an open-label study with two infusions of 1,000 mg RTX. Prednisone dose was tapered according to clinical improvement from a median of 10 mg at baseline to 5 mg at 9 and 12 months. Conventional disease-modifying antirheumatic drugs were kept stable. Subsets of CD19+ B cells were assessed by flow cytometry according to their IgD and CD27 surface expression. Their absolute number and relative frequency in PB were followed every 3 months and were determined in parallel in synovial tissue (n = 3) or synovial fluid (n = 3) in the case of florid arthritis. Results Six of 35 patients fulfilled the European League Against Rheumatism criteria for moderate clinical response, and 19 others for good clinical response. All PB B-cell fractions decreased significantly in number (P < 0.001) after the first infusion. Disease activity developed independently of the total B-cell number. B-cell repopulation was dominated in quantity by CD27-IgD+ 'naïve' B cells. The low number of CD27+IgD- class-switched memory B cells (MemB) in the blood, together with sustained reduction of rheumatoid factor serum concentrations, correlated with good clinical response. Class-switched MemB were found accumulated in flaring joints. Conclusions The present data support the hypothesis that control of adaptive immune processes involving germinal centre-derived, antigen, and T-cell-dependently matured B cells is essential for successful RTX treatment.