Periodic averaging theorems for various types of equations

We prove a periodic averaging theorem for generalized ordinary differential equations and show that averaging theorems for ordinary differential equations with impulses and for dynamic equations on time scales follow easily from this general theorem. We also present a periodic averaging theorem for a large class of retarded equations.

The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

Kurzweil integral for Riesz space-valued functions: Uniform convergence theorem

Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.

Prevalence of celiac disease among blood donors in Sao Paulo - the most populated city in Brazil

OBJECTIVE: Celiac disease is a permanent enteropathy caused by the ingestion of gluten, which leads to an immune-mediated inflammation of the small intestine mucosa. The prevalence of celiac disease varies among different nations and ethnic backgrounds, and its diversity is determined by genetic and environmental factors. Sao Paulo city is one of the largest cities in the world, with a vast population and an important history of internal migratory flow from other Brazilian regions, as well as immigration from other, primarily European, countries, resulting in significant miscegenation. The aim of the present study was to estimate the prevalence of adults with undiagnosed celiac disease among blood donors of Sao Paulo by collecting information on the ancestry of the population studied. METHODS: The prevalence of celiac disease was assessed by screening for positive IgA transglutaminase and IgA endomysium antibodies in 4,000 donors (volunteers) in the Fundacao Pro-Sangue Blood Center of Sao Paulo, Sao Paulo, Brazil. The antibody-positive subjects were asked to undergo a small bowel biopsy. RESULTS: Of the 4,000 subjects, twenty-four had positive tests, although both antibody tests were not always concordant. For example, ten subjects were positive for IgA tissue transglutaminase only. In twenty-one positive patients, duodenal biopsies were performed, and the diagnosis of celiac disease was confirmed in fourteen patients (Marsh criteria modified by Oberhuber). In this group, 67% claimed to have European ancestry, mainly from Italy, Portugal and Spain. CONCLUSION: The prevalence of celiac disease is at least 1: 286 among supposedly healthy blood bank volunteers in Sao Paulo, Brazil.

Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described.

High precision astrometry mission for the detection and characterization of nearby habitable planetary systems with the Nearby Earth Astrometric Telescope (NEAT)

A complete census of planetary systems around a volume-limited sample of solar-type stars (FGK dwarfs) in the Solar neighborhood (d a parts per thousand currency signaEuro parts per thousand 15 pc) with uniform sensitivity down to Earth-mass planets within their Habitable Zones out to several AUs would be a major milestone in extrasolar planets astrophysics. This fundamental goal can be achieved with a mission concept such as NEAT-the Nearby Earth Astrometric Telescope. NEAT is designed to carry out space-borne extremely-high-precision astrometric measurements at the 0.05 mu as (1 sigma) accuracy level, sufficient to detect dynamical effects due to orbiting planets of mass even lower than Earth's around the nearest stars. Such a survey mission would provide the actual planetary masses and the full orbital geometry for all the components of the detected planetary systems down to the Earth-mass limit. The NEAT performance limits can be achieved by carrying out differential astrometry between the targets and a set of suitable reference stars in the field. The NEAT instrument design consists of an off-axis parabola single-mirror telescope (D = 1 m), a detector with a large field of view located 40 m away from the telescope and made of 8 small movable CCDs located around a fixed central CCD, and an interferometric calibration system monitoring dynamical Young's fringes originating from metrology fibers located at the primary mirror. The mission profile is driven by the fact that the two main modules of the payload, the telescope and the focal plane, must be located 40 m away leading to the choice of a formation flying option as the reference mission, and of a deployable boom option as an alternative choice. The proposed mission architecture relies on the use of two satellites, of about 700 kg each, operating at L2 for 5 years, flying in formation and offering a capability of more than 20,000 reconfigurations. The two satellites will be launched in a stacked configuration using a Soyuz ST launch vehicle. The NEAT primary science program will encompass an astrometric survey of our 200 closest F-, G- and K-type stellar neighbors, with an average of 50 visits each distributed over the nominal mission duration. The main survey operation will use approximately 70% of the mission lifetime. The remaining 30% of NEAT observing time might be allocated, for example, to improve the characterization of the architecture of selected planetary systems around nearby targets of specific interest (low-mass stars, young stars, etc.) discovered by Gaia, ground-based high-precision radial-velocity surveys, and other programs. With its exquisite, surgical astrometric precision, NEAT holds the promise to provide the first thorough census for Earth-mass planets around stars in the immediate vicinity of our Sun.

SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

Molecular measurement of BCR-ABL transcript variations in chronic myeloid leukemia patients in cytogenetic remission

Abstract Background The monitoring of BCR-ABL transcript levels by real-time quantitative polymerase chain reaction (RT-qPCR) has become important to assess minimal residual disease (MRD) and standard of care in the treatment of chronic myeloid leukemia (CML). In this study, we performed a prospective, sequential analysis using RT-qPCR monitoring of BCR-ABL gene rearrangements in blood samples from 91 CML patients in chronic phase (CP) who achieved complete cytogenetic remission (CCyR) and major molecular remission (MMR) throughout imatinib treatment. Methods The absolute level of BCR-ABL transcript from peripheral blood was serially measured every 4 to 12 weeks by RT-qPCR. Only level variations > 0.5%, according to the international scale, was considered positive. Sequential cytogenetic analysis was also performed in bone marrow samples from all patients using standard protocols. Results Based on sequential analysis of BCR-ABL transcripts, the 91 patients were divided into three categories: (A) 57 (62.6%) had no variation on sequential analysis; (B) 30 (32.9%) had a single positive variation result obtained in a single sample; and (C) 4 (4.39%) had variations of BCR-ABL transcripts in at least two consecutive samples. Of the 34 patients who had elevated levels of transcripts (group B and C), 19 (55.8%) had a < 1% of BCR-ABL/BCR ratio, 13 (38.2%) patients had a 1% to 10% increase and 2 patients had a >10% increase of RT-qPCR. The last two patients had lost a CCyR, and none of them showed mutations in the ABL gene. Transient cytogenetic alterations in Ph-negative cells were observed in five (5.5%) patients, and none of whom lost CCyR. Conclusions Despite an increase levels of BCR-ABL/BCR ratio variations by RT-qPCR, the majority of CML patients with MMR remained in CCyR. Thus, such single variations should neither be considered predictive of subsequent failure and nor an indication for altering imatinib dose or switching to second generation therapy. Changing of imatinib on the basis of BCR-ABL/BCR% sustained increase and mutational studies is a prudent approach for preserving other therapeutic options in imatinib-resistant patients.

Clinical judgment to estimate pretest probability in the diagnosis of Cushing's syndrome under a Bayesian perspective

OBJECTIVE: To estimate the pretest probability of Cushing's syndrome (CS) diagnosis by a Bayesian approach using intuitive clinical judgment. MATERIALS AND METHODS: Physicians were requested, in seven endocrinology meetings, to answer three questions: "Based on your personal expertise, after obtaining clinical history and physical examination, without using laboratorial tests, what is your probability of diagnosing Cushing's Syndrome?"; "For how long have you been practicing Endocrinology?"; and "Where do you work?". A Bayesian beta regression, using the WinBugs software was employed. RESULTS: We obtained 294 questionnaires. The mean pretest probability of CS diagnosis was 51.6% (95%CI: 48.7-54.3). The probability was directly related to experience in endocrinology, but not with the place of work. CONCLUSION: Pretest probability of CS diagnosis was estimated using a Bayesian methodology. Although pretest likelihood can be context-dependent, experience based on years of practice may help the practitioner to diagnosis CS. Arq Bras Endocrinol Metab. 2012;56(9):633-7

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.

Prevalence of celiac disease among blood donors in São Paulo: the most populated city in Brazil

OBJECTIVE: Celiac disease is a permanent enteropathy caused by the ingestion of gluten, which leads to an immunemediated inflammation of the small intestine mucosa. The prevalence of celiac disease varies among different nations and ethnic backgrounds, and its diversity is determined by genetic and environmental factors. São Paulo city is one of the largest cities in the world, with a vast population and an important history of internal migratory flow from other Brazilian regions, as well as immigration from other, primarily European, countries, resulting in significant miscegenation. The aim of the present study was to estimate the prevalence of adults with undiagnosed celiac disease among blood donors of São Paulo by collecting information on the ancestry of the population studied. METHODS: The prevalence of celiac disease was assessed by screening for positive IgA transglutaminase and IgA endomysium antibodies in 4,000 donors (volunteers) in the Fundação Pró-Sangue Blood Center of São Paulo, São Paulo, Brazil. The antibody-positive subjects were asked to undergo a small bowel biopsy. RESULTS: Of the 4,000 subjects, twenty-four had positive tests, although both antibody tests were not always concordant. For example, ten subjects were positive for IgA tissue transglutaminase only. In twenty-one positive patients, duodenal biopsies were performed, and the diagnosis of celiac disease was confirmed in fourteen patients (Marsh criteria modified by Oberhuber). In this group, 67% claimed to have European ancestry, mainly from Italy, Portugal and Spain. CONCLUSION: The prevalence of celiac disease is at least 1:286 among supposedly healthy blood bank volunteers in São Paulo, Brazil.