Positive Ricci Curvature on Highly Connected Manifolds

Peer reviewed

Positive Ricci Curvature on Highly Connected Manifolds

Peer reviewed

Credit risk & forward price models

Doutoramento em Gestão

A mathematical model of the early visual system and border completion via subriemannian Hamiltonian geodesics

In this thesis, we aim to discuss a simple mathematical model for the edge detection mechanism and the boundary completion problem in the human brain in a differential geometry framework. We describe the columnar structure of the primary visual cortex as the fiber bundle R2 × S1, the orientation bundle, and by introducing a first vector field on it, explain the edge detection process. Edges are detected through a lift from the domain in R2 into the manifold R2 × S1 and are horizontal to a completely non-integrable distribution. Therefore, we can construct a subriemannian structure on the manifold R2 × S1, through which we retrieve perceived smooth contours as subriemannian geodesics, solutions to Hamilton’s equations. To do so, in the first chapter, we illustrate the functioning of the most fundamental structures of the early visual system in the brain, from the retina to the primary visual cortex. We proceed with introducing the necessary concepts of differential and subriemannian geometry in chapters two and three. We finally implement our model in chapter four, where we conclude, comparing our results with the experimental findings of Heyes, Fields, and Hess on the existence of an association field.

代微積拾級Dai wei ji shi ji.Loomis' Analytical Geometry and Differential and Integral Calculus.

Traduction de Wylie, rédigée par Li Shan lan ; préfaces Chinoises des deux traducteurs (1859) ; préface anglaise, écrite à Shang hai par A. Wylie (juillet 1859). Liste de termes techniques en anglais et en Chinois. Gravé à la maison Mo hai (1859).18 livres.

3-D geometry reconstruction using a color image stereo pair and partial differential equations

[EN] In this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a color image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next, we propose a new model for the disparity estimation based on an energy functional. We look for the local minima of the energy using the associate Euler-Langrage partial differential equations. This model is a generalization to color image of the model developed in, with some changes in the strategy to avoid the irrelevant local minima. We present some numerical experiences of 3-D reconstruction, using this method some real stereo pairs.

Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

The differential and integral calculus : containing differentiation, integration, development, series, differential equations, differences, summation, equations of differences, calculus of variations, definite integrals,--with applications to algebra, plane geometry, solid geometry, and mechanics. Also, Elementary illustrations of the differential and integral calculus /

First issued in 25 parts, July 15, 1836, to June 1, 1842.

A treatise on infinitesimal calculus, containing differential and integral calculus, calculus of variations, applications to algebra and geometry, and analytical mechanics.

Vol. 3 and 4 form the author's Treatise on analytical mechanics.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

GEVREY SOLVABILITY AND GEVREY REGULARITY IN DIFFERENTIAL COMPLEXES ASSOCIATED TO LOCALLY INTEGRABLE STRUCTURES

In this work we study some properties of the differential complex associated to a locally integrable (involutive) structure acting on forms with Gevrey coefficients. Among other results we prove that, for such complexes, Gevrey solvability follows from smooth solvability under the sole assumption of a regularity condition. As a consequence we obtain the proof of the Gevrey solvability for a first order linear PDE with real-analytic coefficients satisfying the Nirenberg-Treves condition (P).

Global solutions for abstract impulsive neutral differential equations

We study the existence of mild solutions for a class of impulsive neutral functional differential equation defined on the whole real axis. Some concrete applications to ordinary and partial neutral differential equations with impulses are considered. (C) 2010 Elsevier Ltd. All rights reserved.

A prospective study evaluating the efficacy of the artificial sphincter AMS 800 for the treatment of postradical prostatectomy urinary incontinence and the correlation between preoperative urodynamic and surgical outcomes

OBJECTIVES We have evaluated prospectively the long-term efficacy of the artificial urinary sphincter (AUS) AMS 800 for the treatment postradical prostatectomy urinary incontinence (PRPUI) patients. We also evaluated the correlation between preoperative urodynamic findings and surgical outcomes. METHODS From May 1997 to April 2003, 40 consecutive patients with PRPUI caused by intrinsic sphincter deficiency (ISD) were treated with the AMS 800. Mean age was 68.3 +/- 6.3 years. Continence status was evaluated on the basis of pad count, impact of urinary incontinence on the quality of life, complications, and surgical revisions. Preoperative urodynamic findings were correlated with surgical outcomes. RESULTS Follow-up ranged from 27 to 132 months (mean = 53.4 +/- 21.4 months). There was a significant reduction in pad count from 4.0 +/- 0.9 to 0.62 +/- 1.07 diapers per day (P <0.001) leading to continence in 90%. There was a significant reduction on the impact of incontinence decreasing from 5.0 +/- 0.7 to 1.4 +/- 0.93 (P <0.001) in a visual analogue scale (VAS). Surgical revision rate was 20%. Preoperative urodynamics was useful to identify sphincter deficiency. Except by a tendency of worse results in patients with reduced bladder compliance (RBC), other urodynamic parameters did not correlate with a worse surgical outcome. CONCLUSIONS The AMS 800 offers good long-term continence to most PRPUI patients. Preoperative findings like detrusor hyperactivity (DH), impaired detrusor contraction (IDC), low Valsalva leak point pressure, bladder outlet obstruction (BOO), and mild RBC were not associated with worse surgical outcomes.

Differential diagnosis of oocysts of Hammondia-like organisms of dogs and cats by PCR-RFLP analysis of 70-kilodalton heat shock protein (HSP70) gene

Organisms of the genera Toxoplasma, Hammondia and Neospora, the Hammondia-like organisms, are closely related coccidian with similarly sized oocysts. Therefore, a diagnosis based on microscopy of oocysts in feces is not a method of choice for species identification of these important parasites. In this paper, we present a polymerase chain reaction coupled with restriction fragment length polymorphism (PCR-RFLP) method to differentially diagnose oocysts of Toxoplasma gondii from oocyst of Hammondia hammondi. Another PCR-RFLP was designed to differentiate oocysts of Hammondia heydorni from oocysts of Neospora spp. Both PCR-RFLP are based on nucleotide sequences of the Hsp70 coding gene. In conclusion, we presented two alternative molecular diagnostic assays that can be successfully applied for the differentiation of oocysts of Hammondia-like organisms shed by felids and canids.

Differential expression of CDC25 phosphatases splice variants in human breast cancer cells

Background: CDC25 phosphatases control cell cycle progression by activating cyclin dependent kinases. The three CDC25 isoforms encoding genes are submitted to alternative splicing events which generate at least two variants for CDC25A and five for both CDC25B and CDC25C. An over-expression of CDC25 was reported in several types of cancer, including breast cancer, and is often associated with a poor prognosis. Nevertheless, most of the previous studies did not address the expression of CDC25 splice variants. Here, we evaluated CDC25 spliced transcripts expression in anti-cancerous drug-sensitive and resistant breast cancer cell lines in order to identify potential breast cancer biomarkers. Methods: CDC25 splice variants mRNA levels were evaluated by semi-quantitative RT-PCR and by an original real-time RT-PCR assay. Results: CDC25 spliced transcripts are differentially expres-sed in the breast cancer cell lines studied. An up-regulation of CDC25A2 variant and an increase of the CDC25C5/C1 ratio are associated to the multidrug-resistance in VCREMS and DOXOR breast cancer cells, compared to their sensitive counterpart cell line MCF-7. Additionally, CDC25B2 tran-script is exclusively over-expressed in VCREMS resistant cells and could therefore be involved in the development of certain type of drug resistance. Conclusions: CDC25 splice variants could represent interesting potential breast cancer prognostic biomarkers.