A Numerical method for the semilinear stochastic transport equation

Trabalho apresentado no XXXV CNMAC, Natal-RN, 2014.

Kinetic energy conserving integrators for Gaussian thermostatted SLLOD

A new integration scheme is developed for nonequilibrium molecular dynamics simulations where the temperature is constrained by a Gaussian thermostat. The utility of the scheme is demonstrated by its application to the SLLOD algorithm which is the standard nonequilibrium molecular dynamics algorithm for studying shear flow. Unlike conventional integrators, the new integrators are constructed using operator-splitting techniques to ensure stability and that little or no drift in the kinetic energy occurs. Moreover, they require minimum computer memory and are straightforward to program. Numerical experiments show that the efficiency and stability of the new integrators compare favorably with conventional integrators such as the Runge-Kutta and Gear predictor-corrector methods. (C) 1999 American Institute of Physics. [S0021-9606(99)50125-6].

CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Design of Digital Fractional-Order Integrators and Differentiators by Least Squares

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04

Hypermedia-based Web Services as System Integrators

As we move more closely to the practical concept of the Internet of Things and, our reliance on public and private APIs increases, web services and their related topics have become utterly crucial to the informatics community. However, the question about which style of web services would best solve a particular problem, can raise signi cant and multifarious debates. There can be found two implementation styles that highlight themselves: the RPC-oriented style represented by the SOAP protocol’s implementations and the hypermedia style, which is represented by the REST architectural style’s implementations. As we search examples of already established web services, we can nd a handful of robust and reliable public and private SOAP APIs, nevertheless, it seems that RESTful services are gaining popularity in the enterprise community. For the current generation of developers that work on informatics solutions, REST seems to represent a fundamental and straightforward alternative and even, a more deep-rooted approach than SOAP. But are they comparable? Do both approaches have each speci c best suitable scenarios? Such study is brie y carried out in the present document’s chapters, starting with the respective background study, following an analysis of the hypermedia approach and an instantiation of its architecture, in a particular case study applied in a BPM context.

Financing exponential growth at H3

H3 is a fast-food chain that introduced the concept of gourmet hamburgers in the Portuguese market. This case-study illustrates its financing strategy that supported an exponential growth represented by opening 33 restaurants within approximately 3 years of its inception. H3 is now faced with the challenge of structuring its foreign ventures and change its financial approach. The main covered topics are the options an entrepreneur has for financing a new venture and how it evolves along the life cycle and different business approaches, namely franchising. It aims to be used as a learning tool in courses such as entrepreneurial finance.

Double-Exponential Model of a Photovoltaic Cell with Temperature Dependence

The purpose of the research is the creation of mathematical models in MATLAB based on the double exponential model of the photovoltaic cell. The developed model allows for different physical and environmental parameters. An equivalent circuit of the model includes a photocurrent source, two diodes, and a series and parallel resistance. The paper presents the simulation results for each parameter. The simulation data are displayed graphically and numerical results are saved in a file.

Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

This paper shows that certain quotients of entire functions are characteristic functions. Under some conditions, we provide expressions for the densities of such characteristic functions which turn out to be generalized Dirichlet series which in turn can be expressed as an infinite linear combination of exponential or Laplace densities. We apply these results to several examples.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Repression of flagellar genes in exponential phase by CsgD and CpxR, two crucial modulators of Escherichia coli biofilm formation.

Escherichia coli adapts its lifestyle to the variations of environmental growth conditions, swapping between swimming motility or biofilm formation. The stationary-phase sigma factor RpoS is an important regulator of this switch, since it stimulates adhesion and represses flagellar biosynthesis. By measuring the dynamics of gene expression, we show that RpoS inhibits the transcription of the flagellar sigma factor, FliA, in exponential growth phase. RpoS also partially controls the expression of CsgD and CpxR, two transcription factors important for bacterial adhesion. We demonstrate that these two regulators repress the transcription of fliA, flgM, and tar and that this regulation is dependent on the growth medium. CsgD binds to the flgM and fliA promoters around their -10 promoter element, strongly suggesting direct repression. We show that CsgD and CpxR also affect the expression of other known modulators of cell motility. We propose an updated structure of the regulatory network controlling the choice between adhesion and motility.

On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.