An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

MA167exam01pdf

Exam questions and solutions in PDF

MA167exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

Off-diagonal helicity density matrix elements for vector mesons produced in polarized e+e- processes

Final-state qq̄ interactions give origin to nonzero values of the off-diagonal element ρ1,-1 of the helicity density matrix of vector mesons produced in e+e- annihilations, as has been confirmed by recent OPAL data on φ, D*, and K*. New predictions are given for ρ1,-1 of several mesons produced at large XE and small pT - i.e., collinear with the parent jet - in the annihilation of polarized e+ and e-; the results depend strongly on the elementary dynamics and allow further nontrivial tests of the standard model.

A single chart with supplementary runs rules for monitoring the mean vector and the covariance matrix of multivariate processes

The MRMAX chart is a single chart based on the standardized sample means and sample ranges for monitoring the mean vector and the covariance matrix of multivariate processes. User's familiarity with the computation of these statistics is a point in favor of the MRMAX chart. As a single chart, the recently proposed MRMAX chart is very appropriate for supplementary runs rules. In this article, we compare the supplemented MRMAX chart and the synthetic MRMAX chart with the standard MRMAX chart. The supplementary and the synthetic runs rules enhance the performance of the MRMAX chart. © 2013 Elsevier Ltd.

Weighted geometric mean of large-scale matrices: numerical analysis and algorithms

Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

On derivatives and norms of generalized matrix functions and respective symmetric powers

In recent papers, the authors obtained formulas for directional derivatives of all orders, of the immanant and of the m-th xi-symmetric tensor power of an operator and a matrix, when xi is a character of the full symmetric group. The operator norm of these derivatives was also calculated. In this paper, similar results are established for generalized matrix functions and for every symmetric tensor power.

A new look at the Heston characteristic function

A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factorization of the moment generating function as product of Bessel type factors, and an approximating sequence to the law of log-spot is deduced.

Offering planning process development: Bridging the Offering Gaps and Consolidating Top Priority Needs in Product Offering

The aim of this Thesis is to study how to manage the front-end of the offering planning process. This includes actual process development and methods to gather and analyze information to achieve the best outcome in customer oriented product offering. Study is carried out in two parts: theoretical part and company related part. Theoretical framework is created introducing different types of approaches to manage product planning processes. Products are seen as platforms and they are broken down to subsystems to show different parts of the development. With the help of the matrix-based approaches product platform related information is gathered and analyzed. In this kind of analysis business/market drivers and cus-tomer/competitor information are connected with product subsystems. This gives possibilities to study product gaps/needs and possible future ideas/scenarios in different customer segments. Company related part consists of offering planning process development in real company environment. Process formation includes documents and tools that guide planning from the information gathering to the prioritization and decision making.

Development of Collaborative Product Structure Management

The purpose of this thesis is to develop an environment or network that enables effective collaborative product structure management among stakeholders in each unit, throughout the entire product lifecycle and product data management. This thesis uses framework models as an approach to the problem. Framework model methods for development of collaborative product structure management are proposed in this study, there are three unique models depicted to support collaborative product structure management: organization model, process model and product model. In the organization model, the formation of product data management system (eDSTAT) key user network is specified. In the process model, development is based on the case company’s product development matrix. In the product model framework, product model management, product knowledge management and design knowledge management are defined as development tools and collaboration is based on web-based product structure management. Collaborative management is executed using all these approaches. A case study from an actual project at the case company is presented as an implementation; this is to verify the models’ applicability. A computer assisted design tool and the web-based product structure manager, have been used as tools of this collaboration with the support of the key user. The current PDM system, eDSTAT, is used as a piloting case for key user role. The result of this development is that the role of key user as a collaboration channel is defined and established. The key user is able to provide one on one support for the elevator projects. Also the management activities are improved through the application of process workflow by following criteria for each project milestone. The development shows effectiveness of product structure management in product lifecycle, improved production process by eliminating barriers (e.g. improvement of two-way communication) during design phase and production phase. The key user role is applicable on a global scale in the company.

The role of PPARgamma in cartilage growth and development using cartilage-specific PPARgamma knockout mice

Le cartilage est un tissu conjonctif composé d’une seule sorte de cellule nommée chondrocytes. Ce tissu offre une fondation pour la formation des os. Les os longs se développent par l'ossification endochondral. Ce processus implique la coordination entre la prolifération, la différenciation et l'apoptose des chondrocytes, et résulte au remplacement du cartilage par l'os. Des anomalies au niveau du squelette et des défauts liés à l’âge tels que l’arthrose (OA) apparaissent lorsqu’il y a une perturbation dans l’équilibre du processus de développement. À ce jour, les mécanismes exacts contrôlant la fonction et le comportement des chondrocytes pendant la croissance et le développement du cartilage sont inconnus. Le récepteur activateur de la prolifération des peroxysomes (PPAR) gamma est un facteur de transcription impliqué dans l'homéostasie des lipides. Plus récemment, son implication a aussi été suggérée dans l'homéostasie osseuse. Cependant, le rôle de PPARγ in vivo dans la croissance et le développement du cartilage est inconnu. Donc, pour la première fois, cette étude examine le rôle spécifique de PPARγ in vivo dans la croissance et le développement du cartilage. Les souris utilisées pour l’étude avaient une délétion conditionnelle au cartilage du gène PPARγ. Ces dernières ont été générées en employant le système LoxP/Cre. Les analyses des souris ayant une délétion au PPARγ aux stades embryonnaire et adulte démontrent une réduction de la croissance des os longs, une diminution des dépôts de calcium dans l’os, de la densité osseuse et de la vascularisation, un délai dans l’ossification primaire et secondaire, une diminution cellulaire, une perte d’organisation colonnaire et une diminution des zones hypertrophiques, une désorganisation des plaques de croissance et des chondrocytes déformés. De plus, la prolifération et la différenciation des chondrocytes sont anormales. Les chondrocytes et les explants isolés du cartilage mutant démontrent une expression réduite du facteur de croissance endothélial vasculaire (VEGF)-A et des éléments de production de la matrice extracellulaire. Une augmentation de l’expression de la métalloprotéinase matricielle (MMP)-13 est aussi observée. Dans les souris âgées ayant une délétion au PPARγ, y est aussi noté des phénotypes qui ressemblent à ceux de l’OA tel que la dégradation du cartilage et l'inflammation de la membrane synoviale, ainsi qu’une augmentation de l’expression de MMP-13 et des néoépitopes générés par les MMPs. Nos résultats démontrent que le PPARγ est nécessaire pour le développement et l’homéostasie du squelette. PPARγ est un régulateur essentiel pour la physiologie du cartilage durant les stades de croissance, de développement et de vieillissement.

MA167exam00pdf

Exam questions and solutions in PDF

MA167exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

Leontief Model Analysis with Fuzzy Parameters by Basic Matrixes Method

The basic matrixes method is suggested for the Leontief model analysis (LM) with some of its components indistinctly given. LM can be construed as a forecast task of product’s expenses-output on the basis of the known statistic information at indistinctly given several elements’ meanings of technological matrix, restriction vector and variables’ limits. Elements of technological matrix, right parts of restriction vector LM can occur as functions of some arguments. In this case the task’s dynamic analog occurs. LM essential complication lies in inclusion of variables restriction and criterion function in it.

An Iterative Method for the Matrix Principal n-th Root

In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.