Applied Mathematics and Computational Science

Abstract. Soft-cardinality spectra (SC spectra) is a new method of approximation for text strings in linear time, which divides text strings into character q-grams of different sizes. The method allows simultaneous use of weighting at term and q-gram levels. SC spectra in combination with resemblance coefficients allows the construction of a family of text similarity functions that only use the surface information of the texts and weights obtained in the same text collection. These similarity measures can be used in various tasks of natural ...

We propose an infeasible interior proximal method for solving variational inequality problems with maximal monotone operators and linear constraints. The interior proximal method proposed by Auslender, Teboulle and Ben-Tiba [3] is a proximal method using a distance-like barrier function and it has a global convergence property under mild assumptions. However, this method is applicable only to problems whose feasible region has nonempty interior. The algorithm we propose is applicable to problems whose feasible region may have empty interior. Moreover, a new kind of inexact scheme is used. We present a full convergence analysis for our algorithm. Mathematical subject classification: 90C51, 65K10, 47J20, 49J40, 49J52, 49J53.

... a Department of Basic Science, Benha Higher Institute of Technology, Benha University 13512, Egypt. b Department of Engineering Mathematics and Physics, Faculty of Engineering, CairoUniversity, Giza-Egypt. Received 1 March 2006; revised 3 May 2006. ...

In this paper we introduce COV, a novel information retrieval (IR) algorithm for massive databases based on vector space modeling and spectral analysis of the covariance matrix, for the document vectors, to reduce the scale of the problem. Since the dimension of the covariance matrix depends on the attribute space and is independent of the number of documents, COV can be applied to databases that are too massive for methods based on the singular value decomposition of the document-attribute matrix, such as latent semantic indexing (LSI). In addition to improved scalability, theoretical considerations indicate that results from our algorithm tend to be more accurate than those from LSI, particularly in detecting subtle differences in document vectors. We demonstrate the power and accuracy of COV through an important topic in data mining, known as outlier cluster detection. We propose two new algorithms for detecting major and outlier clusters in databases—the first is based on LSI, and the second on COV. Our implementation studies indicate that our cluster detection algorithms outperform the basic LSI and COV algorithm in detecting outlier clusters.

Emphasis of the study is to empirically analyze the impacts of macroeconomic variables on economic growth in case of some selected Asian countries. For this purpose annual data is taken from 1990 to 2010. It is a panel data analysis and by estimating the model it is found that in case of the sample countries economic growth is positively affected by foreign direct investment and saving rate while exports in the sample period have negative impacts on economic growth and labor force and tax rate have no impacts on economic growth.

Dynamically changing background ("dynamic background") still presents a great challenge to many motion-based video surveillance systems. In the context of event detection, it is a major source of false alarms. There is a strong need from the security industry either to detect and suppress these false alarms, or dampen the effects of background changes, so as to increase the sensitivity to meaningful events of interest. In this paper, we restrict our focus to one of the most common causes of dynamic background changes: that of swaying tree branches and their shadows under windy conditions. Considering the ultimate goal in a video analytics pipeline, we formulate a new dynamic background detection problem as a signal processing alternative to the previously described but unreliable computer vision-based approaches. Within this new framework, we directly reduce the number of false alarms by testing if the detected events are due to characteristic background motions. In addition, we introduce a new dataset suitable for the evaluation of dynamic background detection. It consists of real-world events detected by a commercial surveillance system from two static surveillance cameras. The research question we address is whether dynamic background can be detected reliably and efficiently using simple motion features and in the presence of similar but meaningful events such as loitering. Inspired by the tree aerodynamics theory, we propose a novel method named local variation persistence (LVP), that captures the key characteristics of swaying motions. The method is posed as a convex optimization problem whose variable is the local variation. We derive a computationally efficient algorithm for solving the optimization problem, the solution of which is then used to form a powerful detection statistic. On our newly collected dataset, we demonstrate that the proposed LVP achieves excellent detection results and outperforms the best alternative adapted from existing art in the dynamic background literature.

In this work, we introduce an algebraic operation between bounded Hessenberg matrices and we analyze some of its properties. We call this operation mm-sum and we obtain an expression for it that involves the Cholesky factorization of the corresponding Hermitian positive definite matrices associated with the Hessenberg components.This work extends a method to obtain the Hessenberg matrix of the sum of measures from the Hessenberg matrices of the individual measures, introduced recently by the authors for subnormal matrices, to matrices which are not necessarily subnormal.Moreover, we give some examples and we obtain the explicit formula for the mm-sum of a weighted shift. In particular, we construct an interesting example: a subnormal Hessenberg matrix obtained as the mm-sum of two not subnormal Hessenberg matrices.► We introduce an algebraic operation, mm-sum, between bounded Hessenberg matrices. ► The mm-sum is obtained from sums of Hermitian positive definite matrices associated. ► The mm-sum expression involves the Cholesky factors of the associated HPD matrices. ► We analyze some properties of the mm-sum as subnormality or hyponormality. ► We obtain the explicit formula for the mm-sum of a weighted shift.

The large claims reinsurance treaties ECOMOR and LCR are well known not to be very popular. They have been largely neglected by most reinsurers because of their technical complexity. In this paper, we derive new mathematical results connected to asymptotic problems of these reinsurance forms. Perhaps these results can reopen the discussion on the usefulness of including the largest claims

In this paper, we have combined the ideas of the False Position (FP) and Artificial Bee Colony (ABC) algorithms to find a fast and novel method for solving nonlinear equations. Additionally, to illustrate the efficiency of the proposed method, several benchmark functions are solved and compared with other methods such as ABC, PSO and GA.

This chapter is devoted to introducing the theories of interval algebra to people who are interested in applying the interval methods to uncertainty analysis in science and engineering. In view of this purpose, we shall introduce the key concepts of the algebraic theories of intervals that form the foundations of the interval techniques as they are now practised, provide a historical and epistemological background of interval mathematics and uncertainty in science and technology, and finally describe some typical applications that clarify the need for interval computations to cope with uncertainty in a wide variety of scientific disciplines.

Keywords. Interval mathematics, Uncertainty, Quantitative Knowledge, Reliability, Complex interval arithmetic, Machine interval arithmetic, Interval automatic differentiation, Computer graphics, Ray tracing, Interval root isolation.

Recommended Citation:

Hend Dawood. Interval Mathematics as a Potential Weapon against Uncertainty. In S. Chakraverty, editor, Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems. chapter 1, pages 1-38. IGI Global, Hershey, PA, 2014. ISBN 978-1-4666-4991-0.

The final publication is available at IGI Global via http://dx.doi.org/10.4018/978-1-4666-4991-0.ch001

The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the
field of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is
a three-dimensional phenomenon.