Recent trends in random number and random vector generation

A survey of recent work in the areas of uniform pseudorandom number and uniform pseudorandom vector generation is presented. The emphasis is on methods for which a detailed theory is available. A progress report on the construction of quasirandom points for efficient multidimensional numerical integration is also given.     

Recent trends in infant mortality in China [abstract

The China 1988 Two per Thousand Survey data on infant mortality are evaluated for validity as far back as the 1950s. Existing data available from official statistics of registration and census materials have been found to be inadequate for the coverage between the 1950s and 1980. The conclusion is that the 2 per 1000 data are valid for the study of the pace, distribution, and causes of the decline of infant mortality in China between the 1950s and 1988. The sample of more than 500,000 women included 2 ever-married women aged 15-57 years for every 1000 population and their pregnancy histories by province. The data are considered suitable for multivariate analysis and time-series analysis. Validity is examine for omitted events and misplaced events and age selectivity. Data analysis shows that infant mortality declined at a different pace across provinces. The result of the Great Leap Forward and the associated famine was great excess infant mortality in general, which occurred in only some provinces. The age pattern of infant mortality shows an upward concave pattern, which also varies across provinces. The sex differences in mortality vary across provinces, and the potential meaning is discussed. Analysis indicates that the declines in infant mortality occurred before the early 1970s and consequently before substantial economic development. These economic conditions and infant mortality decline have occurred in China and in Cuba.     

A reverse engineering approach to the Weil representation

We describe a new approach to the Weil representation attached to a symplectic group over a finite or a local field. We dissect the representation into small pieces, study how they work, and put them back together. This way, we obtain a reversed construction of that of T. Thomas, skipping most of the literature on which the latter is based.     

Database reverse engineering: From requirements to CARE tools

This paper analyzes the requirements that CASE tools should meet for effective database reverse engineering (DBRE), and proposes a general architecture for data-centered applications reverse engineering CASE environments. First, the paper describes a generic DBMS-independent DBRE methodology, then it analyzes the main characteristics of DBRE activities in order to collect a set of desirable requirements. Finally, it describes DB-MAIN, an operational CASE tool developed according to these requirements. The main features of this tool that are described in this paper are its unique generic specification model, its repository, its transformation toolkit, its user interface, the text processors, the assistants, the methodological control and its functional extensibility. Finally, the paper describes five real-world projects in which the methodology and the CASE tool were applied. This is a heavily revised and extended version of “Requirements for Information System Reverse Engineering Support” by J.-L. Hainaut, V. Englebert, J. Henrard, J.-M. Hick, D. Roland, which first appeared in the Proceedings of the Second Working Conference on Reverse Engineering, IEEE Computer Society Press, pp. 136–145, July 1995. This paper presents some results of the DB-MAIN project. This project is partially supported by the Région Wallonne, the European Union, and by a consortium comprising ACEC-OSI (Be), ARIANE-II (Be), Banque UCL (Lux), BBL (Be), Centre de recherche public H. Tudor (Lux), CGER (Be), Cockerill-Sambre (Be), CONCIS (Fr), D'Ieteren (Be), DIGITAL, EDF (Fr), EPFL (CH), Groupe S (Be), IBM, OBLOG Software (Port), ORIGIN (Be), Ville de Namur (Be), Winterthur (Be), 3 Suisses (Be). The DB-Process subproject is supported by the Communauté Fran?aise de Belgique.     

Strongest postcondition semantics as the formal basis for reverse engineering

Reverse engineering of program code is the process of constructing a higher level abstraction of an implementation in order to facilitate the understanding of a system that may be in a “legacy” or “geriatric” state. Changing architectures and improvements in programming methods, including formal methods in software development and object-oriented programming, have prompted a need to reverse engineer and re-engineer program code. This paper describes the application of the strongest postcondition predicate transformer (sp) as the formal basis for the reverse engineering of imperative program code. This work is supported in part by the National Science Foundation grants CCR-9407318, CCR-9209873, and CDA-9312389. This author is supported in part by a NASA Graduate Student Researchers Program Fellowship.     

An integer optimization approach for reverse engineering of gene regulatory networks

Gene regulatory networks are a common tool to describe the chemical interactions between genes in a living cell. This paper considers the Weighted Gene Regulatory Network (WGRN) problem, which consists in identifying a reduced set of interesting candidate regulatory elements which can explain the expression of all other genes. We provide an integer programming formulation based on a graph model and derive from it a branch-and-bound algorithm which exploits the Lagrangian relaxation of suitable constraints. This allows to determine lower bounds tighter than CPLEX on most benchmark instances, with the exception of the sparser ones. In order to determine feasible solutions for the problem, which appears to be a hard task for general-purpose solvers, we also develop and compare two metaheuristic approaches, namely a Tabu Search and a Variable Neighborhood Search algorithm. The experiments performed on both of them suggest that diversification is a key feature to solve the problem.     

A survey: Recent results,conjectures, and open problems in labeling graphs

In this paper we organize and summarize much of the work done on graceful and harmonious labelings of graphs. Many open problems and conjectures are included.     

Recent optimization models and trends in location,relocation, and dispatching of emergency medical vehicles

Over the past 10 years, a considerable amount of research has been devoted to the development of models to support decision making in the particular yet important context of Emergency Medical Services (EMS). More specifically, the need for advanced strategies to take into account the uncertainty and dynamism inherent to EMS, as well as the pertinence of socially oriented objectives, such as equity, and patient medical outcomes, have brought new and exciting challenges to the field. In this context, this paper summarizes and discusses modern modeling approaches to address problems related to ambulance fleet management, particularly those related to vehicle location and relocation, as well as dispatching decisions. Although it reviews early works on static ambulance location problems, this review concentrates on recent approaches to address tactical and operational decisions, and the interaction between these two types of decisions. Finally, it concludes on the current state of the art and identifies promising research avenues in the field.     

Modelling issues of a holistic finite element approach in the virtual engineering design process

In the paper methods for the coupling of different meshed local domains of a product model, which occur in an adaptivity process are compared. The properties of the applied coupling methods are demonstrated on finite element models from structural mechanics to point out the advantages and disadvantages of the methods in a model adaptivity process in the field of automotive engineering. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Domination in a digraph and in its reverse

Let D be a digraph. By γ(D) we denote the domintaion number of D and by D⁻ we denote a digraph obtained by reversing all the arcs of D. In this paper we prove that for every δ≥3 and k≥1 there exists a simple strongly connected δ-regular digraph D_δ,k such that . Analogous theorem is obtained for total domination number provided that δ≥4.     

Derived sequences and reverse mathematics

One of the earliest applications of transfinite numbers is in the construction of derived sequences by Cantor [2]. In [6], the existence of derived sequences for countable closed sets is proved in ATR₀. This existence theorem is an intermediate step in a proof that a statement concerning topological comparability is equivalent to ATR₀. In actuality, the full strength of ATR₀ is used in proving the existence theorem. To show this, we will derive a statement known to be equivalent to ATR₀, using only RCA₀ and the assertion that every countable closed set has a derived sequence. We will use three of the subsystems of second order arithmetic defined by H. Friedman ([3], [4]), which can be roughly characterized by the strength of their set comprehension axioms. RCA₀ includes comprehension for Δ definable sets, ACA₀ includes comprehension for arithmetical sets, and ATR₀ appends to ACA₀ a comprehension scheme for sets defined by transfinite recursion on arithmetical formulas. MSC: 03F35, 54B99.     

Pincherle's theorem in reverse mathematics and computability theory

We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first ‘local-to-global’ principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms are necessary to prove Pincherle's theorem, does not have an unique or unambiguous answer, in contrast to compactness. We establish similar differences for the computational properties of compactness and Pincherle's theorem. We establish the same differences for other local-to-global principles, even going back to Weierstrass. We also greatly sharpen the known computational power of compactness, for the most shared with Pincherle's theorem however. Finally, countable choice plays an important role in the previous, we therefore study this axiom together with the intimately related Lindelöf lemma.