Structure of weak Descartes systems

A weak Descartes system is a basis of functions such that every ordered subset is a weak Tchebycheff system, the canonical example being the usual spline basis involving truncated power functions. By examining the intervals of degeneracy for a WD-system, we show that it is possible to produce a new basis that has a simple and convenient structure similar to the spline basis.     

Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials

We give a Descartes’-like bound on the number of positive solutions to a system of fewnomials that holds when its exponent vectors are not in convex position and a sign condition is satisfied. This was discovered while developing algorithms and software for computing the Gale transform of a fewnomial system, which is our main goal. This software is a component of a package we are developing for Khovanskii-Rolle continuation, which is a numerical algorithm to compute the real solutions to a system of fewnomials.     

The nucleolus of a standard tree game revisited: a study of its monotonicity and computational properties

This paper introduces yet another algorithm to compute the nucleolus of a standard tree game. One advantage of this algorithm is that it provides a very intuitive interpretation of the nucleolus, under which the players participate in a joint enterprize in which each group sends a member to help the community. Another advantage is that it demonstrates monotonicity properties of the nucleolus within this class of games. As a consequence the nucleolus of a tree game can be extended to a population monotonic allocation scheme.     

The relevance of system dynamics to engineering systems design

With the recent advent of new technology using micro computers for the centralised monitoring of information, the scope for totally automatic, real time control of large engineering systems has been advanced. We are entering a period which, retrospectively, may well be seen as the era of control; where for the first time it is both feasible and necessary to design system in terms of the way in which they will be operated, as well as in the traditional terms of their capacity requirements. However, before such comprehensive design can be undertaken compatible advances are required in information usage technology.The purpose of this paper is to demonstrate how the subject of System Dynamics can be used to assist with this problem, though its capacity to model information feedback and hence to model and test alternative system control rules based on the information retrieved. This type of application in the hard system area of engineering provides a strong contrast to the more usual applications of System Dynamics in softer socio-economic systems.The problem described is taken from the coal mining industry and related to the design of large scale underground conveyor belt systems used for the clearance of coal from mines. The demonstration presented, therefore, concerns research in this field, but has considerable scope for application in the general area of large scale bulk handling system.Of particular importance in the results is an indication of the potential savings in physical capacity which can stem from the careful design and implementation of control in such systems.     

The history and ideas of Marxism: the relevance for OR

Journal of the Operational Research Society - The paper examines the origins of Marxism in Europe in the second half of the 19th century in the context of the industrial and political revolutions...     

Descartes and the birth of analytic geometry

The traditional thesis that analytic geometry evolved from the concepts of axes of reference, co-ordinates, and loci, is rejected. The origins of this science are re-defined in terms of Egyptian, Greek, Babylonian, and Arabic influences merging in Vieta's Isagoge in artem analyticam (1591) and culminating in a work of his pupil Ghetaldi published posthumously in 1630. Descartes' Vera mathesis, conceived over a decade earlier, served to revive and strengthen the important link with logic and thereby to extend the field of application of this analytic method to the corporeal and moral worlds.     

The Conley conjecture for Hamiltonian systems on the cotangent bundle and its analogue for Lagrangian systems

In this paper, the Conley conjecture, which was recently proved by Franks and Handel [J. Franks, M. Handel, Periodic points of Hamiltonian surface diffeomorphism, Geom. Topol. 7 (2003) 713-756] (for surfaces of positive genus), Hingston [N. Hingston, Subharmonic solutions of Hamiltonian equations on tori, Ann. Math., in press] (for tori) and Ginzburg [V.L. Ginzburg, The Conley conjecture, arXiv: math.SG/0610956v1] (for closed symplectically aspherical manifolds), is proved for C¹-Hamiltonian systems on the cotangent bundle of a C³-smooth compact manifold M without boundary, of a time 1-periodic C²-smooth Hamiltonian H:R×T^*M→R which is strongly convex and has quadratic growth on the fibers. Namely, we show that such a Hamiltonian system has an infinite sequence of contractible integral periodic solutions such that any one of them cannot be obtained from others by iterations. If H also satisfies H(−t,q,−p)=H(t,q,p) for any (t,q,p)∈R×T^*M, it is shown that the time-1-map of the Hamiltonian system (if exists) has infinitely many periodic points siting in the zero section of T^*M. If M is C⁵-smooth and dimM>1, H is of C⁴ class and independent of time t, then for any τ>0 the corresponding system has an infinite sequence of contractible periodic solutions of periods of integral multiple of τ such that any one of them cannot be obtained from others by iterations or rotations. These results are obtained by proving similar results for the Lagrangian system of the Fenchel transform of H, L:R×TM→R, which is proved to be strongly convex and to have quadratic growth in the velocities yet.     

Stochastic equations for complex systems

Book Reviews

Stochastic equations for complex systemsA. V. Skorohod: D. Reidel, Dordrecht, 1988     

The workshop on p-adic methods for modeling of complex systems

We present a brief information on “The Workshop on p-Adic Methods for Modeling of Complex Systems”, which was held in the Center for Interdisciplinary Research (Zentrum für interdisziplinäre Forshung — ZiF), Bielefeld University, Bielefeld, Germany, April 15–19, 2013.     

The coninvolutory decomposition and its computation for a complex matrix

A complex, square matrix E is called coninvolutory if EE = I, where E denotes complex conjugate of the matrix E and I is an identity matrix. In this paper we introduce the coninvolutory decomposition of a complex matrix and investigate a Newton iteration for computing the coninvolutory factor. A simple numerical example illustrates our results.     

GMDH algorithms for complex systems modelling

At present, GMDH algorithms give us a way to identify and forecast economic processes in the case of noised and short input sampling. In contrast to neural networks, the results are explicit mathematical models, obtained in a relatively short time. For ill-defined objects with very big noises, better results are obtained by analog complexing methods. Nets with active neurons should be applied to increase accuracy. Active neurons are able, during the self-organizing process, to estimate which inputs are necessary to minimize the given objective function of the neuron. In the neuronet with such neurons, we have a twofold multilayered structure: neurons themselves are multilayered, and they will be united into a multilayered network.

SelfOrganize! is an easy-to-use modelling tool which realizes twice-multilayered neu-ronets and enables the creation of time series, single input/single output, multi-input/single output and multi-input/multi-output systems (system of equations). Successful applications are shown in the field of analysis and prediction of characteristics of stock markets in financial risk control modelling.     

New architectures for constructed complex systems

This paper is an overview of our research program in intelligent systems. Our object of study is constructed complex systems, which are software and hardware systems mediated or managed by computers. We describe how biological systems provide stiff competition for constructed complex systems in the areas of autonomy and intelligence, robustness, adaptability, and communication. We describe our computationally reflective integration infrastructure, called ‘wrappings', and show how it can provide many of the necessary flexibilities. We also describe two directions of research in computational semiotics, which for us means the study of the use of symbols by computing systems. We describe our ‘conceptual categories', which are a method of knowledge representation that supports these flexibilities, and some new results on symbol systems, which leads to some new mathematical questions about what can be represented in formal systems and how they can be extended automatically. These are then combined to describe our architecture, which we are currently in the process of implementing.     

Generalized isochronous centers for complex systems

In this paper, the definition of generalized isochronous center is given in order to study unitedly real isochronous center and linearizability of polynomial differential systems. An algorithm to compute generalized period constants is obtained, which is a good method to find the necessary conditions of generalized isochronous center for any rational resonance ratio. Its two linear recursive formulas are symbolic and easy to realize with computer algebraic system. The function of time-angle difference is introduced to prove the sufficient conditions. As the application, a class of real cubic Kolmogorov system is investigated and the generalized isochronous center conditions of the origin are obtained.