Evolving a predator–prey ecosystem of mathematical expressions with grammatical evolution

This article describes the use of grammatical evolution to obtain a predator–prey ecosystem of artificial beings associated with mathematical functions, whose fitness is also defined mathematically. The system supports the simultaneous evolution of several ecological niches and through the use of standard measurements, makes it possible to explore the influence of the number of niches and the values of several parameters on “biological” diversity and similar functions. Sensitivity analysis tests have been made to find the effect of assigning different constant values to the genetic parameters that rule the evolution of the system and the predator–prey interaction or of replacing them by functions of time. One of the parameters (predator efficiency) was found to have a critical range, outside which the ecologies are unstable; two others (genetic shortening rate and predator–prey fitness comparison logistic amplitude) are critical just at one side of the range), the others are not critical. The system seems quite robust, even when one or more parameters are made variable during a single experiment, without leaving their critical ranges. Our results also suggest that some of the features of biological evolution depend more on the genetic substrate and natural selection than on the actual phenotypic expression of that substrate. © 2014 Wiley Periodicals, Inc. Complexity 20: 66–83, 2015     

Information Management,Organization and Managerial Effectiveness

In this paper we argue that information management is not only about managing the information resources of an organization as an economic activity; it is also about the use that individuals make of their information inputs and outputs. The discussion centres on individual managers, particularly on how successful they are in converting information into effective action. The management of complexity is seen as the cornerstone of managerial activities; managers are always faced with the problem of matching their limited information-processing capacity to the much larger information space implied by their responsibilities and commitments. It is argued that managers can employ at least three possible strategies to achieve an adequate matching: they can make adjustments to the organization structure; they can design their organizational conversations; and they can aim at a good manager-to-task fit.     

Bifurcations of the Hamiltonian Fourfold 1:1 Resonance with Toroidal Symmetry

This paper deals with the analysis of Hamiltonian Hopf as well as saddle-center bifurcations in 4-DOF systems defined by perturbed isotropic oscillators (1:1:1:1 resonance), in the presence of two quadratic symmetries Ξ and L ₁. When we normalize the system with respect to the quadratic part of the energy and carry out a reduction with respect to a three-torus group we end up with a 1-DOF system with several parameters on the thrice reduced phase space. Then, we focus our analysis on the evolution of relative equilibria around singular points of this reduced phase space. In particular, dealing with the Hamiltonian Hopf bifurcation the ‘geometric approach’ is used, following the steps set up by one of the authors in the context of 3-DOF systems. In order to see the interplay between integrals and physical parameters in the analysis of bifurcations, we consider as a perturbation a one-parameter family, which in particular includes one of the classical Stark–Zeeman models (parallel case) in three dimensions.     

Biologically guided intensity modulated radiation therapy planning optimization with fraction-size dose constraints

Although intensity modulated radiation therapy plans are optimized as a single overall treatment plan, they are delivered over 30–50 treatment sessions (fractions) and both cumulative and per-fraction dose constraints apply. Recent advances in imaging technology provide more insight on tumour biology that has been traditionally disregarded in planning. The current practice of delivering physical dose distributions across the tumour may potentially be improved by dose distributions guided by the biological responses of the tumour points. The biological optimization models developed and tested in this paper generate treatment plans reacting to the tumour biology prior to the treatment as well as the changing tumour biology throughout the treatment while satisfying both cumulative and fraction-size dose limits. Complete computational testing of the proposed methods would require an array of clinical data sets with tumour biology information. Finding no open source ones in the literature, the authors sought proof of concept by testing on a simulated head-and-neck case adapted from a more standard one in the CERR library by blending it with available tumour biology data from a published study. The results show computed biologically optimized plans improve on tumour control obtained by traditional plans ignoring biology, and that such improvements persist under likely uncertainty in sensitivity values. Furthermore, adaptive plans using biological information improve on non-adaptive methods.     

Constraints on the fundamental topological parameters of spatial tessellations

Tessellations of that use convex polyhedral cells to fill the space can be extremely complicated, especially if they are not “facet‐to‐facet”, that is, if the facets of a cell do not necessarily coincide with the facets of that cell's neighbours. In a recent paper 15 , we have developed a theory which covers these complicated cases, at least with respect to their combinatorial topology. The theory required seven parameters, three of which suffice for facet‐to‐facet cases; the remaining four parameters are needed for the awkward adjacency concepts that arise in the general case. This current paper establishes constraints that apply to these seven parameters and so defines a permissible region within their seven‐dimensional space, a region which we discover is not bounded. Our constraints in the relatively simple facet‐to‐facet case are also new.     

Structural and functional growth in self‐reproducing cellular automata

In this article, we analyze the dynamics of change in two‐dimensional self‐reproducers, identifying the processes that drive their evolution. We show that changes in self‐reproducers structure and behavior depend on their genetic memory. This consists of distinct yet interlinked components determining their form and function. In some cases these components degrade gracefully, changing only slightly; in others the changes destroy the original structure and function of the self‐reproducer. We sketch these processes at the genotype and the phenotype level—showing that they follow distinct trajectories within mutation space and quantifying the degree of change produced by different trajectories. We show that changes in structure and behavior depend on the interplay between the genotype and the phenotype. This determines universal structures, from which it is possible to construct a great number of self‐reproducing systems, as we observe in biology. Creative processes of change produce divergent and/or convergent methods for the generation of self‐reproducers. Divergence involves the creation of completely new information convergence involves local change and specialization of the structures concerned. © 2006 Wiley Periodicals, Inc. Complexity 11: 12–29, 2006     

Phase-field models for fluid mixtures

The paper investigates the modelling of phase transitions in multiphase fluid mixtures. The order parameter is identified with the set of concentrations and is a phase field in that it varies smoothly in the space region. This in turn requires that the continuity equations be regarded as constraints on the pertinent fields. The phase field is viewed as an internal variable whose evolution is subject to thermodynamic requirements. The second law allows for an extra entropy flux which proves to be proportional to the time derivative of the order parameter. Previous papers on the subject are revisited. It follows that their recourse to external mass supplies or to ad-hoc entropy fluxes can be avoided. The analogy of the phase-field model, with that of mixtures with mass–density gradients and extra entropy flux, is emphasized.     

The geometrical interpretation of uncertainty relation in Minkowski space

Clifford algebraic geometry corresponds to Minkowski space. Using the discrete structure of Minkowski space, we can abstract a class n-dimensional hyperbolic Hilbert phase space. To discussing the causality of physical event in Minkowski space, we can obtain the geometrical interpretation of uncertainty relation.     

Dynamical systems which realize given random bi-sequences of points on their orbits

A dynamical system consists of a phase space of possible states, together with an evolution rule that determines all future states and all past states given a state at any particular moment. In this paper, we show that for any countable random infinite bi-sequences of states of some phase space, there exists an evolution rule in C⁰-topology which realizes precisely the given sequences of states on their orbits and satisfies some regular conditions on the times to realize the states.     

DYNAMICS OF SPATIAL EXPLOITATION: A METAPOPULATION APPROACH

ABSTRACT. In this paper we present a bioeconomic model of a harvesting industry operating over a heterogeneous environment comprised of discrete biological populations interconnected by dispersal processes. The model generalizes the Gordon [1954]/Smith [1968] model of open-access rent dissipation by accounting for intertemporal and spatial “Ricardian” patterns of exploitation. This model yields a simple, but insightful, framework from which one can investigate factors that contribute to the evolution of resource exploitation patterns over space and time. For example, we find that exploitation patterns are driven by biological and fleet dispersal and biological and economic heterogeneity. We conclude that one cannot really understand the biological processes operating in an exploited system without knowing as much about the harvesting system as about the biological system.     

An assessment of a days off decomposition approach to personnel shift scheduling

This paper studies a two-phase decomposition approach to solving the personnel scheduling problem. The first phase creates a days-off-schedule, indicating working days and days off for each employee. The second phase assigns shifts to the working days in the days-off-schedule. This decomposition is motivated by the fact that personnel scheduling constraints are often divided into two categories: one specifies constraints on working days and days off, while the other specifies constraints on shift assignments. To assess the consequences of the decomposition approach, we apply it to public benchmark instances, and compare this to solving the personnel scheduling problem directly. In all steps we use mathematical programming. We also study the extension that includes night shifts in the first phase of the decomposition. We present a detailed results analysis, and analyze the effect of various instance parameters on the decompositions’ results. In general, we observe that the decompositions significantly reduce the computation time, but the quality, though often good, depends strongly on the instance at hand. Our analysis identifies which aspects in the instance can jeopardize the quality.     

A set oriented definition of finite-time Lyapunov exponents and coherent sets

The problem of phase space transport, which is of interest from both the theoretical and practical point of view, has been investigated extensively using geometric and probabilistic methods. Two important tools to study this problem that have emerged in recent years are finite-time Lyapunov exponents (FTLE) and the Perron–Frobenius operator. The FTLE measures the averaged local stretching around reference trajectories. Regions with high stretching are used to identify phase space transport barriers. One probabilistic method is to consider the spectrum of the Perron–Frobenius operator of the flow to identify almost-invariant densities. These almost-invariant densities are used to identify almost invariant sets. In this paper, a set-oriented definition of the FTLE is proposed which is applicable to phase space sets of finite size and reduces to the usual definition of FTLE in the limit of infinitesimal phase space elements. This definition offers a straightforward connection between the evolution of probability densities and finite-time stretching experienced by phase space curves. This definition also addresses some concerns with the standard computation of the FTLE. For the case of autonomous and periodic vector fields we provide a simplified method to calculate the set-oriented FTLE using the Perron–Frobenius operator. Based on the new definition of the FTLE we propose a simple definition of finite-time coherent sets applicable to vector fields of general time-dependence, which are the analogues of almost-invariant sets in autonomous and time-periodic vector fields. The coherent sets we identify will necessarily be separated from one another by ridges of high FTLE, providing a link between the framework of coherent sets and that of codimension one Lagrangian coherent structures. Our identification of coherent sets is applied to three examples.     

Modeling and simulation of cell populations interaction

Regenerative medicine and cell therapy provide great hopes for the use of adult and stem cells. The latter are far less present in tissue than the former and must be expanded using cell culture. Stem cells culture requires the conservation of their proliferation and self-renewal capabilities. Still, the complex interaction between cell populations, for example in primary cell cultures, are not well-known and may account for part of the variability of such cultures. In order to represent and understand the evolution of cultured stem cells, we present here a mathematical model of cell proliferation and differentiation. Based on the formalism of cellular automata, this model simulates the evolution of several cell classes (which may represent either different levels of differentiation or different cell types) in an environment modeling the growth medium. We model the cell cycle as on the one hand a quiescence phase during which a cell rests, and on the other hand a division phase during which the cell starts the division process. In order to represent cell–cell interaction, the transition probability between those phases depends on the local composition of the growth medium depending itself on neighboring cells. An interaction between cellular populations is represented by a quantitative parameter which has a direct impact on cellular proliferation. Differentiation results in a change of the cell class and depends on the biological model studied : it may result from an asymmetric division or be a consequence of the local composition of the growth medium. This mathematical model aims at a better understanding of the interactions between cell populations in a culture. By defining constraints on the potential or the type of the cells at the end of a culture, it will then be possible to find optimal experimental conditions for cell production.     

Evolution equations,singular dispersion relations,and moving eigenvalues

A new approach for finding the class of integrable evolution equations associated with a given eigenvalue problem is developed. The key point to note is that the squares of the eigenfunctions form a natural basis in which to expand the solutions of the evolution equation. Once this step is taken, the class of integrable equations may usually be read off by inspection. Of particular interest are those equations for which the bound state eigenvalues are not invariant but move in a way prescribed by the coefficients of the evolution equation. The corresponding solitons have the property that they retain their identity on collision with other solution components, but this identity is no longer a constant one. The Hamiltonian structure and the causality properties of these systems are also explored.     

Conic mixed-integer rounding cuts

A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures of second-order conic sets. These cuts can be readily incorporated in branch-and-bound algorithms that solve either second-order conic programming or linear programming relaxations of conic integer programs at the nodes of the branch-and-bound tree. Central to our approach is a reformulation of the second-order conic constraints with polyhedral second-order conic constraints in a higher dimensional space. In this representation the cuts we develop are linear, even though they are nonlinear in the original space of variables. This feature leads to a computationally efficient implementation of nonlinear cuts for conic mixed-integer programming. The reformulation also allows the use of polyhedral methods for conic integer programming. We report computational results on solving unstructured second-order conic mixed-integer problems as well as mean–variance capital budgeting problems and least-squares estimation problems with binary inputs. Our computational experiments show that conic mixed-integer rounding cuts are very effective in reducing the integrality gap of continuous relaxations of conic mixed-integer programs and, hence, improving their solvability. This research has been supported, in part, by Grant # DMI0700203 from the National Science Foundation.     

Constrained Optimization: Projected Gradient Flows

We consider a dynamical system approach to solve finite-dimensional smooth optimization problems with a compact and connected feasible set. In fact, by the well-known technique of equalizing inequality constraints using quadratic slack variables, we transform a general optimization problem into an associated problem without inequality constraints in a higher-dimensional space. We compute the projected gradient for the latter problem and consider its projection on the feasible set in the original, lower-dimensional space. In this way, we obtain an ordinary differential equation in the original variables, which is specially adapted to treat inequality constraints (for the idea, see Jongen and Stein, Frontiers in Global Optimization, pp. 223–236, Kluwer Academic, Dordrecht, 2003). The article shows that the derived ordinary differential equation possesses the basic properties which make it appropriate to solve the underlying optimization problem: the longtime behavior of its trajectories becomes stationary, all singularities are critical points, and the stable singularities are exactly the local minima. Finally, we sketch two numerical methods based on our approach.     

Construction of the viability kernel for a generalized dynamical system

The problem of the approximate construction of the viability kernel for a generalized dynamical system, the evolution of which is specified directly by an attainability set, is investigated under phase constraints. A backward grid method, based on the substitution of the phase space by pixels and a consideration of “inverse” attainability sets, is proposed. The convergence of the method is proved.     

Comparison of two variances under inequality constraints by using empirical likelihood method

In this article, the empirical likelihood introduced by Owen Biometrika, 75, 237-249 （1988） is applied to test the variances of two populations under inequality constraints on the parameter space. One reason that we do the research is because many literatures in this area are limited to testing the mean of one population or means of more than one populations; the other but much more important reason is： even if two or more populations are considered, the parameter space is always without constraint. In reality, parameter space with some kind of constraints can be met everywhere. Nuisance parameter is unavoidable in this case and makes the estimators unstable. Therefore the analysis on it becomes rather complicated. We focus our work on the relatively complicated testing issue over two variances under inequality constraints, leaving the issue over two means to be its simple ratiocination. We prove that the limiting distribution of the empirical likelihood ratio test statistic is either a single chi-square distribution or the mixture of two equally weighted chi-square distributions.     

Linearly constrained reconstruction of functions by kernels with applications to machine learning

This paper investigates the approximation of multivariate functions from data via linear combinations of translates of a positive definite kernel from a reproducing kernel Hilbert space. If standard interpolation conditions are relaxed by Chebyshev-type constraints, one can minimize the norm of the approximant in the Hilbert space under these constraints. By standard arguments of optimization theory, the solutions will take a simple form, based on the data related to the active constraints, called support vectors in the context of machine learning. The corresponding quadratic programming problems are investigated to some extent. Using monotonicity results concerning the Hilbert space norm, iterative techniques based on small quadratic subproblems on active sets are shown to be finite, even if they drop part of their previous information and even if they are used for infinite data, e.g., in the context of online learning. Numerical experiments confirm the theoretical results. Dedicated to C.A. Micchelli at the occasion of his 60th birthday Mathematics subject classifications (2000) 65D05, 65D10, 41A15, 41A17, 41A27, 41A30, 41A40, 41A63.