A STATE‐SPACE MODEL FOR UNIVARIATE ORDINAL‐VALUED TIME SERIES

Abstract A state‐space model was developed to analyze a univariate time series of ordinal‐valued flower phenology data. Flower abundance, recorded as either “none,”“some,” or “much,” was observed each month on trees in a lowland Costa Rican rain forest to investigate flowering patterns of different species. Data from a single Capparis pittieri and daily rain measurements are used to demonstrate the model. A method to obtain maximum likelihood estimates of the parameters and the use of predicted probability differences to assess goodness of fit are described. Opportunities for improving the model are also discussed.     

Using self‐dissimilarity to quantify complexity

For many systems characterized as “complex” the patterns exhibited on different scales differ markedly from one another. For example, the biomass distribution in a human body “looks very different” depending on the scale at which one examines it. Conversely, the patterns at different scales in “simple” systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self‐dissimilarity between the patterns of a system at various scales constitute a complexity “signature” of that system. Here we present a novel quantification of self‐dissimilarity. This signature can, if desired, incorporate a novel information‐theoretic measure of the distance between probability distributions that we derive here. Whatever distance measure is chosen, our quantification of self‐dissimilarity can be measured for many kinds of real‐world data. This allows comparisons of the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. species densities in a rain forest vs. capital density in an economy, etc.). Moreover, in contrast to many other suggested complexity measures, evaluating the self‐dissimilarity of a system does not require one to already have a model of the system. These facts may allow self‐dissimilarity signatures to be used as the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self‐dissimilarity, we present several numerical experiments. In particular, we show that the underlying structure of the logistic map is picked out by the self‐dissimilarity signature of time series produced by that map. © 2007 Wiley Periodicals, Inc. Complexity 12: 77–85, 2007     

Numerical aspects of X‐SIMP‐based topology optimization

The discretization of topology design problems on the basis of the finite‐element‐method results in general in large‐scale combinatorial optimization problems, which are usually relaxed by the introduction of a continuous material density function as design variable. To avoid optimal designs containing unfavourable microstructures such as the well‐known “checkerboard” patterns, the relaxed problem can be regularized by the X‐SIMP‐approach, which penalizes intermediate density values as well as high density gradients within the design domain. In this context we discuss numerical aspects of the X‐SIMP‐based regularization such as the discretization of the regularized problem, the formulation of the corresponding stiffness matrix and the numerical solution of the discretized problem. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

ANALYSIS OF SENSITIVITY AND UNCERTAINTY IN AN INDIVIDUAL‐BASED MODEL OF A THREATENED WILDLIFE SPECIES

Sensitivity analysis—determination of how prediction variables affect response variables—of individual‐based models (IBMs) are few but important to the interpretation of model output. We present sensitivity analysis of a spatially explicit IBM (HexSim) of a threatened species, the Northern Spotted Owl (NSO; Strix occidentalis caurina) in Washington, USA. We explored sensitivity to HexSim variables representing habitat quality, movement, dispersal, and model architecture; previous NSO studies have well established sensitivity of model output to vital rate variation. We developed “normative” (expected) model settings from field studies, and then varied the values of ≥ 1 input parameter at a time by ±10% and ±50% of their normative values to determine influence on response variables of population size and trend. We determined time to population equilibration and dynamics of populations above and below carrying capacity. Recovery time from small population size to carrying capacity greatly exceeded decay time from an overpopulated condition, suggesting lag time required to repopulate newly available habitat. Response variables were most sensitive to input parameters of habitat quality which are well‐studied for this species and controllable by management. HexSim thus seems useful for evaluating potential NSO population responses to landscape patterns for which good empirical information is available.     

Spatio‐temporal Pattern Formation in Chemical Reactions

In our paper numerical simulations of chemical pattern in ionic reaction‐diffusion‐migration system assuming a “self‐consistent” electric field are presented. Chemical waves as well as stationary concentration pattern arise due to an interplay of an autocatalytic chemical reaction with transport processes. Concentration gradient inside the chemical pattern lead to electric diffusion‐potential which in turn affect the patterns. Thus, the model equations take the general form of the Fokker‐Planck equation.     

A MODEL OF CHINOOK SALMON POPULATION DYNAMICS INCORPORATING SIZE‐SELECTIVE EXPLOITATION AND INHERITANCE OF POLYGENIC CORRELATED TRAITS

Abstract Concern regarding the potential for selective fisheries to degrade desirable characteristics of exploited fish populations is growing worldwide. Although the occurrence of fishery‐induced evolution in a wild population has not been irrefutably documented, considerable theoretical and empirical evidence for that possibility exists. Environmental conditions influence survival and growth in many species and may mask comparatively subtle trends induced by selective exploitation, especially given the evolutionarily short time series of data available from many fisheries. Modeling may be the most efficient investigative tool under such conditions. Motivated by public concern that large‐mesh gillnet fisheries may be altering Chinook salmon in western Alaska, we constructed a stochastic model of the population dynamics of Chinook salmon. The model contained several individually based components and incorporated size‐selective exploitation, assortative mating, size‐dependent female fecundity, density‐dependent survival, and the heritability of size and age. Substantial reductions in mean size and age were observed under all scenarios. Concurrently reducing directional selection and increasing spawning abundance was most effective in stimulating population recovery. Use of this model has potential to improve our ability to investigate the consequences of selective exploitation and aid development of improved management strategies to more effectively sustain fish and fisheries into the future.     

Agent‐based computational models and generative social science

This article argues that the agent‐based computational model permits a distinctive approach to social science for which the term “generative” is suitable. In defending this terminology, features distinguishing the approach from both “inductive” and “deductive” science are given. Then, the following specific contributions to social science are discussed: The agent‐based computational model is a new tool for empirical research. It offers a natural environment for the study of connectionist phenomena in social science. Agent‐based modeling provides a powerful way to address certain enduring—and especially interdisciplinary—questions. It allows one to subject certain core theories—such as neoclassical microeconomics—to important types of stress (e.g., the effect of evolving preferences). It permits one to study how rules of individual behavior give rise—or “map up”—to macroscopic regularities and organizations. In turn, one can employ laboratory behavioral research findings to select among competing agent‐based (“bottom up”) models. The agent‐based approach may well have the important effect of decoupling individual rationality from macroscopic equilibrium and of separating decision science from social science more generally. Agent‐based modeling offers powerful new forms of hybrid theoretical‐computational work; these are particularly relevant to the study of non‐equilibrium systems. The agent‐based approach invites the interpretation of society as a distributed computational device, and in turn the interpretation of social dynamics as a type of computation. This interpretation raises important foundational issues in social science—some related to intractability, and some to undecidability proper. Finally, since “emergence” figures prominently in this literature, I take up the connection between agent‐based modeling and classical emergentism, criticizing the latter and arguing that the two are incompatible. © 1999 John Wiley & Sons, Inc.     

A reduced theory for thin‐film micromagnetics

Micromagnetics is a nonlocal, nonconvex variational problem. Its minimizer represents the ground‐state magnetization pattern of a ferromagnetic body under a specified external field. This paper identifies a physically relevant thin‐film limit and shows that the limiting behavior is described by a certain “reduced” variational problem. Our main result is the Γ‐convergence of suitably scaled three‐dimensional micromagnetic problems to a two‐dimensional reduced problem; this implies, in particular, convergence of minimizers for any value of the external field. The reduced problem is degenerate but convex; as a result, it determines some (but not all) features of the ground‐state magnetization pattern in the associated thin‐film limit. © 2002 Wiley Periodicals, Inc.     

HABITAT PATCH OCCUPANCY DYNAMICS OF GLAUCOUS‐WINGED GULLS (LARUS GLAUCESCENS) II: A CONTINUOUS‐TIME MODEL

ABSTRACT. The diurnal distribution and abundance dynamics of loafing Glaucous‐winged Gulls (Larus glaucescens) were examined at Protection Island National Wildlife Refuge, Strait of Juan de Fuca, Washington. Asynchronous movement of gulls among three habitat patches dedicated to loafing was modeled as a function of environmental variables using differential equations. Multiple time scale analysis led to the derivation of algebraic models for habitat patch occupancy dynamics. The models were parameterized with hourly census data collected from each habitat patch, and the resulting model predictions were compared with observed census data. A four‐compartment model explained 41% of the variability in the data. Models that predict the dynamics of organism distribution and abundance enhance understanding of the temporal and spatial organization of ecological systems, as well as the decision‐making process in natural resource management.     

The computational complexity of two‐state spin systems

The subject of this article is spin‐systems as studied in statistical physics. We focus on the case of two spins. This case encompasses models of physical interest, such as the classical Ising model (ferromagnetic or antiferromagnetic, with or without an applied magnetic field) and the hard‐core gas model. There are three degrees of freedom, corresponding to our parameters β, γ, and μ. Informally, β represents the weights of edges joining pairs of “spin blue” sites, γ represents the weight of edges joining pairs of “spin green” sites, and μ represents the weight of “spin green” sites. We study the complexity of (approximately) computing the partition function in terms of these parameters. We pay special attention to the symmetric case μ = 1. Exact computation of the partition function Z is NP‐hard except in the trivial case βγ = 1, so we concentrate on the issue of whether Z can be computed within small relative error in polynomial time. We show that there is a fully polynomial randomised approximation scheme (FPRAS) for the partition function in the “ferromagnetic” region βγ ≥ 1, but (unless RP = NP) there is no FPRAS in the “antiferromagnetic” region corresponding to the square defined by 0 < β < 1 and 0 < γ < 1. Neither of these “natural” regions—neither the hyperbola nor the square—marks the boundary between tractable and intractable. In one direction, we provide an FPRAS for the partition function within a region which extends well away from the hyperbola. In the other direction, we exhibit two tiny, symmetric, intractable regions extending beyond the antiferromagnetic region. We also extend our results to the asymmetric case μ ≠ 1. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 133–154, 2003     

Catch‐to‐stock dependence: The case of small pelagic fishery with bounded harvesting effort

Biologic characteristics of schooling fish species explain why the rates of harvesting in pelagic fisheries are not proportional to the existent stock size and may exhibit no variation between the periods of fish abundance and scarcity. Therefore, the stock‐dependent nonlinearities in catchability must be reflected in the design of flexible fishing policies, which target the sustainable exploitation of this important natural resource. In this study, such nonlinearities are expressed through eventual variability of the “catch‐to‐stock” parameter that measures the sensitivity of an additional catch yield to marginal changes in the fish‐stock level. Using the optimal control modeling framework, we establish that each value of the “catch‐to‐stock” parameter generates a unique steady‐state size of the fish stock and the latter engenders an optimal fishing policy that can be sustained as long as the “catch‐to‐stock” parameter remains unchanged. We also prove the continuous dependence of the steady‐state stock and underlying fishing policy upon the mentioned “catch‐to‐stock” parameter and then focus on the analysis of the equilibrium responses to changes in this parameter induced by external perturbations. Recommendations for Resource Managers

• Marginal catches of pelagic fish stocks do not react in a linear way to changes in existing stock level, and the latter is captured in our model by the “catch‐to‐stock” parameter . Each observable value of engenders a unique steady‐state stock size that defines an optimal fishing policy, which can be sustained as long as remains unchanged.
• The ability of fishery managers to detect variations in the levels of hyperstability expressed by the “catch‐to‐stock” parameter may help them to anticipate new equilibrium responses in stock evolution and to make timely adjustments in the fishing policy.
• Plausible estimations of the “catch‐to‐stock” parameter , as well as detection of its possible alterations, can be carried out within the framework of Management Strategy Evaluation (MSE) approach where different data collected inside and outside the fishery are contrasted via the validation of a relatively simple decision‐making model (presented in this paper) coupled with other “operation models” of higher complexity.
• If the “catch‐to‐stock” parameter cannot be reasonably assessed (), the fishery managers may rely upon the lower bound of stationary stock size, which depends on economic and biological factors (such as the present and future economic values of the exploited fish stock, its marginal productivity, and underlying dynamics of biological growth).

     

WITHIN‐GENERATIONAL AND DIVERSITY‐DEPENDENT EFFECTS IN AN INDIVIDUAL‐BASED MODEL OF PREDATOR‐PREY INTERACTION

ABSTRACT. In this paper we report the use of an individual‐based model of predator‐prey interaction to explore the effects of “within generational” and ‘between generational’ updating of a system level variable. We also report the importance of diversity within the simulated populations. Our findings support those of Grimm and Uchmánski [1994] in regard to the importance of the timing of system level variables, and support Grimm and Uchmañski and others in regard to the importance of the level of diversity across the population. The significance of these findings is emphasized by the fundamental differences between our model and that of Grimm and Uchmánski in regard to the assumptions made about resource flow in the system. This paper was presented at the 2004 Research Modeling Association World Conference on Natural Resource Modeling in Melbourne, Australia.     

Boolos‐style proofs of limitative theorems

Boolos's proof of incompleteness is extended straightforwardly to yield simple “diagonalization‐free” proofs of some classical limitative theorems of logic. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mixed and hybrid formulations for the three‐dimensional magnetostatic problem

We propose mixed and hybrid formulations for the three‐dimensional magnetostatic problem. Such formulations are obtained by coupling finite element method inside the magnetic materials with a boundary element method. We present a formulation where the magnetic field is the state variable and the boundary approach uses a scalar Dirichlet‐Neumann map to describe the exterior domain. Also, we propose a second formulation where the magnetic induction is the state variable and a vectorial Dirichlet‐Neumann map is used to describe the outer field. Numerical discretizations with “edge” and “face” elements are proposed, and for each discrete problem we study an “inf‐sup” condition. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 85–104, 2002     

Extended Kaczmarz‐like methods with oblique projections

In this paper we describe two “sparse preconditioning” techniques for accelerating the convergence of Kaczmarzlike algorithms. The first method, uses projections with respect to the “energy scalar product” generated by an appropriate symmetric and positive definite matrix. The second one starts from some recent results of Y. Censor and T. Elfving on “sparsity pattern oriented” (SPO) oblique projections and uses an “algebraic multigrid interpolationlike” construction of the (SPO) family. Numerical experiments are described on a system comming from a bioelectric field simulation problem.     

On time‐dependent behaviour of controlled turbulent flow with separation and reattachment

Results from numerical simulations of separating and reattaching turbulent boundary layer flow over a backwardfacing step are analysed with respect to the time‐dependent flow behaviour. Beside the well‐known roll‐up of the separated shear‐layer (“Kelvin‐Helmholtz instability”) and the ejection of subsequently formed large‐scale structures (denoted as “shedding”), another unsteady phenomenon which is commonly called “flapping” can be observed. Additionally, the effects of open‐loop passive and active flow control methods are investigated.     

Remarks on Leray's self‐similar solutions to the 3D magnetohydrodynamic equations

In this note, we examine small self‐similar solutions of the 3D incompressible magnetohydrodynamic equations in homogenous function spaces and show the uniqueness of self‐similar solutions when the velocity field is small in some homogeneous function spaces. This extend the recent results given by C. He and Z. Xin. “On the self‐similar solutions of the magneto‐hydro‐dynamic equations. Acta Mathematica Scientia, série B English Edition 2009; 29 (3): 583–598”. It is a natural way to extend the space widely and improve the previous results. Copyright © 2013 John Wiley & Sons, Ltd.     

Some 3‐connected 4‐edge‐critical non‐Hamiltonian graphs

Let γ(G) be the domination number of graph G, thus a graph G is k‐edge‐critical if γ (G) = k, and for every nonadjacent pair of vertices u and υ, γ(G + uυ) = k?1. In Chapter 16 of the book “Domination in Graphs—Advanced Topics,” D. Sumner cites a conjecture of E. Wojcicka under the form “3‐connected 4‐critical graphs are Hamiltonian and perhaps, in general (i.e., for any k ≥ 4), (k?1)‐connected, k‐edge‐critical graphs are Hamiltonian.” In this paper, we prove that the conjecture is not true for k = 4 by constructing a class of 3‐connected 4‐edge‐critical non‐Hamiltonian graphs. © 2005 Wiley Periodicals, Inc.     

Analysis and numerics for an age‐ and sex‐structured population model

We study a linear model of McKendrick‐von Foerster‐Keyfitz type for the temporal development of the age structure of a two‐sex human population. For the underlying system of partial integro‐differential equations, we exploit the semigroup theory to show the classical well‐posedness and asymptotic stability in a Hilbert space framework under appropriate conditions on the age‐specific mortality and fertility moduli. Finally, we propose an implicit finite difference scheme to numerically solve this problem and prove its convergence under minimal regularity assumptions. A real data application is also given. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 706–736, 2016     

Development and Field Test of the Modified Draw‐a‐Scientist Test and the Draw‐a‐Scientist Rubric

Even long before children are able to verbalize which careers may be interesting to them, they collect and store ideas about scientists. For these reasons, asking children to draw a scientist has become an accepted method to provide a glimpse into how children represent and identify with those in the science fields. Years later, these representations may translate into students' career choices. Since 1995, children's illustrations of scientists have been assessed by the Draw‐a‐Scientist Checklist (DAST‐C). The checklist was created from the common aspects or features found in illustrations from previous studies and were based initially on the scientists, broken down into “stereotypical” and “alternative” images shown in the drawings. The purpose of this article is to describe the development, field test, and reliability of the modified DAST Test and the DAST Rubric designed as an improvement of the DAST‐C to provide a more appropriate method of assessing students' drawings of scientists. The combination of the modified DAST and the DAST Rubric brings more refinement as it enables clarities to emerge and subsequently increased detail to what one could ascertain from students about their mental images of scientists.