A computational and combinatorial exposé of plethystic calculus

In recent years, plethystic calculus has emerged as a powerful technical tool for studying symmetric polynomials. In particular, some striking recent advances in the theory of Macdonald polynomials have relied heavily on plethystic computations. The main purpose of this article is to give a detailed explanation of a method for finding combinatorial interpretations of many commonly occurring plethystic expressions, which utilizes expansions in terms of quasisymmetric functions. To aid newcomers to plethysm, we also provide a self-contained exposition of the fundamental computational rules underlying plethystic calculus. Although these rules are well-known, their proofs can be difficult to extract from the literature. Our treatment emphasizes concrete calculations and the central role played by evaluation homomorphisms arising from the universal mapping property for polynomial rings.     

Linear transformations to decrease computational requirements of solving some known linear programming models

Imposing additional weight restrictions increases the degeneracy and computational complexity of solving Data Envelopment Analysis (DEA) models, a known class of linear programming models. In this paper some linear transformations to reduce these problems are provided.     

A computational determination of the Cowper–Symonds parameters from a single Taylor test

A novel technique for the dynamic characterization of metals from a single Taylor impact test is proposed. This computational characterization procedure is based on the formulation and solution of a first class inverse problem, in which the silhouette of the Taylor specimen’s final shape is expressed as a vector of its geometrical moments and used as input parameter. The inverse characterization problem is reduced to an optimization problem where the optimum material parameters for the Cowper–Symonds material model are determined. The optimization process is performed by a range adaptation real-coded genetic algorithm. Numerical example for the characterisation of 1018 steel is implemented and presented to validate the methodology presented in this paper. The effectiveness and simplicity of the proposed characterization procedure makes it an appropriate tool for the characterization of metals at high strain rates.     

How to get the timing right. A computational model of the effects of the timing of contacts on team cohesion in demographically diverse teams

Lau and Murnighan’s faultline theory explains negative effects of demographic diversity on team performance as consequence of strong demographic faultlines. If demographic differences between group members are correlated across various dimensions, the team is likely to show a “subgroup split” that inhibits communication and effective collaboration between team members. Our paper proposes a rigorous formal and computational reconstruction of the theory. Our model integrates four elementary mechanisms of social interaction, homophily, heterophobia, social influence and rejection into a computational representation of the dynamics of both opinions and social relations in the team. Computational experiments demonstrate that the central claims of faultline theory are consistent with the model. We show furthermore that the model highlights a new structural condition that may give managers a handle to temper the negative effects of strong demographic faultlines. We call this condition the timing of contacts. Computational analyses reveal that negative effects of strong faultlines critically depend on who is when brought in contact with whom in the process of social interactions in the team. More specifically, we demonstrate that faultlines have hardly negative effects when teams are initially split into demographically homogeneous subteams that are merged only when a local consensus has developed.     

Do some chemotaxis-growth models possess Lyapunov functionals?

In spirit of a result by W. Alt from 1980 we give some sufficient criteria that guarantee the existence of Lyapunov functionals for parabolic cross-diffusion models including chemotaxis-growth models with non-diffusive chemotactic signals (resp. with non-diffusive memory).     

Do efficiency scores depend on input mix? A statistical test and empirical illustration

In this paper we examine the possibility of using the standard Kruskal-Wallis (KW) rank test in order to evaluate whether the distribution of efficiency scores resulting from Data Envelopment Analysis (DEA) is independent of the input (or output) mix of the observations. Since the DEA frontier is estimated, many standard assumptions for evaluating the KW test statistic are violated. Therefore, we propose to explore its statistical properties by the use of simulation studies. The simulations are performed conditional on the observed input mixes. The method, unlike existing approaches in the literature, is also applicable when comparing distributions of efficiency scores in more than two groups and does not rely on bootstrapping of, or questionable distributional assumptions about, the efficiency scores. The approach is illustrated using an empirical case of demolition projects. Since the assumption of mix independence is rejected the implication is that it, for example, is impossible to determine whether machine intensive project are more or less efficient than labor intensive projects.     

Is politics power or policy oriented? A comparative analysis of dynamic access models in policy networks*

We will show that these base models and some intermediate ones result in fundamentally different network structures and predicted outcomes. Moreover, we will show that the policy driven models do fundamentally better than the power driven models.

In policy networks actors use access relations to influence preferences of other actors. Establishment and shifts of access relations and their consequences for outcomes of decisions are the main focal points in this paper. Unlike most policy network studies, we therefore do not take the network and its relations as given and constant. Instead we device computer simulation models to account for the dynamics in policy networks. We compare different models and investigate the resulting network structures and predicted outcomes of decisions. The choice among the alternative models is made by their correspondence with empirical network structures and actual outcomes of decisions.

In our models, we assume that all relevant actors aim at policy outcomes as close as possible to their own preferences. Policy outcomes are determined by the preferences of the final decision makers at the moment of the vote. In general, only a small fraction of the actors takes part in the final vote. Most actors have therefore to rely on access relations for directly or indirectly shaping the preferences of the final decision makers. For this purpose actors make access requests to other actors. An access relation is assumed to be established if such a request is accepted by the other actor.

Access relations require time and resources. Actors are therefore assumed to be restricted in the number of access requests they can make and the number of requests they can accept Moreover, due to incomplete information and simultaneous actions by other actors, actors have to make simplifying assumptions in the selection of their “best” requests and learn by experience.

We device two base models that correspond to two basic views on the nature of political processes. In the first view politics is seen as power driven. Corresponding to this view, actors aim at access relations with the most powerful actors in the field. They estimate their likelihood of success by comparing their own resources with those of the target actors. Power also determines the order in which actors accept requests. In the second view, policy matters and actors roughly estimate the effects access relations might have on the outcome of decisions. Actors select requests to “bolster” their own preference as much as possible.     

A strong convergence theorem for common fixed points of two relatively nonexpansive mappings and its applications

In this paper, a projection iterative scheme is introduced for the approximation method for finding common fixed points of two relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space and, by using the iterative scheme, we obtain a strong convergence theorem and some applications of the main result. Our results extend the corresponding works given by some authors.     

Niche width and scale in organizational competition: A computational approach

In some organizational applications, the principle of allocation (PoA) and scale advantage (SA) oppose each other. While PoA implies that organizations with wide niches get punished, SA holds that large organizations gain an advantage because of scale efficiencies. The opposition occurs because many large organizations also possess wide niches. However, analyzing these theoretical mechanisms implies a possible trade-off between niche width and size: if both PoA and SA are strong, then organizations must be either focused or large to survive, resulting in a dual market structure, as proposed by the theory of resource partitioning. This article develops a computational model used to study this trade-off, and investigates the properties of organizational populations with low/high SA and low/high PoA. The model generates three expected core “corner” solutions: (1) the dominance of large organizations in the strong SA setting; (2) the proliferation of narrow-niche organizations in the strong PoA setting; and (3) a bifurcated or dual market structure if both SA and PoA are present. The model also allows us to identify circumstances under which narrow-niche (specialists) or wide-niche (generalists) organizations thrive. We also use the model to examine the claim that concentrated resource distributions are more likely to generate partitioned or bifurcated populations. We also investigate the consequences of environments comprised of ordered versus unordered positions.     

On the mathematical formulation of the problem of reassembling fragmented objects: two new theorems

In this paper two new theorems are proved in association with the problem of matching three dimensional solid bodies. Rigorous mathematical criteria are given in order to test if two such bodies actually match in a certain position. Since this problem finds important application to the actual problem of reassembling fragmented objects e.g. archaeological, special care is taken to account for small gaps between matching fragments and fuzziness of the matching parameters.     

A Cramér-von Mises test for symmetry of the error distribution in asymptotically stationary stochastic models

This paper has to do with a Cramér-von Mises test for symmetry of the error distribution in a class of absolutely regular and non-necessarily stationary heteroscedastic models. The test statistic is based on the empirical characteristic function. Its convergence, as well as that of the residual-based empirical distribution function are established. From these results, the null cumulative distribution function of the test statistic is approximated. A simulation experiment shows that the test performs well on the examples tested.     

Is mortality or interest rate the most important risk in annuity models? A comparison of sensitivity analysis methods

Demographic and financial factors are key risk-drivers for insurance companies and pension funds. This paper proposes a systematic investigation for deepening our understanding how these risk drivers affect the annuity cost. We employ local and global sensitivity methods. For local sensitivity, we derive closed form expressions for the differential importance measures of perturbed annuities and connect them to the entropy of the annuity cost. For global sensitivity, we compare variance-based, moment-independent sensitivity measures and Shapley effects. In particular, moment-independent sensitivity measures and Shapley effects are compared for the first time in the case of dependent risk factors. Our framework encompasses and extends several previous results on the sensitivity analysis of annuity models. From a methodological viewpoint, the techniques compared in this paper can support analysts in building annuity models and in verifying the impact of risk drivers in their models. Numerical results using the U.S. 1990 and the U.K. 1990–1994 mortality tables show that the demographic factor is the most important risk source in low-interest rate contexts. However, when uncertainty on the two risk sources is taken into account, the financial factor becomes the global key-driver of risk. Also, interactions among the two factors appear quantitatively significant.     

Stability in predator – prey models and discretization of a modified Volterra – Lotka model

We consider n  2 populations of animals that are living in mutual predator – prey relations or are pairwise neutral to each other. We assume the temporal development of the population densities to be described by a system of differential equations which has an equilibrium state solution. We derive sufficient conditions for this equilibrium state to be stable by Lyapunov's method. The results supplement those published elsewhere.

Further we consider a modification of the Volterra – Lotka model which admits an asymptotically stable steady state solution. This model is discretized in two ways and we investigate how small the time step size has to be chosen in order to guarantee that the steady state solution is an attractive fixed point of the discretized model. This investigation is connected with the determination of the model parameters from given data.     

Do investors like to diversify? A study of Markowitz preferences

We study rankings of completely and partially diversified portfolios and also of specialized assets when investors follow so-called Markowitz preferences. It turns out that diversification strategies for Markowitz investors are more complex than in the case of risk-averse and risk-inclined investors, whose investment strategies have been extensively investigated in the literature. In particular, we observe that for Markowitz investors, preferences toward risk vary depending on their sensitivities toward gains and losses. For example, it turns out that, unlike in the case of risk-averse and risk-inclined investors, Markowitz investors might prefer investing their entire wealth in just one asset. This finding helps us to better understand some financial anomalies and puzzles, such as the well known diversification puzzle, which notes that some investors tend to concentrate on investing in only a few assets instead of choosing the seemingly more attractive complete diversification.     

Ethics outside,within, or beyond OR models?

Since ethical concerns are calling for more attention within Operational Research, we present three approaches to combine Operational Research models with ethics. Our intention is to clarify the trade-offs faced by the OR community, in particular the tension between the scientific legitimacy of OR models (ethics outside OR models) and the integration of ethics within models (ethics within OR models). Presenting and discussing an approach that combines OR models with the process of OR (ethics beyond OR models), we suggest rigorous ways to express the relation between ethics and OR models. As our work is exploratory, we are trying to avoid a dogmatic attitude and call for further research. We argue that there are interesting avenues for research at the theoretical, methodological and applied levels and that the OR community can contribute to an innovative, constructive and responsible social dialogue about its ethics.     

Editable machine learning models? A rule-based framework for user studies of explainability

Advances in Data Analysis and Classification - So far, most user studies dealing with comprehensibility of machine learning models have used questionnaires or surveys to acquire input from...     

A characterization of arithmetical invariants by the monoid of relations

The investigation and classification of non-unique factorization phenomena have attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P. García-Sánchez, together with several co-authors, derived a method to calculate the catenary and tame degree from the monoid of relations, and they applied this method successfully in the case of numerical monoids. In this paper, we investigate the algebraic structure of this approach. Thereby, we dispense with the restriction to finitely generated monoids and give applications to other invariants of non-unique factorizations, such as the elasticity and the set of distances.     

Nonsmooth exclusion test for finding all solutions of nonlinear equations

A new approach is proposed for finding all real solutions of systems of nonlinear equations with bound constraints. The zero finding problem is converted to a global optimization problem whose global minima with zero objective value, if any, correspond to all solutions of the original problem. A branch-and-bound algorithm is used with McCormick’s nonsmooth convex relaxations to generate lower bounds. An inclusion relation between the solution set of the relaxed problem and that of the original nonconvex problem is established which motivates a method to generate automatically, starting points for a local Newton-type method. A damped-Newton method with natural level functions employing the restrictive monotonicity test is employed to find solutions robustly and rapidly. Due to the special structure of the objective function, the solution of the convex lower bounding problem yields a nonsmooth root exclusion test which is found to perform better than earlier interval-analysis based exclusion tests. Both the componentwise Krawczyk operator and interval-Newton operator with Gauss-Seidel based root inclusion and exclusion tests are also embedded in the proposed algorithm to refine the variable bounds for efficient fathoming of the search space. The performance of the algorithm on a variety of test problems from the literature is presented, and for most of them, the first solution is found at the first iteration of the algorithm due to the good starting point generation.     

Agent-based and multi-agent simulations: coming of age or in search of an identity?

The promise of agent-based for explicating properties of social systems has not yet been fully realized. Agent models sometimes provide only a veneer of, rather than substantive engagement with, social behavior. The problem will be illustrated with Axelrod’s model for evolution of ethnocentrism (a biological model) versus Schelling’s model for spatial segregation based on preferences (a cultural model). The examples show the need to incorporate both the biological and cultural basis for behavior through a schema that includes behavior based on cultural/cognitive processing of information and behavior based on biological/cognitive processing of information. An example of an agent-based model that implements decision making in this manner is discussed. The model accounts for heterogeneity in behavior outcomes and leads to two main predictions: (1) small scale, hunter-gatherer societies in resource scarce environments will have stable adaptations less affected by variation in resource abundance in comparison to groups in resource rich regions where inter-group conflict is more likely and (2) the relationship between community size, population size and administrative complexity will have two distinct patterns, one for patrilineally organized societies and the other for matrilineally organized societies. Both predictions have been verified empirically.     

Solitary wave solutions of two nonlinear physical models by tanh–coth method

In this work, we established the exact solutions for some nonlinear physical models. The tanh–coth method was used to construct solitary wave solutions of nonlinear evolution equations. The tanh–coth method presents a wider applicability for handling nonlinear wave equations.