Approximate Analysis of Decentralized, Multi-Stage, Pull-Type Production/Inventory Systems

We consider a decentralized, pull-type manufacturing system with each stage having its own input and output stock keeping activities. Material handling between stages is carried out according to a fixed quantity, non-constant withdrawal cycle. We approximate the system behavior using a two-node decomposition approach, which decomposes the system into smaller subsystems. The analysis of two-node subsystems is achieved using a matrix-recursive approach due to phase-type modeling of certain random variables. Our solution algorithm resolved a major difficulty (due to batch transfers) in the analytical approach to study multi-stage manufacturing systems. We also discuss system behavior and suggest several rules-of-thumb to improve system performance.     

Complex impure systems: Sheaves,freeways, and chains

Fundamental to the approach of Complex Impure Systems is the definition of the concept of an s‐impure set as a set of perceptual beliefs or denotative significances (relative beings) of material and/or energetic real objects (absolute beings). But any Subject not only the subject S perceives objects O as significances, and he perceives the existing relations between these significances or, alternatively, he infers them. The study of these relations, conceived not as a singular relation between singular objects, but as sheaves of relations in both directions and forming relational freeways, will be studied here. In this work, we approach the structure of the system, from a synchronous point of view, as a first approach to this class of systems. © 2016 Wiley Periodicals, Inc. Complexity 21: 387–400, 2016     

Multiple-Spacecraft Reconfiguration Through Collision Avoidance,Bouncing, and Stalemate

We consider constrained multiple-spacecraft reconfigurations outside a gravity well in deep space. As opposed to the single-spacecraft scenario, such reconfigurations involve collision avoidance constraints that can be embedded in a nonconvex, state-constrained optimal control problem. Due to the difficulties in solving this general class of optimal control problems, we adopt a heuristically motivated approach to multiple-spacecraft reconfigurations. Then, we proceed to prove the convergence properties of the proposed approach for reconfigurations involving an arbitrary number of spacecraft.     

Learning Trajectories,Lesson Planning,Affordances, and Constraints in the Design and Enactment of Mathematics Teaching

Recent reform efforts in mathematics education have stimulated a focus on learning trajectories. At the same time, a global increase in high-stakes testing has influenced instructional practices. This study investigated how four fourth grade teachers within a school planned and enacted lessons to understand what mediated their planning and teaching decisions. Findings reveal that three of these teachers, who were veteran teachers, used a testing trajectory approach with decisions mediated by preparing students for high-stakes tests. The fourth teacher, a novice, attempted to use a learning trajectory approach to support student understanding. Results reveal that high-stakes testing played a crucial role in teachers' instructional decisions. Based on the findings, we provide a framework for a testing trajectory approach that the veteran teachers used to make instructional decisions. Further research is needed to understand how to support teachers to prepare students for testing using effective teaching practices.     

Migration Policies, Selection Pressure, and Parallel Evolutionary Algorithms

This paper investigates how the policy used to select migrants and the individuals they replace affects the selection pressure in parallel evolutionary algorithms (EAs) with multiple populations. The four possible combinations of random and fitness-based emigration and replacement of existing individuals are considered. The investigation follows two approaches. The first is to calculate the takeover time under the four migration policies. This approach makes several simplifying assumptions, but the qualitative conclusions that are derived from the calculations are confirmed by the second approach. The second approach consists on quantifying the increase in the selection intensity. The selection intensity is a domain-independent adimensional quantity that can be used to compare the selection pressure of common selection methods with the pressure caused by migration. The results may help to avoid excessively high (or low) selection pressures that may cause the search to fail, and offer a plausible explanation to the frequent claims of superlinear speedups in parallel EAs.     

Social rationality,separability, and equity under uncertainty

Harsanyi (1955) proved that, in the context of uncertainty, social rationality and the Pareto principle impose severe constraints on the degree of priority for the worst-off that can be adopted in the social evaluation. Since then, the literature has hesitated between an ex ante approach that relaxes rationality (Diamond, 1967) and an ex post approach that fails the Pareto principle (Hammond, 1983; Broome, 1991). The Hammond–Broome ex post approach conveniently retains the separable form of utilitarianism but does not make it explicit how to give priority to the worst-off, and how much disrespect of individual preferences this implies. Fleurbaey (2010) studies how to incorporate a priority for the worst-off in an explicit formulation, but leaves aside the issue of ex ante equity in lotteries, retaining a restrictive form of consequentialism. We extend the analysis to a framework allowing for ex ante equity considerations to play a role in the ex post evaluation, and find a richer configuration of possible criteria. But the general outlook of the Harsanyian dilemma is confirmed in this more general setting.     

Approach Spaces, Limit Tower Spaces, and Probabilistic Convergence Spaces

The category LTS of limit tower spaces is defined and shown to be isomorphic to the category CAP of convergence approach spaces. The full subcategory of LTS determined by the objects satisfying a diagonal axiom due to Cook and Fischer is shown to be isomorphic to the category AP of approach spaces. A family of isomorphisms is also obtained between LTS and certain full subcategories of the category PCS of probabilistic convergence spaces.     

Pseudo-linear systems, Lie algebras, and stability

The stability of pseudo-linear systems is considered by usinga diagonal-dominance approach coupled with the theory of semisimpleLie algebras and the Cartan decomposition     

Commutation relations,homomorphisms, and differential equations

We present an algebraic approach to the theory of ordinary differential equations and indicate a method for constructing first integrals of such equations.     

Completeness, Sections and Selections

In this paper, we develop a general approach to set-valued semi-continuous selections which is based on order-like arguments rather than on classical approximations. The approach works nice in a number of situations demonstrating the genesis of such selection properties of set-valued mappings. In particular, it allows to generalize several known results, also to get some new results about sections of set-valued mappings.      

Focused ultrasonic therapy planning: Metamodeling,optimization, visualization

We present a generic approach for focused ultrasonic therapy planning on the basis of numerical simulation, multi-objective optimization, stochastic analysis and visualization in virtual environments. A realistic test case is used to demonstrate the approach. RBF metamodeling of simulation results is performed for continuous representation of two optimization objectives. The non-convex Pareto front of the objectives is determined by means of non-dominated set and local improvement algorithms. Uncertainties of metamodeling are estimated by means of a cross-validation procedure. The 3D visualization in virtual environment framework Avango allows detailed inspection of MRT images, the corresponding material model and spatial distribution of the resulting thermal dose.     

The utility of nonequilibrium statistical mechanics,specifically transport theory,for modeling cohort data

This article introduces a new case‐based density approach to modeling big data longitudinally, which uses ordinary differential equations and the linear advection partial differential equations (PDE) to treat macroscopic, dynamical change as a transport issue of aggregate cases across continuous time. The novelty of this approach comes from its unique data‐driven treatment of cases: which are K dimensional vectors; where the velocity vector for each case is computed according to its particular measurements on some set of empirically defined social, psychological, or biological variables. The three main strengths of this approach are its ability to: (1) translate the data driven, nonlinear trajectories of microscopic constituents (cases) into the linear movement of macroscopic trajectories, which take the form of densities; (2) detect the presence of multiple, complex steady state behaviors, including sinks, spiraling sources, saddles, periodic orbits, and attractor points; and (3) predict the motion of novel cases and time instances. To demonstrate the utility of this approach, we used it to model a recognized cohort dynamic: the longitudinal relationship between a country's per capita gross domestic product (GDP) and its longevity rates. Data for the model came from the widely used Gapminder dataset. Empirical results, including the strength of the model's fit and the novelty of its results (particularly on a topic of such extensive study) support the utility of our new approach. © 2014 Wiley Periodicals, Inc. Complexity 20: 45–57, 2015     

Design,Concepts, and State of the Art of the swMATH Service

In this paper, the concepts and design for an efficient information service for mathematical software and further mathematical research data are presented. The publication-based approach and the web-based approach are the main building blocks of the service and will be discussed. Heuristic methods are used for identification, extraction, and ranking of information about software and other mathematical research data. The methods provide not only information about the research data but also link software and mathematical research data to the scientific context.     

Robust inversion, dimensionality reduction, and randomized sampling

We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only viable, however, for a least-squares misfit, which is sensitive to outliers in the data and artifacts unexplained by the forward model. This motivates us to propose a robust formulation based on the Student’s t-distribution of the error. We demonstrate how the corresponding penalty function, together with the sampling approach, can obtain good results for a large-scale seismic inverse problem with 50 % corrupted data.     

Estimation,modeling, and aggregation of missing survey data for prioritizing customer voices

It is widely acknowledged that understanding and prioritizing the voice of customer is a critical step in new product development. In this work, we propose a novel approach to handle missing and incomplete data while combining information from different surveys for prioritizing customer voices. Our new approach comprises of the following stages: estimating and representing missing and incomplete data; estimating intervals for the criteria used in analyzing data; mapping data on criteria to a common scale; modeling interval data using interval belief structure; and aggregating evidence and ranking customer voices using the interval evidential reasoning algorithm. We demonstrate our approach using a case study from automotive domain with a given criteria hierarchy for analyzing data from three different surveys. We propose new optimization formulations for estimating intervals of the criteria used in our case study and logical yet pragmatic transformation functions for mapping criteria values to a common scale.     

Weighted Norm Inequalities for Convolutions, Differential Operators, and Generalized Hypergeometric Functions

The recent work on discrete inequalities with the binomially made weights leads to a sharp weighted norm inequality for convolutions of complex-valued functions on a finite interval. This result and the Hadamard-type modifications of power series provide the basis for an integral approach to solution-kernel estimates for Volterra convolution equations and for various integro-differential and special function applications. The development of this approach and the new weighted norm inequalities for linear differential operators and generalized hypergeometric functions are presented in this paper.     

Stability,structural stability,and games: Toward a theory of differential hypergames

Differential games (DG's) are investigated from a stability point of view. Several resemblances between the theory of optimal control and that of structural stability suggest a differential game approach in which the operators have conflicting interests regarding the stability of the system only. This qualitative approach adds several interesting new features. The solution of a differential game is defined to be the equilibrium position of a dynamical system in the framework of a given stability theory: this is the differential hypergame (DHG). Three types of DHG are discussed: abstract structural DHG, Liapunov DHG, and Popov DHG. The first makes the connection between DG and the catastrophe theory of Thom; the second makes the connection between the value function approach and Liapunov theory; and the third provides invariant properties for DG's. To illustrate the fact that the theory sketched here may find interesting applications, the up-to-date problem of the world economy is outlined.This research was supported by the National Research Council of Canada.     

Canonical transformations,umbral calculus,and orthogonal theory

We present a theory of representations of canonical transformations which links together the theories of evolution semigroups, Hamiltonian flows, umbral operators, and cross-sequences. We also present a different approach to the orthogonal theory of moment systems.     

Morse inequalities, a function space integral approach

In this paper we prove the Morse inequalities in the non-degenerate and degenerate cases. Like the approach of J.-M. Bismut, ours is based on the idea suggested by Witten. In fact, if anything, our approach is closer to Witten's original idea than Bismut's.