Initial Conditions and the ‘Open Systems’ Argument against Laws of Nature

This article attacks ‘open systems’ arguments that because constant conjunctions are not generally observed in the real world of open systems we should be highly skeptical that universal laws exist. This work differs from other critiques of open system arguments against laws of nature by not focusing on laws themselves, but rather on the inference from open systems. We argue that open system arguments fail for two related reasons: 1) because they cannot account for the ‘systems’ central to their argument (nor the implied systems labeled ‘exogenous factors’ in relation to the system of interest) and 2) they are nomocentric, fixated on laws while ignoring initial and antecedent conditions that are able to account for systems and exogenous factors within a fundamentalist framework.     

Gradient boosting for convex cone predict and optimize problems

Prediction models are traditionally optimized independently from decision-based optimization. Conversely, a ‘smart predict then optimize’ (SPO) framework optimizes prediction models to minimize downstream decision regret. In this paper we present dboost, the first general purpose implementation of smart gradient boosting for ‘predict, then optimize’ problems. The framework supports convex quadratic cone programming and gradient boosting is performed by implicit differentiation of a custom fixed-point mapping. Experiments comparing with state-of-the-art SPO methods show that dboost can further reduce out-of-sample decision regret.     

Achieving ‘Desirable and Feasible’ Change: An Application of Soft Systems Methodology

Rational intervention in human affairs, if it is to constitute not only action but also research, so that future interventions may be made more effective, needs a well-defined methodological framework. Soft systems methodology (S.S.M.) provides one such framework. S.S.M. is doubly systemic: it is itself a learning system, and within that system it uses systems models, models of human activity systems. It accepts that such models are not models of parts of the real world, only models of ways of perceiving the real world, that is to say, models relevant to debate about ‘reality’ (one man's ‘terrorism’ is another's ‘freedom fighting’).S.S.M. is here illustrated by means of an account of a systems study of change in the information function of a sophisticated science-based company. The study is described from the point of view of a professional analyst who was helping a team of three managers carry out the study. The course of the study is described, and a separate commentary relates its activity to the seven stages of S.S.M. The study involved three cycles round stages 2–3–4–5 of S.S.M., the stages in which models of relevant human activity systems are built and compared with the real world in order to construct a rich debate about changes whose introduction in the problem situation world be both (systemically) desirable and (culturally) feasible.     

From Optimizing to Learning: A Development of Systems Thinking for the 1990s

In any subject concerned with rational intervention in human affairs, theory must lead to practice; but practice is the source of theory: neither theory nor practice is prime. We can examine this ‘groundless’ relation by asking what intellectual framework F is applied in what methodology M to what area of application A? If we do this for O.R., systems analysis, systems engineering etc., we see that F and M have changed dramatically between the 1950s and the 1980s, yielding the ‘hard’ and ‘soft’ traditions of systems thinking. The ‘hard’ tradition, based on goal seeking, is examined in the work of Simon and contrasted with the ‘soft’ tradition, based on learning, as exemplified in the work of Vickers and the development of soft systems methodology. The two are complementary, but the relation between them is that the ‘hard’ is a special case of ‘soft’ systems thinking. This analysis makes sense of the recent history of management science and helps to prepare us for the 1990s.     

An Algorithm for Solving the Linear Goal Programming Problem by Solving its Dual

Goal programming, and in particular lexicographic goal programming (i.e. goal programming within a so-called ‘pre-emptive priority’ structure or having non-Archimedean weights), has become one of the most widely used of the approaches for multi-objective mathematical programming. While also applicable to non-linear or integer models, most of the literature has considered the lexicographic linear goal-programming model and its solution via primal simplex-based methods. However, in many cases, enhanced efficiency (and significant additional flexibility) may be gained via an investigation of the dual of this problem. In this paper we consider an algorithm for solving such a dual and also indicate how it may be implemented on conventional (i.e. single objective) simplex software.     

A Cantorian potential theory for describing dynamical systems on El Naschie’s space–time

In this paper we analyze classical systems, in which motion is not on a classical continuous path, but rather on a Cantorian one. Starting from El Naschie’s space–time we introduce a mathematical approach based on a potential to describe the interaction system-support. We study some relevant force fields on Cantorian space and analyze the differences with respect to the analogous case on a continuum in the context of Lagrangian formulation. Here we confirm the idea proposed by the first author in dynamical systems on El Naschie’s ϵ^(∞) Cantorian space–time that a Cantorian space could explain some relevant stochastic and quantum processes, if the space acts as an harmonic oscillating support, such as that found in Nature. This means that a quantum process could sometimes be explained as a classical one, but on a nondifferential and discontinuous support. We consider the validity of this point of view, that in principle could be more realistic, because it describes the real nature of matter and space. These do not exist in Euclidean space or curved Riemanian space–time, but in a Cantorian one. The consequence of this point of view could be extended in many fields such as biomathematics, structural engineering, physics, astronomy, biology and so on.     

Improved gradient method for monotone and lipschitz continuous mappings in banach spaces

Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space E and {A_n}_(n∈N) be a family of monotone and Lipschitz continuos mappings of C into E~*. In this article, we consider the improved gradient method by the hybrid method in mathematical programming [10] for solving the variational inequality problem for{A_n} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.     

Simulation modelling is 50! Do we need a reality check?

Simulation modelling is a fascinating research field. The techniques and tools of simulation modelling have been used to research and investigate the behaviour of various systems in a wide range of areas such as commerce, computer networks, defence, health, manufacturing and transportation. Indeed, the study of the use of these techniques and tools, and the development of new forms of these, are a rich source of research in their own right. Simulation modelling is about to reach the 50th anniversary of the development of GSP (General Simulation Program), the first simulation modelling language (Tocher and Owen, 1960). There have been several historical accounts of simulation modelling research. To complement these, we have performed a review of the recent history of simulation modelling. This study targeted three leading journals dedicated to this field. These are the ACM Transactions of Modeling and Computer Simulation, Simulation: Transactions of The Society for Modeling and Simulation International and Simulation Modelling Practice and Theory (formerly Simulation Practice and Theory). The study covered the first 6 years of this century (2000–2005) and included 576 papers. The key observation of this work was the relative lack of ‘real world’ involvement in simulation modelling research and an even greater lack of evidence of ‘real world’ benefit, arguably very alarming outcomes for an applied field. To further investigate this observation two additional surveys were carried out, one to study if real world papers appeared in the more widely known OR/MS literature (837 papers in 12 journals) and one to study if such papers appeared in Manufacturing and Logistics, an application area closely associated with simulation modelling (1077 papers in 10 journals). The results of these surveys confirmed our observations. We ask if this is the natural evolution of a field that has existed for half a century or an indication of a worrying problem? This paper reports on our findings and discusses whether or not simulation modelling research urgently needs to face a ‘reality check.’     

Mathematical programming based heuristics for improving LP-generated classifiers for the multiclass supervised classification problem

Mathematical programming is used as a nonparametric approach to supervised classification. However, mathematical programming formulations that minimize the number of misclassifications on the design dataset suffer from computational difficulties. We present mathematical programming based heuristics for finding classifiers with a small number of misclassifications on the design dataset with multiple classes. The basic idea is to improve an LP-generated classifier with respect to the number of misclassifications on the design dataset. The heuristics are evaluated computationally on both simulated and real world datasets.     

Some integer programs arising in the design of main frame computers

In this paper we describe and discuss a problem that arises in the (global) design of a main frame computer. The task is to assign certain functional units to a given number of so called multi chip modules or printed circuit boards taking into account many technical constraints and minimizing a complex objective function. We describe the real world problem. A thorough mathematical modelling of all aspects of this problem results in a rather complicated integer program that seems to be hopelessly difficult — at least for the present state of integer programming technology. We introduce several relaxations of the general model, which are alsoNP-hard, but seem to be more easily accessible. The mathematical relations between the relaxations and the exact formulation of the problem are discussed as well.On leave from University of São Paulo, Brazil.     

Reduced order modeling of nonlinear time periodic systems subjected to external periodic excitations

In this work, new methodologies for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov–Floquet (L–F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and nonlinearity takes the form of quasiperiodic functions. The techniques proposed here construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system.Specifically, two methods are discussed to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’. The second novel technique proposed here extends the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on this extended invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via extended invariant manifold approach is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handling systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. It is anticipated that these order reduction techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.     

Enhancing the image of mathematics by association with simple pleasures from real world contexts

Those who market people or products choose their images very carefully. They create positive associations in the public's mind by photographing their clients with sporting heroes or national icons. In this paper we present a variety of evidence to show that a major and overlooked reason for teachers' use and choice of real world problems is to take advantage of this ‘halo effect’ to improve studients' attitude towards learning mathematics. Analysis of interviews, reports, and results of a brief survey from teachers of middle secondary school classes indicate that they place a very high priority on positive attitudes and hence both choose and enhance real world problems to promote studients' affective engagement through simple pleasures. Pleasant sensory stimuli, generally non-cognitive and peripheral to the situation to be modelled, are used to promote a positive view of mathematics. This is a good strategy for creating enjoyable and memorable lessons, but there is a danger that it may override more substantive learning goals.     

Mathematical programming in rough environment

Classical mathematics is usually crisp while most real-life problems are not; therefore, classical mathematics is usually not suitable for dealing with real-life problems. In this article, we present a systematic and focused study of the application of rough sets (Z. Pawlak, Rough sets, In. J. Comput. Informa. Sci. 11 (1982), pp. 341–356.) to a basic area of decision theory, namely ‘mathematical programming’. This new framework concerns mathematical programming in a rough environment and is called ‘rough programming’ (L. Baoding, Theory and Practice of Uncertain Programming, 1st ed., Physica-Verlag, Heidelberg, 2002; E.A. Youness, Characterizing solutions of rough programming problems, Eut. J. Oper. Res. 168 (2006), pp. 1019–1029). It implies the existence of the roughness in any part of the problem as a result of the leakage, uncertainty and vagueness in the available information. We classify rough programming problems into three classes according to the place of the roughness. In rough programming, wherever roughness exists, new concepts like rough feasibility and rough optimality come to the front of our interest. The study of convexity for rough programming problems plays a key role in understanding global optimality in a rough environment. For this, a theoretical framework of convexity in rough programming and conceptualization of the solution is created on the lines of their crisp counterparts.     

Modeling, inference and optimization of regulatory networks based on time series data

In this survey paper, we present advances achieved during the last years in the development and use of OR, in particular, optimization methods in the new gene-environment and eco-finance networks, based on usually finite data series, with an emphasis on uncertainty in them and in the interactions of the model items. Indeed, our networks represent models in the form of time-continuous and time-discrete dynamics, whose unknown parameters we estimate under constraints on complexity and regularization by various kinds of optimization techniques, ranging from linear, mixed-integer, spline, semi-infinite and robust optimization to conic, e.g., semi-definite programming. We present different kinds of uncertainties and a new time-discretization technique, address aspects of data preprocessing and of stability, related aspects from game theory and financial mathematics, we work out structural frontiers and discuss chances for future research and OR application in our real world.     

Model Design Based on the Systems Approach

It is shown how the (extended) systems approach can be successfully used to design mathematical models in a highly systematic way. The systems approach supports interdisciplinarity in that it encourages participation of non-mathematicians in the model design process. The systems approach also leads to a clear documentation of a model.The basic principle explained in this paper is that indices of a model represent elements of an element set of a system, and that variables and constants of a model represent attributes of the elements. Multi-indexed variables and constants refer to attributes of ‘complex entities’ (from extended systems terminology) which cover the information between the elements.     

The Blackett Memorial Lecture 18 November 1997

It is argued that movement toward the ‘control’ aspects of management should be effected to expand OR/MS activities beyond their present (almost exclusive) emphasis on ‘planning’ functions. This will involve increasing the amount of empirical-inferential approaches to research (based on ex-post data) as one way to help bring this about. Examples of such empirical-inferential research activities in OR/MS are supplied by reference to the early (founding) work of PMS Blackett and others on high-level policy problems during World War II. Extensions to the control function are evidenced in the work of Robert Fetter and others in the development of Diagnostic Related Groups on which the Prospective Payment Systems are based with large and important impacts on the health care delivery systems in the USA as well as other countries. Other examples covered include the use of OR concepts in the early ‘turnaround’ of Federal Express from failure to success. Other new methods will nevertheless be needed to extend and improve presently available OR/MS approaches. Some of these possibilities are illustrated with Data Envelopment Analysis. Ways to combine DEA with commonly used statistical methods are described to show how new and old methods may be combined to further enhance their power and range. Similar relations of DEA to other OR/MS approaches are now being studied, some of which are presently occurring with ‘fuzzy sets’ and ‘multiple objective programming.’     

Where is Difference? Processes of Mathematical Remediation through a Constructivist Lens

In this study, we challenge the deficit perspective on mathematical knowing and learning for children labeled as LD, focusing on their struggles not as a within student attribute, but rather as within teacher-learner interactions. We present two cases of fifth-grade students labeled LD as they interacted with a researcher-teacher during two constructivist-oriented teaching experiments designed to foster a concept of unit fraction. Data analysis revealed three main types of interactions, and how they changed over time, which seemed to support the students’ learning: Assess, Cause and Effect Reflection, and Comparison/Prediction Reflection. We thus argue for an intervention in interaction that occurs in the instructional process for students with LD, which should replace attempts to “fix” ‘deficiencies’ that we claim to contribute to disabling such students.     

Posynomial geometric programming with interval exponents and coefficients

Geometric programming provides a powerful tool for solving nonlinear problems where nonlinear relations can be well presented by an exponential or power function. In the real world, many applications of geometric programming are engineering design problems in which some of the problem parameters are estimates of actual values. This paper develops a solution method when the exponents in the objective function, the cost and the constraint coefficients, and the right-hand sides are imprecise and represented as interval data. Since the parameters of the problem are imprecise, the objective value should be imprecise as well. A pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the objective values. Based on the duality theorem and by applying a variable separation technique, the pair of two-level mathematical programs is transformed into a pair of ordinary one-level geometric programs. Solving the pair of geometric programs produces the interval of the objective value. The ability of calculating the bounds of the objective value developed in this paper might help lead to more realistic modeling efforts in engineering optimization areas.     

Mathematic education in a cultural setting

The paper develops some proposals for curriculum development in mathematics based on an analysis of the intercultural transmission of mathematical knowledge. By introducing a concept of culture which calls for an analysis of individual and social behaviours, we are lead to recognize ‘ethnomathematics’ as a form of structured knowledge and to recognize ‘matheracy’ as a characteristic behaviour of human beings. Upon these two concepts, we introduce a theoretical framework for curriculum development in mathematics.

Curricular space is conceptualized as a three‐dimensional space with components, contents, methods and objectives considered solidarily. This relies upon an epistemology of action, based on an integration of episteme, techne and praxis. This allows for an approach in which theory and practice are in a dialectical relationship. Special reference is made to the problems of mathematical education for culturally differentiated groups, and in particular to the situation in third‐world countries.     

A directed topic model applied to call center improvement

We propose subject matter expert refined topic (SMERT) allocation, a generative probabilistic model applicable to clustering freestyle text. SMERT models are three‐level hierarchical Bayesian models in which each item is modeled as a finite mixture over a set of topics. In addition to discrete data inputs, we introduce binomial inputs. These ‘high‐level’ data inputs permit the ‘boosting’ or affirming of terms in the topic definitions and the ‘zapping’ of other terms. We also present a collapsed Gibbs sampler for efficient estimation. The methods are illustrated using real world data from a call center. Also, we compare SMERT with three alternative approaches and two criteria. Copyright © 2015 John Wiley & Sons, Ltd.