Interesting Class Of Problems Research Articles

Sample size calculations for the experimental comparison of multiple algorithms on multiple problem instances

This work presents a statistically principled method for estimating the required number of instances in the experimental comparison of multiple algorithms on a given problem class of interest. This approach generalises earlier results by allowing researchers to design experiments based on the desired best, worst, mean or median-case statistical power to detect differences between algorithms larger than a certain threshold. Holm’s step-down procedure is used to maintain the overall significance level controlled at desired levels, without resulting in overly conservative experiments. This paper also presents an approach for sampling each algorithm on each instance, based on optimal sample size ratios that minimise the total required number of runs subject to a desired accuracy in the estimation of paired differences. A case study investigating the effect of 21 variants of a custom-tailored Simulated Annealing for a class of scheduling problems is used to illustrate the application of the proposed methods for sample size calculations in the experimental comparison of algorithms.

Moral Uncertainty Over Policy Evaluation

When performing intertemporal cost-benefit analyses of policies, both in terms of climate change and other long-term problems, the discounting problem becomes critical. The question is how to weight intertemporal costs and benefits to generate present value equivalents. This thesis argues that those best placed to answer the discounting problem are domain experts, not moral philosophers or the public at large. It does this by arguing that the discounting problem is a special case of an interesting class of problems, those which are both what I call morally complex and quantitative.

Sample size estimation for power and accuracy in the experimental comparison of algorithms

Experimental comparisons of performance represent an important aspect of research on optimization algorithms. In this work we present a methodology for defining the required sample sizes for designing experiments with desired statistical properties for the comparison of two methods on a given problem class. The proposed approach allows the experimenter to define desired levels of accuracy for estimates of mean performance differences on individual problem instances, as well as the desired statistical power for comparing mean performances over a problem class of interest. The method calculates the required number of problem instances, and runs the algorithms on each test instance so that the accuracy of the estimated differences in performance is controlled at the predefined level. Two examples illustrate the application of the proposed method, and its ability to achieve the desired statistical properties with a methodologically sound definition of the relevant sample sizes.

Nonlinear Dynamics in Chemical Reaction Engineering: In Celebration of Moshe Sheintuch's 70th Birthday

This special issue of the Israel Journal of Chemistry is dedicated to Moshe Sheintuch, one of the pioneers in the field of nonlinear dynamics of chemical reactors. Moshe, who turned 70 in July of 2017, is Professor Emeritus at the Chemical Engineering Department at the Technion – Israel Institute of Technology, where he has worked since 1977. A central theme in his versatile research, which spans more than three decades, is the analysis of increasingly complex dynamic regimes in chemical reactors. Moshe's career started with the analysis of chemical oscillations in heterogeneous catalysis. This was the “golden age” of nonlinear dynamics in chemistry, when most of the nonlinear effects predicted by mathematicians were being systematically confirmed in experiments with homogeneous reacting systems, including chemical oscillations in solutions and gas phase combustion. Moshe's research was devoted to examining these phenomena and their possible practical applications in real chemical reactors. Moshe's work on nonlinear chemical dynamics investigated the effects on interphase transport, which plays a critical role in heterogeneous catalysis and electrochemistry. He showed how these effects can both destroy the patterns that exist in homogeneous reactors and create new spatiotemporal regimes. Most notably, he discovered the emergence of symmetry broken states, such as standing fronts and antiphase oscillations, in chemical systems under global control and predicted, over three decades ago, their plausible role in biological systems (1–3). The full significance of these patterns has been understood only recently, in the context of the analysis of symmetry breaking in cell biology. Indeed, many of the processes involved in directed cell migration and asymmetrical localization of intracellular proteins can be successfully interpreted using the theory developed by Sheintuch and his colleagues (4, 5). Another set of important results is related to the analysis of propagating reaction fronts and pulses. Moshe's experiments revealed the existence of such patterns in a packed bed catalytic reactor, a workhorse of chemical industry (6–8). In addition to explaining how such patterns arise through the interplay of interphase transport and chemistry, he proposed several strategies for harnessing these patterns in novel reactor configurations (9–14). These are just two key examples from the list of Moshe's contributions to nonlinear analysis of chemical reactors. The field of nonlinear chemical dynamics is in excellent shape and continues to offer exciting problems to the new generation of scientists and engineers. This collection of articles is a snapshot of the current research. The topics range from the mathematics of chemical reaction networks (paper by Craciun), to propagating chemical waves (papers by Pribyl and colleagues, and Yochelis), and studies of nonlinear dynamics on networks (paper by Kiss). A new research direction use nonlinear dynamics in the design of new materials (papers by Steinbock and Kuksenok). Another class of interesting problems comes from the efforts to systematically engineer nonlinear regimes starting from individual reactions; see the reviews by Taylor, Epstein, and Semenov. Finally, even though the practical uses of nonlinear dynamics in chemical industry are still rare, there has been a recent resurgence of interest in periodic operation chemical reactors. The reviews by Simakov et al and Morgenstein and Petkovska present theoretical progress in this area. Given the fact that biology provides numerous of examples of successful uses of nonlinear patterns (see the review of traveling waves during embryonic cell cycles by Di Talia), the efforts to emulate this success in chemical industry are worth pursuing. Studies of nonlinear dynamics in chemistry have gone a long way since Moshe started his research career. We argue that some of the most exciting developments are still to come, enabled by the recent advances in monitoring multivariable chemical dynamics in chemical reactors and living systems. Furthermore, we are yet to establish truly predictive models, which can be used to design and control nonlinear dynamics of chemical systems to the extent accomplished in electrical engineering and optics. How does one start to construct and validate such models? This question often arises in conversations with Moshe. He recommends starting with the simplest possible model, analyzing it completely, and adding realistic details as needed. This approach served him well throughout his distinguished career and continues to be an excellent example for his students and colleagues. However, the recent revolution in information technology and big data may disrupt long held conventions (see the review by Kevrekidis). We wish both Moshe and the entire field of nonlinear chemical dynamics many more healthy and productive years.

For Bayesians, Rational Modesty Requires Imprecision

G Belot (2013) has recently developed a novel argument against Bayesianism. He shows that there is an interesting class of problems that, intuitively, no rational belief forming method is likely to get right. But a Bayesian agent’s credence, before the problem starts, that she will get the problem right has to be 1. This is an implausible kind of immodesty on the part of Bayesians.1 My aim is to show that while this is a good argument against traditional, precise Bayesians, the argument doesn’t neatly extend to imprecise Bayesians. As such, Belot’s argument is a reason to prefer imprecise Bayesianism to precise Bayesianism. For present purposes, the precise Bayesian agent has just two defining characteristics. First, their credences in all propositions are given by a particular countably additive probability function. Second, those credences are updated by conditionalisation as new information comes in. These commitments are quite strong in some respects. They say that there is a single probability function that supplies the agent’s credences no matter which question is being investigated, and no matter how little evidence the agent has before the investigation is started. The everyday statistician, even one who is sympathetic to Bayesian approaches, may feel no need to sign up for anything this strong. But many philosophers seem to be interested in varieties of Bayesianism that are just this strong. For instance, there has been extensive discussion in recent epistemology of whether various epistemological approaches, such as dogmatism, can be

Dynamic problems for metamaterials: Review of existing models and ideas for further research

Metamaterials are materials especially engineered to have a peculiar physical behaviour, to be exploited for some well-specified technological application. In this context we focus on the conception of general micro-structured continua, with particular attention to piezoelectromechanical structures, having a strong coupling between macroscopic motion and some internal degrees of freedom, which may be electric or, more generally, related to some micro-motion. An interesting class of problems in this context regards the design of wave-guides aimed to control wave propagation.The description of the state of the art is followed by some hints addressed to describe some possible research developments and in particular to design optimal design techniques for bone reconstruction or systems which may block wave propagation in some frequency ranges, in both linear and non-linear fields.

Short messages

This paper has three purposes. The first one is to explain to a general audience what is involved in retrieving a web page or performing some other complex network transaction, and what can make it slow, and why the problem of slowness is likely to get worse as networked applications become more complex. The second is to describe, to those who program networked applications, certain facts that we have learnt from modelling communication networks, notably the fact of heavy-tailed distributions in traffic, which may allow more efficient applications to be written. The third is to describe to network modellers an interesting class of problems relating to algorithm design for communication networks.

Reliable Numerical Computation in Civil Engineering

Civil engineering is a field – as are many other engineering sciences – where most of the methods used for solving optimization problems are based on experience and experiments, and models using local information, but drawn from global models. The present work outlines an interesting class of problems from this field, and initiates some possible ways to solve those problems utilizing the wide tool capabilities of interval arithmetic for error handling and interval branch-and-bound algorithms to solve the original or modified industrial models automating civil engineers' work. The investigations are in the first state but are promising both in a theoretical and in a practical sense.

Normal and sinkless petri nets

We examine both the modeling power of normal and sinkless Petri nets and the computational complexities of various classical decision problems with respect to these two classes. We argue that although neither normal nor sinkless Petri nets are strictly more powerful than persistent Petri nets, they nonetheless are both capable of modeling a more interesting class of problems. On the other hand, we give strong evidence that normal and sinkless Petri nets are easier to analyze than persistent Petri nets. In so doing, we apply techniques originally developed for conflict-free Petri nets—a class defined solely in terms of the structure of the net—to sinkless Petri nets—a class defined in terms of the behavior of the net. As a result, we give the first comprehensive complexity analysis of a class of potentially unbounded Petri nets defined in terms of their behavior.

Vectorization of Linear Recurrence Relations

In this paper the usefulness of the partition method [S. C. Chen, D. J. Kuck, and A. H. Sameh, ACM Trans. Math. Software, 4 (1978), pp. 270–277], [H. H. Wang, ACM Trans. Math. Software, 7 (1981), pp. 170–183] for solving linear bidiagonal systems on vector computers is studied. It is shown that the method is numerically stable for an interesting class of problems. For different vector computers suitable variants of the method are computed and upper bounds for their performance are presented. Also reported are some actually observed performances in a FORTRAN environment.

Real-Time Analog-Digital Computation

The relative advantages of analog and digital tech niques in simulating complex, nonlinear systems in real-time are discussed. A hybrid configuration is suggested consisting of a basic digital computer and peripheral, high-speed analog elements used on a time-shared basis under the control of the digital program. Programs for function generation and for the solution of the aircraft roll equation are presented to illustrate the operation of the hybrid computer and the significant increase in the effective computing speed of the digital computer that results from the incorporation of peripheral analog elements. Further gains can be made by tailoring the order code and logic of the digital computer to the specific prob lem class of interest. The hypothesis is presented that a hybrid computer is technically feasible today that would be competitive with analog techniques on the basis of both cost and the ability to simulate natural aircraft frequencies in real-time. Moreover, such a computer would offer substantial advantages with respect to accuracy, dynamic range, flexibility, size, power consumption, and reliability.

Real-Time Analog-Digital Computation

The relative advantages of analog and digital techniques in simulating complex, nonlinear systems in real-time are discussed. A hybrid configuration is suggested consisting of a basic digital computer and peripheral, high-speed analog elements used on a time-shared basis under the control of the digital program. Programs for function generation and for the solution of the aircraft roll equation are presented to illustrate the operation of the hybrid computer and the significant increase in the effective computing speed of the digital computer that results from the incorporation of peripheral analog elements. Further gains can be made by tailoring the order code and logic of the digital computer to the specific problem class of interest. The hypothesis is presented that a hybrid computer is technically feasible today that would be competitive with analog techniques on the basis of both cost and the ability to simulate natural aircraft frequencies in real-time. Moreover, such a computer would offer substantial advantages with respect to accuracy, dynamic range, flexibility, size, power consumption, and reliability.

Notes on a Combinatorial Problem of B. O. Koopman

AT the recent International Conference on Operational Research, B. 0. Koopman' posed an interesting class of problems in the Combinatorial Analysis of Operations. Koopman defined the class of problem and then considered a simple example of that class, obtaining rough upper and lower limits to the numerical quantity required. In these notes I consider this simple example and obtain limits which are closer than those obtained by Koopman. Lastly, I consider the class of problems to which the approximate methods given here may be extended.

An Algebraic Treatment of the Theorem of Closure

1. Among the classic theorems concerning the proj ective properties of a pair of conics, perhaps the most interesting is one due to Poncelet, viz. the theorem that if a polygon of n sides can be circumscribed about one conic and at the same time inscribed in a second conic, it is possible to construct an infinite number of such polygons for the given pair of conics. A very elegant demonstration of this theorem may be made by the use of elliptic functions, but a parallel algebraic treatment is also possible. From an algebraic point of view, we have here but one example of a certain interesting class of problems in elimination. We shall mention the general algebraic problem, but shall carry through the details only in the hyperelliptic case. Except in so far as is necessary to make the algebraic steps clear no discussion will be -made of the numerous geometric corollaries that suggest themselves. The present treatment is an attempt to reduce the problem to its simplest form and to prove the theorems needed with a minimum of algebraic machinery. Little emphasis is placed upon the numerous features which serve to individualize the elliptic within the general hyperelliptic problem. The functions considered are those well-known in the transcendental theory, although the methods of proof are of necessity largely new. Constant use has been made of the remarkably clearly written Traite des Fonctions Elliptiques by Halphen. It should be noted that not only are the operations used in this paper algebraic, but that except for a single irrationality, it, every step is essentially rational. Neither the notions of geometric continuity nor of convergence of series are required at any stage. Thus the present discussion is applicable in its entirety to finite fields, a statement which does not hold true of the algebraic treatments already published. Extensive references to the literature on the problem of closure in the elliptic case may be found in the Encyklopddie der Math. Wiss., III, C 1, p. 45 ff., the Encyk. der Geometrie (Simon), p. 105 ff. and in Pascal's Repertorium, IIF, p. 238 ff. Modern algebraic treatments of the Poncelet Polygons are given by 97