A note on contributions concerning nonseparable spaces with respect to signal processing within Bayesian frameworks

In this paper, we discuss the study of some signal processing problems within Bayesian frameworks and semigroups theory, in the case where the Banach space under consideration may be nonseparable. For applications, the suggested approach may be of interest in situations where approximation in the norm of the space is not possible. We describe the idea for the case of the abstract Cauchy problem for the evolution equation and provide more detailed example of the diffusion equation with the initial data in the nonseparable Morrey space.     

Empirical Likelihood Type Confidence Intervals Under Random Censorship

In this paper a simple way to obtain empirical likelihood type confidenceintervals for the mean under random censorship is suggested. An extension tothe more general case where the functional of interest is an M-functional isdiscussed and the proposed technique is used to construct confidenceintervals for quantiles. The results of a simulation study carried out toassess the accuracy of these inferential procedures are also given.     

Consistent conjectures in a dynamic model of non-renewable resource management

We consider a model of non-renewable resource extraction where players do not know their opponents’ utility functions and form conjectures on the behavior of others. Two forms of beliefs are introduced, one based on the state of the resource, the other on this state and on the others’ strategy (their consumption). We focus on consistent equilibria, where beliefs must be consistent with observed past plays. Closed form expressions of the optimal policies are derived. Comparisons are made with the full information benchmark case. With strategy and state based beliefs, the agents may behave more (respectively, less) aggressively than in the non-cooperative benchmark depending on the initial consumption level. When initial consumption is low, the optimal consumption path lies below that of the cooperative benchmark. We conclude the analysis by discussing the impact of public policies on the agents’ choice of consumption patterns, and the robustness of the results for the case of renewable resources.     

A Goal Programming Model for Staff Scheduling at a Telecommunications Center

In this paper, a mathematical model is developed to solve a staff scheduling problem for a telecommunications center. Currently, weekly schedules are manually produced. The manual nature of the process and the large number of constraints and goals lead to a situation where the used schedules are both inefficient and unfair. A zero-one linear goal programming model is suggested to find an optimized cyclical schedule. The center objectives as well as the engineers’ preferences are taken into account. The developed model had to produce balanced schedules that provide the required coverage while satisfying fairness considerations, in terms of weekends off, working night shifts, isolated days on, and isolated days off. A staffing analysis and mathematical properties have been developed to find the optimal parameters of the staff scheduling model. A 6-week scheduling period has been suggested instead of the current weekly period. Work patterns have been suggested to improve schedules quality. These work patterns have been mathematically formulated as a set of soft constraints. The suggested mathematical model has been implemented using Lingo software. The optimal cyclical schedule has been found. It significantly increases both efficiency and staff satisfaction. The suggested approach can be used for any similar staff scheduling problem.     

Envy-free rights assignments and self-oriented preferences

Very recently a new solution to Sen's “Impossibility of a Paretian liberal” has been suggested where the focus is on the rights assignments per se (Austen-Smith, 1979). It was shown that the concept of fairness, when applied to rights, admits the existence of social decision functions which satisfy Sen's original conditions. Unfortunately this result collapses when individuals have rights over more than one pair of alternatives.In order to obtain possibility results for this more general case the present paper proposes to restrict individuals' preference orderings. It is proved that envy-free collective choice rules exist if individual preferences are self-oriented and if, in addition, people attach primary importance to their own private sphere alternatives. These restrictions are quite severe, but they may be justified if one values the absence of envy in rights allocations very highly.     

Four solution techniques for a general one machine scheduling problem: A comparative study

Gelders and Kleindorfer suggested a generalized detailed scheduling cost structure, based on the sum of weighted tardiness and weighted flowtime. They solved the single-machine scheduling problem using a transportation scheme to obtain lower bounds in their branch and bound approach. Recently, Fisher, Baker, Rinnooy Kan and Srinivasan reported attractive computation times with general algorithms adapted to the total tardiness problem for the single-machine case. In this paper four algorithms are adapted to the generalized cost structure mentioned above and extensive computational results are presented.This investigation shows that much is to be expected from the dual approach for more complex scheduling problems while dynamic programming deserves a new research effort because of its efficiency in special structured problems and/or problems where a posteriori precedence relations (dominance criteria) can be developed.     

Criterion of unitary similarity of minimal passive scattering systems with a given transfer function

We establish necessary and sufficient conditions under which all minimal passive scattering systems that have a given transfer operator function are unitarily equivalent. These conditions can be significantly simplified in special cases important for applications, in particular, in the case where a transfer function is rational and in a more general case where this function is pseudoextendable.     

Coping strategies applied to comprehend multistep arithmetic word problems by students with above-average numeracy skills and below-average reading skills

This article discusses how 13-year-old students with above-average numeracy skills and below-average reading skills cope with comprehending word problems. Compared to other students who are proficient in numeracy and are skilled readers, these students are more disadvantaged when solving single-step and multistep arithmetic word problems. The difference is smaller for single-step word problems. Analysis of large-scale data as well as a case study suggested that students used knowledge of stereotype item formats and keywords to cope with comprehending word problems. Instances where students used prior experiences to form predispositions to word problems were observed in the case study. In addition, analyses in both studies revealed that errors caused by overuse of keywords were more frequent among the students with below-average reading skills.     

Unveiling connectivity patterns of categories in complex systems: An application to human needs in urban places

We present a methodology based on weighted networks and dependence coefficients aimed at revealing connectivity patterns between categories. As a case study, it is applied to an urban place and at two spatial levels—neighborhood and square—where categories correspond to human needs. Our results show that diverse spatial levels present different and nontrivial patterns of need emergence. A numerical model indicates that these patterns depend on the probability distribution of weights. We suggest that this way of analyzing the connectivity of categories (human needs in our case study) in social and ecological systems can be used to define new strategies to cope with complex processes, such as those related to transition management and governance, urban-making, and integrated planning.     

Volatility estimation for stochastic project value models

One of the key parameters in modeling capital budgeting decisions for investments with embedded options is the project volatility. Most often, however, there is no market or historical data available to provide an accurate estimate for this parameter. A common approach to estimating the project volatility in such instances is to use a Monte Carlo simulation where one or more sources of uncertainty are consolidated into a single stochastic process for the project cash flows, from which the volatility parameter can be determined. Nonetheless, the simulation estimation method originally suggested for this purpose systematically overstates the project volatility, which can result in incorrect option values and non-optimal investment decisions. Examples that illustrate this issue numerically have appeared in several recent papers, along with revised estimation methods that address this problem. In this article, we extend that work by showing analytically the source of the overestimation bias and the adjustment necessary to remove it. We then generalize this development for the cases of levered cash flows and non-constant volatility. In each case, we use an example problem to show how a revised estimation methodology can be applied.     

Asymptotic behavior of dynamic equations ontime scales

As a way to unify a discussion of many kinds of problems for equations in the contionous and discrete case(but also in order to reveal discrepancies between both cases), a theory of "time scales" was proposed and developed by Sulbach and Hilger. In our paper we investigate the asymptoic behaviour of so-called dynamic equations on time scales, and sych dynamic equations are differentialequations in the continous case and difference equations in the discrete case. We offer a perturbation result that leads to a time scales version of Levinson's Fundamental Lemma. Crucial are a dichotomy condition and a growth condition on the perturbation. Also, in the case that Levinson's result cannot be applied immediately, we suggest several preliminary transformations that might lead to a situation where Levinson's lemma is applicable. Such tranformations have been suggested by Harris and Lutz in the continuous case and by Benzaid and Lutz in the discrete case. Both those cases are covered by our theory, plus cases "in between". Examples for such cases will also be discussed in this paper.     

Two canonical wedge problems for the Helmholtz equation

Boundary-transmission problems for two-dimensional Helmholtz equations in a quadrant and its complement, respectively, are considered in a Sobolev space setting. The first problem of a quadrant with Dirichlet condition on one face and transmission condition on the other is solved in closed form for the case where all the quadrants are occupied by the same medium. Unique solvability can also be shown in the case of two different media up to exceptional cases of wave numbers, while the Fredholm property holds in general. In the second problem, transmission conditions are prescribed on both faces. Similar results are obtained in the one-medium case, but the two-media case turns out to be more complicated and the equivalent system of boundary pseudodifferential equations cannot be completely analysed by this reasoning.     

The variable radius covering problem

In this paper we propose a covering problem where the covering radius of a facility is controlled by the decision-maker; the cost of achieving a certain covering distance is assumed to be a monotonically increasing function of the distance (i.e., it costs more to establish a facility with a greater covering radius). The problem is to cover all demand points at a minimum cost by finding optimal number, locations and coverage radii for the facilities. Both, the planar and discrete versions of the model are considered. Heuristic approaches are suggested for solving large problems in the plane. These methods were tested on a set of planar problems. Mathematical programming formulations are proposed for the discrete problem, and a solution approach is suggested and tested.     

On scalarization of vector optimization type problems

We consider scalarization issues for vector problems in the case where the preference relation is represented by a rather arbitrary set. An algorithm for weights choice for a priori unknown preference relations is suggested. Some examples of applications to vector optimization, game equilibrium, and variational inequalities are described.     

Counting Prime Juggling Patterns

Juggling patterns can be described by a closed walk in a (directed) state graph, where each vertex (or state) is a landing pattern for the balls and directed edges connect states that can occur consecutively. The number of such patterns of length n is well known, but a long-standing problem is to count the number of prime juggling patterns (those juggling patterns corresponding to cycles in the state graph). For the case of \(b=2\) balls we give an expression for the number of prime juggling patterns of length n by establishing a connection with partitions of n into distinct parts. From this we show the number of two-ball prime juggling patterns of length n is \((\gamma -o(1))2^n\) where \(\gamma =1.32963879259\ldots \). For larger b we show there are at least \(b^{n-1}\) prime cycles of length n.     

Asymptotic properties of conditional maximum likelihood estimator in a certain exponential model

The conditional maximum likelihood estimator is suggested as an alternative to the maximum likelihood estimator and is favorable for an estimator of a dispersion parameter in the normal distribution, the inverse-Gaussian distribution, and so on. However, it is not clear whether the conditional maximum likelihood estimator is asymptotically efficient in general. Consider the case where it is asymptotically efficient and its asymptotic covariance depends only on an objective parameter in an exponential model. This remand implies that the exponential model possesses a certain parallel foliation. In this situation, this paper investigates asymptotic properties of the conditional maximum likelihood estimator and compares the conditional maximum likelihood estimator with the maximum likelihood estimator. We see that the bias of the former is more robust than that of the latter and that two estimators are very close, especially in the sense of bias-corrected version. The mean Pythagorean relation is also discussed.     

Quadratic programming with M-Matrices

In this paper, we study the problem of quadratic programming with M-matrices. We describe (1) an effective algorithm for the case where the variables are subject to a lower-bound constraint, and (2) an analogous algorithm for the case where the variables are subject to lower-and-upper-bound constraints. We demonstrate the special monotone behavior of the iterate and gradient vectors. The result on the gradient vector is new. It leads us to consider a simple updating procedure which preserves the monotonicity of both vectors. The procedures uses the fact that an M-matrix has a nonnegative inverse. Two new algorithms are then constructed by incorporating this updating procedure into the two given algorithms. We give numerical examples which show that the new methods can be more efficient than the original ones.     

Allocating energy in a first-to-n match

This paper models a decision where a player must allocate limitedenergy over a contest of uncertain length. The motivating exampleis a squash match where one of the players is not as fit asthe other. Should a player's energy be concentrated in the earlygames of the match? Should it be spread evenly over all possiblegames? Or should it be conserved for the end of the match? Wemodel this as a decision problem where, in each game, the decision-makermust determine how much energy to expend. We assume that thereare only a small number of discrete energy choices for eachgame and that the more energy the decision-maker expends, themore likely he is to win that game. We solve for the optimaldecision with dynamic programming. With only two possible energychoices for each game, we show that it does not matter how energyis expended. In the case where there are three or more energychoices, we show how to take advantage of the structure of theproblem to determine the optimal sequence of decisions. As forpractical advice, the model suggests that when the decision-makerfalls behind in a match, he ought to switch to a more conservativeapproach by dividing his remaining energy evenly among all thepossible remaining games. Received 14 May 2003. Revised 5 January 2004.     

The Möbius function of separable and decomposable permutations

We give a recursive formula for the Möbius function of an interval [σ,π] in the poset of permutations ordered by pattern containment in the case where π is a decomposable permutation, that is, consists of two blocks where the first one contains all the letters 1,2,…,k for some k. This leads to many special cases of more explicit formulas. It also gives rise to a computationally efficient formula for the Möbius function in the case where σ and π are separable permutations. A permutation is separable if it can be generated from the permutation 1 by successive sums and skew sums or, equivalently, if it avoids the patterns 2413 and 3142.We also show that the Möbius function in the poset of separable permutations admits a combinatorial interpretation in terms of normal embeddings among permutations. A consequence of this interpretation is that the Möbius function of an interval [σ,π] of separable permutations is bounded by the number of occurrences of σ as a pattern in π. Another consequence is that for any separable permutation π the Möbius function of (1,π) is either 0, 1 or −1.