Inference about the number of contributors to a DNA mixture: Comparative analyses of a Bayesian network approach and the maximum allele count method.

In the forensic examination of DNA mixtures, the question of how to set the total number of contributors (N) presents a topic of ongoing interest. Part of the discussion gravitates around issues of bias, in particular when assessments of the number of contributors are not made prior to considering the genotypic configuration of potential donors. Further complication may stem from the observation that, in some cases, there may be numbers of contributors that are incompatible with the set of alleles seen in the profile of a mixed crime stain, given the genotype of a potential contributor. In such situations, procedures that take a single and fixed number contributors as their output can lead to inferential impasses. Assessing the number of contributors within a probabilistic framework can help avoiding such complication. Using elements of decision theory, this paper analyses two strategies for inference on the number of contributors. One procedure is deterministic and focuses on the minimum number of contributors required to 'explain' an observed set of alleles. The other procedure is probabilistic using Bayes' theorem and provides a probability distribution for a set of numbers of contributors, based on the set of observed alleles as well as their respective rates of occurrence. The discussion concentrates on mixed stains of varying quality (i.e., different numbers of loci for which genotyping information is available). A so-called qualitative interpretation is pursued since quantitative information such as peak area and height data are not taken into account. The competing procedures are compared using a standard scoring rule that penalizes the degree of divergence between a given agreed value for N, that is the number of contributors, and the actual value taken by N. Using only modest assumptions and a discussion with reference to a casework example, this paper reports on analyses using simulation techniques and graphical models (i.e., Bayesian networks) to point out that setting the number of contributors to a mixed crime stain in probabilistic terms is, for the conditions assumed in this study, preferable to a decision policy that uses categoric assumptions about N.

Splitting statistical potentials into meaningful scoring functions: testing the prediction of near-native structures from decoy conformations

Background: Recent advances on high-throughput technologies have produced a vast amount of protein sequences, while the number of high-resolution structures has seen a limited increase. This has impelled the production of many strategies to built protein structures from its sequence, generating a considerable amount of alternative models. The selection of the closest model to the native conformation has thus become crucial for structure prediction. Several methods have been developed to score protein models by energies, knowledge-based potentials and combination of both.Results: Here, we present and demonstrate a theory to split the knowledge-based potentials in scoring terms biologically meaningful and to combine them in new scores to predict near-native structures. Our strategy allows circumventing the problem of defining the reference state. In this approach we give the proof for a simple and linear application that can be further improved by optimizing the combination of Zscores. Using the simplest composite score () we obtained predictions similar to state-of-the-art methods. Besides, our approach has the advantage of identifying the most relevant terms involved in the stability of the protein structure. Finally, we also use the composite Zscores to assess the conformation of models and to detect local errors.Conclusion: We have introduced a method to split knowledge-based potentials and to solve the problem of defining a reference state. The new scores have detected near-native structures as accurately as state-of-art methods and have been successful to identify wrongly modeled regions of many near-native conformations.

ILS-ESP An efficient, simple, and parameter-free algorithm for solving the permutation flow-shop problem

From a managerial point of view, the more effcient, simple, and parameter-free (ESP) an algorithm is, the more likely it will be used in practice for solving real-life problems. Following this principle, an ESP algorithm for solving the Permutation Flowshop Sequencing Problem (PFSP) is proposed in this article. Using an Iterated Local Search (ILS) framework, the so-called ILS-ESP algorithm is able to compete in performance with other well-known ILS-based approaches, which are considered among the most effcient algorithms for the PFSP. However, while other similar approaches still employ several parameters that can affect their performance if not properly chosen, our algorithm does not require any particular fine-tuning process since it uses basic "common sense" rules for the local search, perturbation, and acceptance criterion stages of the ILS metaheuristic. Our approach defines a new operator for the ILS perturbation process, a new acceptance criterion based on extremely simple and transparent rules, and a biased randomization process of the initial solution to randomly generate different alternative initial solutions of similar quality -which is attained by applying a biased randomization to a classical PFSP heuristic. This diversification of the initial solution aims at avoiding poorly designed starting points and, thus, allows the methodology to take advantage of current trends in parallel and distributed computing. A set of extensive tests, based on literature benchmarks, has been carried out in order to validate our algorithm and compare it against other approaches. These tests show that our parameter-free algorithm is able to compete with state-of-the-art metaheuristics for the PFSP. Also, the experiments show that, when using parallel computing, it is possible to improve the top ILS-based metaheuristic by just incorporating to it our biased randomization process with a high-quality pseudo-random number generator.

On prediction of individual sequences

Sequential randomized prediction of an arbitrary binary sequence isinvestigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss, i.e., to make (almost) as few mistakes as the best ``expert'' in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction problem and empirical process theory. First, in the special case of static (memoryless) experts, we completely characterize the minimax relative loss in terms of the maximum of an associated Rademacher process. Then we show general upper and lower bounds on the minimaxrelative loss in terms of the geometry of the class of experts. As main examples, we determine the exact order of magnitude of the minimax relative loss for the class of autoregressive linear predictors and for the class of Markov experts.

Minimax lower bounds for the two-armed bandit problem

We obtain minimax lower bounds on the regret for the classicaltwo--armed bandit problem. We provide a finite--sample minimax version of the well--known log $n$ asymptotic lower bound of Lai and Robbins. Also, in contrast to the log $n$ asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable configurations of the two arms. That is, we show that for {\sl every} allocation rule and for {\sl every} $n$, there is a configuration such that the regret at time $n$ is at least 1 -- $\epsilon$ times the regret of random guessing, where $\epsilon$ is any small positive constant.

Solving two production scheduling problems with sequence-dependent set-up times

In today’s competitive markets, the importance of goodscheduling strategies in manufacturing companies lead to theneed of developing efficient methods to solve complexscheduling problems.In this paper, we studied two production scheduling problemswith sequence-dependent setups times. The setup times areone of the most common complications in scheduling problems,and are usually associated with cleaning operations andchanging tools and shapes in machines.The first problem considered is a single-machine schedulingwith release dates, sequence-dependent setup times anddelivery times. The performance measure is the maximumlateness.The second problem is a job-shop scheduling problem withsequence-dependent setup times where the objective is tominimize the makespan.We present several priority dispatching rules for bothproblems, followed by a study of their performance. Finally,conclusions and directions of future research are presented.

Locating emergency services with different priorities: The priority queuing covering location problem

Previous covering models for emergency service consider all the calls to be of the sameimportance and impose the same waiting time constraints independently of the service's priority.This type of constraint is clearly inappropriate in many contexts. For example, in urban medicalemergency services, calls that involve danger to human life deserve higher priority over calls formore routine incidents. A realistic model in such a context should allow prioritizing the calls forservice.In this paper a covering model which considers different priority levels is formulated andsolved. The model heritages its formulation from previous research on Maximum CoverageModels and incorporates results from Queuing Theory, in particular Priority Queuing. Theadditional complexity incorporated in the model justifies the use of a heuristic procedure.

Adaptive approach heuristics for the generalized assignment problem

The Generalized Assignment Problem consists in assigning a setof tasks to a set of agents with minimum cost. Each agent hasa limited amount of a single resource and each task must beassigned to one and only one agent, requiring a certain amountof the resource of the agent. We present new metaheuristics forthe generalized assignment problem based on hybrid approaches.One metaheuristic is a MAX-MIN Ant System (MMAS), an improvedversion of the Ant System, which was recently proposed byStutzle and Hoos to combinatorial optimization problems, and itcan be seen has an adaptive sampling algorithm that takes inconsideration the experience gathered in earlier iterations ofthe algorithm. Moreover, the latter heuristic is combined withlocal search and tabu search heuristics to improve the search.A greedy randomized adaptive search heuristic (GRASP) is alsoproposed. Several neighborhoods are studied, including one basedon ejection chains that produces good moves withoutincreasing the computational effort. We present computationalresults of the comparative performance, followed by concludingremarks and ideas on future research in generalized assignmentrelated problems.

Driver scheduling problem modelling

The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, for example buses, trains, plane or boat drivers or pilots, for the transportation of passengers or goods. This is a complex problem because it involves several constraints related to labour and company rules and can also present different evaluation criteria and objectives. Being able to develop an adequate model for this problem that can represent the real problem as close as possible is an important research area.The main objective of this research work is to present new mathematical models to the DSP problem that represent all the complexity of the drivers scheduling problem, and also demonstrate that the solutions of these models can be easily implemented in real situations. This issue has been recognized by several authors and as important problem in Public Transportation. The most well-known and general formulation for the DSP is a Set Partition/Set Covering Model (SPP/SCP). However, to a large extend these models simplify some of the specific business aspects and issues of real problems. This makes it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually to be implemented in real situations. Based on extensive passenger transportation experience in bus companies in Portugal, we propose new alternative models to formulate the DSP problem. These models are also based on Set Partitioning/Covering Models; however, they take into account the bus operator issues and the perspective opinions and environment of the user.We follow the steps of the Operations Research Methodology which consist of: Identify the Problem; Understand the System; Formulate a Mathematical Model; Verify the Model; Select the Best Alternative; Present the Results of theAnalysis and Implement and Evaluate. All the processes are done with close participation and involvement of the final users from different transportation companies. The planner s opinion and main criticisms are used to improve the proposed model in a continuous enrichment process. The final objective is to have a model that can be incorporated into an information system to be used as an automatic tool to produce driver schedules. Therefore, the criteria for evaluating the models is the capacity to generate real and useful schedules that can be implemented without many manual adjustments or modifications. We have considered the following as measures of the quality of the model: simplicity, solution quality and applicability. We tested the alternative models with a set of real data obtained from several different transportation companies and analyzed the optimal schedules obtained with respect to the applicability of the solution to the real situation. To do this, the schedules were analyzed by the planners to determine their quality and applicability. The main result of this work is the proposition of new mathematical models for the DSP that better represent the realities of the passenger transportation operators and lead to better schedules that can be implemented directly in real situations.

Firm investment in imperfect capital markets: A structural estimation

We set up a dynamic model of firm investment in which liquidity constraintsenter explicity into the firm's maximization problem. The optimal policyrules are incorporated into a maximum likelihood procedure which estimatesthe structural parameters of the model. Investment is positively related tothe firm's internal financial position when the firm is relatively poor. This relationship disappears for wealthy firms, which can reach theirdesired level of investment. Borrowing is an increasing function of financial position for poor firms. This relationship is reversed as a firm's financial position improves, and large firms hold little debt.Liquidity constrained firms may be unused credits lines and the capacity toinvest further if they desire. However the fear that liquidity constraintswill become binding in the future induces them to invest only when internalresources increase.We estimate the structural parameters of the model and use them to quantifythe importance of liquidity constraints on firms' investment. We find thatliquidity constraints matter significantly for the investment decisions of firms. If firms can finance investment by issuing fresh equity, rather than with internal funds or debt, average capital stock is almost 35% higher overa period of 20 years. Transitory shocks to internal funds have a sustained effect on the capital stock. This effect lasts for several periods and ismore persistent for small firms than for large firms. A 10% negative shock to firm fundamentals reduces the capital stock of firms which face liquidityconstraints by almost 8% over a period as opposed to only 3.5% for firms which do not face these constraints.

Metaheuristics for the bus-driver scheduling problem

We present new metaheuristics for solving real crew scheduling problemsin a public transportation bus company. Since the crews of thesecompanies are drivers, we will designate the problem by the bus-driverscheduling problem. Crew scheduling problems are well known and severalmathematical programming based techniques have been proposed to solvethem, in particular using the set-covering formulation. However, inpractice, there exists the need for improvement in terms of computationalefficiency and capacity of solving large-scale instances. Moreover, thereal bus-driver scheduling problems that we consider can present variantaspects of the set covering, as for example a different objectivefunction, implying that alternative solutions methods have to bedeveloped. We propose metaheuristics based on the following approaches:GRASP (greedy randomized adaptive search procedure), tabu search andgenetic algorithms. These metaheuristics also present some innovationfeatures based on and genetic algorithms. These metaheuristics alsopresent some innovation features based on the structure of the crewscheduling problem, that guide the search efficiently and able them tofind good solutions. Some of these new features can also be applied inthe development of heuristics to other combinatorial optimizationproblems. A summary of computational results with real-data problems ispresented.

The generalized index of maximum and minimum level and its application in decision making

[spa] El índice del máximo y el mínimo nivel es una técnica muy útil, especialmente para toma de decisiones, que usa la distancia de Hamming y el coeficiente de adecuación en el mismo problema. En este trabajo, se propone una generalización a través de utilizar medias generalizadas y cuasi aritméticas. A estos operadores de agregación, se les denominará el índice del máximo y el mínimo nivel medio ponderado ordenado generalizado (GOWAIMAM) y cuasi aritmético (Quasi-OWAIMAM). Estos nuevos operadores generalizan una amplia gama de casos particulares como el índice del máximo y el mínimo nivel generalizado (GIMAM), el OWAIMAM, y otros. También se desarrolla una aplicación en la toma de decisiones sobre selección de productos.

Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

The generalized index of maximum and minimum level and its application in decision making

[spa] El índice del máximo y el mínimo nivel es una técnica muy útil, especialmente para toma de decisiones, que usa la distancia de Hamming y el coeficiente de adecuación en el mismo problema. En este trabajo, se propone una generalización a través de utilizar medias generalizadas y cuasi aritméticas. A estos operadores de agregación, se les denominará el índice del máximo y el mínimo nivel medio ponderado ordenado generalizado (GOWAIMAM) y cuasi aritmético (Quasi-OWAIMAM). Estos nuevos operadores generalizan una amplia gama de casos particulares como el índice del máximo y el mínimo nivel generalizado (GIMAM), el OWAIMAM, y otros. También se desarrolla una aplicación en la toma de decisiones sobre selección de productos.

A test of Jessor's problem behavior theory in a Eurasian and a Western European developmental context.

PURPOSE: The current study tested the applicability of Jessor's problem behavior theory (PBT) in national probability samples from Georgia and Switzerland. Comparisons focused on (1) the applicability of the problem behavior syndrome (PBS) in both developmental contexts, and (2) on the applicability of employing a set of theory-driven risk and protective factors in the prediction of problem behaviors. METHODS: School-based questionnaire data were collected from n = 18,239 adolescents in Georgia (n = 9499) and Switzerland (n = 8740) following the same protocol. Participants rated five measures of problem behaviors (alcohol and drug use, problems because of alcohol and drug use, and deviance), three risk factors (future uncertainty, depression, and stress), and three protective factors (family, peer, and school attachment). Final study samples included n = 9043 Georgian youth (mean age = 15.57; 58.8% females) and n = 8348 Swiss youth (mean age = 17.95; 48.5% females). Data analyses were completed using structural equation modeling, path analyses, and post hoc z-tests for comparisons of regression coefficients. RESULTS: Findings indicated that the PBS replicated in both samples, and that theory-driven risk and protective factors accounted for 13% and 10% in Georgian and Swiss samples, respectively in the PBS, net the effects by demographic variables. Follow-up z-tests provided evidence of some differences in the magnitude, but not direction, in five of six individual paths by country. CONCLUSION: PBT and the PBS find empirical support in these Eurasian and Western European samples; thus, Jessor's theory holds value and promise in understanding the etiology of adolescent problem behaviors outside of the United States.