On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

Exact and approximate stepdown methods for multiple hypothesis testing

Consider the problem of testing k hypotheses simultaneously. In this paper,we discuss finite and large sample theory of stepdown methods that providecontrol of the familywise error rate (FWE). In order to improve upon theBonferroni method or Holm's (1979) stepdown method, Westfall and Young(1993) make eective use of resampling to construct stepdown methods thatimplicitly estimate the dependence structure of the test statistics. However,their methods depend on an assumption called subset pivotality. The goalof this paper is to construct general stepdown methods that do not requiresuch an assumption. In order to accomplish this, we take a close look atwhat makes stepdown procedures work, and a key component is a monotonicityrequirement of critical values. By imposing such monotonicity on estimatedcritical values (which is not an assumption on the model but an assumptionon the method), it is demonstrated that the problem of constructing a validmultiple test procedure which controls the FWE can be reduced to the problemof contructing a single test which controls the usual probability of a Type 1error. This reduction allows us to draw upon an enormous resamplingliterature as a general means of test contruction.

Assigning proctors to exams with scatter search

In this paper we present an algorithm to assign proctors toexams. This NP-hard problem is related to the generalized assignmentproblem with multiple objectives. The problem consists of assigningteaching assistants to proctor final exams at a university. We formulatethis problem as a multiobjective integer program (IP) with a preferencefunction and a workload-fairness function. We then consider also a weightedobjective that combines both functions. We develop a scatter searchprocedure and compare its outcome with solutions found by solving theIP model with CPLEX 6.5. Our test problems are real instances from aUniversity in Spain.

Multiple prisoner's dilemma games with (out) an outside option: An experimental study

Experiments in which subjects play simultaneously several finite prisoner's dilemma supergames with and without an outside optionreveal that: (i) subjects use probabilistic start and endeffect behaviour, (ii) the freedom to choose whether to play the prisoner's dilemma game enhances cooperation, (iii) if the payoff for simultaneous defection is negative, subjects' tendency to avoid losses leads them to cooperate; while this tendency makes them stick to mutual defection if its payoff is positive.

Computation of multiple correspondence analysis, with code in R

The generalization of simple correspondence analysis, for two categorical variables, to multiple correspondence analysis where they may be three or more variables, is not straighforward, both from a mathematical and computational point of view. In this paper we detail the exact computational steps involved in performing a multiple correspondence analysis, including the special aspects of adjusting the principal inertias to correct the percentages of inertia, supplementary points and subset analysis. Furthermore, we give the algorithm for joint correspondence analysis where the cross-tabulations of all unique pairs of variables are analysed jointly. The code in the R language for every step of the computations is given, as well as the results of each computation.

Multiple correspondence analysis of a subset of response categories

In the analysis of multivariate categorical data, typically the analysis of questionnaire data, it is often advantageous, for substantive and technical reasons, to analyse a subset of response categories. In multiple correspondence analysis, where each category is coded as a column of an indicator matrix or row and column of Burt matrix, it is not correct to simply analyse the corresponding submatrix of data, since the whole geometric structure is different for the submatrix . A simple modification of the correspondence analysis algorithm allows the overall geometric structure of the complete data set to be retained while calculating the solution for the selected subset of points. This strategy is useful for analysing patterns of response amongst any subset of categories and relating these patterns to demographic factors, especially for studying patterns of particular responses such as missing and neutral responses. The methodology is illustrated using data from the International Social Survey Program on Family and Changing Gender Roles in 1994.

Contracting externalities and multiple equilibria in sectors: Theory and evidence

We consider an economy where the production technology has constantreturns to scale but where in the descentralized equilibrium thereare aggregate increasing returns to scale. The result follows froma positive contracting externality among firms. If a firms issurrounded by more firms, employees have more opportunitiesoutside their own firm. This improves employees' incentives toinvest in the presence of ex post renegotiation at the firm level,at not cost. Our leading result is that if a region is sparselypopulated or if the degree of development in the region is lowenough, there are multiple equilibria in the level of sectorialemployment. From the theoretical model we derive a non-linearfirst-order censored difference equation for sectoral employment.Our results are strongly consistent with the multiple equilibriahypothesis and the existence of a sectoral critical scale (belowwich the sector follows a delocation process). The scale of theregions' population and the degree of development reduce thecritical scale of the sector.

Case study of intracerebral plasmacytoma as an initial presentation of multiple myeloma.

Cerebral involvement is an uncommon complication of multiple myeloma. We report on a 64-year-old man hospitalized for a partial seizure. MRI showed two intracerebral lesions, which proved to be plasmacytomas. After complete staging, we retained the diagnosis of immunoglobulin G lambda-type multiple myeloma with CNS involvement. Cytogenetic analysis of plasma cells detected a deletion in the p53 gene at 17p13.1. Despite cranial radiotherapy and systemic chemotherapy, the patient's disease progressed rapidly and he died five months after diagnosis. What makes this case unusual is that overt multiple myeloma had been absent before cerebral involvement was discovered. It confirms the extremely poor prognosis of patients with CNS myeloma even in the presence of aggressive treatment. Cytogenetic abnormalities could be a marker of chromosomal and genetic instability, conferring to multiple myeloma a more aggressive profile.

Contrasting the functional properties of GABAergic axon terminals with single and multiple synapses in the thalamus

Diverse sources of GABAergic inhibition are a major feature of cortical networks, but distinct inhibitory input systems have not been systematically characterized in the thalamus. Here, we contrasted the properties of two independent GABAergic pathways in the posterior thalamic nucleus of rat, one input from the reticular thalamic nucleus (nRT), and one "extrareticular" input from the anterior pretectal nucleus (APT). The vast majority of nRT-thalamic terminals formed single synapses per postsynaptic target and innervated thin distal dendrites of relay cells. In contrast, single APT-thalamic terminals formed synaptic contacts exclusively via multiple, closely spaced synapses on thick relay cell dendrites. Quantal analysis demonstrated that the two inputs displayed comparable quantal amplitudes, release probabilities, and multiple release sites. The morphological and physiological data together indicated multiple, single-site contacts for nRT and multisite contacts for APT axons. The contrasting synaptic arrangements of the two pathways were paralleled by different short-term plasticities. The multisite APT-thalamic pathway showed larger charge transfer during 50-100 Hz stimulation compared with the nRT pathway and a greater persistent inhibition accruing during stimulation trains. Our results demonstrate that the two inhibitory systems are morpho-functionally distinct and suggest and that multisite GABAergic terminals are tailored for maintained synaptic inhibition even at high presynaptic firing rates. These data explain the efficacy of extrareticular inhibition in timing relay cell activity in sensory and motor thalamic nuclei. Finally, based on the classic nomenclature and the difference between reticular and extrareticular terminals, we define a novel, multisite GABAergic terminal type (F3) in the thalamus.

Multiple sclerosis-related trigeminal neuralgia: a prospective series of 43 patients treated with gamma knife surgery with more than one year of follow-up.

BACKGROUND: Trigeminal neuralgia (TN) related to multiple sclerosis (MS) is more difficult to manage pharmacologically and surgically. OBJECTIVE: This article aims to evaluate the safety and efficacy of Gamma Knife surgery (GKS) in this special group of patients. METHODS: Between July 1992 and November 2010, 43 cases with more than 1 year of follow-up were operated with GKS for TN related to MS and prospectively evaluated in the Timone University Hospital, Marseille, France. Radiosurgery using the Gamma Knife (model B or C or Perfexion) was performed. A single 4-mm isocenter was positioned at a median distance of 8 mm (range 5.7-14.7) anterior to the emergence of the nerve. A median maximum dose of 85 Gy (range 75-90) was delivered. RESULTS: The median follow-up period was 53.8 months (12-157.1). Thirty-nine patients (90.7%) were initially pain free. Their actuarial probability of remaining pain free without medication at 6 months, 1, 3, 5 and 10 years was 87.2, 71.8, 43.1, 38.3 and 20.5%, respectively, and remained stable till 12 years. The hypoesthesia actuarial rate at 6 months, 1 and 2 years was 11.5, 11.5 and 16%, and remained stable till 12 years. CONCLUSIONS: GKS proved safe and effective in this special group of patients.

From correspondence analysis to multiple and joint correspondence analysis

The generalization of simple (two-variable) correspondence analysis to more than two categorical variables, commonly referred to as multiple correspondence analysis, is neither obvious nor well-defined. We present two alternative ways of generalizing correspondence analysis, one based on the quantification of the variables and intercorrelation relationships, and the other based on the geometric ideas of simple correspondence analysis. We propose a version of multiple correspondence analysis, with adjusted principal inertias, as the method of choice for the geometric definition, since it contains simple correspondence analysis as an exact special case, which is not the situation of the standard generalizations. We also clarify the issue of supplementary point representation and the properties of joint correspondence analysis, a method that visualizes all two-way relationships between the variables. The methodology is illustrated using data on attitudes to science from the International Social Survey Program on Environment in 1993.

Multiple filtering devices for the estimation of cyclical DSGE models

We propose a method to estimate time invariant cyclical DSGE models using the informationprovided by a variety of filters. We treat data filtered with alternative procedures as contaminated proxies of the relevant model-based quantities and estimate structural and non-structuralparameters jointly using a signal extraction approach. We employ simulated data to illustratethe properties of the procedure and compare our conclusions with those obtained when just onefilter is used. We revisit the role of money in the transmission of monetary business cycles.

A simple model of multiple equilibria based on risk

This paper shows how risk may aggravate fluctuations in economies with imperfect insurance and multiple assets. A two period job matching model is studied, in which risk averse agents act both as workers and as entrepreneurs. They choose between two types of investment: one type is riskless, while the other is a risky activity that creates jobs.Equilibrium is unique under full insurance. If investment is fully insured but unemployment risk is uninsured, then precautionary saving behavior dampens output fluctuations. However, if both investment and employment are uninsured, then an increase in unemployment gives agents an incentive to shift investment away from the risky asset, further increasing unemployment. This positive feedback may lead to multiple Pareto ranked equilibria. An overlapping generations version of the model may exhibit poverty traps or persistent multiplicity. Greater insurance is doubly beneficial in this context since it can both prevent multiplicity and promote risky investment.

Location of multiple server common service centers or public facilities for minimizing general congestion and travel cost functions

We propose a model and solution methods, for locating a fixed number ofmultiple-server, congestible common service centers or congestible publicfacilities. Locations are chosen so to minimize consumers congestion (orqueuing) and travel costs, considering that all the demand must be served.Customers choose the facilities to which they travel in order to receiveservice at minimum travel and congestion cost. As a proxy for thiscriterion, total travel and waiting costs are minimized. The travel costis a general function of the origin and destination of the demand, whilethe congestion cost is a general function of the number of customers inqueue at the facilities.