bluuebunny/crossref_metadata_2025_split huggingface dataset:
Grain size in script and teaching: Literacy acquisition in Ge'ez and Latin
Authors: ASFAHA YONAS MESFUN , KURVERS JEANNE , KROON SJAAK 
Published: July 2009

ABSTRACTThe study investigated reading in four African languages that use either syllabic Ge'ez (Tigrinya and Tigre languages) or alphabetic Latin scripts (Kunama and Saho). A sample of 385 Grade 1 children were given letter knowledge, word reading, and spelling tasks to investigate differences at the script and language levels. Results showed that the syllable based Ge'ez script was easier to learn than the phoneme-based Latin despite the bigger number of basic units in Ge'ez. Moreover, the syllable based teaching of alphabetic Saho produced better results than alphabetic teaching of Kunama. These findings are discussed using the psycholinguistic grain size theory. The outcomes confirm the importance of the availability of phonological units in learning to read.
On the Foundations of Nash Equilibrium
Authors: Jørgen Jacobsen Hans 
Published: July 2009

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with therecommendationof strategies, and focus instead entirely on the positive theory ofprediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction ofactual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations,conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.
Reliabilities of Consecutive-2 Graphs
Authors: Du D.Z. , Hwang F. K. 
Published: July 2009

A consecutive-2 graph is a graph where each vertex is associated with a failure probability and the graph is considered failed if any two adjacent vertices both fail. Recently, the problem of computing reliability for general consecutive-2 graph was shown to be #P-complete while polynomial algorithms exist for trees. In this paper, we give a linear time algorithm for a class of graphs including forests and cycles.For a given set of failure probabilities qi, the assignment of qi to the vertices of a given graph is optimal if it maximizes the reliability of that graph. It is known that optimal assignments for trees require messy computations while linear algorithms exist for lines and stars. In this paper, we prove that the optimal reliability of any n−tree is bounded between those of an n−line and an n−star.
Approximations in Renewal Theory
Authors: Ross Sheldon M. 
Published: July 2009

A renewal process [N(t), t ≥ 0] with interarrival times Xi, for i ≥ 1 and renewal function m (t) is considered. Let Gn, λ denote the gamma distribution with parameters n and λ–that is, dGn, λ(x) = λε–λx(λx)n-1/(n – 1)In Section 1 we show how m(t) can be approximated by f m(s) dGn, n/t(s). In addition, we show that these approximations constitute an increasing sequence of lower bounds when the interarrival distribution has the decreasing failure rate property. In Section 2 we show how the integrated renewal function can be approximated in a similar fashion by a decreasing sequence of upper bounds. In Section 3 we consider the problem of approximating the residual life (also called excess life) and the renewal age distribution and their means, and in Section 4 we consider the distribution of N(t). Finally, in Section 5 we remark on the relationship between our approximations and the Feller technique for inverting a Laplace transform.
Dynamic Repair Allocation for a k−Out−of−n System Maintained by Distinguishable Repairmen
Authors: Katehakis Michael N. , Melolidakis Costis 
Published: July 2009

We consider a K-out-of-N system maintained by R repairmen, where the lifetime of the ith component is an exponentially distributed random variable with parameter μi. Repairmen are distinguishable, and the time it takes the rth repairman to repair a failed component is an exponentially distributed random variable with parameter λr. Repaired components are as good as new and preemptions are allowed. We show that the policy that assigns the faster repairmen to the most reliable components is optimal with respect to several optimality criteria.The approach we take in establishing stochastic optimality with respect to the number of functioning components is of wide applicability to different classes of stochastic optimization problems.
When Many Wrongs Make a Right
Authors: Lippman Steven A. , Mamer John W. 
Published: July 2009

When confronted by a sequence of independent, identical, favorable-though- risky investments, a risk-averse agent will in fact elect to invest as part of a large syndicate even if he or she would not undertake even one of the investments by himself or herself. This willingness to invest emanates from the risk reduction associated with the risk pooling effected by the syndicate. Our first two theorems describe the syndicate size needed to induce the agent's participation.The consequence of adding risks is considered next. We demonstrate that the agent will undertake a large number of these independent investments by himself or herself even if each investment taken by itself constitutes a poor risk. The conditions needed to ensure this somewhat surprising result are (a) moment bounds on the investments, and (b) either a polynomial or an exponential bound on the lower tail of the agent's utility function. Finally, we draw the connection between this result, proper risk aversion, and monotonicity of the agent's absolute aversion to risk.
Balance of Recurrece Order in Time-Inhomogenous Markov Chains with Application to Simulated Annealing
Authors: Connors D. P. , Kumar P. R. 
Published: July 2009

We define a notion of order of recurrence for the states and transitions of a general class of time-inhomogeneous Markov chains with transition probabilities proportional to powers of a small vanishing parameter. These orders are shown to satisfy a balance equation across every edge cut in the associated graph. The resulting order balance equations allow computation of the orders of recurrence of the states, and thereby the determination of the asymptotic behavior of the Markov chain.The method of optimization by simulated annealing is a special case of such Markov processes, and can therefore be treated by means of these balance equations. In particular, in this special situation we show that there holds a detailed balance of order of recurrence across every edge in the graph. Moreover, the sum of the order of recurrence of a state and its cost is shown to be a constant in each connected set of recurrent states. By this approach, we determine the necessary and sufficient condition on the “rate of cooling” to guarantee that a minimum of the optimization problem is hit with probability one. Moreover, the rates of convergence of the probabilities can be deduced from the orders of recurrence.
Stochastic Decision Theory
Authors: Cockett J. Robin B. , Zrida Jalel , Birdwell J. Douglas 
Published: July 2009

The manipulations and basic results of stochastic decision theory are introduced. The manipulations of idempotence, transposition, and repetition, introduced for deterministic decision trees, can be used to manipulate stochastic trees. However, there are two major differences. First, in order to obtain a complete set of manipulations it is necessary to introduce an additional rule calledindifference. Second, these identities must be treated as rules of inference. Not all the rules can be soundly applied in both directions; in particular, idempotence is a one-way rule.A manipulation of a stochastic decision tree not only alters the structure of the tree, but also the probability distributions associated with the tree. This allows probability calculation to be viewed as structural manipulation. In particular, a retrieval corresponds to a conditional probability calculation. The algorithm for doing this calculation has, therefore, many applications. For example, the solution to the classical state-estimation problem and the retrieval of information from probabilistic or uncertain knowledge bases may both be viewed as an application of this algorithm.The main result of this paper is that these manipulations are complete and sound. In order to prove this result, it is necessary to have a semantic setting for these theories. The setting chosen is the category ofdescription spaceswhich is a generalization of the category of bounded measure spaces with maps which do not increase measure. The proof of this result exploits the retrieval properties of stochastic terms and its relationship to conditional probability calculations in the models.
Asymptotic Properties of a Recursive Procedure for Simultaneous Estimation
Authors: Reiman Martin I. 
Published: July 2009

In this paper we consider a problem that arises in estimating the heavy traffic limit of a sojourn time distribution in a queueing network during the course of a medium traffic simulation. We need to estimate α =E[f(γ,M)], where γ is an unknown constant andMa random variable. More specifically, we are given an iid sequence of random vectors {(Xi,Mi), 1 ≤ i ≤ n}, with γ =E[Xi] andMihaving the same distribution asM.For known γ, we have a standard estimation problem, which we describe here. The standard estimate is unbiased and asymptotically (asn→ 8 ) consistent. There is also a central limit theorem for this estimator. For unknown γ, we provide two estimation procedures, one that requires two passes through the data (as well as storage of {Mi, 1 ≤ i ≤ n}), and another one, which is recursive, requiring only one pass through and bounded storage. The estimators obtained from these two procedures are shown to be strongly consistent, and central limit theorems are also proven for them.
Quicker Convergence for Iterative Numerical Solutions to Stochastic Problems: Probabilistic Interpretations, Ordering Heuristics, and Parallel Processing
Authors: Greenberg Albert G. , Vanderbei Robert J. 
Published: July 2009

Gauss-Seidel is a general method for solving a system of equations (possibly nonlinear). It makes repeated sweeps through the variables; within a sweep as each new estimate for a variable is computed, the current estimate for that variable is replaced with the new estimate immediately, instead of on completion of the sweep. The idea is to use new data as soon as it is computed. Gauss- Seidel is often efficient for computing the invariant measure of a Markov chain (especially if the transition matrix is sparse), and for computing the value function in optimal control problems. In many applications the computation can be significantly improved by appropriately ordering the variables within each sweep. A simple heuristic is presented here for computing an ordering that quickens convergence. In parallel processing, several variables must be computed simultaneously, which appears to work against Gauss-Seidel. Simple asynchronous parallel Gauss-Seidel methods are presented here. Experiments indicate that the methods retain the benefit of a good ordering, while further speeding up convergence by a factor of P if P processors participate.In this paper, we focus on the optimal stopping problem. A probabilistic interpretation of the Gauss-Seidel (and the Jacobi) method for computing the value function is given, which motivates our ordering heuristic. However, the ordering heuristic and parallel processing methods apply in a broader context, in particular, to the important problem of computing the invariant measure of a Markov chain.
On the Optimality of Trunk Reservation in Overflow Processes
Authors: Nguyen Viên 
Published: July 2009

This paper discusses an optimal dynamic policy for a queueing system with M servers, no waiting room, and two types of customers. Customer types differ with respect to the reward that is paid on commencement of service, but service times are exponentially distributed with the same mean for both types of customers. The arrival stream of one customer type is generated by a Poisson process, and the other customer type arrives according to the overflow process of an M/M/m/m queue. The objective is to determine a policy for admitting customers to maximize the expected long-run average reward.By posing the problem in the framework of Markov decision processes and exploiting properties of submodular functions, the optimal policy is shown to be a “generalized trunk reservation policy”; in other words, the optimal policy accepts higher-paying customers whenever possible and accepts lower-paying customers only if fewer than c1 servers are busy, where i is the number of busy servers in the overflow queue. Computational issues are also discussed. More specifically, approximations of the overflow process by an interrupted Poisson process and a Poisson process are investigated.
Storage-Limited Queues in Heavy Traffic
Authors: Coffman E. G. , Pukhalskii A. A. , Reiman M. I. 
Published: July 2009

This paper models primary computer storage in the context of a general (GI/GI/l) queueing system. Queued items are described by sizes, or storage requirements, as well as by arrival and service times; the sum of the sizes of the items in the system is the occupied storage. Capacity constraints are represented by two different protocols for determining whether an arriving item is admitted to the system: (1) an item is accepted if and only if at its arrival time the currently occupied storage does not exceed a given constantC> 0, and (2) an item is accepted if and only if at its arrival time the occupied storage is at mostC, and the occupied storage plus the item's size is at mostC(l + ε) for some given ε > 0. We prove for both systems that in heavy traffic the occupied storage, suitably normalized, converges weakly to reflected Brownian motion with boundaries at 0 and atC. A distinctive feature of the proof is the characterization of reflected Brownian motion as a limit of unrestricted penalized processes.These results make more plausible an earlier conjecture of the authors, i.e., that one obtains the same heavy traffic limit when the admission rule is: accept an item if and only if at its arrival time the occupied storage plus the item's size is no greater thanC.
Product-Type Probability Bounds of Higher Order
Authors: Block Hentry W. , Costigan Tim , Sampson Allan R. 
Published: July 2009

GIaz and Johnson [14] introduce ith-order product-type approximations, βi, i =1,…n − 1, for Pn = P(X1 ≤c1, X2 ≤ c2,…Xn≤ cn) and show that Pn≥ βn−1 ≥ βn−2 ≥… ≥ β2 ≥ β1 when X is MTP2. In this article, it is shown thatunder weaker positive dependence conditions. For multivariate normal distributions, these conditions reduce to cov(Xi,Xj) ≥ 0 for 1 ≤ i < j ≤ n and cov(Xi,Xj| Xj−1) ≥ 0 for 1 ≤ i < j − 1, j = 3,…,n. This is applied to group sequential analysis with bivariate normal responses. Conditions for Pn ≥ β3 ≥ β2 ≥β1 are also derived. Bound conditions are also obtained that ensure that product-type approximations are nested lower bounds to upper orthant probabilities P(X1 > C1,…,Xn > cn). It is shown that these conditions are satisfied for the multivariate exponential distribution of Marshall and Olkin [20].
Optimal Sampling for Identifying a Cluster: An Application in Sorting
Authors: Gal Shmuel , Sheinwald Dafna 
Published: July 2009

We consider the following problem. For a given population of m items, we have to make a decision whether or not the population includes a relatively large cluster of identical items. This decision affects the effectiveness of a subsequent computational process, depending on the actual existence of the cluster and its size. To make a good decision, we use a statistical sample which should indicate the existence of a cluster and find a representative thereof. This paper describes the optimal sampling technique to be used in such a case, given the cost of the sampling and the potential gain in speed of the subsequent process. The optimal fixed sample size is specified, as well as the optimal sequential sampling, along with characterizing the dependence of the cost function on the truncation point.For the case that the a priori distribution of the cluster proportion is known, we present formulae by which the optimal sampling procedures can be easily calculated. For the common situation in which the a priori distribution is not known, we present, in the case of a fixed sample size, a tight upper bound for the sample size, which is independent of the a priori distribution, and for the case of the sequential sampling, we present an approximately optimal truncation point, which is also independent of the a priori distribution.The situation described arose in connection with choosing the best sorting method, an application that will be described in full detail. The most interesting practical result is that for our application truncating the sequential procedure at 35 observations, out of a population of 25,000–30,000 items, guarantees that in our sorting application we are always within 2.1% of the optimal cost independently of the a priori distribution.
On Queues with Interarrival Times Proportional to Service Times
Authors: Cidon Israel , Guréin Roch , Khamisy Asad , Sidi Moshe 
Published: July 2009

We analyze a family of queueing systems where the interarrival timeIn+1between customersnandn+ 1 depends on the service timeBnof customern. Specifically, we consider cases where the dependency betweenIn+1andBnis aproportionalityrelation andBnis an exponentially distributed random variable. Such dependencies arise in the context of packet-switched networks that use rate policing functions to regulate the amount of data that can arrive to a link within any given time interval. These controls result in significant dependencies between the amount of work brought in by customers/packets and the time between successive customers. The models developed in the paper and the associated solutions are, however, of independent interest and are potentially applicable to other environments.Several scenarios that consist of adding an independent random variable to the interarrival time, allowing the proportionality to be random and the combination of the two are considered. In all cases, we provide expressions for the Laplace-Stieltjes Transform of the waiting time of a customer in the system. Numerical results are provided and compared to those of an equivalent system without dependencies.
An Aggregation/Disaggregation Algorithm for Stochastic Automata Networks
Authors: Buchholz Peter 
Published: July 2009

Stochastic automata networks (SANs) have recently received much attention in the literature as a means to analyze complex Markov chains in an efficient way. The main advantage of SANs over most other paradigms is that they allow a very compact description of the generator matrix by means of much smaller matrices for single automata. This representation can be exploited in different iterative techniques to compute the stationary solution. However, the set of applicable solution methods for SANs is restricted, because a solution method has to respect the specific representation of the generator matrix to exploit the compact representation. In particular, aggregation/disaggregation (a/d) methods cannot be applied in their usual realization for SANs without losing the possibility to exploit the compact representation of the generator matrix.In this paper, a new a/d algorithm for SANs is introduced. The algorithm differs significantly from standard a/d methods because the parts to be aggregated are defined in a completely different way, exploiting the structure of the generator matrix of a SAN. Aggregation is performed with respect to single automata or sets of automata, which are the basic parts generating a SAN. It is shown that the new algorithm is efficient even if the automata are not loosely coupled.
Rainflow Cycles for Switching Processes with Markov Structure
Authors: Johannesson Pär 
Published: July 2009

The concept of rainflow cycles is often used in fatigue of materials for analyzing load processes. Methods are developed for computation of the rainflow matrix for a random load that is changing properties over time due to changes of the system dynamics; for example, for a random vehicle load it could reflect different driving conditions. The random load is modeled by a switching process with Markov regime; that is, the random load changes properties according to a hidden (not observed) Markov chain.An algorithm is developed for a switching process where each part of the load is modeled by a Markov chain. As only the local extremes are of importance for rainflow analysis, another approach is to model the sequence of turning points by a Markov chain. The main result of this paper is an algorithm for computation of the rainflow matrix for a switching process where each part is described by a Markov chain of turning points. The algorithms are illustrated by numerical examples.
The Maximum of a Random Walk and Its Application to Rectangle Packing
Authors: Coffman E. G. , Flajolet Philippe , Flatto Leopold , Hofri Micha 
Published: July 2009

Let S0,…,Sn be a symmetric random walk that starts at the origin (S0 = 0) and takes steps uniformly distributed on [— 1,+1]. We study the large-n behavior of the expected maximum excursion and prove the estimate,where c = 0.297952.... This estimate applies to the problem of packing n rectangles into a unit-width strip; in particular, it makes much more precise the known upper bound on the expected minimum height, O(n½), when the rectangle sides are 2n independent uniform random draws from [0,1].
The Law of Arms-Control and International Supervision
Authors: Myjer Eric P.J. 
Published: July 2009

“[…]for in the international community the rule of law generally ranks second after politics.”“Basis van goede verstandhouding kan slechts het recht zijn. Recht alleen kan goede houdingen bestendigen, geschillen voorkomen of bevredigend oplossen. Onrecht, geweld en anarchie voeren tot ondergang, omdat er kiem van destructie zit in al wat niet rechtens is.”
The Judging of War Criminals:Individual Responsibility and Jurisdiction
Authors: Kooijmans Peter H. 
Published: July 2009

In a recent interview with a Dutch newspaper, Lord Owen, until the beginning of June Co-Chairman of the International Conference on the Former Yugoslavia, said:[W]e were instructed by the conference to make recommendations on the establishment of a war crimes tribunal. We decided that this tribunal should be completely disconnected from the negotiating process. It should have a life of its own in order to enable us the negotiators for the UN and the EU to say that we had nothing to do with it in case the matter would be brought up to us.