Zeev Barzily

PLANNING THE ROUTE SYSTEM FOR URBAN BUSES

Abstract It is assumed that the number of buses to be operated during the various periods of the day, which is the primary factor determining costs, has already been determined and is a problem constraint. The method determines the frequencies on each route but no attempt at scheduling is made. The city is divided into zones and the number of journeys to be made by the public between each pair of zones is a data input expressed in matrix form. The objective function, to be minimized, is the sum of the journey time (which includes allowance for transfer times) plus discomfort penalties proportional to the number of passengers who cannot find seats. The planning method has two phases. In the first, desirable routes, which may be added to an initial set of routes, are generated; and routes, which may be deleted from the augmented set of routes, are pointed out. The routes to be added are selected from a set of candidate routes each of which is based on a route skeleton consisting of four zones with the extremes restricted to a set of terminal zones. In the second phase, optimal frequencies for a set of routes, under the constraint of a given number of available buses, are determined by a gradient method. The optimal value of the objective function in the second phase serves as a more accurate evaluator of a generated set of routes. Fortran programs implementing the two phases have been run for the Haifa area which was represented by 41 zones. The route determining algorithm produces a set of routes in 3 min C.P.U. on an I.B.M. 360 50 . The frequency program effectively minimized the objective function for 20 routes in 15 min run time on an I.B.M. 360 44 . There is strong evidence that the programs provide useful results and they appear to be useful planning tools.

Bayes procedures for detecting a shift in the probability of success in a series of Bernoulli trials

Abstract The determination of a stopping rule for the detection of the time of an increase in the success probability of a sequence of independent Bernoulli trials is discussed. Both success probabilities are assumed unknown. A Bayesian approach is applied; the distribution of the location of the shift in the success probability is assumed geometric and the success probabilities are assumed to have known joint prior distribution. The costs involved are penalties for late or early stoppings. The nature of the optimal dynamic programming solution is discussed and a procedure for obtaining a suboptimal stopping rule is determined. The results indicate that the detection procedure is quite effective.

Resampling approach for cluster model selection

In cluster analysis, selecting the number of clusters is an “ill-posed” problem of crucial importance. In this paper we propose a re-sampling method for assessing cluster stability. Our model suggests that samples’ occurrences in clusters can be considered as realizations of the same random variable in the case of the “true” number of clusters. Thus, similarity between different cluster solutions is measured by means of compound and simple probability metrics. Compound criteria result in validation rules employing the stability content of clusters. Simple probability metrics, in particular those based on kernels, provide more flexible geometrical criteria. We analyze several applications of probability metrics combined with methods intended to simulate cluster occurrences. Numerical experiments are provided to demonstrate and compare the different metrics and simulation approaches.

An application of the minimal spanning tree approach to the cluster stability problem

Among the areas of data and text mining which are employed today in OR, science, economy and technology, clustering theory serves as a preprocessing step in the data analyzing. An important component of clustering theory is determination of the true number of clusters. This problem has not been satisfactorily solved. In our paper, this problem is addressed by the cluster stability approach. For several possible numbers of clusters, we estimate the stability of the partitions obtained from clustering of samples. Partitions are considered consistent if their clusters are stable. Clusters validity is measured by the total number of edges, in the clusters’ minimal spanning trees, connecting points from different samples. Actually, we use the Friedman and Rafsky two sample test statistic. The homogeneity hypothesis of well mingled samples, within the clusters, leads to an asymptotic normal distribution of the considered statistic. Resting upon this fact, the standard score of the mentioned edges quantity is set, and the partition quality is represented by the worst cluster, corresponding to the minimal standard score value. It is natural to expect that the true number of clusters can be characterized by the empirical distribution having the shortest left tail. The proposed methodology sequentially creates the described distribution and estimates its left-asymmetry. Several presented numerical experiments demonstrate the ability of the approach to detect the true number of clusters.

CLUSTER STABILITY ESTIMATION BASED ON A MINIMAL SPANNING TREES APPROACH

Among the areas of data and text mining which are employed today in science, economy and technology, clustering theory serves as a preprocessing step in the data analyzing. However, there are many open questions still waiting for a theoretical and practical treatment, e.g., the problem of determining the true number of clusters has not been satisfactorily solved. In the current paper, this problem is addressed by the cluster stability approach. For several possible numbers of clusters we estimate the stability of partitions obtained from clustering of samples. Partitions are considered consistent if their clusters are stable. Clusters validity is measured as the total number of edges, in the clusters’ minimal spanning trees, connecting points from different samples. Actually, we use the Friedman and Rafsky two sample test statistic. The homogeneity hypothesis, of well mingled samples within the clusters, leads to asymptotic normal distribution of the considered statistic. Resting upon this fact, the stand...

Energy-Efficient Predictive Jamming Holes Detection Protocol for Wireless Sensor Networks

Wireless sensor networks (WSN) are practical implementations of distributed computing ad-hoc wireless networks. Typically empowered with scarce energy resources and limited computing power, they are mainly used for in situ data acquisition and monitoring of the deployment area. As such, they are susceptible to various forms of jamming, at the physical and data link layer. Of special interest are the moving jammers, which impose added strain on the WSN. We developed a detection protocol that takes into consideration the jammers behavior and accordingly adopts new routes, in order to maximize the WSN life. We simulated our algorithm, which is an improvement of the well known LEACH energy- efficient routing protocol, vs. the original LEACH. We have found a significant improvement of the WSN lifetime, offering a proved improvement in the resilience of WSN against moving jamming attacks.

A cluster stability criteria based on the two-sample test concept

A method for assessing cluster stability is presented in this paper. We hypothesize that if one uses a “consistent” clustering algorithm to partition several independent samples then the clustered samples should be identically distributed. We use the two sample energy test approach for analyzing this hypothesis. Such a test is not very efficient in the clustering problems because outliers in the samples and limitations of the clustering algorithms heavily contribute to the noise level. Thus, we repeat calculating the value of the test statistic many times and an empirical distribution of this statistic is obtained. We choose the value of the “true” number of clusters as the one which yields the most concentrated distribution. Results of the numerical experiments are reported.

On Application of a Probabilistic K-Nearest Neighbors Model for Cluster Validation Problem

K-Nearest Neighbors is a widely used technique for classifying and clustering data. In the current article, we address the cluster stability problem based upon probabilistic characteristics of this approach. We estimate the stability of partitions obtained from clustering pairs of samples. Partitions are presumed to be consistent if their clusters are stable. Clusters validity is quantified through the amount of K-Nearest Neighbors belonging to the points sample. The null-hypothesis, of the well-mixed samples within the clusters, suggests Binomial Distribution of this quantity with K trials and the success probability 0.5. A cluster is represented by a summarizing index, of the p-values calculated over all cluster objects, under the null hypothesis for the alternative, and the partition quality is evaluated via the worst partition cluster. The true number of clusters is attained by the empirical index distribution having maximal suitable asymmetry. The proposed methodology offers to produce the index distributions sequentially and to assess their asymmetry. Numerical experiments exhibit a good capability of the methodology to expose the true number of clusters.

On Platoon Formation on Two-Lane Roads,

Abstract : An approximate model for the study of platoon formation on two-lane highways is discussed in detail. The model assumes that the two-lane highway is divided in each traffic direction into alternating road sections of fixed lengths. The passing in one type of section is unrestricted and the passing in the other one is prohibited. It is assumed that there are slow and fast vehicles on the highway and the inputs follow independent Poisson processes. The results include the distribution of the number of vehicles in a platoon and the average speed of a typical fast vehicle. (Author)

Hidden ancient repeats in DNA: Mapping and quantification

We have shown, in a previous paper, that tandem repeating sequences, especially triplet repeats, play a very important role in gene evolution. This result led to the formulation of the following hypothesis: most of the genomic sequences evolved through everlasting acts of tandem repeat expansions with subsequent accumulation of changes. In order to estimate how much of the observed sequences have the repeat origin we describe the adaptation of a text segmentation algorithm, based on dynamic programming, to the mapping of the ancient expansion events. The algorithm maximizes the segmentation cost, calculated as the similarity of obtained fragments to the putative repeat sequence. In the first application of the algorithm to segmentations of genomic sequences, a significant difference between the natural sequences and the corresponding shuffled sequences is detected. The natural fragments are longer and more similar to the putative repeat sequences. As our analysis shows, the coding sequences allow for repeats only when the size of the repeated words is divisible by three. In contrast, in the non-coding sequences, all repeated word sizes are present. It was estimated, that in Escherichia coli K12 genome, about 35.5% of sequence can be detectably traced to original simple repeat ancestors. The results shed light on the genomic sequence organization, and strongly confirm the hypothesis about the crucial role of triplet expansions in gene origin and evolution.