On a New Approach for Finding All the Modified Cut-Sets in an Incompatibility Graph
TL;DR: The problem involving the compatibility relation in a broader perspective is considered and a new approach for finding aU the modified cut-sets of the incompatibility graph of a set having a compatibility relation between its different pairs of elements is suggested.
Abstract: The compatibility relation occurs in many different disciplines in science and engineering. When a compatibility relation exists between pairs of elements in a set, an important problem is to derive the collection of aU those elements that form maximal compatibles. If the set of elements with the compatibility relation can be visualized as a compatibility graph of which the different nodes represent the elements of the set, the only edges of the graph being the nonoriented lines joining pairs of elements with the compatibility relation, then the problem of deriving the maximal compatibles becomes identical to the graph theory problem of finding all the maximal complete subgraphs in a symmetric graph. Recently, in connection with simplifying incompletely specified sequential machines, where a kind of compatibility relation also exists between pairs of internal states, Das and Sheng proposed a method for deriving the different maximal compatibles through finding all of the modified cut-sets of the incompatibility graph of the machine. This paper, without confining itself to only incompletely specified machines, considers the problem involving the compatibility relation in a broader perspective and suggests a new approach for finding aU the modified cut-sets of the incompatibility graph of a set having a compatibility relation between its different pairs of elements.
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TL;DR: In this article, the results of a search for events containing at least one long-lived particle that decays at a significant distance from its production point into two leptons or into five or more charged particles are presented.
Abstract: Many extensions of the Standard Model posit the existence of heavy particles with long lifetimes. This article presents the results of a search for events containing at least one long-lived particle that decays at a significant distance from its production point into two leptons or into five or more charged particles. This analysis uses a data sample of proton-proton collisions at root s = 8 TeV corresponding to an integrated luminosity of 20.3 fb(-1) collected in 2012 by the ATLAS detector operating at the Large Hadron Collider. No events are observed in any of the signal regions, and limits are set on model parameters within supersymmetric scenarios involving R-parity violation, split supersymmetry, and gauge mediation. In some of the search channels, the trigger and search strategy are based only on the decay products of individual long-lived particles, irrespective of the rest of the event. In these cases, the provided limits can easily be reinterpreted in different scenarios.
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...The selected tracks are used to construct a multitrack DV by means of an algorithm based on the incompatibilitygraph approach [55]....
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...In order to resolve such ambiguities, an iterative process based on the incompatibility graph approach [75] is applied....
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Abstract: This paper reviews classical and adaptive methods of track and vertex reconstruction in particle physics experiments. Adaptive methods have been developed to meet the experimental challenges at high-energy colliders, in particular, the CERN Large Hadron Collider. They can be characterized by the obliteration of the traditional boundaries between pattern recognition and statistical estimation, by the competition between different hypotheses about what constitutes a track or a vertex, and by a high level of flexibility and robustness achieved with a minimum of assumptions about the data. The theoretical background of some of the adaptive methods is described, and it is shown that there is a close connection between the two main branches of adaptive methods: neural networks and deformable templates, on the one hand, and robust stochastic filters with annealing, on the other hand. As both classical and adaptive methods of track and vertex reconstruction presuppose precise knowledge of the positions of the sensitive detector elements, the paper includes an overview of detector alignment methods and a survey of the alignment strategies employed by past and current experiments.
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Cites methods from "On a New Approach for Finding All t..."
...An algorithm that solves this problem is given by Das 1973 ....
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References
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Book•
01 Jan 1961
524 citations
"On a New Approach for Finding All t..." refers methods in this paper
...Borrowing the concept ofcut-set fromgraphtheory[ 17 ], amodified cut-set wasdefined inthefollowing way....
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TL;DR: A partially enumerative solution to the problem of reducing the number of rows in a flow table in which some of the entries are unspecified is presented and a rough indication of the efficiency of the given procedures is obtained.
Abstract: Given a sequential switching function in the form of a flow table in which some of the entries are unspecified, the problem of reducing the number of rows in that flow table is extremely complex, and cannot, in general, be solved by any simple extension of the methods used for completely specified functions. An analysis of the problem is presented, and a partially enumerative solution is evolved. A rough indication of the efficiency of the given procedures may be obtained from the fact that these techniques have been successfully applied to approximately two dozen tables ranging up to about 15 rows. No solution required more than two hours.
305 citations
"On a New Approach for Finding All t..." refers background in this paper
...Fig. 2 . Incompatibility graphoffive elements....
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...Intheareaofsequential switching theory, forthe minimization ofincompletely specified sequential machines, akindofbinary relation R,called thecompatibility relation between thedifferent ordered pairsof internal states, isdefined [ 2 ]-[14]....
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...Theorem 2 :Inanedge-inclusion table corresponding toanincompatibility grapheverycolumncontains two andonlytwonodes....
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...elements consist ofk different isolated subgraphs I,, 12,**,Ik,whereeachsubgraph 1i, i=1, 2 ,....
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...Thetotal numberofedgesinthesubgraphisn(n-1)/ 2 . A complete subgraph Cmofasymmetric graphC isamaximalcomplete subgraph ifand onlyifthere doesnotexist anynodeinCoutside ofthe subgraph Cmwhichisadjacent toallthenodesofCm....
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285 citations
TL;DR: A method is illustrated for minimizing the number of internal states in incompletely specified sequential networks and it is shown that only some compatibility classes (prime compatibility classes) need be considered as members of a solution.
Abstract: A method is illustrated for minimizing the number of internal states in incompletely specified sequential networks. The minimization algorithm applies to any type of incompletely specified flow table. It is shown that only some compatibility classes (prime compatibility classes) need be considered as members of a solution. The selection of prime classes may be obtained as the solution of an integer linear program or by tabular techniques that are an extension of those used in the selection of prime implicants.
163 citations
TL;DR: The feasibility of this program depends on the CYCLE time, the REQUIRED MINIMAL GREEN TIMES and the PAIRWISE INCOMPATIBILITIES and thePAIRWise InCOMPatIBILITIES.
125 citations
"On a New Approach for Finding All t..." refers background in this paper
...Another interesting exampleinwhichanidentical typeofcompatibility relation occurs isinconnection withscheduling oftraffic lights whereanimportant problem istodetermine themaximum flowoftraffic through anintersection during the various traffic light phases[ 16 ]....
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