scholarly journals Dynamic Threshold Strategy for Universal Best Choice Problem

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Jakub Kozik
Keyword(s):  
Partially Ordered Sets ◽  
Dynamic Threshold ◽  
Ordered Sets ◽  
Threshold Strategy ◽  
Choice Problem ◽  
Best Choice Problem ◽  
Partial Analysis ◽  
Probability Of Success ◽  
New Strategy ◽  
International Audience

International audience We propose a new strategy for universal best choice problem for partially ordered sets. We present its partial analysis which is sufficient to prove that the probability of success with this strategy is asymptotically strictly greater than 1/4, which is the value of the best universal strategy known so far.

scholarly journals Operations on partially ordered sets and rational identities of type A

2013 ◽  
Vol Vol. 15 no. 2 (Combinatorics) ◽  
Author(s):  
Adrien Boussicault
Keyword(s):  
Partially Ordered Sets ◽  
Rational Functions ◽  
Hasse Diagram ◽  
Linear Extensions ◽  
Ordered Sets ◽  
Closed Expression ◽  
Schubert Polynomials ◽  
Special Cases ◽  
The Family ◽  
International Audience

Combinatorics International audience We consider the family of rational functions ψw= ∏( xwi - xwi+1 )-1 indexed by words with no repetition. We study the combinatorics of the sums ΨP of the functions ψw when w describes the linear extensions of a given poset P. In particular, we point out the connexions between some transformations on posets and elementary operations on the fraction ΨP. We prove that the denominator of ΨP has a closed expression in terms of the Hasse diagram of P, and we compute its numerator in some special cases. We show that the computation of ΨP can be reduced to the case of bipartite posets. Finally, we compute the numerators associated to some special bipartite graphs as Schubert polynomials.

Percolation and best-choice problem for powers of paths

2017 ◽  
Vol 54 (2) ◽  
pp. 343-362
Author(s):  
Fabricio Siqueira Benevides ◽  
Małgorzata Sulkowska
Keyword(s):  
Optimal Algorithm ◽  
Random Order ◽  
Upper And Lower Bounds ◽  
Directed Path ◽  
Choice Problem ◽  
Percolation Process ◽  
Best Choice Problem ◽  
Probability Of Success ◽  
Maximal Vertex ◽  
A Site

AbstractThe vertices of thekth power of a directed path withnvertices are exposed one by one to a selector in some random order. At any time the selector can see the graph induced by the vertices that have already appeared. The selector's aim is to choose online the maximal vertex (i.e. the vertex with no outgoing edges). We give upper and lower bounds for the asymptotic behaviour ofpn,kn1/(k+1), wherepn,kis the probability of success under the optimal algorithm. In order to derive the upper bound, we consider a model in which the selector obtains some extra information about the edges that have already appeared. We give the exact asymptotics of the probability of success under the optimal algorithm in this case. In order to derive the lower bound, we analyse a site percolation process on a sequence of thekth powers of a directed path withnvertices.

scholarly journals Arrangements Of Minors In The Positive Grassmannian And a Triangulation of The Hypersimplex

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Miriam Farber ◽  
Yelena Mandelshtam
Keyword(s):  
Dual Graph ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Grid Structure ◽  
Partially Ordered ◽  
Entire Collection ◽  
Nous Montrons ◽  
International Audience ◽  
Nous Examinons

International audience The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive Grassmannian. It was previously shown that arrangements of equal minors of largest value are in bijection with the simplices in a certain triangulation of the hypersimplex that was studied by Stanley, Sturmfels, Lam and Postnikov. Here we investigate the entire set of arrangements and its relations with this triangulation. First, we show that second largest minors correspond to the facets of the simplices. We then introduce the notion of cubical distance on the dual graph of the triangulation, and study its relations with the arrangement of t-th largest minors. Finally, we show that arrangements of largest minors induce a structure of partially ordered sets on the entire collection of minors. We use the Lam and Postnikov circuit triangulation of the hypersimplex to describe a 2-dimensional grid structure of this poset. La structure des mineurs nuls et non nuls dans la Grassmannienne amène à une combinatoire très riche dematroïdes. Dans cet article, nous examinons la structure encore plus riche des égalités et inégalités possibles entreles mineurs de la Grassmannienne positive. Il a été montré précédemment que les arrangements de mineurs égauxde valeur maximale sont en bijection avec les simplexes d’une certaine triangulation de l’hypersimplexe étudiée parStanley, Sturmfels, Lam et Postnikov. Nous examinons ici l’ensemble total des arrangements et ses relations aveccette triangulation. Tout d’abord, nous montrons que les deuxièmes plus grands mineurs correspondent aux facettesdes simplexes. Nous introduisons ensuite la notion de distance cubique sur le graphe dual de la triangulation, et nousétudions ses relations avec l’arrangement des t-ièmes plus grands mineurs. Enfin, nous montrons que les arrangementsde mineurs maximaux induisent une structure d’ensemble partiellement ordonn´e sur la collection totale des mineurs.Nous utilisons la triangulation-circuit de Lam et Postnikov de l’hypersimplexe pour décrire une structure de réseau2-dimensionnel sur ce poset.

To the spectral theory of partially ordered sets

2018 ◽  
Vol 60 (3) ◽  
pp. 578-598
Author(s):  
Yu. L. Ershov ◽  
M. V. Schwidefsky
Keyword(s):  
Spectral Theory ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

Modelling Nondeterministic Concurrent Processes with Event Structures

1991 ◽  
Vol 14 (1) ◽  
pp. 39-73
Author(s):  
Rita Loogen ◽  
Ursula Goltz
Keyword(s):  
Dynamic Behaviour ◽  
Partially Ordered Sets ◽  
Parallel Composition ◽  
Ordered Sets ◽  
Communicating Sequential Processes ◽  
Partially Ordered ◽  
Event Structures ◽  
Transition Relation ◽  
Concurrent Processes ◽  
Sequential Processes

We present a non-interleaving model for non deterministic concurrent processes that is based on labelled event structures. We define operators on labelled event structures like parallel composition, nondeterministic combination, choice, prefixing and hiding. These operators correspond to the operations of the “Theory of Communicating Sequential Processes” (TCSP). Infinite processes are defined using the metric approach. The dynamic behaviour of event structures is defined by a transition relation which describes the execution of partially ordered sets of actions, abstracting from internal events.

Estimating the area under a receiver operating characteristic curve using partially ordered sets

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ehsan Zamanzade ◽  
Xinlei Wang
Keyword(s):  
Roc Curve ◽  
Characteristic Curve ◽  
Partially Ordered Sets ◽  
Sampling Technique ◽  
Real Data ◽  
Cost Effective ◽  
Ordered Sets ◽  
Operating Characteristics ◽  
Partially Ordered ◽  
Receiver Operating

AbstractRanked set sampling (RSS), known as a cost-effective sampling technique, requires that the ranker gives a complete ranking of the units in each set. Frey (2012) proposed a modification of RSS based on partially ordered sets, referred to as RSS-t in this paper, to allow the ranker to declare ties as much as he/she wishes. We consider the problem of estimating the area under a receiver operating characteristics (ROC) curve using RSS-t samples. The area under the ROC curve (AUC) is commonly used as a measure for the effectiveness of diagnostic markers. We develop six nonparametric estimators of the AUC with/without utilizing tie information based on different approaches. We then compare the estimators using a Monte Carlo simulation and an empirical study with real data from the National Health and Nutrition Examination Survey. The results show that utilizing tie information increases the efficiency of estimating the AUC. Suggestions about when to choose which estimator are also made available to practitioners.

scholarly journals Model Checking Existential Logic on Partially Ordered Sets

2016 ◽  
Vol 17 (2) ◽  
pp. 1-35 ◽  
Author(s):  
Simone Bova ◽  
Robert Ganian ◽  
Stefan Szeider
Keyword(s):  
Model Checking ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

Planar zero divisor graphs of partially ordered sets

2012 ◽  
Vol 137 (1-2) ◽  
pp. 27-35 ◽  
Author(s):  
M. Afkhami ◽  
Z. Barati ◽  
K. Khashyarmanesh
Keyword(s):  
Zero Divisor ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered

scholarly journals An inequality for partially ordered sets

1990 ◽  
Vol 54 (1) ◽  
pp. 123-128 ◽  
Author(s):  
István Beck
Keyword(s):  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Partially Ordered
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