scholarly journals A lower bound on the value of entangled binary games

2010 ◽  
Vol 10 (11&12) ◽  
pp. 911-924
Author(s):  
Salman Beigi
Keyword(s):  
Lower Bound ◽  
Optimal Strategy ◽  
A Priori ◽  
Semidefinite Program ◽  
Property A ◽  
Marginal Distributions ◽  
Winning Probability ◽  
Questions And Answers ◽  
Binary Games ◽  
Binary Game

A two-player one-round binary game consists of two cooperative players who each replies by one bit to a message that he receives privately; they win the game if both questions and answers satisfy some predetermined property. A game is called entangled if the players are allowed to share a priori entanglement. It is well-known that the maximum winning probability (value) of entangled XOR-games (binary games in which the predetermined property depends only on the XOR of the two output bits) can be computed by a semidefinite program. In this paper we extend this result in the following sense; if a binary game is uniform, meaning that in an optimal strategy the marginal distributions of the output of each player are uniform, then its entangled value can be efficiently computed by a semidefinite program. We also introduce a lower bound on the entangled value of a general two-player one-round game; this bound depends on the size of the output set of each player and can be computed by a semidefinite program. In particular, we show that if the game is binary, $\omega_q$ is its entangled value, and $\omega_{sdp}$ is the optimum value of the corresponding semidefinite program, then $0.68\,\omega_{sdp} < \omega_q \leq \omega_{sdp}$.

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

scholarly journals A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 282 ◽  
Author(s):  
Andrea Coladangelo
Keyword(s):  
Optimal Strategy ◽  
Elementary Proof ◽  
Quantum Correlations ◽  
Entangled State ◽  
Finitely Presented Groups ◽  
Self Testing ◽  
Question And Answer ◽  
Questions And Answers ◽  
Non Local ◽  
Finitely Presented

We describe a two-player non-local game, with a fixed small number of questions and answers, such that an ϵ-close to optimal strategy requires an entangled state of dimension 2Ω(ϵ−1/8). Our non-local game is inspired by the three-player non-local game of Ji, Leung and Vidick \cite{ji2018three}. It reduces the number of players from three to two, as well as the question and answer set sizes. Moreover, it provides an (arguably) elementary proof of the non-closure of the set of quantum correlations, based on embezzlement and self-testing. In contrast, previous proofs \cite{slofstra2019set, dykema2017non, musat2018non} involved representation theoretic machinery for finitely-presented groups and C∗-algebras.

Broadcasting in Unlabeled Tori

1998 ◽  
Vol 08 (02) ◽  
pp. 177-188 ◽  
Author(s):  
Krzysztof Diks ◽  
Evangelos Kranakis ◽  
Andrzej Pelc
Keyword(s):  
Lower Bound ◽  
A Priori ◽  
Message Complexity ◽  
Arbitrary Size ◽  
Broadcasting Algorithm

We consider broadcasting a message from one node to all other nodes of an asynchronous totally unlabeled torus: neither nodes nor links have a priori assigned labels but they know the topology and the size of the torus. Nodes can send messages of arbitrary size and we are interested in minimizing the total number of messages. A naive broadcasting algorithm in a n × n totally unlabeled torus uses 3n2 + 1 messages, while the obvious lower bound is n2 - 1. The main result of this paper is a broadcasting algorithm using 2n2 + O(n) messages. We also give a lower bound of 1.04n2 - O(n) messages. This is the first result on message complexity of broadcasting in totally unlabeled networks.

scholarly journals On-line Search in Two-Dimensional Environment

2019 ◽  
Vol 63 (8) ◽  
pp. 1819-1848
Author(s):  
Dariusz Dereniowski ◽  
Dorota Osula
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Mobile Agents ◽  
Line Search ◽  
Search Strategy ◽  
A Priori ◽  
Two Dimensional ◽  
Pursuit Evasion ◽  
On Line ◽  
Evasion Problem

Abstract We consider the following on-line pursuit-evasion problem. A team of mobile agents called searchers starts at an arbitrary node of an unknown network. Their goal is to execute a search strategy that guarantees capturing a fast and invisible intruder regardless of its movements using as few searchers as possible. We require that the strategy is connected and monotone, that is, at each point of the execution the part of the graph that is guaranteed to be free of the fugitive is connected and whenever some node gains a property that it cannot be occupied by the fugitive, the strategy must operate in such a way to keep this property till its end. As a way of modeling two-dimensional shapes, we restrict our attention to networks that are embedded into partial grids: nodes are placed on the plane at integer coordinates and only nodes at distance one can be adjacent. Agents do not have any knowledge about the graph a priori, but they recognize the direction of the incident edge (up, down, left or right). We give an on-line algorithm for the searchers that allows them to compute a connected and monotone strategy that guarantees searching any unknown partial grid with the use of $O(\sqrt {n})$ O ( n ) searchers, where n is the number of nodes in the grid. As for a lower bound, there exist partial grids that require ${\varOmega }(\sqrt {n})$ Ω ( n ) searchers. Moreover, we prove that for each on-line searching algorithm there is a partial grid that forces the algorithm to use ${\varOmega }(\sqrt {n})$ Ω ( n ) searchers but $O(\log n)$ O ( log n ) searchers are sufficient in the off-line scenario. This gives a lower bound on ${\varOmega }(\sqrt {n}/\log n)$ Ω ( n / log n ) in terms of achievable competitive ratio of any on-line algorithm.

scholarly journals Measurement of Interobserver Disagreement: Correction of Cohen’s Kappa for Negative Values

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Tarald O. Kvålseth
Keyword(s):  
Lower Bound ◽  
Statistical Inference ◽  
Lower Bounds ◽  
Interobserver Agreement ◽  
Negative Coefficient ◽  
Cohen’S Kappa ◽  
Marginal Distributions ◽  
Numerical Examples ◽  
Cohen's Kappa ◽  
Alternative Measures

As measures of interobserver agreement for both nominal and ordinal categories, Cohen’s kappa coefficients appear to be the most widely used with simple and meaningful interpretations. However, for negative coefficient values when (the probability of) observed disagreement exceeds chance-expected disagreement, no fixed lower bounds exist for the kappa coefficients and their interpretations are no longer meaningful and may be entirely misleading. In this paper, alternative measures of disagreement (or negative agreement) are proposed as simple corrections or modifications of Cohen’s kappa coefficients. The new coefficients have a fixed lower bound of −1 that can be attained irrespective of the marginal distributions. A coefficient is formulated for the case when the classification categories are nominal and a weighted coefficient is proposed for ordinal categories. Besides coefficients for the overall disagreement across categories, disagreement coefficients for individual categories are presented. Statistical inference procedures are developed and numerical examples are provided.

scholarly journals Analytical and Numerical Evaluation of Co-Scheduling Strategies and Their Application

2021 ◽  
Author(s):  
Ruslan Kuchumov ◽  
Vladimir Korkhov
Keyword(s):  
Optimal Strategy ◽  
High Performance ◽  
A Priori ◽  
Scheduling Problem ◽  
Heuristic Strategies ◽  
Accuracy Of Measurement ◽  
Online Strategy ◽  
Scheduling Strategies ◽  
Priori Information ◽  
Computational Resources

Applications in high-performance computing (HPC) may not use all available computational resources, leaving some of them underutilized. By co-scheduling, i.e. running more than one application on the same computational node, it is possible to improve resource utilization and overall throughput. Some applications may have conflicting requirements on resources and co-scheduling may cause performance degradation, so it is important to take it into account in scheduling decisions. In this paper, we formalized co-scheduling problem and proposed multiple scheduling strategies to solve it: an optimal strategy, an online strategy and heuristic strategies. These strategies vary in terms of the optimality of the solution they produce and a priori information about the system they require. We showed theoretically that the online strategy provides schedules with a competitive ratio that has a constant upper limit. This allowed us to solve the co-scheduling problem using heuristic strategies that approximate this online strategy. Numerical simulations showed how heuristic strategies compare to the optimal strategy for different input systems. We proposed a method for measuring input parameters of the model in practice and evaluated this method on HPC benchmark applications. We showed high accuracy of measurement method, which allows to apply proposed scheduling strategies in scheduler implementation.

scholarly journals Analytical and Numerical Evaluation of Co-Scheduling Strategies and Their Application

Computers ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 122
Author(s):  
Ruslan Kuchumov ◽  
Vladimir Korkhov
Keyword(s):  
Optimal Strategy ◽  
High Performance ◽  
A Priori ◽  
Scheduling Problem ◽  
Heuristic Strategies ◽  
Online Strategy ◽  
Scheduling Strategies ◽  
Priori Information ◽  
Computational Resources ◽  
Performance Computing

Applications in high-performance computing (HPC) may not use all available computational resources, leaving some of them underutilized. By co-scheduling, i.e., running more than one application on the same computational node, it is possible to improve resource utilization and overall throughput. Some applications may have conflicting requirements on resources and co-scheduling may cause performance degradation, so it is important to take it into account in scheduling decisions. In this paper, we formalize the co-scheduling problem and propose multiple scheduling strategies to solve it: an optimal strategy, an online strategy and heuristic strategies. These strategies vary in terms of the optimality of the solution they produce and a priori information about the system they require. We show theoretically that the online strategy provides schedules with a competitive ratio that has a constant upper limit. This allows us to solve the co-scheduling problem using heuristic strategies that approximate this online strategy. Numerical simulations show how heuristic strategies compare to the optimal strategy for different input systems. We propose a method for measuring input parameters of the model in practice and evaluate this method on HPC benchmark applications. We show the high accuracy of the measurement method, which allows us to apply the proposed scheduling strategies in the scheduler implementation.

scholarly journals Minimal energy for elastic inclusions

2010 ◽  
Vol 467 (2127) ◽  
pp. 695-717 ◽  
Author(s):  
Hans Knüpfer ◽  
Robert V. Kohn
Keyword(s):  
Lower Bound ◽  
Elastic Energy ◽  
A Priori ◽  
Isoperimetric Problem ◽  
Minimal Energy ◽  
Fixed Volume ◽  
Optimal Energy ◽  
Non Local ◽  
Elastic Inclusions ◽  
Local Term

We consider a variant of the isoperimetric problem with a non-local term representing elastic energy. More precisely, our aim is to analyse the optimal energy of an inclusion of a fixed volume the energy of which is determined by surface and elastic energies. This problem has been studied extensively in the physical/metallurgical literature; however, the analysis has mainly been either (i) numerical, or (ii) restricted to a specific set of inclusion shapes, e.g. ellipsoids. In this article, we prove a lower bound for the energy, with no a priori hypothesis on the shape (or even number) of the inclusions.

A priori lower bound for the minimal eigenvalue of a Sturm-Liouville problem with boundary conditions of the second type

2015 ◽  
Vol 97 (5-6) ◽  
pp. 846-853
Author(s):  
A. A. Vladimirov ◽  
E. S. Karulina
Keyword(s):  
Lower Bound ◽  
Boundary Conditions ◽  
A Priori ◽  
Liouville Problem ◽  
Minimal Eigenvalue ◽  
Sturm Liouville

scholarly journals Singularity Formation in the Inviscid Burgers Equation

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 848
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
Lower Bound ◽  
Nonlinear Equation ◽  
Burgers Equation ◽  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Singularity Formation ◽  
Priori Estimates ◽  
Inviscid Burgers Equation ◽  
Stability Type

We provide a lower bound for the blow up time of the H2 norm of the entropy solutions of the inviscid Burgers equation in terms of the H2 norm of the initial datum. This shows an interesting symmetry of the Burgers equation: the invariance of the space H2 under the action of such nonlinear equation. The argument is based on a priori estimates of energy and stability type for the (viscous) Burgers equation.

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