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In distributed systems where strong consistency is costly when not impossible, causal consistency provides a valuable abstraction to represent program executions as partial orders. In addition to the sequential program order of ea...
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In distributed systems where strong consistency is costly when not impossible, causal consistency provides a valuable abstraction to represent program executions as partial orders. In addition to the sequential program order of each computing entity, causal order also contains the semantic links between the events that affect the shared objects messages emission and reception in a communication channel, reads and writes on a shared register. Usual approaches based on semantic links are very difficult to adapt to other data types such as queues or counters because they require a specific analysis of causal dependencies for each data type. This paper presents a new approach to define causal consistency for any abstract data type based on sequential specifications. It explores, formalizes and studies the differences between three variations of causal consistency and highlights them in the light of PRAM, eventual consistency and sequential consistency: weak causal consistency, that captures the notion of causality preservation when focusing on convergence; causal convergence that mixes weak causal consistency and convergence; and causal consistency, that coincides with causal memory when applied to shared memory.
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When checking the inconsistency level of a positive reciprocal matrix Saaty uses a deterministic criterion based on two parameters, a benchmark (the average), and a consistency level, usually 10%. Using results from a simulation e...
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When checking the inconsistency level of a positive reciprocal matrix Saaty uses a deterministic criterion based on two parameters, a benchmark (the average), and a consistency level, usually 10%. Using results from a simulation experiment with 100,000 positive random reciprocal matrices of size varying from 3 to 15, we developed a probabilistic criterion and compare it to Saaty's index. We found that if a positive reciprocal matrix is consistent according to the deterministic criterion is also consistent according to the probabilistic criterion only if we accept a higher than usual probability of Type I error. Reducing this error implies that the benchmark must be a small percentile of the probability distribution of the consistency index. (C) 2007 Elsevier B.V. All rights reserved.
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Consistency of choice is a fundamental and recurring theme in decision theory, social choice theory, behavioral economics, and psychological sciences. The purpose of this paper is to study the consistency of choice independent of ...
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Consistency of choice is a fundamental and recurring theme in decision theory, social choice theory, behavioral economics, and psychological sciences. The purpose of this paper is to study the consistency of choice independent of the particular decision model at hand. Consistency is viewed as an inherently logical concept that is fundamentally void of connotation and is thus disentangled from traditional rationality or consistency conditions imposed on decision models. The proposed formalization of consistency takes two forms: internal consistency, which refers to the property that a choice model does not generate contradictory statements; and semantic consistency, which refers to the idea that a theory's predictions are valid with respect to some observed data. In addressing semantic consistency, the relationship between theory and data is analyzed in terms of so-called duality mappings, which allow a passage between the two universes in a way that consistency is preserved. The formalization of consistency concepts relies on adapting the revealed preference theory to the context-dependent setting. The paper concludes by discussing the implications of the proposed framework and how it relates to classical revealed preference theory and other formalizations of the relationship between the theory and reality of choice.
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We extend the reduced games introduced by Davis and Maschler (Naval Res. Log. Q. 12:223-259, 1965) and Moulin (J. Econ. Theory. 36:120-148, 1985) to multichoice transferable-utility games. First, we provide an example to illustrat...
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We extend the reduced games introduced by Davis and Maschler (Naval Res. Log. Q. 12:223-259, 1965) and Moulin (J. Econ. Theory. 36:120-148, 1985) to multichoice transferable-utility games. First, we provide an example to illustrate that the core proposed by van den Nouweland et al. (Math Methods Oper. Res. 41:289-311, 1995) violates related consistency properties. Further, we propose the minimal consistent extensions of the core and the maximal consistent subsolutions of the core. We also provide an axiomatization based on related consistency properties and its converse.
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Seven simple and advanced dynamic polymorphic functions were considered to develop a dominant height growth model for Spanish and Tunisian cork oak forests. Data from 115 stem analyses performed in two regions in each country were...
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Seven simple and advanced dynamic polymorphic functions were considered to develop a dominant height growth model for Spanish and Tunisian cork oak forests. Data from 115 stem analyses performed in two regions in each country were used to fit the equations. Parameter estimates were obtained using the Dummy variable method. Both numerical, graphical and biological consistency were used to compare alternative models. The dynamic equation finally selected was derived from the Hossfeld model by considering the shape parameter to be related to site productivity. An analysis of the dominant height growth patterns between the two countries indicated that the same dominant height growth model was valid for both countries. This dominant height growth model allows estimation of dominant height with a level of reliability of at least 83% from an age of 15 years for a prediction interval of less than 40 years.
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Abstract It is shown for the first time in this paper, that Kleinberg’s (2002) (self-contradictory) axiomatic system for distance-based clustering fails (that is one of the data transforming axioms, consistency axiom, turns out t...
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Abstract It is shown for the first time in this paper, that Kleinberg’s (2002) (self-contradictory) axiomatic system for distance-based clustering fails (that is one of the data transforming axioms, consistency axiom, turns out to be identity transformation) in fixed-dimensional Euclidean space due to the consistency axiom limitations and that its replacement with inner-consistency or outer consistency does not help if continuous data transformations are required. Therefore we formulate a new, sound axiomatic framework for cluster analysis in the fixed dimensional Euclidean space, suitable for k-means like algorithms. The system incorporates centric consistency axiom and motion consistency axiom which induce clustering preserving transformations useful e.g. for deriving new labelled sets for testing clustering procedures. It is suitable for continuous data transformations so that labelled data with small perturbations can be derived. Unlike Kleinberg’s consistency, the new axioms do not lead the data outside of Euclidean space nor cause increase in data dimensionality. Our cluster preserving transformations have linear complexity in data transformation and checking. They are in practice less restrictive, less rigid than Kleinberg’s consistency as they do not enforce inter-cluster distance increase and inner cluster distance decrease when performing clustering preserving transformation.
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CP solvers predominantly use arc consistency (AC) as the default propagation method for binary constraints. Many stronger consistencies, such as triangle consistencies (e.g. RPC and maxRPC) exist, but their use is limited despite ...
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CP solvers predominantly use arc consistency (AC) as the default propagation method for binary constraints. Many stronger consistencies, such as triangle consistencies (e.g. RPC and maxRPC) exist, but their use is limited despite results showing that they outperform AC on many problems. This is due to the intricacies involved in incorporating them into solvers. On the other hand, singleton consistencies such as SAC can be easily crafted into solvers but they are too expensive in practice. Seeking a balance between the efficiency of triangle consistencies and the ease of implementation of singleton ones, we study the family of neighborhood singleton consistencies (NSCs) which extends the recently proposed neighborhood SAC (NSAC). We propose several new members of this family and study them both theoretically and experimentally. Our theroretical results show that the pruning power of the proposed NSCs ranges between that of RPC and (3,1)-consistency. Using a very simple algorithm for the implementation of NSCs, we demonstrate that certain members of the NSC family are quite competitive as general-purpose propagation methods for binary constraints, significantly outperforming the existing propagation techniques on some problem classes.
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In this paper we completely answer the following question: for given A is an element of B(H, K), C is an element of B(H, K) does there exist operators T is an element of B(H, L) and S is an element of B(K) such that the operator [...
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In this paper we completely answer the following question: for given A is an element of B(H, K), C is an element of B(H, K) does there exist operators T is an element of B(H, L) and S is an element of B(K) such that the operator [A C T S] is consistent in invertibility and Fredholmness?
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We extend the reduced games introduced by Davis and Maschler (Naval Res Log Q 12:223-259, 1965) and Moulin (J Econ Theory 36:120-148, 1985) to multi-choice non-transferable utility games and define two related properties of consis...
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We extend the reduced games introduced by Davis and Maschler (Naval Res Log Q 12:223-259, 1965) and Moulin (J Econ Theory 36:120-148, 1985) to multi-choice non-transferable utility games and define two related properties of consistency. We also show that the core proposed by Hwang and Li (Math Methods Oper Res 61:33-40, 2005) violates these two consistency properties. In order to investigate how seriously it violates these two consistency properties, we provide consistent extensions and consistent subsolutions of the core.
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The paper is a continuation of [Z. Adamowicz, Fund. Math. 242 (2018)]. We consider conservativity questions between, on the one hand, arithmetical theories in which the operations of successor, addition and multiplication are not ...
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The paper is a continuation of [Z. Adamowicz, Fund. Math. 242 (2018)]. We consider conservativity questions between, on the one hand, arithmetical theories in which the operations of successor, addition and multiplication are not provably total and which are fragments of the bounded arithmetic theory I Delta(0) and, on the other hand, extensions of those theories to subtheories of Buss's bounded arithmetic S-2. These questions are related to the problem of finite axiomatizability of a version of I Delta(0) in which the totality of the operations is not assumed.
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