The Experts below are selected from a list of 261 Experts worldwide ranked by ideXlab platform
Diego Martínez - One of the best experts on this subject based on the ideXlab platform.
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Amenability and paradoxicality in semigroups and C⁎-algebras
Journal of Functional Analysis, 2020Co-Authors: Pere Ara, Fernando Lledó, Diego MartínezAbstract:Abstract We analyze the dichotomy amenable/paradoxical in the context of (discrete, countable, unital) semigroups and corresponding semigroup rings. We consider also Folner type characterizations of amenability and give an example of a semigroup whose semigroup ring is algebraically amenable but has no Folner sequence. In the context of inverse semigroups S we give a characterization of invariant measures on S (in the sense of Day) in terms of two notions: domain measurability and localization. Given a unital representation of S in terms of partial bijections on some set X we define a natural generalization of the uniform Roe algebra of a group, which we denote by R X . We show that the following notions are then equivalent: (1) X is domain measurable; (2) X is not paradoxical; (3) X satisfies the domain Folner condition; (4) there is an algebraically amenable dense*-subalgebra of R X ; (5) R X has an amenable trace; (6) R X is not properly infinite and (7) [ 0 ] ≠ [ 1 ] in the K 0 -group of R X . We also show that any tracial state on R X is amenable. Moreover, taking into account the localization condition, we give several C*-algebraic characterizations of the amenability of X. Finally, we show that for a certain class of inverse semigroups, the quasidiagonality of C r ⁎ ( X ) implies the amenability of X. The Reverse Implication (which is a natural generalization of Rosenberg's conjecture to this context) is false.
Francisco Montes - One of the best experts on this subject based on the ideXlab platform.
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Random set and coverage measure
Advances in Applied Probability, 1991Co-Authors: Guillermo Ayala, Juan Ferrandiz, Francisco MontesAbstract:It is well known that a random set determines its random coverage measure. The paper gives a necessary and sufficient condition for the Reverse Implication. An equivalent formulation of the condition constitutes a first step in the search for a way to recognize a random measure as being the random coverage measure of a random set.
Dj Smith - One of the best experts on this subject based on the ideXlab platform.
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Twin prime correlations from the pair correlation of Riemann zeros
Journal of Physics A: Mathematical and Theoretical, 2019Co-Authors: Jp Keating, Dj SmithAbstract:We establish, via a formal/heuristic Fourier inversion calculation, that the Hardy-Littlewood twin prime conjecture is equivalent to an asymptotic formula for the two-point correlation function of Riemann zeros at a height $E$ on the critical line. Previously it was known that the Hardy-Littlewood conjecture implies the pair correlation formula, and we show that the Reverse Implication also holds. A smooth form of the Hardy-Littlewood conjecture is obtained by inverting the $E \rightarrow \infty$ limit of the two-point correlation function and the precise form of the conjecture is found by including asymptotically lower order terms in the two-point correlation function formula.
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Twin prime correlations from the pair correlation of Riemann zeros
'IOP Publishing', 2019Co-Authors: Jp Keating, Dj SmithAbstract:We establish, via a heuristic Fourier inversion calculation, that the Hardy–Littlewood twin prime conjecture is equivalent to an asymptotic formula for the two-point correlation function of Riemann zeros at a height E on the critical line. Previously it was known that the Hardy–Littlewood conjecture implies the pair correlation formula, and we show that the Reverse Implication also holds. An averaged form of the Hardy–Littlewood conjecture is obtained by inverting the limit of the two-point correlation function and the precise form of the conjecture is found by including asymptotically lower order terms in the two-point correlation function formula
Sam Sanders - One of the best experts on this subject based on the ideXlab platform.
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LFCS - Lifting Recursive Counterexamples to Higher-Order Arithmetic
Logical Foundations of Computer Science, 2019Co-Authors: Sam SandersAbstract:In classical computability theory, a recursive counterexample to a theorem shows that the latter does not hold when restricted to computable objects. These counterexamples are highly useful in the Reverse Mathematics program, where the aim of the latter is to determine the minimal axioms needed to prove a given theorem of ordinary mathematics. Indeed, recursive counterexamples often (help) establish the ‘Reverse’ Implication in the typical equivalence between said minimal axioms and the theorem at hand. The aforementioned is generally formulated in the language of second-order arithmetic and we show in this paper that recursive counterexamples are readily modified to provide similar Implications in higher-order arithmetic. For instance, the higher-order analogue of ‘sequence’ is the topological notion of ‘net’, also known as ‘Moore-Smith sequence’. Our results on metric spaces suggest that the latter can only be reasonably studied in weak systems via representations (aka codes) in the language of second-order arithmetic.
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Lifting recursive counterexamples to higher-order arithmetic
arXiv: Logic, 2019Co-Authors: Sam SandersAbstract:In classical computability theory, a recursive counterexample to a theorem shows that the latter does not hold when restricted to computable objects. These counterexamples are highly useful in the Reverse Mathematics program, where the aim of the latter is to determine the minimal axioms needed to prove a given theorem of ordinary mathematics. Indeed, recursive counterexamples often (help) establish the 'Reverse' Implication in the typical equivalence between said minimal axioms and the theorem at hand. The aforementioned is generally formulated in the language of second-order arithmetic. In this paper, we show that recursive counterexamples are readily modified to provide similar Implications in higher-order arithmetic. For instance, the higher-order analogue of 'sequence' is the topological notion of 'net', also known as 'Moore-Smith sequence'. Finally, our results on metric spaces suggest that the latter can only be reasonably studied in weak systems via representations (aka codes) in the language of second-order arithmetic.
Pascal Jordan - One of the best experts on this subject based on the ideXlab platform.
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the counterintuitive impact of responses and response times on parameter estimates in the drift diffusion model
British Journal of Mathematical and Statistical Psychology, 2020Co-Authors: Pascal JordanAbstract:Given a drift diffusion model with unknown drift and boundary parameters, we analyse the behaviour of maximum likelihood estimates with respect to changes of responses and response times. It is shown analytically that a single fast response time can dominate the estimation in that no matter how many correct answers a test taker provides, the estimate of the drift (ability) parameter decreases to zero. In addition, it is shown that although higher drift rates imply shorter response times, the Reverse Implication does not hold for the estimates: shorter response times can decrease the drift rate estimate. In the light of these analytical results, we illustrate the actual impact of the findings in a small simulation for a mental rotation test. The method of analysis outlined is applicable to a broader range of models, and we emphasize the need to further check currently used reaction time models within this framework.
