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In this paper, we prove a Hoeffding-like inequality for the survival function of a sum of symmetric independent identically distributed random variables, taking values in a segment [—b, b] of the reals. The symmetric case is rele...
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In this paper, we prove a Hoeffding-like inequality for the survival function of a sum of symmetric independent identically distributed random variables, taking values in a segment [—b, b] of the reals. The symmetric case is relevant to the auditing practice and is an important case study for further investigations. The bounds as given by Hoeffding in 1963 cannot be improved upon unless we restrict the class of random variables, for instance, by assuming the law of the random variables to be symmetric with respect to their mean, which we may assume to be zero. The main result in this paper is an improvement of the Hoeffding bound for i.i.d. random variables which are bounded and have a (upper bound for the) variance by further assuming that they have a symmetric law.
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The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime power conductor. In particular, these bounds imply Minkowski's conjecture for totally real number fields of conductor pr, where ...
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The aim of this paper is to give upper bounds for the Euclidean minima of abelian fields of odd prime power conductor. In particular, these bounds imply Minkowski's conjecture for totally real number fields of conductor pr, where p is an odd prime number and r ≥ 2.
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It is shown that the minimal distance d of a binary self-dual code of length nor=6 exist precisely for n...
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It is shown that the minimal distance d of a binary self-dual code of length nor=6 exist precisely for n收起
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Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative q-entropy is generally unbounded for q > 1. Upper bounds on the quantum relative q-entropy in ...
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Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative q-entropy is generally unbounded for q > 1. Upper bounds on the quantum relative q-entropy in terms of norm distancesbetween its arguments are obtained in finite-dimensional context. These bounds characterize a continuity property in the sense of Fannes.
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A spherical code is a finite set X of points lying on the unit sphere of R/sup n/. For such a set, we define /spl rho/(X) as the minimum of the squared distances /spl par/x-y/spl par//sup 2/, when x, y/spl isin/X and x/spl ne/y. D...
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A spherical code is a finite set X of points lying on the unit sphere of R/sup n/. For such a set, we define /spl rho/(X) as the minimum of the squared distances /spl par/x-y/spl par//sup 2/, when x, y/spl isin/X and x/spl ne/y. Define R(/spl rho/)=lim sup n/spl rarr//spl infin/, /spl rho/(X)=p log/sub 2/CardX/n. Chabauty in 1953 and Shannon in 1959 have given a lower bound for R(/spl rho/), namely, R(/spl rho/)收起
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Our purpose in this paper is to construct three types of single-hidden layer feed-forward neural networks (FNNs) with optimized piecewise linear activation functions and fixed weights and to present the ideal upper and lower bound...
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Our purpose in this paper is to construct three types of single-hidden layer feed-forward neural networks (FNNs) with optimized piecewise linear activation functions and fixed weights and to present the ideal upper and lower bound estimations on the approximation accuracy of the FNNs, for continuous function defined on bounded intervals. We also prove these three types of single-hidden layer FNNs can interpolate any bounded and measurable functions. Our approach compared with existing methods does not require training. Our conclusions not only uncover the inherent properties of approximation of the FNNs, but also reveal the latent relationship among the precision of approximation, the number of hidden units and the smoothness of the target function. Finally, we demonstrate some numerical results that show good agreement with theory.
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Consider the random subset Chi of Nu obtained by selecting independently each integer with a probability delta. Consider a finite class F of finite sets. We describe a combinatorial quantity that is of the same order as E sup(F ep...
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Consider the random subset Chi of Nu obtained by selecting independently each integer with a probability delta. Consider a finite class F of finite sets. We describe a combinatorial quantity that is of the same order as E sup(F epsilon F) card (Chi boolean AND F). We then give a related result allowing to compute the supremum of the empirical process on a class of sets.
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Entropy production is a key quantity characterizing nonequilibrium systems. However, it can often be difficult to compute in practice, as it requires detailed information about the system and the dynamics it undergoes. This become...
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Entropy production is a key quantity characterizing nonequilibrium systems. However, it can often be difficult to compute in practice, as it requires detailed information about the system and the dynamics it undergoes. This becomes even more difficult in the quantum domain and if one is interested in generic nonequilibrium reservoirs, for which the standard thermal recipes no longer apply. In this paper, we derive an upper bound for the entropy production in terms of the entropy flux for a class of systems for which the flux is given in terms of a system’s observable. Since currents are often easily accessible in this class of systems, this bound should prove useful for estimating the entropy production in a broad variety of processes. We illustrate the applicability of the bound by considering a three-level maser engine and a system interacting with a squeezed bath.
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It is a challenging task to detect genuine multipartite nonlocality (GMNL). In this paper, the problem is considered via computing the maximal quantum value of Svetlichny operators for three-qubit systems and a tight upper bound i...
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It is a challenging task to detect genuine multipartite nonlocality (GMNL). In this paper, the problem is considered via computing the maximal quantum value of Svetlichny operators for three-qubit systems and a tight upper bound is obtained. The constraints on the quantum states for the tightness of the bound are also presented. The approach enables us to give the necessary and sufficient conditions of violating the Svetlichny inequality (SI) for several quantum states, including the white and color noised Greenberger-Horne-Zeilinger (GHZ) states. The relation between the genuine multipartite entanglement concurrence and the maximal quantum value of the Svetlichny operators for mixed GHZ class states is also discussed. As the SI is useful for the investigation of GMNL, our results give an effective and operational method to detect the GMNL for three-qubit mixed states.
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Let G=(V,E) be a graph. A signed dominating function on G is a function f:V→{-1,1} such that for each vV, where N[v] is the closed neighborhood of v. The weight of a signed dominating function f is . A signed dominating function ...
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Let G=(V,E) be a graph. A signed dominating function on G is a function f:V→{-1,1} such that for each vV, where N[v] is the closed neighborhood of v. The weight of a signed dominating function f is . A signed dominating function f is minimal if there exists no signed dominating function g such that g≠f and g(v)f(v) for each vV. The upper signed domination number of a graph G, denoted by Γs(G), equals the maximum weight of a minimal signed dominating function of G. In this paper, we establish an tight upper bound for Γs(G) in terms of minimum degree and maximum degree. Our result is a generalization of those for regular graphs and nearly regular graphs obtained in [O. Favaron, Signed domination in regular graphs, Discrete Math. 158 (1996) 287–293] and [C.X. Wang, J.Z. Mao, Some more remarks on domination in cubic graphs, Discrete Math. 237 (2001) 193–197], respectively.
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