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Asymptotic Behaviors of Support Vector Machines with Gaussian Kernel
"... Support vector machines (SVMs) with the Gaussian (RBF) kernel have been popular for practical use. Model selection in this class of SVMs involves two hyperparameters: the penalty parameter C and the kernel width σ. This paper analyzes the behavior of the SVM classifier when these hyperparameters tak ..."
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Cited by 161 (8 self)
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Support vector machines (SVMs) with the Gaussian (RBF) kernel have been popular for practical use. Model selection in this class of SVMs involves two hyperparameters: the penalty parameter C and the kernel width σ. This paper analyzes the behavior of the SVM classifier when these hyperparameters
On the asymptotic behavior of the DurbinWatson statistic for ARX processes in adaptive tracking
 International Journal of Adaptive Control and Signal Processing, DOI: 10.1002/acs.2424
"... the asymptotic behavior of the DurbinWatson ..."
Asymptotic behavior of random determinants
 in the Laguerre, Gram and Jacobi ensembles, arXiv math.PR/0607767
, 2007
"... Abstract. We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble (MANOVA). If n is the size of the sample, r ≤ n the ..."
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Cited by 10 (6 self)
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Abstract. We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble (MANOVA). If n is the size of the sample, r ≤ n the number of variates and Xn,r such a matrix, a generalization of the Bartletttype theorems gives a decomposition of det Xn,r into a product of r independent gamma or beta random variables. For n fixed, we study the evolution as r grows, and then take the limit of large r and n with r/n = t ≤ 1. We derive limit theorems for the sequence of processes with independent increments {n −1 log detX n,⌊nt⌋, t ∈ [0, T]}n for T ≤ 1: convergence in probability, invariance principle, large deviations. Since the logarithm of the determinant is a linear statistic of the empirical spectral distribution, we connect the results for marginals (fixed t) with those obtained by the spectral method. Actually, all the results hold true for log gases or β models, if we define the determinant as the product of charges. The classical matrix models (real, complex, and quaternionic) correspond to the particular values β = 1, 2, 4 of the Dyson parameter. 1.
Asymptotic Behavior of the ZZW Embedding Construction
"... We analyze asymptotic behavior of the embedding construction for steganography proposed by Zhang, Zhang, and Wang (ZZW) at 10th Information Hiding by deriving a closedform expression for the limit between embedding efficiency of the ZZW construction and the theoretical upper bound as a function of r ..."
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Cited by 10 (2 self)
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We analyze asymptotic behavior of the embedding construction for steganography proposed by Zhang, Zhang, and Wang (ZZW) at 10th Information Hiding by deriving a closedform expression for the limit between embedding efficiency of the ZZW construction and the theoretical upper bound as a function
Asymptotic behavior of flows in networks
 Forum Math
"... (Communicated by KarlHermann Neeb) Abstract. Using functional analytical and graph theoretical methods, we extend the results of [12] to more general transport processes in networks allowing space dependent velocities and absorption. We characterize asymptotic periodicity and convergence to an equi ..."
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Cited by 4 (2 self)
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(Communicated by KarlHermann Neeb) Abstract. Using functional analytical and graph theoretical methods, we extend the results of [12] to more general transport processes in networks allowing space dependent velocities and absorption. We characterize asymptotic periodicity and convergence
Uncertainty Principles and Asymptotic Behavior
, 2004
"... Various uncertainty principles for univariate functions are studied, including classes of such principles not considered before. It is shown that in many cases for which the lower bound on the uncertainty is not attained, it is approached by the sequence p k (t) = (1+cos t) , k = 1; 2; : : : , wit ..."
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Cited by 6 (1 self)
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Various uncertainty principles for univariate functions are studied, including classes of such principles not considered before. It is shown that in many cases for which the lower bound on the uncertainty is not attained, it is approached by the sequence p k (t) = (1+cos t) , k = 1; 2; : : : , with order O as k ! 1. By considering Riemann sums, we show that for functions whose Fourier coecients are sampled from the Gaussian with spacing h, the uncertainty approaches the lower bound as h ! 0 with order O(h ), whereas earlier work had shown at best O(h). We deduce that, for any 0 < < 1, there is a sequence of polynomials q k of degree k such that q k (cos t), k = 1; 2; : : : , has uncertainty which approaches the lower bound with order O as k ! 1. We also establish a general uncertainty principle for n pairs of operators on a Hilbert space, n = 2; 3; : : : , which allows us to extend the above univariate uncertainty principles to such principles for functions of n variables. Furthermore we deduce an uncertainty principle for functions on the sphere S , n = 2; 3; : : : , generalizing known results for radial functions and for realvalued functions on . By considering the above work on univariate uncertainty principles, we can similarly derive, for all our multivariate uncertainty principles, sequences of functions for which the lower bound on the uncertainty is approached.
ASYMPTOTIC BEHAVIOR OF LINEAR RECURRENCES
"... 4a, 5a gives three steps more than a, 0, a, 2a. Hences we can have many sets of four numbers of the form 0, a, b9 c having the same number of steps. However, we can tell the number of steps of the reduced set 0, a, b9 c in the following cases: 0, 0, 0, a (a> 0) five rows; 0, 0, a, a (a> 0) fou ..."
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Cited by 3 (0 self)
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4a, 5a gives three steps more than a, 0, a, 2a. Hences we can have many sets of four numbers of the form 0, a, b9 c having the same number of steps. However, we can tell the number of steps of the reduced set 0, a, b9 c in the following cases: 0, 0, 0, a (a> 0) five rows; 0, 0, a, a (a> 0) four rows; 0, 0, a, b (a < b < _ 2a) f ive rows; 0, 0, a, 2a + x (x> 0) seven rows; 0, 0, a, na + x (n _> 3) seven rows; 0, a, 0, a (a> 0) three rows; 0, a, 0, b (a ^ b) five rows; 0, a, £, c (ba + c, a = c> 0) three rows; Q9 a, b, c (b ~ a + e, a ± a) four rows; 0, a9 b, c (c = a + &, a = b> 0) four rows; 0, a, &, c (<? = a + &, a < b) six rows; and 0, a, b9 c (c = a + b, a> b) four rows. From the above, it is clear that the only case which presents difficulty in deciding the number of steps without actual calculation is 0, a, b, c (aba £ 0, b ^ a + c 9 o £ a + b), where we can assume a < o.
Asymptotic behavior of grafting rays
, 2007
"... Abstract. In this paper we study the convergence behavior of grafting rays to the Thurston boundary of Teichmüller space. When the grafting is done along a weighted system of simple closed curves or along a maximal uniquely ergodic lamination this behavior is the same as for Teichmüller geodesics an ..."
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Cited by 2 (0 self)
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Abstract. In this paper we study the convergence behavior of grafting rays to the Thurston boundary of Teichmüller space. When the grafting is done along a weighted system of simple closed curves or along a maximal uniquely ergodic lamination this behavior is the same as for Teichmüller geodesics
Asymptotic behavior of the number of lost messages
 SIAM J. Appl. Math
, 2004
"... Abstract. The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a packet results in the loss of the entire message. ..."
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Cited by 14 (12 self)
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Abstract. The goal of the paper is to study asymptotic behavior of the number of lost messages. Long messages are assumed to be divided into a random number of packets which are transmitted independently of one another. An error in transmission of a packet results in the loss of the entire message
Results 11  20
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