Displaying 1061 – 1080 of 1507

Showing per page

Optimality conditions for maximizers of the information divergence from an exponential family

František Matúš (2007)

Kybernetika

The information divergence of a probability measure P from an exponential family over a finite set is defined as infimum of the divergences of P from Q subject to Q . All directional derivatives of the divergence from are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The first order conditions for P to be a maximizer of the divergence from are presented, including new ones when P  is not projectable to .

Optimality of the Width- w Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases

Clemens Heuberger, Daniel Krenn (2013)

Journal de Théorie des Nombres de Bordeaux

We consider digit expansions j = 0 - 1 Φ j ( d j ) with an endomorphism Φ of an Abelian group. In such a numeral system, the w -NAF condition (each block of w consecutive digits contains at most one nonzero) is shown to minimise the Hamming weight over all expansions with the same digit set if and only if it fulfills the subadditivity condition (the sum of every two expansions of weight 1 admits an optimal w -NAF).This result is then applied to imaginary quadratic bases, which are used for scalar multiplication in elliptic...

Optimally approximating exponential families

Johannes Rauh (2013)

Kybernetika

This article studies exponential families on finite sets such that the information divergence D ( P ) of an arbitrary probability distribution from is bounded by some constant D > 0 . A particular class of low-dimensional exponential families that have low values of D can be obtained from partitions of the state space. The main results concern optimality properties of these partition exponential families. The case where D = log ( 2 ) is studied in detail. This case is special, because if D < log ( 2 ) , then contains all probability...

Order statistics and ( r , s ) -entropy measures

María Dolores Esteban, Domingo Morales, Leandro Pardo, María Luisa Menéndez (1994)

Applications of Mathematics

K. M. Wong and S. Chen [9] analyzed the Shannon entropy of a sequence of random variables under order restrictions. Using ( r , s ) -entropies, I. J. Taneja [8], these results are generalized. Upper and lower bounds to the entropy reduction when the sequence is ordered and conditions under which they are achieved are derived. Theorems are presented showing the difference between the average entropy of the individual order statistics and the entropy of a member of the original independent identically distributed...

Output synchronization of multi-agent port-Hamiltonian systems with link dynamics

Bing Wang, Xinghu Wang, Honghua Wang (2016)

Kybernetika

In this paper, the output synchronization control is considered for multi-agent port-Hamiltonian systems with link dynamics. By using Hamiltonian energy function and Casimir function comprehensively, the design method is proposed to overcome the difficulties taken by link dynamics. The Hamiltonian function is used to handle the dynamic of agent, while the Casimir function is constructed to deal with the dynamic of link. Thus the Lyapunov function is generated by modifying the Hamiltonian function...

Parallel implementation of local thresholding in Mitrion-C

Tomasz Kryjak, Marek Gorgoń (2010)

International Journal of Applied Mathematics and Computer Science

Mitrion-C based implementations of three image processing algorithms: a look-up table operation, simple local thresholding and Sauvola's local thresholding are described. Implementation results, performance of the design and FPGA logic utilization are discussed.

Parametric logarithmic type image processing for contrast based auto-focus in extreme lighting conditions

Corneliu Florea, Laura Florea (2013)

International Journal of Applied Mathematics and Computer Science

While most of state-of-the-art image processing techniques were built under the so-called classical linear image processing, an alternative that presents superior behavior for specific applications comes in the form of Logarithmic Type Image Processing (LTIP). This refers to mathematical models constructed for the representation and processing of gray tones images. In this paper we describe a general mathematical framework that allows extensions of these models by various means while preserving...

Parity codes

Paulo E. D. Pinto, Fábio Protti, Jayme L. Szwarcfiter (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Motivated by a problem posed by Hamming in 1980, we define even codes. They are Huffman type prefix codes with the additional property of being able to detect the occurrence of an odd number of 1-bit errors in the message. We characterize optimal even codes and describe a simple method for constructing the optimal codes. Further, we compare optimal even codes with Huffman codes for equal frequencies. We show that the maximum encoding in an optimal even code is at most two bits larger than the maximum...

Parity codes

Paulo E. D. Pinto, Fábio Protti, Jayme L. Szwarcfiter (2010)

RAIRO - Theoretical Informatics and Applications

Motivated by a problem posed by Hamming in 1980, we define even codes. They are Huffman type prefix codes with the additional property of being able to detect the occurrence of an odd number of 1-bit errors in the message. We characterize optimal even codes and describe a simple method for constructing the optimal codes. Further, we compare optimal even codes with Huffman codes for equal frequencies. We show that the maximum encoding in an optimal even code is at most two bits larger than the maximum...

Currently displaying 1061 – 1080 of 1507