Related papers: Convolutions power of a characteristic function
Depthwise convolution and grouped convolution has been successfully applied to improve the efficiency of convolutional neural network (CNN). We suggest that these models can be considered as special cases of a generalized convolution…
By applying the derivative operators to Chu-Vandermonde convolution, several general harmonic number identities are established.
In this paper, we define new type of convolution and correlation theorems associated with the offset linear canonical transform (OLCT). Additionally, we discuss their applications in multiplicative filter design, which may prove useful in…
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
New families of unit memory as well as multi-memory convolutional codes are constructed algebraically in this paper. These convolutional codes are derived from the class of group character codes. The proposed codes have basic generator…
We study higher moments of convolutions of the characteristic function of a set, which generalize a classical notion of the additive energy. Such quantities appear in many problems of additive combinatorics as well as in number theory. In…
The Mat\'ern covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Mat\'ern class is that it is possible to get precise control over the degree of…
A new characterization for power function distributions is obtained which is based on products of order statistics. This result may be considered as a generalization of some recent results for contractions. We note that in this new result…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities.…
Formulas to calculate multivector exponentials in a base-free representation and in a orthonormal basis are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on the analysis of roots of characteristic…
The article provides a survey on convolutional codes stressing the connections to module theory and systems theory. Constructions of codes with maximal possible distance and distance profile are provided. The article will appear as book…
In this paper we show how to construct new convolutional codes from old ones by applying the well-known techniques: puncturing, extending, expanding, direct sum, the (u|u + v) construction and the product code construction. By applying…
The QCDNUM program numerically solves the evolution equations for parton densities and fragmentation functions in perturbative QCD. Un-polarised parton densities can be evolved up to next-to-next-to-leading order in powers of the strong…
Correlation-immune (CI) multi-output Boolean functions have the property of keeping the same output distribution when some input variables are fixed. Recently, a new application of CI functions has appeared in the system of resisting…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
Deep learning based on deep neural networks has been very successful in many practical applications, but it lacks enough theoretical understanding due to the network architectures and structures. In this paper we establish some analysis for…
The Qth-power algorithm produces a useful canonical P-module presentation for the integral closures of certain integral extensions of $P:=\mathbf{F}[x_n,...,x_1]$, a polyonomial ring over the finite field $\mathbf{F}:=\mathbf{Z}_q$ of $q$…
Linear recurrence operators in characteristic $p$ are classified by their $p$-curvature. For a recurrence operator $L$, denote by $\chi(L)$ the characteristic polynomial of its $p$-curvature. We can obtain information about the…
A probability inequality is proved for n-fold convolutions of a smooth cumulative distribution function on (0,infinity)x...x(0,infinity), which is multivariate totally positive of order 2 (MTP2). This inequality is better than an inequality…
A mathematical development of the Walsh transform, Walsh basis, and Walsh coefficients is given. The author was prompted to write this by a wish to give a unified treatment of epistatic coordinates as they are used in evolutionary biology.…