Journal of Approximation Theory, ISSN 0021-9045, 05/2016, Volume 205, pp. 1 - 24

We establish formulas for the b-adic Walsh coefficients of functions in Cα[0,1] for an integer α≥1 and give upper bounds on the Walsh coefficients of these...

Walsh coefficient | Walsh series | Sobolev space | Smooth function | MATHEMATICS | ORDER | DISCREPANCY BOUNDS | DIGITAL SEQUENCES | F-2 | RULES | Mathematics - Numerical Analysis

Walsh coefficient | Walsh series | Sobolev space | Smooth function | MATHEMATICS | ORDER | DISCREPANCY BOUNDS | DIGITAL SEQUENCES | F-2 | RULES | Mathematics - Numerical Analysis

Journal Article

Siberian Mathematical Journal, ISSN 0037-4466, 5/2016, Volume 57, Issue 3, pp. 505 - 512

We prove that, given a sequence {ak}k=1 ∞ with a k ↓ 0 and {ak}k=1 ∞ ∉ l 2, reals 0 < ε < 1 and p ∈ [1, 2], and f ∈ L p(0, 1), we can find f ∈ L p(0, 1) with...

Mathematics, general | Mathematics | 1) space | Fourier coefficients | L p | Walsh system | SYSTEM | MATHEMATICS | SERIES | CONVERGENCE | L-p(0,1) space | NONLINEAR APPROXIMATION

Mathematics, general | Mathematics | 1) space | Fourier coefficients | L p | Walsh system | SYSTEM | MATHEMATICS | SERIES | CONVERGENCE | L-p(0,1) space | NONLINEAR APPROXIMATION

Journal Article

Bulletin of the Australian Mathematical Society, ISSN 0004-9727, 12/2009, Volume 80, Issue 3, pp. 430 - 453

We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further,...

smooth function | wavelet | Walsh coefficient | Walsh series | sobolev space | MATHEMATICS | INTEGRATION | SPACES | RULES

smooth function | wavelet | Walsh coefficient | Walsh series | sobolev space | MATHEMATICS | INTEGRATION | SPACES | RULES

Journal Article

Journal of Contemporary Mathematical Analysis, ISSN 1068-3623, 1/2016, Volume 51, Issue 1, pp. 21 - 33

The paper proves that for any ε > 0 there exists ameasurable set E ⊂ [0, 1] with measure |E| > 1 − ε such that for each f ∈ L1[0, 1] there is a function...

Mathematics, general | Mathematics | Fourier coefficients | Walsh system | convergence in L 1 -norm | convergence in L | norm | MATHEMATICS | convergence in L-1-norm | Fourier analysis | Research | Mathematical research | Walsh functions

Mathematics, general | Mathematics | Fourier coefficients | Walsh system | convergence in L 1 -norm | convergence in L | norm | MATHEMATICS | convergence in L-1-norm | Fourier analysis | Research | Mathematical research | Walsh functions

Journal Article

Discrete Mathematics and Applications, ISSN 0924-9265, 10/2016, Volume 26, Issue 5, pp. 259 - 272

We obtain achievable lower and upper bounds for the sums of modules of Walsh coefficients of Boolean functions of nvariables. An average value of such sums in...

Boolean functions | filtering generators | Walsh coefficients

Boolean functions | filtering generators | Walsh coefficients

Journal Article

Designs, Codes and Cryptography, ISSN 0925-1022, 11/2014, Volume 73, Issue 2, pp. 299 - 318

We generalize to the arithmetic Walsh transform (AWT) some results which were previously known for the Walsh–Hadamard transform of Boolean functions. We first...

Information and Communication, Circuits | Data Encryption | 11E95 | Boolean function | Mathematics | Poisson summation formula | Resilience | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Arithmetic Walsh transform | Coding and Information Theory | 94A60 | Combinatorics | 94C10 | 94A55 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Computer science

Information and Communication, Circuits | Data Encryption | 11E95 | Boolean function | Mathematics | Poisson summation formula | Resilience | Data Structures, Cryptology and Information Theory | Discrete Mathematics in Computer Science | Arithmetic Walsh transform | Coding and Information Theory | 94A60 | Combinatorics | 94C10 | 94A55 | MATHEMATICS, APPLIED | COMPUTER SCIENCE, THEORY & METHODS | Computer science

Journal Article

Numerische Mathematik, ISSN 0029-599X, 10/2011, Volume 119, Issue 2, pp. 271 - 297

In this paper we construct polynomial lattice rules which have, in some sense, small gain coefficients using a component-by-component approach. The gain...

65D30 | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Numerical Analysis | 65D32 | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 65C05 | HILBERT-SPACES | MATHEMATICS, APPLIED | QUADRATURE | NUMERICAL-INTEGRATION | DISCREPANCY | VARIANCE | ALGORITHMS | WALSH-SERIES | BY-COMPONENT CONSTRUCTION | MULTIVARIATE INTEGRATION | POINT SETS

65D30 | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Numerical Analysis | 65D32 | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | Mathematics, general | Mathematics | 65C05 | HILBERT-SPACES | MATHEMATICS, APPLIED | QUADRATURE | NUMERICAL-INTEGRATION | DISCREPANCY | VARIANCE | ALGORITHMS | WALSH-SERIES | BY-COMPONENT CONSTRUCTION | MULTIVARIATE INTEGRATION | POINT SETS

Journal Article

Hiroshima Mathematical Journal, ISSN 0018-2079, 07/2017, Volume 47, Issue 2, pp. 155 - 179

In this paper we give a new Koksma-Hlawka type inequality for QuasiMonte Carlo (QMC) integration. QMC integration of a function f :[0; 1)(s) -> R by a finite...

Koksma-Hlaka inequality | Walsh coefficients | Quasi-Monte Carlo integration | SMOOTH FUNCTIONS | SPACES | ALGORITHMS | POINT SETS | MATHEMATICS | ORDER | POLYNOMIAL LATTICE RULES | CONSTRUCTION | ERROR | EFFICIENT

Koksma-Hlaka inequality | Walsh coefficients | Quasi-Monte Carlo integration | SMOOTH FUNCTIONS | SPACES | ALGORITHMS | POINT SETS | MATHEMATICS | ORDER | POLYNOMIAL LATTICE RULES | CONSTRUCTION | ERROR | EFFICIENT

Journal Article

Sbornik Mathematics, ISSN 1064-5616, 2012, Volume 203, Issue 9, pp. 1295 - 1309

The paper is concerned with the behaviour of the coefficients of multiple Walsh-Paley series that are cube convergent to a finite sum. It is shown that even an...

Cube convergence | Multiple Walsh-Paley series | Cantor-Lebesgue theorem | MATHEMATICS | multiple Walsh-Paley series | cube convergence | TRIGONOMETRIC SERIES | UNIQUENESS

Cube convergence | Multiple Walsh-Paley series | Cantor-Lebesgue theorem | MATHEMATICS | multiple Walsh-Paley series | cube convergence | TRIGONOMETRIC SERIES | UNIQUENESS

Journal Article

Applicable Algebra in Engineering, Communication and Computing, ISSN 0938-1279, 12/2011, Volume 22, Issue 5, pp. 359 - 366

Are there other Boolean functions having two distinct Walsh coefficients except affine Boolean functions and maximal nonlinear (i.e. bent) Boolean functions?...

Walsh spectrum | Computer Hardware | Computer Science | Artificial Intelligence (incl. Robotics) | Boolean function | Bent Boolean function | Theory of Computation | Symbolic and Algebraic Manipulation | Affine Boolean function | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS | Access control | Computer science | Universities and colleges

Walsh spectrum | Computer Hardware | Computer Science | Artificial Intelligence (incl. Robotics) | Boolean function | Bent Boolean function | Theory of Computation | Symbolic and Algebraic Manipulation | Affine Boolean function | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS | Access control | Computer science | Universities and colleges

Journal Article

Journal of Mathematical Sciences (Japan), ISSN 1340-5705, 2016, Volume 23, Issue 4, pp. 727 - 740

Journal Article

Sbornik Mathematics, ISSN 1064-5616, 2012, Volume 203, Issue 3, pp. 351 - 379

This work continues the author's investigations of the convergence of greedy algorithms from the standpoint of classical results on correction of functions. In...

Greedy algorithm | Correction of functions | Fourier coefficients | Nonlinear approximation | MATHEMATICS | WALSH SYSTEM | RESPECT | nonlinear approximation | SERIES | correction of functions | CONVERGENCE | greedy algorithm | L-P

Greedy algorithm | Correction of functions | Fourier coefficients | Nonlinear approximation | MATHEMATICS | WALSH SYSTEM | RESPECT | nonlinear approximation | SERIES | correction of functions | CONVERGENCE | greedy algorithm | L-P

Journal Article

Symmetry, ISSN 2073-8994, 12/2019, Volume 12, Issue 1, p. 52

Proof of ownership on multimedia data exposes users to significant threats due to a myriad of transmission channel attacks over distributed computing...

fast walsh–hadamard transform | coefficient ordering | gaussian mapping | singular value decomposition | key mapping

fast walsh–hadamard transform | coefficient ordering | gaussian mapping | singular value decomposition | key mapping

Journal Article

Journal of Computer and System Sciences, ISSN 0022-0000, 2011, Volume 77, Issue 6, pp. 1039 - 1053

A k-bounded pseudo-Boolean function is a real-valued function on { 0 , 1 } n that can be expressed as a sum of functions depending on at most k input bits. The...

Pseudo-Boolean function | Walsh analysis | Graph finding | Fourier coefficients | Learning polynomials | Linkage discovery | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTER SCIENCE, THEORY & METHODS | EFFICIENT | DNF | Algorithms | Queries | Equivalence | Upper bounds | Mathematical analysis | Images | Fourier analysis | Mathematical models

Pseudo-Boolean function | Walsh analysis | Graph finding | Fourier coefficients | Learning polynomials | Linkage discovery | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | COMPUTER SCIENCE, THEORY & METHODS | EFFICIENT | DNF | Algorithms | Queries | Equivalence | Upper bounds | Mathematical analysis | Images | Fourier analysis | Mathematical models

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 10/2012, Volume 82, Issue 10, pp. 1815 - 1822

This work is concerned with robust estimation in a semiparametric varying-coefficient partially linear model when the underlying error distribution deviates...

Walsh-average | Robust nonparametric regression | Semiparametric composite quantile estimator | Asymptotic efficiency | Local linear regression | PARTIALLY LINEAR-MODELS | STATISTICS & PROBABILITY | SELECTION | EFFICIENT

Walsh-average | Robust nonparametric regression | Semiparametric composite quantile estimator | Asymptotic efficiency | Local linear regression | PARTIALLY LINEAR-MODELS | STATISTICS & PROBABILITY | SELECTION | EFFICIENT

Journal Article

Russian Mathematics, ISSN 1066-369X, 8/2013, Volume 57, Issue 8, pp. 10 - 19

We consider Fourier coefficients for functions of bounded variation with respect to general orthonormal systems (GONS). We show that in general case the...

Walsh system | trigonometric system | Mathematics, general | Mathematics | Haar system | Fourier series | Fourier coefficients

Walsh system | trigonometric system | Mathematics, general | Mathematics | Haar system | Fourier series | Fourier coefficients

Journal Article

Proceedings of SPIE - The International Society for Optical Engineering, ISSN 0277-786X, 2015, Volume 9255

Conference Proceeding

Cryptography and Communications, ISSN 1936-2447, 12/2014, Volume 6, Issue 4, pp. 335 - 358

We study the relationship between the Walsh Transform of a Boolean function and its Algebraic Normal Form(ANF), and present algorithms that compute the Walsh...

Information and Communication, Circuits | 06E30 | Data Structures, Cryptology and Information Theory | Walsh coefficient | Mathematics of Computing | Computer Science | Coding and Information Theory | Communications Engineering, Networks | Boolean function | Gupta-Sarkar’s algorithm | 94C10 | Algebraic normal form | Gupta-Sarkar's algorithm | MATHEMATICS, APPLIED | TRANSFORM | COMPUTER SCIENCE, THEORY & METHODS | Algorithms

Information and Communication, Circuits | 06E30 | Data Structures, Cryptology and Information Theory | Walsh coefficient | Mathematics of Computing | Computer Science | Coding and Information Theory | Communications Engineering, Networks | Boolean function | Gupta-Sarkar’s algorithm | 94C10 | Algebraic normal form | Gupta-Sarkar's algorithm | MATHEMATICS, APPLIED | TRANSFORM | COMPUTER SCIENCE, THEORY & METHODS | Algorithms

Journal Article

Journal of the Korean Statistical Society, ISSN 1226-3192, 03/2015, Volume 44, Issue 1, pp. 95 - 110

A shrinkage-type variable selection procedure for varying coefficient models is routinely established in the least-squares (LS) framework. Although the LS...

Walsh-average | Oracle property | Asymptotic relative efficiency | Varying coefficient model | Variable selection | Robust BIC-type criterion | STATISTICS & PROBABILITY | LONGITUDINAL DATA | COMPOSITE QUANTILE REGRESSION | ORACLE PROPERTIES | SHRINKAGE | LASSO | EFFICIENT | Research | Variables (Mathematics) | Mathematical research | Least squares | 통계학

Walsh-average | Oracle property | Asymptotic relative efficiency | Varying coefficient model | Variable selection | Robust BIC-type criterion | STATISTICS & PROBABILITY | LONGITUDINAL DATA | COMPOSITE QUANTILE REGRESSION | ORACLE PROPERTIES | SHRINKAGE | LASSO | EFFICIENT | Research | Variables (Mathematics) | Mathematical research | Least squares | 통계학

Journal Article

20.
Full Text
Local rank estimation and related test for varying-coefficient partially linear models

Journal of Nonparametric Statistics, ISSN 1048-5252, 01/2014, Volume 26, Issue 1, pp. 187 - 206

This paper develops a robust estimation procedure for the varying-coefficient partially linear model via local rank technique. The new procedure provides a...

local rank estimation | asymptotic efficiency | test | varying-coefficient partially linear model | STATISTICS & PROBABILITY | QUANTILE REGRESSION | EFFICIENT ESTIMATION | WALSH-AVERAGE REGRESSION | SELECTION | Errors | Monte Carlo methods | Computer simulation | Least squares method | Mathematical analysis | Samples | Statistical tests | Nonparametric statistics

local rank estimation | asymptotic efficiency | test | varying-coefficient partially linear model | STATISTICS & PROBABILITY | QUANTILE REGRESSION | EFFICIENT ESTIMATION | WALSH-AVERAGE REGRESSION | SELECTION | Errors | Monte Carlo methods | Computer simulation | Least squares method | Mathematical analysis | Samples | Statistical tests | Nonparametric statistics

Journal Article

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