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An Algorithm for Testing Asummability of Boolean functions

IEEE Transactions on Computers 1974年第2期C-23卷 188-191页

作者： Chander, Suresh Department of Electrical Engineering College of Technology G. P. Pant University of Agriculture and Technology Pantnagar India

An algorithm is described in this note to determine whether a switching function is asummable or not. The algorithm is efficient and simple for testing 2-asummability. Copyright © 1974 by The Institute of Electri... 详细信息

关键词： 2-asummability m-asummability number system radix threshold functions

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Upper bounds on Fourier entropy 21st

Upper bounds on Fourier entropy

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21st Annual International Computing and Combinatorics Conference (COCOON)

作者： Chakraborty, Sourav Kulkarni, Raghav Lokam, Satyanarayana V. Saurabh, Nitin Chennai Math Inst Madras Tamil Nadu India Ctr Quantum Technol Singapore Singapore Microsoft Res India Bangalore Karnataka India Inst Math Sci Madras Tamil Nadu India

ISBN: (纸本)9783319213972

Given a function f : (0,1}(n) -> {+1, -1), its Fourier Entropy is defined to be - Sigma(s) (f) over cap (S)(2) log (f) over cap (S)(2), where (f) over cap denotes the Fourier transform of f. In the analysis of Boolean functions, an outstanding open question is a conjecture of Friedgut and Kalai, 1996 [3], called the Fourier Entropy Influence (FEI) Conjecture, asserting that the Fourier Entropy of any Boolean function f is bounded above, up to a constant factor, by the total influence (= average sensitivity) of f. In this paper we give several upper bounds on the Fourier Entropy. We first give upper bounds on the Fourier Entropy of Boolean functions in terms of several complexity measures that are known to be bigger than the influence. These complexity measures include, among others, the logarithm of the number of leaves and the average depth of a parity decision tree. We then show that for the class of Linear threshold functions (LTF), the Fourier Entropy is O(root n). It is known that the average sensitivity for the class of LTF is Theta(root n). We also establish a bound of O-d(n(1-1/4d+6)) for general degree-d polynomial threshold functions. Our proof is based on a new upper bound on the derivative of noise sensitivity. Next we proceed to show that the FEI Conjecture holds for read-once formulas that use AND, OR, XOR, and NOT gates. The last result is independent of a result due to O'Donnell and Tan [1] for read-once formulas with arbitrary gates of bounded fan-in, but our proof is completely elementary and very different from theirs. Finally, we give a general bound involving the first and second moments of sensitivities of a function (average sensitivity being the first moment), which holds for real-valued functions as well. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Boolean functions Fourier entropy Noise sensitivity Influence Read-once formulas Decision trees threshold functions

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Using Wavelet Analysis for Signal Processing of Information Transmission Systems

Using Wavelet Analysis for Signal Processing of Information ...

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2024 Systems of Signal Synchronization, Generating and Processing in Telecommunications, SYNCHROINFO 2024

作者： Manonina, I.V. Shestakov, V.V. Moscow Technical University of Communications and Informatics Moscow Russia

ISBN: (纸本)9798350373448

Currently, the use of wavelet analysis makes it possible to solve various problems in the formation and processing of information, perform measurement tasks, and perform compression and regeneration of signals with low distortion. For example, with of wavelet processing it is possible to carry out effective pattern recognition with better performance than with multivariate statistical analysis;for digital information processing systems allows you to develop modern methods and algorithms for signal processing to solve radar and hydroacoustic problems;for infocommunication systems, wavelet analysis allows solving problems of generating, transmitting, receiving and processing information in real time, being a relevant and necessary solution for digital information transmission systems;performing basic algorithms for spectral analysis, filtering and signal synthesis, which allows for more economical use of technical resources;obtain more efficient methods of processing, compression and regeneration of signals transmitted over digital communication channels with low distortion. The article discusses methods of threshold wavelet signal processing using various threshold functions. A subsequent comparative analysis was also carried out for the selected communication signal by determining the risk assessment. © 2024 IEEE.

关键词： Noise component Risk assessment threshold functions thresholding method Wavelet analysis

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Design and implementation of a robust noise removal system in ECG signals using dual-tree complex wavelet transform

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BIOMEDICAL SIGNAL PROCESSING AND CONTROL 2021年 63卷

作者： Prashar, Navdeep Sood, Meenakshi Jain, Shruti Bahra Univ Dept Elect & Commun Engn Solan 173234 Himachal Prades India NITTTR Dept CDC Chandigarh 16009 India Jaypee Univ Informat Technol Dept Elect & Commun Engn Solan 173234 Himachal Prades India

The key deliverable for any health monitoring system that offers telecardiology services is the recovery of the ECG signal related to cardiac diagnostics. Accurate analysis and diagnosis of heart diseases become difficult due to noises and artifacts. Therefore, a need for noise removal which is an inverse problem arises that leads to reliable signal recovery tasks. In this paper, authors have provided a detailed evaluation of the effect of the choice of the threshold value, threshold algorithm, and distribution function to evaluate the ECG signal denoising performance employing Dual tree complex wavelet transform (DTCWT). In this research work, eight different sets of threshold value selection rules along with six distinct threshold functions are implemented and evaluated on MIT-BIH arrhythmia database. Authors have proposed an estimator that yields efficient results than a conventional estimator using Gaussian distribution function and extended the work to Normal distribution. The results show that the Universal modified threshold level-dependent threshold value selection with Non -Negative Garrote threshold function delivers higher performance in terms of SNR, lower values of MSE and PRD. The proposed approach accomplished good performance evaluation results as 58.23 dB, SNR and 9.63e-08, MSE in comparison with the 48.65 dB, SNR and 8.75e-07, MSE using conventional method for the normal distribution function. The novelty of this work also lies in an exhaustive empirical comparative analysis with the existing research work using the same database with the proposed normal distribution technique.

关键词： Dual-tree complex wavelet transform threshold functions threshold values Distribution function Electrocardiogram

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QUASIPOLYNOMIAL NORMALISATION IN DEEP INFERENCE VIA ATOMIC FLOWS AND threshold FORMULAE

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LOGICAL METHODS IN COMPUTER SCIENCE 2016年第2期12卷

作者： Bruscoli, Paola Guglielmi, Alessio Gundersen, Tom Parigot, Michel Univ Bath Bath BA2 7AY Avon England Red Hat Inc Raleigh NC 27601 USA CNRS Lab PPS UMR 7126 Paris France Univ Paris 07 F-75221 Paris 05 France

Jerabek showed that cuts in classical propositional logic proofs in deep inference can be eliminated in quasipolynomial time. The proof is indirect and it relies on a result of Atserias, Galesi and Pudlak about monotone sequent calculus and a correspondence between that system and cut-free deep-inference proofs. In this paper we give a direct proof of Jerabek's result: we give a quasipolynomial-time cut-elimination procedure for classical propositional logic in deep inference. The main new ingredient is the use of a computational trace of deep-inference proofs called atomic flows, which are both very simple (they only trace structural rules and forget logical rules) and strong enough to faithfully represent the cut-elimination procedure.

关键词： Proof theory proof complexity deep inference threshold functions

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Compressed bitmap indexes: beyond unions and intersections

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SOFTWARE-PRACTICE & EXPERIENCE 2016年第2期46卷 167-198页

作者： Kaser, Owen Lemire, Daniel Univ New Brunswick Dept CSAS St John NB E2L 4L5 Canada Univ Quebec TELUQ LICEF Montreal PQ H3C 3P8 Canada

Compressed bitmap indexes are used to speed up simple aggregate queries in databases. Indeed, set operations like intersections, unions and complements can be represented as logical operations (AND, OR and NOT) that are ideally suited for bitmaps. However, it is less obvious how to apply bitmaps to more advanced queries. For example, we might seek products in a store that meet some, but maybe not all, criteria. Such threshold queries generalize intersections and unions;they are often used in information-retrieval and data-mining applications. We introduce new algorithms that are sometimes three orders of magnitude faster than a naive approach. Our work shows that bitmap indexes are more broadly applicable than is commonly believed. Copyright (c) 2014 John Wiley & Sons, Ltd.

关键词： T-overlap queries compressed bitmaps threshold functions symmetric functions Opt-threshold queries

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Average-Case Lower Bounds and Satisfiability Algorithms for Small threshold Circuits

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THEORY OF COMPUTING 2018年 14卷

作者： Chen, Ruiwen Santhanam, Rahul Srinivasan, Srikanth Simon Fraser Univ Burnaby BC Canada Univ Oxford Dept Comp Sci Oxford England Indian Inst Technol Dept Math Bombay Maharashtra India

We show average-case lower bounds for explicit Boolean functions against bounded-depth threshold circuits with a superlinear number of wires. We show that for each integer d > 1, there is a constant epsilon(d) > 0 such that the Parity function on n bits has correlation at most n(1+epsilon d) with depth-d threshold circuits which have at most n(1+)(epsilon d) wires, and the Generalized Andreev function on n bits has correlation at most exp(-n(epsilon d)) with depth-d threshold circuits which have at most n(1+)(epsilon d) wires. Previously, only worst-case lower bounds in this setting were known (Impagliazzo, Paturi, and Saks (SICOMP 1997)). We use our ideas to make progress on several related questions. We give satisfiability algorithms beating brute force search for depth-d threshold circuits with a superlinear number of wires. These are the first such algorithms for depth greater than 2. We also show that Parity on n bits cannot be computed by polynomial-size AC(0) circuits with n(0(1)) general threshold gates. Previously no lower bound for Parity in this setting could handle more than log(n) gates. This result also implies subexponential-time learning algorithms for AC(0) with n(0(1)) threshold gates under the uniform distribution. In addition, we give almost optimal bounds for the number of gates in a depth-d threshold circuit computing Parity on average, and show average-case lower bounds for threshold formulas of any depth. Our techniques include adaptive random restrictions, anti-concentration and the structural theory of linear threshold functions, and bounded-read Chernoff bounds.

关键词： complexity theory circuit complexity correlation bounds threshold functions random restrictions learning SAT

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Input-Dependent threshold Function for an Actuator Fault Detection Filter

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IFAC Proceedings Volumes 2005年第1期38卷 211-216页

作者： Héctor Rotstein Ryan Ingvalson Tamas Keviczky Gary Balas Rafael and the Dept. of Electrical Engineering The Technion Haifa 3200 Israel Dept. of Aerospace Engineering University of Minnesota MN55455 USA

The flight control system is a safety-critical component of an UAV and hence should include a level of fault detection (FD) and controller reconfiguration to be used in case a faulty condition is declared. This paper reports the design of a FD filter for the lateral channel of an UAV. The main theoretical contribution is a new threshold function that enhances the fault detection capabilities in the face of substantial model uncertainty. Simulation result shows that the new threshold function in combination with a fault detection filter can detect a fault in the lateral channel of an UAV flight control.

关键词： Fault detection H-infinity control Aerospace computer control threshold functions Uncertainty

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GRIDS IN RANDOM GRAPHS

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RANDOM STRUCTURES & ALGORITHMS 1994年第2期5卷 329-336页

作者： DELAVEGA, WF MANOUSSAKIS, Y Laboratoire de Recherche en Informatique Université de Paris-Sud Centre d'Orsay 91405 Orsay Cedex France

threshold probabilities for the existence in a random graph on n vertices of a graph isomorphic to a given graph of order Cn and average degree at least three are investigated. In particular it is proved that the random graph G(n, p) on n vertices with edge probability p = ((1 + epsilon) log n/n)1/2, epsilon < 1, contains a square grid on epsilonn/2 vertices. (C) 1994 John Wiley & Sons, Inc.

关键词： RANDOM GRAPHS threshold functions

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Upper Bounds on Probability thresholds for Asymmetric Ramsey Properties

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RANDOM STRUCTURES & ALGORITHMS 2014年第1期44卷 1-28页

作者： Kohayakawa, Yoshiharu Schacht, Mathias Spoehel, Reto Univ Sao Paulo Inst Matemat & Estat BR-05508090 Sao Paulo Brazil Univ Hamburg Fachbereich Math D-20146 Hamburg Germany Max Planck Inst Informat Algorithms & Complex Grp D-66123 Saarbrucken Germany

Given two graphs G and H, we investigate for which functions p=p(n) the random graph Gn,p (the binomial random graph on n vertices with edge probability p) satisfies with probability 1-o(1) that every red-blue-coloring of its edges contains a red copy of G or a blue copy of H. We prove a general upper bound on the threshold for this property under the assumption that the denser of the two graphs satisfies a certain balancedness condition. Our result partially confirms a conjecture by the first author and Kreuter, and together with earlier lower bound results establishes the exact order of magnitude of the threshold for the case in which G and H are complete graphs of arbitrary size. In our proof we present an alternative to the so-called deletion method, which was introduced by Rodl and Ruciski in their study of symmetric Ramsey properties of random graphs (i.e. the case G = H), and has been used in many proofs of similar results since *** (c) 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 1-28, 2014

关键词： Ramsey theory random graphs threshold functions non-diagonal Ramsey properties

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