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On the arithmetic complexity of computing Grobner bases of comaximal determinantal ideals

JOURNAL OF ALGEBRA 2025年 668卷 233-264页

作者： Gopalakrishnan, Sriram Sorbonne Univ 4 Pl Jussieu F-75005 Paris France Univ Waterloo 200 Univ Ave W Waterloo ON N2L 3G1 Canada

Let M be an nxn matrix of homogeneous linear forms over a field k. If the ideal In-2(M) generated by minors of size n-1 is Cohen-Macaulay, then the Gulliksen-Negard complex is a free resolution of In-2(M). It has recently been shown that by taking into account the syzygy modules for In-2(M) which can be obtained from this complex, one can derive a refined signature-based Grobner basis algorithm DetGB which avoids reductions to zero when computing a grevlex Grobner basis for In-2(M). In this paper, we establish sharp complexity bounds on DetGB. To accomplish this, we prove several results on the sizes of reduced grevlex Grobner bases of reverse lexicographic ideals, thanks to which we obtain two main complexity results which rely on conjectures similar to that of Froberg. The first one states that, in the zero-dimensional case, the size of the reduced grevlex Grobner basis of In-2(M) is bounded from below by n(6) asymptotically. The second, also in the zero-dimensional case, states that the complexity of DetGB is bounded from above by n(2 omega+3) asymptotically, where 2 <=omega <= 3 is any complexity exponent for matrix multiplication over k. (c) 2025 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// ***/licenses/by/4.0/).

关键词： Grobner basis Polynomial system solving Determinantal ideals arithmetic complexity

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The arithmetic complexity of online grocery shopping: the moderating role of product pictures

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INDUSTRIAL MANAGEMENT & DATA SYSTEMS 2019年第6期119卷 1206-1222页

作者： Desrochers, Camille Leger, Pierre-Majorique Fredette, Marc Mirhoseini, Seyedmohammadmahdi Senecal, Sylvain Ecole Hautes Etud Commerciales Dept Informat Technol Montreal PQ Canada Ecole Hautes Etud Commerciales Dept Decis Sci Montreal PQ Canada Ecole Hautes Etud Commerciales Dept Mkt Montreal PQ Canada

Purpose Online grocery shopping possesses characteristics that can make it more difficult than regular online shopping. There are numerous buying decisions to make each shopping session, there are large ranges of product types to choose from and there is varied arithmetical complexity. The purpose of this paper is to examine how such characteristics influence the attitude of consumers toward online grocery shopping websites. Design/methodology/approach The authors hypothesized that the product type (search or experience product), the task arithmetic complexity, and the attention and cognitive load associated with browsing through product pictures have an effect on the attitude of online shoppers toward these websites. To test the hypotheses, 31 subjects participated in a within-subject laboratory experiment. Findings The results suggest that visual attention to product pictures has a positive effect on the attitude of online shoppers toward a website when they are shopping for experience goods, but that it has a negative effect on their attitude toward a website when the task arithmetic complexity is greater. They also suggest that the cognitive load associated with browsing through product pictures has a negative effect on the attitude of online shoppers toward a website when they are shopping for experience goods, and that greater cognitive load variation has a positive effect on their attitude toward a website when arithmetic task complexity is greater. Originality/value Results reinforce the relevance of enriching the study of self-reported measures of the user experience on e-commerce sites with automatic measures.

关键词： Uncertainty Human computer interaction Electronic commerce Visual attention Eyetracking Online grocery arithmetic complexity Attitude towards the site Pupil dilation

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Hardware Architectures for Computing Eigendecomposition-Based Discrete Fractional Fourier Transforms with Reduced arithmetic complexity

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2024年第1期43卷 593-614页

作者： Bispo, Breno C. de Oliveira Neto, Jose R. Lima, Juliano B. Univ Fed Pernambuco Dept Elect & Syst Recife PE Brazil Univ Fed Pernambuco Dept Mech Engn Recife PE Brazil

The fractional Fourier transform (FrFT) is a useful mathematical tool for signal and image processing. In some applications, the eigendecomposition-based discrete FrFT (DFrFT) is suitable due to its properties of orthogonality, additivity, reversibility and approximation of continuous FrFT. Although recent studies have introduced reduced arithmetic complexity algorithms for DFrFT computation, which are attractive for real-time and low-power consumption practical scenarios, reliable hardware architectures in this context are gaps in the literature. In this paper, we present two hardware architectures based on the referred algorithms to obtain N-point DFrFT (N = 4L, L is a positive integer). We validate and compare the performance of such architectures by employing field-programmable gate array implementations, co-designed with an embedded hard processor unit. In particular, we carry out computer experiments where synthesis, error and latency analyses are performed, and consider an application related to compact signal representation.

关键词： Field programmable gate array Discrete fractional Fourier transform Hardware implementation arithmetic complexity

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Computation of an eigendecomposition-based discrete fractional Fourier transform with reduced arithmetic complexity

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SIGNAL PROCESSING 2019年 165卷 72-82页

作者： de Oliveira Neto, Jose R. Lima, Juliano B. da Silva, Gilson J., Jr. Campello de Souza, Ricardo M. Univ Fed Pernambuco Dept Mech Engn Ave Arquitetura S-NCidade Univ BR-50740550 Recife PE Brazil Univ Fed Pernambuco Dept Elect & Syst Ave Arquitetura S-NCidade Univ BR-50740550 Recife PE Brazil

In this paper, we introduce a method for computing an eigendecomposition-based discrete fractional Fourier transform (DFrFT) with reduced arithmetic complexity, when compared to the O(N-2) complexity of the corresponding direct computation. Our approach exploits properties of a recently introduced closed-form Hermite-Gaussian-like discrete Fourier transform eigenbasis, which is used to define the DFrFT, and includes a rounding strategy. The proposed (exact) technique requires a slightly lower number of multiplications and half or less additions than what is required by other state-of-the-art methods;if the referred rounding strategy is applied, up to 65% of multiplications can be avoided. We validate our results by means of computer experiments where the application of the transform in signal filtering and compact representation is considered. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Discrete fractional Fourier transforms Hermite-Gaussian eigenvectors Fast algorithms arithmetic complexity

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arithmetic complexity of direct solvers for banded systems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2003年第4期80卷 473-478页

作者： Chawla, MM Evans, DJ Kuwait Univ Dept Math & Comp Sci Safat 13060 Kuwait Nottingham Trent Univ Fac Engn & Comp Nottingham NG1 4BU England

We report on arithmetic complexity of direct solvers for beta-semiband n x n systems. If GT denotes grand total of all operations of additions, multiplications and divisions, then in each case GT = p(beta)n - q(beta), where p(beta) and q(beta) are nonnegative polynomials of degree two and three, respectively. If divisors are not saved, GT reported here saves precisely n operations. Partial pivoting for banded systems can increase the operations counts significantly. We give these counts, and for multiple right-hand sides. For beta = 1 and n - 1, our results agree with known counts. Some interesting observations follow from the obtained counts.

关键词： banded systems arithmetic complexity LU elimination partial pivoting Choleski root-free symmetric elimination

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Modulation of neural activities by the complexity of mental arithmetic: An MEG study

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International Congress Series 2007年 1300卷 539-542页

作者： Kou, Hiroko Iwaki, Sunao Institute for Human Science and Biomedical Engineering National Institute of Advanced Industrial Science and Technology (AIST) Japan

Recent fMRI studies have revealed the involvement of frontal/prefrontal and parietal regions in the mental arithmetic. However it remains unclear how the spatiotemporal characteristics of the neural activities in these regions during arithmetic operations were modulated by the complexity of mental calculations. In this study, we used magnetoencephalography (MEG) to investigate the spatiotemporal cortical activities during mental calculations and their modulation by arithmetic complexity. Increased neural activities in the bilateral frontal/prefrontal and the parietal regions during arithmetic operations were observed in the latencies around 700-900 ms. The activities in the bilateral prefrontal and the left parietal areas in the same latencies were found to be complexity-dependent. Our current results are in agreement with previous fMRI studies and adding further insight into the temporal characteristics of the neural activities in these regions. © 2007 Elsevier B.V. All rights reserved.

关键词： arithmetic complexity Mental arithmetic Neuromagnetic measurement Parietal cortex Prefrontal cortex

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A new complexity bound for the least-squares problem

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1996年第12期31卷 15-16页

作者： Li, L Department of Information Systems Engineering Aomori University Aomori 030 Japan

For a least-squares problem of m degree polynomial regression with n measured values (n greater than or equal to m + 1), the traditional methods need O(n(2)m) arithmetic operations. We prove that the arithmetic comple... 详细信息

关键词： arithmetic complexity least-squares problem

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Majority Logic Formulations for Parallel Adder Designs at Reduced Delay and Circuit complexity

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IEEE TRANSACTIONS ON COMPUTERS 2017年第10期66卷 1824-1830页

作者： Pudi, Vikramkumar Sridharan, K. Lombardi, Fabrizio Nanyang Technol Univ Hardware Embedded Syst Lab Singapore 639798 Singapore Indian Inst Technol Madras Dept Elect Engn Madras 600036 Tamil Nadu India Northeastern Univ Elect & Comp Engn Boston MA 02115 USA

The design of high-performance adders has experienced a renewed interest in the last few years;among high performance schemes, parallel prefix adders constitute an important class. They require a logarithmic number of stages and are typically realized using AND-OR logic;moreover with the emergence of new device technologies based on majority logic, new and improved adder designs are possible. However, the best existing majority gate-based prefix adder incurs a delay of 2log(2)(n) - 1 (due to the nth carry);this is only marginally better than a design using only AND-OR gates (the latter design has a 2log(2)(n) + 1 gate delay). This paper initially shows that this delay is caused by the output carry equation in majority gate-based adders that is still largely defined in terms of AND-OR gates. In this paper, two new majority gate-based recursive techniques are proposed. The first technique relies on a novel formulation of the majority gate-based equations in the used group generate and group propagate hardware;this results in a new definition for the output carry, thus reducing the delay. The second contribution of this manuscript utilizes recursive properties of majority gates (through a novel operator) to reduce the circuit complexity of prefix adder designs. Overall, the proposed techniques result in the calculation of the output carry of an n-bit adder with only a majority gate delay of log(2)(n) + 1. This leads to a reduction of 40percent in delay and 30percent in circuit complexity (in terms of the number of majority gates) for multi-bit addition in comparison to the best existing designs found in the technical literature.

关键词： Adder carry majority voting logic emerging technologies arithmetic complexity

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Low-complexity DST approximation for VVC standard using Particle Swarm Optimization 31

Low-complexity DST approximation for VVC standard using Part...

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Conference on Pattern Recognition and Tracking XXXI

作者： Ben Jdidia, Sonda Sallem, Amin Belghith, Fatma Masmoudi, Nouri Jridi, Maher Alfalou, Ayman Univ Sfax LETI ENIS Sfax 3038 Tunisia LabISEN Equipe Vis 20 Rue Cuirasse Bretagne CS 42807 F-29228 Brest 2 France

ISBN: (数字)9781510635784

ISBN: (纸本)9781510635784

The standardization of the Versatile Video Coding (VVC) is still carrying out. Its first version is planned to be finished by the end of 2020. VVC promises higher coding efficiency than the High Efficiency Video Coding (HEVC) due to the improvements of the different coding tools. The adaptive Multiple Transform (AMT) is one of the major enhancements of the transform module of the VVC where five transform types have been introduced. However, the encoder and decoder complexities have been increased dramatically. This paper discusses one solution for codec complexity alleviation by considering transform approximation. It focuses on the approximation of the DST of type VII. The proposed approximation consists in applying the Particle Swarm Optimization (PSO) algorithm to the target transform in order to get an approximate matrix with low computational complexity requirements. This algorithm is used to cope with traditional approximation techniques based on constrained optimization of the DST transform. The proposed transform has shown a significant computational complexity reduction with no quality degradation and a tolerable BD-rate loss.

关键词： Versatile Video Coding (VVC) Discrete Sine Transform (DST) approximate computing arithmetic complexity Metaheuristics Particle Swarm Optimization (PSO)

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Low complexity channel estimation with pilot symbol assisted modulation

Low complexity channel estimation with pilot symbol assisted...

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8th International Symposium on Signal Processing and Its Applications

作者： Benjillali, M Szczecinski, L INRS EMT Montreal PQ Canada

ISBN: (纸本)0780392434

Pilot symbol assisted modulation (PSAM) allows the channel estimation in fast-fading channels. The approaches proposed up to now were mainly concerned with the robustness and simplicity of adaptation of the channel estimators. In this paper we analyze the techniques presented in the literature from the complexity and performance points of view. As a result, we show that using linear interpolation the complexity of the channel estimation may be strightforwardly reduced by order of magnitude without compromising the performance. For channels with very fast fading, we propose a new method which offers a simple trade-off between performance and complexity. Numerical simulations are shown to illustrate the analysis.

关键词： PSAM channel estimation smoothing interpolation arithmetic complexity

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