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Polynomial Multiplication over Binary Fields Using Charlier Polynomial Representation with Low Space Complexity [chapter]

Sedat Akleylek, Murat Cenk, Ferruh Özbudak
2010 Lecture Notes in Computer Science  
We show that multiplication in Charlier polynomial representation can be performed with subquadratic space complexity.  ...  One can obtain binomial or trinomial irreducible polynomials in Charlier polynomial representation which allows us faster modular reduction over binary fields when there is no desirable such low weight  ...  This representation is based on Charlier polynomials. We show that multiplication in Charlier polynomial representation can be performed with subquadratic space complexity.  ... 
doi:10.1007/978-3-642-17401-8_17 fatcat:v22z3uazqvbtxjzodkercsdqxq

Vision-Based Human Detection Techniques: A Descriptive Review

Shahriar Shakir Sumit, Dayang Rohaya Awang Rambli, Seyedali Mirjalili
2021 IEEE Access  
b: Challenges The TP's common issue is that the calculation of coefficients is vulnerable to numerical instability for higher polynomial order [132] . 3) Charlier polynomials Charlier polynomials (CHPs  ...  combined HoG features with LBP (Local Binary Pattern)  ... 
doi:10.1109/access.2021.3063028 fatcat:bklvpd5sqraq7pb3xe7w5sueli

Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance [article]

Yanjun Han, Jiantao Jiao, Tsachy Weissman
2018 arXiv   pre-print
complexity for the entropy, power sum and support size functionals.  ...  Instead of doing best polynomial approximation explicitly as in existing literature of functional estimation, the plug-in approach conducts polynomial approximation implicitly and attains the optimal sample  ...  Proof [Proof of Lemma 30] The Charlier polynomial c k (u, a) for u ∈ N is defined as c k (u, a) T Tony Cai and Mark G Low.  ... 
arXiv:1802.08405v2 fatcat:o2t4oveyd5djpkscnpt3igh3zm

Review of thek-body embedded ensembles of Gaussian random matrices

L Benet, H A Weidenm ller
2003 Journal of Physics A: Mathematical and General  
properties, and the ergodic properties of these ensembles: moments methods, numerical simulations, the replica trick, the eigenvector decomposition of the matrix of second moments and supersymmetry, the binary  ...  LB has profited from discussions with J.  ...  In a representation of Hilbert space spanned by Slater determinants of single-particle wave functions (solutions of the mean-field equations), the residual twobody interaction has non-vanishing matrix  ... 
doi:10.1088/0305-4470/36/12/340 fatcat:gebaxjhhjfbqtkrcu4la2xvmra

Universality and Fourth Moment Theorem for homogeneous sums. Orthogonal polynomials and apolarity [article]

Rosaria Simone
2017 arXiv   pre-print
Specifically, Part I deals with the Lindberg method of influence functions in free probability spaces.  ...  Then, by focusing on apolarity. a unifying representation for (generalized) sequences of orthogonal polynomials (in any number of variables) is achieved and explicit formulae for the moments of the random  ...  free kurtosis, over a free probability space (A, ϕ).  ... 
arXiv:1705.03294v1 fatcat:qhwbeaepbncn7lywmayehi7ghi

Long-term capture orbits for low-energy space missions

Stefano Carletta, Mauro Pontani, Paolo Teofilatto
2018 Celestial mechanics & dynamical astronomy  
binary star systems.  ...  In the framework of the space debris problem, in order to mitigate the already critical situation in the Low Earth Orbit (LEO) region, and, more generally, to preserve the circumterrestrial environment  ...  DIMARE SpaceDys (Italy) Title: "Use of a semi-linear method to predict the impact corridor on ground" Abstract.  ... 
doi:10.1007/s10569-018-9843-7 fatcat:mie5p3lzircr7pxb3xj2monqqi

Master equations and the theory of stochastic path integrals

Markus F Weber, Erwin Frey
2017 Reports on progress in physics (Print)  
To make our review accessible to a broad community, we have used the language of probability theory rather than quantum (field) theory.  ...  This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals.  ...  Besides Hermite polynomials, Ohkubo also proposed the use of Charlier polynomials and mentioned their relation with certain birth-death processes [301] . 2.2.3. Intermezzo: The unit vector basis.  ... 
doi:10.1088/1361-6633/aa5ae2 pmid:28306551 fatcat:k35hjryscjg73jg2b5edmij2ia

Invariants of the Hilbert Transform for 23-Hilbert Problem

Peter Matveevich Mazurkin
2016 Social Science Research Network  
Thus the wave equations with variables amplitude and the period of fluctuation are designed from the generalized invariant and its fragments.  ...  Everyone wavelet this algebraic equation contains two fundamental physical constants -the number e of time or Napier and the number π of space or Archimedes.  ...  Thus the multiple-factor analysis of data is made by the binary relations on the sum wavelets.  ... 
doi:10.2139/ssrn.2755451 fatcat:hyrdu5o26fahvo5bputu6d4wcu

ChebLieNet: Invariant Spectral Graph NNs Turned Equivariant by Riemannian Geometry on Lie Groups [article]

Hugo Aguettaz, Erik J. Bekkers, Michaël Defferrard
2021 arXiv   pre-print
Group equivariance is achieved via equivariant and invariant operators on graphs with anisotropic left-invariant Riemannian distance-based affinities encoded on the edges.  ...  Surfing on the success of graph- and group-based neural networks, we take advantage of the recent developments in the geometric deep learning field to derive a new approach to exploit any anisotropies  ...  We also thank all the people working at SURFsara 6 , for letting us use Lisa, their excellent computation service.  ... 
arXiv:2111.12139v1 fatcat:z3pdrmv6j5eytkptsin44yr3zm

Best Subset Binary Prediction [article]

Le-Yu Chen, Sokbae Lee
2018 arXiv   pre-print
We illustrate usefulness of the best subset binary prediction approach via Monte Carlo simulations and an empirical application of the work-trip transportation mode choice.  ...  We consider a variable selection problem for the prediction of binary outcomes.  ...  Introduction Prediction of binary outcomes is an important topic in economics and various scientific fields.  ... 
arXiv:1610.02738v7 fatcat:handhpaddfhvjmbhms46wx6mre

Best subset binary prediction

Le-Yu Chen, Sokbae Lee
2018 Journal of Econometrics  
Abstract We consider a variable selection problem for the prediction of binary outcomes.  ...  Introduction Prediction of binary outcomes is an important topic in economics and various scientific fields.  ...  , CARS) seems comparable to that of a more complex model using a richer set of covariates.  ... 
doi:10.1016/j.jeconom.2018.05.001 fatcat:g3lfthcwxjdk3k4xgwwninf66a

Eigenvalues and Low Energy Eigenvectors of Quantum Many-Body Systems [article]

Ramis Movassagh
2012 arXiv   pre-print
I first give an overview of the thesis and Matrix Product States (MPS) representation of quantum spin chains with an improvement on the conventional notation.  ...  I first give the necessary background on frustration free (FF) Hamiltonians, real and imaginary time evolution within MPS representation and a numerical implementation.  ...  MPS allows for a systematic truncation of the Hilbert space to capture the low energy properties with controllable accuracy.  ... 
arXiv:1211.4908v1 fatcat:bg42moy5wnapxgnvmyeh5hw3yu

Quantum Signatures of Solar System Dynamics [article]

Arkady L. Kholodenko
2008 arXiv   pre-print
In short, the rationale for its birth lies in simplicity with which the same type of calculations are done using new methods capable of taking care of resonances.  ...  In this paper new uses of Heisenberg's ideas are found.  ...  According to the imposed rules we are allowed to watch only the motion of crossections. 57 He was awarded the Fields medal for these studies.  ... 
arXiv:0707.3992v4 fatcat:jo4dkx35ibdphegnc3awlqyoau

On Fitting Finite Dirichlet Mixture Using ECM and MML [chapter]

Nizar Bouguila, Djemel Ziou
2005 Lecture Notes in Computer Science  
Numerical results are illustrated for the models under consideration. 2 Pair-copula constructions of multiple dependence.  ...  We study a fluid system with single on/off source in which the active (on) and silent periods (off) follow General and Exponential distributions respectively.  ...  A new approach to Poisson approximation problems is proposed based on properties of Charlier polynomials and Parseval's identity.  ... 
doi:10.1007/11551188_19 fatcat:gtzi5u6emvfyxea3zbklobnvom

Reviews and Descriptions of Tables and Books

1956 Mathematics of Computation  
This machine has the unpleasant characteristic of leaving more space between adjacent columns than rows. The tables were developed for use with the RAYDAC.  ...  The calculating program thus described operates at a fixed binary point and uses 40 binary digits.  ...  Acknowledgment of help in computation is given, but no indication of checks of accuracy or of means used. There are no aids to interpolation.  ... 
doi:10.1090/s0025-5718-56-99306-1 fatcat:hg3tjkqavrbczc3jeyfsjaaalq
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