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Fast n-fold Boolean Convolution via Additive Combinatorics
[article]

2021
*
arXiv
*
pre-print

At the heart of our approach lies a careful usage of Kneser's theorem from

arXiv:2105.03968v1
fatcat:pggfrzoumres7fuvr3cbj7gsr4
*Additive**Combinatorics*, and a new deterministic almost linear output-sensitive algorithm for non-negative sparse*convolution*. ... We consider the problem of computing the*Boolean**convolution*(with wraparound) of*n*vectors of dimension m, or, equivalently, the problem of computing the sumset A_1+A_2+...+A_n for A_1,...,A_n ⊆ℤ_m. ... necessary.*n*-*Fold**Boolean**Convolution*versus*n*-*Fold**Convolution*. ...##
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Fast n-Fold Boolean Convolution via Additive Combinatorics

2021

At the heart of our approach lies a careful usage of Kneser's theorem from

doi:10.4230/lipics.icalp.2021.41
fatcat:vykxgb3tfvff7hgvuwbosu6ory
*Additive**Combinatorics*, and a new deterministic almost linear output-sensitive algorithm for non-negative sparse*convolution*. ... We consider the problem of computing the*Boolean**convolution*(with wraparound) of*n*vectors of dimension m, or, equivalently, the problem of computing the sumset A₁+A₂+...+A_n for A₁,...,A_n ⊆ ℤ_m. ...*n*-*Fold**Boolean**Convolution**via**Additive**Combinatorics*is a divisor of m. ...##
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Symbolic Calculus in Mathematical Statistics: A Review
[article]

2015
*
arXiv
*
pre-print

The symbolic representation of Sheffer polynomial sequences allows us to carry out a unifying theory of classical,

arXiv:1512.08379v1
fatcat:6osh6azvlfc5zgbosdfdx3o6nu
*Boolean*and free cumulants. ... One of the main tools is a formal generalization of the*convolution*of identical probability distributions, which allows us to employ compound Poisson random variables in various topics that are only somewhat ... Cumulants A probability measure P is infinitely divisible if for any positive integer*n*there is a probability measure P*n*such that P = (P*n*)*n** , where (P*n*)*n** denotes the*n*-*fold**convolution*of ...##
###
How Iris Recognition Works

2004
*
IEEE transactions on circuits and systems for video technology (Print)
*

Fig. 11 . 11 The (8 2 8)

doi:10.1109/tcsvt.2003.818350
fatcat:hbjy2hsi65b5rnsxlk2rkmpuce
*convolution*kernel for*fast*focus assessment. Fig. 12 . 12 The 2-D Fourier power spectrum of the*convolution*kernel used for rapid focus assessment. ... This "best of*n*" test skews the distribution to the left and reduces its mean from about 0.5 to 0.458. ...##
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On the Fourier transform of a quantitative trait: Implications for compressive sensing
[article]

2021
*
arXiv
*
pre-print

It uses the theory of real-valued

arXiv:2101.01234v2
fatcat:stwh35cji5ftzkf4oof6jmaf3i
*Boolean*functions in a systematic way to translate trait data into the Fourier domain. ... This theory provides a theoretical underpinning for systematic use of*Boolean*function machinery to dissect the dependency of a trait on the genome and environment. ... linear measurements*via*a sensing/measurement matrix A of size M ×*N*, with M <*N*. ...##
###
Counting Problems in Parameterized Complexity

2019
*
International Symposium on Parameterized and Exact Computation
*

[40] , which asserts that counting satisfying assignments to

doi:10.4230/lipics.ipec.2018.1
dblp:conf/iwpec/Curticapean18
fatcat:tdfs7zngzrgv5fixf2qawrccuy
*Boolean*3-CNF-formulas requires time 2 Ω(*n*) . ... For computing sub(H, G) and thin patterns H, an*additional*improvement to f (k) •*n*0.46k+2pw(H)+O (1) time is possible, where pw(H) denotes the pathwidth of H [9] . ...##
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Convex polytopes: Extremal constructions and 𝑓-vector shapes
[chapter]

2007
*
Geometric Combinatorics
*

of P is

doi:10.1090/pcms/013/10
fatcat:h7csttz7njdf7b5afatcnlzyk4
*boolean*. ... But let's not get too ambitious too*fast*. ...##
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Fast Feasible and Unfeasible Matrix Multiplication
[article]

2018
*
arXiv
*
pre-print

*Fast*matrix-by-matrix multiplication (hereafter MM) is a highly recognized research subject. ... unbounded sizes, cover the progress in decreasing the exponents of MM, comment on its impact on the theory and practice of computing, and recall various fundamental concepts and techniques supporting

*fast*... Let m =

*n*in order to simplify the estimates. Algorithm 1:

*Convolution*

*via*Evaluation, Interpolation, and FFT. INITIALIZATION. ...

##
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Convex Polytopes: Extremal Constructions and f-Vector Shapes
[article]

2005
*
arXiv
*
pre-print

of P is

arXiv:math/0411400v2
fatcat:6wu6oczw7nabpn22lusd2cpo7i
*boolean*. ... (See also Springborn [68] for an*additional*discussion of uniqueness.) 1.3. Steinitz' theorem*via*circle packings Theorem 1.3 (The Koebe-Andreev-Thurston theorem). ...##
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Cumulative index volumes 1–100

1992
*
Theoretical Computer Science
*

-295
Blum,

doi:10.1016/0304-3975(92)90292-n
fatcat:ekwes6owtrco3lkfkiqagnketq
*N*., A*Boolean*function requiring 3n network size (No&) 28 (3) ( 1984) 337-345 Blum,*N*., An*n*( r?) ... Robert, Systolic*convolution*of arithmetic functions 95 (2) ( 1992) 207-229 Quong, R.W.,*Fast*average-case pattern matching by multiplexing sparse tables 92 ( 1) ( 1992) I65- 179 Rabani, Y. ...##
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Euler Calculus with Applications to Signals and Sensing
[article]

2012
*
arXiv
*
pre-print

We work over R

arXiv:1202.0275v1
fatcat:puy3hkehzva3vjnqlrdppi7jtm
*n**via*induction on*n*. ... Equation (17.1) and compared to true values. (5) Various advanced transforms are available, including*addition*of noise, smoothing*via**convolution*with Gaussians , and other integral transforms (using ...##
###
If the Current Clique Algorithms are Optimal, so is Valiant's Parser
[article]

2015
*
arXiv
*
pre-print

Lee showed that any algorithm for a more general parsing problem with running time O(|G|·

arXiv:1504.01431v2
fatcat:6mvl4a2ewjd55gipq7hhvxvslm
*n*^3-ε) can be converted into a surprising subcubic algorithm for*Boolean*Matrix Multiplication. ... complexity of a fundamental problem, our reduction has led us to similar lower bounds for more modern and well-studied cubic time problems for which faster algorithms are highly desirable in practice: RNA*Folding*... recursive algorithm that is able to utilize many*fast**boolean*matrix multiplications to speed up the computation of the dynamic programming table from the CYK algorithm. ...##
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Abstracts of Presentations

2001
*
Brain and Cognition
*

For a

doi:10.1006/brcg.2000.1285
fatcat:k6c2qcfpubdxzjdkbgzktkigz4
*boolean*ring B, a quatient ring B[X 1 , . . . , X*n*]/ X 2 1 −X 1 , . . . , X 2*n*−X*n*is called a*boolean*polynomial ring. ... The arbitrary order of differentiation is found according to the Riemann-Liouville definition, whereas the generalized Cauchy*n*-*fold*integral is adopted for arbitrary order of integration. ... For evaluating such a series to*N*digits of accuracy, the numerator and the denominator computed by binary splitting have size O(*N*log*N*) even though the reduced fraction may only have size O(*N*). ...##
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A Treatise on Quantum Clifford Algebras
[article]

2002
*
arXiv
*
pre-print

We discuss Hopf algebra versus Hopf gebra, the latter emerging naturally from a bi-

arXiv:math/0202059v1
fatcat:jkwwzx2jajfmpertrsv7hwnoty
*convolution*. ... Since we saw that the*convolution*establishes a group like structure*via*the*convolution*and finally the Hopf gebra. ... The whole*combinatorics*of this process is encoded in this singe and harmless looking equation! The crucial point is to investigate what kind of physical reason is behind this*additional*reordering. ...##
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Quiver Mutations, Seiberg Duality and Machine Learning
[article]

2020
*
arXiv
*
pre-print

In

arXiv:2006.10783v1
fatcat:4rgfpwjnzzh3fjo3glxsgscdty
*addition*, we evaluate the relative advantages of Naive Bayes classifiers versus*Convolutional*Neural Networks. ... Finally, we also investigate how the results are affected by the inclusion of*additional*data, such as ranks of gauge/flavor groups and certain variables motivated by the existence of underlying Diophantine ... Figure 2 .1 also illustrates the*addition*of a meson. 3. Ranks. The rank of the dualized node transforms as*N*j =*N*f j −*N*j , (2.1) where*N*f j is the number of flavors at the dualized node j. ...
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