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Even Kernels

Aviezri Fraenkel
1994 Electronic Journal of Combinatorics  
Given a graph $G = (V,E)$, an even kernel is a nonempty independent subset $V' \subseteq V$, such that every vertex of $G$ is adjacent to an even number (possibly 0) of vertices in $V'$.  ...  It is proved that the question of whether a graph has an even kernel is NP-complete. The motivation stems from combinatorial game theory.  ...  Thus an even kernel may exist nonuniquely.  ... 
doi:10.37236/1185 fatcat:qve7xjfnmbg2zbeaipsdlspd4a

Even-order pseudoprocesses on a circle and related Poisson kernels [article]

Enzo Orsingher, Bruno Toaldo
2013 arXiv   pre-print
By composing the circular pseudoprocesses with positively-skewed stable processes we arrive at genuine circular processes whose distribution, in the form of Poisson kernels, is obtained.  ...  We here examine even-order pseudoprocesses wrapped up on circles and derive their explicit signed density measures.  ...  to the Poisson kernel.  ... 
arXiv:1212.5786v3 fatcat:xdyoaynvdzdg5dg3s37ko7xp7m

Convolution with even-sized kernels and symmetric padding [article]

Shuang Wu, Guanrui Wang, Pei Tang, Feng Chen, Luping Shi
2019 arXiv   pre-print
Besides, 3x3 kernels dominate the spatial representation in these models, whereas even-sized kernels (2x2, 4x4) are rarely adopted.  ...  Symmetric padding releases the generalization capabilities of even-sized kernels at little computational cost, making them outperform 3x3 kernels in image classification and generation tasks.  ...  Related work Even-sized kernel Since even-sized kernels are integer multiples of 2, they are mostly applied together with stride 2 to rescale images, which can avoid the checkerboard artifact (Odena et  ... 
arXiv:1903.08385v2 fatcat:rerc5vn7enhr5jeqe2dtmuhlqe

Exclusive evolution kernels in two-loop order: parity even sector

A.V. Belitsky, D. Müller
1999 Physics Letters B  
We complete the construction of the non-forward evolution kernels in next-to-leading order responsible for the scale dependence of e.g. parity even singlet distribution amplitudes.  ...  In the present note we address the flavour singlet parity even case which is responsible for the evolution of the vector distribution amplitude. Anatomy of NLO evolution kernels.  ...  It is worth mentioning that our result for the evolution kernels in the parity even singlet sector possesses the correct conformal moments in both the physical and unphysical sectors.  ... 
doi:10.1016/s0370-2693(99)01003-5 fatcat:b7ovgdyalbfujpxq423qcedjvm

Heat kernels and the index theorems on even and odd dimensional manifolds [article]

Weiping Zhang
2003 arXiv   pre-print
In this talk, we review the heat kernel approach to the Atiyah-Singer index theorem for Dirac operators on closed manifolds, as well as the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds  ...  Heat kernels and the index theorems on even dimensional manifolds We start with a smooth closed oriented 2n-dimensional manifold M and two smooth complex vector bundles E, F over M , on which there is  ...  The index theorem for Dirac operators on even dimensional manifolds with boundary Let M be a smooth compact oriented even dimensional spin manifold with (nonempty) smooth boundary ∂M .  ... 
arXiv:math/0304269v1 fatcat:ryqp5n734bhozmf7hdm6v7myri

Linear bounds for Calderón-Zygmund operators with even kernel on UMD spaces [article]

Sandra Pott, Andrei Stoica
2013 arXiv   pre-print
We prove that this is indeed the case for sufficiently smooth Calderón-Zygmund operators with cancellation, associated to an even kernel.  ...  Let K be an even standard kernel with smoothness δ > 1/2 and T be a Calderón-Zygmund operator on R associated to K.  ...  Since T is associated to a real-valued even kernel K, T * , and hence also Re T = 1 2 (T + T * ), are associated to K.  ... 
arXiv:1310.7864v1 fatcat:dkhqym65hfeull5f2oiy7o5uw4

The Clifford–Fourier integral kernel in even dimensional Euclidean space

Fred Brackx, Nele De Schepper, Frank Sommen
2010 Journal of Mathematical Analysis and Applications  
In the even dimensional case, this allows us to express the Clifford-Fourier transform in terms of the Fourier-Bessel transform, leading to a closed form of the Clifford-Fourier integral kernel.  ...  , we find F H − = c m Q(−Γ ξ ) I + S 2 + Q(−Γ ξ + I) I − S 2 F bes . (9) Closed form for the Clifford-Fourier integral kernel in the even dimensional case By means of Eqs  ...  Theorem 1 ..I + S 2 JI − S 2 J 122 The integral kernel of the Clifford-Fourier transform F H ± in case of even dimension is given byc m Q(−Γ ξ ) I + S 2 J (x ∧ ξ ) ∓ Q(−Γ ξ + I) I − S 2 J (x ∧ ξ ) (10)  ... 
doi:10.1016/j.jmaa.2009.12.008 fatcat:kv66cxd2cfcgjhticbt4xl7qpa

On a property of singular integrals with even positive kernels

St. Ruscheweyh, K.-J. Wirths
1981 Journal of Approximation Theory  
ProoJ: We show that every zero of f is of even multiplicity which implies the assertion.  ...  our conjecture for the kernel x@. .)  ... 
doi:10.1016/0021-9045(81)90064-2 fatcat:l7xcz3fffzhqhopz73wiigoyra

Estimates for the maximal singular integral in terms of the singular integral:the case of even kernels [article]

Joan Mateu, Joan Orobitg, Joan Verdera
2010 arXiv   pre-print
Our main result states that, for even operators, both are equivalent to a purely algebraic condition formulated in terms of the expansion of the kernel in spherical harmonics.  ...  We show now a method to construct even kernels in R 3 that satisfy condition (iii) in the Theorem. It can be easily adapted to any dimension.  ...  Recall that the kernel of our singular integral is K(x) = Ω(x) |x| n = P (x) |x| n+d , where P is an even homogeneous harmonic polynomial of degree d ≥ 2.  ... 
arXiv:0707.4610v2 fatcat:vaiccd6edfgztmtbe2mpempb5m

Nuclear masses in extended kernel ridge regression with odd-even effects [article]

X. H. Wu and L. H. Guo and P. W. Zhao
2021 arXiv   pre-print
The kernel ridge regression (KRR) approach is extended to include the odd-even effects in nuclear mass predictions by remodulating the kernel function without introducing new weight parameters and inputs  ...  extended KRR approach can avoid the risk of worsening the mass predictions for nuclei at large extrapolation distances, and meanwhile, it provides a smooth extrapolation behavior with respect to the odd and even  ...  Summary In summary, the kernel ridge regression approach has been extended to include the odd-even effects in nuclear mass predictions by remodulating the kernel function.  ... 
arXiv:2105.10634v1 fatcat:txo5qiqs3ncybecynsmzitq4b4

Nuclear masses in extended kernel ridge regression with odd-even effects

X.H. Wu, L.H. Guo, P.W. Zhao
2021 Physics Letters B  
The kernel ridge regression (KRR) approach is extended to include the odd-even effects in nuclear mass predictions by remodulating the kernel function without introducing new weight parameters and inputs  ...  extended KRR approach can avoid the risk of worsening the mass predictions for nuclei at large extrapolation distances, and meanwhile, it provides a smooth extrapolation behavior with respect to the odd and even  ...  Summary In summary, the kernel ridge regression approach has been extended to include the odd-even effects in nuclear mass predictions by remodulating the kernel function.  ... 
doi:10.1016/j.physletb.2021.136387 fatcat:f75v6be5afbvtcnskuurdnetpu

Identification of Volterra Kernels of Nonlinear Systems by Separating Odd- and Even-Order Kernels
非線形システムの偶数次及び奇数次Volterra核の分離同定

Min LIU, Eiji NISHIYAMA, Hiroshi KASHIWAGI
1998 Transactions of the Society of Instrument and Control Engineers  
In order to obtain the Volterra kernels, in this paper ,the authors propose a new method for identifying of odd-and even-order Volterra kernels by use of M-sequences and correlation function.  ...  Many classes of non-linear systems can be represented by Volterra kernels.  ... 
doi:10.9746/sicetr1965.34.1266 fatcat:n4s7qv3kk5bhpde2wbqr5yqfre

Estimates for the maximal singular integral in terms of the singular integral: the case of even kernels

Joan Mateu, Joan Orobitg, Joan Verdera
2011 Annals of Mathematics  
Our main result characterizes the L 2 and pointwise inequalities in terms of an algebraic condition expressed in terms of the kernel Ω(x) |x| n of T , where Ω is an even homogeneous function of degree  ...  As in the previous section, we want to obtain an expression for the kernel K(x) off the unit ball B.  ...  Now, we show a method to construct even kernels in R 3 that satisfy condition (iii) in the theorem. It can be easily adapted to any dimension.  ... 
doi:10.4007/annals.2011.174.3.2 fatcat:xsettlo3erfpzp3qu3wpbokwym

Identifying Odd/Even-Order Binary Kernel Slices for a Nonlinear System Using Inverse Repeat m-Sequences

Jin-yan Hu, Gang Yan, Tao Wang
2015 Computational and Mathematical Methods in Medicine  
We then derive the properties of the inverse repeat (IR) m-sequence and propose a method of using IR m-sequence as an input to separately estimate odd- and even-order kernel slices to reduce the chance  ...  of kernel-slice overlapping.  ...  1 − ⋅ ⋅ ⋅ − −1 ] . (25) Therefore, (24) becomes [ ], or the even-order Volterra kernels are also excluded from the odd-order binary kernel slices.  ... 
doi:10.1155/2015/454638 pmid:25873988 pmcid:PMC4385604 fatcat:4u2izpm5a5am7pcukbveeqfscy

Sleep's Kernel: Surprisingly small sections of brain, and even neuronal and glial networks in a dish, display many electrical indicators of sleep

James M Krueger, Sandip Roy
2016 The Scientist  
But if the column was in the sleep-like state (high-magnitude ERP), the animals would fail to lick the sucrose when stimulated and would sometimes lick it even when their whisker was not flicked. 4 Even  ...  Researchers have even documented sleep-like behavior in cultures of glial and neural cells.  ... 
pmid:27695161 pmcid:PMC5044876 fatcat:ktk5rorm2ba4ncjpu4a6seexjy
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