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On linear sets of minimum size
[article]

2020
*
arXiv
*
pre-print

An 𝔽_q-

arXiv:2005.10931v2
fatcat:7nnzdwxtrnfaxl3awncvctocde
*linear**set**of*rank k*on*a projective line PG(1,q^h), containing at least*one*point*of*weight*one*, has*size*at least q^k-1+1 (see [J. De Beule and G. ... Van De Voorde, The*minimum**size**of*a*linear**set*, J. Comb. Theory, Ser: A 164 (2019), 109-124.]). The classical example*of*such a*set*is given by a club. ... In particular, we thank*one**of*the referees for pointing out the link with references [3] and [6] . ...##
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Systematic Misestimation of Machine Learning Performance in Neuroimaging Studies of Depression
[article]

2021
*
arXiv
*
pre-print

Specifically, for small sample

arXiv:1912.06686v2
fatcat:pabizhpcnzeh5b67hhm5aw6asa
*sizes*(N = 20), we observe accuracies*of*up to 95 %. For medium sample*sizes*(N = 100) accuracies up to 75 % were found. ... Here, we systematically investigated this effect focusing*on**one**of*the most heavily studied questions in the field, namely the classification*of*patients suffering from major depressive disorder (MDD) ... This work is part*of*the German multicenter consortium "Neurobiology*of*Affective Disorders. ...##
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Alphabet-Dependent Bounds for Linear Locally Repairable Codes Based on Residual Codes

2019
*
IEEE Transactions on Information Theory
*

Furthermore, an upper bound

doi:10.1109/tit.2019.2911595
fatcat:6vjacd6srbhjzmouv47tkcsbkm
*on*the asymptotic rate-distance tradeoff*of*LRCs is derived, and yields the tightest known upper bound for large relative*minimum*distances. ... In this paper, a novel definition*of*locality is proposed to keep track*of*the precise number*of*nodes required for a local repair when the repair*sets*do not yield MDS codes. ... The first author would like to thank the Department*of*Electrical and Computer Engineering at the Technical University*of*Munich for hosting him while part*of*this work was carried out. ...##
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Comparative Linear Classification Splicing

2017
*
JOURNAL OF ADVANCES IN MATHEMATICS
*

The comparative classification performance

doi:10.24297/jam.v13i4.6258
fatcat:jcspdujitzfhnn3fw33d7cap4i
*of*the Fisher*linear*classification analysis and its spliced versions when the data*set*are contaminated are investigated. ... The simulation results revealed that the robust Fisher's approach based*on*the*minimum*covariance determinant estimates outperformed the other procedures; a good competitor to this technique is the winsorized ... The half*set*i h strictly depends*on*the arithmetic*of*the sample*size*and sample dimension. These robust estimates are computed based*on*the clean data*set*selected by the half*set*. ...##
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On a Minimum Linear Classification Problem

2006
*
Journal of Global Optimization
*

We study the following

doi:10.1007/s10898-005-8465-2
fatcat:jloiaaue7bd5dp3fb4t3qlxnn4
*linear*classification problem in signal processing: Given a*set*B*of*n black point and a*set*W*of*m white points in the plane (m = O(n)), compute a*minimum*number*of*lines L such ... We call this the*Minimum**Linear*Classification (MLC) problem. ... Consequently, MLF has a solution*of**size*K if and only if the*minimum**linear*classification problem has a solution*of**size*2K. This reduction clearly takes polynomial time. ...##
###
Alphabet-Dependent Bounds for Linear Locally Repairable Codes Based on Residual Codes
[article]

2018
*
arXiv
*
pre-print

In this paper, a novel definition

arXiv:1810.08510v1
fatcat:mpuhksuu7ng55o72fcb7hgdx2i
*of*locality is proposed to address the imprecision*on*the number*of*nodes contacted during the repair process. ... Several works have thus been done to understand optimal rate-distance tradeoff and only recently the*size**of*the alphabet has been taken into account. ... where we replace the condition*on*the*size*by a condition*on*the dimension. 1) i ∈ R i , 2) H(R i ) = log q (|{c Ri : c ∈ C}|) ≤ κ, 3) The*minimum*distance*of*the restriction*of*C to the*set*R i is at ...##
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Linear-time Kernelization for Feedback Vertex Set
[article]

2017
*
arXiv
*
pre-print

This is the first

arXiv:1608.01463v3
fatcat:qg7pomkxnzbyve4tsexgyq53uy
*linear*-time polynomial-*size*kernel for Feedback Vertex*Set*. ... k^2), (2) k'≤ k, and (3) G has a feedback vertex*set**of**size*at most k if and only if G' has a feedback vertex*set**of**size*at most k'. ... A vertex*set*S ⊆ V is called a feedback vertex*set*if G − S is a forest. We denote the*size**of*the*minimum*feedback vertex*set**of*G by fvs(G). ...##
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On the Stopping Distance and Stopping Redundancy of Product Codes

2008
*
IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences
*

In this paper, the number

doi:10.1093/ietfec/e91-a.8.2167
fatcat:7kycehgtu5btxktmlfq76ufhpi
*of**minimum*stopping*sets**of*a product code is determined by the number*of*the*minimum*stopping*sets**of*the corresponding component codes. ... Let us define the concept*of*a stopping*set*in the next section. The*size**of*the smallest non-empty stopping*set*in a parity-check MSC(2010): Primary: 94B25; Secondary: 94B35. ... A stopping*set**of*the smallest*size*is called a*minimum*stopping*set*. ...##
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Classification of the extremal formally self-dual even codes of length 30

2010
*
Advances in Mathematics of Communications
*

Let C be a binary [n, k, d] code and let c be a codeword

doi:10.3934/amc.2010.4.433
fatcat:vuu7kw3hozfjzaydxhf2enipm4
*of*weight d. Then As the residual code can be considered as a punctured code*on*a*set**of*coordinates, its dual distance is at least d ⊥ . ... Theorem 2. [8] Let C be a binary [n, k, d] code and let c be a codeword*of*weight Actually, we consider a residual code with respect to a codeword*of**minimum*weight. ... The resulting code is still*linear*, its length is n − 1, if d > 1 its dimension is k, and its*minimum*weight is d or d − 1. In general a code C can be punctured*on*a coordinate*set*T*of**size*t. ...##
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Partial permutation decoding for binary linear Hadamard codes

2014
*
Electronic Notes in Discrete Mathematics
*

A method to obtain s-PD-

doi:10.1016/j.endm.2014.08.006
fatcat:cjdbeojlmzglffg2jr2hk3fykq
*sets**of**size*s + 1 for partial permutation decoding for the binary*linear*Hadamard codes H m*of*length 2 m , for all m ≥ 4 and 1 < s ≤ (2 m − m − 1)/(1 + m) , is described. ... Moreover, a recursive construction to obtain s-PD-*sets**of**size*s + 1 for H m+1*of*length 2 m+1 , from a given s-PD-*set**of*the same*size*for the Hadamard code*of*half length H m is also established. ... Bound*on*the*minimum**size**of*s-PD-*sets*for H m There is a well-known bound*on*the*minimum**size**of*PD-*sets*for*linear*codes based*on*the length, the dimension and the*minimum*distance*of*such codes. ...##
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Optimum Group Size Selection for Launch Vehicle Sections Linear Assembly by Selective Assembly Method

2015
*
International Journal of Engineering Research and
*

Moreover there is a chance

doi:10.17577/ijertv4is060752
fatcat:hghq2thnpve2ni6abfnmpootcq
*of*few sections*of*particular group may become surplus due to non-utilisation. ... This method is very much effective where the process variability*of*assembly is too large in spite*of*precisely machined components. ... ACKNOWLEDGMENT Authors thank the authorities*of*ASL, DRDO, Hyderabad for granting permission to carryout the research work in and publish in journals ...##
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Minimum Fill-In and Treewidth for Graphs Modularly Decomposable into Chordal Graphs
[chapter]

1998
*
Lecture Notes in Computer Science
*

We show that a

doi:10.1007/10692760_28
fatcat:uozdparxgvbmpo2vizsvnebqd4
*minimum*ll-in ordering*of*a graph can be determined in*linear*time if it can be modularly decomposed into chordal graphs. This generalizes results*of*2]. ... We show that the treewidth*of*these graphs can be determined in O((n + m) log n) time. ... Theorem 1 The*size**of*a*minimum*ll-in*of*a modulated chordal graph can be determined in*linear*time. Proof:*One*determines the*sizes**of*the*minimum*ll-ins*of*all overlap-free modules X recursively. ...##
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Two-point method uncertainty during control and measurement of cylindrical element diameters

2018
*
Journal of Physics, Conference Series
*

*of*measurements

*of*average, maximum and

*minimum*

*linear*

*sizes*

*of*elements by the twopoint method. ... material

*minimum*

*size*

*of*the shaft D LМ only for

*one*

*of*the details translational motion. ...

##
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Learning semilinear sets from examples and via queries

1992
*
Theoretical Computer Science
*

., Learning semilinear

doi:10.1016/0304-3975(92)90123-w
fatcat:banw5gxzgjgetpjx7quidelin4
*sets*from examples and via queries, Theoretical Computer Science 104 (1992) 207-233. ... Find*minimum*-*size*representations (FMR) Instance: A finite subset E*of*Nk. Question: Find the*minimum*-*size*representation*of*a*linear**set*which contains all elements*of*E. ...*linear**set*Lu and any conjectured semilinear*set*S'. queries whether or not Lu r S' can be made, the family*of**linear**sets*is learnable in polynomial time*of*the*minimum**size**of*representations and the ...##
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Page 418 of Biological Reviews Vol. 84, Issue 3
[page]

2009
*
Biological Reviews
*

These isoclines may be

*linear*or non-*linear*, depending*on*the form*of*the equations that underlie them. ... In Fig. 2, we consider the maximum group*size**set*by an animal’s ability to meet its time allocations (derived directly from the output*of*the time budgets model), and the*minimum*viable group*size*(representing ...
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