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On linear sets of minimum size [article]

Dibyayoti Jena, Geertrui Van de Voorde
2020 arXiv   pre-print
An 𝔽_q-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] .  ... 
arXiv:2005.10931v2 fatcat:7nnzdwxtrnfaxl3awncvctocde

Systematic Misestimation of Machine Learning Performance in Neuroimaging Studies of Depression [article]

Claas Flint, Micah Cearns, Nils Opel, Ronny Redlich, David M. A. Mehler, Daniel Emden, Nils R. Winter, Ramona Leenings, Simon B. Eickhoff, Tilo Kircher, Axel Krug, Igor Nenadic (+6 others)
2021 arXiv   pre-print
Specifically, for small sample 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.  ... 
arXiv:1912.06686v2 fatcat:pabizhpcnzeh5b67hhm5aw6asa

Alphabet-Dependent Bounds for Linear Locally Repairable Codes Based on Residual Codes

Matthias Grezet, Ragnar Freij-Hollanti, Thomas Westerback, Camilla Hollanti
2019 IEEE Transactions on Information Theory  
Furthermore, an upper bound 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.  ... 
doi:10.1109/tit.2019.2911595 fatcat:6vjacd6srbhjzmouv47tkcsbkm

Comparative Linear Classification Splicing

Fred Zin
2017 JOURNAL OF ADVANCES IN MATHEMATICS  
The comparative classification performance 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.  ... 
doi:10.24297/jam.v13i4.6258 fatcat:jcspdujitzfhnn3fw33d7cap4i

On a Minimum Linear Classification Problem

Bing Lu, Hongwei Du, Xiaohua Jia, Yinfeng Xu, Binhai Zhu
2006 Journal of Global Optimization  
We study the following 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.  ... 
doi:10.1007/s10898-005-8465-2 fatcat:jloiaaue7bd5dp3fb4t3qlxnn4

Alphabet-Dependent Bounds for Linear Locally Repairable Codes Based on Residual Codes [article]

Matthias Grezet, Ragnar Freij-Hollanti, Thomas Westerbäck, and Camilla Hollanti
2018 arXiv   pre-print
In this paper, a novel definition 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  ... 
arXiv:1810.08510v1 fatcat:mpuhksuu7ng55o72fcb7hgdx2i

Linear-time Kernelization for Feedback Vertex Set [article]

Yoichi Iwata
2017 arXiv   pre-print
This is the first 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).  ... 
arXiv:1608.01463v3 fatcat:qg7pomkxnzbyve4tsexgyq53uy

On the Stopping Distance and Stopping Redundancy of Product Codes

M. HIVADI, M. ESMAEILI
2008 IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences  
In this paper, the number 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.  ... 
doi:10.1093/ietfec/e91-a.8.2167 fatcat:7kycehgtu5btxktmlfq76ufhpi

Classification of the extremal formally self-dual even codes of length 30

Stefka Bouyuklieva, Iliya Bouyukliev
2010 Advances in Mathematics of Communications  
Let C be a binary [n, k, d] code and let c be a codeword 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.  ... 
doi:10.3934/amc.2010.4.433 fatcat:vuu7kw3hozfjzaydxhf2enipm4

Partial permutation decoding for binary linear Hadamard codes

R.D. Barrolleta, M. Villanueva
2014 Electronic Notes in Discrete Mathematics  
A method to obtain s-PD-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.  ... 
doi:10.1016/j.endm.2014.08.006 fatcat:cjdbeojlmzglffg2jr2hk3fykq

Optimum Group Size Selection for Launch Vehicle Sections Linear Assembly by Selective Assembly Method

N Manickam, Tarak Nath De
2015 International Journal of Engineering Research and  
Moreover there is a chance 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  ... 
doi:10.17577/ijertv4is060752 fatcat:hghq2thnpve2ni6abfnmpootcq

Minimum Fill-In and Treewidth for Graphs Modularly Decomposable into Chordal Graphs [chapter]

Elias Dahlhaus
1998 Lecture Notes in Computer Science  
We show that a 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.  ... 
doi:10.1007/10692760_28 fatcat:uozdparxgvbmpo2vizsvnebqd4

Two-point method uncertainty during control and measurement of cylindrical element diameters

V I Glukhov, V V Shalay, H. Radev
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.  ... 
doi:10.1088/1742-6596/998/1/012011 fatcat:dnvnjnjvgbfjtb22ybdtjpolqq

Learning semilinear sets from examples and via queries

Yuji Takada
1992 Theoretical Computer Science  
., Learning semilinear 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  ... 
doi:10.1016/0304-3975(92)90123-w fatcat:banw5gxzgjgetpjx7quidelin4

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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