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Convex subsets of 2n and bounded truth-table reducibility

1978
*
Discrete Mathematics
*

The second half

doi:10.1016/0012-365x(78)90145-0
fatcat:y35hsncpvfamfewprrohsc4kya
*of*the paper con".ins applications to recursion theory; in particular, canonical forms fcr certain minimum-norm*bounded*-*truth*-*table*reductions are obtained. ... Let 2* her the set*of*n-tuples*of*O's*and*l's, partially ordered componentwise. ... This is the case In the*bounded*-*truth*-*table**reducibility**of*recursion theory; in the second half*of*the paper th\: decomposition theorem will be applied to obtain a canonical form for '%hortecUt"*bounded*-*truth*-*table*...##
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A special case of mahler's conjecture

1998
*
Discrete & Computational Geometry
*

This is the case

doi:10.1007/pl00000076
fatcat:g7mtekcplbhudelis6zpsuebpe
*of*polytopes with at most*2n*+ 2 vertices (or facets). Mahler's conjecture is proved in this case for n < 8*and*the minimal bodies are characterized. * M. A. ... A special case*of*Mahler's conjecture on the volume-product*of*symmetric*convex*bodies in n-dimensional Euclidean space is treated here. ... Introduction*and*Statement*of*the Results A well-known problem in the theory*of**convex*sets is the one*of*finding an exact lower*bound*for the product*of*n-dimensional volumes volprod(K) = voln (K) VOln ...##
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Improved Multi-Class Cost-Sensitive Boosting via Estimation of the Minimum-Risk Class
[article]

2016
*
arXiv
*
pre-print

We evaluate our method on a variety

arXiv:1607.03547v2
fatcat:y5ebtcywyrgtdly3y2mxbydkny
*of*datasets: a collection*of*synthetic planar data, common UCI datasets, MNIST digits, SUN scenes,*and*CUB-200 birds. ... Our method jointly optimizes binary weak learners*and*their corresponding output vectors, requiring classes to share features at each iteration. ... (GT means ground*truth*, PRED is prediction)*Table*1 : 1 REBEL misclassification errors on SUN-6*and*CUB datasets using different tree depths. ...##
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Dimension, Halfspaces, and the Density of Hard Sets

2010
*
Theory of Computing Systems
*

The class

doi:10.1007/s00224-010-9288-1
fatcat:lxzs47achrbtxfkblayfh2olum
*of*problems which*reduce*to nondense sets via an iterated reduction that composes a*bounded*-query*truth*-*table*reduction with a conjunctive reduction. ... We use the connection between resource-*bounded*dimension*and*the online mistake-*bound*model*of*learning to show that the following classes have polynomial-time dimension zero. 1. ... For k queries, there are 2 2 k*truth*-*table*conditions. ...##
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Stochastic Primal-Dual Deep Unrolling
[article]

2022
*
arXiv
*
pre-print

The proposed learned stochastic primal-dual (LSPD) network only uses

arXiv:2110.10093v4
fatcat:burgt5aqozdjzi2lgccjx2vqwy
*subsets**of*the forward*and*adjoint operators*and*offers considerable computational efficiency. ... We develop a stochastic (ordered-*subsets*) variant*of*the classical learned primal-dual (LPD), which is a state-*of*-the-art unrolling network for tomographic image reconstruction. ... We partition the forward*and*adjoint operators into m*subsets*,*and*also the corresponding measurement data. In each layer, we use only one*of*the*subsets*, in a cycling order. ...##
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Formularless Logic Function

2013
*
Open Journal of Discrete Mathematics
*

To do that the

doi:10.4236/ojdm.2013.31005
fatcat:u2yqz5r735fi7bsqisah5et77m
*reduced*(compact) description*of*values is determined in the*truth**table*or in the statement*of*the problem. ... The concept*of*computability is defined more exactly*and*illustrated as an example*of*Boolean functions*and*cryptanalysis. To define a Boolean function is not necessary to record its formula. ... It is possible to bypass the step*of*creating a*truth**table**and*go to the task*of*the logical functions*of*the meaningful statement*of*problem. ...##
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Locally consistent constraint satisfaction problems

2005
*
Theoretical Computer Science
*

Our results yield a robust deterministic algorithm (for a fixed set ) running in time linear in the size

doi:10.1016/j.tcs.2005.09.012
fatcat:an54fhcj5jatnpmotaq2j2lrtm
*of*the input*and*1/ which finds either an inconsistent set*of*constraints (*of*size*bounded*by the ... function*of*) or a*truth*assignment which satisfies the fraction*of*at least ∞ ( ) −*of*the given constraints. ... Thilikos for suggesting the version*of*the problem considered in this paper. The detailed comments*of*the anonymous referee that helped to improve the paper are greatly appreciated. ...##
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Locally Consistent Constraint Satisfaction Problems
[chapter]

2004
*
Lecture Notes in Computer Science
*

Our results yield a robust deterministic algorithm (for a fixed set ) running in time linear in the size

doi:10.1007/978-3-540-27836-8_41
fatcat:posjfcldrvcqleb2dvlftpmvwi
*of*the input*and*1/ which finds either an inconsistent set*of*constraints (*of*size*bounded*by the ... function*of*) or a*truth*assignment which satisfies the fraction*of*at least ∞ ( ) −*of*the given constraints. ... Thilikos for suggesting the version*of*the problem considered in this paper. The detailed comments*of*the anonymous referee that helped to improve the paper are greatly appreciated. ...##
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A convex optimization approach to robust fundamental matrix estimation

2015
*
2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
*

The main result

doi:10.1109/cvpr.2015.7298829
dblp:conf/cvpr/ChengLCS15
fatcat:iiu3r3pt2zfjvamvn64widorrq
*of*the paper shows that this non-*convex*problem can be solved by solving a sequence*of**convex*semi-definite programs, obtained by exploiting a combination*of*polynomial optimization tools ... A general nonconvex framework is proposed that explicitly takes into account the rank-2 constraint on the fundamental matrix*and*the presence*of*noise*and*outliers. ...*Table*1 . 1 Mean*and*Standard Deviation*of*Precision (%)*Table*2. ...##
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Optimal Shape Control via L_∞ Loss for Composite Fuselage Assembly
[article]

2019
*
arXiv
*
pre-print

From statistical point

arXiv:1911.03592v1
fatcat:r3qlgyjrejec5fwtiedf77krxe
*of*view, this can be formulated as the ℓ_∞ loss based linear regression,*and*under some standard assumptions, such as the restricted eigenvalue (RE) conditions,*and*the light tailed ... noise, the non-asymptotic estimation error*of*the ℓ_1 regularized ℓ_∞ linear model is derived to be the order*of*O(σ√(Slog p/n)), which meets the upper-*bound*in the existing literature. ... The p−value is also listed in*Table*2 . As shown in*Table*2 , compared with [10] , the proposed method significantly*reduces*the maximum gap (MG)*and*RMS gap (RMSG) for two fuselage assembly. ...##
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A bounded uncertainty approach to cooperative localization using relative bearing constraints

2007
*
2007 IEEE/RSJ International Conference on Intelligent Robots and Systems
*

The scheme produces

doi:10.1109/iros.2007.4399398
dblp:conf/iros/TaylorS07
fatcat:ldvxnfe4mrd5xbrnpy4vip6ujm
*bounded*uncertainty estimates for the relative configuration*of*the team by using*convex*optimization techniques to approximate the projection*of*this feasible set onto various subspaces ... In this framework, range*and*bearing measurements obtained by the robots are viewed as constraints which implicitly define a set*of*feasible solutions in the joint configuration space*of*the robot team ... The authors gratefully acknowledge the support*of*an ARO MURI DAAD-19-02-1-0383 "Adaptive Coordinated Control*of*Intelligent Multi-Agent Teams (ACCLIMATE)". ...##
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On phase retrieval via matrix completion and the estimation of low rank PSD matrices

2019
*
Inverse Problems
*

Given underdetermined measurements

doi:10.1088/1361-6420/ab4e6d
fatcat:xhkyg5aypzddhc6jqyttgkseoq
*of*a positive semi-definite (PSD) matrix X*of*known low rank K, we present a new algorithm to estimate X based on recent advances in non-*convex*optimization schemes. ... Moreover, we provide a theory for how oversampling affects the stability*of*the lifted inverse problem. ... Figure 6 . 6 Normalized reconstruction error (distance to ground*truth*) as function*of*normalized noise, 3 masks. Figure 7 . 7 Residual*Table*1 . 1 Reweighted nuclear norm eigenvalues*table*. ...##
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On phase retrieval via matrix completion and the estimation of low rank PSD matrices
[article]

2019
*
arXiv
*
pre-print

Given underdetermined measurements

arXiv:1907.09537v2
fatcat:s3zlguchfbfm7c6xsga5ziv4j4
*of*a Positive Semi-Definite (PSD) matrix X*of*known low rank K, we present a new algorithm to estimate X based on recent advances in non-*convex*optimization schemes. ... Moreover, we provide theory for how oversampling affects the stability*of*the lifted inverse problem. ... Notation M N will denote the set*of*N ×N complex matrices*and*H N the*subset**of*Hermitian (i.e. self-adjoint) matrices. ...##
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On a multiplier conjecture for univalent functions

1990
*
Transactions of the American Mathematical Society
*

, the class

doi:10.1090/s0002-9947-1990-0991960-7
fatcat:kagldlnwy5ayjdd3ks43ib6se4
*of*close-to-*convex*functions,*and*show its*truth*for a number*of*special members*of*:;g. ... Let SC be the set*of*normalized univalent functions,*and*let :;g be the*subset**of*SC containing functions with the property: We present*and*discuss the following conjecture: For f E :;g , g, h E co(SC) ... , y* denote the*subsets**of*~ whose members are univalent, close-to-*convex*,*and*starlike in j[)), respectively. ...##
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On a Multiplier Conjecture for Univalent Functions

1990
*
Transactions of the American Mathematical Society
*

, the class

doi:10.2307/2001537
fatcat:4qzucg2nwna6bgusre4msc2x64
*of*close-to-*convex*functions,*and*show its*truth*for a number*of*special members*of*:;g. ... Let SC be the set*of*normalized univalent functions,*and*let :;g be the*subset**of*SC containing functions with the property: We present*and*discuss the following conjecture: For f E :;g , g, h E co(SC) ... , y* denote the*subsets**of*~ whose members are univalent, close-to-*convex*,*and*starlike in j[)), respectively. ...
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