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Convex subsets of 2n and bounded truth-table reducibility

Louise Hay
1978 Discrete Mathematics  
The second half 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  ... 
doi:10.1016/0012-365x(78)90145-0 fatcat:y35hsncpvfamfewprrohsc4kya

A special case of mahler's conjecture

M. A. Lopez, S. Reisner
1998 Discrete & Computational Geometry  
This is the case 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  ... 
doi:10.1007/pl00000076 fatcat:g7mtekcplbhudelis6zpsuebpe

Improved Multi-Class Cost-Sensitive Boosting via Estimation of the Minimum-Risk Class [article]

Ron Appel, Xavier Burgos-Artizzu, Pietro Perona
2016 arXiv   pre-print
We evaluate our method on a variety 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.  ... 
arXiv:1607.03547v2 fatcat:y5ebtcywyrgtdly3y2mxbydkny

Dimension, Halfspaces, and the Density of Hard Sets

Ryan C. Harkins, John M. Hitchcock
2010 Theory of Computing Systems  
The class 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.  ... 
doi:10.1007/s00224-010-9288-1 fatcat:lxzs47achrbtxfkblayfh2olum

Stochastic Primal-Dual Deep Unrolling [article]

Junqi Tang, Subhadip Mukherjee, Carola-Bibiane Schönlieb
2022 arXiv   pre-print
The proposed learned stochastic primal-dual (LSPD) network only uses 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.  ... 
arXiv:2110.10093v4 fatcat:burgt5aqozdjzi2lgccjx2vqwy

Formularless Logic Function

Alexey Nikolayevitch Teterin
2013 Open Journal of Discrete Mathematics  
To do that the 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.  ... 
doi:10.4236/ojdm.2013.31005 fatcat:u2yqz5r735fi7bsqisah5et77m

Locally consistent constraint satisfaction problems

Zdeněk Dvořák, Daniel Král', Ondřej Pangrác
2005 Theoretical Computer Science  
Our results yield a robust deterministic algorithm (for a fixed set ) running in time linear in the size 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.  ... 
doi:10.1016/j.tcs.2005.09.012 fatcat:an54fhcj5jatnpmotaq2j2lrtm

Locally Consistent Constraint Satisfaction Problems [chapter]

Zdeněk Dvořák, Daniel Král', Ondřej Pangrác
2004 Lecture Notes in Computer Science  
Our results yield a robust deterministic algorithm (for a fixed set ) running in time linear in the size 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.  ... 
doi:10.1007/978-3-540-27836-8_41 fatcat:posjfcldrvcqleb2dvlftpmvwi

A convex optimization approach to robust fundamental matrix estimation

Y. Cheng, J. A. Lopez, O. Camps, M. Sznaier
2015 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
The main result 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.  ... 
doi:10.1109/cvpr.2015.7298829 dblp:conf/cvpr/ChengLCS15 fatcat:iiu3r3pt2zfjvamvn64widorrq

Optimal Shape Control via L_∞ Loss for Composite Fuselage Assembly [article]

Juan Du, Shanshan Cao, Jeffrey H. Hunt, Xiaoming Huo
2019 arXiv   pre-print
From statistical point 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.  ... 
arXiv:1911.03592v1 fatcat:r3qlgyjrejec5fwtiedf77krxe

A bounded uncertainty approach to cooperative localization using relative bearing constraints

Camillo J. Taylor, John Spletzer
2007 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems  
The scheme produces 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)".  ... 
doi:10.1109/iros.2007.4399398 dblp:conf/iros/TaylorS07 fatcat:ldvxnfe4mrd5xbrnpy4vip6ujm

On phase retrieval via matrix completion and the estimation of low rank PSD matrices

Marcus Carlsson, Daniele Gerosa
2019 Inverse Problems  
Given underdetermined measurements 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.  ... 
doi:10.1088/1361-6420/ab4e6d fatcat:xhkyg5aypzddhc6jqyttgkseoq

On phase retrieval via matrix completion and the estimation of low rank PSD matrices [article]

Marcus Carlsson, Daniele Gerosa
2019 arXiv   pre-print
Given underdetermined measurements 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.  ... 
arXiv:1907.09537v2 fatcat:s3zlguchfbfm7c6xsga5ziv4j4

On a multiplier conjecture for univalent functions

V. Gruenberg, F. Rønning, St. Ruscheweyh
1990 Transactions of the American Mathematical Society  
, the class 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.  ... 
doi:10.1090/s0002-9947-1990-0991960-7 fatcat:kagldlnwy5ayjdd3ks43ib6se4

On a Multiplier Conjecture for Univalent Functions

V. Gruenberg, F. Ronning, St. Ruscheweyh
1990 Transactions of the American Mathematical Society  
, the class 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.  ... 
doi:10.2307/2001537 fatcat:4qzucg2nwna6bgusre4msc2x64
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