Convex (0,1)-matrices and their epitopes
نویسندگان
چکیده
We investigate (0,1)-matrices that are convex, which means the ones consecutive in every row and column. These matrices occur discrete tomography. The notion of ranked essential sets, known for permutation matrices, is extended to convex sets. show a number results class C(R,S) with given column sum vectors R S. Also, it shown set uniquely determines matrix C(R,S).
منابع مشابه
Singular values of convex functions of matrices
Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$ are nonzero matrices and each $X_{i}$ is positive semidefinite. It is shown that if $f$ is a nonnegative increasing convex function on $left[ 0,infty right) $ satisfying $fleft( 0right) =0 $, then $$2s_{j}left( fleft( fra...
متن کاملReconstruction of hv-convex binary matrices from their absorbed projections
The reconstruction of hv-convex binary matrices from their absorbed projections is considered. Although this problem is NP-hard if the non-absorbed row and column sums are available, it is proved that such a reconstruction problem can be solved in polynomial time from absorbed projections when the absorption is represented by =(1+ √ 5)=2. Also a reconstruction algorithm is given to determine th...
متن کاملRandom Laplacian Matrices and Convex Relaxations
Abstract. The largest eigenvalue of a matrix is always larger or equal than its largest diagonal entry. We show that for a large class of random Laplacian matrices, this bound is essentially tight: the largest eigenvalue is, up to lower order terms, often the size of the largest diagonal entry. Besides being a simple tool to obtain precise estimates on the largest eigenvalue of a large class of...
متن کاملConvex Sets of Nonsingular and P–matrices
We show that the set r(A,B) (resp. c(A,B)) of square matrices whose rows (resp. columns) are independent convex combinations of ∗Work supported in part by Office of Naval Research contract N00014–90–J–1739 and NSF grant DMS 90–00899. †Work partially supported by NSERC grant 6–53121. Part of the work was done while this author was a Visiting Assistant Professor at the College of William and Mary.
متن کاملConvex Sets and their Applications
The main objective of this Workshop was to bring together in Banff eminent and emerging researchers from the three main branches of Convex Geometry: Discrete, Analytical and Applied. There has not been such a unifying conference in the past fifteen years. The organizers believe that this objective was met during the week of March 4 9. First, of the thirty-nine participants, one third represente...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2021
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2021.02.038