Standard Loading Profile in Matrix Rigidity Sensing
نویسندگان
چکیده
منابع مشابه
Matrix Rigidity
The rigidity of a matrix M is the function R M (r), which, for a given r, gives the minimum number of entries of M which one has to change in order to reduce its rank to at most r. This notion has been introduced by Valiant in 1977 in connection with the complexity of computing linear forms. Despite more than 20 years of research, very little is known about the rigidity of matrices. Nonlinear l...
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Consider the following problem: Given an n×n matrix A and an input x, compute Ax. This problem has a simple algorithm which runs in time O(n). The question thus is: Is this is the best possible ? Valiant showed ([12]) that if an n × n matrix A is rigid, then the smallest straight line program computing Ax is either super-linear size, or has super logarithmic depth. Roughly a matrix of rank n is...
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We study the problem of identifying conditions under which a divergence free matrix field takes values in some prescribed sets of matrices K. We treat in detail the case when K is made of two or three matrices. Our results are parallel to those on curl free matrices. In that case Ball and James showed rigidity when K is made of two matrices and Tartar proved lack of rigidity when K is made of f...
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The rigidity of a matrix is deened to be the number of entries in the matrix that have to be changed in order to reduce its rank below a certain value. Using a simple combinatorial lemma, we show that one must alter at least c n 2 r log n r entries of an n n-Cauchy matrix to reduce its rank below r, for some constant c. In the second part of the paper we apply our combinatorial lemma to matrice...
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In this paper we give an explicit construction of n × n matrices over finite fields which are somewhat rigid, in that if we change at most k entries in each row, its rank remains at least Cn(logq k)/k, where q is the size of the field and C is an absolute constant. Our matrices satify a somewhat stronger property, we which explain and call “strong rigidity.” We introduce and briefly discuss str...
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ژورنال
عنوان ژورنال: Biophysical Journal
سال: 2018
ISSN: 0006-3495
DOI: 10.1016/j.bpj.2018.01.017