1,067 research outputs found
Towards a robust algorithm to determine topological domains from colocalization data
One of the most important tasks in understanding the complex spatial
organization of the genome consists in extracting information about this
spatial organization, the function and structure of chromatin topological
domains from existing experimental data, in particular, from genome
colocalization (Hi-C) matrices. Here we present an algorithm allowing to reveal
the underlying hierarchical domain structure of a polymer conformation from
analyzing the modularity of colocalization matrices. We also test this
algorithm on several model polymer structures: equilibrium globules, random
fractal globules and regular fractal (Peano) conformations. We define what we
call a spectrum of cluster borders, and show that these spectra behave
strikingly differently for equilibrium and fractal conformations, allowing us
to suggest an additional criterion to identify fractal polymer conformations
Relative blocking in posets
Poset-theoretic generalizations of set-theoretic committee constructions are
presented. The structure of the corresponding subposets is described. Sequences
of irreducible fractions associated to the principal order ideals of finite
bounded posets are considered and those related to the Boolean lattices are
explored; it is shown that such sequences inherit all the familiar properties
of the Farey sequences.Comment: 29 pages. Corrected version of original publication which is
available at http://www.springerlink.com, see Corrigendu
Some New Bounds For Cover-Free Families Through Biclique Cover
An cover-free family is a family of subsets of a finite set
such that the intersection of any members of the family contains at least
elements that are not in the union of any other members. The minimum
number of elements for which there exists an with blocks is
denoted by .
In this paper, we show that the value of is equal to the
-biclique covering number of the bipartite graph whose vertices
are all - and -subsets of a -element set, where a -subset is
adjacent to an -subset if their intersection is empty. Next, we introduce
some new bounds for . For instance, we show that for
and
where is a constant satisfies the
well-known bound . Also, we
determine the exact value of for some values of . Finally, we
show that whenever there exists a Hadamard matrix of
order 4d
A max-flow approach to improved lower bounds for quadratic unconstrained binary optimization (QUBO)
AbstractThe “roof dual” of a QUBO (Quadratic Unconstrained Binary Optimization) problem has been introduced in [P.L. Hammer, P. Hansen, B. Simeone, Roof duality, complementation and persistency in quadratic 0–1 optimization, Mathematical Programming 28 (1984) 121–155]; it provides a bound to the optimum value, along with a polynomial test of the sharpness of this bound, and (due to a “persistency” result) it also determines the values of some of the variables at the optimum. In this paper we provide a graph-theoretic approach to provide bounds, which includes as a special case the roof dual bound, and show that these bounds can be computed in O(n3) time by using network flow techniques. We also obtain a decomposition theorem for quadratic pseudo-Boolean functions, improving the persistency result of [P.L. Hammer, P. Hansen, B. Simeone, Roof duality, complementation and persistency in quadratic 0–1 optimization, Mathematical Programming 28 (1984) 121–155]. Finally, we show that the proposed bounds (including roof duality) can be applied in an iterated way to obtain significantly better bounds. Computational experiments on problems up to thousands of variables are presented
- …