Related papers: Factorization of network reliability with perfect …
In this paper we give a new formula for the $n$-th power of a $2\times2$ matrix. More precisely, we prove the following: Let $A= \left ( \begin{matrix} a & b \\ c & d \end{matrix} \right )$ be an arbitrary $2\times2$ matrix, $T=a+d$ its…
We obtain sharp estimates on the connectivity of complex affine hypersurfaces in terms of the decomposition of the defining equation as a sum of weighted homogeneous components relative to some weight system.
Inspired by practical importance of social networks, economic networks, biological networks and so on, studies on large and complex networks have attracted a surge of attentions in the recent years. Link prediction is a fundamental issue to…
The exact calculation of network reliability in a probabilistic context has been a long-standing issue of practical importance, but a difficult one, even for planar graphs, with perfect nodes and with edges of identical reliability p. Many…
We introduce a connectivity function for infinite matroids with properties similar to the connectivity function of a finite matroid, such as submodularity and invariance under duality. As an application we use it to extend Tutte's linking…
Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive factorizations of translations of those matrices. We show that…
In this note, we give a necessary and sufficient condition for a matrix A in M to be finitely G-determined, where M is the ring of 2 x 2 matrices whose entries are formal power series over an infinite field, and G is a group acting on M by…
We prove an identity relating the permanent of a rank $2$ matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
This is the first installment of an exposition of an ACL2 formalization of elementary linear algebra, focusing on aspects of the subject that apply to matrices over an arbitrary commutative ring with identity, in anticipation of a future…
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
The connectivity properties of a weight-bearing network are exploited to enhance it's capacity. We study a 2-d network of sites where the weight-bearing capacity of a given site depends on the capacities of the sites connected to it in the…
The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…
In this paper we extend and prove in detail the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with counting (CMSOL) from B. Godlin, T. Kotek and J.A. Makowsky (2008) and J.A.…
The calculation of network reliability in a probabilistic context has long been an issue of practical and academic importance. Conventional approaches (determination of bounds, sums of disjoint products algorithms, Monte Carlo evaluations,…
In this paper we prove that a matrix property of nettedness (all 2x2 cells satisfy a recurrence) is preserved for powers of such a matrix, where the coefficients are all instances of the same sequence. Also, we find an n-dimensional analog…
In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…
We introduce a novel approach to description of networks/graphs. It is based on an analogue physical model which is dynamically evolved. This evolution depends on the connectivity matrix and readily brings out many qualitative features of…
In this paper we investigate the algebraic structure of the truth tables of all bracketed formulae with n distinct variables connected by the binary connective of implication.