Related papers: Samuelson's Webs
The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. We determine the maximum order of reduced triangle-free…
Let $\sigma_b(X_{m,d}(\mathbb {C}))(\mathbb {R})$, $b(m+1) < \binom{m+d}{m}$, denote the set of all degree $d$ real homogeneous polynomials in $m+1$ variables (i.e. real symmetric tensors of format $(m+1)\times ... \times (m+1)$, $d$ times)…
With the explosion of social media in the last few years, web pages nowadays include different social network buttons where users can express if they support or recommend content. Those social buttons are very visual and their…
We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank.
In this paper we further develop the theory of matrices over the extended tropical semiring. Introducing a notion of tropical linear dependence allows for a natural definition of matrix rank in a sense that coincides with the notions of…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
This paper is devoted to the online dominating set problem and its variants. We believe the paper represents the first systematic study of the effect of two limitations of online algorithms: making irrevocable decisions while not knowing…
We provide a counterexample to a recent conjecture that the minimum rank of every sign pattern matrix can be realized by a rational matrix. We use one of the equivalences of the conjecture and some results from projective geometry. As a…
We argue that the spiral can, in presence of a maximum principle, be of maximal rank at a boundary, but does not preserve hypoellipticity.
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. In this paper we propose a systematic study of basic properties of signature tensors, starting from their rank, symmetries and conciseness. We…
The majority of Semantic Web search engines retrieve information by focusing on the use of concepts and relations restricted to the query provided by the user. By trying to guess the implicit meaning between these concepts and relations,…
We prove that general unions of singularity schemes of multiplicity two in the projective plane have maximal rank.
In this paper we define and study self-similar ranked fragmentations. We first show that any ranked fragmentation is the image of some partition-valued fragmentation, and that there is in fact a one-to-one correspondence between the laws of…
Let $\mathcal{A} \rightarrow S$ be an abelian scheme over an irreducible variety over $\mathbb{C}$ of relative dimension $g$. For any simply-connected subset $\Delta$ of $S^{\mathrm{an}}$ one can define the Betti map from…
We investigate the new, Turing-complete class of layered systems, whose lefthand sides of rules can only be overlapped at a multiset of disjoint or equal positions. Layered systems define a natural notion of rank for terms: the maximal…
The topological structures of the Internet and the Web have received considerable attention. However, there has been little research on the topological properties of individual web sites. In this paper, we consider whether web sites (as…
An open problem in graphical Gaussian models is to determine the smallest number of observations needed to guarantee the existence of the maximum likelihood estimator of the covariance matrix with probability one. In this paper we formalize…
With the advent of the information age, the scale of data on the Internet is getting larger and larger, and it is full of text, images, videos, and other information. Different from social media data and news data, scientific research…
Finding the most probable explanation for observed variables in a Bayesian network is a notoriously intractable problem, particularly if there are hidden variables in the network. In this paper we examine the complexity of a related…
We show that computing the minimum rank of a sign pattern matrix is NP hard. Our proof is based on a simple but useful connection between minimum ranks of sign pattern matrices and the stretchability problem for pseudolines arrangements. In…