We consider the question of how to solve inverse problems of the form ex(0) = x(t) for an unkown matrix A, given measurements of x(t) at different time points. Problems of this form have applications in reverse engineering gene networks. In particular, we examine the cases where A is circulant and Toeplitz. We are also able to extend our findings of the circulant case to some generalizations of...

Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding methods traditionally suffer from high computation and storage costs in such a scenario. To address this problem, we propose Circulant Binary Embedding (CBE) wh...

In this paper, the concept of continuous multifunctions for digraphs is introduced. It turns out that a digraph multifunction is continuous if and only if it is strong. We introduce the notion of dismantlable digraphs and show that it does generalize the dismantlable graphs and posets. Generalizing various previous results, we show that any dismantlable digraph has the almost fixed point proper...

Many science phenomena are described as interacting particle systems (IPS). The mean field limit (MFL) of large all-to-all coupled deterministic IPS is given by the solution a PDE, Vlasov Equation (VE). Yet, many applications demand on networks/graphs. In this paper, we interested in sequence directed graphs, or digraphs for short. It interesting to know, how associated with influences macrosco...

"A 4-dimensional Riemannian manifold equipped with an additional tensor structure, whose fourth power is the identity, considered. This structure has a circulant matrix respect to some basis, i.e. circulant, and it acts as isometry metric. The product associated considered studied. Conditions for metric, which imply that belongs each of basic classes Staikova-Gribachev's classi cation, are obta...