What distribution of graphical degree sequence is invariant under “scaling”? Are these graphs always power-law graphs? We show the answer is a surprising “yes” for sparse graphs if we ignore isolated vertices, or more generally, the vertices with degrees less than a fixed constant k. We obtain a concentration result on the degree sequence of a random induced subgraph. The case of hypergraphs (o...

What distribution of graphical degree sequence is invariant under “scaling”? Are these graphs always power-law graphs? We show the answer is a surprising “yes” for sparse graphs if we ignore isolated vertices, or more generally, the vertices with degrees less than a fixed constant k. We obtain a concentration result on the degree sequence of a random induced subgraph. The case of hypergraphs (o...

The Process Hitting (PH) is a recently introduced framework to model concurrent processes. Its major originality lies in a specific restriction on the causality of actions, which makes the formal analysis of very large systems tractable. PH is suitable to model Biological Regulatory Networks (BRNs) with complete or partial knowledge of cooperations between regulators by defining the most permis...

This paper explores Answer Set Programming (ASP) for stream reasoning with data retrieved continuously from sensors. We describe a proof-of-concept with an example of using declarative models to recognize car on-road situations.

Transmission of a vertex v connected graph G is the sum distances from to all other vertices in G. Graph transmission irregular (TI) if no two its have same transmission, and interval (ITI) it TI transmissions form sequence consecutive integers. Here we give positive answer question Dobrynin [Appl Math Comput 340 (2019), 1–4] whether infinite families ITI graphs exist.

Many sequences of binomial coefficients share various unimodality properties. In this paper we consider the unimodality problem of a sequence of binomial coefficients located in a ray or a transversal of the Pascal triangle. Our results give in particular an affirmative answer to a conjecture of Belbachir et al which asserts that such a sequence of binomial coefficients must be unimodal. We als...

We define an integer graded symplectic Floer cohomology and a spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopies. Such an integer graded Floer cohomology is an integral lifting of the usual Floer-Oh cohomology with ZΣ(L) grading. As one of applications of the spectral sequence, we offer an affirmative answer to an Audin’s question for oriented, ...

The effective use of ASP solvers is essential for enhancing efficiency and scalability. The incidence matrix is a simple representation used in Constraint Programming (CP) and Integer Linear Programming for modeling combinatorial problems. Generating test cases for event-sequence testing is to find a sequence covering array (SCA). In this paper, we consider the problem of finding optimal sequen...