For first passage percolation in Zd with large d, we construct a path connecting the origin to {x1 = 1}, whose passage time has optimal order log d/d. Besides, an improved lower bound for the "diagonal" speed of the cluster combined with a result by Dhar (1988) shows that the limiting shape in FPP with exponential passage times (and thus that of Eden model) is not the euclidian ball in dimensio...

Let / be any fixed positive integer and a a sentence in the first-order predicate calculus of/unary functions. For positive integers n, an «-structure is a model with universe {0,1,...,« 1} and/unary functions, and p(n,a) is the ratio of the number of «-structures satisfying a to n"f, the number of «-structures. We show that lim„_00/i(«, a) exists for all such a, and its value is given by an ex...

A temporal graph is a graph in which connections between vertices are active at specific times, and such temporal information leads to completely new patterns and knowledge that are not present in a non-temporal graph. In this paper, we study traversal problems in a temporal graph. Graph traversals, such as DFS and BFS, are basic operations for processing and studying a graph. While both DFS an...

We investigate a construction schema for first-order logical systems, called “form logic”. Form logic allows us to overcome the dualistic commitment of predicate logic to individual constants and predicates. Dualism is replaced by a pluralism of terms of different “logical forms”. Individual form-logical systems are generated by the determination of a range of logical forms and of the formbased...

We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension, i. e. it represents ⊥. Our calculus establishes that a graph has empty extension by converting it to a normal form, which is expanded to other graphs until we...

The relationship between videogames and violent behaviour was analysed in a representative sample of 9889 Norwegian youth ageing from 13 to 18 years. Videogames were separated in eight different categories. A hypothesis of the relationship between videogames and violence was put forward as a starting – point for reasoning. A unique correlation between violent videogames, specifying first person...

This paper continues the research on determining a maximum cardinality set of edgeand node-disjoint paths between a source cell and a target cell in P systems. We review the previous solution [3], based on depth-first search (DFS), and we propose a faster solution, based on breadth-first search (BFS), which leverages the parallel and distributed characteristics of P systems. The runtime complex...

This work introduces the idea of breadth-first generation of infinite trees and languages. It is orthogonal to usual descriptions by classical objects such as automata and grammars which refer more naturally to a depth-first approach. This idea is brought into play with periodic inputs, a case that comes from the study of rational base number systems which correspond to specific inputs derived ...

An abstraction mapping over clausal form theories in first-order predicate calculus is presented that involves the renaming of predicate symbols. This renaming is not 1-1, in the sense that several predicate symbols Ri,.. . , Rn from the original theory are all replaced by a single symbol R in the abstract theory. In order to preserve consistency, however, the clauses that distinguish the Rj's ...

Identification and characterization of gene regulatory binding motifs is one of the fundamental tasks toward systematically understanding the molecular mechanisms of transcriptional regulation. Recently, the problem has been abstracted as the challenge planted (l,d)-motif problem. Previous studies have developed numerous methods to solve the problem. But most of them need to specify the length ...