Recent data identify distinct components of social cognition associated with five brain regions. In posterior temporal cortex, the extrastriate body area is associated with perceiving the form of other human bodies. A nearby region in the posterior superior temporal sulcus is involved in interpreting the motions of a human body in terms of goals. A distinct region at the temporo-parietal juncti...

In the Graph Realization Problem (GRP), one is given a graph G, a set of non-negative edge-weights, and an integer d. The goal is to find, if possible, a realization of G in the Euclidian space R, such that the distance between any two vertices is the assigned edge weight. The problem has many applications in mathematics and computer science, but is NP-hard when the dimension d is fixed. Charac...

The concept of a k-pairable graph was introduced by Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In this talk, we introduce a special class of k-pairable graphs which are called uniquely pairable graphs. Then we give a characterization of uniquely pairable graphs in terms of the prime factor decomposi...

There exists a model in a countable language having a unique element which is not definable in Lω1,ω. We answer problem 10.12 from the updated version of Arnie Miller’s problem list, [3]. Definition For a structure M and a ∈ M, we say that a is definable over Lω1,ω if there is a formul ψ ∈ Lω1,ω such that for all b ∈ M a = b ⇔ M |= ψ(b). Theorem 0.1 There is a countable language L and a model M...

in this paper, we introduce the new notion of strongly j-clean rings associatedwith polynomial identity g(x) = 0, as a generalization of strongly j-clean rings. we denotestrongly j-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-j-cleanrings. next, we investigate some properties of strongly g(x)-j-clean.

Let P1, . . . ,Pn be properties of graphs. A (P1, . . . ,Pn)-partition of a graph G is a partition of the vertex set V (G) into subsets V1, . . . , Vn such that the subgraph G[Vi] induced by Vi has property Pi; i = 1, . . . , n. A graph G is said to be uniquely (P1, . . . ,Pn)-partitionable if G has exactly one (P1, . . . ,Pn)-partition. A property P is called hereditary if every subgraph of ev...

The question of efficient characterization of inclusion neighbourhood is crucial in some methods for learning (equivalence classes of) Bayesian networks. In this paper, neighbouring equivalence classes of a given equivalence class of Bayesian networks are characterized efficiently in terms of the respective essential graph. One can distinguish two kinds of inclusion neighbours: upper and lower ...