The aim of this paper is to introduce fuzzy ($e$, almost) $e^{*}$-regular spaces in $check{S}$ostak's fuzzy topological spaces. Using the $r$-fuzzy $e$-closed sets, we define $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points and their properties. Moreover, we investigate the relations among $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points, $r$-fuzzy ($e$, almost) $e^{*}$-regular spaces a...

objectives: autism spectrum disorder (asd) is a group of neurodevelopment syndromes with impairments in social communications and restrictive or repetitive behaviors. neurofeedback is a new method that may regulate neuro and metabolic function in brain. this study is semi-experimental, with pre and post test.  methods: in 26 children with asd, 40 sessions of neurofeedback were done. brain waves...

The infinite grid is the Cayley graph of Z × Z with the usual generators. In this paper, the Ihara zeta function for the infinite grid is computed using elliptic integrals and theta functions. The zeta function of the grid extends to an analytic, multivalued function which satisfies a functional equation. The set of singularities in its domain is finite. The grid zeta function is the first comp...

The stability number α(G) for a given graph G is the size of a maximum stable set in G. The Lovász theta number provides an upper bound on α(G) and can be computed in polynomial time as the optimal value of the Lovász semidefinite program. In this paper, we show that restricting the matrix variable in the Lovász semidefinite program to be rank-one and rank-two, respectively, yields a pair of co...

The $q$-Coloring problem asks whether the vertices of a graph can be properly colored with $q$ colors. Lokshtanov et al. [SODA 2011] showed that on graphs feedback vertex set size $k$ cannot solved in time $\mathcal{O}^*((q-\varepsilon)^k)$, for any $\varepsilon > 0$, unless Strong Exponential-Time Hypothesis (SETH) fails. In this paper we perform fine-grained analysis complexity respect to hie...

The aim of the paper is to first investigate some properties of the hyperspace $theta(X)$, and then in the next article it deals with some detailed study of a special type of subspace $downarrowtheta C(X)$ of the space $theta (Xtimes mathbb I)$.

The famous Lovász theta number θ(G) is expressed as the optimal solution of a semidefinite program. As such, it can be computed in polynomial time to an arbitrary precision. Nevertheless, computing it in practice yields some difficulties as the size of the graph gets larger and larger, despite recent significant advances of semidefinite programming (SDP) solvers. We present a way around SDP whi...

OBJECTIVE Neuroimaging research suggested a mixed pattern of functional connectivity abnormalities in developmental dyslexia. We examined differences in the topological properties of functional networks between 29 dyslexics and 15 typically reading controls in 3rd grade using graph analysis. Graph metrics characterize brain networks in terms of integration and segregation. METHOD We used EEG ...

Abstract Given a graph $H$ and positive integer $n$ , the Turán number $\mathrm{ex}(n,H)$ is maximum of edges in an -vertex that does not contain as subgraph. A real $r\in (1,2)$ called exponent if there exists bipartite such $\mathrm{ex}(n,H)=\Theta (n^r)$ . long-standing conjecture Erdős Simonovits states $1+\frac{p}{q}$ for all integers $p$ $q$ with $q\gt p$ In this paper, we show $q \gt p^{...

The topological architecture of brain connectivity has been well-characterized by graph theory based analysis. However, previous studies have primarily built brain graphs based on a single modality of brain imaging data. Here we develop a framework to construct multi-modal brain graphs using concurrent EEG-fMRI data which are simultaneously collected during eyes open (EO) and eyes closed (EC) r...