Transcranial direct current stimulation (tDCS) is a neuromodulation technique that can alter cortical excitability and modulate behaviour in a polarity-dependent way. Despite the widespread use of this method in the neuroscience field, its effects on ongoing local or global (network level) neuronal activity are still not foreseeable. A way to shed light on the neuronal mechanisms underlying the...

In this paper we show that the θ-graph with 4 cones has constant stretch factor, i.e., there is a path between any pair of vertices in this graph whose length is at most a constant times the Euclidean distance between that pair of vertices. This is the last θ-graph for which it was not known whether its stretch factor was bounded.

The cycles of a graph give natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges adjacent one cycle if only they every which appear together. An orderable matroid is whose set circuits admits such ordering. In this paper, we consider the question determining matroids orderable. Although able answer for non-binary matroids, it remains open binary matroi...

We study a family of random permutation models on the Hamming graph $H(2,n)$ (i.e., $2$-fold Cartesian product complete graphs), containing interchange process and cycle-weighted with parameter $\theta > 0$. This contains walk representation quantum Heisenberg ferromagnet. show that in these cycle structure permutations undergoes \textit{phase transition} -- when number transpositions defining ...

in this paper, some results of singh, gopalakrishna and kulkarni (1970s) have been extended to higher order derivatives. it has been shown that, if $sumlimits_{a}theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $t(r, f)sim t(r, f^{(k)}), rrightarrowinfty$ if $theta(infty, f)=1$ and $t(r, f)sim (k+1)t(r, f^{(k)}), rrightarrowinfty$ if $th...

We investigate hierarchies of semidefinite approximations for the chromatic number χ(G) of a graph G. We introduce an operator Ψ mapping any graph parameter β(G), nested between the stability number α(G) and χ(G), to a new graph parameter Ψ β (G), nested between α(G) and χ(G); Ψ β (G) is polynomial time computable if β(G) is. As an application, there is no polynomial time computable graph param...

in the paper‎, ‎some new existence theorems of maximal elements for‎ ‎$mathscr{f}_{c,theta}$-mappings and $mathscr{f}_{c,theta}$-majorized mappings are established‎. ‎as applications, ‎some new existence theorems of equilibrium points for‎ ‎one-person games‎, ‎qualitative games and generalized games are obtained‎. ‎our results unify and generalize most known results‎ ‎in recent literature‎.

Let $Q_d$ be the $d$-dimensional Hamming cube and $N=|V(Q_d)|=2^d$. An independent set $I$ in is called balanced if contains same number of even odd vertices. We show that logarithm sets is
 \[(1-\Theta(1/\sqrt d))N/2.\]
 The key ingredient proof an improved version "Sapozhenko's graph container lemma".

A semidefinite relaxation σ(Γ) for the problem of finding the maximum number κ(Γ) of edges in a complete bipartite subgraph of a bipartite graph Γ = (V1 ∪ V2, E) is considered. For a large class of graphs, the relaxation is better than the LP-relaxation described in [9]. It is shown that σ(Γ) is bounded from above by the Lovász theta function θ(LQ(Γ)) of the graph LQ(Γ) related to the line grap...

A semideenite relaxation (?) for the problem of nding the maximum number (?) of edges in a complete bipartite subgraph of a bipartite graph ? = (V1 V2; E) is considered. For a large class of graphs, the relaxation is better than the LP-relaxation described in 8]. It is shown that (?) is bounded from above by the Lovv asz theta function (LQ(?)) of the graph LQ(?) related to the line graph of ?. ...