The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$theta$-open sets and $e$-$theta$-closure operator which are defined by Özkoç and Aslım [10] called weakly $eR$-open functions and $e$-$theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topolo...

Let $(X, \tau)$ and $(Y, \sigma)$ be topological spaces in which no separation axioms are assumed, unless explicitly stated if $\mathcal{I}$ is an ideal on $X$.Given a multifunction $F\colon (X, \tau)\rightarrow (Y, \sigma)$, $\alpha,\beta$ operators \tau)$, $\theta,\delta$ proper $X$. We introduce study upper lower $(\alpha, \beta,\theta,\delta,\mathcal{I})$-continuous multifunctions.A said to...

In this research, we investigate the subject of path-finding. A pruned version of visibility graph based on Candidate Vertices is formulated, followed by a new visibility check technique. Such combination enables us to quickly identify the useful vertices and thus find the optimal path more efficiently. The algorithm proposed is demonstrated on various path-finding cases. The performance of the...

Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a subgraph. We show that the maximum value of the correlations for classical, quantum, and more general theories is the independence number, the Lovász number...

We study the spanning properties of Theta-Theta graphs. Similar in spirit with the Yao-Yao graphs, Theta-Theta graphs partition the space around each vertex into a set of k cones, for some fixed integer k > 1, and select at most one edge per cone. The difference is in the way edges are selected. Yao-Yao graphs select an edge of minimum length, whereas Theta-Theta graphs select an edge of minimu...

In this study, we investigated the neural correlates of a visual working memory task. Two experiments were carried out using scalp electroencephalography (EEG) and Electrocorticography (ECoG), respectively. In each trial, participants judged whether a test face had been among a small set of recently studied faces. We used a combination of hidden semi-Markov models (HSMMs) and multi-variate patt...

In 2004, Karoński, Łuczak and Thomason proposed 1-2-3-Conjecture: For every nice graph G there is an edge weighting function w:E(G)→{1,2,3} such that the induced vertex coloring proper. After that, total versions of this conjecture were suggested in literature recently, Kalkowski et al. have generalized to hypergraphs. paper, some previously known results on are improved. Moreover, affirmative ...

This paper introduces a biologically realistic mathematical, computational model of theta (≈5 Hz) rhythm generation in the hippocampal CA1 region and some of its possible further applications in drug discovery and in robotic/computational models of navigation. The model shown here uses the conductance based description of nerve cells: populations of basket cells, alveus/lacunosum-moleculare int...

We prove the reducibility of 1-D quantum harmonic oscillators in $\mathbb R$ perturbed by a quasi-periodic time potential $V(x,\omega t)$ under following conditions, namely there is $C>0$ such that \begin{equation*} |V(x,\theta)|\le C,\quad|x\partial_xV(x,\theta)|\le C,\quad\forall~(x,\theta)\in\mathbb R\times\mathbb T_\sigma^n. \end{equation*} The corresponding perturbation matrix $(P_i^j(\the...

The medial septum/vertical limb of diagonal band complex (MS/vDB) consists of cholinergic, GABAergic, and glutamatergic neurons that project to the hippocampus and functionally regulate attention, memory, and cognitive processes. Using tyrosine hydroxlase (TH) immunocytochemistry and dark-field light microscopy, we found that the MS/vDB is innervated by a sparse network of TH-immunoreactive (pu...