BACKGROUND To understand neurophysiological mechanisms underlying cognitive dysfunction in low-grade glioma (LGG) patients by evaluating the spatial structure of 'resting-state' brain networks with graph theory. METHODS Standardized tests measuring 6 neurocognitive domains were administered in 17 LGG patients and 17 healthy controls. Magnetoencephalography (MEG) recordings were conducted duri...

We study the use of quantum entanglement in the zero-error source-channel coding problem. Here, Alice and Bob are connected by a noisy classical one-way channel, and are given correlated inputs from a random source. Their goal is for Bob to learn Alice’s input while using the channel as little as possible. In the zero-error regime, the optimal rates of source codes and channel codes are given b...

For every constant $d \geq 3$ and $\epsilon > 0$, we give a deterministic $\operatorname{poly}(n)$-time algorithm that outputs $d$-regular graph on $\Theta(n)$ vertices is $\eps$-near-Ramanujan; i.e., its eigenvalues are bounded in magnitude by $2\sqrt{d-1} + \epsilon$ (excluding the single trivial eigenvalue of $d$).

We improve by an exponential factor the best known asymptotic upper bound for the density of sets avoiding 1 in Euclidean space. This result is obtained by a combination of an analytic bound that is an analogue of Lovász theta number and of a combinatorial argument involving finite subgraphs of the unit distance graph. In turn, we straightforwardly obtain an asymptotic improvement for the measu...

Let X0 be an irreducible projective nodal curve with only one singular point, and let P0 be a line bundle on X0. The moduli SUX0(r;P0) of rank r vector bundles on X0 with determinant P0 is not compact. In [A], using the technique of Kausz ([K1], [K2]), we constructed a compactification GSL2B(X0;P0) of SUX0(2;P0), and studied its structure. Surprisingly, despite its seemingly natural definition,...

We present a new approach for gluing tours over certain tight, 3-edge cuts. Gluing cuts has been used in algorithms finding Hamilton cycles special graph classes and proving bounds 2-edge-connected subgraph problem, but not much was known this direction connected multigraphs. apply to the traveling salesman problem (TSP) case when objective function of subtour elimination relaxation is minimize...

In the paper we consider degree, spectral, and semidefinite bounds on the stability number of a graph. The bounds are obtained via reformulations and variants of the inverse theta function, a notion recently introduced by the author in a previous work.

In this report, some results on semidefinite programming relaxation of graph coloring are summarized. Two algorithms on semicoloring/coloring are described in detail for 3-colorable graphs. The relation between semidefinite programming relaxation and the Lovász theta function is simply introduced.

In Bayesian applications, there is a huge interest in rapid and accurate estimation of the posterior distribution, particularly for high dimensional or hierarchical models. this article, we propose to use optimization solve joint distribution (random transport plan) between two random variables, $\theta$ from $\beta$ simple multivariate uniform. Specifically, obtain an approximate estimate cond...