Introduction: Quantitative assessments of the effects induced by repetitive transcranial magnetic stimulation (rTMS) are crucial to develop more efficient and personalized treatments. Objectives: To determine the spectral powers of different subbands of EEG correlated with treatment response to rTMS.   Materials and Methods: the spectral powers of different...

0. Introduction. Let X be a non-singular, connected, projective curve defined over an algebraically closed field k. Let U denote the set of isomorphism classes of stable vector bundles on X with given degree d and rank r. In the sixties, C.S. Seshadri and D. Mumford ([14], [17] and [18]) supplied U with a natural structure of quasi-projective variety, together with a natural compactification U ...

Euclidean n-component φ theories whose Hamiltonians areO(n) symmetric except for quadratic symmetry breaking boundary terms are studied in the film geometry R×[0, L]. The boundary terms imply the Robin boundary conditions ∂nφα = c̊ (j) α φα at the boundary planes Bj=1 at z = 0 and Bj=2 at z = L. Particular attention is paid to the cases in which mj of the n variables c̊ (j) α associated with plan...

Abstract We study the a central limit theorem for sums of independent tensor powers, $\frac{1}{\sqrt{d}}\sum \limits _{i=1}^d X_i^{\otimes p}$. focus on high-dimensional regime where $X_i \in{\mathbb{R}}^n$ and $n$ may scale with $d$. Our main result is proposed threshold convergence. Specifically, we show that, under some regularity assumption, if $n^{2p-1}\ll d$, then normalized sum converges...