The center of a connected graph G is the set of nodes of G for which the maximum distance to any other node of G is as small as possible. If G is a simply connected set of lattice points (\pixels") with graph structure deened by 4-neighbor adjacency, we show that the center of G is either a 2-by-2 square block, a diagonal staircase, or a (dotted) diagonal line with no gaps. The authors thank Fr...

This study examines the temporal and directional characteristics of child-adult vocal exchanges in day-long naturalistic recordings of autism and typical control groups. In both populations, adults responded frequently (on average about 40% of responses) within 1s or less, a time thought to be conducive for contingency learning by the child. However, the time to adult response tended to be long...

Two-dimensional (2D) spectroscopy is used to study the interactions between energy levels in both the field of optics and nuclear magnetic resonance (NMR). Conventionally, the strength of interaction between two levels is inferred from the value of their common off-diagonal peak in the 2D spectrum, which is termed the cross peak. However, stronger diagonal peaks often have long tails that exten...

The solvability of the Riemann–Hilbert boundary value problem on the real line is described in the case when its matrix coefficient admits a Wiener–Hopf-type factorization with bounded outer factors, but rather general diagonal elements of its middle factor. This covers, in particular, the almost periodic setting, when the factorization multiples belong to the algebra generated by the functions...

There is an error in the last sentence of the “Validation on factual statements” section of the Results. The sentence should read: With this method we estimate that, in the four subject areas, true statements are assigned higher truth values than false ones with probability 95%, 98%, 100%, and 95%, respectively. Fig 4 is incorrect. Please view the corrected figure below. For each confusion matr...

Multivariate spectral gradient method is proposed for solving unconstrained optimization problems. Combined with some quasi-Newton property multivariate spectral gradient method allows an individual adaptive stepsize along each coordinate direction, which guarantees that the method is finitely convergent for positive definite quadratics. Especially, it converges no more than two steps for posit...

The paper presents the results of research electromagnetic mutual coupling impact on structure correlation matrices in multiantenna communication systems. Classical structures employed most up-to-date systems descriptions and designs usually assume unit autocorrelation exponentially decreasing cross-correlation antenna elements receiving/transmitting array. At same time numerous studies had sho...