Electrocortical group neuron activity describe changes in neurotransmision cause by different factors. Such changes could by qualitative described by spectral analysis of electrocortical activity as a variation of relative spectral power in different frequency ranges. We used fractal dimension to compare treated animals with control to quantitativily describe degree of pathophysiological state....

Abstract A celebrated theorem of Douglas Lind states that a positive real number is equal to the spectral radius some integral primitive matrix, if and only if, it Perron algebraic integer. Given p , we prove there an irreducible matrix with dimension bounded above in terms degree, ratio first two largest Galois conjugates, arithmetic information about ring integers its field. This can be taken...

We study simple random walk on the class of planar maps which can be encoded by a two-dimensional with i.i.d.. increments or Brownian motion via “mating-of-trees” type bijection. This includes uniform infinite triangulation (UIPT), infinite-volume limits weighted number spanning trees, bipolar orientations, Schnyder woods they admit, and ?-mated-CRT map for ??(0,2). For each these maps, we obta...