Eigenvector localization for random band matrices with power law band width

It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction of standard basis vectors, provided the band width $W$ raised to a power $\mu$ remains smaller than the matrix size $N$. For a Gaussian band ensemble, with matrix elements given by i.i.d. centered Gaussians within a band of width $W$, the estimate $\mu \le 8$ holds.Comment: 30 pages; corrected typo

Neuroelectronic Systems: Binding Neurons to Electric Circuits

This paper is devoted to description of a new type of information system based on interaction of biological neurons and electronic components – neuroelectronic (NE) system. Main features and components, like neural network sensor, of NE are briefly put into consideration followed with an example of electric interaction between neural network of a snail Lymnaea Stagnalis neurons and electronic MOSFET sensor

Notes on Stein-Sahi representations and some problems of non L2L^2 harmonic analysis

We discuss one natural class of kernels on pseudo-Riemannian symmetric spaces.Comment: 40p

About possibility to locate an EQ epicenter using parameters of ELF/ULF preseismic emission

A relation between parameters of preseismic ULF/ELF emissions and EQ is studied. The magnetic data measured at Karymshino station (Kamchatka, Russia) along with data on local seismic activity during eight years of observations (2001–2008) are taken for the analysis. Source azimuth is detected in different techniques, based on the analysis of the total field and its polarized pulsed component. The latter technique shows a better accuracy in the source azimuth detection. The errors of the method are associated with existence of non-seismic sources and with use of one-point observation. The second error can be eliminated by development of multi-point observations

Coherent frequentism

By representing the range of fair betting odds according to a pair of confidence set estimators, dual probability measures on parameter space called frequentist posteriors secure the coherence of subjective inference without any prior distribution. The closure of the set of expected losses corresponding to the dual frequentist posteriors constrains decisions without arbitrarily forcing optimization under all circumstances. This decision theory reduces to those that maximize expected utility when the pair of frequentist posteriors is induced by an exact or approximate confidence set estimator or when an automatic reduction rule is applied to the pair. In such cases, the resulting frequentist posterior is coherent in the sense that, as a probability distribution of the parameter of interest, it satisfies the axioms of the decision-theoretic and logic-theoretic systems typically cited in support of the Bayesian posterior. Unlike the p-value, the confidence level of an interval hypothesis derived from such a measure is suitable as an estimator of the indicator of hypothesis truth since it converges in sample-space probability to 1 if the hypothesis is true or to 0 otherwise under general conditions.Comment: The confidence-measure theory of inference and decision is explicitly extended to vector parameters of interest. The derivation of upper and lower confidence levels from valid and nonconservative set estimators is formalize