Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

Language processing within the human medial temporal lobe

Although the hippocampal formation is essential for verbal memory, it is not fully understood how it contributes to language comprehension. We recorded event-related potentials (ERPs) directly from two substructures of the medial temporal lobe (MTL), the rhinal cortex and the hippocampus proper, while epilepsy patients listened to sentences that either were correct or contained semantic or syntactic violations. Semantic violations elicited a large negative ERP response peaking at approximately 400 ms in the rhinal cortex. In contrast, syntactically incorrect sentences elicited a negative deflection of 500-800 ms in the hippocampus proper. The results suggest that functionally distinct aspects of integration in language comprehension are supported by different MTL structures: the rhinal cortex is involved in semantic integration, whereas the hippocampus proper subserves processes of syntactic integration. An analysis of phase synchronization within the gamma band between rhinal and hippocampal recording sites showed that both of the above-mentioned ERP components were preceded by an increase of phase synchronization. In contrast to these short phasic increases of phase synchronization in both violation conditions, correct sentences were associated with a long-lasting synchronization in a late time window, possibly reflecting the integration of semantic and syntactic information as required for normal comprehension

Scale-invariance of human EEG signals in sleep

We investigate the dynamical properties of electroencephalogram (EEG) signals of human in sleep. By using a modified random walk method, We demonstrate that the scale-invariance is embedded in EEG signals after a detrending procedure. Further more, we study the dynamical evolution of probability density function (PDF) of the detrended EEG signals by nonextensive statistical modeling. It displays scale-independent property, which is markedly different from the turbulent-like scale-dependent PDF evolution.Comment: 4 pages and 6 figure

General Framework for phase synchronization through localized sets

We present an approach which enables to identify phase synchronization in coupled chaotic oscillators without having to explicitly measure the phase. We show that if one defines a typical event in one oscillator and then observes another one whenever this event occurs, these observations give rise to a localized set. Our result provides a general and easy way to identify PS, which can also be used to oscillators that possess multiple time scales. We illustrate our approach in networks of chemically coupled neurons. We show that clusters of phase synchronous neurons may emerge before the onset of phase synchronization in the whole network, producing a suitable environment for information exchanging. Furthermore, we show the relation between the localized sets and the amount of information that coupled chaotic oscillator can exchange

Positronium S state spectrum: analytic results at O(m alpha^6)

We present an analytic calculation of the O(m alpha^6) recoil and radiative recoil corrections to energy levels of positronium nS states and their hyperfine splitting. A complete analytic formula valid to O(m alpha^6) is given for the spectrum of S states. Technical aspects of the calculation are discussed in detail. Theoretical predictions are given for various energy intervals and compared with experimental results.Comment: 29 pages, revte

A new intracellular serine protease inhibitor expressed in the rat pituitary gland complexes with granzyme B

AbstractWe have cloned a novel serpin (raPIT5a) from a rat pituitary cDNA library which is structurally related to members of the ovalbumin subfamily of serine protease inhibitors. This new cDNA encodes a 374-amino acid protein, designated raPIT5a. raPIT5a was expressed in specific cells in the intermediate and anterior lobes of the pituitary. Recombinant raPIT5a was not secreted suggesting raPIT5a functions to inhibit intracellular proteases. Recombinant raPIT5a formed an SDS-stable complex with human granzyme B, a serine protease which induces apoptosis by activating members of the caspase enzyme family. These data suggest raPIT5a may have a role in regulating granzyme B or related enzymes and apoptosis in the pituitary gland

Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions

We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a pair of basic realizations of the algebra of N=2 pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is identified with either a boson-phermion or a boson-abnormal-phermion exchange symmetry. We further establish the physical equivalence (non-equivalence) of phermions (abnormal phermions) with ordinary fermions, describe the underlying Lie algebras, and study multi-particle systems of abnormal phermions. The latter provides a certain bosonization of multi-fermion systems.Comment: 20 pages, to appear in J.Phys.

How model sets can be determined by their two-point and three-point correlations

We show that real model sets with real internal spaces are determined, up to translation and changes of density zero by their two- and three-point correlations. We also show that there exist pairs of real (even one dimensional) aperiodic model sets with internal spaces that are products of real spaces and finite cyclic groups whose two- and three-point correlations are identical but which are not related by either translation or inversion of their windows. All these examples are pure point diffractive. Placed in the context of ergodic uniformly discrete point processes, the result is that real point processes of model sets based on real internal windows are determined by their second and third moments.Comment: 19 page

Edge overload breakdown in evolving networks

We investigate growing networks based on Barabasi and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. the load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, as the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than preferential attachment (as defines the Barabasi and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.