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

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

Noncommutative Lattices and Their Continuum Limits

We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra \cc(M) of continuous functions on $M$. We show how to recover the space $M$ and the algebra \cc(M) from a projective system of noncommutative lattices and an inductive system of noncommutative $C^*$-algebras, respectively.Comment: 22 pages, 8 Figures included in the LaTeX Source New version, minor modifications (typos corrected) and a correction in the list of author

Theta phase synchronization between the human hippocampus and prefrontal cortex increases during encoding of unexpected information: A case study

Events that violate predictions are thought to not only modulate activity within the hippocampus and PFC but also enhance communication between the two regions. Scalp and intracranial EEG studies have shown that oscillations in the theta frequency band are enhanced during processing of contextually unexpected information. Some theories suggest that the hippocampus and PFC interact during processing of unexpected events, and it is possible that theta oscillations may mediate these interactions. Here, we had the rare opportunity to conduct simultaneous electrophysiological recordings from the human hippocampus and PFC from two patients undergoing presurgical evaluation for pharmacoresistant epilepsy. Recordings were conducted during a task that involved encoding of contextually expected and unexpected visual stimuli. Across both patients, hippocampal–prefrontal theta phase synchronization was significantly higher during encoding of contextually unexpected study items, relative to contextually expected study items. Furthermore, the hippocampal–prefrontal theta phase synchronization was larger for contextually unexpected items that were later remembered compared with later forgotten items. Moreover, we did not find increased theta synchronization between the PFC and rhinal cortex, suggesting that the observed effects were specific to prefrontal–hippocampal interactions. Our findings are consistent with the idea that theta oscillations orchestrate communication between the hippocampus and PFC in support of enhanced encoding of contextually deviant information

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

Cardiac myosin binding protein-C variants in paediatric-onset hypertrophic cardiomyopathy: natural history and clinical outcomes

Background: Variants in the cardiac myosin-binding protein C gene (MYBPC3) are a common cause of hypertrophic cardiomyopathy (HCM) in adults and have been associated with late-onset disease, but there are limited data on their role in paediatric-onset HCM. The objective of this study was to describe natural history and clinical outcomes in a large cohort of children with HCM and pathogenic/likely pathogenic (P/LP) MYBPC3 variants. / Methods and results: Longitudinal data from 62 consecutive patients diagnosed with HCM under 18 years of age and carrying at least one P/LP MYBPC3 variant were collected from a single specialist referral centre. The primary patient outcome was a major adverse cardiac event (MACE). Median age at diagnosis was 10 (IQR: 2–14) years, with 12 patients (19.4%) diagnosed in infancy. Forty-seven (75%) were boy and 31 (50%) were probands. Median length of follow-up was 3.1 (IQR: 1.6–6.9) years. Nine patients (14.5%) experienced an MACE during follow-up and five (8%) died. Twenty patients (32.3%) had evidence of ventricular arrhythmia, including 6 patients (9.7%) presenting with out-of-hospital cardiac arrest. Five-year freedom from MACE for those with a single or two MYBPC3 variants was 95.2% (95% CI: 78.6% to 98.5%) and 68.4% (95% CI: 40.6% to 88.9%), respectively (HR 4.65, 95% CI: 1.16 to 18.66, p=0.03). / Conclusions: MYBPC3 variants can cause childhood-onset disease, which is frequently associated with life-threatening ventricular arrhythmia. Clinical outcomes in this cohort vary substantially from aetiologically and genetically mixed paediatric HCM cohorts described previously, highlighting the importance of identifying specific genetic subtypes for clinical management of childhood HCM

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

Random graphs with arbitrary degree distributions and their applications

Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in the past. In this paper we develop in detail the theory of random graphs with arbitrary degree distributions. In addition to simple undirected, unipartite graphs, we examine the properties of directed and bipartite graphs. Among other results, we derive exact expressions for the position of the phase transition at which a giant component first forms, the mean component size, the size of the giant component if there is one, the mean number of vertices a certain distance away from a randomly chosen vertex, and the average vertex-vertex distance within a graph. We apply our theory to some real-world graphs, including the world-wide web and collaboration graphs of scientists and Fortune 1000 company directors. We demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.Comment: 19 pages, 11 figures, some new material added in this version along with minor updates and correction

Statistical mechanics of complex networks

Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks is governed by robust organizing principles. Here we review the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, we discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, as well as the interplay between topology and the network's robustness against failures and attacks.Comment: 54 pages, submitted to Reviews of Modern Physic

Some Like It Fat: Comparative Ultrastructure of the Embryo in Two Demosponges of the Genus Mycale (Order Poecilosclerida) from Antarctica and the Caribbean

0000-0002-7993-1523© 2015 Riesgo et al. This is an open access article distributed under the terms of the Creative Commons Attribution License [4.0], which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article