Poisson-to-Wigner crossover transition in the nearest-neighbor spacing statistics of random points on fractals

We show that the nearest-neighbor spacing distribution for a model that consists of random points uniformly distributed on a self-similar fractal is the Brody distribution of random matrix theory. In the usual context of Hamiltonian systems, the Brody parameter does not have a definite physical meaning, but in the model considered here, the Brody parameter is actually the fractal dimension. Exploiting this result, we introduce a new model for a crossover transition between Poisson and Wigner statistics: random points on a continuous family of self-similar curves with fractal dimension between 1 and 2. The implications to quantum chaos are discussed, and a connection to conservative classical chaos is introduced.Comment: Low-resolution figure is included here. Full resolution image available (upon request) from the author

Many Roads to Synchrony: Natural Time Scales and Their Algorithms

We consider two important time scales---the Markov and cryptic orders---that monitor how an observer synchronizes to a finitary stochastic process. We show how to compute these orders exactly and that they are most efficiently calculated from the epsilon-machine, a process's minimal unifilar model. Surprisingly, though the Markov order is a basic concept from stochastic process theory, it is not a probabilistic property of a process. Rather, it is a topological property and, moreover, it is not computable from any finite-state model other than the epsilon-machine. Via an exhaustive survey, we close by demonstrating that infinite Markov and infinite cryptic orders are a dominant feature in the space of finite-memory processes. We draw out the roles played in statistical mechanical spin systems by these two complementary length scales.Comment: 17 pages, 16 figures: http://cse.ucdavis.edu/~cmg/compmech/pubs/kro.htm. Santa Fe Institute Working Paper 10-11-02

Quaternary Structure Defines a Large Class of Amyloid-β Oligomers Neutralized by Sequestration

SummaryThe accumulation of amyloid-β (Aβ) as amyloid fibrils and toxic oligomers is an important step in the development of Alzheimer’s disease (AD). However, there are numerous potentially toxic oligomers and little is known about their neurological effects when generated in the living brain. Here we show that Aβ oligomers can be assigned to one of at least two classes (type 1 and type 2) based on their temporal, spatial, and structural relationships to amyloid fibrils. The type 2 oligomers are related to amyloid fibrils and represent the majority of oligomers generated in vivo, but they remain confined to the vicinity of amyloid plaques and do not impair cognition at levels relevant to AD. Type 1 oligomers are unrelated to amyloid fibrils and may have greater potential to cause global neural dysfunction in AD because they are dispersed. These results refine our understanding of the pathogenicity of Aβ oligomers in vivo

Results from the CERN pilot CLOUD experiment

During a 4-week run in October–November 2006, a pilot experiment was performed at the CERN Proton Synchrotron in preparation for the Cosmics Leaving OUtdoor Droplets (CLOUD) experiment, whose aim is to study the possible influence of cosmic rays on clouds. The purpose of the pilot experiment was firstly to carry out exploratory measurements of the effect of ionising particle radiation on aerosol formation from trace H2SO4 vapour and secondly to provide technical input for the CLOUD design. A total of 44 nucleation bursts were produced and recorded, with formation rates of particles above the 3 nm detection threshold of between 0.1 and 100 cm -3 s -1, and growth rates between 2 and 37 nm h -1. The corresponding H2O concentrations were typically around 106 cm -3 or less. The experimentally-measured formation rates and htwosofour concentrations are comparable to those found in the atmosphere, supporting the idea that sulphuric acid is involved in the nucleation of atmospheric aerosols. However, sulphuric acid alone is not able to explain the observed rapid growth rates, which suggests the presence of additional trace vapours in the aerosol chamber, whose identity is unknown. By analysing the charged fraction, a few of the aerosol bursts appear to have a contribution from ion-induced nucleation and ion-ion recombination to form neutral clusters. Some indications were also found for the accelerator beam timing and intensity to influence the aerosol particle formation rate at the highest experimental SO2 concentrations of 6 ppb, although none was found at lower concentrations. Overall, the exploratory measurements provide suggestive evidence for ion-induced nucleation or ion-ion recombination as sources of aerosol particles. However in order to quantify the conditions under which ion processes become significant, improvements are needed in controlling the experimental variables and in the reproducibility of the experiments. Finally, concerning technical aspects, the most important lessons for the CLOUD design include the stringent requirement of internal cleanliness of the aerosol chamber, as well as maintenance of extremely stable temperatures (variations below 0.1 °C

Critical statistics for non-Hermitian matrices

We introduce a generalized ensemble of nonhermitian matrices interpolating between the Gaussian Unitary Ensemble, the Ginibre ensemble and the Poisson ensemble. The joint eigenvalue distribution of this model is obtained by means of an extension of the Itzykson-Zuber formula to general complex matrices. Its correlation functions are studied both in the case of weak nonhermiticity and in the case of strong nonhermiticity. In the weak nonhermiticity limit we show that the spectral correlations in the bulk of the spectrum display critical statistics: the asymptotic linear behavior of the number variance is already approached for energy differences of the order of the eigenvalue spacing. To lowest order, its slope does not depend on the degree of nonhermiticity. Close the edge, the spectral correlations are similar to the Hermitian case. In the strong nonhermiticity limit the crossover behavior from the Ginibre ensemble to the Poisson ensemble first appears close to the surface of the spectrum. Our model may be relevant for the description of the spectral correlations of an open disordered system close to an Anderson transition.Comment: 25 pages, 6 figure

Efficient RF/microwave modeling of discontinuities in chip packages and boards

A methodology for efficient modeling of discontinuities in chip packages and boards at RF/microwave frequencies is discussed. It commences with a novel approach for defining the boundaries of all geometrical discontinuities in chip packages and boards, because defining the boundaries of discontinuities ensures efficient RF/microwave modeling and measurement of the discontinuities themselves as well as the chip packages and boards in which they are found. It also leads to a reduction in the cost of fabrication of test structures needed for their characterization. Based on the 3D full wave electromagnetic (EM) field computation results of the discontinuities, their electrical parameters were extracted. To validate the modeling technique, test structures were designed, fabricated and measured. A good correlation was obtained between the computed and measured results

Bump arrays for RF applications modeling methodology

The advantages offered by area array packages over peripherally leaded packaging approaches were discussed. The advantages arises from the use of bump arrays for signal transmission from the chip to the package and the package to the board. The design requires accurate electrical models for bump arrays that account for their parasitic effects in the GHz range. It was shown that the electrical parameters extracted from a single bump and two-coupled bumps could be used to characterize any bump array

A novel modelling methodology of bump arrays for RF and high-speed applications

A novel methodology for electrical modelling of bump arrays up to a frequency of 30GHz is presented. It starts with the development of an equivalent circuit model for a single bump. Based on the radio frequency (RF) modelling of this bump, equivalent circuit models were developed for any two parallel or diagonal bumps, which account for their electromagnetic (EM) interactions. These models were then extended to characterise three-coupled bumps in linear and triangular configurations. For these bump arrangements, it was proven, that considering pitches used in RF and high-speed packages, effects of EM coupling between outwardly-placed bumps on EM interaction between the adjacent ones can be neglected. It is actually on this basis, that a combination of all the electrical models developed can be used to characterise any bump array, irrespective of the number of bumps in the array. This was validated using a bump array consisting of four-coupled bumps