Uniform asymptotics of the coefficients of unitary moment polynomials

Keating and Snaith showed that the $2k^{th}$ absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by a polynomial of degree $k^2$. In this article, uniform asymptotics for the coefficients of that polynomial are derived, and a maximal coefficient is located. Some of the asymptotics are given in explicit form. Numerical data to support these calculations are presented. Some apparent connections between random matrix theory and the Riemann zeta function are discussed.Comment: 31 pages, 1 figure, 2 tables. A few minor misprints fixe

Entropy of complex relevant components of Boolean networks

Boolean network models of strongly connected modules are capable of capturing the high regulatory complexity of many biological gene regulatory circuits. We study numerically the previously introduced basin entropy, a parameter for the dynamical uncertainty or information storage capacity of a network as well as the average transient time in random relevant components as a function of their connectivity. We also demonstrate that basin entropy can be estimated from time-series data and is therefore also applicable to non-deterministic networks models.Comment: 8 pages, 6 figure

The Ammann-Beenker tilings revisited

This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all be seen as digitization of two-dimensional planes in the four-dimensional Euclidean space. This family contains the Ammann-Beenker tilings as the solution of a simple optimization problem.Comment: 7 pages, 4 figure

Semi-autonomous competency assessment of powered mobility device users

This paper describes a stand-alone sensor package and algorithms for aiding the assessment by an occupational therapist whether a person has the capacity to safely and effectively operate a powered mobility device such as a walking aid or a wheelchair. The sensor package employed consists of a laser range finder, an RGB camera and an inertial measurement unit that can be attached to any mobility device with minimal modifications. Algorithms for capturing the data received by the sensor package and for generating the map of the environment as well as the trajectory of the mobility device have been developed. Such information presents occupational therapists with the capability to provide a quantitative assessment of whether patients are ready to be safely deployed with mobile aids for their daily activities. Preliminary evaluation of the sensor package and associated algorithms based on experiments, conducted at the premises of the Prince of Wales Hospital in Sydney, are presented. © 2011 IEEE

What is a crystal?

Almost 25 years have passed since Shechtman discovered quasicrystals, and 15 years since the Commission on Aperiodic Crystals of the International Union of Crystallography put forth a provisional definition of the term crystal to mean ``any solid having an essentially discrete diffraction diagram.'' Have we learned enough about crystallinity in the last 25 years, or do we need more time to explore additional physical systems? There is much confusion and contradiction in the literature in using the term crystal. Are we ready now to propose a permanent definition for crystal to be used by all? I argue that time has come to put a sense of order in all the confusion.Comment: Submitted to Zeitschrift fuer Kristallographi

Правове регулювання повторного шлюбу у римському та ранньовізантійському праві

В статті досліджується традиційна проблема інституту повторного шлюбу в контексті його еволюції на засадах античних та християнських цінностей.В статье исследуется традиционная проблема института повторного брака в контексте его эволюции на принципах античных и христианских ценностей.In the article the traditional problem of institute of the deuterogamy is probed in the context of its evolution on principles of ancient and christian values

Is Your Error My Concern? An Event-Related Potential Study on Own and Observed Error Detection in Cooperation and Competition

Electroencephalogram studies have identified an error-related event-related potential (ERP) component known as the error-related negativity or ERN, thought to result from the detection of a loss of reward during performance monitoring. However, as own errors are always associated with a loss of reward, disentangling whether the ERN is error- or reward-dependent has proven to be a difficult endeavor. Recently, an ERN has also been demonstrated following the observation of other’s errors. Importantly, other people’s errors can be associated with loss or gain depending on the cooperative or competitive context in which they are made. The aim of the current ERP study was to disentangle the error- or reward-dependency of performance monitoring. Twelve pairs (N = 24) of participants performed and observed a speeded-choice-reaction task in two contexts. Own errors were always associated with a loss of reward. Observed errors in the cooperative context also yielded a loss of reward, but observed errors in the competitive context resulted in a gain. The results showed that the ERN was present following all types of errors independent of who made the error and the outcome of the action. Consequently, the current study demonstrates that performance monitoring as reflected by the ERN is error-specific and not directly dependent on reward