Quadratic Forms on Complex Random Matrices and Multiple-Antenna Systems

This research published in the foremost international journal in information theory and shows interplay between complex random matrix and multiantenna information theory. Dr T. Ratnarajah is leader in this area of research and his work has been contributed in the development of graduate curricula (course reader) in Massachusetts Institute of Technology (MIT), USA, By Professor Alan Edelman. The course name is "The Mathematics and Applications of Random Matrices", see http://web.mit.edu/18.338/www/projects.html

New results on a classical operator

It is remarkable how the classical Volterra integral operator, which was one of the first operators which attracted mathematicians' attention, is still worth of being studied. In this essentially survey work, by collecting some of the very recent results related to the Volterra operator, we show that there are new (and not so new) concepts that are becoming known only at the present days. Discovering whether the Volterra operator satisfies or not a given operator property leads to new methods and ideas that are useful in the setting of Concrete Operator Theory as well as the one of General Operator Theory. In particular, a wide variety of techniques like summability kernels, theory of entire functions, Gaussian cylindrical measures, approximation theory, Laguerre and Legendre polynomials are needed to analyze different properties of the Volterra operator. We also include a characterization of the commutator of the Volterra operator acting on L-P[0, 1], 1

Sensory and intrinsic coordination of movement

A recently generalized theory of perceptual guidance (general tau theory) was used to analyse coordination in skilled movement. The theory posits that (i) guiding movement entails controlling closure of spatial and/or force gaps between effecters and goals, by sensing and regulating the tau s of the gaps (the time-to-closure at current closure rate), (ii) a principal way of coordinating movements is keeping the rs of different gaps in constant ratio (known as tau-coupling), and (iii) intrinsically paced movements are guided and coordinated by tau-coupling onto a tau-guide, tau(g), generated in the nervous system and described by the equation tau(g) = 0.5(t-T-2/t) where T is the duration of the body movement and t is the time from the start of the movement. Kinematic analysis of hand to mouth movements by human adults, with eyes open or closed, indicated that hand guidance was achieved by maintaining, during 80-85% of the movement, the tau-couplings tau(alpha)-tau(t) and tau(t)-tau(g), where tau(t) is tau of the hand-mouth gap, tau(alpha) is tau of the angular gap to be closed by steering the hand and tau(g) is an intrinsic tau-guide.

Neonatal control of sucking pressures

Human newborns appear to regulate sucking pressure when bottle feeding by employing, with similar precision, the same principle of control evidenced by adults in skilled behavior, such as reaching (Lee et al., 1998a). In particular, the present study of 12 full-term newborn infants indicated that the intraoral sucking pressures followed an internal dynamic prototype - an intrinsic tau-guide. The intrinsic tau-guide, a recent hypothesis of general tau theory is a time-varying quantity, tau(g), assumed to be generated within the nervous system. It corresponds to some quantity (e.g., electrical charge), chang ing with a constant second-order temporal derivative from a rest level to a goal level, in the sense that tau(g) equals tau of the gap between the quantity and its goal level at each time t. (tau of a gap is the rime-to-closure of the gap at the current closure-rate.) According to the hypoth esis, the infant senses tau(p), the tau of the gap between the current intraoral pressure and its goal level, and regulates intraoral pressure so that tau(p) and tau(g) remain coupled in a constant ratio, k; i.e., tau(p) = k tau(g). With k in the range 0-1, the tau-coupling would result in a bell-shaped rate of change pressure profile, as was, in fact, found. More specifically, the high mean r(2) values obtained when regressing tau(p) on tau(g), for both the increasing and decreasing suction periods of the infants' suck, supported a strong tau-coupling between tau(p) and tau(g). The mean k values were significantly higher In the Increasing suction period, indicating that the ending of the movement was more forceful, a finding which makes sense given the different functions of the two periods of the suck.

Temporal guidance of musicians’ performance movement is an acquired skill

The ancillary (non-sounding) body movements made by expert musicians during performance have been shown to indicate expressive, emotional, and structural features of the music to observers, even if the sound of the performance is absent. If such ancillary body movements are a component of skilled musical performance, then it should follow that acquiring the temporal control of such movements is a feature of musical skill acquisition. This proposition is tested using measures derived from a theory of temporal guidance of movement, “General Tau Theory” (Lee in Ecol Psychol 10:221–250, 1998; Lee et al. in Exp Brain Res 139:151–159, 2001), to compare movements made during performances of intermediate-level clarinetists before and after learning a new piece of music. Results indicate that the temporal control of ancillary body movements made by participants was stronger in performances after the music had been learned and was closer to the measures of temporal control found for an expert musician’s movements. These findings provide evidence that the temporal control of musicians’ ancillary body movements develops with musical learning. These results have implications for other skillful behaviors and nonverbal communication.