The full infinite dimensional moment problem on semi-algebraic sets of generalized functions

We consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure.

Design of delay-tolerant space–time codes with limited feedback

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. Such a timing mismatch may cause rank deficiency of the conventional space-time codes and, thus, performance degradation. One efficient way to overcome such an issue is the delay-tolerant space-time codes (DT-STCs). The existing DT-STCs are designed assuming that the transmitter has no knowledge about the channels. In this paper, we show how the performance of DT-STCs can be improved by utilizing some feedback information. A general framework for designing DT-STC with limited feedback is first proposed, allowing for flexible system parameters such as the number of transmit/receive antennas, modulated symbols, and the length of codewords. Then, a new design method is proposed by combining Lloyd's algorithm and the stochastic gradient-descent algorithm to obtain optimal codebook of STCs, particularly for systems with linear minimum-mean-square-error receiver. Finally, simulation results confirm the performance of the newly designed DT-STCs with limited feedback.

Accurate delay analysis in prioritised wireless sensor networks for generalized packet arrival

This letter presents an accurate delay analysis in prioritised wireless sensor networks (WSN). The analysis is an enhancement of the existing analysis proposed by Choobkar and Dilmaghani, which is only applicable to the case where the lower priority nodes always have packets to send in the empty slots of the higher priority node. The proposed analysis is applicable for any pattern of packet arrival, which includes the general case where the lower priority nodes may or may not have packets to send in the empty slots of the higher priority nodes. Evaluation of both analyses showed that the proposed delay analysis has better accuracy over the full range of loads and provides an excellent match to simulation results.

Atypically rightward cerebral asymmetry in male adults with autism stratifies individuals with and without language delay

In humans, both language and fine motor skills are associated with left-hemisphere specialization, whereas visuospatial skills are associated with right-hemisphere specialization. Individuals with autism spectrum conditions (ASC) show a profile of deficits and strengths that involves these lateralized cognitive functions. Here we test the hypothesis that regions implicated in these functions are atypically rightward lateralized in individuals with ASC and, that such atypicality is associated with functional performance. Participants included 67 male, right-handed adults with ASC and 69 age- and IQ-matched neurotypical males. We assessed group differences in structural asymmetries in cortical regions of interest with voxel-based analysis of grey matter volumes, followed by correlational analyses with measures of language, motor and visuospatial skills. We found stronger rightward lateralization within the inferior parietal lobule and reduced leftward lateralization extending along the auditory cortex comprising the planum temporale, Heschl's gyrus, posterior supramarginal gyrus, and parietal operculum, which was more pronounced in ASC individuals with delayed language onset compared to those without. Planned correlational analyses showed that for individuals with ASC, reduced leftward asymmetry in the auditory region was associated with more childhood social reciprocity difficulties. We conclude that atypical cerebral structural asymmetry is a potential candidate neurophenotype of ASC