Critical points and resonance of hyperplane arrangements

If F is a master function corresponding to a hyperplane arrangement A and a collection of weights y, we investigate the relationship between the critical set of F, the variety defined by the vanishing of the one-form w = d log F, and the resonance of y. For arrangements satisfying certain conditions, we show that if y is resonant in dimension p, then the critical set of F has codimension at most p. These include all free arrangements and all rank 3 arrangements.Comment: revised version, Canadian Journal of Mathematics, to appea

Public injecting and public amenity in an inner-city suburb of Melbourne, Australia

Background: Public drug markets and injecting impose significant burden on individuals and the community. This study aimed to document public injecting and amenity in North Richmond, an inner-city suburb of Melbourne, Australia. Methods: A rapid assessment methodology was employed. Data comprised: secondary data on drug use indicators, structured observations and interviews with key stakeholders. Primary data were collected from May to October 2012. Quantitative data are summarised using descriptive statistics. Basic content analysis was performed on interview transcripts. Results: An average of 1843 needle–syringes (NS) were collected per month from syringe disposal bins and street-sweeps in the period January–December 2012. Discarded NS and other injecting paraphernalia were observed in a variety of locations. Stakeholder interviews indicated substantial concerns over the presence of NS and witnessing injecting and overdose. Discussion: Public injecting is widespread, frequent, and highly visible in North Richmond and has a substantial negative effect on public amenity. The research identified two main priorities: (1) enhance access to harm reduction services and materials; and (2) improve public amenity. Among other responses, the study findings support the introduction of a supervised injecting facility (SIF) as a viable component of a comprehensive harm reduction response to illicit drug use in this area

Critical Points and Resonance of Hyperplane Arrangements

If $\Phi_\lambda$ is a master function corresponding to a hyperplane arrangement $\mathcal A$ and a collection of weights $\lambda$, we investigate the relationship between the critical set of $\Phi_\lambda$, the variety defined by the vanishing of the one-form $\omega_\lambda=\operatorname{d} \log \Phi_\lambda$, and the resonance of $\lambda$. For arrangements satisfying certain conditions, we show that if $\lambda$ is resonant in dimension $p$, then the critical set of $\Phi_\lambda$ has codimension at most $p$. These include all free arrangements and all rank $3$ arrangements

The role of perceived source location in auditory stream segregation: separation affects sound organization, common fate does not

The human auditory system is capable of grouping sounds originating from different sound sources into coherent auditory streams, a process termed auditory stream segregation. Several cues can influence auditory stream segregation, but the full set of cues and the way in which they are integrated is still unknown. In the current study, we tested whether auditory motion can serve as a cue for segregating sequences of tones. Our hypothesis was that, following the principle of common fate, sounds emitted by sources moving together in space along similar trajectories will be more likely to be grouped into a single auditory stream, while sounds emitted by independently moving sources will more often be heard as two streams. Stimuli were derived from sound recordings in which the sound source motion was induced by walking humans. Although the results showed a clear effect of spatial separation, auditory motion had a negligible influence on stream segregation. Hence, auditory motion may not be used as a primitive cue in auditory stream segregation

Varying levels of clonality and ploidy create barriers to gene flow and challenges for conservation of an Australian arid-zone ecosystem engineer, Acacia loderi

Acacia loderi, the ecosystem engineer of the endangered Acacia loderi Shrublands in arid eastern Australia, spans a persistent (\u3e 15 000 year) but poorly studied landscape feature, the Darling River. We investigated the genetic structure of 19 stands of eight to \u3e 1000 plants separated by \u3c 300 km to test for variation in life histories between semi-arid and arid stands to the east and west of the Darling River, respectively. Eight of nine stands east of the Darling were exclusively sexual, whereas most of those to the west were clonal. Three western stands were monoclonal, two were polyploid, and one was a diverse mix of diploid and triploid phenotypes. Bayesian analysis revealed a complex genetic structure within the western stands, whereas the eastern stands formed only two genetic clusters. Conservation of small stands may require augmentation of genotypic diversity. However, most genotypic diversity resides within the eastern stands. Although arid zone stands of A. loderi are not always clonal, clonality and polyploidy are more common in the arid west. Clear demarcation of life histories either side of the Darling River may reflect ancient or contemporary effects of physical disturbance associated with the river channel, or cryptic environmental differences, with sexual and asexual reproduction, respectively, at a selective premium in the semi-arid east and arid west. The restricted distribution of clones and variation in clonality and polyploidy suggests that smaller stands may be vulnerable and warrant individual management

A robust sound perception model suitable for neuromorphic implementation

Coath M, Sheik S, Chicca E, Indiveri G, Denham S, Wennekers T. A robust sound perception model suitable for neuromorphic implementation. Neuromorphic Engineering. 2014;7(278):1-10.We have recently demonstrated the emergence of dynamic feature sensitivity through exposure to formative stimuli in a real-time neuromorphic system implementing a hybrid analog/digital network of spiking neurons. This network, inspired by models of auditory processing in mammals, includes several mutually connected layers with distance-dependent transmission delays and learning in the form of spike timing dependent plasticity, which effects stimulus-driven changes in the network connectivity. Here we present results that demonstrate that the network is robust to a range of variations in the stimulus pattern, such as are found in naturalistic stimuli and neural responses. This robustness is a property critical to the development of realistic, electronic neuromorphic systems. We analyze the variability of the response of the network to “noisy” stimuli which allows us to characterize the acuity in information-theoretic terms. This provides an objective basis for the quantitative comparison of networks, their connectivity patterns, and learning strategies, which can inform future design decisions. We also show, using stimuli derived from speech samples, that the principles are robust to other challenges, such as variable presentation rate, that would have to be met by systems deployed in the real world. Finally we demonstrate the potential applicability of the approach to real sounds

Single- and double-scattering production of four muons in ultraperipheral PbPb collisions at the Large Hadron Collider

We discuss production of two $\mu^+\mu^-$ pairs in ultraperipheral ultrarelativistic heavy ion collisions at the LHC. We take into account electromagnetic (two-photon) double-scattering production and for a first time direct $\gamma\gamma$ production of four muons in one scattering. We study the unexplored process $\gamma \gamma \to \mu^+\mu^-\mu^+\mu^-$. We present predictions for total and differential cross sections. Measurable nuclear cross sections are obtained and corresponding differential distributions and counting rates are presented.Comment: 13 pages, 11 figures, 1 tabl

On the Rational Type 0f Moment Angle Complexes

In this note it is shown that the moment angle complexes Z(K;(D^2,,S^1)) which are rationally elliptic are a product of odd spheres and a diskComment: This version avoids the use of an incorrect result from the literature in the proof of Theorem 1.3. There is some text overlap with arXiv:1410.645