A note on the algebraic growth rate of Poincar\'e series for Kleinian groups

In this note we employ infinite ergodic theory to derive estimates for the algebraic growth rate of the Poincar\'e series for a Kleinian group at its critical exponent of convergence.Comment: 8 page

Traces in complex hyperbolic geometry.

We discuss the relationship between the geometry of complex hyperbolic manifolds and orbifolds and the traces of elements of the corresponding subgroup of SU(2, 1). We begin by showing how geometrical information about individual isometries is encoded by their trace. We then consider traces for groups Γ of isometries in two specific cases. First, we consider the case where Γ is a free group on two generators, which we view as the fundamental group of a three holed sphere. We indicate how to use this analysis to give complex hyperbolic Fenchel-Nielsen coordinates. Secondly, we consider the case where Γ is a triangle group generated by complex reflections in three complex lines. We keep in mind similar results from the more familiar setting of Fuchsian and Kleinian groups and we explain those examples from our point of view

Methods to estimate the cost effectiveness threshold for the NHS

This presentation was delivered by Professor Mark Sculpher from the University of York, UK on 6th September 2011, as part of the HERG Seminar Series. The speaker is a Professor of Health Economics

The effect of neural adaptation of population coding accuracy

Most neurons in the primary visual cortex initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. The functional consequences of adaptation are unclear. Typically a reduction of firing rate would reduce single neuron accuracy as less spikes are available for decoding, but it has been suggested that on the population level, adaptation increases coding accuracy. This question requires careful analysis as adaptation not only changes the firing rates of neurons, but also the neural variability and correlations between neurons, which affect coding accuracy as well. We calculate the coding accuracy using a computational model that implements two forms of adaptation: spike frequency adaptation and synaptic adaptation in the form of short-term synaptic plasticity. We find that the net effect of adaptation is subtle and heterogeneous. Depending on adaptation mechanism and test stimulus, adaptation can either increase or decrease coding accuracy. We discuss the neurophysiological and psychophysical implications of the findings and relate it to published experimental data.Comment: 35 pages, 8 figure

Optical characterization of marine phytoplankton assemblages within surface waters of the western Arctic Ocean.

An extensive data set of measurements within the Chukchi and Beaufort Seas is used to characterize the optical properties of seawater associated with different phytoplankton communities. Hierarchical cluster analysis of diagnostic pigment concentrations partitioned stations into four distinct surface phytoplankton communities based on taxonomic composition and average cell size. Concurrent optical measurements of spectral absorption and backscattering coefficients and remote-sensing reflectance were used to characterize the magnitudes and spectral shapes of seawater optical properties associated with each phytoplankton assemblage. The results demonstrate measurable differences among communities in the average spectral shapes of the phytoplankton absorption coefficient. Similar or smaller differences were also observed in the spectral shapes of nonphytoplankton absorption coefficients and the particulate backscattering coefficient. Phytoplankton on average, however, contributed only 25% or less to the total absorption coefficient of seawater. Our analyses indicate that the interplay between the magnitudes and relative contributions of all optically significant constituents generally dampens any influence of varying phytoplankton absorption spectral shapes on the total absorption coefficient, yet there is still a marked discrimination observed in the spectral shape of the ratio of the total backscattering to total absorption coefficient and remote-sensing reflectance among the phytoplankton assemblages. These spectral variations arise mainly from differences in the bio-optical environment in which specific communities were found, as opposed to differences in the spectral shapes of phytoplankton optical properties per se. These results suggest potential approaches for the development of algorithms to assess phytoplankton community composition from measurements of seawater optical properties in western Arctic waters

Exploring the ethics of human-centred design

This seminar was delivered on 27th April 2012 by Dr Marc Steen, a senior scientist in human-centred design, co-design, open innovation and innovation management at TNO, a not-for profit organization for research and innovation in The Netherlands (www.tno.nl). He earned MSc, MTD and PhD degrees in Industrial Design Engineering at Delft University of Technology. Before joining TNO, he worked at Philips and KPN. Marc works in international projects TA2 (www.ta2-project.eu) and WeCare (www.wecare-project.eu) and for national and international clients. He is particularly interested in questions concerning creativity and cooperation, participation and empowerment, and ethics and reflexivity. The presentation was hosted at Brunel University as part of the Human Centred Design Institute (HCDI) Research Seminar Series. HCDI is a University Research Centre (URC) that brings together expertise in Human-centred Design which combines methodologies and technologies from design, engineering, computer science, artificial intelligence and philosophy. Human-centred Design leads to machines, systems and products which are physically, cognitively and emotionally intuitive to their users. The Human Centre Design seminar series are events designed to encourage communication and teamwork with colleagues across the university and experts leaders in human-centred related topics.This seminar will explore the ethics of human-centred design (HCD), where HCD is meant to refer to innovation processes that include user involvement and co-design (ISO 13407). Based on critical reflection in several HCD projects, and drawing from three schools of ethics, the idea is explored that the process of HCD has intrinsic ethical qualities: Ethics-of-alterity (Levinas, Derrida) helps to see HCD as a fragile encounter between other and self; Pragmatist ethics (Dewey) helps to construe HCD as a process of joint inquiry and imagination; and Virtue ethics (Aristotle) helps to understand the virtues of cooperation, curiosity, creativity and care. In addition, reflexivity is proposed as a way for practitioners to cope more mindfully with the ethical qualities, so that HCD projects can more effectively promote participation and empowerment, and help people to flourish. Moreover, one idea for future research is proposed: To study the relationships between our ways of organizing HCD, processes of participation and empowerment, and the effects on actually improving people’s well-being

A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Limiting modular symbols and their fractal geometry

In this paper we use fractal geometry to investigate boundary aspects of the first homology group for finite coverings of the modular surface. We obtain a complete description of algebraically invisible parts of this homology group. More precisely, we first show that for any modular subgroup the geodesic forward dynamic on the associated surface admits a canonical symbolic representation by a finitely irreducible shift space. We then use this representation to derive an `almost complete' multifractal description of the higher--dimensional level sets arising from Manin--Marcolli's limiting modular symbols.Comment: 20 pages, 1 figur

Acquisition of visual priors and induced hallucinations in chronic schizophrenia

Prominent theories suggest that symptoms of schizophrenia stem from learning deficiencies resulting in distorted internal models of the world. To test these theories further, we used a visual statistical learning task known to induce rapid implicit learning of the stimulus statistics. In this task, participants are presented with a field of coherently moving dots and are asked to report the presented direction of the dots (estimation task), and whether they saw any dots or not (detection task). Two of the directions were more frequently presented than the others. In controls, the implicit acquisition of the stimuli statistics influences their perception in two ways: (i) motion directions are perceived as being more similar to the most frequently presented directions than they really are (estimation biases); and (ii) in the absence of stimuli, participants sometimes report perceiving the most frequently presented directions (a form of hallucinations). Such behaviour is consistent with probabilistic inference, i.e. combining learnt perceptual priors with sensory evidence. We investigated whether patients with chronic, stable, treated schizophrenia (n = 20) differ from controls (n = 23) in the acquisition of the perceptual priors and/or their influence on perception. We found that although patients were slower than controls, they showed comparable acquisition of perceptual priors, approximating the stimulus statistics. This suggests that patients have no statistical learning deficits in our task. This may reflect our patients’ relative wellbeing on antipsychotic medication. Intriguingly, however, patients experienced significantly fewer (P = 0.016) hallucinations of the most frequently presented directions than controls when the stimulus was absent or when it was very weak (prior-based lapse estimations). This suggests that prior expectations had less influence on patients’ perception than on controls when stimuli were absent or below perceptual threshold