Cohomology of U(2,1) representation varieties of surface groups

In this paper we use the Morse theory of the Yang-Mills-Higgs functional on the singular space of Higgs bundles on Riemann surfaces to compute the equivariant cohomology of the space of semistable U(2,1) and SU(2,1) Higgs bundles with fixed Toledo invariant. In the non-coprime case this gives new results about the topology of the U(2,1) and SU(2,1) character varieties of surface groups. The main results are a calculation of the equivariant Poincare polynomials, a Kirwan surjectivity theorem in the non-fixed determinant case, and a description of the action of the Torelli group on the equivariant cohomology of the character variety. This builds on earlier work for stable pairs and rank 2 Higgs bundles.Comment: 34 page

Collaborating on Referring Expressions

This paper presents a computational model of how conversational participants collaborate in order to make a referring action successful. The model is based on the view of language as goal-directed behavior. We propose that the content of a referring expression can be accounted for by the planning paradigm. Not only does this approach allow the processes of building referring expressions and identifying their referents to be captured by plan construction and plan inference, it also allows us to account for how participants clarify a referring expression by using meta-actions that reason about and manipulate the plan derivation that corresponds to the referring expression. To account for how clarification goals arise and how inferred clarification plans affect the agent, we propose that the agents are in a certain state of mind, and that this state includes an intention to achieve the goal of referring and a plan that the agents are currently considering. It is this mental state that sanctions the adoption of goals and the acceptance of inferred plans, and so acts as a link between understanding and generation.Comment: 32 pages, 2 figures, to appear in Computation Linguistics 21-

Additive Extensions of a Quantum Channel

We study extensions of a quantum channel whose one-way capacities are described by a single-letter formula. This provides a simple technique for generating powerful upper bounds on the capacities of a general quantum channel. We apply this technique to two qubit channels of particular interest--the depolarizing channel and the channel with independent phase and amplitude noise. Our study of the latter demonstrates that the key rate of BB84 with one-way post-processing and quantum bit error rate q cannot exceed H(1/2-2q(1-q)) - H(2q(1-q)).Comment: 6 pages, one figur

Unlocking medical leadership’s potential:a multilevel virtuous circle?

Background and aim: Medical leadership (ML) has been introduced in many countries, promising to support healthcare services improvement and help further system reform through effective leadership behaviours. Despite some evidence of its success, such lofty promises remain unfulfilled. Method: Couched in extant international literature, this paper provides a conceptual framework to analyse ML's potential in the context of healthcare's complex, multifaceted setting. Results: We identify four interrelated levels of analysis, or domains, that influence ML's potential to transform healthcare delivery. These are the healthcare ecosystem domain, the professional domain, the organisational domain and the individual doctor domain. We discuss the tensions between the various actors working in and across these domains and argue that greater multilevel and multistakeholder collaborative working in healthcare is necessary to reprofessionalise and transform healthcare ecosystems

Classical signature of quantum annealing

A pair of recent articles concluded that the D-Wave One machine actually operates in the quantum regime, rather than performing some classical evolution. Here we give a classical model that leads to the same behaviors used in those works to infer quantum effects. Thus, the evidence presented does not demonstrate the presence of quantum effects.Comment: 8 pages, 3 pdf figure

How epigenetic evolution can guide genetic evolution (abstract)

The expression level of a gene in future generations can be modified both by genetic mutations and by the attachment of methyl groups to the DNA. Since the DNA methylation pattern along a genome is inherited, methylation patterns constitute a significant epigenetic inheritance mechanism that is subject to evolution by natural selection. The variation rate of methylation patterns is generally higher than that of DNA which suggests that evolution of methylation patterns might be more rapid than that of genetic evolution. But, common consequences of methylation, such as reduced expression of methylated genes, could also be produced by genetic changes and these would have higher heritability. The question we address in this work is how the evolution of epigenetic methylation-dependent phenotypes might interact with the evolution of genetic DNA-determined phenotypes. There is no biological mechanism known to directly transfer methyl groups into equivalent DNA changes. However, in principle an indirect mechanism could cause evolved methylation patterns to enable the subsequent evolution of equivalent genetic patterns in a manner analogous to the Baldwin effect (Baldwin, Am. Nat., 30:441-451, 1896; Jablonka et al, TREE, 13:206-210, 1998). The Baldwin effect describes how non-heritable acquired characteristics can influence the evolution of equivalent genetic characteristics without any direct Lamarckian inheritance of acquired characters. This occurs because the ability to acquire or learn a new behaviour changes the selective pressures acting on genetic changes. Specifically, genetic changes that support this behaviour, e.g. by reducing learning time by making a small part of the behaviour genetically innate, may be selected for when the learning mechanism is present even though these same genetic changes may not be selected for when the learning mechanism is absent. Over generations, the modified selection pressures so produced can cause genetic assimilation of a phenotype that was previously acquired, even to the extent of making the acquisition mechanism subsequently redundant. Thus a learned behaviour can guide the evolution of an equivalent innate behaviour (Hinton & Nowlan, Complex Systems, 1: 495-502, 1987). In the Baldwin effect a rapid mechanism of lifetime adaptation guides the relatively slow genetic evolution of the same behaviour. By analogy, Jablonka et al have suggested that “genetic adaptations may be guided by heritable induced or learnt phenotypic adaptations”. Here we hypothesise that “inherited epigenetic variations may be able to ‘hold’ an adapted state for long enough to allow similar genetic variations to catch up”, as they put it, even if the epigenetic variations are not induced or learnt but simply evolved by natural selection on methylation patterns. We assume that an individual may only express one phenotype in its lifetime, but that a given genome will persist relatively unchanged on a timescale that allows its methylome to adapt by natural selection. Thus, in contrast to the Baldwin effect, in this case two mechanisms of evolution by natural selection are coupled — one acting at a different variation rate from the other. We present a simple model to illustrate how a rapidly evolving methylome can guide a slowly evolving but highly-heritable genome. This is used to show that methylome evolution can enable genetic evolution to cross fitness valleys that would otherwise require multiple genetic changes that were each selected against. This finding suggests that the relatively rapid evolution of methylation patterns can produce novel phenotypes that are subsequently genetically assimilated in DNA evolution without direct transfer or appeal to induced phenotypes. This can enable the genetic evolution of new phenotypes that would not be found by genetic evolution alone, even if methylation is not significant in the ultimate phenotype

A model for phenotype change in a stochastic framework

some species, an inducible secondary phenotype will develop some time after the environmental change that evokes it. Nishimura (2006) [4] showed how an individual organism should optimize the time it takes to respond to an environmental change ("waiting time''). If the optimal waiting time is considered to act over the population, there are implications for the expected value of the mean fitness in that population. A stochastic predator-prey model is proposed in which the prey have a fixed initial energy budget. Fitness is the product of survival probability and the energy remaining for non-defensive purposes. The model is placed in the stochastic domain by assuming that the waiting time in the population is a normally distributed random variable because of biological variance inherent in mounting the response. It is found that the value of the mean waiting time that maximises fitness depends linearly on the variance of the waiting time

The quantum capacity with symmetric side channels

We present an upper bound for the quantum channel capacity that is both additive and convex. Our bound can be interpreted as the capacity of a channel for high-fidelity quantum communication when assisted by a family of channels that have no capacity on their own. This family of assistance channels, which we call symmetric side channels, consists of all channels mapping symmetrically to their output and environment. The bound seems to be quite tight, and for degradable quantum channels it coincides with the unassisted channel capacity. Using this symmetric side channel capacity, we find new upper bounds on the capacity of the depolarizing channel. We also briefly indicate an analogous notion for distilling entanglement using the same class of (one-way) channels, yielding one of the few entanglement measures that is monotonic under local operations with one-way classical communication (1-LOCC), but not under the more general class of local operations with classical communication (LOCC).Comment: 10 pages, 4 figure