Renormalization and blow up for charge one equivariant critical wave maps

We prove the existence of equivariant finite time blow up solutions for the wave map problem from 2+1 dimensions into the 2-sphere. These solutions are the sum of a dynamically rescaled ground-state harmonic map plus a radiation term. The local energy of the latter tends to zero as time approaches blow up time. This is accomplished by first "renormalizing" the rescaled ground state harmonic map profile by solving an elliptic equation, followed by a perturbative analysis

Memetic Multilevel Hypergraph Partitioning

Hypergraph partitioning has a wide range of important applications such as VLSI design or scientific computing. With focus on solution quality, we develop the first multilevel memetic algorithm to tackle the problem. Key components of our contribution are new effective multilevel recombination and mutation operations that provide a large amount of diversity. We perform a wide range of experiments on a benchmark set containing instances from application areas such VLSI, SAT solving, social networks, and scientific computing. Compared to the state-of-the-art hypergraph partitioning tools hMetis, PaToH, and KaHyPar, our new algorithm computes the best result on almost all instances

H\"older Continuity of the Integrated Density of States for the Fibonacci Hamiltonian

We prove H\"older continuity of the integrated density of states for the Fibonacci Hamiltonian for any positive coupling, and obtain the asymptotics of the H\"older exponents for large and small couplings.Comment: 18 page

Imitation in Large Games

In games with a large number of players where players may have overlapping objectives, the analysis of stable outcomes typically depends on player types. A special case is when a large part of the player population consists of imitation types: that of players who imitate choice of other (optimizing) types. Game theorists typically study the evolution of such games in dynamical systems with imitation rules. In the setting of games of infinite duration on finite graphs with preference orderings on outcomes for player types, we explore the possibility of imitation as a viable strategy. In our setup, the optimising players play bounded memory strategies and the imitators play according to specifications given by automata. We present algorithmic results on the eventual survival of types

The value of real world evidence: the case of medical cannabis

Randomised controlled trials (RCTs) have long been considered the gold standard of medical evidence. In relation to cannabis based medicinal products (CBMPs), this focus on RCTs has led to very restrictive guidelines in the UK, which are limiting patient access. There is general agreement that RCT evidence in relation to CBPMs is insufficient at present. As well as commercial reasons, a major problem is that RCTs do not lend themselves well to the study of whole plant medicines. One solution to this challenge is the use of real world evidence (RWE) with patient reported outcomes (PROs) to widen the evidence base. Such data increasingly highlights the positive impact medical cannabis can have on patients’ lives. This paper outlines the value of this approach which involves the study of interventions and patients longitudinally under medical care. In relation to CBMPs, RWE has a broad range of advantages. These include the study of larger groups of patients, the use of a broader range and ratio of components of CBMPs, and the inclusion of more and rarer medical conditions. Importantly, and in contrast to RCTs, patients with significant comorbidities–and from a wider demographic profile–can also be studied, so providing higher ecological validity and increasing patient numbers, whilst offering significant cost savings. We conclude by outlining 12 key recommendations of the value of RWE in relation to medical cannabis. We hope that this paper will help policymakers and prescribers understand the importance of RWE in relation to medical cannabis and help them develop approaches to overcome the current situation which is detrimental to patients

On the Dynamics of solitons in the nonlinear Schroedinger equation

We study the behavior of the soliton solutions of the equation i((\partial{\psi})/(\partialt))=-(1/(2m)){\Delta}{\psi}+(1/2)W_{{\epsilon}}'({\psi})+V(x){\psi} where W_{{\epsilon}}' is a suitable nonlinear term which is singular for {\epsilon}=0. We use the "strong" nonlinearity to obtain results on existence, shape, stability and dynamics of the soliton. The main result of this paper (Theorem 1) shows that for {\epsilon}\to0 the orbit of our soliton approaches the orbit of a classical particle in a potential V(x).Comment: 29 page

Spectral Analysis for Matrix Hamiltonian Operators

In this work, we study the spectral properties of matrix Hamiltonians generated by linearizing the nonlinear Schr\"odinger equation about soliton solutions. By a numerically assisted proof, we show that there are no embedded eigenvalues for the three dimensional cubic equation. Though we focus on a proof of the 3d cubic problem, this work presents a new algorithm for verifying certain spectral properties needed to study soliton stability. Source code for verification of our comptuations, and for further experimentation, are available at http://www.math.toronto.edu/simpson/files/spec_prop_code.tgz.Comment: 57 pages, 22 figures, typos fixe

Evolution of the complex refractive index in the UV spectral region in ageing secondary organic aerosol

The chemical and physical properties of secondary organic aerosol (SOA) formed by the photochemical degradation of biogenic and anthropogenic volatile organic compounds (VOC) are as yet still poorly constrained. The evolution of the complex refractive index (RI) of SOA, formed from purely biogenic VOC and mixtures of biogenic and anthropogenic VOC, was studied over a diurnal cycle in the SAPHIR photochemical outdoor chamber in Jülich, Germany. The correlation of RI with SOA chemical and physical properties such as oxidation level and volatility was examined. The RI was retrieved by a newly developed broadband cavity-enhanced spectrometer for aerosol optical extinction measurements in the UV spectral region (360 to 420 nm). Chemical composition and volatility of the particles were monitored by a high-resolution time-of-flight aerosol mass spectrometer, and a volatility tandem differential mobility analyzer. SOA was formed by ozonolysis of either (i) a mixture of biogenic VOC (α-pinene and limonene), (ii) biogenic VOC mixture with subsequent addition of an anthropogenic VOC (<i>p</i>-xylene-d₁₀), or (iii) a mixture of biogenic and anthropogenic VOC. The SOA aged by ozone/OH reactions up to 29.5 h was found to be non-absorbing in all cases. The SOA with <i>p</i>-xylene-d₁₀ showed an increase of the scattering component of the RI correlated with an increase of the O / C ratio and with an increase in the SOA density. There was a greater increase in the scattering component of the RI when the SOA was produced from the mixture of biogenic VOCs and anthropogenic VOC than from the sequential addition of the VOCs after approximately the same ageing time. The increase of the scattering component was inversely correlated with the SOA volatility. Two RI retrievals determined for the pure biogenic SOA showed a constant RI for up to 5 h of ageing. Mass spectral characterization shows the three types of the SOA formed in this study have a significant amount of semivolatile components. The influence of anthropogenic VOCs on the oxygenated organic aerosol as well as the atmospheric implications are discussed

Structural models of genome-wide covariance identify multiple common dimensions in autism

Common genetic variation has been associated with multiple symptoms in Autism Spectrum Disorder (ASD). However, our knowledge of shared genetic factor structures contributing to this highly heterogeneous neurodevelopmental condition is limited. Here, we developed a structural equation modelling framework to directly model genome-wide covariance across core and non-core ASD phenotypes, studying autistic individuals of European descent using a case-only design. We identified three independent genetic factors most strongly linked to language/cognition, behaviour and motor development, respectively, when studying a population-representative sample (N=5,331). These analyses revealed novel associations. For example, developmental delay in acquiring personal-social skills was inversely related to language, while developmental motor delay was linked to self-injurious behaviour. We largely confirmed the three-factorial structure in independent ASD-simplex families (N=1,946), but uncovered simplex-specific genetic overlap between behaviour and language phenotypes. Thus, the common genetic architecture in ASD is multi-dimensional and contributes, in combination with ascertainment-specific patterns, to phenotypic heterogeneity

Biases in the perceived timing of perisaccadic perceptual and motor events

Subjects typically experience the temporal interval immediately following a saccade as longer than a comparable control interval. One explanation of this effect is that the brain antedates the perceptual onset of a saccade target to around the time of saccade initiation. This could explain the apparent continuity of visual perception across eye movements. Thisantedating account was tested in three experiments in which subjects made saccades of differing extents and then judged either the duration or the temporal order of key events. Postsaccadic stimuli underwent subjective temporal lengthening and had early perceived onsets. A temporally advanced awareness of saccade completion was also found, independently of antedating effects. These results provide convergent evidence supporting antedating and differentiating it from other temporal biases