Positive Transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps

In this paper we will develop a general approach which shows that generalized "critical relations" of families of locally defined holomorphic maps on the complex plane unfold transversally. The main idea is to define a transfer operator, which is a local analogue of the Thurston pullback operator, using holomorphic motions. Assuming a so-called lifting property is satisfied, we obtain information about the spectrum of this transfer operator and thus about transversality. An important new feature of our method is that it is not global: the maps we consider are only required to be defined and holomorphic on a neighbourhood of some finite set. We will illustrate this method by obtaining transversality for a wide class of one-parameter families of interval and circle maps, for example for maps with flat critical points, but also for maps with complex analytic extensions such as certain polynomial-like maps. As in Tsujii's approach \cite{Tsu0,Tsu1}, for real maps we obtain {\em positive} transversality (where $>0$ holds instead of just $\ne 0$), and thus monotonicity of entropy for these families, and also (as an easy application) for the real quadratic family. This method additionally gives results for unimodal families of the form $x\mapsto |x|^\ell+c$ for $\ell>1$ not necessarily an even integer and $c$ real

Topological Entanglement Entropy of a Bose-Hubbard Spin Liquid

The Landau paradigm of classifying phases by broken symmetries was demonstrated to be incomplete when it was realized that different quantum Hall states could only be distinguished by more subtle, topological properties. Today, the role of topology as an underlying description of order has branched out to include topological band insulators, and certain featureless gapped Mott insulators with a topological degeneracy in the groundstate wavefunction. Despite intense focus, very few candidates for these topologically ordered "spin liquids" exist. The main difficulty in finding systems that harbour spin liquid states is the very fact that they violate the Landau paradigm, making conventional order parameters non-existent. Here, we uncover a spin liquid phase in a Bose-Hubbard model on the kagome lattice, and measure its topological order directly via the topological entanglement entropy. This is the first smoking-gun demonstration of a non-trivial spin liquid, identified through its entanglement entropy as a gapped groundstate with emergent Z2 gauge symmetry.Comment: 4+ pages, 3 figure

Positron kinetics in an idealized PET environment

The kinetic theory of non-relativistic positrons in an idealized positron emission tomography PET environment is developed by solving the Boltzmann equation, allowing for coherent and incoherent elastic, inelastic, ionizing and annihilating collisions through positronium formation. An analytic expression is obtained for the positronium formation rate, as a function of distance from a spherical source, in terms of the solutions of the general kinetic eigenvalue problem. Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue. Comparisons are made with the 'gas-phase' assumption used in current models in which coherent scattering is suppressed. Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations

Characteristic Energy of the Coulomb Interactions and the Pileup of States

Tunneling data on $\mathrm{La_{1.28}Sr_{1.72}Mn_2O_7}$ crystals confirm Coulomb interaction effects through the $\sqrt{\mathrm{E}}$ dependence of the density of states. Importantly, the data and analysis at high energy, E, show a pileup of states: most of the states removed from near the Fermi level are found between ~40 and 130 meV, from which we infer the possibility of universal behavior. The agreement of our tunneling data with recent photoemission results further confirms our analysis.Comment: 4 pages, 4 figures, submitted to PR

Identifying Topological Order by Entanglement Entropy

Topological phases are unique states of matter incorporating long-range quantum entanglement, hosting exotic excitations with fractional quantum statistics. We report a practical method to identify topological phases in arbitrary realistic models by accurately calculating the Topological Entanglement Entropy (TEE) using the Density Matrix Renormalization Group (DMRG). We argue that the DMRG algorithm naturally produces a minimally entangled state, from amongst the quasi-degenerate ground states in a topological phase. This proposal both explains the success of this method, and the absence of ground state degeneracy found in prior DMRG sightings of topological phases. We demonstrate the effectiveness of the calculational procedure by obtaining the TEE for several microscopic models, with an accuracy of order $10^{-3}$ when the circumference of the cylinder is around ten times the correlation length. As an example, we definitively show the ground state of the quantum $S=1/2$ antiferromagnet on the kagom\'e lattice is a topological spin liquid, and strongly constrain the full identification of this phase of matter.Comment: 20 pages, 6 figure

The fire toxicity of polyurethane foams [Review]

Polyurethane is widely used, with its two major applications, soft furnishings and insulation, having low thermal inertia, and hence enhanced flammability. In addition to their flammability, polyurethanes form carbon monoxide, hydrogen cyanide and other toxic products on decomposition and combustion. The chemistry of polyurethane foams and their thermal decomposition are discussed in order to assess the relationship between the chemical and physical composition of the foam and the toxic products generated during their decomposition. The toxic product generation during flaming combustion of polyurethane foams is reviewed, in order to relate the yields of toxic products and the overall fire toxicity to the fire conditions. The methods of assessment of fire toxicity are outlined in order to understand how the fire toxicity of polyurethane foams may be quantified. In particular, the ventilation condition has a critical effect on the yield of the two major asphyxiants, carbon monoxide and hydrogen cyanid

Is Bacterial Persistence a Social Trait?

The ability of bacteria to evolve resistance to antibiotics has been much reported in recent years. It is less well-known that within populations of bacteria there are cells which are resistant due to a non-inherited phenotypic switch to a slow-growing state. Although such ‘persister’ cells are receiving increasing attention, the evolutionary forces involved have been relatively ignored. Persistence has a direct benefit to cells because it allows survival during catastrophes–a form of bet-hedging. However, persistence can also provide an indirect benefit to other individuals, because the reduced growth rate can reduce competition for limiting resources. This raises the possibility that persistence is a social trait, which can be influenced by kin selection. We develop a theoretical model to investigate the social consequences of persistence. We predict that selection for persistence is increased when: (a) cells are related (e.g. a single, clonal lineage); and (b) resources are scarce. Our model allows us to predict how the level of persistence should vary with time, across populations, in response to intervention strategies and the level of competition. More generally, our results clarify the links between persistence and other bet-hedging or social behaviours

Epidemiological trends in nosocomial candidemia in intensive care

BACKGROUND: Infection represents a frequent complication among patients in Intensive Care Units (ICUs) and mortality is high. In particular, the incidence of fungal infections, especially due to Candida spp., has been increasing during the last years. METHODS: In a retrospective study we studied the etiology of candidemia in critically ill patients over a five-year period (1999–2003) in the ICU of the San Martino University Hospital in Genoa, Italy. RESULTS: In total, 182 episodes of candidaemia were identified, with an average incidence of 2.22 episodes/10 000 patient-days/year (range 1.25–3.06 episodes). Incidence of candidemia increased during the study period from 1.25 in 1999 to 3.06/10 000 patient-days/year in 2003. Overall, 40% of the fungemia episodes (74/182) were due to C.albicans, followed by C. parapsilosis(23%), C.glabrata (15%), C.tropicalis (9%) and other species (13%). Candidemia due to non-albicans species increased and this was apparently correlated with an increasing use of azoles for prophylaxis or empirical treatment. CONCLUSION: The study demonstrates a shift in the species of Candida causing fungemia in a medical and surgical ICU population during a 5 year period. The knowledge of the local epidemiological trends in Candida species isolated in blood cultures is important to guide therapeutic choices

A Risk Score for Predicting Multiple Sclerosis

Multiple sclerosis (MS) develops as a result of environmental influences on the genetically susceptible. Siblings of people with MS have an increased risk of both MS and demonstrating asymptomatic changes in keeping with MS. We set out to develop an MS risk score integrating both genetic and environmental risk factors. We used this score to identify siblings at extremes of MS risk and attempted to validate the score using brain MRI.78 probands with MS, 121 of their unaffected siblings and 103 healthy controls were studied. Personal history was taken, and serological and genetic analysis using the illumina immunochip was performed. Odds ratios for MS associated with each risk factor were derived from existing literature, and the log values of the odds ratios from each of the risk factors were combined in an additive model to provide an overall score. Scores were initially calculated using log odds ratio from the HLA-DRB1*1501 allele only, secondly using data from all MS-associated SNPs identified in the 2011 GWAS. Subjects with extreme risk scores underwent validation studies. MRI was performed on selected individuals.There was a significant difference in the both risk scores between people with MS, their unaffected siblings and healthy controls (p<0.0005). Unaffected siblings had a risk score intermediate to people with MS and controls (p<0.0005). The best performing risk score generated an AUC of 0.82 (95%CI 0.75–0.88).The risk score demonstrates an AUC on the threshold for clinical utility. Our score enables the identification of a high-risk sibling group to inform pre-symptomatic longitudinal studies