Freezing transitions and the density of states of 2D random Dirac Hamiltonians

Using an exact mapping to disordered Coulomb gases, we introduce a novel method to study two dimensional Dirac fermions with quenched disorder in two dimensions which allows to treat non perturbative freezing phenomena. For purely random gauge disorder it is known that the exact zero energy eigenstate exhibits a freezing-like transition at a threshold value of disorder $\sigma=\sigma_{th}=2$. Here we compute the dynamical exponent $z$ which characterizes the critical behaviour of the density of states around zero energy, and find that it also exhibits a phase transition. Specifically, we find that $\rho(E=0 + i \epsilon) \sim \epsilon^{2/z-1}$ (and $\rho(E) \sim E^{2/z-1}$) with $z=1 + \sigma$ for $\sigma < 2$ and $z=\sqrt{8 \sigma} - 1$ for $\sigma > 2$. For a finite system size $L<\epsilon^{-1/z}$ we find large sample to sample fluctuations with a typical $\rho_{\epsilon}(0) \sim L^{z-2}$. Adding a scalar random potential of small variance $\delta$, as in the corresponding quantum Hall system, yields a finite noncritical $\rho(0) \sim \delta^{\alpha}$ whose scaling exponent $\alpha$ exhibits two transitions, one at $\sigma_{th}/4$ and the other at $\sigma_{th}$. These transitions are shown to be related to the one of a directed polymer on a Cayley tree with random signs (or complex) Boltzmann weights. Some observations are made for the strong disorder regime relevant to describe transport in the quantum Hall system

Cardiac magnetic resonance T1 and extracellular volume mapping with motion correction and co-registration based on fast elastic image registration

OBJECTIVE: Our aim was to investigate the technical feasibility of a novel motion compensation method for cardiac magntic resonance (MR) T1 and extracellular volume fraction (ECV) mapping. MATERIALS AND METHODS: Native and post-contrast T1 maps were obtained using modified look-locker inversion recovery (MOLLI) pulse sequences with acquisition scheme defined in seconds. A nonrigid, nonparametric, fast elastic registration method was applied to generate motion-corrected T1 maps and subsequently ECV maps. Qualitative rating was performed based on T1 fitting-error maps and overlay images. Local deformation vector fields were produced for quantitative assessment. Intra- and inter-observer reproducibility were compared with and without motion compensation. RESULTS: Eighty-two T1 and 39 ECV maps were obtained in 21 patients with diverse myocardial diseases. Approximately 60% demonstrated clear quality improvement after motion correction for T1 mapping, particularly for the poor-rating cases (23% before vs 2% after). Approximately 67% showed further improvement with co-registration in ECV mapping. Although T1 and ECV values were not clinically significantly different before and after motion compensation, there was improved intra- and inter-observer reproducibility after motion compensation. CONCLUSIONS: Automated motion correction and co-registration improved the qualitative assessment and reproducibility of cardiac MR T1 and ECV measurements, allowing for more reliable ECV mapping

Conductance Distributions in Random Resistor Networks: Self Averaging and Disorder Lengths

The self averaging properties of conductance $g$ are explored in random resistor networks with a broad distribution of bond strengths P(g)\simg^{\mu-1}. Distributions of equivalent conductances are estimated numerically on hierarchical lattices as a function of size $L$ and distribution tail parameter $\mu$. For networks above the percolation threshold, convergence to a Gaussian basin is always the case, except in the limit $\mu$ --> 0. A {\it disorder length} $\xi_D$ is identified beyond which the system is effectively homogeneous. This length diverges as $\xi_D \sim |\mu|^{-\nu}$ ($\nu$ is the regular percolation correlation length exponent) as $\mu$-->0. This suggest that exactly the same critical behavior can be induced by geometrical disorder and bu strong bond disorder with the bond occupation probability $p$$\mu$. Only lattices at the percolation threshold have renormalized probability distribution in a {\it Levy-like} basin. At the threshold the disorder length diverges at a vritical tail strength $\mu_c$ as $|\mu-\mu_c|^{-z}$, with $z=3.2\pm 0.1$, a new exponent. Critical path analysis is used in a generalized form to give form to give the macroscopic conductance for lattice above $p_c$.Comment: 16 pages plain TeX file, 6 figures available upon request.IBC-1603-01

The Influence of Physiological Status on age Prediction of Anopheles Arabiensis Using Near Infra-red spectroscopy

Determining the age of malaria vectors is essential for evaluating the impact of interventions that reduce the survival of wild mosquito populations and for estimating changes in vectorial capacity. Near infra-red spectroscopy (NIRS) is a simple and non-destructive method that has been used to determine the age and species of Anopheles gambiae s.l. by analyzing differences in absorption spectra. The spectra are affected by biochemical changes that occur during the life of a mosquito and could be influenced by senescence and also the life history of the mosquito, i.e., mating, blood feeding and egg-laying events. To better understand these changes, we evaluated the influence of mosquito physiological status on NIR energy absorption spectra. Mosquitoes were kept in individual cups to permit record keeping of each individual insect’s life history. Mosquitoes of the same chronological age, but at different physiological stages, were scanned and compared using cross-validations. We observed a slight trend within some physiological stages that suggest older insects tend to be predicted as being physiologically more mature. It was advantageous to include mosquitoes of different chronological ages and physiological stages in calibrations, as it increases the robustness of the model resulting in better age predictions. Progression through different physiological statuses of An. arabiensis influences the chronological age prediction by the NIRS. Entomologists that wish to use NIR technology to predict the age of field-caught An. gambiae s.l from their study area should use a calibration developed from their field strain using mosquitoes of diverse chronological ages and physiological stages to increase the robustness and accuracy of the predictions.\u

Lowering the recommended maximal wall thickness threshold improves diagnostic sensitivity in Asians with hypertrophic cardiomyopathy

BACKGROUND: Hypertrophic cardiomyopathy (HCM) is defined as left ventricular end-diastolic maximal wall thickness (WTMax) ≥15.0 mm, without accounting for ethnicity, sex, and body size. It is well-established that Asians have smaller hearts than do Caucasians. OBJECTIVES: This study aims to examine the implications of this single absolute WTMax threshold on the diagnosis of HCM in Asians. METHODS: The study consisted of 360 healthy volunteers (male: n = 174; age: 50 ± 12 years) and 114 genetically characterized patients with HCM (male: n = 83; age: 52 ± 13 years; genotype-positive, n = 39). All participants underwent cardiovascular magnetic resonance. WTMax was measured semiautomatically at end-diastole according to the standard 16 myocardial segments. RESULTS: Healthy male volunteers had increased WTMax compared with that of female volunteers (8.4 ± 1.2 mm vs 6.6 ± 1.1 mm, respectively; P 15.0 mm (specificity of 100% and sensitivity of 51%). Lowering WTMax thresholds to 10.0 mm in female patients and 12.0 mm in male patients did not affect specificity (100%) but significantly improved sensitivity (84%). Despite lower left ventricular mass, female patients with HCM demonstrated more features of adverse cardiac remodeling than did male patients: increased myocardial fibrosis, higher asymmetric ratio, and disproportionately worse myocardial strain. CONCLUSIONS: The study highlights cautious application of guideline-recommended WTMax to diagnose HCM in Asians. Lowering WTMax to account for ethnicity and sex improves diagnostic sensitivity without compromising specificity

Functional Renormalization Group and the Field Theory of Disordered Elastic Systems

We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the renormalization group functions beyond 1-loop order. Even worse, observables such as the 2-point correlation function exhibit the same problem already at 1-loop order. These difficulties are due to the non-analyticity of the renormalized disorder correlator at zero temperature, which is inherent to the physics beyond the Larkin length, characterized by many metastable states. As a result, 2-loop diagrams, which involve derivatives of the disorder correlator at the non-analytic point, are naively "ambiguous''. We examine several routes out of this dilemma, which lead to a unique renormalizable field-theory at 2-loop order. It is also the only theory consistent with the potentiality of the problem. The beta-function differs from previous work and the one at depinning by novel "anomalous terms''. For interfaces and random bond disorder we find a roughness exponent zeta = 0.20829804 epsilon + 0.006858 epsilon^2, epsilon = 4-d. For random field disorder we find zeta = epsilon/3 and compute universal amplitudes to order epsilon^2. For periodic systems we evaluate the universal amplitude of the 2-point function. We also clarify the dependence of universal amplitudes on the boundary conditions at large scale. All predictions are in good agreement with numerical and exact results, and an improvement over one loop. Finally we calculate higher correlation functions, which turn out to be equivalent to those at depinning to leading order in epsilon.Comment: 42 pages, 41 figure

Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior

Quantum anti-Zeno effect without wave function reduction

We study the measurement-induced enhancement of the spontaneous decay (called quantum anti-Zeno effect) for a two-level subsystem, where measurements are treated as couplings between the excited state and an auxiliary state rather than the von Neumann's wave function reduction. The photon radiated in a fast decay of the atom, from the auxiliary state to the excited state, triggers a quasi-measurement, as opposed to a projection measurement. Our use of the term "quasi-measurement" refers to a "coupling-based measurement". Such frequent quasi-measurements result in an exponential decay of the survival probability of atomic initial state with a photon emission following each quasi-measurement. Our calculations show that the effective decay rate is of the same form as the one based on projection measurements. What is more important, the survival probability of the atomic initial state which is obtained by tracing over all the photon states is equivalent to the survival probability of the atomic initial state with a photon emission following each quasi-measurement to the order under consideration. That is because the contributions from those states with photon number less than the number of quasi-measurements originate from higher-order processes.Comment: 7 pages, 3 figure

A Decidable Fragment in Separation Logic with Inductive Predicates and Arithmetic

Singapore National Research Foundatio