Computing singularities of perturbation series

Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the perturbed Hamiltonian on a vector, and does not rely on the terms in the perturbation series. Some illustrative model problems are studied, including a Helium-like model with $\delta$-function interactions for which M{\o}ller--Plesset perturbation theory is considered and the radius of convergence found.Comment: 11 figures, submitte

Solitary coherent structures in viscoelastic shear flow: computation and mechanism

Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large wavelengths, and show hysteresis in the Weissenberg number, similar to experimentally observed ``diwhirl'' patterns. Based on the computed velocity and stress fields, we elucidate a heuristic, fully nonlinear mechanism for these flows. We propose that these localized, fully nonlinear structures comprise fundamental building blocks for complex spatiotemporal dynamics in the flow of elastic liquids.Comment: 5 pages text and 4 figures. Submitted to Physical Review Letter

Coarse Bifurcation Diagrams via Microscopic Simulators: A State-Feedback Control-Based Approach

The arc-length continuation framework is used for the design of state feedback control laws that enable a microscopic simulator trace its own open-loop coarse bifurcation diagram. The steering of the system along solution branches is achieved through the manipulation of the bifurcation parameter, which becomes our actuator. The design approach is based on the assumption that the eigenvalues of the linearized system can be decomposed into two well separated clusters: one containing eigenvalues with large negative real parts and one containing (possibly unstable) eigenvalues close to the origin

Density function associated with nonlinear bifurcating map

In the class of nonlinear one-parameter real maps we study those with bifurcation that exhibits period doubling cascade. The fixed points of such a map form a finite discrete real set with dimension (2^n)m, where m is the (odd) number of "primary branches" of the map in the non-chaotic region and n is a non-negative integer. We associate with this map a nonlinear dynamical system whose Hamiltonian matrix is real, tridiagonal and symmetric. The density of states of the system is calculated and shown to have a number of separated bands equals to (2^n-1)m for n not equal 0, in which case the density has m bands. The location of the bands depends only on the map parameter and the odd/even ordering of the fixed points in the set. Polynomials orthogonal with respect to this density (weight) function are constructed. The logistic map is taken as an illustrative example.Comment: 8 pages of text, 9 figures (one in color

A non-parametric structural hybrid modeling approach for electricity prices

We develop a stochastic model of zonal/regional electricity prices, designed to reflect information in fuel forward curves and aggregated capacity and load as well as zonal or regional price spreads. We use a nonparametric model of the supply stack that captures heat rates and fuel prices for all generators in the market operator territory, combined with an adjustment term to approximate congestion and other zone-specific behavior. The approach requires minimal calibration effort, is readily adaptable to changing market conditions and regulations, and retains sufficient tractability for the purpose of forward price calibration. The model is illustrated for the spot and forward electricity prices of the PS zone in the PJM market, and the set of time-dependent risk premiums are inferred and analyzed

Simulation models predict that school-age children are responsible for most human-to-mosquito Plasmodium falciparum transmission in southern Malawi

Abstract Background Malaria persists in some high-transmission areas despite extensive control efforts. Progress toward elimination may require effective targeting of specific human populations that act as key transmission reservoirs. Methods Parameterized using molecular-based Plasmodium falciparum infection data from cross-sectional community studies in southern Malawi, a simulation model was developed to predict the proportions of human-to-mosquito transmission arising from (a) children under 5 years old (U5s), (b) school-age children (SAC, 5–15 years), (c) young adults (16–30 years), and (d) adults > 30 years. The model incorporates mosquito biting heterogeneity and differential infectivity (i.e. probability that a blood-fed mosquito develops oocysts) by age and gametocyte density. Results The model predicted that SAC were responsible for more than 60% of new mosquito infections in both dry and rainy seasons, even though they comprise only 30% of this southern Malawi population. Young adults were the second largest contributors, while U5s and adults over 30 were each responsible for < 10% of transmission. While the specific predicted values are sensitive to the relative infectiousness of SAC, this group remained the most important contributor to mosquito infections under all realistic estimates. Conclusions These results suggest that U5 children play a small role compared to SAC in maintaining P. falciparum transmission in southern Malawi. Models that assume biting homogeneity overestimate the importance of U5s. To reduce transmission, interventions will need to reach more SAC and young adults. This publicly available model can be used by others to estimate age-specific transmission contributions in epidemiologically similar sites with local parameter estimates of P. falciparum prevalence and bed net use.https://deepblue.lib.umich.edu/bitstream/2027.42/143001/1/12936_2018_Article_2295.pd

A histological method for quantifying Plasmodium falciparum in the brain in fatal paediatric cerebral malaria

Background: The sequestration of Plasmodium falciparum-infected erythrocytes in brain microvasculature through cytoadherence to endothelium, is the hallmark of the definitive diagnosis of cerebral malaria and plays a critical role in malaria pathogenesis. The complex pathophysiology, which leads each patient to the final outcome of cerebral malaria, is multifaceted and thus, metrics to delineate specific patterns within cerebral malaria are needed to further parse patients. Methods: A method was developed for quantification utilizing counts of capillary contents (early-stage parasites, late-stage parasites and fibrin) from histological preparations of brain tissue after death, and compared it to the standard approach, in which the percentage of parasitized vessels in cross-section is determined. Results: Within the initial cohort of 50 patients, two different observers agreed closely on the percentage of vessels parasitized, pigmented parasites and pigment globules (ICC = 0.795-0.970). Correlations between observers for correct diagnostic classification were high (Kendall’s tau-b = 0.8779, Kappa = 0.8413). When these methods were applied prospectively to a second set of 50 autopsy samples, they revealed a heterogeneous distribution of sequestered parasites in the brain with pigmented parasites and pigment globules present in the cerebellum > cortex > brainstem. There was no difference in the distribution of early stages of parasites or in the percentage of vessels parasitized across the same sites. The second cohort of cases was also used to test a previously published classification and regression tree (CART) analysis; the quantitative data alone were able to accurately classify and distinguish cerebral malaria from non-cerebral malaria. Classification errors occurred within a subclassification of cerebral malaria (CM1 vs CM2). A repeat CART analysis for the second cohort generated slightly different classification rules with more accurate subclassification, although misclassification still occurred. Conclusions: The traditional measure of parasite sequestration in falciparum malaria, the percentage of vessels parasitized, is the most reliable and consistent for the general diagnosis of cerebral malaria. Methods that involve quantitative measures of different life cycle stages are useful for distinguishing patterns within the cerebral malaria population; these subclassifications may be important for studies of disease pathogenesis and ancillary treatment

HIV coinfection influences the inflammatory response but not the outcome of cerebral malaria in Malawian children

This work was supported by grants from the NIH (T.E.T., 5R01AI034969-14) and a Clinical Fellowship from The Wellcome Trust, United Kingdom (C.A.M, 88758). The Malawi-Liverpool-Wellcome Clinical Research Programme is supported by core funding from The Wellcome Trust, UK.Objectives. Study of the effect of HIV on disease progression in heterogeneous severe malaria syndromes with imprecise diagnostic criteria has led to varying results. Characteristic retinopathy refines cerebral malaria (CM) diagnosis, enabling more precise exploration of the hypothesis that HIV decreases the cytokine response in CM, leading to higher parasite density and a poor outcome. Methods. We retrospectively reviewed data on clinical progression and laboratory parameters in 877 retinopathy-positive CM cases admitted 1996-2011 (14.4% HIV-infected) to a large hospital in Malawi. Admission plasma levels of TNF, interleukin-10, and soluble intercellular adhesion molecule (sICAM-1) were measured by ELISA in 135 retinopathy-positive CM cases. Results. HIV-infected CM cases had lower median plasma levels of TNF (p=0.008), interleukin-10 (p=0.045) and sICAM-1 (p=0.04) than HIV-uninfected cases. Although HIV-infected children were older and more likely to have co-morbidities, HIV-status did not significantly affect parasite density (p=0.90) or outcome (24.8% infected, vs. 18.5% uninfected; p=0.13). Conclusions. In this well-characterised CM cohort, HIV-coinfection was associated with marked blunting of the inflammatory response but did not affect parasite density or outcome. These data highlight the complex influence of HIV on severe malaria and bring into question systemic inflammation as a primary driver of pathogenesis in human CM.Publisher PDFPeer reviewe