Parallel algorithm with spectral convergence for nonlinear integro-differential equations

We discuss a numerical algorithm for solving nonlinear integro-differential equations, and illustrate our findings for the particular case of Volterra type equations. The algorithm combines a perturbation approach meant to render a linearized version of the problem and a spectral method where unknown functions are expanded in terms of Chebyshev polynomials (El-gendi's method). This approach is shown to be suitable for the calculation of two-point Green functions required in next to leading order studies of time-dependent quantum field theory.Comment: 15 pages, 9 figure

Sighting of critically endangered Red-headed vulture Sarcogyps calvus (Scopoli, 1786) in Palamau Tiger Reserve, Jharkhand, India

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A new diagrammatic representation for correlation functions in the in-in formalism

In this paper we provide an alternative method to compute correlation functions in the in-in formalism, with a modified set of Feynman rules to compute loop corrections. The diagrammatic expansion is based on an iterative solution of the equation of motion for the quantum operators with only retarded propagators, which makes each diagram intrinsically local (whereas in the standard case locality is the result of several cancellations) and endowed with a straightforward physical interpretation. While the final result is strictly equivalent, as a bonus the formulation presented here also contains less graphs than other diagrammatic approaches to in-in correlation functions. Our method is particularly suitable for applications to cosmology.Comment: 14 pages, matches the published version. includes a modified version of axodraw.sty that works with the Revtex4 clas

Bayesian Estimation Via Sequential Monte Carlo Sampling-Constrained Dynamic Systems

Nonlinear and non-Gaussian processes with constraints are commonly encountered in dynamic estimation problems. Methods for solving such problems either ignore the constraints or rely on crude approximations of the model or probability distributions. Such approximations may reduce the accuracy of the estimates since they often fail to capture the variety of probability distributions encountered in constrained linear and nonlinear dynamic systems. This article describes a practical approach that overcomes these shortcomings via a novel extension of sequential Monte Carlo (SMC) sampling or particle filtering. Inequality constraints are imposed by accept/reject steps in the algorithm. The proposed approach provides samples representing the posterior distribution at each time point, and is shown to satisfy the same theoretical properties as unconstrained SMC. Illustrative examples show that results of the proposed approach are at least as accurate as moving horizon estimation, but computationally more efficient and in addition, the approach indicates the uncertainty associated with these estimates

Guillain-Barré syndrome after tetanus toxoid, reduced diphtheria toxoid and acellular pertussis vaccine: a case report

<p>Abstract</p> <p>Introduction</p> <p>The association of Guillain-Barré syndrome with vaccination has been described in the literature; it is infrequent and controversial. An association with swine influenza, influenza, hepatitis and tetanus vaccination has been documented in few case reports.</p> <p>Case presentation</p> <p>A 40-year-old Caucasian man sustained a small right temporal epidural hematoma and nondisplaced right skull fractures after a fall from a roof. He was managed conservatively; a tetanus toxoid, reduced diphtheria toxoid and acellular pertussis vaccine was administered and a week later he was discharged home. A few days after his discharge, he experienced weakness and numbness in his legs, which progressed to involve his arms. Three weeks after his initial fall, he was readmitted with quadriparesis. A lumbar puncture revealed a cerebrospinal fluid protein of 790 mg/dL and one white blood cell. We diagnosed Guillain-Barré syndrome. Our patient was treated with intravenous immunoglobulin. Three months later his muscle strength had improved, but he continued to have tingling in his hands and feet and used a walker intermittently.</p> <p>Conclusion</p> <p>To the best of our knowledge, this is the first case of Guillain-Barré syndrome to be reported in the English literature after administration of tetanus toxoid, reduced diphtheria toxoid and acellular pertussis vaccine.</p

WRKY6 restricts Piriformospora indica-stimulated and phosphate-induced root development in Arabidopsis

BACKGROUND: Arabidopsis root growth is stimulated by Piriformospora indica, phosphate limitation and inactivation of the WRKY6 transcription factor. Combinations of these factors induce unexpected alterations in root and shoot growth, root architecture and root gene expression profiles. RESULTS: The results demonstrate that P. indica promotes phosphate uptake and root development under Pi limitation in wrky6 mutant. This is associated with the stimulation of PHOSPHATE1 expression and ethylene production. Expression profiles from the roots of wrky6 seedlings identified genes involved in hormone metabolism, transport, meristem, cell and plastid proliferation, and growth regulation. 25 miRNAs were also up-regulated in these roots. We generated and discuss here a list of common genes which are regulated in growing roots and which are common to all three growth stimuli investigated in this study. CONCLUSION: Since root development of wrky6 plants exposed to P. indica under phosphate limitation is strongly promoted, we propose that common genes which respond to all three growth stimuli are central for the control of root growth and architecture. They can be tested for optimizing root growth in model and agricultural plants. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12870-015-0673-4) contains supplementary material, which is available to authorized users

Shear viscosity of hot scalar field theory in the real-time formalism

Within the closed time path formalism a general nonperturbative expression is derived which resums through the Bethe-Salpter equation all leading order contributions to the shear viscosity in hot scalar field theory. Using a previously derived generalized fluctuation-dissipation theorem for nonlinear response functions in the real-time formalism, it is shown that the Bethe-Salpeter equation decouples in the so-called (r,a) basis. The general result is applied to scalar field theory with pure lambda*phi**4 and mixed g*phi**3+lambda*phi**4 interactions. In both cases our calculation confirms the leading order expression for the shear viscosity previously obtained in the imaginary time formalism.Comment: Expanded introduction and conclusions. Several references and a footnote added. Fig.5 and its discussion in the text modified to avoid double counting. Signs in Eqs. (45) and (53) correcte

A Generalized Fluctuation-Dissipation Theorem for Nonlinear Response Functions

A nonlinear generalization of the Fluctuation-Dissipation Theorem (FDT) for the n-point Green functions and the amputated 1PI vertex functions at finite temperature is derived in the framework of the Closed Time Path formalism. We verify that this generalized FDT coincides with known results for n=2 and 3. New explicit relations among the 4-point nonlinear response and correlation (fluctuation) functions are presented.Comment: 34 pages, Revte