Extrapolated High-Order Propagators for Path Integral Monte Carlo Simulations

We present a new class of high-order imaginary time propagators for path-integral Monte Carlo simulations by subtracting lower order propagators. By requiring all terms of the extrapolated propagator be sampled uniformly, the subtraction only affects the potential part of the path integral. The negligible violation of positivity of the resulting path integral at small time steps has no discernable affect on the accuracy of our method. Thus in principle arbitrarily high order algorithms can be devised for path-integral Monte Carlo simulations. We verify this claim is by showing that fourth, sixth, and eighth order convergence can indeed be achieved in solving for the ground state of strongly interacting quantum many-body systems such as bulk liquid $^4$He.Comment: 9 pages and 3 figures. Submitted to J. Chem. Phy

OPTIMISATION OF THE FELGE TO HANDSTAND ON PARALLEL BARS

The felge, or undersomersault, to handstand on parallel bars has become an important skill in Men’s Artistic Gymnastics as it forms the basis of many complex variations. To receive no deductions from the judges, the felge must be performed without demonstrating the use of strength to achieve the final handstand position. Two male gymnasts each performed nine trials of the felge from handstand to handstand while data were recorded using an automatic motion capture system. The highest and lowest scoring trials of each gymnast, as determined by four international judges, were chosen for further analysis. The technique used by each gymnast was optimised using a computer simulation model so that the final handstand position could be achieved with straight arms. Two separate optimisations found different techniques identified in the coaching literature that are used by gymnasts. Although the stoop stalder technique used by the two gymnasts was found to be more demanding than the clear circle technique in terms of the strength required, it offered the potential for more consistent performance and future developments in skill complexity

Entropic effects in large-scale Monte Carlo simulations

The efficiency of Monte Carlo samplers is dictated not only by energetic effects, such as large barriers, but also by entropic effects that are due to the sheer volume that is sampled. The latter effects appear in the form of an entropic mismatch or divergence between the direct and reverse trial moves. We provide lower and upper bounds for the average acceptance probability in terms of the Renyi divergence of order 1/2. We show that the asymptotic finitude of the entropic divergence is the necessary and sufficient condition for non-vanishing acceptance probabilities in the limit of large dimensions. Furthermore, we demonstrate that the upper bound is reasonably tight by showing that the exponent is asymptotically exact for systems made up of a large number of independent and identically distributed subsystems. For the last statement, we provide an alternative proof that relies on the reformulation of the acceptance probability as a large deviation problem. The reformulation also leads to a class of low-variance estimators for strongly asymmetric distributions. We show that the entropy divergence causes a decay in the average displacements with the number of dimensions n that are simultaneously updated. For systems that have a well-defined thermodynamic limit, the decay is demonstrated to be n^{-1/2} for random-walk Monte Carlo and n^{-1/6} for Smart Monte Carlo (SMC). Numerical simulations of the LJ_38 cluster show that SMC is virtually as efficient as the Markov chain implementation of the Gibbs sampler, which is normally utilized for Lennard-Jones clusters. An application of the entropic inequalities to the parallel tempering method demonstrates that the number of replicas increases as the square root of the heat capacity of the system.Comment: minor corrections; the best compromise for the value of the epsilon parameter in Eq. A9 is now shown to be log(2); 13 pages, 4 figures, to appear in PR

The Vascularization Pattern of the Colon and Surgical Decision in Esophageal Reconstruction with Colon. A Selective SMA and IMA Arteriographic Study

Rezumat Pattern-ul de vascularizaåie al colonului aei decizia chirurgicalã în reconstrucåia esofagianã cu colon -studiu arteriografic selectiv al AMS aei AMI Introducere: Indiferent de tehnica reconstructivã, conceptele de fundamentare din reconstrucåia visceralã au ca baza principalã suportul vascular necesar pentru grefonul de substituåie. Particularitãåile vasculare individuale pot înclina sau chiar obliga chirurgul la o anumitã opåiune cãtre unul sau altul dintre procedee. De aceea, vascularizaåia este, fãrã îndoialã, factorul care dominã mobilizarea colonului pentru reconstrucåia esofagianã. Material aei metodã: Studiul nostru arteriografic aei-a propus o investigaåie asupra tiparului vascular al celor douã surse principale ce participã prin vasele emergente la irigarea arterialã a colonului: a. mezentericã superioarã (AMS) respectiv a. mezentericã inferioarã (AMI). Nu am avut în vedere selectarea pacienåilor dupã un anumit criteriu dupã cum nu am realizat nici o excludere dintr-un anumit considerent. Lotul de studiu a constat din 49 de pacienåi care s-au prezentat în clinicã pentru o tehnicã reconstructivã, toåi aparåinând perioadei 2000-2010. În intervalul 1981-2012, au fost efectuate 187 de tehnici reconstructive pentru o indicaåie postcausticã. Din totalul de 49 de pacienåi, 11 bolnavi suferiserã intervenåii chirurgicale abdominale majore iar dintre aceaetia, 5 cu tentative nereuaeite de reconstrucåie. Rezultate: Din cei 49 de pacienåi la care s-a efectuat explorarea, arteriografia a evidenåiat o situaåie favorabilã reconstrucåiei la 31 dintre aceştia. La ceilalåi 18 pacienåi au fost identificate anomalii ori distribuåii atipice, 5 ale AMS respectiv 13 ale AMI. Decizia operatorie a fost ajustatã la 22 de bolnavi. Un lucru important de semnalat dpdv predictiv asupra viscerul de mobilizat: nu am avut necroze de grefon la pacienåii cu examinare arteriograficã preoperatorie. Concluzii: Dictate de necesitatea unei bune mobilizãri, ligaturile arteriale trebuie adaptate şi modificate în funcåie de particularitãåile de distribuåie vascularã, astfel încât sã se menåinã un flux sangvin suficient în arcada marginalã pânã la nivelul secåiunilor colice şi, implicit, în arterele drepte din vecinãtatea acestora. main grounds the mandatory vascular support for the graft replacement. Individual vascular particularities can influence or even oblige the surgeon to choose a certain procedure. This is why the vascularization is beyond doubt the dominant factor in mobilizing the colon for reconstruction. Material and method: Our arteriographic study entails an investigation upon the vascularization pattern of the two main sources that participate in the arterial irrigation of the colon via the emerging vessels: superior mesenteric artery (SMA) and inferior mesenteric artery (IMA). We did not consider certain patients upon a specific criterion; also, we did not exclude any patients due to various reasons. We took into account 49 patients as study group, all of them having registered into the clinic for a reconstructive technique, throughout the years from 2000 to 2010. From 1981 to 2012 there have been 187 reconstructive techniques performed due to post caustic pathology. From a total of 49 patients, 11 had suffered major abdominal surgeries, 5 of which had had unsuccessful reconstructive attempts. Results: Out of the 49 patients on whom we have performed the exploration, arteriography showed a favorable situation for reconstruction in 31 of them. In the other 18 patients anomalies or atypical distributions were identified, in 5 of the SMA and in 13 of the IMA, respectively. Operative decision was modified in 22 patients. One important thing to note from the point of view of the segment to be moved: we had no graft necrosis in patients with preoperative arteriographic examination. Conclusions: Due to the need for good mobilization, arterial ligations should be adjusted and modified depending on the particular vascular distribution, to maintain a sufficient blood flow in the marginal artery, in order to reach the colic sections and the straight arteries near them. Abbreviations: SMA -superior mesenteric artery; IMAinferior mesenteric artery; ICa -ileocolic artery; RCa -right colic artery; MCa -middle colic artery; LCa -left colic artery; LC acc.a -left accessory colic artery (or middle left colic artery); ILCa -inferior left colic artery; S trunk -sigmoidian trunk; Sa -sigmoidian artery; SRa -superior rectal arter

On the efficient Monte Carlo implementation of path integrals

We demonstrate that the Levy-Ciesielski implementation of Lie-Trotter products enjoys several properties that make it extremely suitable for path-integral Monte Carlo simulations: fast computation of paths, fast Monte Carlo sampling, and the ability to use different numbers of time slices for the different degrees of freedom, commensurate with the quantum effects. It is demonstrated that a Monte Carlo simulation for which particles or small groups of variables are updated in a sequential fashion has a statistical efficiency that is always comparable to or better than that of an all-particle or all-variable update sampler. The sequential sampler results in significant computational savings if updating a variable costs only a fraction of the cost for updating all variables simultaneously or if the variables are independent. In the Levy-Ciesielski representation, the path variables are grouped in a small number of layers, with the variables from the same layer being statistically independent. The superior performance of the fast sampling algorithm is shown to be a consequence of these observations. Both mathematical arguments and numerical simulations are employed in order to quantify the computational advantages of the sequential sampler, the Levy-Ciesielski implementation of path integrals, and the fast sampling algorithm.Comment: 14 pages, 3 figures; submitted to Phys. Rev.

Moments of spectral functions: Monte Carlo evaluation and verification

The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable against time whenever the potential function is arbitrarily smooth. Here, I demonstrate that the numerical differentiation of the estimating functionals can be more successfully implemented by means of pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial interpolant), which utilize information from the entire interval $(-\beta \hbar / 2, \beta \hbar/2)$. The algorithmic detail that leads to robust numerical approximations is the fact that the path integral action and not the actual estimating functional are interpolated. Although the resulting approximation to the estimating functional is non-linear, the derivatives can be computed from it in a fast and stable way by contour integration in the complex plane, with the help of the Cauchy integral formula (e.g., by Lyness' method). An interesting aspect of the present development is that Hamburger's conditions for a finite sequence of numbers to be a moment sequence provide the necessary and sufficient criteria for the computed data to be compatible with the existence of an inversion algorithm. Finally, the issue of appearance of the sign problem in the computation of moments, albeit in a milder form than for other quantities, is addressed.Comment: 13 pages, 2 figure

Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is ``experimental'', I only provide a ``physicist's'' proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in the Appendix, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present article is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now treated as independent from their continuous version; new examples of discrete short-time approximations of order three and four are given; a new appendix containing a short review on Brownian motion has been added; also, some additional explanations are provided here and there; this is the last version; to appear in Phys. Rev.

Codynamics of Four Variables Involved in Dengue Transmission and Its Control by Community Intervention: A System of Four Difference Equations

In the case of Dengue transmission and control, the interaction of nature and society is captured by a system of difference equations. For the purpose of studying the dynamics of these interactions, four variables involved in a Dengue epidemic: proportion of infected people (P), number of mosquitoes involved in transmission (M), mosquito habitats (H) and population awareness (A), are linked in a system of difference equations: [equation omitted]. The constraints have socio-ecological meaning. The initial conditions are such that 0 P0 1; (M0;H0;A0) (0; 0; 0), the parameters l,a, c, r 2 (0; 1), and the parameters f, i, b and p are positive. The paper is concerned with the analysis of solutions of the above system for p = q. We studied the global asymptotic stability of the degenerate equilibrium. We also propose extensions of the above model and some open problems. We explored the role of memory in community awareness by numerical simulations. When the memory parameter is large, the proportion of infected people decreases and stabilizes at zero. Below a critical point we observe periodic oscillations

Pro-inflammatory endothelial cell dysfunction is associated with intersectin-1s down-regulation

<p>Abstract</p> <p>Background</p> <p>The response of lung microvascular endothelial cells (ECs) to lipopolysaccharide (LPS) is central to the pathogenesis of lung injury. It is dual in nature, with one facet that is pro-inflammatory and another that is cyto-protective. In previous work, overexpression of the anti-apoptotic Bcl-X_L rescued ECs from apoptosis triggered by siRNA knockdown of intersectin-1s (ITSN-1s), a pro-survival protein crucial for ECs function. Here we further characterized the cyto-protective EC response to LPS and pro-inflammatory dysfunction.</p> <p>Methods and Results</p> <p>Electron microscopy (EM) analyses of LPS-exposed ECs revealed an activated/dysfunctional phenotype, while a biotin assay for caveolae internalization followed by biochemical quantification indicated that LPS causes a 40% inhibition in biotin uptake compared to controls. Quantitative PCR and Western blotting were used to evaluate the mRNA and protein expression, respectively, for several regulatory proteins of intrinsic apoptosis, including ITSN-1s. The decrease in ITSN-1s mRNA and protein expression were countered by Bcl-X_L and survivin upregulation, as well as Bim downregulation, events thought to protect ECs from impending apoptosis. Absence of apoptosis was confirmed by TUNEL and lack of cytochrome c (cyt c) efflux from mitochondria. Moreover, LPS exposure caused induction and activation of inducible nitric oxide synthase (iNOS) and a mitochondrial variant (mtNOS), as well as augmented mitochondrial NO production as measured by an oxidation oxyhemoglobin (oxyHb) assay applied on mitochondrial-enriched fractions prepared from LPS-exposed ECs. Interestingly, expression of myc-ITSN-1s rescued caveolae endocytosis and reversed induction of iNOS expression.</p> <p>Conclusion</p> <p>Our results suggest that ITSN-1s deficiency is relevant for the pro-inflammatory ECs dysfunction induced by LPS.</p