Stratified Kelvin–Helmholtz turbulence of compressible shear flows

We study scaling laws of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin–Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16 3842) and three-dimensional (with a spatial resolution of 5123) configurations utilizing different compressibility characteristics such as shocks. For three-dimensional turbulence, we find that both the kinetic energy and density-weighted energy spectra follow the classical Kolmogorov k−5∕3 inertial scaling. This phenomenon is observed due to the fact that the power density spectrum of three-dimensional turbulence yields the same k−5∕3 scaling. However, we demonstrate that there is a significant difference between these two spectra in two-dimensional turbulence since the power density spectrum yields a k−5∕3 scaling. This difference may be assumed to be a reason for the k−7∕3 scaling observed in the two-dimensional density-weight kinetic every spectra for high compressibility as compared to the k−3 scaling traditionally assumed with incompressible flows. Further inquiries are made to validate the statistical behavior of the various configurations studied through the use of the Helmholtz decomposition of both the kinetic velocity and density-weighted velocity fields. We observe that the scaling results are invariant with respect to the compressibility parameter when the density-weighted definition is used. Our two-dimensional results also confirm that a large inertial range of the solenoidal component with the k−3 scaling can be obtained when we simulate with a lower compressibility parameter; however, the compressive spectrum converges to k−2 for a larger compressibility parameter

Gopakumar-Vafa invariants via vanishing cycles

In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. We also give a counter-example to the Kiem-Li conjectures, where our invariants match the predicted answer. Finally, we give examples where our invariant matches the expected answer in cases where the cycle is non-reduced, non-planar, or non-primitive.Comment: 63 pages, many improvements of the exposition following referee comments, final version to appear in Inventione

A L\'evy input fluid queue with input and workload regulation

We consider a queuing model with the workload evolving between consecutive i.i.d.\ exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y_i(t)$ that is reflected at zero, and where the environment $i$ equals 0 or 1. When the exponential clock $e_q^{(i)}$ ends, the workload, as well as the L\'evy input process, are modified; this modification may depend on the current value of the workload, the maximum and the minimum workload observed during the previous cycle, and the environment $i$ of the L\'evy input process itself during the previous cycle. We analyse the steady-state workload distribution for this model. The main theme of the analysis is the systematic application of non-trivial functionals, derived within the framework of fluctuation theory of L\'evy processes, to workload and queuing models

An open and parallel multiresolution framework using block-based adaptive grids

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid computations. The implementation of the scheme is fully parallel using MPI with a hybrid data structure. Load balancing relies on space filling curves techniques. Validation tests for 2D advection equations allow to assess the precision and performance of the developed code. Computations of the compressible Navier-Stokes equations for a temporally developing 2D mixing layer illustrate the properties of the code for nonlinear multi-scale problems. The code is open source

Convergence of the all-time supremum of a L\'evy process in the heavy-traffic regime

In this paper we derive a technique of obtaining limit theorems for suprema of L\'evy processes from their random walk counterparts. For each $a>0$, let $\{Y^{(a)}_n:n\ge 1\}$ be a sequence of independent and identically distributed random variables and $\{X^{(a)}_t:t\ge 0\}$ be a L\'evy processes such that $X_1^{(a)}\stackrel{d}{=} Y_1^{(a)}$, $\mathbb E X_1^{(a)}<0$ and $\mathbb E X_1^{(a)}\uparrow0$ as $a\downarrow0$. Let $S^{(a)}_n=\sum_{k=1}^n Y^{(a)}_k$. Then, under some mild assumptions, $\Delta(a)\max_{n\ge 0} S_n^{(a)}\stackrel{d}{\to} R\iff\Delta(a)\sup_{t\ge 0} X^{(a)}_t\stackrel{d}{\to} R$, for some random variable $R$ and some function $\Delta(\cdot)$. We utilize this result to present a number of limit theorems for suprema of L\'evy processes in the heavy-traffic regime

A Novel Biclustering Approach to Association Rule Mining for Predicting HIV-1–Human Protein Interactions

Identification of potential viral-host protein interactions is a vital and useful approach towards development of new drugs targeting those interactions. In recent days, computational tools are being utilized for predicting viral-host interactions. Recently a database containing records of experimentally validated interactions between a set of HIV-1 proteins and a set of human proteins has been published. The problem of predicting new interactions based on this database is usually posed as a classification problem. However, posing the problem as a classification one suffers from the lack of biologically validated negative interactions. Therefore it will be beneficial to use the existing database for predicting new viral-host interactions without the need of negative samples. Motivated by this, in this article, the HIV-1–human protein interaction database has been analyzed using association rule mining. The main objective is to identify a set of association rules both among the HIV-1 proteins and among the human proteins, and use these rules for predicting new interactions. In this regard, a novel association rule mining technique based on biclustering has been proposed for discovering frequent closed itemsets followed by the association rules from the adjacency matrix of the HIV-1–human interaction network. Novel HIV-1–human interactions have been predicted based on the discovered association rules and tested for biological significance. For validation of the predicted new interactions, gene ontology-based and pathway-based studies have been performed. These studies show that the human proteins which are predicted to interact with a particular viral protein share many common biological activities. Moreover, literature survey has been used for validation purpose to identify some predicted interactions that are already validated experimentally but not present in the database. Comparison with other prediction methods is also discussed

Detecting a conditional extrme value model

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value model assumes a domain of attraction condition on a sub-collection of the components of a multivariate random vector. This model has been studied in \cite{heffernan:tawn:2004,heffernan:resnick:2007,das:resnick:2008a}. In this paper we propose three statistics which act as tools to detect this model in a bivariate set-up. In addition, the proposed statistics also help to distinguish between two forms of the limit measure that is obtained in the model.Comment: 21 pages, 4 figure

D-brane Deconstructions in IIB Orientifolds

With model building applications in mind, we collect and develop basic techniques to analyze the landscape of D7-branes in type IIB compact Calabi-Yau orientifolds, in three different pictures: F-theory, the D7 worldvolume theory and D9-anti-D9 tachyon condensation. A significant complication is that consistent D7-branes in the presence of O7^- planes are generically singular, with singularities locally modeled by the Whitney Umbrella. This invalidates the standard formulae for charges, moduli space and flux lattice dimensions. We infer the correct formulae by comparison to F-theory and derive them independently and more generally from the tachyon picture, and relate these numbers to the closed string massless spectrum of the orientifold compactification in an interesting way. We furthermore give concrete recipes to explicitly and systematically construct nontrivial D-brane worldvolume flux vacua in arbitrary Calabi-Yau orientifolds, illustrate how to read off D-brane flux content, enhanced gauge groups and charged matter spectra from tachyon matrices, and demonstrate how brane recombination in general leads to flux creation, as required by charge conservation and by equivalence of geometric and gauge theory moduli spaces.Comment: 49 pages, v2: two references adde

Predictors of Poor Perinatal Outcome following Maternal Perception of Reduced Fetal Movements: A Prospective Cohort Study

Background Maternal perception of reduced fetal movement (RFM) is associated with increased risk of stillbirth and fetal growth restriction (FGR). RFM is thought to represent fetal compensation to conserve energy due to insufficient oxygen and nutrient transfer resulting from placental insufficiency. Objective To identify predictors of poor perinatal outcome after maternal perception of reduced fetal movements (RFM). Design Prospective cohort study. Methods 305 women presenting with RFM after 28 weeks of gestation were recruited. Demographic factors and clinical history were recorded and ultrasound performed to assess fetal biometry, liquor volume and umbilical artery Doppler. A maternal serum sample was obtained for measurement of placentally-derived or modified proteins including: alpha fetoprotein (AFP), human chorionic gonadotrophin (hCG), human placental lactogen (hPL), ischaemia-modified albumin (IMA), pregnancy associated plasma protein A (PAPP-A) and progesterone. Factors related to poor perinatal outcome were determined by logistic regression. Results 22.1% of pregnancies ended in a poor perinatal outcome after RFM. The most common complication was small-for-gestational age infants. Pregnancy outcome after maternal perception of RFM was related to amount of fetal activity while being monitored, abnormal fetal heart rate trace, diastolic blood pressure, estimated fetal weight, liquor volume, serum hCG and hPL. Following multiple logistic regression abnormal fetal heart rate trace (Odds ratio 7.08, 95% Confidence Interval 1.31–38.18), (OR) diastolic blood pressure (OR 1.04 (95% CI 1.01–1.09), estimated fetal weight centile (OR 0.95, 95% CI 0.94–0.97) and log maternal serum hPL (OR 0.13, 95% CI 0.02–0.99) were independently related to pregnancy outcome. hPL was related to placental mass. Conclusion Poor perinatal outcome after maternal perception of RFM is closely related to factors which are connected to placental dysfunction. Novel tests of placental function and associated fetal response may provide improved means to detect fetuses at greatest risk of poor perinatal outcome after RFM