On the Critical Behavior of D1-brane Theories

We study renormalization-group flow patterns in theories arising on D1-branes in various supersymmetry-breaking backgrounds. We argue that the theory of N D1-branes transverse to an orbifold space can be fine-tuned to flow to the corresponding orbifold conformal field theory in the infrared, for particular values of the couplings and theta angles which we determine using the discrete symmetries of the model. By calculating various nonplanar contributions to the scalar potential in the worldvolume theory, we show that fine-tuning is in fact required at finite N, as would be generically expected. We further comment on the presence of singular conformal field theories (such as those whose target space includes a ``throat'' described by an exactly solvable CFT) in the non-supersymmetric context. Throughout the analysis two applications are considered: to gauge theory/gravity duality and to linear sigma model techniques for studying worldsheet string theory.Comment: 23 pages in harvmac big, 8 figure

Non-Gaussianity in Island Cosmology

In this paper we fully calculate the non-Gaussianity of primordial curvature perturbation of island universe by using the second order perturbation equation. We find that for the spectral index $n_s\simeq 0.96$, which is favored by current observations, the non-Gaussianity level $f_{NL}$ seen in island will generally lie between 30 $\sim$ 60, which may be tested by the coming observations. In the landscape, the island universe is one of anthropically acceptable cosmological histories. Thus the results obtained in some sense means the coming observations, especially the measurement of non-Gaussianity, will be significant to make clear how our position in the landscape is populated.Comment: 5 pages, 1 eps figure, some discussions added, published versio

Open string instantons and relative stable morphisms

We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri and Vafa from the point of view of physics. By using the method of virtual localization, we successfully reproduce their results for multiple covers of a holomorphic disc, whose boundary lies in a Lagrangian submanifold of a Calabi-Yau 3-fold, by Riemann surfaces with arbitrary genera and number of boundary components. In particular we show that in the case we consider there are no open string instantons with more than one boundary component ending on the Lagrangian submanifold.Comment: This is the version published by Geometry & Topology Monographs on 22 April 200

Descartes' rule of signs and the identifiability of population demographic models from genomic variation data

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the "folded" SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes' rule of signs for polynomials to the Laplace transform of piecewise continuous functions.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1264 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Scope and Mechanistic Study of the Ruthenium-Catalyzed \u3cem\u3eortho\u3c/em\u3e-C−H Bond Activation and Cyclization Reactions of Arylamines with Terminal Alkynes

The cationic ruthenium hydride complex [(PCy3)2(CO)(CH3CN)2RuH]+BF4- was found to be a highly effective catalyst for the C−H bond activation reaction of arylamines and terminal alkynes. The regioselective catalytic synthesis of substituted quinoline and quinoxaline derivatives was achieved from the ortho-C−H bond activation reaction of arylamines and terminal alkynes by using the catalyst Ru3(CO)12/HBF4·OEt2. The normal isotope effect (kCH/kCD = 2.5) was observed for the reaction of C6H5NH2 and C6D5NH2 with propyne. A highly negative Hammett value (ρ = −4.4) was obtained from the correlation of the relative rates from a series of meta-substituted anilines, m-XC6H4NH2, with σp in the presence of Ru3(CO)12/HBF4·OEt2 (3 mol % Ru, 1:3 molar ratio). The deuterium labeling studies from the reactions of both indoline and acyclic arylamines with DC⋮CPh showed that the alkyne C−H bond activation step is reversible. The crossover experiment from the reaction of 1-(2-amino-1-phenyl)pyrrole with DC⋮CPh and HC⋮CC6H4-p-OMe led to preferential deuterium incorporation to the phenyl-substituted quinoline product. A mechanism involving rate-determining ortho-C−H bond activation and intramolecular C−N bond formation steps via an unsaturated cationic ruthenium acetylide complex has been proposed

Fundamental limits on the accuracy of demographic inference based on the sample frequency spectrum

The sample frequency spectrum (SFS) of DNA sequences from a collection of individuals is a summary statistic which is commonly used for parametric inference in population genetics. Despite the popularity of SFS-based inference methods, currently little is known about the information-theoretic limit on the estimation accuracy as a function of sample size. Here, we show that using the SFS to estimate the size history of a population has a minimax error of at least $O(1/\log s)$, where $s$ is the number of independent segregating sites used in the analysis. This rate is exponentially worse than known convergence rates for many classical estimation problems in statistics. Another surprising aspect of our theoretical bound is that it does not depend on the dimension of the SFS, which is related to the number of sampled individuals. This means that, for a fixed number $s$ of segregating sites considered, using more individuals does not help to reduce the minimax error bound. Our result pertains to populations that have experienced a bottleneck, and we argue that it can be expected to apply to many populations in nature.Comment: 17 pages, 1 figur

Quilting Stochastic Kronecker Product Graphs to Generate Multiplicative Attribute Graphs

We describe the first sub-quadratic sampling algorithm for the Multiplicative Attribute Graph Model (MAGM) of Kim and Leskovec (2010). We exploit the close connection between MAGM and the Kronecker Product Graph Model (KPGM) of Leskovec et al. (2010), and show that to sample a graph from a MAGM it suffices to sample small number of KPGM graphs and \emph{quilt} them together. Under a restricted set of technical conditions our algorithm runs in $O((\log_2(n))^3 |E|)$ time, where $n$ is the number of nodes and $|E|$ is the number of edges in the sampled graph. We demonstrate the scalability of our algorithm via extensive empirical evaluation; we can sample a MAGM graph with 8 million nodes and 20 billion edges in under 6 hours

An asymptotic sampling formula for the coalescent with Recombination

Ewens sampling formula (ESF) is a one-parameter family of probability distributions with a number of intriguing combinatorial connections. This elegant closed-form formula first arose in biology as the stationary probability distribution of a sample configuration at one locus under the infinite-alleles model of mutation. Since its discovery in the early 1970s, the ESF has been used in various biological applications, and has sparked several interesting mathematical generalizations. In the population genetics community, extending the underlying random-mating model to include recombination has received much attention in the past, but no general closed-form sampling formula is currently known even for the simplest extension, that is, a model with two loci. In this paper, we show that it is possible to obtain useful closed-form results in the case the population-scaled recombination rate $\rho$ is large but not necessarily infinite. Specifically, we consider an asymptotic expansion of the two-locus sampling formula in inverse powers of $\rho$ and obtain closed-form expressions for the first few terms in the expansion. Our asymptotic sampling formula applies to arbitrary sample sizes and configurations.Comment: Published in at http://dx.doi.org/10.1214/09-AAP646 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Study of numerical simulation method modelling gas injection into fractured reservoirs

Purpose. Fractures are the main flow channels in fractured reservoirs. The rapid flow characteristics of gas are outstanding in fractures. It is a major technical problem in the current oilfield development to calculate and accurately describe the fluid flow of this type of reservoir. Methods. This paper improves the calculation model of oil-water-gas phase equilibrium. Based on the discrete fracture net-work model, the numerical simulation mathematical model, numerical model and solution method of nitrogen injection were established. Findings. A simple discrete fracture network model was designed. Numerical simulations verify the correctness of the method. Originality. A fast solution method for gas injection numerical simulation based on discrete crack network model is proposed. Practical implications. The fractured reservoir numerical simulation method can accurately describe the flow of oil, water and gas in the fracture, which lays a foundation for the gas injection development mechanism and gas injection optimization research.Мета. Розробка нової методики чисельного моделювання впорскування газу у тріщинуваті колектори на основі моделі дискретної мережі тріщин. Методика. Для досягнення поставленої мети виконано критичний аналіз відомих методів моделювання, що довів відсутність на сьогоднішній день ефективних методів. Для дослідження проблемних питань у статті застосовано метод розрахунку фазової рівноваги на основі вільної енергії Гіббса як основи для чисельного моделювання закачування газу. Використовували ітераційний метод Ньютона для визначення складу кожної фази в мінімумі вільної енергії Гіббса. Результати. На основі моделі дискретної мережі тріщин сформовані математична модель, чисельна модель і метод рішення для чисельного моделювання закачування газу у тріщинуваті колектори. Правильність методу підтверджується спрощеною моделлю мережі дискретного руйнування. Результати чисельного моделювання узгоджуються з результатами теоретичних розрахунків. Отримана імітаційна модель дискретної мережі тріщин. Встановлено рівняння збереження маси нафти, води, газу та закачаного газу у тріщинах і матриці. Створено рівняння багатофазного потоку рідини у різних середовищах. Наукова новизна. Розроблено новий науково-методичний підхід до розрахунку та чисельного моделювання впорскування газу у тріщинуваті колектори, що враховує дискретну модель мережі тріщин. Практична значимість. Методика чисельного моделювання поведінки тріщинуватого колектору може точно описати потоки нафти, води і газу у тріщині, що сприяє більш детальному вивченню механізму розвитку впорскування газу та його оптимізації.Цель. Разработка новой методики численного моделирования впрыскивания газа в трещиноватые коллекторы на основе модели дискретной сети трещин. Методика. Для достижения поставленной цели выполнен критический анализ известных методов моделирования, доказавший отсутствие на сегодняшний день эффективных методов. Для исследования проблемных вопросов в статье применен метод расчета фазового равновесия на основе свободной энергии Гиббса как основа для численного моделирования закачки газа. Использовали итерационный метод Ньютона для определения состава каждой фазы в минимуме свободной энергии Гиббса. Результаты. На основе модели дискретной сети трещин сформированы математическая модель, численная модель и метод решения для численного моделирования закачки газа в трещиноватые коллекторы. Правильность метода подтверждается упрощенной моделью сети дискретного разрушения. Результаты численного моделирования согласуются с результатами теоретических расчетов. Получена имитационная модель дискретной сети трещин. Установлены уравнения сохранения массы нефти, воды, газа и закачанного газа в трещинах и матрице. Создано уравнение многофазного потока жидкости в различных средах. Научная новизна. Разработан новый научно-методический подход к расчету и численному моделированию впрыскивания газа в трещиноватые коллекторы, учитывающий дискретную модель сети трещин. Практическая значимость. Методика численного моделирования поведения трещиноватого коллектора может точно описать потоки нефти, воды и газа в трещине, что способствует более детальному изучению механизма развития впрыскивания газа и его оптимизации.Project supported by National Science Foundation (No. 51674285), Major National Science and Technology Special Projects (2016ZX05014-004)