BPS Quivers and Spectra of Complete {\mathcal{N} = 2} Quantum Field Theories

We study the BPS spectra of ${\mathcal{N}=2}$ N = 2 complete quantum field theories in four dimensions. For examples that can be described by a pair of M5 branes on a punctured Riemann surface we explain how triangulations of the surface fix a BPS quiver and superpotential for the theory. The BPS spectrum can then be determined by solving the quantum mechanics problem encoded by the quiver. By analyzing the structure of this quantum mechanics we show that all asymptotically free examples, Argyres-Douglas models, and theories defined by punctured spheres and tori have a chamber with finitely many BPS states. In all such cases we determine the spectrum.     

Application of Multivariate Techniques in Optimization of Spectroanalytical Methods

Abstract

The present article describes fundamentals and applications of multivariate techniques used for the optimization of analytical procedures and systems involving spectroanalytical methods such as flame atomic absorption spectrometry (FAAS), electrothermal atomic absorption spectrometry (ETAAS), inductively coupled plasma optical emission spectrometry (ICP OES), and inductively coupled plasma mass spectrometry (ICP‐MS), considering the main steps of a chemical analysis. This way, applications of experimental designs in optimization of sampling systems, digestion procedures, preconcentration procedures, instrumental parameters of quantification steps of analytical methods, and robustness tests have been summarized in this work.     

Optimization methodology assessment for the inlet velocity profile of a hydraulic turbine draft tube: part I—computer optimization techniques

In recent years, numerical and experimental investigations on the draft tube performance have confirmed the importance of the inlet swirling flow created by the runner vanes. The results indicate that it is still a challenge to get the optimal flow distribution at the draft tube inlet which gives the best machine performance over a range of operation points. Consequently, there is a need to adjust the runner-draft tube coupling to minimize the losses arising from the inlet flow distribution. This paper focus on establishing an optimization methodology for maximizing the draft tube performance as a function of the inlet velocity profile. The overall work is divides into two parts: The part one establish the inlet velocity parametrization, the numerical optimization set-up and the objective function definition. The part two validate the numerical CFD draft tube model. These steps are represented by the coupling of the commercial softwares MATLAB, FLUENT and iSIGHT. It is considered that this proved methodology will help to find a inlet velocity profile shape which will be able to suppress or mitigate the undesirable draft tube flow characteristics.     

Binary Image Compression via Monochromatic Pattern Substitution: Sequential and Parallel Implementations

We present a method for compressing binary images via monochromatic pattern substitution. Such method has no relevant loss of compression effectiveness if the image is partitioned into up to a thousand blocks, approximately, and each block is compressed independently. Therefore, it can be implemented on a distributed system with no interprocessor communication. In the theoretical context of unbounded parallelism, interprocessor communication is needed. Compression effectiveness has a bell-shaped behaviour which is again competitive with the sequential performance when the highest degree of parallelism is reached. Finally, the method has a speed-up if applied sequentially to an image partitioned into up to 256 blocks. It follows that such speed-up can be applied to a parallel implementation on a small scale system.     

A probabilistic model associated with the pressureless gas dynamics

Using a method of stochastic perturbation of a Langevin system associated with the non-viscous Burgers equation we introduce a system of PDE that can be considered as a regularization of the pressureless gas dynamics describing sticky particles. By means of this regularization we describe how starting from smooth data a δ-singularity arises in the component of density. Namely, we find the asymptotics of solution at the point of the singularity formation as the parameter of stochastic perturbation tends to zero. Then we introduce a generalized solution in the sense of free particles (FP-solution) as a special limit of the solution to the regularized system. This solution corresponds to a medium consisting of non-interacting particles. The FP-solution is a bridging step to constructing solutions to the Riemann problem for the pressureless gas dynamics describing sticky particles. We analyze the difference in the behavior of discontinuous solutions for these two models and the relations between them. In our framework we obtain a unique entropy solution to the Riemann problem in 1D case.     

Classroom note: A simple proof of an interesting Fibonacci generalization

It is reasonably well known that the ratios of consecutive terms of a Fibonacci series converge to the golden ratio. This note presents a simple, complete proof of an interesting generalization of this result to a whole family of ‘precious metal ratios’.     

Hardness of Approximation for Crossing Number

We show that, if $\mathrm{P}\not=\mathrm{NP}$ , there is a constant c ₀>1 such that there is no c ₀-approximation algorithm for the crossing number, even when restricted to 3-regular graphs.     

Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and pfaffians

The classic Cayley identity states that

det(∂)(detX)^s=s(s+1)?(s+n−1)(detX)^s−1$\det (\partial ){(\det X)}^s=s(s+1)?(s+n-1){(\det X)}^{s-1}$

where X=(_xij)$X=(x_{ij})$ is an n×n$n\times n$ matrix of indeterminates and ∂=(∂/∂_xij)$\partial =(\partial /\partial x_{ij})$ is the corresponding matrix of partial derivatives. In this paper we present straightforward algebraic/combinatorial proofs of a variety of Cayley-type identities, both old and new. The most powerful of these proofs employ Grassmann algebra (= exterior algebra) and Grassmann–Berezin integration. Among the new identities proven here are a pair of “diagonal-parametrized” Cayley identities, a pair of “Laplacian-parametrized” Cayley identities, and the “product-parametrized” and “border-parametrized” rectangular Cayley identities.     

The generalized second law in the emergent universe

This Letter studies whether the generalized second law of thermodynamics is fulfilled in the transition from a generic initial Einstein static phase to the inflationary phase, with constant Hubble rate, and from the end of the latter to the conventional era of thermal radiation dominated expansion. As it turns out, the said law is satisfied provided the radiation component does not largely contribute to the total energy of the static phase.     

A suggested statistical test for measuring bivariate nonlinear dependence

We devise a new asymptotic statistical test to assess independence in bivariate continuous distributions. Our approach is based on the Cramér–von Mises test, in which the empirical process is viewed as the Kullback–Leibler divergence, that is, as the distance between the data under the independence hypothesis and the data empirically observed. We derive the theoretical characteristic function of the limit distribution of the test statistic and find the critical values through computer simulation. A Monte Carlo experiment is considered as assessing the validation and power performance of the test by assuming a bivariate nonlinear dependence structure with fat tails. Two extra examples, respectively, consider stationary and conditionally nonstationary series. Results confirm that our suggested test is consistent and powerful in the presence of bivariate nonlinear dependence even if the environment is non-Gaussian. Our case is illustrated with high-frequency data from stocks listed on the NYSE that recently experienced so-called mini-flash crashes.