Isomorphism of graph classes related to the circular-ones property

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, \Gamma-circular-arc graphs, proper circular-arc graphs and convex-round graphs.Comment: 25 pages, 9 figure

Evaporative Deposition Patterns Revisited: Spatial Dimensions of the Deposit

A model accounting for finite spatial dimensions of the deposit patterns in the evaporating sessile drops of colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite volume and hence these dimensions are of the steric origin. Within this model, the geometrical characteristics of the deposition patterns are found as functions of the initial concentration of the solute, the initial geometry of the drop, and the time elapsed from the beginning of the drying process. The model is solved analytically for small initial concentrations of the solute and numerically for arbitrary initial concentrations of the solute. The agreement between our theoretical results and the experimental data is demonstrated, and it is shown that the observed dependence of the deposit dimensions on the experimental parameters can indeed be attributed to the finite dimensions of the solute particles. These results are universal and do not depend on any free or fitting parameters; they are important for understanding the evaporative deposition and may be useful for creating controlled deposition patterns.Comment: 34 pages, 14 figures, LaTeX; submitted to Physical Review

Numerical calculations of diffraction losses in advanced interferometric gravitational wave detectors

Knowledge of the diffraction losses in higher-order modes of large optical cavities is essential for predicting three-mode parametric photon-phonon scattering, which can lead to mechanical instabilities in long-baseline gravitational wave detectors. We explore different numerical methods in order to determine the diffraction losses of the higher-order optical modes. Diffraction losses not only affect the power buildup inside the cavity but also influence the shape and frequency of the mode, which ultimately affect the parametric instability gain. Results depend on both the optical mode shape (order) and the mirror diameter. We also present a physical interpretation of these results

CHIRON - A Fiber Fed Spectrometer for Precise Radial Velocities

The CHIRON optical high-resolution echelle spectrometer was commissioned at the 1.5m telescope at CTIO in 2011. The instrument was designed for high throughput and stability, with the goal of monitoring radial velocities of bright stars with high precision and high cadence for the discovery of low-mass exoplanets. Spectral resolution of R=79,000 is attained when using a slicer with a total (including telescope and detector) efficiency of 6% or higher, while a resolution of R=136,000 is available for bright stars. A fixed spectral range of 415 to 880 nm is covered. The echelle grating is housed in a vacuum enclosure and the instrument temperature is stabilized to +-0.2deg. Stable illumination is provided by an octagonal multimode fiber with excellent light-scrambling properties. An iodine cell is used for wavelength calibration. We describe the main optics, fiber feed, detector, exposure-meter, and other aspects of the instrument, as well as the observing procedure and data reduction.Comment: 15 pages, 10 figures. Accepted by PAS

Quasi-regular sequences and optimal schedules for security games

We study security games in which a defender commits to a mixed strategy for protecting a finite set of targets of different values. An attacker, knowing the defender's strategy, chooses which target to attack and for how long. If the attacker spends time $t$ at a target $i$ of value $\alpha_i$, and if he leaves before the defender visits the target, his utility is $t \cdot \alpha_i$; if the defender visits before he leaves, his utility is 0. The defender's goal is to minimize the attacker's utility. The defender's strategy consists of a schedule for visiting the targets; it takes her unit time to switch between targets. Such games are a simplified model of a number of real-world scenarios such as protecting computer networks from intruders, crops from thieves, etc. We show that optimal defender play for this continuous time security games reduces to the solution of a combinatorial question regarding the existence of infinite sequences over a finite alphabet, with the following properties for each symbol $i$: (1) $i$ constitutes a prescribed fraction $p_i$ of the sequence. (2) The occurrences of $i$ are spread apart close to evenly, in that the ratio of the longest to shortest interval between consecutive occurrences is bounded by a parameter $K$. We call such sequences $K$-quasi-regular. We show that, surprisingly, $2$-quasi-regular sequences suffice for optimal defender play. What is more, even randomized $2$-quasi-regular sequences suffice for optimality. We show that such sequences always exist, and can be calculated efficiently. The question of the least $K$ for which deterministic $K$-quasi-regular sequences exist is fascinating. Using an ergodic theoretical approach, we show that deterministic $3$-quasi-regular sequences always exist. For $2 \leq K < 3$ we do not know whether deterministic $K$-quasi-regular sequences always exist.Comment: to appear in Proc. of SODA 201

Ray trace modeling in a solar secondary concentrator with various inlet shapes"

Este Trabajo Fin de Máster está enfocado a las plantas de energía solar concentrada, las cuales usan heliostatos para concentrar la radiación solar en un área relativamente pequeña, con el fin de calentar un fluido. En este Trabajo Fin de Máster un concentrador secundario forma parte del sistema. El software MIRVAL es utilizado para el trazado de los rayos desde el sol hasta el concentrador secundario. Una vez los rayos entran al concentrador, FORTRAN se utilizará para realizar los cálculos de la trayectoria de los rayos. La forma del concentrador secundario se definirá primero en SOLIDWORKS y después se creará una malla en ANSYS. La potencia absorbida en el concentrador secundario se graficará con MATLAB. Asimismo, se creará una nueva forma de concentrador secundario la cual será añadida al código y simulada. Con varias formas de concentrador secundario, se podrá crear el óptimo en función del campo de heliostatos dado.Departamento de Ingeniería Energética y FluidomecánicaMáster en Ingeniería Industria

Maximum Likelihood Estimation for Linear Gaussian Covariance Models

We study parameter estimation in linear Gaussian covariance models, which are $p$-dimensional Gaussian models with linear constraints on the covariance matrix. Maximum likelihood estimation for this class of models leads to a non-convex optimization problem which typically has many local maxima. Using recent results on the asymptotic distribution of extreme eigenvalues of the Wishart distribution, we provide sufficient conditions for any hill-climbing method to converge to the global maximum. Although we are primarily interested in the case in which $n>\!\!>p$, the proofs of our results utilize large-sample asymptotic theory under the scheme $n/p \to \gamma > 1$. Remarkably, our numerical simulations indicate that our results remain valid for $p$ as small as $2$. An important consequence of this analysis is that for sample sizes $n \simeq 14 p$, maximum likelihood estimation for linear Gaussian covariance models behaves as if it were a convex optimization problem