The spans in Brownian motion

For $d \in \{1,2,3\}$, let $(B^d_t;~ t \geq 0)$ be a $d$-dimensional standard Brownian motion. We study the $d$-Brownian span set Span(d):=\{t-s;~ B^d_s=B^d_t~\mbox{for some}~0 \leq s \leq t\}. We prove that almost surely the random set $Span(d)$ is $\sigma$-compact and dense in $\mathbb{R}_{+}$. In addition, we show that $Span(1)=\mathbb{R}_{+}$ almost surely; the Lebesgue measure of $Span(2)$ is $0$ almost surely and its Hausdorff dimension is $1$ almost surely; and the Hausdorff dimension of $Span(3)$ is $\frac{1}{2}$ almost surely. We also list a number of conjectures and open problems.Comment: 33 pages, 4 figures. This paper is published by http://projecteuclid.org/euclid.aihp/150062403

Sunk costs, market contestability, and the size distribution of firms

This paper offers a new economic explanation for the observed inter-industry differences in the size distribution of firms. The empirical estimates--based on three temporal (1982, 1987, and 1992) cross-sections of the four-digit United States manufacturing industries--indicate that increased market contestability, as signified by low sunk costs, tends to reduce the dispersion of firm sizes. These findings provide support for one of the key predictions of the theory of contestable markets: that market forces under contestability would tend to render any inefficient organization of the industry unsustainable and, consequently, tighten the distribution of firms around the optimum.Markets and Market Access,Economic Theory&Research,Water and Industry,Access to Markets,Debt Markets

Nonlinear Dual-Mode Control of Variable-Speed Wind Turbines with Doubly Fed Induction Generators

This paper presents a feedback/feedforward nonlinear controller for variable-speed wind turbines with doubly fed induction generators. By appropriately adjusting the rotor voltages and the blade pitch angle, the controller simultaneously enables: (a) control of the active power in both the maximum power tracking and power regulation modes, (b) seamless switching between the two modes, and (c) control of the reactive power so that a desirable power factor is maintained. Unlike many existing designs, the controller is developed based on original, nonlinear, electromechanically-coupled models of wind turbines, without attempting approximate linearization. Its development consists of three steps: (i) employ feedback linearization to exactly cancel some of the nonlinearities and perform arbitrary pole placement, (ii) design a speed controller that makes the rotor angular velocity track a desired reference whenever possible, and (iii) introduce a Lyapunov-like function and present a gradient-based approach for minimizing this function. The effectiveness of the controller is demonstrated through simulation of a wind turbine operating under several scenarios.Comment: 14 pages, 9 figures, accepted for publication in IEEE Transactions on Control Systems Technolog

Seismic analysis of 70 Ophiuchi A: A new quantity proposed

The basic intent of this paper is to model 70 Ophiuchi A using the latest asteroseismic observations as complementary constraints and to determine the fundamental parameters of the star. Additionally, we propose a new quantity to lift the degeneracy between the initial chemical composition and stellar age. Using the Yale stellar evolution code (YREC7), we construct a series of stellar evolutionary tracks for the mass range $M$ = 0.85 -- 0.93 $M_{\odot}$ with different composition $Y_{i}$ (0.26 -- 0.30) and $Z_{i}$ (0.017 -- 0.023). Along these tracks, we select a grid of stellar model candidates that fall within the error box in the HR diagram to calculate the theoretical frequencies, the large- and small- frequency separations using the Guenther's stellar pulsation code. Following the asymptotic formula of stellar $p$-modes, we define a quantity $r_{01}$ which is correlated with stellar age. Also, we test it by theoretical adiabatic frequencies of many models. Many detailed models of 70 Ophiuchi A have been listed in Table 3. By combining all non-asteroseismic observations available for 70 Ophiuchi A with these seismological data, we think that Model 60, Model 125 and Model 126, listed in Table 3, are the optimum models presently. Meanwhile, we predict that the radius of this star is about 0.860 -- 0.865 $R_{\odot}$ and the age is about 6.8 -- 7.0 Gyr with mass 0.89 -- 0.90 $M_{\odot}$. Additionally, we prove that the new quantity $r_{01}$ can be a useful indicator of stellar age.Comment: 23 pages, 5 figures, accepted by New Astronom

Gravitino Interactions from Yang-Mills Theory

We fabricate gravitino vertex interactions using as only input on-shell Yang-Mills amplitudes and the Kawai-Lewellen-Tye gauge theory / gravity relations. A useful result of this analysis is simpler tree-level Feynman rules for gravitino scattering than in traditional gauges. All results are explicitly verified until five point scattering.Comment: 17 pages, 10 figures, REVTe

Asteroseismic study of solar-like stars: A method of estimating stellar age

Asteroseismology, as a tool to use the indirect information contained in stellar oscillations to probe the stellar interiors, is an active field of research presently. Stellar age, as a fundamental property of star apart from its mass, is most difficult to estimate. In addition, the estimating of stellar age can provide the chance to study the time evolution of astronomical phenomena. In our poster, we summarize our previous work and further present a method to determine age of low-mass main-sequence star.Comment: 2 pages, 1 figures, submitted to IAUS25

Fitting stochastic epidemic models to gene genealogies using linear noise approximation

Phylodynamics is a set of population genetics tools that aim at reconstructing demographic history of a population based on molecular sequences of individuals sampled from the population of interest. One important task in phylodynamics is to estimate changes in (effective) population size. When applied to infectious disease sequences such estimation of population size trajectories can provide information about changes in the number of infections. To model changes in the number of infected individuals, current phylodynamic methods use non-parametric approaches, parametric approaches, and stochastic modeling in conjunction with likelihood-free Bayesian methods. The first class of methods yields results that are hard-to-interpret epidemiologically. The second class of methods provides estimates of important epidemiological parameters, such as infection and removal/recovery rates, but ignores variation in the dynamics of infectious disease spread. The third class of methods is the most advantageous statistically, but relies on computationally intensive particle filtering techniques that limits its applications. We propose a Bayesian model that combines phylodynamic inference and stochastic epidemic models, and achieves computational tractability by using a linear noise approximation (LNA) --- a technique that allows us to approximate probability densities of stochastic epidemic model trajectories. LNA opens the door for using modern Markov chain Monte Carlo tools to approximate the joint posterior distribution of the disease transmission parameters and of high dimensional vectors describing unobserved changes in the stochastic epidemic model compartment sizes (e.g., numbers of infectious and susceptible individuals). We apply our estimation technique to Ebola genealogies estimated using viral genetic data from the 2014 epidemic in Sierra Leone and Liberia.Comment: 43 pages, 6 figures in the main tex

Emergence of highly-designable protein-backbone conformations in an off-lattice model

Despite the variety of protein sizes, shapes, and backbone configurations found in nature, the design of novel protein folds remains an open problem. Within simple lattice models it has been shown that all structures are not equally suitable for design. Rather, certain structures are distinguished by unusually high designability: the number of amino-acid sequences for which they represent the unique ground state; sequences associated with such structures possess both robustness to mutation and thermodynamic stability. Here we report that highly designable backbone conformations also emerge in a realistic off-lattice model. The highly designable conformations of a chain of 23 amino acids are identified, and found to be remarkably insensitive to model parameters. While some of these conformations correspond closely to known natural protein folds, such as the zinc finger and the helix-turn-helix motifs, others do not resemble known folds and may be candidates for novel fold design.Comment: 7 figure