Heterogeneity and behavioral response in continuous time capture-recapture, with application to street cannabis use in Italy

We propose a general and flexible capture-recapture model in continuous time. Our model incorporates time-heterogeneity, observed and unobserved individual heterogeneity, and behavioral response to capture. Behavioral response can possibly have a delayed onset and a finite-time memory. Estimation of the population size is based on the conditional likelihood after use of the EM algorithm. We develop an application to the estimation of the number of adult cannabinoid users in Italy.Comment: Published in at http://dx.doi.org/10.1214/13-AOAS672 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Reflection Positivity: A Quantum Field Theory Connection

At the heart of constructive quantum field theory lies reflection positivity. Through its use one may extend results for a Euclidean field theory to a relativistic theory. In this dissertation we connect functorial and constructive quantum field theories through reflection positivity. In 2014 Santosh Kandel constructed examples of $d$-dimensional functorial QFTs when $d$ is even. We define functorial reflection positivity and show that this functorial theory is a reflection positive theory. We go on to show that every reflection positive theory produces a reflection positive Hilbert space. Iterated doubles are then introduced and used as a starting point to produce a four dimensional quantum field theory. The $(0+1)$ dimensional theory is then analyzed and shown to correspond to quantum mechanics

Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

Fuzzy {\it discrete event systems} (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems with fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically, (i) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]; {\it max-product} and {\it max-min} automata for modeling fuzzy DESs are considered; (ii) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus present the conditions for the existence of supervisors in fuzzy DESs; (iii) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata; also, we introduce the fuzzy $n$-controllability condition for some practical problems; (iv) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration

Ranking Portfolio Performance: An Application of a Joint Means and Variances Equality Test

We propose a new procedure to rank portfolio performance. Given a set of N portfolios, we use statistical tests of dominance which produce direct mean-variance comparisons between any two portfolios in the set. These tests yield an NxN matrix of pairwise comparisons. A ranking function maps the elements of the comparison matrix into a numerical ranking. To illustrate the procedure we use a set of 133 mutual funds, including the S&P500 index and the CRSP equal and value weighted indexes. We explore the empirical and theoretical relationships between our ranking procedure and the Treynor, Sharpe and Jensen performance measures. In general, the new procedure?s ranking is relatively robust, does not allow for gaming and can be performed with small samples.

Global existence results for complex hyperbolic models of bacterial chemotaxis

Bacteria are able to respond to environmental signals by changing their rules of movement. When we take into account chemical signals in the environment, this behaviour is often called chemotaxis. At the individual-level, chemotaxis consists of several steps. First, the cell detects the extracellular signal using receptors on its membrane. Then, the cell processes the signal information through the intracellular signal transduction network, and finally it responds by altering its motile behaviour accordingly. At the population level, chemotaxis can lead to aggregation of bacteria, travelling waves or pattern formation, and the important task is to explain the population-level behaviour in terms of individual-based models. It has been previously shown that the transport equation framework is suitable for connecting different levels of modelling of bacterial chemotaxis. In this paper, we couple the transport equation for bacteria with the (parabolic/elliptic) equation for the extracellular signals. We prove global existence of solutions for the general hyperbolic chemotaxis models of cells which process the information about the extracellular signal through the intracellular biochemical network and interact by altering the extracellular signal as well. The conditions for global existence in terms of the properties of the signal transduction model are given.Comment: 22 pages, submitted to Discrete and Continuous Dynamical Systems Series

Testing for Stochastic Dominance with Diversification Possibilities

We derive empirical tests for stochastic dominance that allow for diversification betweenchoice alternatives. The tests can be computed using straightforward linearprogramming. Bootstrapping techniques and asymptotic distribution theory canapproximate the sampling properties of the test results and allow for statistical inference.Our results could provide a stimulus to the further proliferation of stochastic dominancefor the problem of portfolio selection and evaluation (as well as other choice problemsunder uncertainty that involve diversification possibilities). An empirical application forUS stock market data illustrates our approach.stochastic dominance;portfolio selection;linear programming;portfolio diversification;portfolio evaluation