Bayesian Analysis of a Two-State Markov Modulated Poisson Process

Abstract

We postulate observations from a Poisson process whose rate parameter modulates between two values determined by an unobserved Markov chain. The theory switches from continuous to discrete time by considering the intervals between observations as a sequence of dependent random variables. A result from hidden Markov models allows us to sample from the posterior distribution of the model parameters given the observed event times using a Gibbs sampler with only two steps per iteration.     

The existence of continuous invariants for linear difference equations

We study real continuous invariants for systems of linear difference equations. We shall prove a conjecture by Ladas about the existence of such invariants. In fact, necessary and sufficient conditions on existence of such invariants will be established. The invariants will be constructed when they exist.     

Comparison of the discriminating power of Raman and surface‐enhanced Raman spectroscopy with established techniques for the examination of liquid and gel inks

The ability to discriminate between inks is important for forensic document analysis. Here, Raman spectroscopy (RS) and surface‐enhanced RS have been compared to the traditional document examination techniques of video spectral comparison and thin layer chromatography on a population of blue and black‐coloured liquid and gel inks. It was found that in most cases, the Raman techniques provided a similar or better discriminating power than the conventional methods. Importantly, this study allowed us to determine whether the same underlying changes in composition were being exploited by the different methods to discriminate between samples. It was found that there was indeed a high degree of commonality in the sample pairs being discriminated by the various techniques. This work can therefore underpin introduction of Raman methods into standard operating procedures for ink analysis since it not only measures the extent of discrimination between samples but can also explain the origin of the spectral changes that are used to distinguish between them. © 2013 John Wiley & Sons Ltd and Crown copyright     

Comparison of Inductively Coupled Plasma with Classical Analytical Techniques in the Analysis of Southern Oregon Lithia Water: Inclusion of a Local Resource in the Undergraduate Chemistry Curriculum

Abstract

Lithia water, a community resource of local historical significance, is described as a central theme in the undergraduate analytical chemistry sequence. A statistical comparison of the classical determination of major cations (Na⁺, K⁺, Ca²⁺, Mg²⁺) and anions (HCO₃ ^?, Cl^?) reinforces statistical and charge‐balance concepts covered in analytical chemistry. Subsequent determination of these major cations by inductively coupled plasma (ICP) enables students to statistically evaluate the presence of bias between instrumental and classical methods. The effect of easily ionized elements on ICP calibration sensitivity and linearity via the use of cesium as an ionization suppressor is reported.     

A unique continuation problem for holomorphic mappings

The authors study analytic discs that are “attached to” a red submanifold having minimal smoothness. They prove a new uniqueness and regularity theorem by using the technique of the Riemann–Hilbert problem. They also present a new method for conatructing families of analytic discs lhat osculate a surface.     

Harmonizing model with transfer tax on water pollution across regional boundaries in a China’s lake basin

This paper presents a bilevel programming framework for a harmonizing model with transfer tax (HMTT) on water pollution across regional boundaries of a lake basin in China, where the administrator is the upper-level decision maker and individual regions consisting of the lake basin are the lower-level decision makers (followers). Leader’s cost is the total pollution reduction cost, whereas each region selfishly minimizes its own cost including reduction cost and transfer cost, given the transfer tax rate imposed by the leader. The HMTT guarantees that the imposed environmental quality standard is met through the transfer tax. Based on the KKT conditions of an auxiliary problem, we obtain that the solution set of the HMTT is nonempty. An algorithm is proposed, with the convergence result, to compute the cost-minimized transfer tax rate along with the reduction quantities of individual regions. Theoretical analysis and a case study for China’s Taihu Lake Basin show that the HMTT is superior to the current model of proportional share of pollution reduction (MPSPR). The HMTT not only solves the problem of conflicts over water pollution across regional boundaries but also utilizes the resources of the lake basin more efficiently.     

Static search games played over graphs and general metric spaces

We define a general game which forms a basis for modelling situations of static search and concealment over regions with spatial structure. The game involves two players, the searching player and the concealing player, and is played over a metric space. Each player simultaneously chooses to deploy at a point in the space; the searching player receiving a payoff of 1 if his opponent lies within a predetermined radius r of his position, the concealing player receiving a payoff of 1 otherwise. The concepts of dominance and equivalence of strategies are examined in the context of this game, before focusing on the more specific case of the game played over a graph. Methods are presented to simplify the analysis of such games, both by means of the iterated elimination of dominated strategies and through consideration of automorphisms of the graph. Lower and upper bounds on the value of the game are presented and optimal mixed strategies are calculated for games played over a particular family of graphs.     

Approximate Hermitian–Einstein connections on principal bundles over a compact Riemann surface

Let $X$ be a compact connected Riemann surface and $G$ a connected reductive complex affine algebraic group. Given a holomorphic principal $G$ -bundle $E_G$ over $X$ , we construct a $C^\infty $ Hermitian structure on $E_G$ together with a $1$ -parameter family of $C^\infty $ automorphisms $\{F_t\}_{t\in \mathbb R }$ of the principal $G$ -bundle $E_G$ with the following property: Let $\nabla ^t$ be the connection on $E_G$ corresponding to the Hermitian structure and the new holomorphic structure on $E_G$ constructed using $F_t$ from the original holomorphic structure. As $t\rightarrow -\infty $ , the connection $\nabla ^t$ converges in $C^\infty $ Fréchet topology to the connection on $E_G$ given by the Hermitian–Einstein connection on the polystable principal bundle associated to $E_G$ . In particular, as $t\rightarrow -\infty $ , the curvature of $\nabla ^t$ converges in $C^\infty $ Fréchet topology to the curvature of the connection on $E_G$ given by the Hermitian–Einstein connection on the polystable principal bundle associated to $E_G$ . The family $\{F_t\}_{t\in \mathbb R }$ is constructed by generalizing the method of [6]. Given a holomorphic vector bundle $E$ on $X$ , in [6] a $1$ -parameter family of $C^\infty $ automorphisms of $E$ is constructed such that as $t\rightarrow -\infty $ , the curvature converges, in $C^0$ topology, to the curvature of the Hermitian–Einstein connection of the associated graded bundle.     

A branch-and-bound method for discretely-constrained mathematical programs with equilibrium constraints

We present a branch-and-bound algorithm for discretely-constrained mathematical programs with equilibrium constraints (DC-MPEC). This is a class of bilevel programs with an integer program in the upper-level and a complementarity problem in the lower-level. The algorithm builds on the work by Gabriel et al. (Journal of the Operational Research Society 61(9):1404–1419, 2010) and uses Benders decomposition to form a master problem and a subproblem. The new dynamic partition scheme that we present ensures that the algorithm converges to the global optimum. Partitioning is done to overcome the non-convexity of the Benders subproblem. In addition Lagrangean relaxation provides bounds that enable fathoming in the branching tree and warm-starting the Benders algorithm. Numerical tests show significantly reduced solution times compared to the original algorithm. When the lower level problem is stochastic our algorithm can easily be further decomposed using scenario decomposition. This is demonstrated on a realistic case.     

Resolutions of subsets of finite sets of points in projective space

Abstract

Eisenbud et al. proved a number of results regarding Gröbner bases and initial ideals of those ideals J in the free associative algebra K ?X ₁,…, X _n ? which contain the commutator ideal. We prove similar results for ideals which contains the anti-commutator ideal (the defining ideal of the exterior algebra). We define one weak notion of generic initial ideals in K ?X ₁,…, X _n ?, and show that generic initial ideals of ideals containing the anti-commutator ideal, or the commutator ideal, are finitely generated.