Conditional VaR estimation using Pearson’s type IV distribution

This paper presents a new value at risk (VaR) estimation model for equity returns time series and tests it extensively on Stock Indices of 14 countries. Two most important stylized facts of such series are volatility clustering, and non-normality as a result of fat tails of the return distribution. While volatility clustering has been extensively studied using the GARCH model and its various extensions, the phenomenon of non-normality has not been comprehensively explored, at least in the context of VaR estimation. A combination of extreme value theory (EVT) and GARCH has been explored to analyze financial data showing non-normal behavior. This paper proposes a combination of the Pearson’s Type IV distribution and the GARCH (1, 1) approach to furnish a new method with superior predictive abilities. The approach is back tested for the entire sample as well as for a holdout sample using rolling windows.     

Effect of time delay on a harvested predator-prey model

The predator-prey systems with harvesting have received a great deal of attentions for last few decades. Incorporating discrete time delays into predator-prey models could induce instability and bifurcation. In this paper we are interested in studying the combined effects of harvesting and discrete time delay on the dynamics of a predator-prey model. A comparative analysis is provided for stability behaviour in absence as well as in presence of time delay. The length of discrete time delay to preserve stability of the model system is obtained. Existence of Hopf-bifurcating small amplitude periodic solutions is derived by taking discrete time delay as a bifurcation parameter.     

Predicting particle trajectories on an electrodynamic screen – Theory and experiment

The electrodynamic screen, or EDS, was first introduced to the electrostatics community in the early 1970's. Since that time, it has been studied by several research groups who have investigated its use as a means to remove unwanted particles from insulator surfaces. In the typical EDS, interdigitated electrodes are embedded or deposited on the surface, then energized by three-phase square or sinusoidal voltages of magnitude 500–1200 V at frequencies between 5 and 200 Hz. The resulting electric field entrains previously deposited particles and moves them laterally across the surface. Electrodynamic screens have been proposed for use on solar cells in Mars and Moon space missions, as well as the removal of dust from renewable-energy solar collectors such as photovoltaic panels, solar reflectors, and mirrors. Though often considered merely a nuisance, dust has the potential to partially or totally obscure the solar flux incident on any solar collector.Development of EDS technology has evolved mostly from a “trial and error” approach to choosing such parameters as electrode spacing, depth, and width, as well as voltage magnitude and frequency. Though some theoretical studies may be found in the literature, a more detailed understanding would be valuable in optimizing EDS performance for a particular application and composition of ambient dust, which may vary with geographical location with respect to size, permittivity, and conductivity. A theoretical understanding of how particles are entrained and made to move on an EDS will facilitate proper choice of relevant parameters in future EDS systems. Our work thus attempts to analyze the motion of dust particles subject to all the forces encountered at the surface of an EDS, including the coulomb and dielectrophoretic forces, as well as aerodynamic drag, gravity, and friction. Previous work has shown that particles entrained in the traveling-wave electrostatic field of an EDS exhibit one of two behaviors: ordered, lateral motion; and semi-chaotic motion. These two behaviors have been found both experimentally and in theoretical simulations. This paper attempts to correlate trajectory computations with video observations of these behaviors as recorded in a laboratory setting.     

Almost sure convergence of sums of maxima and minima of positive random variables

For a sequence of independent and identically distributed positive random variables, the almost sure convergence of sums of maxima (when suitably normalized) to appropriate constants is proved for both bounded and unbounded random variables. A similar result is also proved for sums of minima of such variables.     

On a class of asymptotically optimal nonparametric tests for grouped data I

Summary Generalizing the results of Sen [8], a class of nonparametric tests for the hypothesis of no regression in the multiple linear regression model is obtained here. The asymptotic power properties of the proposed class of tests are studied, and the asymptotic optimality of the tests is established under the conditions of Wald [10]. Applications of the results are also considered. Research supported by National Institutes of Health, Institute of General Medical Sciences, Grant No. 12868-05.     

Admissible and minimax multiparameter estimation in exponential families

Consider p independent distributions each belonging to the one parameter exponential family with distribution functions absolutely continuous with respect to Lebesgue measure. For estimating the natural parameter vector with p ≥ p₀ (p₀ is typically 2 or 3), a general class of estimators dominating the minimum variance unbiased estimator (MVUE) or an estimator which is a known constant multiple of the MVUE is produced under different weighted squared error losses. Included as special cases are some results of Hudson [13] and Berger [5]. Also, for a subfamily of the general exponential family, a class of estimators dominating the MVUE of the mean vector or an estimator which is a known constant multiple of the MVUE is produced. The major tool is to obtain a general solution to a basic differential inequality.     

Comparing predator–prey models with hidden and explicit resources

In this paper two mathematical models are proposed and analyzed to elucidate the influence on a generalist predator of its hidden and explicit resources. Boundedness of the system’s trajectories, feasibility, local and global stability of the equilibria for both models are established, as well as possible local bifurcations. The findings indicate that the relevant behaviour of the system, including switching of stability, extinction and persistence of the involved populations, depends mainly on the reproduction rate of the favorite prey. To achieve full ecosystem survival some balance between the respective grazing pressures exerted by the predator on the prey populations needs to be maintained, while higher grazing pressure just on one species always leads to its extinction.     

A safe harbor can protect an endangered species from its predators

The objective is the study of the dynamics of a prey–predator model where the prey species can migrate between two patches. The specialist predator is confined to the first patch, where it consumes the prey following the simple law of mass action. The prey is further “endangered” in that it suffers from the strong Allee effect, assumed to occur due to the lowering of successful matings. In the second patch the prey grows logistically. The model is formulated in a comprehensive way so as to include specialist as well as generalist predators, as a continuum of possible behaviors. This model described by a set of three ordinary differential equation is an extension of some previous models proposed and analysed in the literature on metapopulation models. The following analysis issues will be addressed: boundedness of the solution, equilibrium feasibility and stability, and dynamic behaviour dependency of the population and environmental parameters. Three types for both equilibria and limit cycles are possible: trivial, predator-free and coexistence. Classical analysis techniques are used and also theoretical and numerical bifurcation analysis. Besides the well-known local bifurcations, also a homoclinic connection as a global bifurcation is calculated. In view of the difficulty in the analysis, only the specialist case will be analysed. The obtained results indicate that the safe harbor can protect the endangered species under certain parametric restrictions.

     

Photochemical Conjugation and One‐Pot Radiolabelling of Antibodies for Immuno‐PET

Monoclonal antibodies (mAbs), immunoglobulin fragments, and other proteins are important scaffolds in the development of radiopharmaceuticals for diagnostic immuno‐positron emission tomography (immuno‐PET) and targeted radioimmunotherapy (RIT). Conventional methods for radiolabelling proteins with metal ions such as ⁶⁸Ga, ⁶⁴Cu, ⁸⁹Zr, and ⁹⁰Y require multi‐step procedures involving pre‐purification, functionalisation with a chelate, and subsequent radiolabelling. Standard coupling chemistries are time‐consuming, difficult to automate, and involve synthesis, isolation, and storage of an intermediate, new molecular entity (the conjugated mAb) whose biochemical properties can differ from those of the parent protein. To circumvent these issues, we developed a photoradiochemical approach that uses fast, chemoselective, light‐induced protein modification under mild conditions with novel metal‐ion‐binding chelates derivatised with aryl azide (ArN₃) groups. Experiments show that one‐pot photochemical conjugation and radiolabelling of formulated mAbs can be achieved in <20 min.     

The trapezoidal cylinder phase: a new mode of self-assembly in liquid-crystalline soft matter

A new rectangular columnar liquid crystalline phase with p2gg lattice is reported, which represents a polygonal cylinder array composed of cylinders with trapezoidal cross section. In these polygonal cylinders, one of the sides has a different length and is composed of a different material than the others. This tiling pattern was obtained in two series of T-shaped facial amphiphilic triblock molecules in which a rigid rod-like p-terphenyl core is substituted laterally by a polar and flexible oligoethylene glycol chain, terminated either by a hydrogen-bonding COOH group or by a Li carboxylate group, and having identical or different alkyl groups in the terminal positions. The trapezoidal cylinder phase provides an improved packing for relatively long and rigid alkyl chains at lower temperature and more space inside the polygonal cylinders than triangular cylinders. This combination of conformational and space-filling effects leads to different phase sequences. The trapezoidal cylinder phases pave the way to a new level of complexity in LC engineering and show the huge potential of the general concept of polyphilic tectons for the design of new complex soft matter structures.