Estimating stochastic volatility diffusion using conditional moments of integrated volatility

We exploit the distributional information contained in high-frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility, the realization of which is effectively approximated by the sum of the squared high-frequency increments of the process. Our simulation evidence indicates that the resulting GMM estimator is highly reliable and accurate. Our empirical implementation based on high-frequency five-minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps. © 2002 Elsevier Science B.V. All rights reserved.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Real-Time and Data-Driven Operation Optimization and Knowledge Discovery for an Enterprise Information System

An enterprise information system (EIS) is an integrated data-applications platform characterized by diverse, heterogeneous, and distributed data sources. For many enterprises, a number of business processes still depend heavily on static rule-based methods and extensive human expertise. Enterprises are faced with the need for optimizing operation scheduling, improving resource utilization, discovering useful knowledge, and making data-driven decisions.

This thesis research is focused on real-time optimization and knowledge discovery that addresses workflow optimization, resource allocation, as well as data-driven predictions of process-execution times, order fulfillment, and enterprise service-level performance. In contrast to prior work on data analytics techniques for enterprise performance optimization, the emphasis here is on realizing scalable and real-time enterprise intelligence based on a combination of heterogeneous system simulation, combinatorial optimization, machine-learning algorithms, and statistical methods.

On-demand digital-print service is a representative enterprise requiring a powerful EIS.We use real-life data from Reischling Press, Inc. (RPI), a digit-print-service provider (PSP), to evaluate our optimization algorithms.

In order to handle the increase in volume and diversity of demands, we first present a high-performance, scalable, and real-time production scheduling algorithm for production automation based on an incremental genetic algorithm (IGA). The objective of this algorithm is to optimize the order dispatching sequence and balance resource utilization. Compared to prior work, this solution is scalable for a high volume of orders and it provides fast scheduling solutions for orders that require complex fulfillment procedures. Experimental results highlight its potential benefit in reducing production inefficiencies and enhancing the productivity of an enterprise.

We next discuss analysis and prediction of different attributes involved in hierarchical components of an enterprise. We start from a study of the fundamental processes related to real-time prediction. Our process-execution time and process status prediction models integrate statistical methods with machine-learning algorithms. In addition to improved prediction accuracy compared to stand-alone machine-learning algorithms, it also performs a probabilistic estimation of the predicted status. An order generally consists of multiple series and parallel processes. We next introduce an order-fulfillment prediction model that combines advantages of multiple classification models by incorporating flexible decision-integration mechanisms. Experimental results show that adopting due dates recommended by the model can significantly reduce enterprise late-delivery ratio. Finally, we investigate service-level attributes that reflect the overall performance of an enterprise. We analyze and decompose time-series data into different components according to their hierarchical periodic nature, perform correlation analysis,

and develop univariate prediction models for each component as well as multivariate models for correlated components. Predictions for the original time series are aggregated from the predictions of its components. In addition to a significant increase in mid-term prediction accuracy, this distributed modeling strategy also improves short-term time-series prediction accuracy.

In summary, this thesis research has led to a set of characterization, optimization, and prediction tools for an EIS to derive insightful knowledge from data and use them as guidance for production management. It is expected to provide solutions for enterprises to increase reconfigurability, accomplish more automated procedures, and obtain data-driven recommendations or effective decisions.

Molecular dynamics simulation of observed c(4x4) and c(4x3) C60 alignments on the Si(100) reconstructed surface.

We have implemented a large-scale classical molecular dynamics simulation at constant temperature to provide a theoretical insight into the results of a recently performed experiment on the monolayer and multi-layer formations of molecular films on the Si(100) reconstructed dimerized surface. Our simulation has successfully reproduced all of the morphologies observed on the monolayer film by this experiment. We have obtained the formation of both c(4 4) and c(4 3) structures of the molecules and have also obtained phase transitions of the former into the latter.

A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

Monotone scheme and boundary conditions for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number

A monotone scheme for finite volume simulation of magnetohydrodynamic internal flows at high Hartmann number is presented. The numerical stability is analysed with respect to the electromagnetic force. Standard central finite differences applied to finite volumes can only be numerically stable if the vector products involved in this force are computed with a scheme using a fully staggered grid. The electromagnetic quantities (electric currents and electric potential) must be shifted by half the grid size from the mechanical ones (velocity and pressure). An integral treatment of the boundary layers is used in conjunction with boundary conditions for electrically conducting walls. The simulations are performed with inhomogeneous electrical conductivities of the walls and reach high Hartmann numbers in three-dimensional simulations, even though a non-adaptive grid is used.

Micromagnetic simulation of domain walls in iron films

The micromagnetic structure and energy of 180° domain walls spanning laminar crystals of iron having (100) or (110) surfaces and ranging in thickness from 145 to 580 nm have been investigated by numerical integration of the Landau-Lifshitz-Gilbert equation. Stable equilibrium structures with two flux symmetries were obtained for both crystal orientations at all thicknesses studied.

Modelling the nano-scale phenomena in condensed matter physics via computer-based numerical simulations

A review of the atomistic modelling of the behaviour of nano-scale structures and processes via molecular dynamics (MD) simulation method of a canonical ensemble is presented. Three areas of application in condensed matter physics are considered. We focus on the adhesive and indentation properties of the solid surfaces in nano-contacts, the nucleation and growth of nano-phase metallic and semi-conducting atomic and molecular films on supporting substrates, and the nano- and multi-scale crack propagation properties of metallic lattices. A set of simulations selected from these fields are discussed, together with a brief introduction to the methodology of the MD simulation. The pertinent inter-atomic potentials that model the energetics of the metallic and semi-conducting systems are also given.

Molecular dynamics simulation of fractures using an N-body potential

Molecular dynamics has been employed to model the fracture of a two dimensional triangular atomic lattice. The N-body Sutton-Chen potential developed for fcc metals and its extended version (Rafii-Tabar and Sutton) for fcc random binary alloys were used for the interatomic interactions. It is shown that at low temperatures cleavage fractures can occur in both an elemental metal and an alloy. At elevated temperatures the nucleation of dislocations is shown to cause a brittle-to-ductile transition. For the brittle crack propagation in the elemental metal, crack propagation speeds have been computed for different stress rates, and a crack instability found to exist as the speed reaches a critical value of about 32% of the Rayleigh wave speed. For the random alloy, we find that the dislocation movement can be affected by the distorted lattice.

Numerical modelling of adsorption of metallic particles on graphite substrate via molecular dynamics simulation

A computer-based numerical modelling of the adsorption process of gas phase metallic particles on the surface of a graphite substrate has been performed via the application of molecular dynamics simulation method. The simulation relates to an extensive STM-based experiment performed in this field, and reproduces part of the experimental results. Both two-body and many-body inter-atomic potentials have been employed. A Morse-type potential describing the metal-carbon interactions at the interface was specifically formulated for this modelling. Intercalation of silver in graphite has been observed as well as the correct alignments of monomers, dimers and two-dimensional islands on the surface. PACS numbers: 02.60.Cb, 07.05.Tp, 68.55.-a, 81.05.Tp

Reliability analysis of flip chip designs via computer simulation

A flip chip component is a silicon chip mounted to a substrate with the active area facing the substrate. This paper presents the results of an investigation into the relationship between a number of important material properties and geometric parameters on the thermal-mechanical fatigue reliability of a standard flip chip design and a flip chip design with the use of microvias. Computer modeling has been used to analyze the mechanical conditions of flip chips under cyclic thermal loading where the Coffin-Manson empirical relationship has been used to predict the life time of the solder interconnects. The material properties and geometry parameters that have been investigated are the Young's modulus, the coefficient of thermal expansion (CTE) of the underfill, the out-of-plane CTE (CTEz) of the substrate, the thickness of the substrate, and the standoff height. When these parameters vary, the predicted life-times are calculated and some of the features of the results are explained. By comparing the predicted lifetimes of the two designs and the strain conditions under thermal loading, the local CTE mismatch has been found to be one of most important factors in defining the reliability of flip chips with microvias.

Parallelisation of electromagnetic simulation codes

In this paper results obtained from the parallelisation of existing 3D electromagnetic Finite Element codes within the ESPRIT HPCN project PARTEL are presented. The parallelisation procedure, based on the Bulk Synchronous Parallel approach, is outlined and the encouraging results obtained in terms of speed-up on some industrially significant test cases are described and discussed.

Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive Finite Element simulations in which we use preconditioned Conjugate Gradient solvers based on domain-decomposition. The load balancing is designed to maintain good partition aspect ratio and we show that cut size is not always the appropriate measure in load balancing. Furthermore, we attempt to answer the question why the aspect ratio of partitions plays an important role for certain solvers. We define and rate different kinds of aspect ratio and present a new center-based partitioning method of calculating the initial distribution which implicitly optimizes this measure. During the adaptive simulation, the load balancer calculates a balancing flow using different versions of the diffusion algorithm and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. Experimental results for Bramble's preconditioner and comparisons to state-of-the-art load balancers show the benefits of the construction.

Macro-segregation of multi-component alloys in shape casting simulation

The objective of this work is to present a new scheme for temperature-solute coupling in a solidification model, where the temperature and concentration fields simultaneously satisfy the macro-scale transport equations and, in the mushy region, meet the constraints imposed by the thermodynamics and the local scale processes. A step-by-step explanation of the macrosegregation algorithm, implemented in the finite volume unstructured mesh multi-physics modelling code PHYSICA, is initially presented and then the proposed scheme is validated against experimental results obtained by Krane for binary and a ternary alloys.