Dist Frequent Next Neighbours: A Distributed Galois Lattice Algorithm for Frequent Closed Itemsets Extraction

The general purpose of this paper is to propose a distributed version of frequent closed itemsets extraction in the context of big data. The goal is to have good performances of frequent closed itemsets extraction as frequent closed item-sets are bases for frequent itemsets. To achieve this goal, we have extended the Galois lattice technique (or concept lattice) in this context. Indeed, Galois lattices are an efficient alternative for extracting closed itemsets which are interesting approaches for generating frequent itemsets. Thus we proposed Dist Frequent Next Neighbour which is a distributed version of the Frequent Next Neighbour concept lattice construction algorithm, which considerably reduces the extraction time by parallelizing the computation of frequent concepts (closed itemsets).

A lattice approach for option pricing under a regime-switching GARCH-jump model

In this study, we consider option pricing under a Markov regime-switching GARCH-jump (RS-GARCH-jump) model. More specifically, we derive the risk neutral dynamics and propose a lattice algorithm to price European and American options in this framework. We also provide a method of parameter estimation in our RS-GARCH-jump setting using historical data on the underlying time series. To measure the pricing performance of the proposed algorithm, we investigate the convergence of the tree-based results to the true option values and show that this algorithm exhibits good convergence. By comparing the pricing results of RS-GARCH-jump model with regime-switching GARCH (RS-GARCH) model, GARCH-jump model, GARCH model, Black–Scholes (BS) model, and Regime-Switching (RS) model, we show that accommodating jump effect and regime switching substantially changes the option prices. The empirical results also show that the RS-GARCH-jump model performs well in explaining option prices and confirm the importance of allowing for both jump components and regime switching.

High Level FPGA Implementation Of Adaptive Signal Segmentation And Autoregressive Modeling Techniques

This thesis contains new FPGA implementations of adaptive signal segmentation and autoregressive modeling techniques. Both designs use Simulink-to-FPGA methodology and have been successfully implemented onto Xilinx Virtex II Pro device. The implementation of adaptive signal segmentation is based on the conventional RLSL algorithm using double-precision floating point arithmetic for internal computation and is programmable for users providing data length and order selection functions. The implemented RLSL design provides very good performance of obtaining accurate conversion factor values with a mean correlation of 99.93% and accurate boundary positions for both synthesized and biomedical signals. The implementation of autoregressive (AR) modeling is based on the Burg-lattice algorithm using fixed point arithmetic. The implemented Burg design with order of 3 provides good performance of calculating AR coefficients of input biomedical signals.

High Level FPGA Implementation Of Adaptive Signal Segmentation And Autoregressive Modeling Techniques

This thesis contains new FPGA implementations of adaptive signal segmentation and autoregressive modeling techniques. Both designs use Simulink-to-FPGA methodology and have been successfully implemented onto Xilinx Virtex II Pro device. The implementation of adaptive signal segmentation is based on the conventional RLSL algorithm using double-precision floating point arithmetic for internal computation and is programmable for users providing data length and order selection functions. The implemented RLSL design provides very good performance of obtaining accurate conversion factor values with a mean correlation of 99.93% and accurate boundary positions for both synthesized and biomedical signals. The implementation of autoregressive (AR) modeling is based on the Burg-lattice algorithm using fixed point arithmetic. The implemented Burg design with order of 3 provides good performance of calculating AR coefficients of input biomedical signals.

Unitary quantum lattice simulations for Maxwell equations in vacuum and in dielectric media

Utilizing the similarity between the spinor representation of the Dirac and the Maxwell equations that has been recognized since the early days of relativistic quantum mechanics, a quantum lattice algorithm (QLA) representation of unitary collision-stream operators of Maxwell's equations is derived for both homogeneous and inhomogeneous media. A second-order accurate 4-spinor scheme is developed and tested successfully for two-dimensional (2-D) propagation of a Gaussian pulse in a uniform medium whereas for normal (1-D) incidence of an electromagnetic Gaussian wave packet onto a dielectric interface requires 8-component spinors because of the coupling between the two electromagnetic polarizations. In particular, the well-known phase change, field amplitudes and profile widths are recovered by the QLA asymptotic profiles without the imposition of electromagnetic boundary conditions at the interface. The QLA simulations yield the time-dependent electromagnetic fields as the wave packet enters and straddles the dielectric boundary. QLA involves unitary interleaved non-commuting collision and streaming operators that can be coded onto a quantum computer: the non-commutation being the very reason why one perturbatively recovers the Maxwell equations.