My specific research interests lie in the area of information assurance,
scientific computing, Monte Carlo and quasi-Monte
Carlo and data science.
- Cyber Security
Security/privacy models/Issues for various computing enviornments,
such as mobile health, cloud computing, insider threat, digital forensics in mobile device and social
- Parallel Computing
Development of random number generators for use on multi-core processors
and GPU and Mobile(handheld) Device. SPRNG library.
- Parallel Quasirandom Numbers
have high degrees of parallelism, can tolerate large latencies,
and usually require considerable computational effort, making them
extremely well suited to parallel, distributed, and even
Grid-based computational environments. In these environments, a
large QMC problem is broken up into many small subproblems. These
subproblems are then scheduled on the parallel, distributed, or
Grid-based environment. In a more traditional instantiation,
these environments are usually a workstation cluster connected by
a local-area network, where the computational workload is cleverly
distributed. Recently, peer-to-peer or Grid computing, the
cooperative use of geographically distributed resources unified to
act as a single powerful computer, has been investigated as an
appropriate computational environment for QMC
applications. The computational
infrastructure developed for quasirandom numbers would be very useful.
- Randomized Quasi-Monte Carlo
Quasi-Monte Carlo methods are a variant of
ordinary Monte Carlo methods that employ highly
uniform quasirandom numbers in place of Monte Carlo's pseudorandom numbers.
Quasi-Monte Carlo methods are now widely used in scientific computation,
especially in estimating integrals over multidimensional domains
and in many different financial computations.
While quasirandom numbers do improve the convergence of
applications like numerical integration, it is by no means trivial
to provide practical error estimates.
In order to provide error
estimates for quasi-Monte Carlo methods, several researchers proposed the use of
Randomized quasi-Monte Carlo methods,
where randomness can be brought to bear on quasirandom sequences
through scrambling and other related randomization techniques.
The core of randomized quasi-Monte Carlo is to find fast and effective
algorithms to randomize (scramble) quasirandom sequences.
The purpose of scrambling in quasi-Monte Carlo is threefold. Primarily, it
provides a practical method to obtain error estimates for quasi-Monte Carlo
based by treating each scrambled sequence as a different and
independent random sample from a family of randomly scrambled
quasirandom numbers. Thus, randomized quasi-Monte Carlo overcomes the main
disadvantage of quasi-Monte Carlo while maintaining the favorable convergence
rate of quasi-Monte Carlo. Secondarily, scrambling gives us an a simple and
unified way to generate quasirandom numbers for parallel,
distributed, and Grid-based computational environments. Finally,
randomized quasi-Monte Carlo provides many more choices of quality quasirandom sequences
for quasi-Monte Carlo applications, and perhaps even optimal choices as a result
of derandomization. These promising characteristics have lead to
considerable work in the area randomized quasi-Monte Carlo. Thus, a careful exploration of
scrambling and derandomization methods coupled with library-level
implementations will play central role in the use of randomized quasi-Monte Carlo
Scrambled Quasirandom Numbers
The Halton sequence along with (t,s)-sequences and
lattice points are the standard quasirandom sequences,
The critical task for randomizing in QMC is to find fast and
effective methods to scramble quasirandom sequences. Various
scrambling methods have been studied, and these basically fall
into two main categories. One is based on randomized shifting.
The other method is based on digital permutations.
Generally speaking, the methods of scrambling quasirandom sequences are based on the construction
of the quasirandom numbers. Digital permutations are mainly used for quasirandom sequences which
are constructed via digital inversion methods, such as Halton sequences and
(t,s)-sequences. Lattice points are constructed by a different method and so
digital permutations are not suitable and shifting is used instead.
I explore the efficacy of various scrambling methods to build a
a library of parallel and distributed quasirandom numbers.
- Computational Finance
Numerical methods are used for a variety of purposes of finance. These includes
risk analysis, the evaluation of securities, and stress testing of portfolios.
The Monte Carlo approach, which uses random sequences, has proved
to be a valuable computational tool in modern finance. But, for
many applications of computational finance, the use of quasirandom
sequences, called quasi-Monte Carlo approach, seems to provide
more faster convergent rate than random sequences. Even though it
is well-known that the distribution of the quasirandom sequence in
high dimensions is not good, the scrambled or optimally scrambled
quasirandom sequence can often improve the quality. Thus the
scrambled and optimal quasirandom sequence can be widely applied
in computational finance.