Hongmei Chi

On the optimal Halton sequence

Quasi-Monte Carlo methods are a variant of ordinary Monte Carlo methods that employ highly uniform quasirandom numbers in place of Monte Carlos pseudorandom numbers. Clearly, the generation of appropriate high-quality quasirandom sequences is crucial to the success of quasi-Monte Carlo methods. The Halton sequence is one of the standard (along with (t,s)-sequences and lattice points) low-discrepancy sequences, and one of its important advantages is that the Halton sequence is easy to implement due to its definition via the radical inverse function. However, the original Halton sequence suffers from correlations between radical inverse functions with different bases used for different dimensions. These correlations result in poorly distributed two-dimensional projections. A standard solution to this phenomenon is to use a randomized (scrambled) version of the Halton sequence. An alternative approach to this is to find an optimal Halton sequence within a family of scrambled sequences. This paper presents a new algorithm for finding an optimal Halton sequence within a linear scrambling space. This optimal sequence is numerically tested and shown empirically to be far superior to the original. In addition, based on analysis and insight into the correlations between dimensions of the Halton sequence, we illustrate why our algorithm is efficient for breaking these correlations. An overview of various algorithms for constructing various optimal Halton sequences is also given.

Mobile health in China: Current status and future development

Mobile health applications offer unique opportunities for monitoring patient progress, providing education materials to patients and family members, receiving personalized prompts and support, collecting ecologically valid data, and using self-management interventions when and where they are needed. Mobile health application services to mental illness have evidenced success in Western countries. However, they are still in the initial stage of development in China. The purpose of this paper is to identify needs for mobile health in China, present major mobile health products and technology in China, introduce mobile and digital psychiatric services, and discuss ethical issues and challenges in mobile health development in a country with the largest population in the world.

Parallel linear congruential generators with Sophie-Germain moduli

Monte Carlo simulations are thought to be very easy to parallelize; however, the quality of these parallel Monte Carlo computations depends greatly on the quality of the parallel random number generators used. Linear congruential generators (LCGs), the most common number-theoretic pseudorandom number generators, with both power-of-two and prime moduli are used in many popular implementations of pseudorandom number generators. Recently, one of the authors of this paper [M. Mascagni, Parallel linear congruential generators with prime moduli, Parallel Comput. 24 (1998) 923-936] developed an explicit parameterization of prime modulus LCGs for use in parallel computations. This approach was based on an explicit enumeration of all the primitive roots modulo the prime modulus for use as unique multipliers in each parallel LCG. In that paper, only Mersenne prime moduli were considered because of the existence of a fast modular multiplication algorithm for primes close to powers-of-two. In the current paper, we investigate the nature of the trade-off implicitly made in the choice of Mersenne primes by comparing them to parameterized Sophie-Germain prime modulus LCGs. While the choice of Mersenne primes trades off initialization time for generation time, the choice of Sophie-Germain primes not only largely reduces initialization time but also provides competitive generation time when an appropriately chosen Sophie-Germain primes are used. The resulting Sophie-Germain prime modulus LCGs have been tested, and incorporated into the Scalable Parallel Random Number Generators SPRNG library [SPRNG. Scalable parallel random number generators, http://sprng.fsu.edu], a widely used random number generation suite for parallel, distributed, and grid-based Monte Carlo computations [M. Mascagni, A. Srinivasan, Computational infrastructure for parallel, distributed, and grid-based Monte Carlo computations, Lect. Notes Comput. Sci. 2907 (2004) 39-52].

On the Scrambled Halton Sequence

The Halton sequence is one of the standard (along with (t, s)-sequences and lattice points) low-discrepancy sequences, and thus is widely used in quasi-Monte Carlo applications. One of its important advantages is that the Halton sequence is easy to implement due to its definition via the radical inverse function. However, the original Halton sequence suffers from correlations between radical inverse functions with different bases used for different dimensions. These correlations result in poorly distributed two-dimensional projections. A standard solution to this is to use a randomized (scrambled) version of the Halton sequence. Here, we analyze the correlations in the standard Halton sequence, and based on this analysis propose a new and simpler modified scrambling algorithm. We also provide a number theoretic criterion to choose the optimal scrambling from among a large family of random scramblings. Based on this criterion, we have found the optimal scrambling for up to 60 dimensions for the Halton sequence. This derandomized Halton sequence is then numerically tested and shown empirically to be far superior to the original sequence.

On the scrambled soboĺ sequence

The Soboĺ sequence is the most popular quasirandom sequence because of its simplicity and efficiency in implementation. We summarize aspects of the scrambling technique applied to Soboĺ sequences and propose a new simpler modified scrambling algorithm, called the multi-digit scrambling scheme. Most proposed scrambling methods randomize a single digit at each iteration. In contrast, our multi-digit scrambling scheme randomizes one point at each iteration, and therefore is more efficient. After the scrambled Soboĺ sequence is produced, we use this sequence to evaluate a particular derivative security, and found that when this sequence is numerically tested, it is shown empirically to be far superior to the original unscrambled sequence.

Research Note: Generating parallel quasirandom sequences via randomization

Quasi-Monte Carlo (QMC) methods are now widely used in scientific computation, especially in estimating integrals over multidimensional domains. One advantage of QMC is that it is easy to parallelize applications, and so the success of any parallel QMC application depends crucially on the quality of parallel quasirandom sequences used. Much of the recent work dealing with parallel QMC methods has been aimed at splitting a single quasirandom sequence into many subsequences. In contrast with this perspective to concentrate on breaking one sequence up, this paper proposes an alternative approach to generating parallel sequences for QMC. This method generates parallel sequences of quasirandom numbers via scrambling. The exact meaning of scrambling depends on the type of parallel quasirandom numbers. In general, we seek to randomize the generator matrix for each quasirandom number generator. Specifically, this paper will discuss how to parallelize the Halton sequence via scrambling. The proposed scheme for generating parallel random number streams is especially good for heterogeneous and unreliable computing environments.

Designing and implementing cloud-based digital forensics hands-on labs

Cloud computing is radically changing the way how information technology services are created, delivered, accessed and managed. The rise of cloud computing not only has exacerbated the problem of scale for digital forensics activities, but also created a brand new front for cybercrime investigation with various challenges. Through this paper, we will give a comprehensive perspective in the integrated framework for the design of cloud-based digital forensics labs, along with scenario and procedures. In addition, those hands-on labs will be tested by training future investigators, current students whose career will be in Information Assurance (IA) related fields.

Computational investigations of scrambled Faure sequences

The Faure sequence is one of the well-known quasi-random sequences used in quasi-Monte Carlo applications. In its original and most basic form, the Faure sequence suffers from correlations between different dimensions. These correlations result in poorly distributed two-dimensional projections. A standard solution to this problem is to use a randomly scrambled version of the Faure sequence. We analyze various scrambling methods and propose a new nonlinear scrambling method, which has similarities with inversive congruential methods for pseudo-random number generation. We demonstrate the usefulness of our scrambling by means of two-dimensional projections and integration problems.

Implementation of a Security Access Control Model for Inter-organizational Healthcare Information Systems

The inability to share information across systems is just one of the major impediments in the health care business that hinders progress towards efficiency and cost-effectiveness. Workflow management systems are very popular and largely being used in a business environment for inter-organizations. This paper investigates workflow involvement of healthcare process in order to support and complement the transition of information and tasks among different healthcare organizations. This research examined dataflow between organizations. The purpose of this study is to propose a security access control model, based on role based access control, for integrating healthcare information systems of various healthcare organizations. A case study among pharmacies, hospitals and clinics is presented in this paper. Our experimental results show that this model is scalable and it can be easily extended to a pervasive computing environment.

Computational investigations of quasirandom sequences in generating test cases for specification-based tests

This paper presents work on generation of specification-driven test cases based on quasirandom (low-discrepancy) sequences instead of pseudorandom numbers. This approach is novel in software testing. This enhanced uniformity of quasirandom sequences leads to faster generation of test cases covering all possibilities. We demonstrate by examples that quasirandom sequences can be a viable alternative to pseudorandom numbers in generating test cases. In this paper, we present a method that can generate test cases from a decision table specification more effectively via quasirandom numbers. Analysis of a simple problem in this paper shows that quasirandom sequences achieve better data than pseudorandom numbers, and have the potential to converge faster and so reduce the computational burden. The use of different quasirandom sequences for generating test cases is presented in this paper