Guan-Shieng Huang

Edit distance for a run-length-encoded string and an uncompressed string

We propose a new algorithm for computing the edit distance of an uncompressed string against a run-length-encoded string. For an uncompressed string of length n and a compressed string with M runs, the algorithm computes their edit distance in time O(Mn). This result directly implies an O(min{mN,Mn}) time algorithm for strings of lengths m and n with M and N runs, respectively. It improves the previous best known time bound O(mN+Mn).

An efficient convergent lattice algorithm for European Asian options

Financial options whose payoff depends critically on historical prices are called path-dependent options. Their prices are usually harder to calculate than options whose prices do not depend on past histories. Asian options are popular path-dependent derivatives, and it has been a long-standing problem to price them efficiently and accurately. No known exact pricing formulas are available to price them under the continuous-time Black-Scholes model. Although approximate pricing formulas exist, they lack accuracy guarantees. Asian options can be priced numerically on the lattice. A lattice divides the time to maturity into n equal-length time steps. The option price computed by the lattice converges to the option value under the Black-Scholes model as n->~. Unfortunately, only subexponential-time algorithms are available if Asian options are to be priced on the lattice without approximations. Efficient approximation algorithms are available for the lattice. The fastest lattice algorithm published in the literature runs in O(n^3^.^5)-time, whereas for the related PDE method, the fastest one runs in O(n^3) time. This paper presents a new lattice algorithm that runs in O(n^2^.^5) time, the best in the literature for such methods. Our algorithm exploits the method of Lagrange multipliers to minimize the approximation error. Numerical results verify its accuracy and the excellent performance.

Two-Literal Logic Programs and Satisfiability Representation of Stable Models: A Comparison

Logic programming with the stable model semantics has been proposed as a constraint programming paradigm for solving constraint satisfaction and other combinatorial problems. In such a language one writes function-free logic programs with negation. Such a program is instantiated to a ground program and its stable models are computed. In this paper, we identify a class of logic programs for which the current techniques in solving SAT problems can be adopted for the computation of stable models efficiently. These logic programs are called 2-literal programs where each rule or constraint consists of at most 2 literals. Many logic programming encodings of graph-theoretic, combinatorial problems given in the literature fall into the class of 2-literal programs. We show that a 2-literal program can be translated to a SAT instance in polynomial time without using extra variables. We report and compare experimental results on solving a number of benchmarks by a stable model generator and by a SAT solver.

A Hormone Receptor-Based Transactivator Bridges Different Binary Systems to Precisely Control Spatial-Temporal Gene Expression in Drosophila

The GAL4/UAS gene expression system is a precise means of targeted gene expression employed to study biological phenomena in Drosophila. A modified GAL4/UAS system can be conditionally regulated using a temporal and regional gene expression targeting (TARGET) system that responds to heat shock induction. However heat shock-related temperature shifts sometimes cause unexpected physiological responses that confound behavioral analyses. We describe here the construction of a drug-inducible version of this system that takes advantage of tissue-specific GAL4 driver lines to yield either RU486-activated LexA-progesterone receptor chimeras (LexPR) or β-estradiol-activated LexA-estrogen receptor chimeras (XVE). Upon induction, these chimeras bind to a LexA operator (LexAop) and activate transgene expression. Using GFP expression as a marker for induction in fly brain cells, both approaches are capable of tightly and precisely modulating transgene expression in a temporal and dosage-dependent manner. Additionally, tissue-specific GAL4 drivers resulted in target gene expression that was restricted to those specific tissues. Constitutive expression of the active PKA catalytic subunit using these systems altered the sleep pattern of flies, demonstrating that both systems can regulate transgene expression that precisely mimics regulation that was previously engineered using the GeneSwitch/UAS system. Unlike the limited number of GeneSwitch drivers, this approach allows for the usage of the multitudinous, tissue-specific GAL4 lines for studying temporal gene regulation and tissue-specific gene expression. Together, these new inducible systems provide additional, highly valuable tools available to study gene function in Drosophila.

Sequence Alignment Algorithms for Run-Length-Encoded Strings

A unified framework is applied to solving various sequence comparison problems for run-length encoded strings. All of these algorithms take O( min {mni¾?,mi¾?n}) time and O( max {m,n}) space, for two strings of lengths mand n, with mi¾? and ni¾? runs, respectively. We assume the linear-gap model and make no assumption on the scoring matrices, which maximizes the applicability of these algorithms. The trace (i.e., the way to align two strings) of an optimal solution can also be recovered within the same time and space bounds.

A metric for rooted trees with unlabeled vertices based on nested parentheses

In this paper, we propose a new metric for rooted trees with unlabeled vertices based on alignments of nested parenthesis strings. We prove that the time complexity for computing this metric is NP-hard and present a 1.5-approximation algorithm for it.

A Practical Edit-Distance Model for RNA Secondary-Structure Comparison

We point out the importance to incorporate affinegappenalties in RNA secondary-structure comparison. Twonotions of affine-gap penalties, one for sequences and the otherfor structures, are developed. A model from Jiang et al. in [JComput Biol, 2002, 9, (2), pp. 371–388] is extended to allowthis facility, and a polynomial-time algorithm is provided inthis paper. Experimental results in this paper revealed that ournew model generates more accurate and biological meaningfulalignments than several existing algorithms.

Boolean rings for intersection-based satisfiability

A potential advantage of using a Boolean-ring formalism for propositional formulae is the large measure of simplification it facilitates. We propose a combined linear and binomial representation for Boolean-ring polynomials with which one can easily apply Gaussian elimination and Horn-clause methods to advantage. We demonstrate that this framework, with its enhanced simplification, is especially amenable to intersection-based learning, as in recursive learning and the method of Stalmarck. Experiments support the idea that problem variables can be eliminated and search trees can be shrunk by incorporating learning in the form of Boolean-ring saturation.

Pricing Asian Options with an Efficient Convergent Approximation Algorithm

Asian options are popular path-dependent derivatives in the financial market. However, how to price them efficiently and accurately has been a longstanding research and practical problem. No known exact pricing formulas are available to price the Asian option. Although approximate pricing formulas exist, they lack accuracy guarantees. Asian options can be priced on the lattice. A lattice divides a time interval into n equal-length time steps. It is known that the value computed by the lattice converges to the true option value as n → ∞. Unfortunately, only subexponential-time algorithms are available if Asian options are to be priced on the lattice without approximations. Efficient approximation algorithms are available for the lattice. The best known in the literature is an O(n 3.5)-time approximation lattice algorithm and an O(n 3)-time approximation PDE algorithm. Our paper suggests an O(n 2.5)-time lattice algorithm. Our algorithm uses a novel technique based on the method of Lagrange multipliers to minimize the approximation error. Numerical results verify the accuracy and the excellent performance of our algorithm.