On Accelerating Monte Carlo Integration Using Orthogonal Projections

Methodology and Computing in Applied Probability - Monte Carlo simulation is an indispensable tool in calculating high-dimensional integrals. Although Monte Carlo integration is notoriously known...     

On the relationship between catalytic residues and their protein contact number

Due to advances in structural biology, an increasing number of protein structures of unknown function have been deposited in Protein Data Bank (PDB). These proteins are usually characterized by novel structures and sequences. Conventional comparative methodology (such as sequence alignment, structure comparison, or template search) is unable to determine their function. Thus, it is important to identify protein's function directly from its structure, but this is not an easy task. One of the strategies used is to analyze whether there are distinctive structure-derived features associated with functional residues. If so, one may be able to identify the functional residues directly from a single structure. Recently, we have shown that protein weighted contact number is related to atomic thermal fluctuations and can be used to derive motional correlations in proteins. In this report, we analyze the weighted contact-number profiles of both catalytic residues and non-catalytic residues for a dataset of 760 structures. We found that catalytic residues have distinct distributions of weighted contact numbers from those of non-catalytic residues. Using this feature, we are able to effectively differentiate catalytic residues from other residues with a single optimized threshold value. Our method is simple to implement and compares favourably with other more sophisticated methods. In addition, we discuss the physics behind the relationship between catalytic residues and their contact numbers as well as other features (such as residue centrality or B-factors) associated with catalytic residues.     

Departure Processes of BMAP/G/1 Queues

A unified approach is applied to analyze the departure processes of finite/infinite BMAP/G/1 queueing systems for both vacationless and vacation arrangements via characterizing the moments, the z-transform of the scaled autocovariance function of interdeparture times C _P (z), and lag n (n1) covariance of interdeparture times. From a structural point of view, knowing departure process helps one to understand the impact of service mechanisms on arrivals. Through numerical experiments, we investigate and discuss how the departure statistics are affected by service and vacation distributions as well as the system capacity. From a practical perspective, output process analysis serves to bridge the nodal performance and connectionwise performance. Our results can be then used to facilitate connection- or networkwise performance analysis in the current high-speed networks.     

Optical Nonlinearities of Phthalocyanines and Naphthalocyanines

The nonlinear absorption and refraction of soluble phthalocyanines and naphthalocyanines have been measured with z-scan technique using 8 ns, 532 nm laser pulses. The excited-state absorption cross-section and the excited-state refractive-index cross section have been estimated under the consideration of laser induced thermal effect. The excited state absorption induced n2 and Re χ⁽³⁾ values are in the range of 10^?12 esu. These observed data are enhanced by the concentrations of both metal substituted Pc's and Nc's, but this increment became very small for the metal free phthalocyanine. During the optical limiting experiments, a 25% linear transmitted solution of R₈PcH² can limit laser pulses to ≤ 120 μJ from incident energies as high as 2.0 mJ, and this limitation moved down to ≤ 50 μJ when replacing R₈PcCu from P₈PcH₂. A similar property has also been observed for the metal substituted naphthalocyanines. The results indicate that both the nonlinear refraction and optical limiting properties should be strongly affected by the metal induced triplet-state nonlinear absorption in both Pc's and Nc's. Moreover, the laser pulses created a self trapped filament inside the solution of this optical limiter, while emitting time-resolved, concentric rings on a projection screen, which could be induced by the thermal lensing effect. The various optical nonlinear properties observed from these materials should make them valuable as an optical limiter.     

The departure process of discrete-time queueing systems with Markovian type inputs

This paper proposes a unified matrix-analytic approach to characterize the output processes of general discrete-time lossless/lossy queueing systems in which time is synchronized/slotted into fixed length intervals called slots. The arrival process can be continuous- or discrete-time Markovian processes. It can be either renewal or non-renewal. The service of a customer commences at the beginning of a slot, consumes a random number of slots, and completes at the end of a later slot. The service times are independent and follow a common and general distribution. Systems with and without server vacations are both treated in this paper. These queueing systems have potential applications in asynchronous transfer mode (ATM) networks, packet radio networks, etc. Since the output process of a node in a queueing network becomes an input process to some node at the next stage, the results of this paper can be used to facilitate end-to-end performance analysis which has attracted more and more attention in the literature. This revised version was published online in June 2006 with corrections to the Cover Date.