The vertex-cover polynomial of a graph

In this paper we define the vertex-cover polynomial Ψ(G,τ) for a graph G. The coefficient of τ^r in this polynomial is the number of vertex covers V′ of G with |V′|=r. We develop a method to calculate Ψ(G,τ). Motivated by a problem in biological systematics, we also consider the mappings f from {1, 2,…,m} into the vertex set V(G) of a graph G, subject to f⁻¹(x)f⁻¹(y)≠ for every edge xy in G. Let F(G,m) be the number of such mappings f. We show that F(G,m) can be determined from Ψ(G,τ).     

A DSC study of the effects of sugars on thermal properties of rice starch gels before and after aging

Thermal characterization of gelatinized binary rice starch-water and ternary starch-sugar-water gels before and after aging was carried out using differential scanning calorimetry. The glass transition temperature of the maximally freeze-concentrated solution (T_g) in both fresh and aged gels was observed to decrease progressively with increasing sugar concentration. Aging of the gels generally shiftedT_g to higher temperatures, but had little or no effect on the ice melting peak temperature (T _m). The presence of various sugars could either accelerate or retard starch (amylopectin) recrystallization, depending on the type and concentration of sugar, as well as on starch/water ratio. A hypothesis based on the dual antiplasticizing-plasticizing effects of sugars was postulated to explain the observed effects. Of the sugars studied, xylose and fructose appeared to display exceptional retardative and accelerative effects, respectively, on retrogradation.This study was funded by a Sixth Malaysia Plan R&D grant under the Intensification of Research Priority Areas (IRPA) Program of the Ministry of Science, Technology and Environment, Malaysia. We thank Dr. Harry Levine and Dr. Louise Slade for giving us the opportunity to contribute a paper to this special issue of JTA.     

Machine Learning Approaches for Metalloproteins

Metalloproteins are a family of proteins characterized by metal ion binding, whereby the presence of these ions confers key catalytic and ligand-binding properties. Due to their ubiquity among biological systems, researchers have made immense efforts to predict the structural and functional roles of metalloproteins. Ultimately, having a comprehensive understanding of metalloproteins will lead to tangible applications, such as designing potent inhibitors in drug discovery. Recently, there has been an acceleration in the number of studies applying machine learning to predict metalloprotein properties, primarily driven by the advent of more sophisticated machine learning algorithms. This review covers how machine learning tools have consolidated and expanded our comprehension of various aspects of metalloproteins (structure, function, stability, ligand-binding interactions, and inhibitors). Future avenues of exploration are also discussed.     

Robust suboptimal control of nonlinear systems

In this paper, we consider a nonlinear dynamic system with uncertain parameters. Our goal is to choose a control function for this system that balances two competing objectives: (i) the system should operate efficiently; and (ii) the system’s performance should be robust with respect to changes in the uncertain parameters. With this in mind, we introduce an optimal control problem with a cost function penalizing both the system cost (a function of the final state reached by the system) and the system sensitivity (the derivative of the system cost with respect to the uncertain parameters). We then show that the system sensitivity can be computed by solving an auxiliary initial value problem. This result allows one to convert the optimal control problem into a standard Mayer problem, which can be solved directly using conventional techniques. We illustrate this approach by solving two example problems using the software MISER3.     

Optimal Control of Nonlinear Fractional-Order Systems with Multiple Time-Varying Delays

Journal of Optimization Theory and Applications - This paper considers an optimal control problem governed by nonlinear fractional-order systems with multiple time-varying delays and subject to...     

Computational algorithm for a distributed optimal control problem of parabolic type with terminal inequality constraints

A computational algorithm for optimal control problems with control and terminal inequality constraints involving first boundary-value problems of parabolic type is presented. The convergence properties are also studied.This work, which was partly supported by the Australian Research Grants Committee, was done during the period when Z. S. Wu was an Honorary Visiting Fellow in the School of Mathematics at the University of New South Wales, Australia.     

A class of optimal state-delay control problems

We consider a general nonlinear time-delay system with state-delays as control variables. The problem of determining optimal values for the state-delays to minimize overall system cost is a non-standard optimal control problem–called an optimal state-delay control problem–that cannot be solved using existing optimal control techniques. We show that this optimal control problem can be formulated as a nonlinear programming problem in which the cost function is an implicit function of the decision variables. We then develop an efficient numerical method for determining the cost function’s gradient. This method, which involves integrating an auxiliary impulsive system backwards in time, can be combined with any standard gradient-based optimization method to solve the optimal state-delay control problem effectively. We conclude the paper by discussing applications of our approach to parameter identification and delayed feedback control.     

Fabrications of hollow nanocubes of Cu(2)O and Cu via reductive self-assembly of CuO nanocrystals

In this work, a template-free synthetic approach for generating single-crystalline hollow nanostructures has been described. Using the small optical band-gap cuprous oxide Cu(2)O as a model case, we demonstrate that, instead of normally known spherical aggregates, primary nanocrystalline particles can first self-aggregate into porous organized solids with a well-defined polyhedral shape according to the oriented attachment mechanism, during which chemical conversion can also be introduced. In contrast to the spherical aggregates, where the nanocrystallites are randomly joined together, the Cu(2)O nanocrystallites in the present case are well organized, maintaining a definite geometric shape and a global crystal symmetry. Due to the presence of intercrystallite space, hollowing and chemical conversion can also be carried out in order to create central space and change the chemical phase of nanostructured polyhedrons. It has been revealed that Ostwald ripening plays a key role in the solid evacuation process. Using this synthetic strategy, we have successfully prepared single-crystal-like Cu(2)O nanocubes and polycrystalline Cu nanocubes with hollow interiors. For the first time, we demonstrate that nanostructured polyhedrons of functional materials with desired interiors can be synthesized in solution via a combination of oriented attachment and Ostwald ripening processes.