Contents Volume 29

Volume Contents

Contents Volume 29     

Monotone paths on polytopes

We investigate the vertex-connectivity of the graph of f-monotone paths on a d-polytopeP with respect to a generic functionalf. The third author has conjectured that this graph is always (d )-connected. We resolve this conjecture positively for simple polytopes and show that the graph is 2-connected for any d-polytope with . However, we disprove the conjecture in general by exhibiting counterexamples for each in which the graph has a vertex of degree two. We also re-examine the Baues problem for cellular strings on polytopes, solved by Billera, Kapranov and Sturmfels. Our analysis shows that their positive result is a direct consequence of shellability of polytopes and is therefore less related to convexity than is at first apparent. Received April 6, 1999 / in final form October 1, 1999 / Published online July 20, 2000     

Determination of antimicrobial activity and resistance to oxidation of moringa peregrina seed oil

The antimicrobial activity of the oil extracted with n-hexane from the seeds of Moringa peregrina was tested against Staphylococcus aureus, S. epidermidis, Pseudomonas aeruginosa, Escherichia coli, Enterobacter cloacae, Klebsiella pneumoniae, Candida albicans, C. tropicalis and C. glabrata. The oil proved effective against all of the tested microorganisms. Standard antibiotics (netilmycin, 5-flucytocine, intraconazole and 7-amino-4-methylcoumarin-3-acetic acid) were used for comparison. The resistance to oxidation of the extracted seed oil was also determined.     

Stereochemically consistent reaction mapping and identification of multiple reaction mechanisms through integer linear optimization

Reaction mappings are of fundamental importance to researchers studying the mechanisms of chemical reactions and analyzing biochemical pathways. We have developed an automated method based on integer linear optimization, ILP, to identify optimal reaction mappings that minimize the number of bond changes. An alternate objective function is also proposed that minimizes the number of bond order changes. In contrast to previous approaches, our method produces mappings that respect stereochemistry. We also show how to locate multiple reaction mappings efficiently and determine which of those mappings correspond to distinct reaction mechanisms by automatically detecting molecular symmetries. We demonstrate our techniques through a number of computational studies on the GRI-Mech, KEGG LIGAND, and BioPath databases. The computational studies indicate that 99% of the 8078 reactions tested can be addressed within 1 CPU hour. The proposed framework has been incorporated into the Web tool DREAM ( http://selene.princeton.edu/dream/ ), which is freely available to the scientific community.     

Computational characterization of zeolite porous networks: an automated approach

An automated method has been developed to fully characterize the three-dimensional structure of zeolite porous networks. The proposed optimization-based approach starts with the crystallographic coordinates of a structure and identifies all portals, channels, and cages in a unit cell, as well as their connectivity. We apply our algorithms to known zeolites, hypothetical zeolites, and zeolite-like structures and use the characterizations to calculate important quantities such as pore size distribution, accessible volume, surface area, and largest cavity and pore limiting diameters. We aggregate this data over many framework types to gain insights about zeolite selectivity. Finally, we develop a continuous-time Markov chain model to estimate the probability of occupancy of adsorption sites throughout the porous network. ZEOMICS, an online database of structure characterizations and web tool for the automated approach is freely available to the scientific community (http://helios.princeton.edu/zeomics/).     

A tri-Hamiltonian formulation of the full Kostant-Toda lattice

We define Poisson structures which lead to a tri-Hamiltonian formulation for the full Kostant-Toda lattice. In addition, a hierarchy of vector fields called master symmetries are constructed and they are used to generate the nonlinear Poisson brackets and other invariants. Various deformation relations are investigated. The results are analogous to results for the finite nonperiodic Toda lattice.     

Transmission problems in contrasting chiral media

Time harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle embedded in a homogeneous chiral environment. The corresponding transmission problem is reduced, with the use of Beltrami fields, to an integral equation over the interface between the obstacle and the surrounding medium. This integral equation is known to be weakly uniquely solvable except for a discrete set of electromagnetic parameters of the obstacle. We establish classical solvability, and in some interesting cases (mirror conjugated and isoimpedant chiral media) it is shown that unique solvability is established without the exception of any set of electromagnetic parameters.     

Tight convex underestimators for {{\mathcal C}^2}-continuous problems: I. univariate functions

A novel method for the convex underestimation of univariate functions is presented in this paper. The method is based on a piecewise application of the well-known αBB underestimator, which produces an overall underestimator that is piecewise convex. Subsequently, two algorithms are used to identify the linear segments needed for the construction of its -continuous convex envelope, which is itself a valid convex underestimator of the original function. The resulting convex underestimators are very tight, and their tightness benefits from finer partitioning of the initial domain. It is theoretically proven that there is always some finite level of partitioning for which the method yields the convex envelope of the function of interest. The method was applied on a set of univariate test functions previously presented in the literature, and the results indicate that the method produces convex underestimators of high quality in terms of both lower bound and tightness over the whole domain under consideration.     

Decomposition based and branch and bound global optimization approaches for the phase equilibrium problem

An increasingly popular approach when solving the phase and chemical equilibrium problem is to pose it as an optimization problem. However, difficulties are encountered due to the highly nonlinear nature of the models used to represent the behavior of the fluids, and because of the existence of multiple local solutions. This work shows how it is possible to guarantee -global solutions for a certain important class of the phase and chemical equilibrium problem, namely when the liquid phase can be modeled using neither the Non-Random Two-Liquid (NRTL) equation, or the UNIversal QUAsi Chemical (UNIQUAC) equation. Ideal vapor phases are easily incorporated into the global optimization framework. A numberof interesting properties are described which drastically alter the structure of the respective problems. For the NRTL equation, it is shown that the formulation can be converted into a biconvex optimization problem. The GOP algorithm of Floudas and Visweswaran [8, 9] can then be used to obtain -global solutions in this case. For the UNIQUAC equation, the new properties show how the objective function can be transformed into the difference of two convex functions (i.e. a D.C. programming problem is obtained), where the concave portion is separable. A branch and bound algorithm based on that of Falk and Soland [6] is used to guarantee convergence to an -global solution. Examples are presented which demonstrate the performance of both algorithms.     

Maximizing the guarded boundary of an Art Gallery is APX-complete

In the Art Gallery problem, given is a polygonal gallery and the goal is to guard the gallery's interior or walls with a number of guards that must be placed strategically in the interior, on walls or on corners of the gallery. Here we consider a more realistic version: exhibits now have size and may have different costs. Moreover the meaning of guarding is relaxed: we use a new concept, that of watching an expensive art item, i.e. overseeing a part of the item. The main result of the paper is that the problem of maximizing the total value of a guarded weighted boundary is APX-complete. This is shown by an appropriate ‘gap-preserving’ reduction from the Max-5-occurrence-3-Sat problem. We also show that this technique can be applied to a number of maximization variations of the art gallery problem. In particular we consider the following problems: given a polygon with or without holes and k available guards, maximize a) the length of walls guarded and b) the total cost of paintings watched or overseen. We prove that all the above problems are APX-complete.