On the Farrell cohomology of mapping class groups

Oblatum 31-X-1991 & 24-II-1992     

Logical testing for rule-base management

We present a procedure to logically reduce simple implications that comprise the rule-base of an expert system. Our method uses topological sorting on a digraph representation that detects logical inconsistency and circular reasoning in linear-time. Then, the sort order provides an efficient method to detect and eliminate forced values and redundant rules. We consider additional diagnostic aids for the rule-base manager, notably how to range the number of propositions that could be true and how to consolodate the rule-base. We than show how the simple case may be extended to logically test a general rule-base with a decomposition principle.     

Calculation of the quark and gluon form factors to three loops in QCD

We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master integrals by using integration-by-parts relations. Our calculation confirms the recent results by Baikov et al. for the three-loop form factors. In addition, we derive the subleading \( \mathcal{O}\left( \varepsilon \right) \) terms for the fermion-loop type contributions to the three-loop form factors which are required for the extraction of the fermionic contributions to the four-loop quark and gluon collinear anomalous dimensions. The finite parts of the form factors are used to determine the hard matching coefficients for the Drell-Yan process and inclusive Higgs-production in soft-collinear effective theory.     

Neighborhood analysis: a case study on curriculum-based course timetabling

In this paper, we present an in-depth analysis of neighborhood relations for local search algorithms. Using a curriculum-based course timetabling problem as a case study, we investigate the search capability of four neighborhoods based on three evaluation criteria: percentage of improving neighbors, improvement strength and search steps. This analysis shows clear correlations of the search performance of a neighborhood with these criteria and provides useful insights on the very nature of the neighborhood. This study helps understand why a neighborhood performs better than another one and why and how some neighborhoods can be favorably combined to increase their search power. This study reduces the existing gap between reporting experimental assessments of local search-based algorithms and understanding their behaviors.     

Integrated exact,hybrid and metaheuristic learning methods for confidentiality protection

A vital task facing government agencies and commercial organizations that report data is to represent the data in a meaningful way and simultaneously to protect the confidentiality of critical components of this data. The challenge is to organize and disseminate data in a form that prevents such critical components from being inferred by groups bent on corporate espionage, to gain competitive advantages, or having a desire to penetrate the security of the information underlying the data. Controlled tabular adjustment is a recently developed approach for protecting sensitive information by imposing a special form of statistical disclosure limitation on tabular data. The underlying model gives rise to a mixed integer linear programming problem involving both continuous and discrete (zero-one) variables. We develop stratified ordered (s-ordered) heuristics and a new meta-heuristic learning approach for solving this model, and compare their performance to previous heuristics and to an exact algorithm embodied in the state-of-the-art ILOG- CPLEX software. Our new approaches are based on partitioning the problem into its discrete and continuous components, first creating an s-ordered heuristic that reduces the number of binary variables through a grouping procedure that combines an exact mathematical programming model with constructive heuristics. To gain further advantages we then replace the mathematical programming model with an evolutionary scatter search approach that makes it possible to extend the method to large problems with over 9000 entries. Finally, we introduce a new metaheuristic learning method that significantly improves the quality of solutions obtained.     

Structure and cation ordering in spinel-type TcCo2O4. An example of a trivalent technetium oxide

The structure of TcCo(2)O(4) has been determined using a combination of synchrotron X-ray and neutron powder diffraction methods. It has an inverse spinel structure where the Tc occupies the octahedral sites. Both the refined Tc-O distance and X-ray absorption spectra suggest the Tc is predominantly trivalent.     

Structures of N,N-dialkoxyamides: pyramidal anomeric amides with low amidicity

The first X-ray structures of two anomeric N,N-dialkoxyamides (2 and 3) have been obtained, which confirm that they are highly pyramidalized at nitrogen and have long N-CO bonds, a characteristic of other anomeric amides and a consequence of drastically reduced amidicity. The crystals also demonstrate chirality at the amide nitrogen in the solid state. The structures are well-predicted by density functional calculations using N,N-dimethoxyacetamide as a model. The amidicity of N,N-dimethoxyacetamide has been estimated by two independent methods, COSNAR and a new transamidation method, which give almost identical resonance stabilization energies of -8.6 kcal mol(-1) and only 47% that of N,N-dimethylacetamide computed at the same level. The total destabilization is composed of a resonance and an inductive contribution, which we have evaluated separately. The electronegative oxygens at nitrogen are responsible for localization of the nitrogen lone pair on the amide nitrogen, a factor that contributes to a loss of resonance over and above the impact of pyramidalization at nitrogen, as well as the fact that N,N-dimethoxyacetamide is predicted to protonate on the carbonyl oxygen in preference to nitrogen.     

A modeling/solution approach for optimal deployment of a weapons arsenal

This paper reports a real-world application of a large-scale assignment/allocation mixed-integer program for optimal deployment and targeting of missiles for the U.S. Strategic Air Command. We provide a NETFORM model that reduces the number of zero-one variables of a standard integer programming formulation by more than two orders of magnitude (by factors approaching 500) and a tailored NETFORM software system that solves problems involving 2,400 zero-one variables and 984,000 continuous variables to within 99.9% of optimality in less than one minute on an IBM 4381.This research was supported in part by the Center for Business Decision Analysis, the Hugh Roy cullen Centennial Chair in Business Administration, and the Office of Naval Research under Contract N00014-87-K-0190. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.