Utility theory in conflict resolution

In this paper, multi-attribute utility theory is extended to accommodate adversarial problem solving situations involving multiple interacting agents. Such situations are resolved by partial goal satisfaction and persuasion, and have only scantily been described in the AI literature. Utility theory is shown to provide a computational framework to (a) generate a compromise solution that partially satisfies the conflicting goals of the agents, (b) evaluate whether a solution is an improvement on a previously rejected one, and (c) determine the effectiveness of persuasive arguments. Our examples are taken from the domain of labor mediation and are implemented in a computer program, called the PERSUADER.     

A note on resolution of rational and hypersurface singularities

It is well known that the exceptional set in a resolution of a rational surface singularity is a tree of rational curves. We generalize the combinatoric part of this statement to higher dimensions and show that the highest cohomologies of the dual complex associated to a resolution of an isolated rational singularity vanish. We also prove that the dual complex associated to a resolution of an isolated hypersurface singularity is simply connected. As a consequence, we show that the dual complex associated to a resolution of a 3-dimensional Gorenstein terminal singularity has the homotopy type of a point.

     

On crepant resolution of some hypersurface singularities and a criterion for UFD

In this article, we find some diagonal hypersurfaces that admit crepant resolutions. We also give a criterion for unique factorization domains.

     

Generalized resolution and cutting planes

This paper illustrates how the application of integer programming to logic can reveal parallels between logic and mathematics and lead to new algorithms for inference in knowledge-based systems. If logical clauses (stating that at least one of a set of literals is true) are written as inequalities, then the resolvent of two clauses corresponds to a certain cutting plane in integer programming. By properly enlarging the class of cutting planes to cover clauses that state that at least a specified number of literals are true, we obtain a generalization of resolution that involves both cancellation-type and circulant-type sums. We show its completeness by proving that it generates all prime implications, generalizing an early result by Quine. This leads to a cutting-plane algorithm as well as a generalized resolution algorithm for checking whether a set of propositions, perhaps representing a knowledge base, logically implies a given proposition. The paper is intended to be readable by persons with either an operations research or an artificial intelligence background.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie-Mellon University. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

Anick resolution and Koszul algebras of finite global dimension

We show how to study a certain associative algebra recently discovered by Iyudu and Shkarin using the Anick resolution. This algebra is a counterexample to the conjecture of Positselski on Koszul algebras of finite global dimension.     

Equivariant resolution of points of indeterminacy

We prove an equivariant form of Hironaka's theorem on elimination of points of indeterminacy. Our argument uses canonical resolution of singularities and an extended version of Sumihiro's equivariant Chow lemma.

     

Bayesian selection of primary resolution and wavelet basis functions for wavelet regression

This paper considers a Bayesian approach to selecting a primary resolution and wavelet basis functions. Most of papers on wavelet shrinkage have been focused on thresholding of wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, it turns out that a proper primary resolution is much affected by the shape of an unknown function rather than by the sample size. In particular, Bayesian approaches to wavelet series suffer from computational burdens if the chosen primary resolution is too high. A surplus primary resolution may result in a poor estimate. In this paper, we propose a simple Bayesian method to determine a primary resolution and wavelet basis functions independently of the sample size. Results from a simulation study demonstrate the promising empirical properties of the proposed approach.     

Bockstein basis and resolution theorems in extension theory

We prove a generalization of the Edwards-Walsh Resolution Theorem:

Theorem. Let G be an abelian group withPG=P, where. Letn∈Nand let K be a connected CW-complex withπn(K)≅G,πk(K)≅0for0?k<n. Then for every compact metrizable space X with XτK (i.e., with K an absolute extensor for X), there exists a compact metrizable space Z and a surjective mapπ:Z→Xsuch that

(a)

π is cell-like,

(b)

dimZ?n, and

(c)

ZτK.

     

On the resolution of 3-dimensional terminal singularities

We show that there is at most one nonrational exceptional divisor with discrepancy 1 over a three-dimensional terminal point of type cD. If such a divisor exists, then it is birationally isomorphic to the surface ¹ × C, where C is a hyperelliptic (for g(C) > 1) curve.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 127–140.Original Russian Text Copyright © 2005 by D. A. Stepanov.This revised version was published online in April 2005 with a corrected issue number.     

Optimization problems in electron microscopy of single particles

Electron Microscopy is a valuable tool for the elucidation of the three-dimensional structure of macromolecular complexes. Knowledge about the macromolecular structure provides important information about its function and how it is carried out. This work addresses the issue of three-dimensional reconstruction of biological macromolecules from electron microscopy images. In particular, it focuses on a methodology known as “single-particles” and makes a thorough review of all those steps that can be expressed as an optimization problem. In spite of important advances in recent years, there are still unresolved challenges in the field that offer an excellent testbed for new and more powerful optimization techniques. AMS Subject Classification 92C55 · 90C90 · 44A12 · 78A15 · 65R32     

Optimization, resolution and application of composite compact finite difference templates

Spectral-like compact finite differencing schemes are capable of achieving high spatial efficiency of complex physics in irregular domains with difficult boundary conditions. Their low-resolution errors are commonly reached through large stencils sizes and/or parameter optimization. The field stencils require boundary (and near boundary) stencils to close the composite template for implicit solution. Present practices often optimize each participating stencil individually with aim toward insuring global stability and/or spectral-like characteristics. However, analyzing each stencil separately incorrectly quantifies the local resolution errors. A new process is proposed that properly quantifies the dispersive and dissipative errors of optimized templates in the spectral domain. The templates are optimized at the boundary and adjacent interior points. Both tri- (five-point) and penta-diagonal (seven-point) compact systems are treated in this fashion. A spectral eigenvalue analysis shows the resultant composites to be numerically stable. An a priori procedure is formulated that quantifies the expected reduction in the local predictive error due specifically to the improved template spatial resolution. Three test problems are selected from the Computational Aeroacoustics workshops to demonstrate their improved predictive accuracy. Finally, the present technique provides closure for exercising the three essential criteria of numerical accuracy, stability and resolution when developing composite compact finite difference templates for practical applications.     

On the modal resolution of kernel density estimators

The ability of a kernel density estimator to resolve modes of the underlying density is investigated. For various bimodal densities and three different kernels, the smallest sample size required for the expectation of an optimally smoothed kernel estimator to be bimodal is determined. The optimality criterion employed is equivalent to asymptotic mean integrated squared error for sufficiently smooth densities.     

Theory and application of conflict resolution with hybrid preference in colored graphs

An algebraic approach is proposed to calculate stabilities in a colored graph with hybrid preference. The algebraic approach establishes a hybrid framework for stability analysis by combining strength of preference and unknown preference. The hybrid system is more general than existing models, which consider preference strength and preference uncertainty separately. Within the hybrid preference structure, matrix representations of four basic stabilities in a colored graph are extended to include mild, strong, and uncertain preference and algorithms are developed to calculate efficiently the inputs essential to the stability definitions. A specific case study, including multiple decision makers and hybrid preference, is used to illustrate how the proposed method can be applied in practice.     

Noncommutative resolution, F-blowups and D-modules

We explain the isomorphism between the G-Hilbert scheme and the F-blowup from the noncommutative viewpoint after Van den Bergh. In doing this, we immediately and naturally arrive at the notion of D-modules. We also find, as a byproduct, a canonical way to construct a noncommutative resolution at least for a few classes of singularities in positive characteristic.     

Study of coals by high resolution solid state nuclear magnetic resonance

By using high resolution solid state nuclear magnetic resonance method, six coal samples coming from four countries were investigated. Twelve structural parameters of these samples were measured and compared withthose of Chinese coals. Spectral editing experiment was carried out and¹⁵N NMR spectrum was obtained. Project supported by the National Natural Science Foundation of China (Grant No. 19774068)and the NEDO’s International Joint Research Program of Japan.     

Optimal partially balanced fractional 2 m 1+m 2 factorial designs of resolution IV

Summary This paper investigates some partially balanced fractional 2 ^m ₁+m ₂ factorial designs of resolution IV derived from partially balanced arrays, which permit estimation of the general mean, all main effects, all two-factor interactions within each set of them _k factors (k=1, 2) and some linear combinations of the two-factor interactions between the sets of them _k ones. In addition, optimal designs with respect to the generalized trace criterion defined by Shirakura (1976,Ann. Statist.,4, 723–735) are presented for each pair (m ₁,m ₂) with 2≦m ₁≦m ₂ andm ₁+m ₂≦6, and for values ofN (the number of observations) in a reasonable range. Partially supported in part by Grants 56530009 (C) and 57530010 (C).     

Further improvement of weakly nonlinear theory of hydrodynamic stability

The problems of the weakly nonlinear theory of hydrodynamic stability has been re-addressed; namely, (i) why is the radius of convergence of its solution too small? (ii) it is not appropriate to use it to deal with the evolution problem of disturbances; the main reason is that the way of calculating the mean flow distortion is inappropriate, (iii) it cannot be used to deal with the initial value problem. Ways of its improvement were proposed. Its correctness was confirmed by its comparison with the results of numerical simulations.     

High resolution quantization and entropy coding of jump processes

We study the quantization problem for certain types of jump processes. The probabilities for the number of jumps are assumed to be bounded by Poisson weights. Otherwise, jump positions and increments can be rather generally distributed and correlated. We show in particular that in many cases entropy coding error and quantization error have distinct rates. Finally, we investigate the quantization problem for the special case of R^d${\mathbb{R}}^d$-valued compound Poisson processes.