Pool resolution is NP-hard to recognize

A pool resolution proof is a dag-like resolution proof which admits a depth-first traversal tree in which no variable is used as a resolution variable twice on any branch. The problem of determining whether a given dag-like resolution proof is a valid pool resolution proof is shown to be NP-complete.     

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.     

Linear resolutions of quadratic monomial ideals

We study the minimal free resolution of a quadratic monomial ideal in the case where the resolution is linear. First, we focus on the squarefree case, namely that of an edge ideal. We provide an explicit minimal free resolution under the assumption that the graph associated with the edge ideal satisfies specific combinatorial conditions. In addition, we construct a regular cellular structure on the resolution. Finally, we extend our results to non-squarefree ideals by means of polarization.     

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.

     

Gröbner basis and free resolution of the ideal of 2-minors of a 2 × n matrix of linear forms *

We give a Gröbner basis for the ideal of 2-minors of a 2 × n utiatrix of linear forms. The minimal free resolution of such an ideal is obtained in [4] when the corresponding Kronecker-Weierstrass normal form has no iiilpotent blocks. For the general case, using this result, the Grobner basis and the Eliahou-Kervaire resolution for stable monomial ideals, we obtain a free resolution with the expected regularity. For a specialization of the defining ideal of ordinary pinch points, as a special case of these ideals, we provide a minimal free resolution explicitly in terms of certain Koszul complex.     

The geometric genus of splice-quotient singularities

We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for splice-quotient singularities with smaller resolution graphs. We also discuss the dimension of the first cohomology groups of certain invertible sheaves on a resolution of a splice-quotient singularity.

     

Reverse time migration for reconstructing extended obstacles in planar acoustic waveguides

We propose a new reverse time migration method for reconstructing extended obstacles in the planar waveguide using acoustic waves at a fixed frequency. We prove the resolution of the reconstruction method in terms of the aperture and the thickness of the waveguide. The resolution analysis implies that the imaginary part of the cross-correlation imaging function is always positive and thus may have better stability properties.Numerical experiments are included to illustrate the powerful imaging quality and to confirm our resolution results.     

子句集的神经网络归结

给出基于神经网络的归结方法。首先将子句集S表示为δ形式，并且用算子对(⊙， )引入两种类型的神经元；然后用这两种神经元构造子句集S的神经网络结构；而后给出基于子句集的神经网络的归结算法；最后证明了该算法的完备性，并用实例进行了验证。     

Enhanced algorithms for implementing the spectral discretization of the vorticity‐velocity‐pressure formulation of Stokes problem

In this paper, we deal with the numerical resolution of spectral discretization of the vorticity‐velocity‐pressure formulation of Stokes problem in a square or a cube provided with nonstandard boundary conditions, which involve the normal component of the velocity and the tangential components of the vorticity. Therefore, we propose two algorithms: the Uzawa algorithm and the global resolution. We implemented the two algorithms and compared their results. With global resolution, we obtained a very good accuracy with a small number of iteration.     

Minimal projective resolutions

In this paper, we present an algorithmic method for computing a projective resolution of a module over an algebra over a field. If the algebra is finite dimensional, and the module is finitely generated, we have a computational way of obtaining a minimal projective resolution, maps included. This resolution turns out to be a graded resolution if our algebra and module are graded. We apply this resolution to the study of the -algebra of the algebra; namely, we present a new method for computing Yoneda products using the constructions of the resolutions. We also use our resolution to prove a case of the ``no loop' conjecture.

     

The multiplicity of abelian covers of splice quotient singularities

From a resolution graph with certain conditions, Neumann and Wahl constructed an equisingular family of surface singularities called splice quotients. For this class some fundamental analytic invariants have been computed from their resolution graph. In this paper we give a method to compute the multiplicity of an abelian covering of a splice quotient from its resolution graph and the Galois group.     

Resolutions for free partially commutative monoids

We construct a free resolution for a free partially commutative monoid and, using this resolution, estimate the homological dimension of the monoid.     

An optimal monotone contention resolution scheme for bipartite matchings via a polyhedral viewpoint

Relaxation and rounding approaches became a standard and extremely versatile tool for constrained submodular function maximization. One of the most common rounding techniques in this context are contention resolution schemes. Such schemes round a fractional point by first rounding each coordinate independently, and then dropping some elements to reach a feasible set. Also the second step, where elements are dropped, is typically randomized. This leads to an additional source of randomization within the procedure, which can complicate the analysis. We suggest a different, polyhedral viewpoint to design contention resolution schemes, which avoids to deal explicitly with the randomization in the second step. This is achieved by focusing on the marginals of a dropping procedure. Apart from avoiding one source of randomization, our viewpoint allows for employing polyhedral techniques. Both can significantly simplify the construction and analysis of contention resolution schemes. We show how, through our framework, one can obtain an optimal monotone contention resolution scheme for bipartite matchings, which has a balancedness of 0.4762. So far, only very few results are known about optimality of monotone contention resolution schemes. Our contention resolution scheme for the bipartite case also improves the lower bound on the correlation gap for bipartite matchings. Furthermore, we derive a monotone contention resolution scheme for matchings that significantly improves over the previously best one. More precisely, we obtain a balancedness of 0.4326, improving on a prior 0.1997-balanced scheme. At the same time, our scheme implies that the currently best lower bound on the correlation gap for matchings is not tight. Our results lead to improved approximation factors for various constrained submodular function maximization problems over a combination of matching constraints with further constraints.

     

On the use of fuzzy inference techniques in assessment models: part I—theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules.     

Terrain map resolution

Studies of land combat processes usually deal with interactions between combatants on (and above) specified terrain. When this involves modeling through computer simulation (or even tracking units in a field test over actual terrain), the terrain is usually represented as a digital terrain map for computational purposes. With a digital terrain map, the terrain surface is represented as a simple surface (often a step function) over a two-dimensional domain covered by a tesselation of squares or hexagons. As the size of the underlying units (let us assume squares) in the domain is reduced, the resolution of the map increases, but the computational cost of preparing, storing and using the map increases exponentially. Thus, there is a question of how high the resolution needs to be for a given application. We study this question from the point of view of accuracy of intervisibility calculations as a function of terrain resolution.The approach involves computation of theoretical total intervisibility with varying levels of terrain resolution over simple “pseudo terrains” having assumed mathematical forms. It is found that intervisibility approximations based on digital terrain rapidly approach the theoretical limiting intervisibility as resolution is increased. Relationships between intervisibility surfaces and current military doctrine concerning location of defending forces at the “military crest” are discussed.     

Truncated resolution model structures

Using the dual of Bousfield-Friedlander localization, we colocalize resolution model structures on cosimplicial objects over a left proper model category to get truncated resolution model structures. These are useful for studying realization and moduli problems in algebraic topology.     

A resolution (minimal model) of the PROP for bialgebras

This paper is concerned with a minimal resolution of the PROP for bialgebras (Hopf algebras without unit, counit and antipode). We prove a theorem about the form of this resolution (Theorem 15) and give, in Section 5, a lot of explicit formulas for the differential.     

Bioriented flags and resolutions of Schubert varieties

We use incidence relations running in two directions in order to construct a Kempf–Laksov type resolution for any Schubert variety of the complete flag manifold but also an embedded resolution for any Schubert variety in the Grassmannian. These constructions are alternatives to the celebrated Bott–Samelson resolutions. The second process led to the introduction of W-flag varieties, algebro-geometric objects that interpolate between the standard flag manifolds and products of Grassmannians, but which are singular in general. The surprising simple desingularization of a particular such type of variety produces an embedded resolution of the Schubert variety within the Grassmannian.