Deconvolving Multivariate Density from Random Field

We consider the problem of estimating a continuous bounded multivariate probability density function (pdf) when the random field X _i , i ∈ Z ^d from the density is contaminated by measurement errors. In particular, the observations Y _i , i ∈ Z ^d are such that Y _i = X _i + ε _i , where the errors ε _i are a sample from a known distribution. We improve the existing results in at least two directions. First, we consider random vectors in contrast to most existing results which are only concerned with univariate random variables. Secondly, and most importantly, while all the existing results focus on the temporal cases (d = 1), we develop the results for random vectors with a certain spatial interaction. Precise asymptotic expressions and bounds on the mean-squared error are established, along with rates of both weak and strong consistencies, for random fields satisfying a variety of mixing conditions. The dependence of the convergence rates on the density of the noise field is also studied. This revised version was published online in June 2006 with corrections to the Cover Date.     

Modeling plant disease with biological control of insect pests

Abstract

Introduction: This article discusses the problem of plant diseases that pose major threat to agriculture in several parts of the World. Herein, our focus is on viruses that are transmitted from one plant to another by insect vectors. We consider predators that prey on insect population leading to reduction in infection transmission of plant diseases. Methods: We formulate and analyze a deterministic model for plant disease by incorporating predators as biological control agents. Existence of equilibria and the stability of the model are discussed in-detail. Basic reproduction number R₀ of the proposed model is also computed and this helps in determining the impact of different key parameters on the transmission dynamics of disease. Additionally, the proposed model is extended to stochastic model and simulation results of both deterministic and stochastic models are compared and analyzed. Results: Our results of stochastic model show the less number of infected plants and insects compared to corresponding results for deterministic model. Also, our results analyze the impact of different key parameters on the equilibrium levels of infected plants and identify the key parameters. Discussion: Presented results are used to conclude and demonstrate that the biological control is effective in reducing the infection transmission of plant disease and there is a need to use plant-insect-specific predators to get desirable results.     

Deciding finiteness for matrix groups over function fields

LetF be a field andt an indeterminate. In this paper we consider aspects of the problem of deciding if a finitely generated subgroup of GL(n,F(t)) is finite. WhenF is a number field, the analysis may be easily reduced to deciding finiteness for subgroups of GL(n,F), for which the results of [1] can be applied. WhenF is a finite field, the situation is more subtle. In this case our main results are a structure theorem generalizing a theorem of Weil and upper bounds on the size of a finite subgroup generated by a fixed number of generators with examples of constructions almost achieving the bounds. We use these results to then give exponential deterministic algorithms for deciding finiteness as well as some preliminary results towards more efficient randomized algorithms. Supported in part by NSF DMS Awards 9404275 and Presidential Faculty Fellowship.     

Eigenvalues and switching algorithms for Quasi-Newton updates

Two switching algorithms QNSWl and QNSW2 are proposed in this paper. These algorithms are developed based on the eigenvalues of matrices which are inertial to the symmetric rank-one (SR1) updates and the BFGS updates. First, theoretical results on the eigenvalues and condition numbers of these matrices are presented. Second, switch-ing mechanisms are then developed based on theoretical results obtained so that each proposed algorithm has the capability of applying appropriate updating formulae at each iterative point during the whole minimization process. Third, the performance of

each of the proposed algorithms is evaluated over a wide range of test problems with variable dimensions. These results are then compared to the results obtained by some well-known minimization packages. Comparative results show that among the tested methods, the QNSW2 algorithm has the best overall performance for the problems examined. In some cases, the number of iterations and the number function/gradient calls required by certain existing methods are more than a four-fold increase over that required by the proposed switching algorithms     

Pure ℓ-Ideals in Lattice-Ordered Rings#

An ?-ideal I of a commutative lattice-ordered ring R with positive identity element is called a pure ?-ideal if R  =  I  + ?( x ) for each x  ∈  I , where ?(x) is the ?-annihilator of x in R . In this article, we give some results on pure ?-ideals and study the ?-ideal structure of a commutative lattice-ordered ring with positive identity element by using pure ?-ideals.     

Bayesian Calibration and Uncertainty Analysis for Computationally Expensive Models Using Optimization and Radial Basis Function Approximation

We presenta Bayesian approach to model calibration when evaluation of the model is computationally expensive. Here, calibration is a nonlinear regression problem: given a data vector Y corresponding to the regression model f(β), find plausible values of β. As an intermediate step, Y and f are embedded into a statistical model allowing transformation and dependence. Typically, this problem is solved by sampling from the posterior distribution of β given Y using MCMC. To reduce computational cost, we limit evaluation of f to a small number of points chosen on a high posterior density region found by optimization.Then,we approximate the logarithm of the posterior density using radial basis functions and use the resulting cheap-to-evaluate surface in MCMC.We illustrate our approach on simulated data for a pollutant diffusion problem and study the frequentist coverage properties of credible intervals. Our experiments indicate that our method can produce results similar to those when the true “expensive” posterior density is sampled by MCMC while reducing computational costs by well over an order of magnitude.     

Distance Geometry Optimization for Protein Structures

We study the performance of the dgsol code for the solution of distance geometry problems with lower and upper bounds on distance constraints. The dgsol code uses only a sparse set of distance constraints, while other algorithms tend to work with a dense set of constraints either by imposing additional bounds or by deducing bounds from the given bounds. Our computational results show that protein structures can be determined by solving a distance geometry problem with dgsol and that the approach based on dgsol is significantly more reliable and efficient than multi-starts with an optimization code.     

On the category Q-Mod

In this paper we consider the category Q-Mod of modules over a given quantale Q. The paper is motivated by constructions and results from the category of modules over a ring. We show that the category Q-Mod is monadic, consider its relation to the category Q-Top of Q-topological spaces and generalize a method of completion of partially ordered sets. Received December 20, 2005; accepted in final form December 4, 2006.     

Coherent Sheaves on P1: their Families and their Deformations Related to a Behavioral Approach to Singular Systems

Recently, Lomadze, Ravi, Rosenthal and Schumacher gave a natural and geometrically meaningful one-to-one correspondence between abstract linar behaviors and coherent sheaves on P ¹. Motivated by their result, here we give a complete picture of the deformation theory of coherent sheaves on P ¹. We use our results to study deformations over the field R obtaining a connectedness result for the real locus of the algebraic parameter spaces.     

Relative Semi-abelian Categories

We define a relative semi-abelian category as a pair (C,E), where C is a pointed category with finite limits, and E is a class of regular epimorphisms in C satisfying certain conditions, stronger than those defining a relative homological category. Some results on the equivalence of the so-called old-style and new-style axioms for the semi-abelian categories are extended to the relative case. Partially supported by the University of Cape Town Research Associateship and Georgia National Science Foundation (GNSF/ST06/3-004).     

On hull classes of <Emphasis Type="Italic">ℓ</Emphasis>-groups and covering classes of spaces

W denotes the category of archimedean ℓ-groups with designated weak unit and ℓ-homomorphisms that preserve the weak unit. Comp denotes the category of compact Hausdorff spaces with continuous maps. The Yosida functor is used to investigate the relationship between hull classes in W and covering classes in Comp. The central idea is that of a hull class whose hull operator preserves boundedness. We demonstrate how the Yosida functor may be used to identify hull classes in W and covering classes in Comp. In addition, we exhibit an array of order preserving bijections between certain families of hull classes and all covering classes, one of which was recently produced by Martínez. Lastly, we apply our results to answer a question of Knox and McGovern about the class of all feebly projectable ℓ-groups.     

The lattice of pseudovarieties of idempotent semigroups and a non-regular analogue

We use classical results on the lattice of varieties of band (idempotent) semigroups to obtain information on the structure of the lattice Ps (DA) of subpseudovarieties of DA, – where DA is the largest pseudovariety of finite semigroups in which all regular semigroups are band semigroups. We bring forward a lattice congruence on Ps (DA), whose quotient is isomorphic to , and whose classes are intervals with effectively computable least and greatest members. Also we characterize the pro-identities satisfied by the members of an important family of subpseudovarieties of DA. Finally, letting V _k be the pseudovariety generated by the k-generated elements of DA (k≥ 1), we use all our results to compute the position of the congruence class of V _k in . Received April 24, 1996; accepted in final form April 3, 1997.     

Generic Global Rigidity

Suppose a finite configuration of labeled points p = (p₁,. . . ,p_n) in E^d is given along with certain pairs of those points determined by a graph G such that the coordinates of the points of p are generic, i.e., algebraically independent over the integers. If another corresponding configuration q = (q₁,. . . ,q_n) in E^d is given such that the corresponding edges of G for p and q have the same length, we provide a sufficient condition to ensure that p and q are congruent in E^d. This condition, together with recent results of Jackson and Jordán, give necessary and sufficient conditions for a graph being generically globally rigid in the plane.     

On the justification of the Reynolds equation,describing isentropic compressible flows through a tiny pore

Abstract We consider the isentropic compressible flow through a tiny pore. Our approach is to adapt the recent results by N. Masmoudi on the homogenization of compressible flows through porous media to our situation. The major difference is in the a priori estimates for the pressure field. We derive the appropriate ones and then Masmoudi’s results allow to conclude the convergence. In this way the compressible Reynolds equation in the lubrication theory is rigorously justified. Keywords: Compressible Navier-Stokes equations, Lubrication, Pressure estimates Mathematics Subject Classification (2000): 35B27, 76M50, 35D05     

Epimorphisms and cowellpoweredness for separated metrically generated theories

For metrically generated constructs X we give an internal characterization of the regular closure operator on X, determined by the subconstruct X ₀, consisting of its T ₀ objects. This allows us to describe the epimorphisms in X ₀ and to show that all the constructs of that type are cowellpowered. We capture many known results but our method also gives solutions in cases where the epimorphism problem was still open. The third author is “research assistant” at the FWO-Vlaanderen.     

Self-similar solutions for the 1-D Schrödinger map on the hyperbolic plane

In this paper, we will study self-similar solutions for X _t = XẋX _ss , the equivalent in the Minkowski 3-space to the localized induction approximation flow, trying to adapt some results given by Gutiérrez, Rivas and Vega. We will show the existence of a one-parameter family of smooth solutions developing a corner in finite time. The main difference with respect to the Euclidean case studied by those authors will be the proof of the boundedness of T, e ₁ and e ₂, the equivalents of T, b and n in . The author was supported by the grant BFI02.135 of the Basque Government and by the project MTM2004-03029 of MEC (Spain) and FEDER.     

变量核分数次积分在Hardy空间的有界性

§ 1　 Introduction and main resultsLet Sn- 1 be the unitsphere in Rn(n≥ 2 ) equipped with normalized Lebesgue measure dσ= dσ(z′) .We say that a functionΩ(x,z) defined on Rn× Rnbelongs to L∞ (Rn)× Lr(Sn- 1 )(r≥ 1 ) ,ifΩ(x,z) satisfies the following two conditions,(i) for any x,z∈Rnandλ>0 ,there hasΩ(x,λz) =Ω(x,z) ;(ii)‖Ω‖L∞(Rn)× Lr(Sn- 1) :=supx∈ Rn∫Sn- 1|Ω(x,z′) | rdσ(z′) 1 / r<∞ .For 0 <α相似文献   

The linear combination of vectors implies the existence of the cross and dot products

Given two vectors u and v, their cross product u × v is a vector perpendicular to u and v. The motivation for this property, however, is never addressed. Here we show that the existence of the cross and dot products and the perpendicularity property follow from the concept of linear combination, which does not involve products of vectors. For our proof we consider the plane generated by a linear combination of uand v. When looking for the coefficients in the linear combination required to reach a desired point on the plane, the solution involves the existence of a normal vector n = u × v. Our results have a bearing on the history of vector analysis, as a product similar to the cross product but without the perpendicularity requirement existed at the same time. These competing products originate in the work of two major nineteen-century mathematicians, W. Hamilton, and H. Grassmann. These historical aspects are discussed in some detail here. We also address certain aspects of the teaching of u × v to undergraduate students, which is known to carry some difficulties. This includes the algebraic and geometric denitions of u × v, the rule for the direction of u × v, and the pseudovectorial nature of u × v.     

On automorphisms of the degrees that preserve jumps

IfF is an automorphism of the degrees of unsolvability that preserves the jump operator, thenF leaves fixed all the degreesc that satisfyc≧0 ⁽³⁾. The results of this paper were part of the author’s PhD thesis (Illinois 1977), supervised by Carl G. Jockusch, Jr.