On bargaining partner selection when communication is restricted

This paper analyzes the optimal selection of a bargaining partner when communication among players is restricted by an exogenously given graph. If players are equally patient, bargaining agreements are immune to players' locations, and the selection of a bargaining partner is not an issue. In contrast, when players differ in their discount factors, both location and impatience matter for bilateral agreements and partner selection becomes an issue. We show that selecting the most impatient neighbor is an equilibrium strategy whenever two players having a common neighbor share their most impatient neighbor. This condition is always satisfied by stratified graphs with no more than three strata. In the absence of this condition, cyclically-stratified graphs with no more than three strata also admit this equilibrium selection rule. Received: November 2000/Final version: January 2002     

Point-weight designs with design conditions on t points

This paper examines some of the properties of point-weight incidence structures, i.e. incidence structures for which every point is assigned a positive integer weight. In particular it examines point-weight designs with a design condition that stipulates that any two “identical” sets of t points must lie on the same number of blocks. We introduce a new class of designs with this property: row-sum designs, and examine the basic properties of row-sum point-weight designs and their similarities to classical (non-point-weight) designs and the point-weight designs of Horne [On point-weighted designs, Ph.D. Thesis, Royal Holloway, University of London, 1996].     

Steiner systems with automorphism groups PSL(2, 71), PSL(2, 83), and P∑L(2, 35)

The first 5-(72, 6, 1) designs with automorphism group PSL(2, 71) were found by Mills [10]. We presently enumerate all 5-(72, 6, 1) designs with this automorphism group. There are in all 926299 non-isomorphic designs. We show that a necessary condition for semiregular5-(v, 6, 1) designs with automorphism group PSL(2, v 1) to exist is thatv=84, 228 (mod 360). In particular, there are exactly 3 non-isomorphic semiregular 5-(84, 6, 1) designs with automorphism group PSL(2, 83). There are at least 6450 non-isomorphic 5-(244, 6, 1) designs with automorphism group PL(2, 3⁵).     

Graphs Satisfying a Richness Condition and One Concerning Forbidden Subgraphs

We characterize several classes of graphs which satify a richness condition (R) and a condition (F) which concerns forbidden subgraphs. In particular we treat the case where (R) is: Each two vertices have a common neighbor. And this in combination with (F): G has no 5-circle C ₅ resp. no 6-circle C ₆ as subgraph. Another result deals with the case where (R) and (F) concern existence or non-existence of circles C _n .     

Robust nonparametric regression estimation

In this paper we define a robust conditional location functional without requiring any moment condition. We apply the nonparametric proposals considered by C. Stone (Ann. Statist. 5 (1977), 595–645) to this functional equation in order to obtain strongly consistent, robust nonparametric estimates of the regression function. We give some examples by using nearest neighbor weights or weights based on kernel methods under no assumptions whatsoever on the probability measure of the vector (X,Y). We also derive strong convergence rates and the asymptotic distribution of the proposed estimates.     

Distribution of integers into k-tuples with prescribed conditions

In this paper, we pose and solve two problems concerning the distribution of given sets of integers into k-tuples with prescribed conditions, which are generalizations of two well-known difference problems of Heffter. Solutions to these two problems play an important role in the authors' construction of neighbor designs for use in serology.     

Facility location problems in the plane based on reverse nearest neighbor queries

For a finite set of points S, the (monochromatic) reverse nearest neighbor (RNN) rule associates with any query point q the subset of points in S that have q as its nearest neighbor. In the bichromatic reverse nearest neighbor (BRNN) rule, sets of red and blue points are given and any blue query is associated with the subset of red points that have it as its nearest blue neighbor. In this paper we introduce and study new optimization problems in the plane based on the bichromatic reverse nearest neighbor (BRNN) rule. We provide efficient algorithms to compute a new blue point under criteria such as: (1) the number of associated red points is maximum (MAXCOV criterion); (2) the maximum distance to the associated red points is minimum (MINMAX criterion); (3) the minimum distance to the associated red points is maximum (MAXMIN criterion). These problems arise in the competitive location area where competing facilities are established. Our solutions use techniques from computational geometry, such as the concept of depth of an arrangement of disks or upper envelope of surface patches in three dimensions.     

The application of invariant theory to the existence of quasi-symmetric designs

Gleason and Mallows and Sloane characterized the weight enumerators of maximal self-orthogonal codes with all weights divisible by 4. We apply these results to obtain a new necessary condition for the existence of 2 − (v, k, λ) designs where the intersection numbers s₁…,s_n satisfy s₁ ≡ s₂ ≡ … ≡ s_n (mod 2). Non-existence of quasi-symmetric 2−(21, 18, 14), 2−(21, 9, 12), and 2−(35, 7, 3) designs follows directly from the theorem. We also eliminate quasi-symmetric 2−(33, 9, 6) designs. We prove that the blocks of quasi-symmetric 2−(19, 9, 16), 2−(20, 10, 18), 2-(20,8, 14), and 2−(22, 8, 12) designs are obtained from octads and dodecads in the [24, 12] Golay code. Finally we eliminate quasi-symmetric 2−(19,9, 16) and 2-(22, 8, 12) designs.     

A quasi‐symmetric 2‐(49,9,6) design

Huffman and Tonchev discovered four non‐isomorphic quasi‐symmetric 2‐(49,9,6) designs. They arise from extremal self‐dual [50,25,10] codes with a certain weight enumerator. In this note, a new quasi‐symmetric 2‐(49,9,6) design is constructed. This is established by finding a new extremal self‐dual [50,25,10] code as a neighbor of one of the four extremal codes discovered by Huffman and Tonchev. A number of new extremal self‐dual [50,25,10] codes with other weight enumerators are also found. © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 173–179, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10007     

Large deviations for functionals of spatial point processes with applications to random packing and spatial graphs

Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. We prove general Donsker–Varadhan large deviation principles (LDP) for such functionals and show that the general result can be applied to prove LDPs for various particular functionals, including those concerned with random packing, nearest neighbor graphs, and lattice versions of the Voronoi and sphere of influence graphs.     

A greedy meshless local Petrov–Galerkin methodbased on radial basis functions

The meshless local Petrov–Galerkin (MLPG) method with global radial basis functions (RBF) as trial approximation leads to a full final linear system and a large condition number. This makes MLPG less efficient when the number of data points is increased. We can overcome this drawback if we avoid using more points from the data site than absolutely necessary. In this article, we equip the MLPG method with the greedy sparse approximation technique of (Schaback, Numercail Algorithms 67 (2014), 531–547) and use it for numerical solution of partial differential equations. This scheme uses as few neighbor nodal values as possible and allows to control the consistency error by explicit calculation. Whatever the given RBF is, the final system is sparse and the algorithm is well‐conditioned. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 847–861, 2016     

非参数回归函数的kn近邻估计的渐近性质及其Bootstrap逼近

本文研究回归函数的kn-近邻估计的渐近性质,得到了回归函数的kn－近邻估计的渐近正态性和它的Bootstrap统计量的相合性,在高阶矩存在的条件下,我们证明了回归函数的kn-近邻估计的Bootstrap逼近比正态逼近更精确。     

Wrap-Around L2-Discrepancy of Random Sampling, Latin Hypercube and Uniform Designs

For comparing random designs and Latin hypercube designs, this paper con- siders a wrap-around version of the L₂-discrepancy (WD). The theoretical expectation and variance of this discrepancy are derived for these two designs. The expectation and variance of Latin hypercube designs are significantly lower than those of the corresponding random designs. We also study construction of the uniform design under the WD and show that one-dimensional uniform design under this discrepancy can be any set of equidistant points. For high dimensional uniform designs we apply the threshold accepting heuristic for finding low discrepancy designs. We also show that the conjecture proposed by K. T. Fang, D. K. J. Lin, P. Winker, and Y. Zhang (2000, Technometrics) is true under the WD when the design is complete.     

Some characterization of locally resistant BIB designs of degree one

Summary This paper investigates locally resistant balanced incomplete block (LRBIB) designs of degree one. A new necessary condition for the existence of such an LRBIB design is presented. This condition yields a complete characterization of affine α-resolvable LRBIB designs of degree one. Furthermore, regarding construction methods of LRBIB designs of degree one, it is shown that Shah and Gujarathi's method (1977,Sankhy?, B39, 406–408) yields the same parameters as Hedayat and John's method (1974,Ann. Statist.,2, 148–158), but their block structures are different and interesting. Partially supported by Grants 59540043 (C) and 60530014 (C).     

Partitions and partial matchings avoiding neighbor patterns

We obtain the generating functions for partial matchings avoiding neighbor alignments and for partial matchings avoiding neighbor alignments and left nestings. We show that there is a bijection between partial matchings avoiding the three neighbor patterns (neighbor alignments, left nestings and right nestings) and set partitions avoiding right nestings via an intermediate structure of upper triangular matrices. Combining our bijection and the bijection given by Dukes and Parviainen between upper triangular matrices and self-modified ascent sequences, we get a bijection between partial matchings avoiding the three neighbor patterns and self-modified ascent sequences.     

Block designs with v = 10, k = 5, λ = 4

It was shown by Singhi that there are 21 nonisomorphic block designs BD (10, 5; 18, 9, 4) which are residual designs of (19, 9, 4) Hadamard designs. In this paper we show that there are no other block designs with these parameters, i.e., each such design is embeddable in a symmetric design. We give a complete list of these designs and their automorphism groups.     

Connectedness of PBIB designs having asymmetrical association schemes

Summary A necessary and sufficient condition for the connectedness ofm-associate partially balanced incomplete block (PBIB) designs having an asymmetrical association scheme is given, only in terms of design parameters, without inner structure parameters of designs. Supported in part by Grant 321-6066-58530013 (Japan).     

Natural neighbor coordinates of points on a surface

Natural neighbor coordinates and natural neighbor interpolation have been introduced by Sibson for interpolating multivariate scattered data. In this paper, we consider the case where the data points belong to a smooth surface , i.e., a (d−1)-manifold of . We show that the natural neighbor coordinates of a point X belonging to tends to behave as a local system of coordinates on the surface when the density of points increases. Our result does not assume any knowledge about the ordering, connectivity or topology of the data points or of the surface. An important ingredient in our proof is the fact that a subset of the vertices of the Voronoi diagram of the data points converges towards the medial axis of when the sampling density increases.     

Strong consistency of nearest neighbor kernel regression estimation for stationary dependent samples

Under quite mild conditions onk _n . the strong consistency is proved for the nearest neighbor density, the nearest neighbor kernel regression and the modified nearest neighbor kernel regression of an a-mixing stationary sequence in time series context. The condition imposed on the mixing coefficients is , . which is simple and weak.     

Invariants and constructions of mendelsohn designs

In this paper we examine Mendelsohn designs and some connections to topology which lead to an easily described algorithm for computing invariants of these designs. The results are applied to designs which have natural group actions. We also use the topology to describe when ordinary two-fold triple systems with a group action lead to Mendelsohn designs with the same group action. Procedures for constructing Mendelsohn designs are also given. In particular, we give necessary and sufficient conditions for constructing 2-(v, 4, 1) Mendelsohn designs.