Training Multilayer Perceptrons Via Minimization of Sum of Ridge Functions

Motivated by the problem of training multilayer perceptrons in neural networks, we consider the problem of minimizing E(x)= _i=1 ⁿ f _i ( _i x), where _i R ^s , 1in, and each f _i ( _i x) is a ridge function. We show that when n is small the problem of minimizing E can be treated as one of minimizing univariate functions, and we use the gradient algorithms for minimizing E when n is moderately large. For large n, we present the online gradient algorithms and especially show the monotonicity and weak convergence of the algorithms.  

The multiplicity of solutions in non-homogeneous boundary value problems

We use a method recently devised by Bolle to establish the existence of an infinite number of solutions for various non-homogeneous boundary value problems. In particular, we consider second order systems, Hamiltonian systems as well as semi-linear partial differential equations. The non-homogeneity can originate in the equation but also from the boundary conditions. The results are more satisfactory than those obtained by the standard “Perturbation from Symmetry” method that was developed – in various forms – in the early eighties by Bahri–Berestycki, Struwe and Rabinowitz. Received: 13 August 1998 / Revised version: 6 July 1999  

Space-time fractional derivative operators

Evolution equations for anomalous diffusion employ fractional derivatives in space and time. Linkage between the space-time variables leads to a new type of fractional derivative operator. This paper develops the mathematical foundations of those operators.

  

Subgraph distances in graphs defined by edge transfers

For two edge-induced subgraphs F and H of the same size in a graph G, the subgraph H can be obtained from F by an edge jump if there exist four distinct vertices u, v, w, and x in G such that uv ε E(F), wx ε E(G) - E(F), and H = F - uv + wx. The subgraph F is j-transformed into H if H can be obtained from F by a sequence of edge jumps. Necessary and sufficient conditions are presented for a graph G to have the property that every edge-induced subgraph of a fixed size in G can be j-transformed into every other edge-induced subgraph of that size. The minimum number of edge jumps required to transform one subgraph into another is called the jump distance. This distance is a metric and can be modeled by a graph. The jump graph J(G) of a graph G is defined as that graph whose vertices are the edges of G and where two vertices of J(G) are adjacent if and only if the corresponding edges of G are independent. For a given graph G, we consider the sequence {{J^k(G)}} of iterated jump graphs and classify each graph as having a convergent, divergent, or terminating sequence.  

Mixed methods for fourth-order elliptic and parabolic problems using radial basis functions

By extending Wendlands meshless Galerkin methods using RBFs, we develop mixed methods for solving fourth-order elliptic and parabolic problems by using RBFs. Similar error estimates as classical mixed finite element methods are proved. AMS subject classification 35G15, 65N12  

Using an Iterated Prisoner's Dilemma with Exit Option to Study Alliance Behavior: Results of a Tournament and Simulation

Nearly half of all strategic alliances fail (Park and Russo, 1996; Dyer et al., 2001), often because of opportunistic behavior by one party or the other. We use a tournament and simulation to study strategies in an iterated prisoner's dilemma game with exit option to shed light on how a firm should react to an opportunistic partner. Our results indicate that a firm should give an alliance partner a second chance following an opportunistic act but that subsequent behavior should be contingent on the value of the next best opportunity outside the alliance. Firms should be more forgiving if the potential benefits from the alliance exceed other opportunities. The strategies were also found to be robust across a wide range of game lengths. The implications of these results for alliance strategies are discussed. Steven E. Phelan received his PhD in economics from La Trobe University (Australia) in 1998. Following five years at the University of Texas at Dallas, he joined the faculty of the University of Nevada Las Vegas in 2003. Dr. Phelan's research interests include competitive dynamics, organizational efficiency, acquisition and alliance performance, and entrepreneurial competence. His methods of choice to study these phenomena include agent-based modelling, experimental game theory, and event studies. Prior to joining academia, Dr. Phelan held executive positions in the telecommunications and airline industries and was a principal partner in Bridges Management Group, a consultancy specializing in strategic investment decisions. Richard J. Arend is a graduate of the University of British Columbia's doctoral program in Policy Analysis and Strategy. He is on the Management faculty of the University of Nevada, Las Vegas, arriving most recently from the Management faculty of New York University's Stern School of Business. Dr. Arend's interests lie in the analysis of unusual modes of firm value creation and destruction, where he has published in several top journals. He is a professional engineer with work and consulting experience in aerospace and computing. Darryl A. Seale joined the faculty of UNLV in 1999, following three years at Kent State University and the University of Alabama in Huntsville. Prior to Alabama, he completed his Ph.D. and M.S. degrees in Business Administration at the University of Arizona, his M.B.A. from Penn State University, and spent over ten years in management and market planning positions in the health care industry. Professor Seale's research interests include strategic decision making, bargaining and negotiation, and behavioral game theory. His research has been funded by the National Science Foundation and has been published in top-tier journals including Management Science, OBHDP, Games and Economic Behavior, and Strategic Management Journal. His teaching interests include business policy/strategy, managerial decision making, and bargaining and negotiation.  

一对普遍的级数变换公式（英）

利用Krasnoselskii-Zabreiko不动点定理获得了非线性三点边值问题{u″（t）＋a（t）u′（t）＋b（t）u（t）＋h（t）f（t）=0,t∈（0,1） u（0）=0,u（1）=αu（η）解的—个新的存在定理．  

Perturbation from symmetry for indefinite semilinear elliptic equations

We prove the existence of an unbounded sequence of solutions for an elliptic equation of the form -Du=lu + a(x)g(u)+f(x), u ? H¹₀(W){-\Delta u=\lambda u + a(x)g(u)+f(x), u\in H^1_0(\Omega)}, where l ? \mathbbR, g(·){\lambda \in \mathbb{R}, g(\cdot)} is subcritical and superlinear at infinity, and a(x) changes sign in Ω; moreover, g( − s) =  − g(s) "s{\forall s}. The proof uses Rabinowitz’s perturbation method applied to a suitably truncated problem; subsequent energy and Morse index estimates allow us to recover the original problem. We consider the case of W ì \mathbbR^N{\Omega\subset \mathbb{R}^N} bounded as well as W = \mathbbR^N,  N\geqslant 3{\Omega=\mathbb{R}^N, \, N\geqslant 3}.  

On the Ramsey Number of Sparse 3-Graphs

We consider a hypergraph generalization of a conjecture of Burr and Erd?s concerning the Ramsey number of graphs with bounded degree. It was shown by Chvátal, Rödl, Trotter, and Szemerédi [The Ramsey number of a graph with bounded maximum degree, J. Combin. Theory Ser. B 34 (1983), no. 3, 239–243] that the Ramsey number R(G) of a graph G of bounded maximum degree is linear in |V(G)|. We derive the analogous result for 3-uniform hypergraphs.