Mann and Ishikawa iterations with errors for non-lipschitzian mappings in Banach spaces

Let C be a nonempty closed convex subset of a uniformly convex Banach space and let T : C → C be completely continuous asymptotically nonexpansive in the intermediate sense. In this paper, we prove that the Ishikawa (and Mann) iteration process with errors converges strongly to some fixed point of T, which generalizes the recent results due to Huang [1].     

The role of convexity in the adaptive control of rapidly time-varying systems

In classical adaptive control the parameters are assumed to be fixed or slowly time-varying. In order to facilitate parameter estimation/tuning it is desirable to have the set of admissible parameters lie in a convex set; if this set is not convex, a common trick is to replace it with its convex hull, but the adaptive control problem is challenging if stabilizability of the set of admissible parameters is lost. However, such a convexity assumption is an artifact of the approach to the problem, rather than an inherent constraint, since most logic-based and supervisory approaches to the problem make no such requirement. On the other hand, here we show that losing stabilizability on the convex hull of the set of admissible parameters plays an important role in the adaptive control of rapidly time-varying systems.     

Extension of a Purely Pulse Control under Boundary Conditions

The control of a linear system under boundary conditions for the choice of a purely pulse program of limited potentialities, the asymptote of the set of admissible controls under different constraint perturbations, and the influence of perturbations on the reachability sets in the space of trajectories generated by admissible controls are studied. The asymptotic insensitivity of the problem under perturbations of boundary conditions is determined.     

The foundations of confounding in epidemiology

A statistically coherent view of confounding motivated by the over controversy over the proper control of confounding in the presence of prior knowledge is presented. Confounding by a covariate C in the presence of data on C is distinguished from confounding in the absence of data on C. A covariate C is defined to be a nonconfounder in the absence of data on C if the population parameter of interest can be unbiasedly estimated (asymptotically) absent data on C. Under this definition, C may be a confounder for some parameters of interest and a nonconfounder for others. If C is a confounder for a parameter of interest that has a causal interpretation, we call C a causal confounder. When data on C are available, C is defined to be a nonconfounder for a particular parameter of interest if and only if inference on the parameter of interest does not depend on the data through C. Bayesians, frequentists and pure likelihoodists will in general agree on the prior knowledge necessary to render C a non-confounder. In particular C will in general be a nonconfounder precisely when the crude data ignoring C are S-sufficient for the parameter of interest. The intuitive view held by many practicing epidemiologists that confounding by C represents a bias of the unadjusted crude estimator is in a sense correct provided inference is performed conditional on approximate ancillary statistics that measure the degree to which associations in the data differ due to sampling variability from those population associations known a priori.     

基于可变连接价格的TCP接入控制研究

本文面向有连接的弹性应用,探讨了基于可变连接价格的TCP接入控制问题.将该问题描述为追求连接阻塞率最小化和活动连接时长最大化的多目标优化问题,分别考察了在连接请求确定到达和随机到达时的连接价格确定问题.提出了在阻塞率不高于某一设定值的情况下,使得单位时间内期望活动连接时长最大化的连接价格调整算法,并给出了基于Socks代理协议的价格协商和接入控制实现方法.     

C- and C-continuous spline-interpolation of a regular triangular net of points

The investigations focus on the construction of a C^k-continuous (k=0,1,2) interpolating spline-surface for a given data set consisting of points P_ijk arranged in a regular triangular net and corresponding barycentric parameter triples (u_i,v_j,w_k). We try to generalize an algorithm by A.W. Overhauser who solved the analogous problem for the case of a univariate data set. As a straightforward generalization does not work out we adapt the Overhauser-construction. We use some blending of basic surfaces with uniquely determined basic functions. This yields a spline-surface with a polynomial parametric representation which display C¹- or C²-continuity along the common curve of two adjacent sub-patches. Local control of the emerging spline surface is provided which means moving one data point P changes only some of the sub-patches around P and does not affect regions lying far away.     

A Nonfeasible Gradient Projection Recurrent Neural Network for Equality-Constrained Optimization Problems

In this paper, a recurrent neural network for both convex and nonconvex equality-constrained optimization problems is proposed, which makes use of a cost gradient projection onto the tangent space of the constraints. The proposed neural network constructs a generically nonfeasible trajectory, satisfying the constraints only as t rarr infin. Local convergence results are given that do not assume convexity of the optimization problem to be solved. Global convergence results are established for convex optimization problems. An exponential convergence rate is shown to hold both for the convex case and the nonconvex case. Numerical results indicate that the proposed method is efficient and accurate.     

A double-sequence iteration process for fixed points of continuous pseudocontractions

Let C be a bounded closed convex nonempty subset of a (real) Hilbert space H. The idea of a double-sequence iteration is introduced, and it is proved that a Mann-type double-sequence iteration process converges strongly to a fixed point of a continuous pseudocontractive map T which maps C into C. Related results deal with the strong convergence of the iteration process to fixed points of nonexpansive maps.     

Existence of solutions for lower semicontinuous quasi-equilibrium problems

In this paper, we deal with the following quasi-equilibrium problem: given a nonempty subset C of a topological vector space X, a nonempty set D, two functions T : C → D, f : X × D → R and a multifunction S : C → 2^X, find such that , and for all . Such a problem, recently introduced in [1], extends and unifies several variational inequality problems, generalized complementarity problems and Nash equilibrium problems. We prove several existence results in which the upper semicontinuity of the multifunction S is not assumed.     

Biquartic C-surface splines over irregular meshes

C¹-surface splines define tangent continuous surfaces from control points in the manner of tensor-product (B-)splines, but allow a wider class of control meshes capable of outlining arbitrary free-form surfaces with or without boundary. In particular, irregular meshes with non-quadrilateral cells and more or fewer than four cells meeting at a point can be input and are treated in the same conceptual frame work as tensor-product B-splines; that is, the mesh points serve as control points of a smooth piecewise polynomial surface representation that is local and evaluates by averaging. Biquartic surface splines extend and complement the definition of C¹-surface splines in a previous paper (Peters, J SLAM J. Numer. Anal. Vol 32 No 2 (1993) 645–666) improving continuity and shape properties in the case where the user chooses to model entirely with four-sided patches. While tangent continuity is guaranteed, it is shown that no polynomial, symmetry-preserving construction with adjustable blends can guarantee its surfaces to lie in the local convex hull of the control mesh for very sharp blends where three patches join. Biquartic C¹-surface splines do as well as possible by guaranteeing the property whenever more than three patches join and whenever the blend exceeds a certain small threshold.     

Assignment of Complete Structural Properties of Linear Systems via Sensor Selection

For x =Ax + Bu , the problem of structural assignment via sensor selection is to find an output equation, y = Cx + Du , such that the resulting system (A, B, C, D) has the pre-specified structural properties, such as the finite and infinite zero structures as well as the invertibility properties. In this paper, we establish a set of necessary and sufficient conditions under which a complete set of system structural properties can be assigned, and an explicit algorithm for constructing the required matrix pair (C, D).     

MPC for tracking piecewise constant references for constrained linear systems

In this paper, a novel model predictive control (MPC) for constrained (non-square) linear systems to track piecewise constant references is presented. This controller ensures constraint satisfaction and asymptotic evolution of the system to any target which is an admissible steady-state. Therefore, any sequence of piecewise admissible setpoints can be tracked without error. If the target steady state is not admissible, the controller steers the system to the closest admissible steady state.These objectives are achieved by: (i) adding an artificial steady state and input as decision variables, (ii) using a modified cost function to penalize the distance from the artificial to the target steady state (iii) considering an extended terminal constraint based on the notion of invariant set for tracking. The control law is derived from the solution of a single quadratic programming problem which is feasible for any target. Furthermore, the proposed controller provides a larger domain of attraction (for a given control horizon) than the standard MPC and can be explicitly computed by means of multiparametric programming tools. On the other hand, the extra degrees of freedom added to the MPC may cause a loss of optimality that can be arbitrarily reduced by an appropriate weighting of the offset cost term.     

An approach to mining bundled commodities

Although bundled commodities are largely existed in supermarket, there are few investigations about bundled commodities mining. In this study, interval-valued association rules as a novel and possible approach to solving the bundled commodities mining issue, is proposed. Properties research based on interval-valued association rules is conducted, and an interval-valued rule pattern: F, ,  is constructed, where F denotes set of interval-valued ruses, and denote the disjunctive operation and conjunctive operation, respectively. Furthermore, one of the properties satisfied by the interval-valued rules: A  C = B  C and A  C = B  C  A = B, where A, B, C are there different rules, is validated and utilized to mine the bundled commodities. Finally, a large-scale software engineering project relative to interval-valued rule mining is implemented to merge flight testing information about aircrafts which validates the technique of mining bundled commodities can be discovered a special relation between objects. These initial investigations provide a researchable framework for bundled commodities mining.     

Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard

Let G=(V,E) be an undirected graph and C a subset of vertices. If the sets B_r(v)∩C, vV (respectively, vVC), are all nonempty and different, where B_r(v) denotes the set of all points within distance r from v, we call C an r-identifying code (respectively, an r-locating-dominating code). We prove that, given a graph G and an integer k, the decision problem of the existence of an r-identifying code, or of an r-locating-dominating code, of size at most k in G, is NP-complete for any r.     

On some dynamical subsets of the rauzy fractal

Let ( ,(+1)_n) be the adic system associated to the substitution: 1 → 12,…,(n − 1) → 1n, n → 1. In Sirvent (1996) it was shown that there exist a subset Cⁿ of and a map h_n: C → Cⁿ such that the dynamical system (C, h_n) is semiconjugate to ( ). In this paper we compute the Hausdorff and Billingsley dimensions of the geometrical realizations of the set Cⁿ on the (n− l)-dimensional torus. We also show that the dynamical system (Cⁿ,h_n) cannot be realized on the (n − 1)-torus.     

On renaming a set of clauses as a Horn set

Let S = {C₁, …, C_m} be a set of clauses in the propositional calculus and let n denote the number of variables appearing these clauses. We present and O(mn) time algorithm to test whether S can be renamed as a Horn set.     

Automatic rotational symmetry determination for shape analysis

The determination of the rotational symmetry of a shape is useful for object recognition and shape analysis in computer vision applications. In this paper, a simple, but effective, algorithm to analyse the rotational symmetry of a given closed-curve shape S is proposed. A circle C with the centroid of S as the circle center and the average radius of S as the circle radius is superimposed on S, resulting in the intersection of C and S at a set of points. By theoretical analysis, the relationship between the order N_s of the rotational symmetry of S and the number of intersection points between C and S is established. All the possible values for N_s are determined. And finally N_s is determined by evaluating the similarity between S and its rotated versions. In the proposed algorithm, only simple pixel operations and second-order moment function computation are involved. Several problems caused by the use of discrete image coordinates are analysed and solved for correct decision-making in the algorithm. Good experimental results are also included.     

Scalable services via egress admission control

Allocating resources for multimedia traffic flows with real-time performance requirements is an important challenge for future packet networks. However, in large-scale networks, individually managing each traffic flow on each of its traversed routers has fundamental scalability limitations, in both the control plane's requirements for signaling, state management, and admission control, and the data plane's requirements for per-flow scheduling mechanisms. In this paper, we develop a scalable architecture and algorithm for quality-of-service management termed egress admission control. In our approach, resource management and admission control are performed only at egress routers, without any coordination among backbone nodes or per-flow management. Our key technique is to develop a framework for admission control under a general “black box” model, which allows for cross traffic that cannot be directly measured, and scheduling policies that may be ill-described across many network nodes. By monitoring and controlling egress routers' class-based arrival and service envelopes, we show how network services can be provisioned via scalable control at the network edge. We illustrate the performance of our approach with a set of simulation experiments using highly bursty traffic flows and find that despite our use of distributed admission control, our approach is able to accurately control the system's admissible region under a wide range of conditions     

A two-layer congestion control protocol for broadband ISDN

In this paper, we present a new, effective connection-oriented congestion control protocol for B-ISDN. The protocol employs the traffic viewpoint hierarchical design approach and is implemented by a two-layer scheme at the call and cell layers. The call layer handles call admission (denial) and provides shortest path connection routing when a call is admitted, while the cell layer allocates switch input buffer space for each traffic type according to each type's cell loss probability grade-of-service requirement. There is a direct interaction between the two layers in processing a connection request. A discrete-time queueing system with geometrically distributed service time and state-dependent Markov modulated Bernoulli process (MMBP) arrivals is established to model heterogeneous networking environments for this protocol and an analytical solution is developed for this queueing system. Numerical results obtained by both analysis and simulation show that the protocol can reduce network congestion as input traffic rates approach switch capacity and, thereby, increase network utilization relative to that possible in the absence of congestion control.     

Preemptive LCFS scheduling in hard real-time applications

We investigate the real-time behaviour of a (discrete time) single server system with preemptive LCFS task scheduling. The main result deals with the probability distribution of a random variable SRD(T), which describes the time the system operates without violating a fixed task service time deadline T. The tree approach, used for the derivation of our results, is also suitable for revisiting problems in queueing theory.

Relying on a simple general probability model, asymptotic formulas concerning all moments of SRD(T) are determined; for instance, the expectation of SRD(T) is proved to grow exponentially in T, i.e., E[SRD(T)]C^TT^3/2 for some > 1.