Symmetrisation of n-operads and compactification of real configuration spaces

It is well known that the forgetful functor from symmetric operads to nonsymmetric operads has a left adjoint Sym₁ given by product with the symmetric group operad. It is also well known that this functor does not affect the category of algebras of the operad. From the point of view of the author's theory of higher operads, the nonsymmetric operads are 1-operads and Sym₁ is the first term of the infinite series of left adjoint functors Symn, called symmetrisation functors, from n-operads to symmetric operads with the property that the category of one object, one arrow, …, one (n−1)-arrow algebras of an n-operad A is isomorphic to the category of algebras of Symn(A).In this paper we consider some geometrical and homotopical aspects of the symmetrisation of n-operads. We follow Getzler and Jones and consider their decomposition of the Fulton-Macpherson operad of compactified real configuration spaces. We construct an n-operadic counterpart of this compactification which we call the Getzler-Jones operad. We study the properties of Getzler-Jones operad and find that it is contractible and cofibrant in an appropriate model category. The symmetrisation of the Getzler-Jones operad turns out to be exactly the operad of Fulton and Macpherson. These results should be considered as an extension of Stasheff's theory of 1-fold loop spaces to n-fold loop spaces n?2. We also show that a space X with an action of a contractible n-operad has a natural structure of an algebra over an operad weakly equivalent to the little n-disks operad. A similar result holds for chain operads. These results generalise the classical Eckman-Hilton argument to arbitrary dimension.Finally, we apply the techniques to the Swiss-Cheese type operads introduced by Voronov and prove analogous results in this case.     

The Problem of Capacity Addition in Multi-user Elastic Demand Communication Networks

In this paper we consider some properties on prices under flow control in a network that is to be shared by noncooperative users. Each user is faced with an optimization problem which is formulated as the minimization of its own criterion subject to constraint on the flows of the other users. The operating points of the network are the Nash equilibria of the underlying routing game. Our objective is to study the behavior of prices of all users when the network designer needs to allocate capacities to network links. For parallel links topologies, we show that degradation of the performances such as prices will not take place, as well as the users may find it beneficial to improve their requests     

BP神经网络在光学相关器相关峰识别中的应用

光学相关识别是图像识别的重要方法，有效识别相关器输出平面的相关峰信号是保证光学相关器图像识别准确性的关键。由于激光器输出功率的波动、光学系统本身的误差以及SLM器件本身带来的噪声，采用一般的阈值方法很难达到理想的效果。该文提出对相关器的输出平面进行预处理，充分考虑相关信号的形状信息，提取感兴趣区域(ROI)，采用BP神经网络对输入矢量进行计算，可达到对相关峰信号和噪声的有效分类识别，从而提高了光学相关器识别的可靠性，降低了误判的概率。     

Scale-Free Properties in Traffic System

In this work, we propose a new model of evolution networks, which is based on the evolution of the traffic flow. In our method, the network growth does not take into account preferential attachment, and the attachment of new node is independent of the degree of nodes. Our aim is that employing the theory of evolution network, we give a further understanding about the dynamical evolution of the traffic flow. We investigate the probability distributions and scaling properties of the proposed model. The simulation results indicate that in the proposed model, the distribution of the output connections can be well described by scale-free distribution. Moreover, the distribution of the connections is largely related to the traffic flow states, such as the exponential distribution (i.e., the scale-free distribution) and random distribution etc.     

Parking Capacity and Pricing in Park'n Ride Trips: A Continuous Equilibrium Network Design Problem

In this paper we consider the problem of designing parking facilities for park'n ride trips. We present a new continuous equilibrium network design problem to decide the capacity and fare of these parking lots at a tactical level. We assume that the parking facilities have already been located and other topological decisions have already been taken.The modeling approach proposed is mathematical programming with equilibrium constraints. In the outer optimization problem, a central Authority evaluates the performance of the transport network for each network design decision. In the inner problem a multimodal traffic assignment with combined modes, formulated as a variational inequality problem, generates the share demand for modes of transportation, and for parking facilities as a function of the design variables of the parking lots. The objective is to make optimal parking investment and pricing decisions in order to minimize the total travel cost in a subnetwork of the multimodal transportation system.We present a new development in model formulation based on the use of generalized parking link cost as a design variable.The bilevel model is solved by a simulated annealing algorithm applied to the continuous and non-negative design decision variables. Numerical tests are reported in order to illustrate the use of the model, and the ability of the approach to solve applications of moderate size.     

Approximating the single source unsplittable min-cost flow problem

In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. Moreover, the total cost must not exceed a given budget. This problem has been introduced by Kleinberg [7] and generalizes several NP-complete problems from various areas in combinatorial optimization such as packing, partitioning, scheduling, load balancing, and virtual-circuit routing. Kolliopoulos and Stein [9] and Dinitz, Garg, and Goemans [4] developed algorithms improving the first approximation results of Kleinberg for the problem of minimizing the violation of edge capacities and for other variants. However, known techniques do not seem to be capable of providing solutions without also violating the cost constraint. We give the first approximation results with hard cost constraints. Moreover, all our results dominate the best known bicriteria approximations. Finally, we provide results on the hardness of approximation for several variants of the problem. Received: August 23, 2000 / Accepted: April 20, 2001?Published online October 2, 2001     

Long-Term Changes in a Heat Exchanger Steel

The steel ASTM A213 P22 is used for superheater outlet header in power plants. During duty cycles lasting over tens of years the temperature is of the order of 545°C and the pressure 125 atm. The microscopic changes in these steels are hard to analyze under working conditions, but they are believed to be responsible for the appearance of creeps in such devices. Investigation of the microscopic modifications will help to predict future failures due to creeps, increasing the reliability and saving a lot of money.We report the investigation of such changes in ASTM A213 P22 steel in use for 30 years as a Superheater header at Haifa power station. The analysis has been carried out using Mössbauer Spectroscopy, X-ray diffraction and optical microscopy. As a result it seems that the morphology and phase change of the carbide phases M₃C/M₇C₃ and M₂₃C₆ are the most prominent changes leading to the material failures.     

On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

基于反向传播神经网络的阻抗断层图像重建新方法

电阻抗成像是通过对物体表面电压、电流的测量来重建物体内部阻抗分布或变化图像的一种新颖计算机断层成像技术。阻抗断层图像重建是一种病态的、非线性的逆问题。提出了一种全新的阻抗断层图像重建方法，它利用反向传播神经网络来表征物体内部阻抗变化位置与物体表面电压变化大小的非线性映射关系，从而可以根据对物体表面测量电压的变化先准确定位阻抗变化区域，再用线性近似方法重建阻抗变化图像，这种方法不仅具有一定的抗噪能力，而且成像精度和空间分辨率都大大好于逆投影方法。     

基于模糊神经网络的自适应PID控制器

提出了一种应用于自适应PID控制器的神经网络与模糊控制相结合的算法,该算法可以有效地解决普通PID控制器依赖于对象的数学模型的缺点,可实现控制系统的在线自适应调整,可满足实时控制的要求。仿真结果表明,基于模糊神经网络整定的PID控制器具有较好的自学习和自适应性,具有较快的响应速度。