Approximation of the Quadratic Set Covering problem

We study in this article the polynomial approximation properties of the Quadratic Set Covering problem. This problem, which arises in many applications, is a natural generalization of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case, and even in classical subcases (when the size of each set or when the frequency of each element is bounded by a constant). Then we focus on the convex case and give both positive and negative approximation results. Finally, we tackle the unweighted version of this problem.     

非线性延时模型及逻辑门优化设计

为了解决信号斜率对逻辑门延时的影响,提出一种基于逻辑努力的非线性逻辑门延时模型.模型引入非线性修正因子,该修正因子通过对仿真数据的模拟,由优化算法求得.针对不同的连线负载,提出模型得到的延时与仿真得到的延时误差小于3％.仿真结果表明,在不同的连线负载下,采用该模型优化设计的译码器延时最小,验证了模型的有效性.     

非高斯噪声驱动下一维双稳系统的逻辑操作

本文以成功率作为逻辑随机共振的测度, 主要研究了非高斯噪声激励下一维双稳系统的逻辑随机共振现象, 并用平均首次通过时间的方法对此现象的机理进行了解释. 研究结果表明: 只有在适当的噪声强度带或关联时间带上, 成功率才会达到共振峰值. 通过对系统参数进行优化, 提高了系统实现逻辑操作的可靠性. 关键词： 逻辑随机共振 一维双稳系统 非高斯噪声 平均首次通过时间     

Mixed integer programming for a special logic constrained optimal control problem

Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L² norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a complicated one, difficulties arise when integrating the additional logical constraints. First, we will present two different ways of modeling the problem, both of them leading us to Mixed Integer Problems. Furthermore, algorithms (Generalized Outer Approximation, Benders Decomposition and Branch and Cut) are applied on each model and results analyzed. We also present a Benders Decomposition algorithm variant that is adapted to our problem (taking into account its particular form) and we will conclude by looking at the optimal solutions obtained in an interesting physical example: the harmonic spring.     

积逻辑系统中的广义重言式

讨论积逻辑系统中的广义重言式理论 ,给出积逻辑系统中子代数和广义重言式的一系列性质。本文的主要结果表明 ,在几个重要的逻辑系统中 ,标准积逻辑系统具有最简单的广义重言式结构 ,而在推理过程中 ,它具有较差的真值传递性。     

On a family of connectives for fuzzy sets

In this paper we find the general solution of the functional equation $\text{S}{}^1\text{(T(x, y), T(x, N(y))) = x}$, where $\text{S}{}^1$ is a t-conorm, T is a t-norm and N is a strong negation on the unit interval. In particular the result yields a family of connectives for fuzzy sets.     

Statistical issues in measurement

Measurement theories are traditionally couched in algebraic terms, which makes them unsuitable for statistical testing. A probabilistic recasting of these theories is proposed here. It is observed then that an axiom of probabilistic measurement has typically the form of a logical polynomial, the structure of which induces a particular partition of the parameter space, giving rise to a calss of statistical problems for which the null hypothesis is a union of convex polyhedrons. This is a consequence of the fact that a logical polynomial can always be rewritten in normal form, that is, as a disjunction of conjunctions. A likelihood ratio method is worked out in a couple of exemplary cases. One of these examples provides a test of transitivity, a property which lies at the heart of ordinal measurement.     

A Structure Theorem for Free Temporal Algebras

In this paper an algebraic version for temporal algebras of the logical filtrations for modal and temporal logics is analysed. A structure theorem for free temporal algebras and also some results with regard to the variety of temporal algebras are obtained.     

基于逻辑输入样本的神经网络算法

本文对确定多层前向神经网络权提出了一种基于逻辑输入样本的直接算法。对于逻辑输入样本,该算法只需一个三层网络实现;否则,需在输入层和隐层间引入一个预处理层以完成输入样本向逻辑向量的转化。由于不引入误差能量函数,该算法避免了BP算法训练过程出现的收敛速度慢和误差陷入局部极小问题。本文还对该算法的正确性作了详细论证并以XOR问题解释其计算过程。     

Genetic algorithm to design logical topologies in reconfigurable WDM networks

A new method to design logical topologies based on genetic algorithms is presented. Not only does the algorithm determine which nodes should be connected by means of lightpaths with the aim of minimizing congestion, but it also solves the routing and wavelength assignment problem. In this way, the algorithm guarantees that the logical topology obtained can be embedded in the optical network subject to the available set of resources. The algorithm is effective in terms of both congestion and fairness. For instance, when compared with other work, the congestion is significantly reduced (from 20% to 75% depending on the matrix of traffic considered), and the fairness, when evaluated in terms of the Jain index, is generally higher than 0.94. Moreover, the algorithm brings advantages when employed in dynamic scenarios where the logical topology is frequently reconfigured, as it is fast and, in contrast to other algorithms previously proposed, the calculation process can be stopped at any time (if required) in order to give the best virtual topology found up to the moment.