On representations of 2-increasing binary aggregation functions

In this paper, we provide two different representations of 2-increasing binary aggregation functions by means of their lower and upper margins and a suitable copula.     

Generating binary trees by Glivenko classes on Tamari lattices

Using algebraic-theoretic results, we give an algorithm for generating binary trees within Glivenko classes in Tamari lattices. Tamari lattices are lattices of binary trees endowed by the well-known rotation transformation.     

Online shape learning using binary search trees

In this paper we propose an online shape learning algorithm based on the self-balancing binary search tree data structure for the storage and retrieval of shape templates. This structure can also be used for classification purposes. We introduce a similarity measure with which we can make decisions on how to traverse the tree and even backtrack through the search path to find more candidate matches. Then we describe every basic operation a binary search tree can perform adapted to such a tree of shapes. Note that as a property of binary search trees, all operations can be performed in O(logn)$O(\log n)$ time and are very efficient. Finally, we present experimental data evaluating the performance of the proposed algorithm and demonstrating the suitability of this data structure for the purpose it was designed to serve.     

Optimization based on a team of automata with binary outputs

This paper presents an algorithm for optimization of a multimodal scalar-argument function based on a team of learning stochastic automata with binary actions (outputs) 0 or 1. The action of the team of automata consists of a digital number which represents the environment input. The probability distribution associated with each automaton is adjusted using a modified version of the Bush-Mosteller reinforcement scheme with a continuous environment response and a time-varying correction factor. The asymptotic properties of this optimization algorithm are presented. An example illustrates the feasibility of this optimization algorithm.     

Lower bounds on the rotation distance of binary trees

The rotation distanced(S,T) between two binary trees S, T of n vertices is the minimum number of rotations to transform S into T. While it is known that d(S,T)?2n−6, a well-known conjecture states that there are trees for which this bound is sharp for any value of n?11. We are unable to prove the conjecture, but we give here some simple criteria for lower bound evaluation, leading for example to individuate some “regular” tree structures for which d(S,T)=3n/2−O(1), or d(S,T)=5n/3−O(1).     

k-Restricted rotation distance between binary trees

The restricted rotation distancedR(S,T) between two binary trees S, T of n vertices is the minimum number of rotations to transform S into T, where rotations take place at the root of S, or at the right child of the root. A sharp upper bound dR(S,T)?4n−8 is known, based on group theory [S. Cleary, J. Taback, Bounding restricted rotation distance, Information Processing Letters 88 (5) (2003) 251-256]. We refine this bound to a sharp dR(S,T)?4n−8−ρS−ρT, where ρS and ρT are the numbers of vertices in the rightmost vertex chains of the two trees, using an elementary transformation algorithm. We then generalize the concept to k-restricted rotation, by allowing rotations to take place at all the vertices of the highest k levels of the tree, and study the new distance for k=2. The case k?3 is essentially open.     

Structured population-based incremental learning

 We investigate a recently developed abstraction of genetic algorithms (GAs) in which a population of GAs in any generation is represented by a single vector whose elements are the probabilities of the corresponding bit positions being equivalent to 1. The process of evolution is represented by learning the elements of the probability vector; the method is clearly linked to the artificial neural network (ANN) method of competitive learning. We use techniques from ANNs to extend the applicability of the method to non-static problems, to multi-objective criteria, to multi-modal problems and to creating an order on a set of sub-populations.     

A note on constructing binary heaps with periodic networks

We consider the problem of constructing binary heaps on constant degree networks performing compare-exchange operations only. The heap data structure, introduced by William and Williams [Comm. ACM 7 (6) (1964) 347-348], has many applications and, therefore, has been intensively studied in sequential and parallel context. In particular, Brodal and Pinotti [Theoret. Comput. Sci. 250 (2001) 235-245] have recently presented two families of comparator networks: the first of depth 4logN and the second of size O(NloglogN) for constructing binary heaps of size N. In this note, we give an new construction of such a network with the running time improved to 3logN. Moreover, the network has a novel property of being 3-periodic, that is, for each unit of time i the same sets of operations are performed in units i and i+3. Then we argue that our construction is optimal with respect to the length of the period, that is, we prove that there is no 2-periodic network that is able to build a binary heap in sublinear time. Finally, we show that our construction can be used to decrease also the depth of the networks with O(NloglogN) size.     

Single-machine scheduling jobs with exponential learning functions

In a manufacturing system workers are involved in doing the same job or activity repeatedly. Hence, the workers start learning more about the job or activity. Because of the learning, the time to complete the job or activity starts decreasing, which is known as “learning effect”. In this paper, an exponential sum-of-actual-processing-time based learning effect is introduced into single-machine scheduling. By the exponential sum-of-actual-processing-time based learning effect, we mean that the processing time of a job is defined by an exponential function of the sum-of-the-actual-processing-time of the already processed jobs. Under the proposed learning model, we show that under a sufficient condition, the makespan minimization problem, the sum of the θth (θ > 0) power of completion times minimization problem, and some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem remain polynomially solvable.     

Source rate encoding mechanisms for binary congestion control

This paper focus on congestion control for best-effort packet-switching networks, where congested routers use 1 bit per packet to communicate with sources. Sources adapt their rates according to the sequence of bits received. Routers do not keep per-flow information but perform selective marking based on the source rate value inserted in each packet. We propose a new strategy for source rate encoding in forward packets, directly applicable to existing network protocols (e.g. IP). The scheme supports differentiated classes with respect to rate allocation. We test, by simulation, this encoding mechanism as well as the performance of the router and source algorithms.     

Best approximations of fitness functions of binary strings

Fitness functions of binary strings (pseudo-boolean functions) canbe represented as polynomials over a set of boolean variables. Weshow that any such function has a unique best approximation in thelinear span of any subset of polynomials. For example, there is aunique best linear approximation and a unique best quadraticapproximation. The error of an approximation here isroot-mean-squared error. If all the details of the function to beapproximated are known, then the approximation can be calculateddirectly. Of more practical importance, we give a method for usingsampling to estimate the coefficients of the approximation, anddescribe its limitations.     

Study on IAC networks models: learning and stability

This paper presents a methodology that uses evolutionary learning in training ‘A’ model networks, a topology based on Interactive Activation and Competition (IAC) neural networks. IAC networks show local knowledge and processing units clustered in pools. The connections among units may assume only 1, 0 or −1. On the other hand, ‘A’ model network uses values in interval [−1, 1]. This feature provides a wider range of applications for this network, including problems which do not show mutually exclusive concepts. However, there is no algorithm to adjust the network weights and still preserve the desired characteristics of the original network. Accordingly, we propose the use of genetic algorithms in a new methodology to obtain the correct weight set for this network. Two examples are used to illustrate the proposed method. Findings are considered consistent and generic enough to allow further applications on similar classes of problems suitable for ‘A’ model IAC Networks.     

Identification and control of gene networks in living organisms via supervised and unsupervised learning

Cells efficiently carry out organic synthesis, energy transduction, and signal processing across a range of environmental conditions and at nanometer scales—rivaling any engineered system. In the cell, these processes are orchestrated by gene networks, which we define broadly as networks of interacting genes, proteins, and metabolites. Understanding how the dynamics of gene networks give rise to cellular functions is a principal challenge in biology, and identifying their structure is the first step towards their control. This knowledge has applications ranging from the improvement of antibiotics, the engineering of microbes for environmental remediation, and the creation of biologically-derived energy sources. In this review, we discuss several methods for the identification of gene networks.     

The Fermat star of binary trees

A Fermat point P is one that minimizes the sum δ of the distances between P and the points of a given set. The resulting arrangement, called here a Fermat star, is a particular Steiner tree with only one intermediate point. We extend these concepts to rooted binary trees under the known rotation distance that measures the difference in shape of such trees. Minimizing δ is hard, due to the intrinsic difficulty of computing the rotation distance. Then we limit our study to establishing significant upper bounds for δ. In particular, for m binary trees of n vertices, we show how to construct efficiently a Fermat star with δ?mn−3m, with a technique inherited from the studies on rotation distance.     

A cooperative game of a pair of learning automata

A cooperative game played in a sequential manner by a pair of learning automata is investigated in this paper. The automata operate in an unknown random environment which gives a common pay-off to the automata. Necessary and sufficient conditions on the functions in the reinforcement scheme are given for absolute monotonicity which enables the expected pay-off to be monotonically increasing in any arbitrary environment. As each participating automaton operates with no information regarding the other partner, the results of the paper are relevant to decentralized control.     

基于局部二值模式和深度学习的人脸识别

针对人脸识别中深度学习直接提取人脸特征时忽略了其局部结构特征的问题,提出一种将分块局部二值模式(LBP)与深度学习相结合的人脸识别方法.首先,将人脸图像分块,利用均匀LBP算子分别提取图像各局部的LBP直方图特征,再按照顺序连接在一起形成整个人脸的LBP纹理特征; 其次,将得到的LBP特征作为深度信念网络(DBN)的输入,逐层训练网络,并在顶层形成分类面; 最后,用训练好的深度信念网络对人脸样本进行识别.在ORL、YALE和FERET人脸库上的实验结果表明,所提算法与采用支持向量机(SVM)的方法相比,在小样本的人脸识别中有很好的识别效果.     

Evolutionary model trees for handling continuous classes in machine learning

Model trees are a particular case of decision trees employed to solve regression problems. They have the advantage of presenting an interpretable output, helping the end-user to get more confidence in the prediction and providing the basis for the end-user to have new insight about the data, confirming or rejecting hypotheses previously formed. Moreover, model trees present an acceptable level of predictive performance in comparison to most techniques used for solving regression problems. Since generating the optimal model tree is an NP-Complete problem, traditional model tree induction algorithms make use of a greedy top-down divide-and-conquer strategy, which may not converge to the global optimal solution. In this paper, we propose a novel algorithm based on the use of the evolutionary algorithms paradigm as an alternate heuristic to generate model trees in order to improve the convergence to globally near-optimal solutions. We call our new approach evolutionary model tree induction (E-Motion). We test its predictive performance using public UCI data sets, and we compare the results to traditional greedy regression/model trees induction algorithms, as well as to other evolutionary approaches. Results show that our method presents a good trade-off between predictive performance and model comprehensibility, which may be crucial in many machine learning applications.