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Acuna, V., Ferreira, C. E., Freire, A. S., & Moreno, E. (2014). Solving the maximum edge biclique packing problem on unbalanced bipartite graphs. Discret Appl. Math., 164, 2–12.
Abstract: A biclique is a complete bipartite graph. Given an (L, R)bipartite graph G = (V, E) and a positive integer k, the maximum edge biclique packing (num') problem consists in finding a set of at most k bicliques, subgraphs of G, such that the bicliques are vertex disjoint with respect to a subset of vertices S, where S E {V, L, R}, and the number of edges inside the bicliques is maximized. The maximum edge biclique (mEs) problem is a special case of the MEBP problem in which k = 1. Several applications of the MEB problem have been studied and, in this paper, we describe applications of the MEBP problem in metabolic networks and product bundling. In these applications the input graphs are very unbalanced (i.e., IRI is considerably greater than ILI), thus we consider carefully this property in our models. We introduce a new formulation for the MEB problem and a branchandprice scheme, using the classical branch rule by Ryan and Foster, for the MEBP problem. Finally, we present computational experiments with instances that come from the described applications and also with randomly generated instances. (C) 2011 Elsevier B.V. All rights reserved.

Allende, H., Salas, R., & Moraga, C. (2003). A robust and effective learning algorithm for feedforward neural networks based on the influence function. Lect. Notes Comput. Sc., 2652, 28–36.
Abstract: The learning process of the Feedforward Artificial Neural Networks relies on the data, though a robustness analysis of the parameter estimates of the model must be done due to the presence of outlying observations in the data. In this paper we seek the robust properties in the parameter estimates in the sense that the influence of aberrant observations or outliers in the estimate is bounded so the neural network is able to model the bulk of data. We also seek a trade off between robustness and efficiency under a Gaussian model. An adaptive learning procedure that seeks both aspects is developed. Finally we show some simulations results applied to the RESEX time series.

Averbakh, I., & Pereira, J. (2018). Lateness Minimization in Pairwise Connectivity Restoration Problems. INFORMS J. Comput., 30(3), 522–538.
Abstract: A network is given whose edges need to be constructed (or restored after a disaster). The lengths of edges represent the required construction/restoration times given available resources, and one unit of length of the network can be constructed per unit of time. All points of the network are accessible for construction at any time. For each pair of vertices, a due date is given. It is required to find a construction schedule that minimizes the maximum lateness of all pairs of vertices, where the lateness of a pair is the difference between the time when the pair becomes connected by an already constructed path and the pair's due date. We introduce the problem and analyze its structural properties, present a mixedinteger linear programming formulation, develop a number of lower bounds that are integrated in a branchandbound algorithm, and discuss results of computational experiments both for instances based on randomly generated networks and for instances based on 2010 Chilean earthquake data.

Barrera, J., Moreno, E., & Varas, S. (2020). A decomposition algorithm for computing income taxes with passthrough entities and its application to the Chilean case. Ann. Oper. Res., 286(12), 545–557.
Abstract: Income tax systems with “passthrough” entities transfer a firm's income to shareholders, which are taxed individually. In 2014, a Chilean tax reform introduced this type of entity and changed to an accrual basis that distributes incomes (but not losses) to shareholders. A crucial step for the Chilean taxation authority is to compute the final income of each individual given the complex network of corporations and companies, usually including cycles between them. In this paper, we show the mathematical conceptualization and the solution to the problem, proving that there is only one way to distribute income to taxpayers. Using the theory of absorbing Markov chains, we define a mathematical model for computing the taxable income of each taxpayer, and we propose a decomposition algorithm for this problem. This approach allows us to compute the solution accurately and to efficiently use computational resources. Finally, we present some characteristics of Chilean taxpayers' network and the computational results of the algorithm using this network.
Keywords: Income taxes; Markov processes; Networks; Algorithms

BorquezParedes, D., Beghelli, A., Leiva, A., & Murrugarra, R. (2018). Does fragmentation avoidance improve the performance of dynamic spectrum allocation in elastic optical networks? Photonic Netw. Commun., 35(3), 287–299.
Abstract: Most spectrum allocation algorithms in elastic optical networks apply a greedy approach: A new connection is allocated as long as there are enough spectrum slots to accommodate it. Recently, a different approach was proposed. Named DeadlockAvoidance (DA), it only establishes a new connection if the portion of spectrum left after allocating it is zero (fulllink utilization) or is big enough to accommodate future requests. Otherwise, the connection request is blocked as a way to avoid fragmentation. The performance of DA has been evaluated in a singlelink scenario, where its performance is not affected by the slot continuity constraint. In this paper, we evaluate for the first time the blocking performance and fragmentation level of DA in a fully dynamic network scenario with different bitrates and number of slots for a single link, a 4node bus and a mesh topology. The performance was evaluated by simulation, and a lower bound was also derived using a continuous Markov chain model. Results are obtained for DA and three greedy algorithms: First Fit, Exact Fit and FirstLast Fit. Results show that DA significantly decreases fragmentation, and thus, it exhibits a much lower blocking due to fragmentation than the greedy algorithms. However, this decrease is compensated by a new type of blocking due to the selective acceptance of connections. As a result, the extra computational complexity of DA does not compensate a gain in performance.

Calderon, F. I., Lozada, A., BorquezParedes, D., Olivares, R., Davalos, E. J., Saavedra, G., et al. (2020). BERAdaptive RMLSA Algorithm for WideArea Flexible Optical Networks. IEEE Access, 8, 128018–128031.
Abstract: Widearea optical networks face significant transmission challenges due to the relentless growth of bandwidth demands experienced nowadays. Network operators must consider the relationship between modulation format and maximum reach for each connection request due to the accumulation of physical layer impairments in optical fiber links, to guarantee a minimum quality of service (QoS) and quality of transmission (QoT) to all connection requests. In this work, we present a BERadaptive solution to solve the routing, modulation format, and spectrum assignment (RMLSA) problem for widearea elastic optical networks. Our main goal is to maximize successful connection requests in widearea networks while choosing modulation formats with the highest efficiency possible. Consequently, our technique uses an adaptive biterrorrate (BER) threshold to achieve communication with the best QoT in the most efficient manner, using the strictest BER value and the modulation format with the smallest bandwidth possible. Additionally, the proposed algorithm relies on 3R regeneration devices to enable longdistances communications if transparent communication cannot be achieved. We assessed our method through simulations for various network conditions, such as the number of regenerators per node, traffic load per user, and BER threshold values. In a scenario without regenerators, the BERAdaptive algorithm performs similarly to the most relaxed fixed BER threshold studied in blocking probability. However, it ensures a higher QoT to most of the connection requests. The proposed algorithm thrives with the use of regenerators, showing the best performance among the studied solutions, enabling longdistance communications with a high QoT and low blocking probability.

ColiniBaldeschi, R., Cominetti, R., & Scarsini, M. (2019). Price of Anarchy for Highly Congested Routing Games in Parallel Networks. Theor. Comput. Syst., 63(1), 90–113.
Abstract: We consider nonatomic routing games with one source and one destination connected by multiple parallel edges. We examine the asymptotic behavior of the price of anarchy as the inflow increases. In accordance with some empirical observations, we prove that under suitable conditions on the costs the price of anarchy is asymptotic to one. We show with some counterexamples that this is not always the case, and that these counterexamples already occur in simple networks with only 2 parallel links.

Cortes, C. E., JaraMoroni, P., Moreno, E., & Pineda, C. (2013). Stochastic transit equilibrium. Transp. Res. Pt. BMethodol., 51, 29–44.
Abstract: We present a transit equilibrium model in which boarding decisions are stochastic. The model incorporates congestion, reflected in higher waiting times at bus stops and increasing invehicle travel time. The stochastic behavior of passengers is introduced through a probability for passengers to choose boarding a specific bus of a certain service. The modeling approach generates a stochastic commonlines problem, in which every line has a chance to be chosen by each passenger. The formulation is a generalization of deterministic transit assignment models where passengers are assumed to travel according to shortest hyperpaths. We prove existence of equilibrium in the simplified case of parallel lines (stochastic commonlines problem) and provide a formulation for a more general network problem (stochastic transit equilibrium). The resulting waiting time and network load expressions are validated through simulation. An algorithm to solve the general stochastic transit equilibrium is proposed and applied to a sample network; the algorithm works well and generates consistent results when considering the stochastic nature of the decisions, which motivates the implementation of the methodology on a realsize network case as the next step of this research. (C) 2013 Elsevier Ltd. All rights reserved.

D'Angelo, G., Di Stefano, G., Navarra, A., Nisse, N., & Suchan, K. (2015). Computing on Rings by Oblivious Robots: A Unified Approach for Different Tasks. Algorithmica, 72(4), 1055–1096.
Abstract: A set of autonomous robots have to collaborate in order to accomplish a common task in a ringtopology where neither nodes nor edges are labeled (that is, the ring is anonymous). We present a unified approach to solve three important problems: the exclusive perpetual exploration, the exclusive perpetual clearing, and the gathering problems. In the first problem, each robot aims at visiting each node infinitely often while avoiding that two robots occupy a same node (exclusivity property); in exclusive perpetual clearing (also known as graph searching), the team of robots aims at clearing the whole ring infinitely often (an edge is cleared if it is traversed by a robot or if both its endpoints are occupied); and in the gathering problem, all robots must eventually occupy the same node. We investigate these tasks in the LookComputeMove model where the robots cannot communicate but can perceive the positions of other robots. Each robot is equipped with visibility sensors and motion actuators, and it operates in asynchronous cycles. In each cycle, a robot takes a snapshot of the current global configuration (Look), then, based on the perceived configuration, takes a decision to stay idle or to move to one of its adjacent nodes (Compute), and in the latter case it eventually moves to this neighbor (Move). Moreover, robots are endowed with very weak capabilities. Namely, they are anonymous, asynchronous, oblivious, uniform (execute the same algorithm) and have no common sense of orientation. In this setting, we devise algorithms that, starting from an exclusive and rigid (i.e. aperiodic and asymmetric) configuration, solve the three above problems in anonymous ringtopologies.

Fernandez, C., Valle, C., Saravia, F., & Allende, H. (2012). Behavior analysis of neural network ensemble algorithm on a virtual machine cluster. Neural Comput. Appl., 21(3), 535–542.
Abstract: Ensemble learning has gained considerable attention in different learning tasks including regression, classification, and clustering problems. One of the drawbacks of the ensemble is the high computational cost of training stages. Resampling local negative correlation (RLNC) is a technique that combines two wellknown methods to generate ensemble diversityresampling and error negative correlationand a finegrain parallel approach that allows us to achieve a satisfactory balance between accuracy and efficiency. In this paper, we introduce a structure of the virtual machine aimed to test diverse selection strategies of parameters in neural ensemble designs, such as RLNC. We assess the parallel performance of this approach on a virtual machine cluster based on the full virtualization paradigm, using speedup and efficiency as performance metrics, for different numbers of processors and training data sizes.

Goles, E., & Montealegre, P. (2014). Computational complexity of threshold automata networks under different updating schemes. Theor. Comput. Sci., 559, 3–19.
Abstract: Given a threshold automata network, as well as an updating scheme over its vertices, we study the computational complexity associated with the prediction of the future state of a vertex. More precisely, we analyze two classes of local functions: the majority and the ANDOR rule (vertices take the AND or the OR logic functions over the state of its neighborhoods). Depending on the updating scheme, we determine the complexity class (NC, P, NP, PSPACE) where the prediction problem belongs. (C) 2014 Elsevier B.V. All rights reserved.

Goles, E., & Montealegre, P. (2015). The complexity of the majority rule on planar graphs. Adv. Appl. Math., 64, 111–123.
Abstract: We study the complexity of the majority rule on planar automata networks. We reduce a special case of the Monotone Circuit Value Problem to the prediction problem of determining if a vertex of a planar graph will change its state when the network is updated with the majority rule. (C) 2014 Elsevier Inc. All rights reserved.
Keywords: Automata networks; Computational complexity; Majority; PCompleteness; NC; Planar graph

Goles, E., & Ruz, G. A. (2015). Dynamics of neural networks over undirected graphs. Neural Netw., 63, 156–169.
Abstract: In this paper we study the dynamical behavior of neural networks such that their interconnections are the incidence matrix of an undirected finite graph G = (V, E) (i.e., the weights belong to {0, 1}). The network may be updated synchronously (every node is updated at the same time), sequentially (nodes are updated one by one in a prescribed order) or in a blocksequential way (a mixture of the previous schemes). We characterize completely the attractors (fixed points or cycles). More precisely, we establish the convergence to fixed points related to a parameter alpha(G), taking into account the number of loops, edges, vertices as well as the minimum number of edges to remove from E in order to obtain a maximum bipartite graph. Roughly, alpha(G') < 0 for any G' subgraph of G implies the convergence to fixed points. Otherwise, cycles appear. Actually, for very simple networks (majority functions updated in a blocksequential scheme such that each block is of minimum cardinality two) we exhibit cycles with nonpolynomial periods. (C) 2014 Elsevier Ltd. All rights reserved.

Goles, E., Lobos, F., Ruz, G. A., & Sene, S. (2020). Attractor landscapes in Boolean networks with firing memory: a theoretical study applied to genetic networks. Nat. Comput., to appear, 25 pp.
Abstract: In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains at its firing state a finite number of steps. We prove in particular that these networks have the same computational power than the classical ones, i.e. any Boolean network with firing memory composed of m vertices can be simulated by a Boolean network by adding vertices. We also prove general results on specific classes of networks. For instance, we show that the existence of at least one delay greater than 1 in disjunctive networks makes such networks have only fixed points as attractors. Moreover, for arbitrary networks composed of two vertices, we characterize the delay phase space, i.e. the delay values such that networks admits limit cycles or fixed points. Finally, we analyze two classical biological models by introducing delays: the model of the immune control of the lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$$\lambda $$\end{document}phage and that of the genetic control of the floral morphogenesis of the plant Arabidopsis thaliana.

Goles, E., Montalva, M., & Ruz, G. A. (2013). Deconstruction and Dynamical Robustness of Regulatory Networks: Application to the Yeast Cell Cycle Networks. Bull. Math. Biol., 75(6), 939–966.
Abstract: Analyzing all the deterministic dynamics of a Boolean regulatory network is a difficult problem since it grows exponentially with the number of nodes. In this paper, we present mathematical and computational tools for analyzing the complete deterministic dynamics of Boolean regulatory networks. For this, the notion of alliance is introduced, which is a subconfiguration of states that remains fixed regardless of the values of the other nodes. Also, equivalent classes are considered, which are sets of updating schedules which have the same dynamics. Using these techniques, we analyze two yeast cell cycle models. Results show the effectiveness of the proposed tools for analyzing update robustness as well as the discovery of new information related to the attractors of the yeast cell cycle models considering all the possible deterministic dynamics, which previously have only been studied considering the parallel updating scheme.
Keywords: Boolean networks; Attractors; Update robustness; Alliances; Dynamics

Goles, E., Montealegre, P., & RiosWilson, M. (2020). On The Effects Of Firing Memory In The Dynamics Of Conjunctive Networks. Discret. Contin. Dyn. Syst., 40(10), 5765–5793.
Abstract: A boolean network is a map F : {0, 1}(n) > {0, 1}(n) that defines a discrete dynamical system by the subsequent iterations of F. Nevertheless, it is thought that this definition is not always reliable in the context of applications, especially in biology. Concerning this issue, models based in the concept of adding asynchronicity to the dynamics were propose. Particularly, we are interested in a approach based in the concept of delay. We focus in a specific type of delay called firing memory and it effects in the dynamics of symmetric (nondirected) conjunctive networks. We find, in the caseis in which the implementation of the delay is not uniform, that all the complexity of the dynamics is somehow encapsulated in the component in which the delay has effect. Thus, we show, in the homogeneous case, that it is possible to exhibit attractors of nonpolynomial period. In addition, we study the prediction problem consisting in, given an initial condition, determinate if a fixed coordinate will eventually change its state. We find again that in the nonhomogeneous case all the complexity is determined by the component that is affected by the delay and we conclude in the homogeneous case that this problem is PSPACEcomplete.

Goles, E., Montealegre, P., & Vera, J. (2016). Naming Game Automata Networks. J. Cell. Autom., 11(56), 497–521.
Abstract: In this paper we introduce automata networks to model some features of the emergence of a vocabulary related with the naming game model. We study the dynamical behaviour (attractors and convergence) of extremal and majority local functions.

Harrison, R., Hernandez, G., & Munoz, R. (2019). A discrete model of market interaction in the presence of social networks and price discrimination. Math. Soc. Sci., 102, 48–58.
Abstract: In this paper, we provide a model to study the equilibrium outcome in a market characterized by the competition between two firms offering horizontally differentiated services, in a context where consumers are the basic unit of decision on the demand side and are related through a social network. In the model, we consider that consumers make optimal choice, participation and consumption decisions, while firms optimally decide their tariffs, eventually using nonlinear pricing schemes. This approach permits us to identify and model two different kinds of network externalities, one associated with tariffmediated network externalities and the other related to participation network externalities. We apply the model to the telecommunication industry, where we study the impact of alternative regulatory interventions. We provide numerical evidence suggesting that policies designed to reduce horizontal differentiation might be more effective than those designed to limit access charges; this result seems robust to the presence of different forms of price discrimination. We should interpret these findings cautiously due to the existence of potential implementation costs for each policy. (C) 2019 Elsevier B.V. All rights reserved.
Keywords: Social networks; Agentbased models; Price discrimination

Henriquez, P. A., & Ruz, G. A. (2018). A noniterative method for pruning hidden neurons in neural networks with random weights. Appl. Soft. Comput., 70, 1109–1121.
Abstract: Neural networks with random weights have the advantage of fast computational time in both training and testing. However, one of the main challenges of single layer feedforward neural networks is the selection of the optimal number of neurons in the hidden layer, since few/many neurons lead to problems of underfitting/overfitting. Adapting Garson's algorithm, this paper introduces a new efficient and fast noniterative algorithm for the selection of neurons in the hidden layer for randomization based neural networks. The proposed approach is divided into three steps: (1) train the network with h hidden neurons, (2) apply Garson's algorithm to the matrix of the hidden layer, and (3) perform pruning reducing hidden layer neurons based on the harmonic mean. Our experiments in regression and classification problems confirmed that the combination of the pruning technique with these types of neural networks improved their predictive performance in terms of mean square error and accuracy. Additionally, we tested our proposed pruning method with neural networks trained under sequential learning algorithms, where Random Vector Functional Link obtained, in general, the best predictive performance compared to online sequential versions of extreme learning machines and single hidden layer neural network with random weights. (C) 2018 Elsevier B.V. All rights reserved.

Kiwi, M., de Espanes, P. M., Rapaport, I., Rica, S., & Theyssier, G. (2014). Strict Majority Bootstrap Percolation in the rwheel. Inf. Process. Lett., 114(6), 277–281.
Abstract: In the strict Majority Bootstrap Percolation process each passive vertex v becomes active if at least [deg(v)+1/2] of its neighbors are active (and thereafter never changes its state). We address the problem of finding graphs for which a small proportion of initial active vertices is likely to eventually make all vertices active. We study the problem on a ring of n vertices augmented with a “central” vertex u. Each vertex in the ring, besides being connected to u, is connected to its r closest neighbors to the left and to the right. We prove that if vertices are initially active with probability p > 1/4 then, for large values of r, percolation occurs with probability arbitrarily close to I as n > infinity. Also, if p < 1/4, then the probability of percolation is bounded away from 1. (c) 2014 Elsevier B.V. All rights reserved.
Keywords: Bootstrap percolation; Interconnection networks
