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Morales, P., Lozada, A., BorquezParedes, D., Olivares, R., Saavedra, G., Leiva, A., et al. (2021). Improving the Performance of SDMEON Through Demand Prioritization: A Comprehensive Analysis. IEEE Access, 9, 63475–63490.
Abstract: This paper studies the impact of demandprioritization on SpaceDivision Multiplexing Elastic Optical Networks (SDMEON). For this purpose, we solve the static Routing, Modulation Level, Spatial Mode, and Spectrum Assignment (RMLSSA) problem using 34 different explainable demandprioritization strategies. Although previous works have applied heuristics or metaheuristics to perform demandprioritization, they have not focused on identifying the best prioritization strategies, their inner operation, and the implications behind their good performance by thorough profiling and impact analysis. We focus on a comprehensive analysis identifying the best explainable strategies to sort network demands in SDMEON, considering the physicallayer impairments found in optical communications. Also, we show that simply using the common shortest path routing might lead to higher resource requirements. Extensive simulation results show that up to 8.33% capacity savings can be achieved on average by balanced routing, up to a 16.69% capacity savings can be achieved using the best performing demandprioritization strategy compared to the worstperforming ones, the most used demandprioritization strategy in the literature (serving demands with higher bandwidth requirements first) is not the bestperforming one but the one sorting based on the path lengths, and using doublecriteria strategies to break ties is key for a good performance. These results are relevant showing that a good combination of routing and demandprioritization heuristics impact significantly on network performance. Additionally, they increase the understanding about the inner workings of good heuristics, a valuable knowledge when network settings forbid using more computationally complex approaches.
Keywords: Modulation; Optical fiber networks; Optical modulation; Routing; Resource management; Bandwidth; Optical variables control; Elastic optical networks; spacedivision multiplexing; resource assignment; network capacity; physicallayer impairments
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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.

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.

Timmermann, T., Gonzalez, B., & Ruz, G. A. (2020). Reconstruction of a gene regulatory network of the induced systemic resistance defense response in Arabidopsis using boolean networks. BMC Bioinformatics, 21(1), 16 pp.
Abstract: Background An important process for plant survival is the immune system. The induced systemic resistance (ISR) triggered by beneficial microbes is an important costeffective defense mechanism by which plants are primed to an eventual pathogen attack. Defense mechanisms such as ISR depend on an accurate and contextspecific regulation of gene expression. Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRNs). Here, we explore the regulatory mechanism of the ISR defense response triggered by the beneficial bacterium Paraburkholderia phytofirmans PsJN in Arabidopsis thaliana plants infected with Pseudomonas syringae DC3000. To achieve this, a GRN underlying the ISR response was inferred using gene expression timeseries data of certain defenserelated genes, differential evolution, and threshold Boolean networks. Results One thousand threshold Boolean networks were inferred that met the restriction of the desired dynamics. From these networks, a consensus network was obtained that helped to find plausible interactions between the genes. A representative network was selected from the consensus network and biological restrictions were applied to it. The dynamics of the selected network showed that the largest attractor, a limit cycle of length 3, represents the final stage of the defense response (12, 18, and 24 h). Also, the structural robustness of the GRN was studied through the networks' attractors. Conclusions A computational intelligence approach was designed to reconstruct a GRN underlying the ISR defense response in plants using gene expression timeseries data of A. thaliana colonized by P. phytofirmans PsJN and subsequently infected with P. syringae DC3000. Using differential evolution, 1000 GRNs from timeseries data were successfully inferred. Through the study of the network dynamics of the selected GRN, it can be concluded that it is structurally robust since three mutations were necessary to completely disarm the Boolean trajectory that represents the biological data. The proposed method to reconstruct GRNs is general and can be used to infer other biologically relevant networks to formulate new biological hypotheses.

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., 19(2), 295–319.
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.

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

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

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.

Ruz, G. A., Zuniga, A., & Goles, E. (2018). A Boolean network model of bacterial quorumsensing systems. Int. J. Data Min. Bioinform., 21(2), 123–144.
Abstract: There are several mathematical models to represent gene regulatory networks, one of the simplest is the Boolean network paradigm. In this paper, we reconstruct a regulatory network of bacterial quorumsensing systems, in particular, we consider Paraburkholderia phytofirmans PsJN which is a plant growth promoting bacteria that produces positive effects in horticultural crops like tomato, potato and grape. To learn the regulatory network from temporal expression pattern of quorumsensing genes at root plants, we present a methodology that considers the training of perceptrons for each gene and then the integration into one Boolean regulatory network. Using the proposed approach, we were able to infer a regulatory network model whose topology and dynamic exhibited was helpful to gain insight on the quorumsensing systems regulation mechanism. We compared our results with REVEAL and BestFit extension algorithm, showing that the proposed neural network approach obtained a more biologically meaningful network and dynamics, demonstrating the effectiveness of the proposed method.

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.

Moreno, S., Pfeiffer, J. J., & Neville, J. (2018). Scalable and exact sampling method for probabilistic generative graph models. Data Min. Knowl. Discov., 32(6), 1561–1596.
Abstract: Interest in modeling complex networks has fueled the development of multiple probabilistic generative graph models (PGGMs). PGGMs are statistical methods that model the network distribution and match common characteristics of real world networks. Recently, scalable sampling algorithms for well known PGGMs, made the analysis of largescale, sparse networks feasible for the first time. However, it has been demonstrated that these scalable sampling algorithms do not sample from the original underlying distribution, and sometimes produce very unlikely graphs. To address this, we extend the algorithm proposed in Moreno et al.(in: IEEE 14th international conference on data mining, pp 440449, 2014) for a single model and develop a general solution for a broad class of PGGMs. Our approach exploits the fact that PGGMs are typically parameterized by a small set of unique probability valuesthis enables fast generation via independent sampling of groups of edges with the same probability value. By sampling within groups, we remove bias due to conditional sampling and probability reallocation. We show that our grouped sampling methods are both provably correct and efficient. Our new algorithm reduces time complexity by avoiding the expensive rejection sampling step previously necessary, and we demonstrate its generality, by outlining implementations for six different PGGMs. We conduct theoretical analysis and empirical evaluation to demonstrate the strengths of our algorithms. We conclude by sampling a network with over a billion edges in 95s on a single processor.

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.

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.

Vera, J. (2017). SelfOrganization of Vocabularies under Different Interaction Orders. Artif. Life, 23(2), 287–294.
Abstract: Traditionally, the formation of vocabularies has been studied by agentbased models (primarily, the naming game) in which random pairs of agents negotiate wordmeaning associations at each discrete time step. This article proposes a first approximation to a novel question: To what extent is the negotiation of wordmeaning associations influenced by the order in which agents interact? Automata networks provide the adequate mathematical framework to explore this question. Computer simulations suggest that on twodimensional lattices the typical features of the formation of wordmeaning associations are recovered under random schemes that update small fractions of the population at the same time; by contrast, if larger subsets of the population are updated, a periodic behavior may appear.
Keywords: Vocabulary; automata networks; interaction orders; naming game

TarifenoGajardo, M., Beghelli, A., & Moreno, E. (2016). AvailabilityDriven Optimal Design of Shared Path Protection in WDM Networks. Networks, 68(3), 224–237.
Abstract: Availability, defined as the fraction of time a network service is operative, is a key network service parameter. Dedicated protection increases availability but also the cost. Shared protection instead decreases the cost, but also the availability. In this article, we formulate and solve an integer linear programming (ILP) model for the problem of minimizing the backup resources required by a sharedprotected static optical network whilst guaranteeing an availability target per connection. The main research challenge is dealing with the nonlinear expression for the availability constraint. Taking the working/backup routes and the availability requirements as input data, the ILP model identifies the set of connections sharing backup resources in any given network link. We also propose a greedy heuristic to solve large instances in much shorter time than the ILP model with low levels of relative error (2.49% average error in the instances studied) and modify the ILP model to evaluate the impact of wavelength conversion. Results show that considering availability requirements can lead up to 56.4% higher backup resource requirements than not considering them at all, highlighting the importance of availability requirements in budget estimation. (C) 2016 Wiley Periodicals, Inc.

Pineda, C., Cortes, C. E., JaraMoroni, P., & Moreno, E. (2016). Integrated traffictransit stochastic equilibrium model with parkandride facilitiesd. Transp. Res. Pt. CEmerg. Technol., 71, 86–107.
Abstract: We propose an Integrated Stochastic Equilibrium model that considers both private automobile traffic and transit networks to incorporate the interactions between these two modes in terms of travel time and generalized costs. In addition, in the general version of the model, travelers are allowed to switch from personal vehicles to mass transit at specific locations in a parkandride scheme. The assignment for traffic equilibrium is based on the Markovian Traffic Equilibrium model of Baillon and Cominetti (2008), whereas the equilibrium of the transit network is represented by the Stochastic Transit Equilibrium model of Cortes et al. (2013). Stochastic travel decisions are made at the node level, thereby avoiding the enumeration of routes or strategies and incorporating various perception and uncertainty issues. We propose a MethodofSuccessiveAverages algorithm to calculate an Integrated Stochastic Equilibrium and conduct numerical experiments to highlight the effect of stochasticity on equilibrium flows and travel times. Our experiments show that higher stochasticity implies greater dispersion of equilibrium flows and longer expected travel times. Results on a real network with mode combination and park and ride facilities provide insights regarding the use of park and ride in terms of number and location, potential modal share of the combined mode option under different circumstances, and travel time impact due to the implementation of such park and ride facilities in a real setting. (C) 2016 Elsevier Ltd. All rights reserved.

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.

Vera, J., & Goles, E. (2016). Automata Networks for Memory Loss Effects in the Formation of Linguistic Conventions. Cogn. Comput., 8(3), 462–466.
Abstract: This work attempts to give new theoretical insights into the absence of intermediate stages in the evolution of language. In particular, a mathematical model, based on automata networks, is proposed with the purpose to answer a crucial question: How a population of language users can reach agreement on linguistic conventions? To describe the appearance of drastic transitions in the development of language, an extremely simple model of working memory is adopted: at each time step, language users simply lose part of their word memories according to a forgetfulness parameter. Through computer simulations on lowdimensional lattices, sharp transitions at critical values of the parameter are described.

Leiva, A., Pavez, N., Beghelli, A., & Olivares, R. (2015). A Joint RSA Algorithm for Dynamic Flexible Optical Networking. IEEE Latin Am. Trans., 13(11), 3531–3537.
Abstract: We propose a novel algorithm to solve the Routing and Spectrum Allocation (RSA) problem in dynamic flexible grid optical networks. Unlike most previous proposals, the algorithm solves the R and SA problems jointly by exhaustively searching the solution space and taking the network state into account. As a result, the shortest possible path with enough spectrum availability is allocated to establish the connections. Simulation results show that, in terms of blocking ratio, our proposal significantly outperforms previously proposed algorithms. In some cases, the performance is better by more than one order of magnitude.

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.
