Abstract: In this work, we provide a procedure that allows us to transform certain kinds of deterministic Boolean networks on minterm or maxterm functions into symmetric ones, so inferring that such symmetrizable networks can present only periodic points of periods 1 or 2. In particular, we deal with generalized parallel (or synchronous) dynamical systems (GPDS) over undirected graphs, i. e., discrete parallel dynamical systems over undirected graphs where some of the self-loops may not appear. We also study the class of anti-symmetric GPDS (which are non-symmetrizable), proving that their periodic orbits have period 4. In addition, we introduce a class of non-symmetrizable systems which admit periodic orbits with arbitrary large periods.

Abstract: The present work proposes a novel Network Optimization problem whose core is to combine both network design and network construction scheduling under uncertainty into a single two-stage robust optimization model. The first-stage decisions correspond to those of a classical network design problem, while the second-stage decisions correspond to those of a network construction scheduling problem (NCS) under uncertainty. The resulting problem, which we will refer to as the Two-Stage Robust Network Design and Construction Problem (2SRNDC), aims at providing a modeling framework in which the design decision not only depends on the design costs (e.g., distances) but also on the corresponding construction plan (e.g., time to provide service to costumers). We provide motivations, mixed integer programming formulations, and an exact algorithm for the 2SRNDC. Experimental results on a large set of instances show the effectiveness of the model in providing robust solutions, and the capability of the proposed algorithm to provide good solutions in reasonable running times. (C) 2017 Elsevier Ltd. All rights reserved.

Abstract: Deterministic Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states are to be updated. We study the robustness of the dynamical behavior of a Boolean network with respect to different update schedules (synchronous, block-sequential, sequential), which can provide modelers with a better understanding of the consequences of changes in this aspect of the model. For a given Boolean network, we define equivalence classes of update schedules with the same dynamical behavior, introducing a labeled graph which helps to understand the dependence of the dynamics with respect to the update, and to identify interactions whose timing may be crucial for the presence of a particular attractor of the system. Several other results on the robustness of update schedules and of dynamical cycles with respect to update schedules are presented. Finally, we prove that our equivalence classes generalize those found in sequential dynamical systems. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

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 mixed-integer linear programming formulation, develop a number of lower bounds that are integrated in a branch-and-bound algorithm, and discuss results of computational experiments both for instances based on randomly generated networks and for instances based on 2010 Chilean earthquake data.

Abstract: Given its wide spectrum of applications, the classical problem of all-terminal network reliability evaluation remains a highly relevant problem in network design. The associated optimization problem-to find a network with the best possible reliability under multiple constraints-presents an even more complex challenge, which has been addressed in the scientific literature but usually under strong assumptions over failures probabilities and/or the network topology. In this work, we propose a novel reliability optimization framework for network design with failures probabilities that are independent but not necessarily identical. We leverage the linear-time evaluation procedure for network reliability in the series-parallel graphs of Satyanarayana and Wood (1985) to formulate the reliability optimization problem as a mixed-integer nonlinear optimization problem. To solve this nonconvex problem, we use classical convex envelopes of bilinear functions, introduce custom cutting planes, and propose a new family of convex envelopes for expressions that appear in the evaluation of network reliability. Furthermore, we exploit the refinements produced by spatial branch-and-bound to locally strengthen our convex relaxations. Our experiments show that, using our framework, one can efficiently obtain optimal solutions in challenging instances of this problem.

Abstract: Network virtualization is a key enabling technology for “Infrastructure as a Service” provisioning, increasing the flexibility and cost savings offered to customers. By extending the concept of server virtualization to the network infrastructure, the allocation of different, independent virtual networks over a single physical network is carried out on demand. A fundamental challenge in network virtualization systems is to choose which physical nodes and links to use for hosting virtual networks in the physical infrastructure, known as the “virtual network allocation” problem. All virtual network allocation proposals on elastic optical networks assume a centralized operation, deploying a single node with access to the network state global information and assigning resources accordingly. However, such configuration might exhibit the inherent problems of centralized systems: survivability and scalability. In this paper, we present a distributed protocol for resource discovery, mapping, and allocation of network virtualization systems. The distributed protocol is generic enough as to be used with different substrate networks. However, in this paper, it has been adapted to work over an elastic optical network infrastructure, where further considerations regarding the spectrum continuity and contiguity constraints must also be taken into account. The distributed protocol is based on the concept of alliances: upon the arrival of a virtual network request, agents located in the physical network nodes compete to form the first alliance able to host the virtual network. Because the first alliances to be formed are also the ones composed by nearby nodes, a good network resource usage is achieved. The feasibility of the distributed protocol was studied by evaluating its ability to successfully establish virtual networks within acceptable time and with low bandwidth consumption from the coordination messages.

Abstract: Multi-band elastic optical networks are a promising alternative to meet the bandwidth demand of the ever-growing Internet traffic. In this letter, we propose a family of band allocation algorithms for multi-band elastic optical networks. Employing simulation, we evaluate the blocking performance of 3 algorithms of such a family and compare their performance with the only heuristic proposed to date. Results show that the three new algorithms outperform the previous proposal, with up to one order of magnitude improvement. We expect these results to help advance the area of dynamic resource allocation in multi-band elastic optical networks.

Abstract: Many decisions involve selecting among many more options than an individual can effectively examine and consider. Therefore, people usually consider smaller and different “choice sets” as viable options. To better understand the processes affecting choice-set formation, we developed a computational model of how households become aware of potential choices in a context for which understanding household decision-making has important public policy implications: market-based reforms in education. In the model, households learn about the schools to which they can send their children through three mechanisms: find out about geographically proximate schools, access to publicly available information, and information gathered from interactions with other households. We calibrated the model using data from four cities in Chile, where students are not required to attend their neighborhood school. We then used the model to conduct hypothetical computational experiments that assessed how each mechanism impacted the sets of schools known to households before they make their choice (their “awareness set”). We found that the inclusion of a social interaction mechanism was crucial for producing simulated awareness sets that matched the awareness sets provided in a survey conducted by the Chilean Ministry of Education. We also found that the social interaction mechanism played the largest role in determining the quality and price range of the choices available in households’ awareness sets. Our findings highlight the importance of social interactions in a stage of decision-making before the direct impact of other individuals is typically made explicit. Moreover, it validates an approach that can be used in future models where understanding how decision-makers become aware of their options may be as important as the way they choose among them.

Abstract: The prognostics and health management disciplines provide an efficient solution to improve a system's durability, taking advantage of its lifespan in functionality before a failure appears. Prognostics are performed to estimate the system or subsystem's remaining useful life (RUL). This estimation can be used as a supply in decision-making within maintenance plans and procedures. This work focuses on prognostics by developing a recurrent neural network and a forecasting method called Prophet to measure the performance quality in RUL estimation. We apply this approach to degradation signals, which do not need to be monotonical. Finally, we test our system using data from new generation telescopes in real-world applications.

Abstract: The flowtime network restoration problem was introduced by Averbakh and Pereira (2012) who presented a Minimum Spanning Tree heuristic, two local search procedures, and an exact branch-and-bound algorithm. This note corrects the computational results in Averbakh and Pereira (2012).