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: 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: 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: Maintenance is one of the critical areas in operations in which a careful balance between preventive costs and the effect of failures is required. Thanks to the increasing data availability, decision-makers can now use models to better estimate, evaluate, and achieve this balance. This work presents a maintenance scheduling model which considers prognostic information provided by a predictive system. In particular, we developed a prescriptive maintenance system based on run-to-failure signal segmentation and a Long Short Term Memory (LSTM) neural network. The LSTM network returns the prediction of the remaining useful life when a fault is present in a component. We incorporate such predictions and their inherent errors in a decision support system based on a stochastic optimization model, incorporating them via chance constraints. These constraints control the number of failed components and consider the physical distance between them to reduce sparsity and minimize the total maintenance cost. We show that this approach can compute solutions for relatively large instances in reasonable computational time through experimental results. Furthermore, the decision-maker can identify the correct operating point depending on the balance between costs and failure probability.

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 in-vehicle 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 common-lines 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 common-lines 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 real-size network case as the next step of this research. (C) 2013 Elsevier Ltd. All rights reserved.

Abstract: We consider physics-informed neural networks (PINNs) (Raissiet al., 2019) for forward physical problems. In order to find optimal PINNs configuration, we introduce a hyper-parameter optimization (HPO) procedure via Gaussian processes-based Bayesian optimization. We apply the HPO to Helmholtz equation for bounded domains and conduct a thorough study, focusing on: (i) performance, (ii) the collocation points density r and (iii) the frequency kappa, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.

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 AND-OR 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.

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 block-sequential 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 block-sequential scheme such that each block is of minimum cardinality two) we exhibit cycles with nonpolynomial periods. (C) 2014 Elsevier Ltd. All rights reserved.