Abstract: In this paper, we investigate potential pathways for achieving deep reductions in CO2 emissions by 2050 in the Chilean electric power system. We simulate the evolution of the power system using a long-term planning model for policy analysis that identifies investments and operation strategies to meet demand and CO2 emissions reductions at the lowest possible cost. The model considers a simplified representation of the main transmission network and representative days to simulate operations considering the variability of demand and renewable resources at different geographical locations. We perform a scenario analysis assuming different ambitious renewable energy and emission reduction targets by 2050. As observed in other studies, we show that the incremental cost of reducing CO2 emissions without carbon capture or offset alternatives increases significantly as the system approaches zero emissions. Indeed, the carbon tax is multiplied by a factor of 4 to eliminate the last Mt of CO2 emissions, i.e., from 2000 to almost 8500 USD/tCO(2) in 2050. This result highlights the importance of implementing technology-neutral mechanisms that help investors identify the most cost-efficient actions to reduce CO2 emissions. Our analysis shows that Carbon Capture and Storage could permit to divide by more than two the total system cost of a 100% renewable scenario. Furthermore, it also illustrates the importance of implementing economy-wide carbon emissions policies that ensure that the incremental costs to reduce CO2 emissions are roughly similar across different sectors of the economy.

Abstract: The Marshall-Olkin (MO) distribution is considered a key model in reliability theory and in risk analysis, where it is used to model the lifetimes of dependent components or entities of a system and dependency is induced by “shocks” that hit one or more components at a time. Of particular interest is the Levy-frailty subfamily of the Marshall-Olkin (LFMO) distribution, since it has few parameters and because the nontrivial dependency structure is driven by an underlying Levy subordinator process. The main contribution of this work is that we derive the precise asymptotic behavior of the upper order statistics of the LFMO distribution. More specifically, we consider a sequence ofnunivariate random variables jointly distributed as a multivariate LFMO distribution and analyze the order statistics of the sequence asngrows. Our main result states that if the underlying Levy subordinator is in the normal domain of attraction of a stable distribution with index of stability alpha then, after certain logarithmic centering and scaling, the upper order statistics converge in distribution to a stable distribution if alpha> 1 or a simple transformation of it if alpha <= 1. Our result can also give easily computable confidence intervals for the last failure times, provided that a proper convergence analysis is carried out first.

Abstract: Natural hazards cause major power outages as a result of spatially-correlated failures of network components. However, these correlations between failures of individual elements are often ignored in probabilistic planning models for optimal network design. We use different types of planning models to demonstrate the impact of ignoring correlations between component failures and the value of flexible transmission assets when power systems are exposed to natural hazards. We consider a network that is hypothetically located in northern Chile, a region that is prone to earthquakes. Using a simulation model, we compute the probabilities of spatially- correlated outages of transmission and substations based on information about historical earthquakes in the area. We determine optimal network designs using a deterministic reliability criterion and probabilistic models that either consider or disregard correlations among component failures. Our results show that the probability of a simultaneous failure of two transmission elements exposed to an earthquake can be up to 15 times higher than the probability simultaneous failure of the same two elements when we only consider independent component failures. Disregarding correlations of component failures changes the optimal network design significantly and increases the expected levels of curtailed demand in scenarios with spatially-correlated failures. We also find that, in some cases, it becomes optimal to invest in HVDC instead of AC transmission lines because the former gives the system operator the flexibility to control power flows in meshed transmission networks. This feature is particularly valuable to systems exposed to natural hazards, where network topologies in post-contingency operating conditions might differ significantly from pre-contingency ones.

Abstract: We address the design problem of a reliable network. Previous work assumes that link failures are independent. We discuss the impact of dropping this assumption. We show that under a common-cause failure model, dependencies between failures can affect the optimal design. We also provide an integer-programming formulation to solve this problem. Furthermore, we discuss how the dependence between the links that participate in the solution and those that do not can be handled. Other dependency models are discussed as well. (C) 2014 Elsevier B.V. All rights reserved.

Abstract: Intelligent transportation, and in particular, fleet management, has been a forefront concern for a plethora of industries. This statement is especially true for the production of commodities, where transportation represents a central element for operational continuity. Additionally, in many industries, and in particular those with hazardous environments, fleet control must satisfy a wide range of security restrictions to ensure that risks are kept at bay and accidents are minimum. Furthermore, in these environments, any decision support tool must cope with noisy and incomplete data and give recommendations every few minutes. In this work, a fast and efficient decision support tool is presented to help fleet managers oversee and control ore trucks, in a mining setting. The main objective of this system is to help managers avoid interactions between ore trucks and personnel buses, one of the most critical security constraints in our case study, keeping a minimum security distance between the two at all times. Furthermore, additional algorithms are developed and implemented, so that this approach can work with real-life noisy GPS data. Through the use of historical data, the performance of this decision support system is studied, validating that it works under the real-life conditions presented by the company. The experimental results show that the proposed approach improved truck and road utilization significantly while allowing the fleet manager to control the security distance required by their procedures.

Abstract: Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable number of functions that appear in practice, and thus obtain tight and tractable approximations to challenging problems. We contribute to this line of work by considering a family of functions that, to the best of our knowledge, has not been considered before in the literature. We call this family ray-concave functions. We show sufficient conditions that allow us to easily compute closed-form expressions for the convex envelope of ray-concave functions over arbitrary polytopes. With these tools, we are able to provide new perspectives to previously known convex envelopes and derive a previously unknown convex envelope for a function that arises in probability contexts.

Abstract: Income tax systems with “pass-through” 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.

Abstract: Background: Interactions between genes and their products give rise to complex circuits known as gene regulatory networks (GRN) that enable cells to process information and respond to external stimuli. Several important processes for life, depend of an accurate and context-specific regulation of gene expression, such as the cell cycle, which can be analyzed through its GRN, where deregulation can lead to cancer in animals or a directed regulation could be applied for biotechnological processes using yeast. An approach to study the robustness of GRN is through the neutral space. In this paper, we explore the neutral space of a Schizosaccharomyces pombe (fission yeast) cell cycle network through an evolution strategy to generate a neutral graph, composed of Boolean regulatory networks that share the same state sequences of the fission yeast cell cycle. Results: Through simulations it was found that in the generated neutral graph, the functional networks that are not in the wildtype connected component have in general a Hamming distance more than 3 with the wildtype, and more than 10 between the other disconnected functional networks. Significant differences were found between the functional networks in the connected component of the wildtype network and the rest of the network, not only at a topological level, but also at the state space level, where significant differences in the distribution of the basin of attraction for the G(1) fixed point was found for deterministic updating schemes. Conclusions: In general, functional networks in the wildtype network connected component, can mutate up to no more than 3 times, then they reach a point of no return where the networks leave the connected component of the wildtype. The proposed method to construct a neutral graph is general and can be used to explore the neutral space of other biologically interesting networks, and also formulate new biological hypotheses studying the functional networks in the wildtype network connected component.