Optimal networks for exact controllability

The exact controllability can be mapped to the problem of maximum algebraic multiplicity of all eigenvalues. In this paper, we focus on the exact controllability of deterministic complex networks. First, we explore the eigenvalues of two famous networks, i.e. the comb-of-comb network and the Farey graph. Due to their special structure, we find that the eigenvalues of each network are mutually distinct, showing that these two networks are optimal networks with respect to exact controllability. Second, we study how to optimize the exact controllability of a deterministic network. Based on the spectral graph theory, we find that reducing the order of duplicate sets or co-duplicate sets which are two special vertex subsets can decrease greatly the exact controllability. This result provides an answer to an open problem of Li et al. [X. F. Li, Z. M. Lu and H. Li, Int. J. Mod. Phys. C 26, 1550028 (2015)]. Finally, we discuss the relation between the topological structure and the multiplicity of two special eigenvalues and the computational complexity of our method.

DEXOM: Diversity-based enumeration of optimal context-specific metabolic networks

The correct identification of metabolic activity in tissues or cells under different environmental or genetic conditions can be extremely elusive due to mechanisms such as post-transcriptional modification of enzymes or different rates in protein degradation, making difficult to perform predictions on the basis of gene expression alone. Context-specific metabolic network reconstruction can overcome these limitations by leveraging the integration of multi-omics data into genome-scale metabolic networks (GSMN). Using the experimental information, context-specific models are reconstructed by extracting from the GSMN the sub-network most consistent with the data, subject to biochemical constraints. One advantage is that these context-specific models have more predictive power since they are tailored to the specific organism and condition, containing only the reactions predicted to be active in such context. A major limitation of this approach is that the available information does not generally allow for an unambiguous characterization of the corresponding optimal metabolic sub-network, i.e., there are usually many different sub-network that optimally fit the experimental data. This set of optimal networks represent alternative explanations of the possible metabolic state. Ignoring the set of possible solutions reduces the ability to obtain relevant information about the metabolism and may bias the interpretation of the true metabolic state. In this work, we formalize the problem of enumeration of optimal metabolic networks, we implement a set of techniques that can be used to enumerate optimal networks, and we introduce DEXOM, a novel strategy for diversity-based extraction of optimal metabolic networks. Instead of enumerating the whole space of optimal metabolic networks, which can be computationally intractable, DEXOM samples solutions from the set of optimal metabolic sub-networks maximizing diversity in order to obtain a good representation of the possible metabolic state. We evaluate the solution diversity of the different techniques using simulated and real datasets, and we show how this method can be used to improve in-silico gene essentiality predictions in Saccharomyces Cerevisiae using diversity-based metabolic network ensembles. Both the code and the data used for this research are publicly available on GitHub1.

Introducing the Ensemble-Based Dual Entropy and Multiobjective Optimization for Hydrometric Network Design Problems: EnDEMO

Entropy applications in hydrometric network design problems have been extensively studied in the most recent decade. Although many studies have successfully found the optimal networks, there have been assumptions which could not be logically integrated into their methodology. One of the major assumptions is the uncertainty that can arise from data processing, such as time series simulation for the potential stations, and the necessary data quantization in entropy calculations. This paper introduces a methodology called ensemble-based dual entropy and multiobjective optimization (EnDEMO), which considers uncertainty from the ensemble generation of the input data. The suggested methodology was applied to design hydrometric networks in the Nelson-Churchill River Basin in central Canada. First, the current network was evaluated by transinformation analysis. Then, the optimal networks were explored using the traditional deterministic network design method and the newly proposed ensemble-based method. Result comparison showed that the most frequently selected stations by EnDEMO were fewer and appeared more reliable for practical use. The maps of station selection frequency from both DEMO and EnDEMO allowed us to identify preferential locations for additional stations; however, EnDEMO provided a more robust outcome than the traditional approach.

An optimization for reducing the size of an existing urban-like monitoring network for retrieving an unknown point source emission

This study presents an optimization methodology for reducing the size of an existing monitoring network of the sensors measuring polluting substances in an urban-like environment in order to estimate an unknown emission source. The methodology is presented by coupling the simulated annealing (SA) algorithm with the renormalization inversion technique and the computational fluid dynamics (CFD) modeling approach. This study presents an application of the renormalization data-assimilation theory for optimally reducing the size of an existing monitoring network in an urban-like environment. The performance of the obtained reduced optimal sensor networks is analyzed by reconstructing the unknown continuous point emission using the concentration measurements from the sensors in that optimized network. This approach is successfully applied and validated with 20 trials of the Mock Urban Setting Test (MUST) tracer field experiment in an urban-like environment. The main results consist of reducing the size of a fixed network of 40 sensors deployed in the MUST experiment. The optimal networks in the MUST urban region are determined, which makes it possible to reduce the size of the original network (40 sensors) to ∼1/3 (13 sensors) and 1∕4 (10 sensors). Using measurements from the reduced optimal networks of 10 and 13 sensors, the averaged location errors are obtained as 19.20 and 17.42 m, respectively, which are comparable to the 14.62 m obtained from the original 40-sensor network. In 80 % of the trials with networks of 10 and 13 sensors, the emission rates are estimated within a factor of 2 of the actual release rates. These are also comparable to the performance of the original network, whereby in 75 % of the trials the releases were estimated within a factor of 2 of the actual emission rates.

Equilibrium Provider Networks: Bargaining and Exclusion in Health Care Markets

We evaluate the consequences of narrow hospital networks in commercial health care markets. We develop a bargaining solution, “Nash-in-Nash with Threat of Replacement,” that captures insurers’ incentives to exclude, and combine it with California data and estimates from Ho and Lee (2017) to simulate equilibrium outcomes under social, consumer, and insurer-optimal networks. Private incentives to exclude generally exceed social incentives, as the insurer benefits from substantially lower negotiated hospital rates. Regulation prohibiting exclusion increases prices and premiums and lowers consumer welfare without significantly affecting social surplus. However, regulation may prevent harm to consumers living close to excluded hospitals. (JEL C78, D85, G22, H75, I11, I13, I18)