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One of the critical steps to characterize metabolic alterations in multifactorial diseases, as well as their heterogeneity across different patients, is the identification of reactions that exhibit significantly different usage (or flux) between cohorts. However, since metabolic fluxes cannot be determined directly, researchers typically use constraint-based metabolic network models, customized on post-genomics datasets. The use of random sampling within the feasible region of metabolic networks is becoming more prevalent for comparing these networks. While many algorithms have been proposed and compared for efficiently and uniformly sampling the feasible region of metabolic networks, their impact on the risk of making false discoveries when comparing different samples has not been investigated yet, and no sampling strategy has been so far specifically designed to mitigate the problem. To be able to precisely assess the False Discovery Rate (FDR), in this work we compared different samples obtained from the very same metabolic model. We compared the FDR obtained for different model scales, sample sizes, parameters of the sampling algorithm, and strategies to filter out non-significant variations. To be able to compare the largely used hit-and-run strategy with the much less investigated corner-based strategy, we first assessed the intrinsic capability of current corner-based algorithms and of a newly proposed one to visit all vertices of a constraint-based region. We show that false discoveries can occur at high rates even for large samples of small-scale networks. However, we demonstrate that a statistical test based on the empirical null distribution of Kullback–Leibler divergence can effectively correct for false discoveries. We also show that our proposed corner-based algorithm is more efficient than state-of-the-art alternatives and much less prone to false discoveries than hit-and-run strategies. We report that the differences in the marginal distributions obt

Constraint-based modelling (CBM) is a computational method used in systems biology to predict metabolic fluxes. However, modelling metabolic fluxes with CBM remains challenging due to the complexity of metabolism and the need for omics data integration. This study introduces scFBApy, a Python-based tool for simulating CBM and the metabolic cooperation between cells. It allows the flux simulation of a population of networks for a target objective, such as biomass production, with or without cooperation. The tool integrates single-cell transcriptomics data using Reaction Activity Scores and uses a denoising algorithm for pre-processing scRNA-seq data. Five real-world scRNA-seq datasets were used to demonstrate the applicability of the pipeline. Results showed that cooperation between cells increased biomass production compared to independent cell simulations. The scFBApy package provides an open-source alternative to MATLAB-based CBM tools.

Characterizing the heterogeneity of cancer metabolism requires the knowledge of metabolic fluxes in different tumor types. These fluxes cannot be directly determined, especially at a sub-cellular level. Still, they can be obtained numerically through constraint-based steady-state models after integrating other high-throughput -omics data, such as transcriptomics. In this work, we proposed to study cancer metabolism through data analysis and machine learning methodologies. To this aim, we considered transcriptomics profiles for a large set of cancer cells. Using a core metabolic network as a scaffold, we generated many feasible flux distributions for each cancer cell. Then, we used cluster analysis to analyze these data. This preliminary analysis revealed three well-separated clusters having different metabolic behaviors.

Flux Variability Analysis (FVA) is an important method to analyze the range of fluxes of a metabolic network. FVA consists in performing a large number of independent optimization problems, to obtain the maximum and minimum flux through each reaction in the network. Although several strategies to make the computation more efficient have been proposed, the computation time of an FVA can still be limiting. We present a two-step procedure to accelerate the FVA computational time that exploits the large presence within metabolic networks of sets of reactions that necessarily have an identical optimal flux value or only differ by a multiplication constant. The first step identifies such sets of reactions. The second step computes the maximum and minimum flux value for just one element of each of set, reducing the total number of optimization problems compared to the classical FVA. We show that, when applied to any metabolic network model included in the BiGG database, our FVA algorithm reduces the total number of optimization problems of about 35 %, and the computation time of FVA of about 30%.

This chapter looks at the issue of black-box constrained optimization where both the objective function and the constraints are unknown and can only be observed pointwise. Both deterministic and probabilistic surrogate models are considered: the latter, more specifically analysed, are based on Gaussian Processes and Bayesian Optimization to handle the exploration–exploitation dilemma and improve sample efficiency. Particularly challenging is the case when the feasible region might be disconnected and the objective function cannot be evaluated outside the feasible region; this situation, known as “partially defined objective function” or “non-computable domains”, requires a novel approach: a first phase is based on the SVM classification in order to learn the feasible region, and a second phase, optimization, is based on a Gaussian Process. This approach is the main focus of this chapter that analyses modelling and computational issues and demonstrates the sample efficiency of the resulting algorithms.

Many web services have a Recommender System to help the users in their choices such as movies to watch or products to buy. The aim is to make accurate predictions on the user preferences depending on his/her past choices. Matrix-factorization is one of the most widely adopted method to build a Recommender System. Like many Machine Learning algorithms, matrix-factorization has a set of hyper-parameters to tune, leading to a complex expensive black-box optimization problem. The objective function maps any possible hyper-parameter configuration to a numeric score quantifying the quality of predictions. In this work, we show how Bayesian Optimization can efficiently optimize three hyper-parameters of a Recommender System: number of latent factors, regularization term and learning rate. A widely adopted acquisition function, namely Expected Improvement, is compared with a variant of Thompson Sampling. Numerical for both a benchmark 2-dimensional test function and a Recommender System evaluated on a benchmark dataset proved that Bayesian Optimization is an efficient tool for improving the predictions of a Recommendation System, but a clear choice between the two acquisition function is not evident.

The objective of this paper is to show how smart water networks enable new strategies for the energy cost management of the network, more precisely Pump Scheduling Optimization. This problem is traditionally solved using mathematical programming and, more recently, nature inspired metaheuristics. The schedules obtained by these methods are typically not robust both respect to random variations in the water demand and the non-linear features of the model. The authors consider three alternative optimization strategies: (i) global optimization of black-box functions, based on a Gaussian model and the use of the hydraulic simulator (EPANET) to evaluate the objective function; (ii) Multi Stage Stochastic Programming, which models the stochastic evolution of the water demand through a scenario analysis to solve an equivalent large scale linear program; and finally (iii), Approximate Dynamic Programming, also known as Reinforcement Learning. With reference to real life experimentation, the last two strategies offer more modeling flexibility, are demand responsive and typically result in more robust solutions (i.e. pump schedules) than mathematical programming. More specifically, Approximate Dynamic Programming works on minimal modelling assumption and can effectively leverage on line data availability into robust on-line Pump Scheduling Optimization.

This paper presents a network analysis approach to assess efficiency and resilience of public transport systems under cascading failures. Results of the two case studies of the RESOLUTE project (i.e., Florence, Italy and the Attika region, Greece) are presented. Failures can be of different types (accidents, infrastructure collapses, attacks, etc.) and can lead to impacts with different severities. The key element of cascading failures is time: as time passes by, more locations or connections of the network can be affected consecutively, as well as change their own condition. The proposed network analysis approach simulates failure propagation and evaluates the associated impacts on the transport system. Analogously to the analysis of road networks proposed in the literature, the network average efficiency and the relative size of the largest connected component have been considered for the analysis of the two RESOLUTE case studies. The cascade is simulated as follows. The node betweenness – the number of shortest paths through that node (i.e. stop/station) – is the “capacity” of that node. The worst-case of the cascading failure is considered. The node with the highest betweenness is the one triggering the cascade: it is removed and the new betweenness for every remaining node is computed, since it changes with the new shortest paths arrangement. All the nodes with betweenness higher than capacity are removed and the process continues until no more nodes can be deleted, that is the end of the cascade. Finally, efficiency and relative size of the largest connected component are computed along the cascade, to compare network at the begin and the end of the cascade. Analysis is repeated by considering the chance to increase node capacity by a given percentage, allowing to assess which is the implied improvement on resilience and on efficiency supporting a more sustainable allocation of financial resources.

This paper presents some results devoted to providing network analysis functionalities for vulnerability assessment in public transportation networks with respect to disruptive events and/or targeted attacks to stations. The results have been obtained on two public transportation networks: the bus network in Florence, Italy, and the transportation network in the Attika region, Greece. The analysis implements a topological approach, based on graph theory, using a multi-graph to model public transportation networks and analyse vulnerabilities with respect to the removal of one or more of their components. Both directed attacks and cascading failures are considered. While the first type of disruptive events is related to a static analysis, where nodes are removed according to a rank related to some centrality measures, the second type is related to a dynamic analysis, where a failure cascade is simulated making unavailable the node with the highest betweenness value. Vulnerability measures are computed as loss of connectivity and efficiency, with respect to both the two different types of disruptive events considered. This study allows to evidence potential vulnerabilities of the urban networks, that must be considered to support the planning process into the creation of resilient structures

This paper presents a network analysis approach to simulate cascading effects in a transit network with the aim to assess its resilience and efficiency. The key element of a cascade is time: as time passes by, more locations or connections of the transit network which are nodes and edges of the associated graph can be affected consecutively as well as change their own condition. Thus, modifications in terms of efficiency and resilience are also dynamically evaluated and analysed along the cascade. Results on the two case studies of the RESOLUTE project (i.e., Florence, in Italy, and the Attika region, in Greece) are presented. Since the two case studies are significantly different, important differences are reflected also on the impacts of the relative cascades, even if they were started in both the two cases from the node with the highest betweenness centrality.