Multivariate McCormick relaxations

McCormick (Math Prog 10(1):147–175, 1976) provides the framework for convex/concave relaxations of factorable functions, via rules for the product of functions and compositions of the form F ∘ f, where F is a univariate function. Herein, the composition theorem is generalized to allow multivariate outer functions F, and theory for the propagation of subgradients is presented. The generalization interprets the McCormick relaxation approach as a decomposition method for the auxiliary variable method. In addition to extending the framework, the new result provides a tool for the proof of relaxations of specific functions. Moreover, a direct consequence is an improved relaxation for the product of two functions, at least as tight as McCormick’s result, and often tighter. The result also allows the direct relaxation of multilinear products of functions. Furthermore, the composition result is applied to obtain improved convex underestimators for the minimum/maximum and the division of two functions for which current relaxations are often weak. These cases can be extended to allow composition of a variety of functions for which relaxations have been proposed

Design of dynamic experiments for black-box model discrimination

Diverse domains of science and engineering require and use mechanistic mathematical models, e.g. systems of differential algebraic equations. Such models often contain uncertain parameters to be estimated from data. Consider a dynamic model discrimination setting where we wish to chose: (i) what is the best mechanistic, time-varying model and (ii) what are the best model parameter estimates. These tasks are often termed model discrimination/selection/validation/verification. Typically, several rival mechanistic models can explain data, so we incorporate available data and also run new experiments to gather more data. Design of dynamic experiments for model discrimination helps optimally collect data. For rival mechanistic models where we have access to gradient information, we extend existing methods to incorporate a wider range of problem uncertainty and show that our proposed approach is equivalent to historical approaches when limiting the types of considered uncertainty. We also consider rival mechanistic models as dynamic black boxes that we can evaluate, e.g. by running legacy code, but where gradient or other advanced information is unavailable. We replace these black-box models with Gaussian process surrogate models and thereby extend the model discrimination setting to additionally incorporate rival black-box model. We also explore the consequences of using Gaussian process surrogates to approximate gradient-based methods

Gibbs-Duhem-Informed Neural Networks for Binary Activity Coefficient Prediction

We propose Gibbs-Duhem-informed neural networks for the prediction of binary activity coefficients at varying compositions. That is, we include the Gibbs-Duhem equation explicitly in the loss function for training neural networks, which is straightforward in standard machine learning (ML) frameworks enabling automatic differentiation. In contrast to recent hybrid ML approaches, our approach does not rely on embedding a specific thermodynamic model inside the neural network and corresponding prediction limitations. Rather, Gibbs-Duhem consistency serves as regularization, with the flexibility of ML models being preserved. Our results show increased thermodynamic consistency and generalization capabilities for activity coefficient predictions by Gibbs-Duhem-informed graph neural networks and matrix completion methods. We also find that the model architecture, particularly the activation function, can have a strong influence on the prediction quality. The approach can be easily extended to account for other thermodynamic consistency conditions

Social cohesion in Europe after the crisis

In the last few years, Europe has been forced to re-think its socio-economic model. Social indicators speak for themselves. Real household income declined significantly between 2008 and 2012, employment rates are lower and the number of people in poverty saw a steady rise with a growing divergence between EU countries. In the eurozone, cuts in public spending and internal devaluation have been the main tools to aim at a correction of unsustainable fiscal positions and a strengthening of competitiveness. It has carried a heavy social price tag. Outside of the eurozone, austerity has also been the prevailing policy, seen as inevitable to avoid economic instability. The crisis has not hit everyone equally. The general losses have been high, but there have also been some quite important redistributive effects. With all the difficulties of defining and measuring 'fairness', it is clear that the adjustment has not been equitable. Apart from issues of market failure, there have been direct increases of inequality within each of the member states. Higher poverty rates have been observed, rises in inequalities between higher and lower income earners as well as intergenerational inequalities between age groups. Long-term consequences are only beginning to surface in the public debate as the most immediate pressures of the crisis are slowly overcome. In this report, the authors first of all look at the results of the survey we have carried out in seven European countries and review perceptions of the socio-economic model. Subsequently, they assess the importance of the social dimension in the broader context of the European growth model. The authors discuss the impact of the structural challenges of globalisation, demography and technological change. They then review the EU’s performance in the crisis. Finally, the authors make a number of recommendations on how to bridge the gap between Europeans‘ expectations and reality

Ensayo aleatorizado del cierre de orejuela izquierda vs varfarina para la prevención de accidentes cerebrovasculares tromboembólicos en pacientes con fibrilación auricular no relacionada con valvulopatía. Estudio PREVAIL

The successful application of poly­(<i>N</i>-vinylcaprolactam)-based microgels requires a profound understanding of their synthesis. For this purpose, a validated process model for the microgels synthesis by precipitation copolymerization with the cross-linker <i>N</i>,<i>N</i>′-methylenebis­(acrylamide) is formulated. Unknown reaction rate constants, reaction enthalpies, and partition coefficients are obtained by quantum mechanical calculations. The remaining parameter values are estimated from reaction calorimetry and Raman spectroscopy measurements of experiments with different monomer/cross-linker compositions. Because of high cross-propagation reaction rate constants, simulations predict a fast incorporation of the cross-linker. This agrees with reaction calorimetry measurements. Furthermore, the gel phase is predicted as the major reaction locus. The model is utilized for a prediction of the internal particle structure regarding its cross-link distribution. The highly cross-linked core reported in the literature corresponds to the predictions of the model

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

A Boolean Approach to Linear Prediction for Signaling Network Modeling

The task of the DREAM4 (Dialogue for Reverse Engineering Assessments and Methods) “Predictive signaling network modeling” challenge was to develop a method that, from single-stimulus/inhibitor data, reconstructs a cause-effect network to be used to predict the protein activity level in multi-stimulus/inhibitor experimental conditions. The method presented in this paper, one of the best performing in this challenge, consists of 3 steps: 1. Boolean tables are inferred from single-stimulus/inhibitor data to classify whether a particular combination of stimulus and inhibitor is affecting the protein. 2. A cause-effect network is reconstructed starting from these tables. 3. Training data are linearly combined according to rules inferred from the reconstructed network. This method, although simple, permits one to achieve a good performance providing reasonable predictions based on a reconstructed network compatible with knowledge from the literature. It can be potentially used to predict how signaling pathways are affected by different ligands and how this response is altered by diseases

Education in Process Systems Engineering: Why it matters more than ever and how it can be structured

This position paper is an outcome of discussions that took place at the third FIPSE Symposium in Rhodes, Greece, between June 20–22, 2016 (http://fi-in-pse.org). The FIPSE objective is to discuss open research challenges in topics of Process Systems Engineering (PSE). Here, we discuss the societal and industrial context in which systems thinking and Process Systems Engineering provide indispensable skills and tools for generating innovative solutions to complex problems. We further highlight the present and future challenges that require systems approaches and tools to address not only ‘grand’ challenges but any complex socio-technical challenge. The current state of Process Systems Engineering (PSE) education in the area of chemical and biochemical engineering is considered. We discuss approaches and content at both the unit learning level and at the curriculum level that will enhance the graduates’ capabilities to meet the future challenges they will be facing. PSE principles are important in their own right, but importantly they provide significant opportunities to aid the integration of learning in the basic and engineering sciences across the whole curriculum. This fact is crucial in curriculum design and implementation, such that our graduates benefit to the maximum extent from their learning