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In this review, the fundamental basis of machine learning (ML) and data mining (DM) are summarized together with the techniques for distilling knowledge from state-of-the-art omics experiments. This includes an introduction to the basic mathematical principles of unsupervised/supervised learning methods, dimensionality reduction techniques, deep neural networks architectures and the applications of these in bioinformatics. Several case studies under evaluation mainly involve next generation sequencing (NGS) experiments, like deciphering gene expression from total and single cell (scRNA-seq) analysis; for the latter, a description of all recent artificial intelligence (AI) methods for the investigation of cell sub-types, biomarkers and imputation techniques are described. Other areas of interest where various ML schemes have been investigated are for providing information regarding transcription factors (TF) binding sites, chromatin organization patterns and RNA binding proteins (RBPs), while analyses on RNA sequence and structure as well as 3D dimensional protein structure predictions with the use of ML are described. Furthermore, we summarize the recent methods of using ML in clinical oncology, when taking into consideration the current omics data with pharmacogenomics to determine personalized treatments. With this review we wish to provide the scientific community with a thorough investigation of main novel ML applications which take into consideration the latest achievements in genomics, thus, unraveling the fundamental mechanisms of biology towards the understanding and cure of diseases.

This paper contributes to the literature on decision making under multiple probability models by studying a class of variational preferences. These preferences are defined in terms of Fréchet mean utility functionals, which are based on the Wasserstein metric in the space of probability models. In order to produce a measure that is the “closest” to all probability models in the given set, we find the barycenter of the set. We derive explicit expressions for the Fréchet–Wasserstein mean utility functionals and show that they can be expressed in terms of an expansion that provides a tractable link between risk aversion and ambiguity aversion. The proposed utility functionals are illustrated in terms of two applications. The first application allows us to define the social discount rate under model uncertainty. In the second application, the functionals are used in risk securitization. The barycenter in this case can be interpreted as the model that maximizes the probability that different decision makers will agree on, which could be useful for designing and pricing a catastrophe bond. This paper was accepted by Manel Baucells, decision analysis.

Economic growth has traditionally been analyzed in the temporal domain, while the spatial dimension is captured by cross-country income differences. Data suggest great inequality in income per capita across countries, and a slight but noticeable increase in inequality across nations between 1960 and 2000. Seeking to explore the mechanism underlying the temporal evolution of the cross sectional distribution of economies, we develop a spatial growth model where saving rates are exogenous. Capital movements across locations are governed by a mechanism under which capital moves toward locations of relatively higher marginal productivity, with a velocity determined by the existing stock of capital. This augments the capital accumulation equation by a nonlinear diffusion term. Our results suggest that under diminishing returns, the growth process leads to a stable spatially nonhomogeneous distribution for per capita capital and income in the long run. Insufficient savings may lead to the emergence of persistent poverty cores where capital stock is depleted in some locations.

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We study rational expectations equilibrium problems and social optimum problems in infinite horizon spatial economies in the context of a Ramsey type capital accumulation problem with geographical spillovers. We identify sufficient local and global conditions for the emergence (or not) of optimal agglomeration, using techniques from monotone operator theory and spectral theory in infinite dimensional Hilbert spaces. We show that agglomerations may emerge, with any type of returns to scale (increasing or decreasing) and with the marginal productivity of private capital increasing or decreasing with respect to the spatial externality. This is a fairly general result indicating the importance of the network structure of the spatial externality relative to the properties of the aggregate production function. Our analytical methods can be used to systematically study optimal potential agglomeration and clustering in dynamic economics. © 2014 Elsevier B.V.

We show that for a specific class of random matching Edgeworthian economies, the expectation of the limiting equilibrium price coincides with the equilibrium price of the related Walrasian economies. This result extends to the study of economies in the presence of uncertainty within the multi-period Arrow-Debreu model, allowing to understand the dynamics of how beliefs survive and propagate through the market.

We study the asymptotic behavior of complex discrete evolution equations of Ginzburg- Landau type. Depending on the nonlinearity and the data of the problem, we find different dynamical behavior ranging from global existence of solutions and global attractors to blow-up in finite time. We provide estimates for the blow-up time, depending not only on the initial data but also on the size of the lattice. Some of the theoretical results are tested by numerical simulations.

The equations for the evolution of electromagnetic fields in chiral media, in the time domain, are nonlocal in time. In this work we study the validity of a singular limit (local in time) approximation for these nonlocal in time equations, by estimating the size of the difference of the fields as predicted by both models. In particular, we establish an a priori estimate for this difference, depending on the time horizon, properties of the domain, spatial properties of the initial data and the source terms and the chirality measure β of the approximating model.