Modeling, Dynamics, Optimization and Bioeconomics III

Large animal facilities generate manure in excess of their production needs leading to excessive nutrient loading. Differences in manure contents of phosphorus and nitrogen relative to crop requirements exacerbate loading of the more abundant nutrient, frequently phosphorus. Current regulations that restrict manure utilization and animal production, but not at crop lands leads to suboptimal resource allocation and under utilization of manure in crop production. The transboundary character of nutrient loading further complicates the management of manure phosphorus and nitrogen. Due to differences in environmental characteristics, upstream and downstream regions may have differing objectives towards controlling nitrogen and phosphorus surpluses. We consider optimal management of manure in a stylized two-agent, two-nutrient and two-region model. We show that trade-offs in managing manure phosphorus and nitrogen, inability to regulate manure applications outside animal farms’ field areas and regional differences in environmental targets can severely impede the effectiveness of regulation. Depending on the environmental and economic characteristics, tightening upstream regulation with respect to the loading of one nutrient might increase the downstream loading of the other and might even decrease the total welfare.

One of the key aspects in the theory of coupled cell networks concerns the existence of synchrony subspaces. That is, subspaces defined in terms of equalities between cell coordinates which are flow-invariant for all coupled cell systems that respect a given coupled cell network structure. We review some recent concepts and results concerning synchrony subspaces on coupled cell networks. The existence of such subspaces naturally restricts the dynamics that can occur at the coupled cell systems, as in general it is the case for any dynamical system admitting flow-invariant spaces. We focus at some of the aspects that make important and special the existence of synchrony subspaces for coupled cell systems. Namely, their existence depend on the network structure and not on the specific form of the differential equations that are chosen to govern the dynamics; the solutions of the restricted coupled cell systems represent dynamics where groups of cells are dynamically behaving exactly in the same way; the restricted coupled cell systems are again coupled cell systems that are consistent with a network structure with a fewer cells. We review some results on how synchrony changes, or it is combined, in evolving networks. More precisely, in networks where their topology changes with time, either to a rewiring of a link, appearance or removal of a link or a node, or by merging smaller networks into larger ones. Finally, we consider the complement network of a network remarking that both networks have the same set of synchrony subspaces.

We propose a two-phase acceleration technique for the solution of Symmetric and Positive Definite linear systems with multiple right-hand sides. In the first phase we compute some partial spectral information related to the ill conditioned part of the given coefficient matrix and, in the second phase, we use this information to improve the convergence of the Conjugate Gradient algorithm. This approach is adequate for large scale problems, like the simulation of time dependent differential equations, where it is necessary to solve consecutively several linear systems with the same coefficient matrix (or with matrices that present very close spectral properties) but with changing right-hand sides. To compute the spectral information, in the first phase, we combine the block Conjugate Gradient algorithm with the Inexact Subspace Iteration to build a purely iterative algorithm, that we call BlockCGSI. We proceed to an inner-outer convergence analysis and we show that it is possible to determine when to stop the inner iteration in order to achieve the targeted invariance in the outer iteration. The spectral information is used in a second phase to remove the effect of the smallest eigenvalues in two different ways: either by building a Spectral Low Rank Update preconditioner, or by performing a deflation of the initial residual in order to remove part of the solution corresponding to the smallest eigenvalues.

Space behaviour is very close to imperfect competition: agglomeration economies lead to increasing returns to scale and physical distance between economic agents and markets causes horizontal product differentiation and prices discrimination in goods markets and in land as a good and as an input. An important target in macroeconomics is the money market analysis, but money market is generally not considered in microeconomic models and hence neither in most spatial models although it affects the location. The main aim of this paper is to introduce the money market in a general equilibrium model to explain the location of consumers and producers around a big monocentric city, where consumers choose optimal quantities of consumption goods, money, land and transport, and households and firms can rationally choose their location in relation to the central market. Results for firms indicate that their locations are generally situated beyond those of households with respect to the central business district, depending on their land needs.

This paper aims to predict energy demand in Spain for the year 2020 and analyzes whether this country will be able to meet the European Union’s greenhouse gas emission reduction commitment. To this purpose, we use climatic data and some variables to measure the economic activity in Spain. The simulated scenario considers that Spain will begin a process of economic recovery which will result in an increase in industrial activity with stable climatic conditions. Several techniques including Simple Linear Regression, Support Vector Machines or Deep Learning have been proposed to estimate and test the model. The EU agreements imply that by 2020 between 20 and 30% of the consumed energy will come from clean and renewable energy sources. The conclusions for this paper show that Spain may be on track to meet its commitments to Europe.

The biodiesel industry is characterized by high fluctuations of the prices and a multiplicity of biological raw material sources. On the other hand, there exist strict quality standards imposed on the final product. Because of these factors, it is important for biodiesel plants to run their processes in the most efficient manner in order to stay competitive. One of the ways to achieve this is the use of model based approaches for design, operation, and control. In this work, that focuses on the latter two areas, a first-principle dynamic model of the main units of a biodiesel plant is developed and applied in two situations: for open-loop simulation as well as for process optimization. The former demonstrates the response observed in the process variables when the plant is subjected to a series of disturbances in the input variables. The later is built in the context of nonlinear model predictive control that determines the optimal profiles of the manipulated variables taking into account process and quality constraints as well as the associated reactant and energy costs.

The paper introduces the Bayesian approach to multivariate regression analysis, from a subjective point of view. A review of non-informative and informative priors adequate to practical situations is carried out. The marginal posteriors of the regression coefficients and the variance factors corresponding to the Laplace, Jeffreys and conjugate priors, as well as the respective modes, are presented. Of note is the fact that Laplace and Jeffreys priors, as it would be expected of non-informative priors, yield maximum posterior estimates of the regression coefficients identical to the maximum likelihood estimate.

This paper examines the effects that professional status and maturity have on the understanding and perception of the true and fair view (TFV) and its True and fair override in Spain. The effects were deduced by a survey conducted on students and auditors. The results show that, while the goal of reaching the TFV is fully integrated into the Spanish accounting system, the implications of such an objective are far from what would be expected. The evidence suggests a practical rejection of the overriding aspect associated with the TFV notion in the EU Directives which is demonstrated by a preference to follow the accounting standards in all cases rather than having to choose when not to apply them in order to achieve this objective. This aversion is logical in a country whose legislation allows little room for flexibility. Finally, the study identifies a pattern of change according to the participant’s professional status and maturity. It is observed that the younger and less professional participants are more concerned with obtaining the TFV than the strict coherence with the accounting standards. However, as the participants evolve according to age and professional status they prefer the TFV to be obtained by a rigorous following of the standards without having to override them, they are also more demanding for a detailed definition of TFV and are much less favourable to the imposition of fines where the TFV is not achieved by following the accounting standards.

This paper examines the disclosure of information provided by FinTech companies (FTC) on the website in order to identify the main topics disclosed. Furthermore, the study analyses if the type of service and the geographical area could have some effect on the level of disclosure. The diversity of issues disclosed on the Internet is categorized in items grouped in self-constructed indices in order to identify the structure of the financial and non-financial information reported and furthermore to quantify the volume of disclosure. The empirical study is based on the analysis of the information reported by companies included in two FinTech top-list. Thus, the sample includes 91 businesses from Europe, Asia and North America. The results of the indices indicate that the total volume of information provided on the website is less than the amount reported in other sectors and other type of businesses. The findings also suggest that there are not any effects due to the type of service or the geographical area, effects traditionally associated in the literature with a major or a minor level of disclosure.

For, \(0<\lambda <1\), consider the transformation \(T(x) = d x \) (mod 1) on the circle \(S^1\), a \(C^1\) function \(A:S^1 \rightarrow \mathbb {R}\), and, the map \(F(x,s) = ( T(x) , \lambda \, s + A(x))\), \((x,s)\in S^1 \times \mathbb {R}\). We denote \(\mathscr {B}= \mathscr {B}_\lambda \) the upper boundary of the attractor (known as fat attractor). We are interested in the regularity of \(\mathscr {B}_\lambda \), and, also in what happens in the limit when \(\lambda \rightarrow 1\). We also address the analysis of the following conjecture which were proposed by R. Bamón, J. Kiwi, J. Rivera-Letelier and R. Urzúa: for any fixed \(\lambda \), \(C^1\) generically on the potential A, the upper boundary \(\mathscr {B}_\lambda \) is formed by a finite number of pieces of smooth unstable manifolds of periodic orbits for F. We show the proof of the conjecture for the class of \(C^2\) potentials A(x) satisfying the twist condition (plus a combinatorial condition). We do not need the generic hypothesis for this result. We present explicit examples. On the other hand, when \(\lambda \) is close to 1 and the potential A is generic a more precise description can be done. In this case the finite number of pieces of \(C^1\) curves on the boundary have some special properties. Having a finite number of pieces on this boundary is an important issue in a problem related to semi-classical limits and micro-support. This was consider in a recent published work by A. Lopes and J. Mohr. Finally, we present the general analysis of the case where A is Lipschitz and its relation with Ergodic Transport.

In this mainly survey paper we consider the Lagrangian \( L(x,v) = \frac{1}{2} \, |v|^2 - V(x) \), and a closed form w on the torus \( \mathbb {T}^n \). For the associated Hamiltonian we consider the the Schrodinger operator \(\mathbf{H}_\beta =\, -\,\frac{1}{2 \beta ^2} \, \varDelta +V\) where \(\beta \) is large real parameter. Moreover, for the given form \(\beta \, w\) we consider the associated twist operator \(\mathbf{H}_\beta ^w\). We denote by \((\mathbf{H}_\beta ^w)^*\) the corresponding backward operator. We are interested in the positive eigenfunction \( \psi _\beta \) associated to the the eigenvalue \( E_\beta \) for the operator \(\mathbf{H}_\beta ^{w} \). We denote \( \psi _\beta ^*\) the positive eigenfunction associated to the eigenvalue \( E_\beta \) for the operator \((\mathbf{H}_\beta ^{w})^* \). Finally, we analyze the asymptotic limit of the probability \(\nu _\beta = \psi _\beta \, \psi _\beta ^*\) on the torus when \(\beta \rightarrow \infty \). The limit probability is a Mather measure. We consider Large deviations properties and we derive a result on Transport Theory. We denote \(L^{-}(x,v) = \frac{1}{2} \, |v|^2 - V(x) - w_x(v) \) and \(L^{+}(x,v) = \frac{1}{2} \, |v|^2 - V(x) + w_x(v) \). We are interest in the transport problem from \(\mu _{-}\) (the Mather measure for \(L^{-}\)) to \(\mu _{+}\) (the Mather measure for \(L^{+}\)) for some natural cost function. In the case the maximizing probability is unique we use a Large Deviation Principle due to N. Anantharaman in order to show that the conjugated sub-solutions u and \(u^*\) define an admissible pair which is optimal for the dual Kantorovich problem.

A fixed bed adsorption mathematical model has been developed to describe the kinetic separation of hexane isomers when they flow through a packed bed containing the microporous Metal-Organic Framework (MOF) ZIF-8 adsorbent. The flow of inert and adsorbable species through the fixed bed is modeled with fundamental differential equations according to the mass and heat conservation laws, a general isotherm to describe adsorption equilibrium and a lumped kinetic mass transfer mechanism between bulk gas phase and the porous solid. It is shown that a proper combination of two characteristic times (the residence time of the gas in the fixed bed, \(\tau _{fb}\) and the characteristic time of diffusion of solutes into the pores \(\tau _{dif}\)) can lead to very different dynamics of fixed bed adsorbers where in a limiting case can gives rise to a spontaneous breakthrough curves of solutes. The numerical simulations of an experimental breakthrough curve with the developed mathematical model clearly explain the complete separation between linear n-Hexane (nHEX) and the respective branched isomers: 3-Methyl-Pentane (3MP) and 2, 2-Dimethyl-Butane (22DMB). The separation is due to significant differences in the diffusivity parameters \(\tau _{dif}\) between 3MP and 22DMB and the residence time of the gas mixture \(\tau _{fb}\) within the fixed bed. This work shows the importance of mathematical modelling for the comprehension and design of adsorption separation processes.

In this paper and following an approach used by two of the authors in (Nassif, N.R., Sheaib, D. (2009) On spectral methods for scalar aged-structured population models.) [5], we present a mathematical model for the tick life cycle based on the McKendrick Partial Differential Equation (PDE). Putting this model using a semi-variational formulation, we derive a Petrov–Galerkin approximation to the solution of the McKendrick PDE, using finite element semi-discretizations that lead to a system of ordinary differential equations in time which computations are carried out using an Euler semi-implicit scheme. The resulting simulations allow us to investigate and understand the dynamics of tick populations. Numerical results are presented illustrating in a realistic way the basic features of the computational model solutions.

In recent years multiple empirical works have been undertaken to analyze the effect of mergers and acquisitions (M&A) on corporate performance, in order to effectively confirm whether M&A are investment projects that are able to create value for the shareholders. Nowadays, the analysis of the M&A value creation is still subjected to a profound debate, especially when studying the implication of time (short-term versus long-term value creation measurement) and the methodology to evaluate the value creation in the long run. In this chapter we propose a comprehensiv e review and in-depth analysis about these open debates, we evaluate the validity of the different methodologies based in calculating the stock abnormal returns provoked by the operation, and we include, as additional contribution, a short study of the implications of this theoretical discussion in a concrete example of sectoral M&A in the digital era, to illustrate the debate.

We study a model of a Cournot duopoly where firms invest in R&D to reduce their production costs. Depending on the parameters, we may find regions with one, two or three Nash equilibria of the investment. Here, we study the effect of the parameters in these regions, in particular, we study the effect of the possible market saturation, the maximum relative cost reduction and the product differentiation, giving special attention to regions with multiple Nash equilibria. We observed that, in general, the competitive region, where both firms invest, is reduced as we increase the possible market saturation and the differentiation of the products and is enlarged when we increase the maximum relative cost reduction.

We consider a logistic growth model with predation and a stochastic perturbation given by a diffusive term with power-type coefficient. The resulting stochastic differential equation (SDE) has the particularity that the standard conditions for the existence and uniqueness of solutions of SDEs do not hold for a large subset of parameter space. Thus, we start by discussing the well posedness of the problem at hand, leading to a detailed characterization for the existence and uniqueness of solutions. We then provide criteria ensuring extinction and persistence of such population. Additionally, we list subsets of parameter space where (absolutely continuous) stationary measures for the SDE under consideration are guaranteed to exist, providing a description for the corresponding densities. We conclude with an application to the optimal management of resources. We consider a real asset such as, for instance, a farm or an aquaculture facility, devoted to the exploration of a unique culture or population whose growth follows a SDE such as described above, and look for the optimal harvesting strategy associated with such culture or population.

In this paper I address the question of whether irreversible pollution accumulation - in a global pollution problem - may be optimal or not. Based on the Tahvonen and Withagen’s article (Tahvonen, Withagen, J Econ Dyn Control, 20:1775–1795, 1996), [16], I set up a model of economic growth where pollution is a byproduct of production, and its natural decay function follows an inverted-U shape, and becomes irreversible for high levels of pollution. Under some parameter’s constellation, the model produces multiplicity of equilibria making local analysis of little relevance. I therefore study the global dynamics of the system using a dynamic programming algorithm, showing that irreversible pollution accumulation cannot be an optimal strategy, unless it is guided by short-term objectives.

There are many approaches to model the biochemical systems deterministically or stochastically. In deterministic approaches, we aim to describe the steady-state behaviours of the system, whereas, under stochastic models, we present the random nature of the system, for instance, during transcription or translation processes. Here, we represent the stochastic modelling approaches of biological networks and explain in details the inference of the model parameters within the Bayesian framework.

We present a constructive proof of the complete nonholonomy of the rolling ellipsoid. The rolling motions are assumed to be over the affine tangent space at a point of the n-ellipsoid and both manifolds are considered embedded in \(\mathbb {R}^{n+1}\), equipped with a metric that results from a convenient deformation of the Euclidean metric. The deformation is defined through a positive definite matrix D whose eigenvalues are the semi-axis of the ellipsoid. The rolling motion has the usual constraints of non-slip and non-twist. Showing that the rolling ellipsoid is a complete nonholonomic system reduces to showing that one can move between two arbitrary admissible configurations by rolling without slipping and without twisting. We exhibit piecewise linear paths on the affine tangent space along which the ellipsoid rolls in order to perform the forbidden motions, twists and slips.

This paper aims to appraise the problem of financial exclusion in Spain after the process of banking system restructuration. The paper proposes a theoretical model for explaining the phenomenon of financial exclusion including both “access difficulties” and “difficulties in the use of financial services” as two dimensions that should be jointly considered. The main contribution of this paper is that it broadens the scope of financial exclusion from a theoretical and empirical point of view, and it also analyses the financial exclusion phenomenon at lower units of analysis that have not been previously explored: urban districts and municipalities. We considered Madrid and Barcelona as our scenarios of analysis. The methodological procedure was carried out in two steps: we first validate our theoretical model by applying canonical correlations, and secondly we carried out Quantile Regressions (QR) to estimate the different impact of financial exclusion’s predictors at different points of the empirical distribution. The empirical results indicate a trend towards low-cost retail banking to serve the segment of less profitable customers and a pattern of branch disappearance more pronounced in those territories vulnerable from a socioeconomic point of view.

Agricultural activity promotes poverty reduction. There is still an important infrastructure investment gap to enhance agricultural productivity. The public-private partnerships arise as a channel to cover it. This article analyzes the relation between public-private investment in infrastructure and agricultural exports in Latin American countries. We use a panel data sample composed by 14 countries observed over the period of 17 years, from 1995 to 2011 to which we apply panel data techniques. Results show that public-private investment in infrastructure has a positive impact on agricultural exports. The impact of private investments more than doubles the impact of public investments. The role of the public sector is crucial to guarantee the positive impacts of public-private investment on the recipient country by providing solid institutions framework and the appropriate investment climate.

As biochemical networks become more popular, the number of simulation tools grows rapidly. Although most of the tools have similar functionality, they differ in their algorithms and capabilities. Here, we present the major simulation tools applied in biochemical networks and describe their supported algorithms with details. We consider that the capacities of each tool in terms of the simulation, inference or visualization of the different types of biological networks, their supported algorithms and the features of these algorithms as well as the mathematical background in all these calculations can be helpful for the researchers when they choose the most appropriate tool for their analyses.