
Chuaqui, M., & Hernandez, R. (2013). The order of a linearly invariant family in Cn. J. Math. Anal. Appl., 398(1), 372–379.
Abstract: We study the (trace) order of the linearly invariant family in the ball Bn defined by parallel to SF parallel to <= alpha, where F : Bn > Cn is locally biholomorphic and SF is the Schwarzian operator. By adapting Pommerenke's approach, we establish a characteristic equation for the extremal mapping that yields an upper bound for the order of the family in terms of alpha and the dimension n. Lower bounds for the order are established in similar terms by means of examples. (C) 2012 Elsevier Inc. All rights reserved.



Chuaqui, M., & Hernandez, R. (2015). AhlforsWeill extensions in several complex variables. J. Reine Angew. Math., 698, 161–179.
Abstract: We derive an AhlforsWeill type extension for a class of holomorphic mappings defined in the ball Bn, generalizing the formula for Nehari mappings in the disk. The class of mappings holomorphic in the ball is defined in terms of the Schwarzian operator. Convexity relative to the Bergman metric plays an essential role, as well as the concept of a weakly linearly convex domain. The extension outside the ball takes values in the projective dual to Cn, that is, in the set of complex hyperplanes.



Chuaqui, M., Hamada, H., Hernandez, R., & Kohr, G. (2014). Pluriharmonic mappings and linearly connected domains in Cn. Isr. J. Math., 200(1), 489–506.
Abstract: In this paper we obtain certain sufficient conditions for the univalence of pluriharmonic mappings defined in the unit ball of Cn . The results are generalizations of conditions of Chuaqui and Hernandez that relate the univalence of planar harmonic mappings with linearly connected domains, and show how such domains can play a role in questions regarding injectivity in higher dimensions. In addition, we extend recent work of Hernandez and Martin on a shear type construction for planar harmonic mappings, by adapting the concept of stable univalence to pluriharmonic mappings of the unit ball into Cn .



Chuaqui, M., Hernandez, R., & Martin, M. J. (2017). Affine and linear invariant families of harmonic mappings. Math. Ann., 367(34), 1099–1122.
Abstract: We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk. By using the famous shear construction of Clunie and SheilSmall, we construct a function to determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class SH of univalent harmonic mappings can be formulated as a question about Schwarzian norm and, in particular, our result shows consistency between the conjectured order of SH and the Schwarzian norm of the harmonic Koebe function.



Ciarreta, A., Nasirov, S., & Silva, C. (2016). The development of market power in the Spanish power generation sector: Perspectives after market liberalization. Energy Policy, 96, 700–710.
Abstract: This paper provides a comprehensive analysis of the market power problem in the Spanish power generation sector and examines how and to which extent the market has developed in terms of market power concerns after the market liberalization reforms. The methodology applied in this study includes typical expost structural and behavioral measures employed to estimate potential for market power, namely: concentration ratios (CR) (for the largest and the three largest suppliers), the HerfindahlHirschman Index (HHI), Entropy, Pivotal Supply Index, the Residual Supply Index and Residual Demand Elasticity (RDE). The results are presented for the two largest Spanish generating companies (Endesa and Iberdrola) acting in the Iberian Electricity Market (MIBEL), and in the Spanish Dayahead electricity market. The results show evidence that these companies have behaved much more competitively in recent periods than in the beginning of the market liberalization. In addition, the paper discusses important structural and regulatory changes through market liberalization processes in the Spanish Day ahead electricity market. (C) 2016 Elsevier Ltd. All rights reserved.



Clerc, M. G., Rica, S., & Tredicce, J. (2011). Instabilities and Nonequilibrium Structures. On the occasion of the 60th birthday of Pierre Coullet. Eur. Phys. J. D, 62(1), 1–4.



Collins, C. J., Vivanco, J. F., Sokn, S. A., Williams, B. O., Burgers, T. A., & Ploeg, H. L. (2015). Fracture healing in mice lacking Pten in osteoblasts: a microcomputed tomography imagebased analysis of the mechanical properties of the femur. J. Biomech., 48(2), 310–317.
Abstract: In the United States, approximately eight million osseous fractures are reported annually, of which 510% fail to create a bony union. Osteoblastspecific deletion of the gene Pten in mice has been found to stimulate bone growth and accelerate fracture healing. Healing rates at four weeks increased in femurs from Pten osteoblast conditional knockout mice (PtenCKO) compared to wildtype mice (WT) of the same genetic strain as measured by an increase in mechanical stiffness and failure load in fourpoint bending tests. Preceding mechanical testing, each femur was imaged using a Skyscan 1172 microcomputed tomography (mu CT) scanner (Skyscan, Kontich, Belgium). The present study used μCT imagebased analysis to test the hypothesis that the increased femoral fracture force and stiffness in PtenCKO were due to greater section properties with the same effective material properties as that of the WT. The second moment of area and section modulus were computed in ImageJ 1.46 (National Institutes of Health) and used to predict the effective flexural modulus and the stress at failure for fourteen pairs of intact and callus WT and twelve pairs of intact and callus PtenCKO femurs. For callus and intact femurs, the failure stress and tissue mineral density of the PtenCKO and WT were not different; however, the section properties of the PtenCKO were more than twice as large 28 days postfracture. It was therefore concluded, when the gene Pten was conditionally knockedout in osteoblasts, the resulting increased bending stiffness and force to fracture were due to increased section properties. (C) 2014 Elsevier Ltd. All rights reserved.



Comisso, L., & Asenjo, F. A. (2014). ThermalInertial Effects on Magnetic Reconnection in Relativistic Pair Plasmas. Phys. Rev. Lett., 113(4), 5 pp.
Abstract: The magnetic reconnection process is studied in relativistic pair plasmas when the thermal and inertial properties of the magnetohydrodynamical fluid are included. We find that in both SweetParker and Petschek relativistic scenarios there is an increase of the reconnection rate owing to the thermalinertial effects, both satisfying causality. To characterize the new effects we define a thermalinertial number which is independent of the relativistic Lundquist number, implying that reconnection can be achieved even for vanishing resistivity as a result of only thermalinertial effects. The current model has fundamental importance for relativistic collisionless reconnection, as it constitutes the simplest way to get reconnection rates faster than those accessible with the sole resistivity.



Concha, A., Mellado, P., MoreraBrenes, B., Costa, C. S., Mahadevan, L., & MongeNajera, J. (2015). Oscillation of the velvet worm slime jet by passive hydrodynamic instability. Nat. Commun., 6, 6 pp.
Abstract: The rapid squirt of a proteinaceous slime jet endows velvet worms (Onychophora) with a unique mechanism for defence from predators and for capturing prey by entangling them in a disordered web that immobilizes their target. However, to date, neither qualitative nor quantitative descriptions have been provided for this unique adaptation. Here we investigate the fast oscillatory motion of the oral papillae and the exiting liquid jet that oscillates with frequencies f similar to 3060 Hz. Using anatomical images, highspeed videography, theoretical analysis and a physical simulacrum, we show that this fast oscillatory motion is the result of an elastohydrodynamic instability driven by the interplay between the elasticity of oral papillae and the fast unsteady flow during squirting. Our results demonstrate how passive strategies can be cleverly harnessed by organisms, while suggesting future oscillating microfluidic devices, as well as novel ways for micro and nanofibre production using bioinspired strategies.



Concha, P. K., Durka, R., Inostroza, C., Merino, N., & Rodriguez, E. K. (2016). Pure Lovelock gravity and ChernSimons theory. Phys. Rev. D, 94(2), 14 pp.
Abstract: We explore the possibility of finding pure Lovelock gravity as a particular limit of a ChernSimons action for a specific expansion of the AdS algebra in odd dimensions. We derive in detail this relation at the level of the action in five and seven dimensions. We provide a general result for higher dimensions and discuss some issues arising from the obtained dynamics.



Concha, P. K., Durka, R., Merino, N., & Rodriguez, E. K. (2016). New family of Maxwell like algebras. Phys. Lett. B, 759, 507–512.
Abstract: We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the Sexpansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license.



Concha, P. K., Fierro, O., & Rodriguez, E. K. (2017). InonuWigner contraction and D=2+1 supergravity. Eur. Phys. J. C, 77(1), 18 pp.
Abstract: We present a generalization of the standard InonuWigner contraction by rescaling not only the generators of a Lie superalgebra but also the arbitrary constants appearing in the components of the invariant tensor. The procedure presented here allows one to obtain explicitly the ChernSimons supergravity action of a contracted superalgebra. In particular we show that the Poincare limit can be performed to a D = 2 + 1 (p, q) AdS ChernSimons supergravity in presence of the exotic form. We also construct a newthreedimensional (2, 0) Maxwell ChernSimons supergravity theory as a particular limit of (2, 0) AdSLorentz supergravity theory. The generalization for N = p + q gravitinos is also considered.



Concha, P. K., Ipinza, M. C., Ravera, L., & Rodriguez, E. K. (2016). On the supersymmetric extension of GaussBonnet like gravity. J. High Energy Phys., (9), 14 pp.
Abstract: We explore the supersymmetry invariance of a supergravity theory in the presence of a nontrivial boundary. The explicit construction of a bulk Lagrangian based on an enlarged superalgebra, known as AdSLorentz, is presented. Using a geometric approach we show that the supersymmetric extension of a GaussBonnet like gravity is required in order to restore the supersymmetry invariance of the theory.



Concha, P. K., Merino, N., & Rodriguez, E. K. (2017). Lovelock gravities from BornInfeld gravity theory. Phys. Lett. B, 765, 395–401.
Abstract: We present a BornInfeld gravity theory based on generalizations of Maxwell symmetries denoted as Cm. We analyze different configuration limits allowing to recover diverse Lovelock gravity actions in six dimensions. Further, the generalization to higher even dimensions is also considered. (C) 2016 The Authors. Published by Elsevier B.V.



Contreras, G. M. (2014). Stochastic volatility models at rho = +/ 1 as second class constrained Hamiltonian systems. Physica A, 405, 289–302.
Abstract: The stochastic volatility models used in the financial world are characterized, in the continuoustime case, by a set of two coupled stochastic differential equations for the underlying asset price S and volatility sigma. In addition, the correlations of the two Brownian movements that drive the stochastic dynamics are measured by the correlation parameter rho (1 <= rho <= 1). This stochastic system is equivalent to the FokkerPlanck equation for the transition probability density of the random variables S and sigma. Solutions for the transition probability density of the Heston stochastic volatility model (Heston, 1993) were explored in Dragulescu and Yakovenko (2002), where the fundamental quantities such as the transition density itself, depend on rho in such a manner that these are divergent for the extreme limit rho = +/ 1. The same divergent behavior appears in Hagan et al. (2002), where the probability density of the SABR model was analyzed. In an option pricing context, the propagator of the bidimensional BlackScholes equation was obtained in Lemmens et al. (2008) in terms of the path integrals, and in this case, the propagator diverges again for the extreme values rho = +/ 1. This paper shows that these similar divergent behaviors are due to a universal property of the stochastic volatility models in the continuum: all of them are second class constrained systems for the most extreme correlated limit rho = +/ 1. In this way, the stochastic dynamics of the rho = +/ 1 cases are different of the rho (1 <= rho <= 1) case, and it cannot be obtained as a continuous limit from the rho not equal +/ 1 regimen. This conclusion is achieved by considering the FokkerPlanck equation or the bidimensional BlackScholes equation as a Euclidean quantum Schrodinger equation. Then, the analysis of the underlying classical mechanics of the quantum model, implies that stochastic volatility models at rho = +/ 1 correspond to a constrained system. To study the dynamics in an appropriate form, Dirac's method for constrained systems (Dirac, 1958, 1967) must be employed, and Dirac's analysis reveals that the constraints are second class. In order to obtain the transition probability density or the option price correctly, one must evaluate the propagator as a constrained Hamiltonian pathintegral (Henneaux and Teitelboim, 1992), in a similar way to the high energy gauge theory models. In fact, for all stochastic volatility models, after integrating over momentum variables, one obtains an effective Euclidean Lagrangian path integral over the volatility alone. The role of the second class constraints is determining the underlying asset price S completely in terms of volatility, so it plays no role in the path integral. In order to examine the effect of the constraints on the dynamics for both extreme limits, the probability density function is evaluated by using semiclassical arguments, in an analogous manner to that developed in Hagan et al. (2002), for the SABR model. (C) 2014 Elsevier B.V. All rights reserved.



Contreras, M., & Hojman, S. A. (2014). Option pricing, stochastic volatility, singular dynamics and constrained path integrals. Physica A, 393, 391–403.
Abstract: Stochastic volatility models have been widely studied and used in the financial world. The Heston model (Heston, 1993) [7] is one of the best known models to deal with this issue. These stochastic volatility models are characterized by the fact that they explicitly depend on a correlation parameter p which relates the two Brownian motions that drive the stochastic dynamics associated to the volatility and the underlying asset. Solutions to the Heston model in the context of option pricing, using a path integral approach, are found in Lemmens et al. (2008) [21] while in Baaquie (2007,1997) [12,13] propagators for different stochastic volatility models are constructed. In all previous cases, the propagator is not defined for extreme cases rho = +/ 1. It is therefore necessary to obtain a solution for these extreme cases and also to understand the origin of the divergence of the propagator. In this paper we study in detail a general class of stochastic volatility models for extreme values rho = +/ 1 and show that in these two cases, the associated classical dynamics corresponds to a system with second class constraints, which must be dealt with using Dirac's method for constrained systems (Dirac, 1958,1967) [22,23] in order to properly obtain the propagator in the form of a Euclidean Hamiltonian path integral (Henneaux and Teitelboim, 1992) [25]. After integrating over momenta, one gets an Euclidean Lagrangian path integral without constraints, which in the case of the Heston model corresponds to a path integral of a repulsive radial harmonic oscillator. In all the cases studied, the price of the underlying asset is completely determined by one of the second class constraints in terms of volatility and plays no active role in the path integral. (C) 2013 Elsevier B.V. All rights reserved.



Contreras, M., Montalva, R., Pellicer, R., & Villena, M. (2010). Dynamic option pricing with endogenous stochastic arbitrage. Physica A, 389(17), 3552–3564.
Abstract: Only few efforts have been made in order to relax one of the key assumptions of the BlackScholes model: the noarbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be shortlived. The purpose of this paper is to develop an option pricing model with endogenous stochastic arbitrage, capable of modelling in a general fashion any future and underlying asset that deviate itself from its market equilibrium. Thus, this investigation calibrates empirically the arbitrage on the futures on the S&P 500 index using transaction data from September 1997 to June 2009, from here a specific type of arbitrage called “arbitrage bubble”, based on a tstep function, is identified and hence used in our model. The theoretical results obtained for Binary and European call options, for this kind of arbitrage, show that an investment strategy that takes advantage of the identified arbitrage possibility can be defined, whenever it is possible to anticipate in relative terms the amplitude and timespan of the process. Finally, the new trajectory of the stock price is analytically estimated for a specific case of arbitrage and some numerical illustrations are developed. We find that the consequences of a finite and small endogenous arbitrage not only change the trajectory of the asset price during the period when it started, but also after the arbitrage bubble has already gone. In this context, our model will allow us to calibrate the BS model to that new trajectory even when the arbitrage already started. (C) 2010 Elsevier B.V. All rights reserved.



Contreras, M., Pellicer, R., & Villena, M. (2017). Dynamic optimization and its relation to classical and quantum constrained systems. Physica A, 479, 12–25.
Abstract: We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum frameworks. Classically, the dynamic optimization problem is equivalent to a classical mechanics constrained system, so we must use the Dirac method to analyze it in a correct way. We find that there are two secondclass constraints in the model: one fix the momenta associated with the control variables, and the other is a reminder of the optimal control law. The dynamic evolution of this constrained system is given by the Dirac's bracket of the canonical variables with the Hamiltonian. This dynamic results to be identical to the unconstrained one given by the Pontryagin equations, which are the correct classical equations of motion for our physical optimization problem. In the same Pontryagin scheme, by imposing a closedloop lambdastrategy, the optimality condition for the action gives a consistency relation, which is associated to the HamiltonJacobiBellman equation of the dynamic programming method. A similar result is achieved by quantizing the classical model. By setting the wave function Psi (x, t) = e(is(x,t)) in the quantum Schrodinger equation, a nonlinear partial equation is obtained for the S function. For the righthand side quantization, this is the HamiltonJacobiBellman equation, when S(x, t) is identified with the optimal value function. Thus, the HamiltonJacobiBellman equation in Bellman's maximum principle, can be interpreted as the quantum approach of the optimization problem. (C) 2017 Elsevier B.V. All rights reserved.



Contreras, M., Pellicer, R., Villena, M., & Ruiz, A. (2010). A quantum model of option pricing: When BlackScholes meets Schrodinger and its semiclassical limit. Physica A, 389(23), 5447–5459.
Abstract: The BlackScholes equation can be interpreted from the point of view of quantum mechanics, as the imaginary time Schrodinger equation of a free particle. When deviations of this state of equilibrium are considered, as a product of some market imperfection, such as: Transaction cost, asymmetric information issues, shortterm volatility, extreme discontinuities, or serial correlations; the classical nonarbitrage assumption of the BlackScholes model is violated, implying a nonriskfree portfolio. From Haven (2002) [1] we know that an arbitrage environment is a necessary condition to embedding the BlackScholes option pricing model in a more general quantum physics setting. The aim of this paper is to propose a new BlackScholesSchrodinger model based on the endogenous arbitrage option pricing formulation introduced by Contreras et al. (2010) [2]. Hence, we derive a more general quantum model of option pricing, that incorporates arbitrage as an external time dependent force, which has an associated potential related to the random dynamic of the underlying asset price. This new resultant model can be interpreted as a Schrodinger equation in imaginary time for a particle of mass 1/sigma(2) with a wave function in an external field force generated by the arbitrage potential. As pointed out above, this new model can be seen as a more general formulation, where the perfect market equilibrium state postulated by the BlackScholes model represent a particular case. Finally, since the Schrodinger equation is in place, we can apply semiclassical methods, of common use in theoretical physics, to find an approximate analytical solution of the BlackScholes equation in the presence of market imperfections, as it is the case of an arbitrage bubble. Here, as a numerical illustration of the potential of this Schrodinger equation analogy, the semiclassical approximation is performed for different arbitrage bubble forms (step, linear and parabolic) and compare with the exact solution of our general quantum model of option pricing. (C) 2010 Elsevier B.V. All rights reserved.



Corral, N., Anrique, N., Fernandes, D., Parrado, C., & Caceres, G. (2012). Power, placement and LEC evaluation to install CSP plants in northern Chile. Renew. Sust. Energ. Rev., 16(9), 6678–6685.
Abstract: Chile is expecting a 5.4% growth in energy consumption per year until 2030, requiring new and better solutions for the upward trend of its electricity demand. This state leads to select and study one of the potential alternatives for electricity generation: concentrated solar power (CSP) plants. Such renewable technology found in Chile a very favorable condition. Recent researches indicate Atacama Desert as one of the best regions for solar energy worldwide, having an average radiation higher than in places where CSP plants are currently implemented, e.g. Spain and USA. The aim of this study is to present an analysis of levelized energy cost (LEC) for different power capacities of CSP plants placed in distinct locations in northern Chile. The results showed that CSP plants can be implemented in Atacama Desert with LECs around 19 (sic)US$/kWh when a gasfired backup and thermal energy storage (TES) systems are fitted. This value increases to approximately 28 (sic)US$/kWh if there is no backup system. (C) 2012 Elsevier Ltd. All rights reserved.

