
Asenjo, F. A., & Hojman, S. A. (2017). Birefringent light propagation on anisotropic cosmological backgrounds. Phys. Rev. D, 96(4), 12 pp.
Abstract: Exact electromagnetic wave solutions to Maxwell equations on anisotropic Bianchi I cosmological spacetime backgrounds are studied. The waves evolving on Bianchi I spacetimes exhibit birefringence (associated with linear polarization) and dispersion. The particular case of a vacuumdominated anisotropic Universe, which reproduces a FriedmannRobertsonWalker Universe (for late times)while, for earlier times, it matches a Kasner Universeis studied. The electromagnetic waves do not, in general, follow null geodesics. This produces a modification of the cosmological redshift, which is then dependent on light polarization, its dispersion, and its nonnull geodesic behavior. New results presented here may help to tackle some issues related to the “horizon” problem.



Asenjo, F. A., & Hojman, S. A. (2017). Class of Exact Solutions for a Cosmological Model of Unified Gravitational and Quintessence Fields. Found. Phys., 47(7), 887–896.
Abstract: A new approach to tackle Einstein equations for an isotropic and homogeneous FriedmannRobertsonWalker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.



Asenjo, F. A., & Hojman, S. A. (2017). Do electromagnetic waves always propagate along null geodesics? Class. Quantum Gravity, 34(20), 12 pp.
Abstract: We find exact solutions to Maxwell equations written in terms of fourvector potentials in nonrotating, as well as in Gdel and Kerr spacetimes. We show that Maxwell equations can be reduced to two uncoupled secondorder differential equations for combinations of the components of the fourvector potential. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in nonrotating spherical symmetric spacetimes, electromagnetic waves travel along null geodesics. However, electromagnetic waves on Gdel and Kerr spacetimes do not exhibit that behavior.



Asenjo, F. A., & Hojman, S. A. (2017). New nonlinear modified massless KleinGordon equation. Eur. Phys. J. C, 77(11), 5 pp.
Abstract: The massless KleinGordon equation on arbitrary curved backgrounds allows for solutions which develop “tails” inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost 60 years ago. A modification of the massless KleinGordon equation is presented, which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits currentcurrent interaction. Its nonlinearity is due to a selfcoupling term which is related to the quantum mechanical Bohm potential.



Asenjo, F. A., & Mahajan, S. M. (2015). Relativistic quantum vorticity of the quadratic form of the Dirac equation. Phys. Scr., 90(1), 4 pp.
Abstract: We explore the fluid version of the quadratic form of the Dirac equation, sometimes called the FeynmanGellMann equation. The dynamics of the quantum spinor field is represented by equations of motion for the fluid density, the velocity field, and the spin field. In analogy with classical relativistic and nonrelativistic quantum theories, the fully relativistic fluid formulation of this equation allows a vortex dynamics. The vortical form is described by a total tensor field that is the weighted combination of the inertial, electromagnetic and quantum forces. The dynamics contrives the quadratic form of the Dirac equation as a total vorticity free system.



Asenjo, F. A., Comisso, L., & Mahajan, S. M. (2015). Generalized magnetofluid connections in pair plasmas. Phys. Plasmas, 22(12), 4 pp.
Abstract: We extend the magnetic connection theorem of ideal magnetohydrodynamics to nonideal relativistic pair plasmas. Adopting a generalized Ohm's law, we prove the existence of generalized magnetofluid connections that are preserved by the plasma dynamics. We show that these connections are related to a general antisymmetric tensor that unifies the electromagnetic and fluid fields. The generalized magnetofluid connections set important constraints on the plasma dynamics by forbidding transitions between configurations with different magnetofluid connectivity. An approximated solution is explicitly shown where the corrections due to current inertial effects are found. (C) 2015 AIP Publishing LLC.



Asenjo, F. A., Erices, C., Gomberoff, A., Hojman, S. A., & Montecinos, A. (2017). Differential geometry approach to asymmetric transmission of light. Opt. Express, 25(22), 26405–26416.
Abstract: In the last ten years, the technology of differential geometry, ubiquitous in gravitational physics, has found its place in the field of optics. It has been successfully used in the design of optical metamaterials through a technique now known as “transformation optics.” This method, however, only applies for the particular class of metamaterials known as impedance matched, that is, materials whose electric permittivity is equal to their magnetic permeability. In that case, the material may be described by a spacetime metric. In the present work we will introduce a generalization of the geometric methods of transformation optics to situations in which the material is not impedance matched. In such situations, the material or more precisely, its constitutive tensorwill not be described by a metric only. We bring in a second tensor, with the local symmetries of the Weyl tensor, the “Wtensor.” In the geometric optics approximation we show how the properties of the Wtensor are related to the asymmetric transmission of the material. We apply this feature to the design of a particularly interesting set of asymmetric materials. These materials are birefringent when light rays approach the material in a given direction, but behave just like vacuum when the rays have the opposite direction with the appropriate polarization (or, in some cases, independently of the polarization). (C) 2017 Optical Society of America



AstorgaElo, M., RamirezFlandes, S., DeLong, E. F., & Ulloa, O. (2015). Genomic potential for nitrogen assimilation in uncultivated members of Prochlorococcus from an anoxic marine zone. Isme J., 9(5), 1264–1267.
Abstract: Cyanobacteria of the genus Prochlorococcus are the most abundant photosynthetic marine organisms and key factors in the global carbon cycle. The understanding of their distribution and ecological importance in oligotrophic tropical and subtropical waters, and their differentiation into distinct ecotypes, is based on genetic and physiological information from several isolates. Currently, all available Prochlorococcus genomes show their incapacity for nitrate utilization. However, environmental sequence data suggest that some uncultivated lineages may have acquired this capacity. Here we report that uncultivated lowlightadapted Prochlorococcus from the nutrientrich, lowlight, anoxic marine zone (AMZ) of the eastern tropical South Pacific have the genetic potential for nitrate uptake and assimilation. All genes involved in this trait were found syntenic with those present in marine Synechococcus. Genomic and phylogenetic analyses also suggest that these genes have not been aquired recently, but perhaps were retained from a common ancestor, highlighting the basal characteristics of the AMZ lineages within Prochlorococcus.



Atkinson, J., & Maurelia, A. (2017). RedundancyBased Trust in QuestionAnswering Systems. Computer, 50(1), 58–65.
Abstract: By combining user preferences, redundancy analysis, and trustnetwork inference, the proposed trust model can augment candidate answers with information about target sources on the basis of connections with other web users and sources. Experiments show that the model is more effective overall than trust analyses based on inference alone.



Bandi, M. M., Concha, A., Wood, R., & Mahadevan, L. (2013). A pendulum in a flowing soap film. Phys. Fluids, 25(4), 6 pp.
Abstract: We consider the dynamics of a pendulum made of a rigid ring attached to an elastic filament immersed in a flowing soap film. The system shows an oscillatory instability whose onset is a function of the flow speed, length of the supporting string, the ring mass, and ring radius. We characterize this system and show that there are different regimes where the frequency is dependent or independent of the pendulum length depending on the relative magnitude of the addedmass. Although the system is an infinitedimensional, we can explain many of our results in terms of a one degreeoffreedom system corresponding to a forced pendulum. Indeed, using the vorticity measured via particle imaging velocimetry allows us to make the model quantitative, and a comparison with our experimental results shows we can capture the basic phenomenology of this system. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4800057]



Barra, F., Lund, F., Mujica, N., & Rica, S. (2012). Shear modulus of an elastic solid under external pressure as a function of temperature: The case of helium. Phys. Rev. B, 85(6), 6 pp.
Abstract: The energy of a dislocation loop in a continuum elastic solid under pressure is considered within the framework of classical mechanics. For a circular loop, this is a function with a maximum at pressures that are well within reach of experimental conditions for solid helium, suggesting, in this case, that dislocation loops can be generated by a pressureassisted thermally activated process. It is also pointed out that pinned dislocation segments can alter the shear response of solid helium by an amount consistent with current measurements, without any unpinning.



Barrera, J., & Fontbona, J. (2010). The Limiting MoveToFront SearchCost In Law Of Large Numbers Asymptotic Regimes. Ann. Appl. Probab., 20(2), 722–752.
Abstract: We explicitly compute the limiting transient distribution of the searchcost in the movetofront Markov chain when the number of objects tends to infinity, for general families of deterministic or random request rates. Our techniques are based on a “law of large numbers for random partitions,” a scaling limit that allows us to exactly compute limiting expectation of empirical functionals of the request probabilities of objects. In particular, we show that the limiting searchcost can be split at an explicit deterministic threshold into one random variable in equilibrium, and a second one related to the initial ordering of the list. Our results ensure the stability of the limiting searchcost under general perturbations of the request probabilities. We provide the description of the limiting transient behavior in several examples where only the stationary regime is known, and discuss the range of validity of our scaling limit.



Barrera, J., & Ycart, B. (2014). Bounds for left and right window cutoffs. ALEALatin Am. J. Probab. Math. Stat., 11(2), 445–458.
Abstract: The location and width of the time window in which a sequence of processes converges to equilibrum are given under conditions of exponential convergence. The location depends on the side: the leftwindow and rightwindow cutoffs may have different locations. Bounds on the distance to equilibrium are given for both sides. Examples prove that the bounds are tight.



Barrera, J., Bertoncini, O., & Fernandez, R. (2009). Abrupt Convergence and Escape Behavior for Birth and Death Chains. J. Stat. Phys., 137(4), 595–623.
Abstract: We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cutoff phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by convergence at asymptotically deterministic times, while the convergence times for the latter are exponentially distributed. We compare and study both phenomena for discretetime birthanddeath chains on a"currency sign with drift towards zero. In particular, this includes energydriven evolutions with energy functions in the form of a single well. Under suitable drift hypotheses, we show that there is both an abrupt convergence towards zero and escape behavior in the other direction. Furthermore, as the evolutions are reversible, the law of the final escape trajectory coincides with the time reverse of the law of cutoff paths. Thus, for evolutions defined by onedimensional energy wells with sufficiently steep walls, cutoff and escape behavior are related by time inversion.



Barrera, J., Cancela, H., & Moreno, E. (2015). Topological optimization of reliable networks under dependent failures. Oper. Res. Lett., 43(2), 132–136.
Abstract: We address the design problem of a reliable network. Previous work assumes that link failures are independent. We discuss the impact of dropping this assumption. We show that under a commoncause failure model, dependencies between failures can affect the optimal design. We also provide an integerprogramming formulation to solve this problem. Furthermore, we discuss how the dependence between the links that participate in the solution and those that do not can be handled. Other dependency models are discussed as well. (C) 2014 Elsevier B.V. All rights reserved.



Barrera, J., HomemDeMello, T., Moreno, E., Pagnoncelli, B. K., & Canessa, G. (2016). Chanceconstrained problems and rare events: an importance sampling approach. Math. Program., 157(1), 153–189.
Abstract: We study chanceconstrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing samplingbased algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. We argue that importance sampling (IS) techniques, combined with a Sample Average Approximation (SAA) approach, can be effectively used in such situations, provided that variance can be reduced uniformly with respect to the decision variables. We give sufficient conditions to obtain such uniform variance reduction, and prove asymptotic convergence of the combined SAAIS approach. As it often happens with IS techniques, the practical performance of the proposed approach relies on exploiting the structure of the problem under study; in our case, we work with a telecommunications problem with Bernoulli input distributions, and show how variance can be reduced uniformly over a suitable approximation of the feasibility set by choosing proper parameters for the IS distributions. Although some of the results are specific to this problem, we are able to draw general insights that can be useful for other classes of problems. We present numerical results to illustrate our findings.



Barrera, J., Moreno, E., & Varas K., S. (2018). A decomposition algorithm for computing income taxes with passthrough entities and its application to the Chilean case. Ann. Oper. Res., to appear.
Abstract: Income tax systems with “passthrough” entities transfer a firm's incomes to the sharehold ers, which are taxed individually. In 2014, a Chilean tax reform introduced this type of entity and changed to an accrual basis that distributes incomes (but not losses) to shareholders. A crucial step for the Chilean taxation authority is to compute the final income of each individual, given the complex network of corporations and companies, usually including cycles between them. In this paper, we show the mathematical conceptualization and the solution to the problem, proving that there is only one way to distribute incomes to taxpayers. Using the theory of absorbing Markov chains, we define a mathematical model for computing the taxable incomes of each taxpayer, and we propose a decomposition algorithm for this problem. This allows us to compute the solution accurately and with the efficient use of computational resources. Finally, we present some characteristics of the Chilean taxpayers' network and computational results of the algorithm using this network.



Barria, A. M., Lardies, M. A., Beckerman, A. P., & Bacigalupe, L. D. (2014). Latitude or biogeographic breaks? Determinants of phenotypic (co)variation in fitnessrelated traits in Betaeus truncatus along the Chilean coast. Mar. Biol., 161(1), 111–118.
Abstract: Ectothermal organisms distributed along environmental gradients in a wide geographical distribution display extensive phenotypic variation. This is particularly pervasive along latitudinal clines, which are linked to gradual changes in environmental factors. Widespread species may also be distributed among biogeographic breaks, which in contrast to smooth clines, often show abrupt changes in phenotypic traits. In species with widespread latitudinal distribution that also encompass important biogeographical breaks, it is not clear which of those factors prevails on shaping the phenotypic variation or if some traits are particularly more sensitive to one or the other. To evaluate this, we measured 4 fitnessrelated traits in 6 populations of the intertidal snapping shrimp Betaeus truncatus, as its distribution along Chile expands over 40A degrees in latitude and three major biogeographical provinces. Here, we statistically evaluated the role of both, latitude and biogeographic breaks, on mean population values of fitnessrelated traits but also on the variances and covariances (i.e., Pmatrix) between them. Overall, our results (1) indicate that latitude is more important than breaks in shaping the phenotypic variation of most of these fitnessrelated traits, (2) show that the differences in the variancecovariance relationship among traits between the extremes of the gradient arises from gradual increases in variance and rather sharp changes in covariance at midlatitudes and (3) show that at present, it is difficult to unambiguously determine whether natural selection or plasticity is responsible for the observed pattern in means, variances and covariances and only further work might disentangle these possibilities.



BarrientosDiaz, L., Gidekel, M., & GutierrezMoraga, A. (2008). Characterization of rhizospheric bacteria isolated from Deschampsia antarctica Desv. World J. Microbiol. Biotechnol., 24(10), 2289–2296.
Abstract: Deschampsia antarctica Desv. is the only gramineae capable of colonizing the Antarctic due to the region's extreme climate and soil environment. In the present research, bacteria colonizing the rhizospheric soil of D. antarctica were isolated and characterized. The soil studies showed that D. antarctica possesses a wide spectrum of psychrotolerant bacteria with extensive and varied antibiotic resistance, as well as heavy metal tolerance. The bacterial strains isolated from the rhizosphere of D. antarctica also produced a diverse pattern of enzymes. Based on the strain identification with partial characterization of the 16S rRNA gene, the majority of the isolates correspond to different Pseudomonas species, and species of the genus Flavobacterium sp. and Arthrobacter sp. The isolated strains collected from this research constitute a unique collection for future, more detailed taxonomic analysis and physiological characterization, contributing to the search for potential biotechnological uses. These findings and others have great potential for developing new biotechnological products from Antarctic microorganisms.



Barros, M., Galea, M., Leiva, V., & SantosNeto, M. (2018). Generalized Tobit models: diagnostics and application in econometrics. J. Appl. Stat., 45(1), 145–167.
Abstract: The standard Tobit model is constructed under the assumption of a normal distribution and has been widely applied in econometrics. Atypical/extreme data have a harmful effect on the maximum likelihood estimates of the standard Tobit model parameters. Then, we need to count with diagnostic tools to evaluate the effect of extreme data. If they are detected, we must have available a Tobit model that is robust to this type of data. The family of elliptically contoured distributions has the Laplace, logistic, normal and Studentt cases as some of its members. This family has been largely used for providing generalizations of models based on the normal distribution, with excellent practical results. In particular, because the Studentt distribution has an additional parameter, we can adjust the kurtosis of the data, providing robust estimates against extreme data. We propose a methodology based on a generalization of the standard Tobit model with errors following elliptical distributions. Diagnostics in the Tobit model with elliptical errors are developed. We derive residuals and global/local influence methods considering several perturbation schemes. This is important because different diagnostic methods can detect different atypical data. We implement the proposed methodology in an R package. We illustrate the methodology with realworld econometrical data by using the R package, which shows its potential applications. The Tobit model based on the Studentt distribution with a small quantity of degrees of freedom displays an excellent performance reducing the influence of extreme cases in the maximum likelihood estimates in the application presented. It provides new empirical evidence on the capabilities of the Studentt distribution for accommodation of atypical data.

