Complex variable positive definite functions

In this paper we develop an appropriate theory of positive definite functions on the complex plane from first principles and show some consequences of positive definiteness for meromorphic functions.

Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Complex Dynamics of defective interfering baculoviruses during serial passage in insect cells

Defective interfering (DI) viruses are thought to cause oscillations in virus levels, known as the ‘Von Magnus effect’. Interference by DI viruses has been proposed to underlie these dynamics, although experimental tests of this idea have not been forthcoming. For the baculoviruses, insect viruses commonly used for the expression of heterologous proteins in insect cells, the molecular mechanisms underlying DI generation have been investigated. However, the dynamics of baculovirus populations harboring DIs have not been studied in detail. In order to address this issue, we used quantitative real-time PCR to determine the levels of helper and DI viruses during 50 serial passages of Autographa californica multiple nucleopolyhedrovirus (AcMNPV) in Sf21 cells. Unexpectedly, the helper and DI viruses changed levels largely in phase, and oscillations were highly irregular, suggesting the presence of chaos. We therefore developed a simple mathematical model of baculovirus-DI dynamics. This theoretical model reproduced patterns qualitatively similar to the experimental data. Although we cannot exclude that experimental variation (noise) plays an important role in generating the observed patterns, the presence of chaos in the model dynamics was confirmed with the computation of the maximal Lyapunov exponent, and a Ruelle-Takens-Newhouse route to chaos was identified at decreasing production of DI viruses, using mutation as a control parameter. Our results contribute to a better understanding of the dynamics of DI baculoviruses, and suggest that changes in virus levels over passages may exhibit chaos.

Catalytic activity of a benzoyl hydrazone based dimeric dicopper(II) complex in catechol and alcohol oxidation reactions

The benzoyl hydrazone based dimeric dicopper(II) complex [Cu2(R)(CH3O)(NO3)]2(CH3O)2 (R-Cu2+), recently reported by us, catalyzes the aerobic oxidation of catechols (catechol (S1), 3,5- itertiarybutylcatechol (S2) and 3-nitrocatechol (S3)) to the corresponding quinones (catecholase like activity), as shown by UV–Vis absorption spectroscopy in methanol/HEPES buffer (pH 8.2) medium at 25 C. The highest activity is observed for the substituted catechol (S2) with the electron donor tertiary butyl group, resulting in a turnover frequency (TOF) value of 1.13 103 h1. The complex R-Cu2+ also exhibits a good catalytic activity in the oxidation (without added solvent) of 1-phenylethanol to acetophenone by But OOH under low power (10 W) microwave (MW) irradiation. 2014 Elsevier B.V. All rights reserved.

Catalytic oxidation of cyclohexane with hydrogen peroxide and a tetracopper(II) complex in an ionic liquid

The catalytic peroxidative oxidation (with H2O2) of cyclohexane in an ionic liquid (IL) using the tetracopper(II) complex [(CuL)2(μ4-O,O′,O′′,O′′′-CDC)]2·2H2O [HL = 2-(2-pyridylmethyleneamino)benzenesulfonic acid, CDC = cyclohexane-1,4-dicarboxylate] as a catalyst is reported. Significant improvements on the catalytic performance, in terms of product yield (up to 36%), TON (up to 529), reaction time, selectivity towards cyclohexanone and easy recycling (negligible loss in activity after three consecutive runs), are observed using 1-butyl-3-methylimidazolium hexafluorophosphate as the chosen IL instead of a molecular organic solvent including the commonly used acetonitrile. The catalytic behaviors in the IL and in different molecular solvents are discussed.

Large pseudoscalar Yukawa couplings in the complex 2HDM

We start by presenting the current status of a complex flavour conserving two-Higgs doublet model. We will focus on some very interesting scenarios where unexpectedly the light Higgs couplings to leptons and to b-quarks can have a large pseudoscalar component with a vanishing scalar component. Predictions for the allowed parameter space at end of the next run with a total collected luminosity of 300 fb(-1) and 3000 fb(-1) are also discussed. These scenarios are not excluded by present data and most probably will survive the next LHC run. However, a measurement of the mixing angle phi(tau), between the scalar and pseudoscalar component of the 125 GeV Higgs, in the decay h -> tau(+)tau(-) will be able to probe many of these scenarios, even with low luminosity. Similarly, a measurement of phi(t) in the vertex (t) over bar th could help to constrain the low tan beta region in the Type I model.

Juggling time concepts: complex metanarrative in Alejandro González Iñárritu’s 21 Grams

ABSTRACT - Starting with the explanation of metanarrative as a sort of self-reflexive storytelling (as defended by Kenneth Weaver Hope in his unpublished PhD. thesis), I propose to talk about enunciative practices that stress the telling more than the told. In line with some metaficcional practices applied to cinema, such as the ‘mindfuck’ film (Jonathan Eig, 2003), the ‘psychological puzzle film’ (Elliot Panek, 2003) and the ‘mind-game film’ (Thomas Elsaesser, 2009), I will address the manipulations that a narrative film endures in order to produce a more fruitful and complex experience for the viewer. I will particularly concentrate on the misrepresentation of time as a way to produce a labyrinthine work of fiction where the linear description of events is replaced by a game of time disclosure. The viewer is thus called upon to reconstruct the order of the various situations portrayed in a process that I call ‘temporal mapping’. However, as the viewer attempts to do this, the film, ironically, because of the intricate nature of the plot and the uncertain status of the characters, resists the attempt. There is a sort of teasing taking place between the film and its spectator: an invitation of decoding that is half-denied until the end, where the puzzle is finally solved. I will use three of Alejandro Iñárritu’s films to better convey my point: Amores perros (2000), 21 Grams (2003) and Babel (2006). I will consider Iñárritu’s methods to produce a non-linear storytelling as a way to stress the importance of time and its validity as one of the elements that make up for a metanarrative experience in films. I will focus especially on 21 Grams, which I consider to be a paragon of the labyrinth.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Two-loop stability of a complex singlet extended Standard Model

Motivated by the dark matter and the baryon asymmetry problems, we analyze a complex singlet extension of the Standard Model with a Z(2) symmetry (which provides a dark matter candidate). After a detailed two-loop calculation of the renormalization group equations for the new scalar sector, we study the radiative stability of the model up to a high energy scale (with the constraint that the 126 GeV Higgs boson found at the LHC is in the spectrum) and find it requires the existence of a new scalar state mixing with the Higgs with a mass larger than 140 GeV. This bound is not very sensitive to the cutoff scale as long as the latter is larger than 10(10) GeV. We then include all experimental and observational constraints/measurements from collider data, from dark matter direct detection experiments, and from the Planck satellite and in addition force stability at least up to the grand unified theory scale, to find that the lower bound is raised to about 170 GeV, while the dark matter particle must be heavier than about 50 GeV.