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.

A high throughput colorimetric assay of beta-1,3-D-glucans by Congo red dye

Mushroom strains contain complex nutritional biomolecules with a wide spectrum of therapeutic and prophylactic properties. Among these compounds, β-d-glucans play an important role in immuno-modulating and anti-tumor activities. The present work involves a novel colorimetric assay method for β-1,3-d-glucans with a triple helix tertiary structure by using Congo red. The specific interaction that occurs between Congo red and β-1,3-d-glucan was detected by bathochromic shift from 488 to 516 nm (> 20 nm) in UV–Vis spectrophotometer. A micro- and high throughput method based on a 96-well microtiter plate was devised which presents several advantages over the published methods since it requires only 1.51 μg of polysaccharides in samples, greater sensitivity, speed, assay of many samples and very cheap. β-d-Glucans of several mushrooms (i.e., Coriolus versicolor, Ganoderma lucidum, Pleurotus ostreatus, Ganoderma carnosum, Hericium erinaceus, Lentinula edodes, Inonotus obliquus, Auricularia auricular, Polyporus umbellatus, Cordyseps sinensis, Agaricus blazei, Poria cocos) were isolated by using a sequence of several extractions with cold and boiling water, acidic and alkaline conditions and quantified by this microtiter plate method. FTIR spectroscopy was used to study the structural features of β-1,3-d-glucans in these mushroom samples as well as the specific interaction of these polysaccharides with Congo red. The effect of NaOH on triple helix conformation of β-1,3-d-glucans was investigated in several mushroom species.

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.

On the applicability of joint inversion of gravity and resistivity data to the study of a tectonic sedimentary basin in Northern Portugal

The Chaves basin is a pull-apart tectonic depression implanted on granites, schists, and graywackes, and filled with a sedimentary sequence of variable thickness. It is a rather complex structure, as it includes an intricate network of faults and hydrogeological systems. The topography of the basement of the Chaves basin still remains unclear, as no drill hole has ever intersected the bottom of the sediments, and resistivity surveys suffer from severe equivalence issues resulting from the geological setting. In this work, a joint inversion approach of 1D resistivity and gravity data designed for layered environments is used to combine the consistent spatial distribution of the gravity data with the depth sensitivity of the resistivity data. A comparison between the results from the inversion of each data set individually and the results from the joint inversion show that although the joint inversion has more difficulty adjusting to the observed data, it provides more realistic and geologically meaningful models than the ones calculated by the inversion of each data set individually. This work provides a contribution for a better understanding of the Chaves basin, while using the opportunity to study further both the advantages and difficulties comprising the application of the method of joint inversion of gravity and resistivity data.

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.

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.

A teaching-learning sequence of colour informed by history and philosophy of science

In this work, we present a teaching-learning sequence on colour intended to a pre-service elementary teacher programme informed by History and Philosophy of Science. Working in a socio-constructivist framework, we made an excursion on the history of colour. Our excursion through history of colour, as well as the reported misconception on colour helps us to inform the constructions of the teaching-learning sequence. We apply a questionnaire both before and after each of the two cycles of action-research in order to assess students’ knowledge evolution on colour and to evaluate our teaching-learning sequence. Finally, we present a discussion on the persistence of deep-rooted alternative conceptions.

Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

A didactic sequence of elementary geometric optics Informed by history and philosophy of science

The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic processwithout a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the teaching and learning process in mathematics but has been used in other disciplinary fields. It will be used in this work in order to clear up the main obstacles in the teachinglearning process of geometric optics. We proceed to argue that since Newton’s approach to optics, in his Book I of Opticks, is independent of the corpuscular or undulatory nature of light, it is the most suitable for a constructivist learning environment. However, Newton’s theory must be subject to a proper didactic transposition to help overcome the referred alternative concepts. Then is described our didactic transposition in order to create knowledge to be taught using a dialogical process between students’ previous knowledge, history of optics and the desired outcomes on geometrical optics in an elementary pre-service teacher training course. Finally, we use the scheme-facet structure of knowledge both to analyse and discuss our results as well as to illuminate shortcomings that must be addressed in our next stage of the inquiry.