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.

Preserving the validity of the two-Higgs-doublet model up to the Planck scale

We examine the constraints on the two Higgs doublet model (2HDM) due to the stability of the scalar potential and absence of Landau poles at energy scales below the Planck scale. We employ the most general 2HDM that incorporates an approximately Standard Model (SM) Higgs boson with a flavor aligned Yukawa sector to eliminate potential tree-level Higgs-mediated flavor changing neutral currents. Using basis independent techniques, we exhibit robust regimes of the 2HDM parameter space with a 125 GeV SM-like Higgs boson that is stable and perturbative up to the Planck scale. Implications for the heavy scalar spectrum are exhibited.

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.

Explosion birth and extinction: Double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models

This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called "box-within-a-box" type. The double big bang bifurcations are related to the existence of flip codimension-2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena.

Search for charged Higgs bosons decaying via H± → τ±ν in fully hadronic final states using pp collision data at √s = 8 TeV with the ATLAS detector

The results of a search for charged Higgs bosons decaying to a τ lepton and a neutrino, H±→τ±ν, are presented. The analysis is based on 19.5 fb−1 of proton--proton collision data at s√=8 TeV collected by the ATLAS experiment at the Large Hadron Collider. Charged Higgs bosons are searched for in events consistent with top-quark pair production or in associated production with a top quark. The final state is characterised by the presence of a hadronic τ decay, missing transverse momentum, b-tagged jets, a hadronically decaying W boson, and the absence of any isolated electrons or muons with high transverse momenta. The data are consistent with the expected background from Standard Model processes. A statistical analysis leads to 95% confidence-level upper limits on the product of branching ratios B(t→bH±)×B(H±→τ±ν), between 0.23% and 1.3% for charged Higgs boson masses in the range 80--160 GeV. It also leads to 95% confidence-level upper limits on the production cross section times branching ratio, σ(pp→tH±+X)×B(H±→τ±ν), between 0.76 pb and 4.5 fb, for charged Higgs boson masses ranging from 180 GeV to 1000 GeV. In the context of different scenarios of the Minimal Supersymmetric Standard Model, these results exclude nearly all values of tanβ above one for charged Higgs boson masses between 80 GeV and 160 GeV, and exclude a region of parameter space with high tanβ for H± masses between 200 GeV and 250 GeV.

ATLAS Run 1 searches for direct pair production of third-generation squarks at the Large Hadron Collider

This paper reviews and extends searches for the direct pair production of the scalar supersymmetric partners of the top and bottom quarks in proton--proton collisions collected by the ATLAS collaboration during the LHC Run 1. Most of the analyses use 20 fb−1 of collisions at a centre-of-mass energy of s√=8 TeV, although in some case an additional 4.7 fb−1 of collision data at s√=7 TeV are used. New analyses are introduced to improve the sensitivity to specific regions of the model parameter space. Since no evidence of third-generation squarks is found, exclusion limits are derived by combining several analyses and are presented in both a simplified model framework, assuming simple decay chains, as well as within the context of more elaborate phenomenological supersymmetric models.

The behavior of money velocity in low and high inflation countries

This paper presents a general equilibrium model of money demand where the velocity of money changes in response to endogenous fluctuations in the interest rate. The parameter space can be divided into two subsets: one where velocity is constant as in standard cash-in-advance models, and another one where velocity fluctuates as in Baumol (1952). The model provides an explanation of why, for a sample of 79 countries, the correlation between the velocity of money and the inflation rate appears to be low, unlike common wisdom would suggest. The reason is the diverse transaction technologies available in different economies.

A Data mining approach to indirect inference

Consider a model with parameter phi, and an auxiliary model with parameter theta. Let phi be a randomly sampled from a given density over the known parameter space. Monte Carlo methods can be used to draw simulated data and compute the corresponding estimate of theta, say theta_tilde. A large set of tuples (phi, theta_tilde) can be generated in this manner. Nonparametric methods may be use to fit the function E(phi|theta_tilde=a), using these tuples. It is proposed to estimate phi using the fitted E(phi|theta_tilde=theta_hat), where theta_hat is the auxiliary estimate, using the real sample data. This is a consistent and asymptotically normally distributed estimator, under certain assumptions. Monte Carlo results for dynamic panel data and vector autoregressions show that this estimator can have very attractive small sample properties. Confidence intervals can be constructed using the quantiles of the phi for which theta_tilde is close to theta_hat. Such confidence intervals are found to have very accurate coverage.

Extended truncated Tweedie-Poisson model

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed poisson distributions and that, other than for the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Considering the extended model also allows one to use the basic maximum likelihood based inference tools when parameter estimates fall in the extended part of the parameter space, and hence when the m.l.e. does not exist under the unextended model. This extended truncated Tweedie-Poisson model is proved to be useful in the analysis of words and species frequency count data.

Weak and Strong Altruism in Trait Groups: Reproductive Suicide, Personal Fitness, and Expected Value

A simple variant of trait group selection, employing predators as the mechanism underlying group selection, supports contingent reproductive suicide as altruism (i.e., behavior lowering personal fitness while augmenting that of another) without kin assortment. The contingent suicidal type may either saturate the population or be polymorphic with a type avoiding suicide, depending on parameters. In addition to contingent suicide, this randomly assorting morph may also exhibit continuously expressed strong altruism (sensu Wilson 1979) usually thought restricted to kin selection. The model will not, however, support a sterile worker caste as such, where sterility occurs before life history events associated with effective altruism; reproductive suicide must remain fundamentally contingent (facultative sensu West Eberhard 1987; Myles 1988) under random assortment. The continuously expressed strong altruism supported by the model may be reinterpreted as probability of arbitrarily committing reproductive suicide, without benefit for another; such arbitrary suicide (a "load" on "adaptive" suicide) is viable only under a more restricted parameter space relative to the necessarily concomitant adaptive contingent suicide.

Circulation of private notes during a currency shortage

This paper provides a search theoretical model that captures two phenomena that have characterized several episodes of monetary history: currency shortages and the circulation of privately issued notes. As usual in these models, the media of exchange are determined as part of the equilibrium. We characterize all the different equilibria and specify the conditions under which there is a currency shortage and/or privately issued notes are used as means of payment. There is multiplicity of equilibria for the entire parameter space, but there always exist an equilibrium in which notes circulate, either alone or together with coins. Hence, credit is a self-fulfilling phenomenon that depends on the beliefs of agents about the acceptability and future repayment of notes. The degree of circulation of coins depends on two crucial parameters, the intrinsic utility of holding coins and the extent with which it is possible to find exchange opportunities in the market.

The variability of money velocity in a generalized cash-in-advance model

This paper presents a general equilibrium model of money demand wherethe velocity of money changes in response to endogenous fluctuations in the interest rate. The parameter space can be divided into two subsets: one where velocity is constant and equal to one as in cash-in-advance models, and another one where velocity fluctuates as in Baumol (1952). Despite its simplicity, in terms of paramaters to calibrate, the model performs surprisingly well. In particular, it approximates the variability of money velocity observed in the U.S. for the post-war period. The model is then used to analyze the welfare costs of inflation under uncertainty. This application calculates the errors derived from computing the costs of inflation with deterministic models. It turns out that the size of this difference is small, at least for the levels of uncertainty estimated for the U.S. economy.

A dynamic model for stem cell homeostasis and patterning in Arabidopsis meristems.

Plants maintain stem cells in their meristems as a source for new undifferentiated cells throughout their life. Meristems are small groups of cells that provide the microenvironment that allows stem cells to prosper. Homeostasis of a stem cell domain within a growing meristem is achieved by signalling between stem cells and surrounding cells. We have here simulated the origin and maintenance of a defined stem cell domain at the tip of Arabidopsis shoot meristems, based on the assumption that meristems are self-organizing systems. The model comprises two coupled feedback regulated genetic systems that control stem cell behaviour. Using a minimal set of spatial parameters, the mathematical model allows to predict the generation, shape and size of the stem cell domain, and the underlying organizing centre. We use the model to explore the parameter space that allows stem cell maintenance, and to simulate the consequences of mutations, gene misexpression and cell ablations.

Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Black holes as fundamental strings: Comparing the absorption of scalars

The recently proposed correspondence principle of Horowitz and Polchinski provides a concrete means to relate (among others) black holes with electric Neveu-SchwarzNeveu-Schwarz charges to fundamental strings and correctly match their entropies. We further test this correspondence by examining the greybody factors in the absorption rates of neutral, minimally coupled scalars by a near extremal black hole. Perhaps surprisingly, the results disagree in general with the absorption by weakly coupled strings. Though this does not disprove the correspondence, it indicates that it might not be simple in this region of the black hole parameter space.