Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method

As originally formulated, the Generalized Alignment Index (GALI) method of chaos detection has so far been applied to distinguish quasiperiodic from chaotic motion in conservative nonlinear dynamical systems. In this paper we extend its realm of applicability by using it to investigate the local dynamics of periodic orbits. We show theoretically and verify numerically that for stable periodic orbits the GALIs tend to zero following particular power laws for Hamiltonian flows, while they fluctuate around non-zero values for symplectic maps. By comparison, the GALIs of unstable periodic orbits tend exponentially to zero, both for flows and maps. We also apply the GALIs for investigating the dynamics in the neighborhood of periodic orbits, and show that for chaotic solutions influenced by the homoclinic tangle of unstable periodic orbits, the GALIs can exhibit a remarkable oscillatory behavior during which their amplitudes change by many orders of magnitude. Finally, we use the GALI method to elucidate further the connection between the dynamics of Hamiltonian flows and symplectic maps. In particular, we show that, using for the computation of GALIs the components of deviation vectors orthogonal to the direction of motion, the indices of stable periodic orbits behave for flows as they do for maps.Comment: 17 pages, 9 figures (accepted for publication in Int. J. of Bifurcation and Chaos

The Inevitability of Corruption in Greek Football

This is an Accepted Manuscript of an article published by Taylor & Francis in Soccer & Society on 14th March 2017, available online: http://www.tandfonline.com/10.1080/14660970.2017.1302936.From the late 1990s corrupt practices in Greek football have been considered to pose a serious threat to the integrity of the sport, with a number of schemes and measures being introduced as a response. The aim of this article is to show why corruption in Greek football is inevitable by offering a detailed account of three football-related corrupt practices and highlighting their contextual parameters, as well as juxtaposing them against the set of measures that have been implemented. By placing corruption in football in the wider landscape of the country and of global football, and examining the political, structural and economic factors that contribute to the overall managerial and financial implications of corruption, we present the reader with the new norm which, in reality, makes corruption the ‘only game in town’

Experimental and Modeled Assessment of Interventions to Reduce PM2.5 in a Residence during aWildfire Event

Increasingly large and frequent wildfires affect air quality even indoors by emitting and dispersing fine/ultrafine particulate matter known to pose health risks to residents. With this health threat, we are working to help the building science community develop simplified tools that may be used to estimate impacts to large numbers of homes based on high-level housing characteristics. In addition to reviewing literature sources, we performed an experiment to evaluate interventions to mitigate degraded indoor air quality. We instrumented one residence for one week during an extreme wildfire event in the Pacific Northwest. Outdoor ambient concentrations of PM2.5 reached historic levels, sustained at over 200 μg/m3 for multiple days. Outdoor and indoor PM2.5 were monitored, and data regarding building characteristics, infiltration, and mechanical system operation were gathered to be consistent with the type of information commonly known for residential energy models. Two conditions were studied: a high-capture minimum efficiency rated value (MERV 13) filter integrated into a central forced air (CFA) system, and a CFA with MERV 13 filtration operating with a portable air cleaner (PAC). With intermittent CFA operation and no PAC, indoor corrected concentrations of PM2.5 reached 280 μg/m3, and indoor/outdoor (I/O) ratios reached a mean of 0.55. The measured I/O ratio was reduced to a mean of 0.22 when both intermittent CFA and the PAC were in operation. Data gathered from the test home were used in a modeling exercise to assess expected I/O ratios from both interventions. The mean modeled I/O ratio for the CFA with an MERV 13 filter was 0.48, and 0.28 when the PAC was added. The model overpredicted the MERV 13 performance and underpredicted the CFA with an MERV 13 filter plus a PAC, though both conditions were predicted within 0.15 standard deviation. The results illustrate the ways that models can be used to estimate indoor PM2.5 concentrations in residences during extreme wildfire smoke events

On error estimates for Galerkin finite element methods for the Camassa-Holm equation

We consider the Camassa-Holm (CH) equation, a nonlinear dispersive wave equation that models one-way propagation of long waves of moderately small amplitude. We discretize in space the periodic initial-value problem for CH (written in its original and in system form), using the standard Galerkin finite element method with smooth splines on a uniform mesh, and prove optimal-order $L^{2}$-error estimates for the semidiscrete approximation. We also consider an initial-boundary-value problem on a finite interval for the system form of CH and analyze the convergence of its standard Galerkin semidiscretization. Using the fourth-order accurate, explicit, "classical" Runge-Kutta scheme for time-stepping, we construct a highly accurate, stable, fully discrete scheme that we employ in numerical experiments to approximate solutions of CH, mainly smooth travelling waves and nonsmooth solitons of the `peakon' type

Brain reward function in people who use cannabis : A systematic review

Rationale: Cannabis is one of the most widely used psychoactive substances globally. Cannabis use can be associated with alterations of reward processing, including affective flattening, apathy, anhedonia, and lower sensitivity to natural rewards in conjunction with higher sensitivity to cannabis-related rewards. Such alterations have been posited to be driven by changes in underlying brain reward pathways, as per prominent neuroscientific theories of addiction. Functional neuroimaging (fMRI) studies have examined brain reward function in cannabis users via the monetary incentive delay (MID) fMRI task; however, this evidence is yet to be systematically synthesised. Objectives: We aimed to systematically integrate the evidence on brain reward function in cannabis users examined by the MID fMRI task; and in relation to metrics of cannabis exposure (e.g., dosage, frequency) and other behavioural variables. Method: We pre-registered the review in PROSPERO and reported it using PRISMA guidelines. Literature searches were conducted in PsycINFO, PubMed, Medline, CINAHL, and Scopus. Results: Nine studies were included, comprising 534 people with mean ages 16-to-28 years, of which 255 were people who use cannabis daily or almost daily, and 279 were controls. The fMRI literature to date led to largely non-significant group differences. A few studies reported group differences in the ventral striatum while participants anticipated rewards and losses; and in the caudate while participants received neutral outcomes. A few studies examined correlations between brain function and withdrawal, dosage, and age of onset; and reported inconsistent findings. Conclusions: There is emerging but inconsistent evidence of altered brain reward function in cannabis users examined with the MID fMRI task. Future fMRI studies are required to confirm if the brain reward system is altered in vulnerable cannabis users who experience a Cannabis Use Disorder, as postulated by prominent neuroscientific theories of addiction

Case series and a systematic review concerning the level of the aortic bifurcation

Background: The aim of this study is to present the level of aortic bifurcation in a sample of Greek origin (case series) and to perform an up-to-date systematic review in the existing literature. Materials and methods: Seventy-six formalin-fixed adult cadavers were dissected and studied in order to research the level of aortic bifurcation. Additionally, PubMed and Google Scholar databases were searched for eligible articles concerning the level of aortic bifurcation for the period up to February 2020. Results: The mean level of aortic bifurcation according to our case series was the lower third of the L4 vertebral body (21/76, 27.6%). The level of aortic bifurcation ranged between the lower third of the L3 vertebral body and the lower third of the L5 body. No statistically significant correlation was found between the two sexes. The systematic review of the literature revealed 31 articles which were considered eligible and a total number of 3537 specimens were retracted. According to the recorded findings the most common mean level of aortic bifurcation was the body of L4 vertebra (1495/3537 cases, 42.2%), while the range of aortic bifurcation was described to occur from upper third of L3 vertebrae to the upper third of the S1 vertebrae in the 52.8% of the cases (1866/3537). Conclusions: The mean level of AA corresponds to the body of L4 and presents a great range (form L3U to S1U). Knowledge of the mean level of aortic bifurcation and its probable ranges is of great significance for interventional radiologists and especially vascular surgeons that deal with aneurism proximal to the aortic bifurcation

Chaotic Dynamics of N-degree of Freedom Hamiltonian Systems

We investigate the connection between local and global dynamics of two N-degree of freedom Hamiltonian systems with different origins describing one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a discretized version of the nonlinear Schrodinger equation related to Bose-Einstein Condensation (BEC). We study solutions starting in the vicinity of simple periodic orbits (SPOs) representing in-phase (IPM) and out-of-phase motion (OPM), which are known in closed form and whose linear stability can be analyzed exactly. Our results verify that as the energy E increases for fixed N, beyond the destabilization threshold of these orbits, all positive Lyapunov exponents exhibit a transition between two power laws, occurring at the same value of E. The destabilization energy E_c per particle goes to zero as N goes to infinity following a simple power-law. However, using SALI, a very efficient indicator we have recently introduced for distinguishing order from chaos, we find that the two Hamiltonians have very different dynamics near their stable SPOs: For example, in the case of the FPU system, as the energy increases for fixed N, the islands of stability around the OPM decrease in size, the orbit destabilizes through period-doubling bifurcation and its eigenvalues move steadily away from -1, while for the BEC model the OPM has islands around it which grow in size before it bifurcates through symmetry breaking, while its real eigenvalues return to +1 at very high energies. Still, when calculating Lyapunov spectra, we find for the OPMs of both Hamiltonians that the Lyapunov exponents decrease following an exponential law and yield extensive Kolmogorov--Sinai entropies per particle, in the thermodynamic limit of fixed energy density E/N with E and N arbitrarily large.Comment: 29 pages, 10 figures, published at International Journal of Bifurcation and Chaos (IJBC

Anatomical study of the common iliac arteries

Background: The common iliac arteries (CIA) are the two terminal branches of the abdominal aorta which supply the pelvis and the lower extremities. The present study aims to examine the morphometric features of the CIA in a cadaveric sample and possible correlations between lengths.Materials and methods: Seventy-six formalin fixed cadavers of Greek origin were dissected in the Department of Anatomy, School of Medicine, National and Kapodistrian University of Athens. In each cadaver dissected, the abdominal aorta and the CIA were identified and their lengths were measured. Also the torso length was measured and the height of each cadaver. All the statistical analysis was done by SPSS 15.0.Results: The mean length of the left CIA was 6.12 cm (SD: ± 1.791, SE: 0.205) and that of the right one was 6.03 cm (SD: ± 1.607, SE: 0.184). The lengths of the CIA differed between the sexes, but no statistically significant difference was observed. Statistically significant differences regarding the torso lengths and body heights were found between the sexes, as well as a statistically strong correlation between the lengths of the left and right CIA in the cadavers dissected.Conclusions: The knowledge of the anatomy and morphology of the CIA is ofgreat clinical significance, given that abnormal course, length or branching pattern of these vessels are not uncommon and their clinical impact may be great. Mostly interventional radiologists and vascular surgeons should be aware of this knowledge