On Gauge Invariance and Spontaneous Symmetry Breaking

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.Comment: 13 pages, latex, no figure

Quantitative analysis of regulatory flexibility under changing environmental conditions

The circadian clock controls 24-h rhythms in many biological processes, allowing appropriate timing of biological rhythms relative to dawn and dusk. Known clock circuits include multiple, interlocked feedback loops. Theory suggested that multiple loops contribute the flexibility for molecular rhythms to track multiple phases of the external cycle. Clear dawn- and dusk-tracking rhythms illustrate the flexibility of timing in Ipomoea nil. Molecular clock components in Arabidopsis thaliana showed complex, photoperiod-dependent regulation, which was analysed by comparison with three contrasting models. A simple, quantitative measure, Dusk Sensitivity, was introduced to compare the behaviour of clock models with varying loop complexity. Evening-expressed clock genes showed photoperiod-dependent dusk sensitivity, as predicted by the three-loop model, whereas the one- and two-loop models tracked dawn and dusk, respectively. Output genes for starch degradation achieved dusk-tracking expression through light regulation, rather than a dusk-tracking rhythm. Model analysis predicted which biochemical processes could be manipulated to extend dusk tracking. Our results reveal how an operating principle of biological regulators applies specifically to the plant circadian clock

Influence of team success, fixture congestion and playing position on physical performance of elite youth soccer players during an international tournament

The purpose of the present study was to examine the influence of team success, fixture congestion and playing position on physical performance of elite youth soccer players during an international tournament. Physical match data was collected from 22 matches for U17 soccer players (n = 112) across 12 clubs during the play-off stage of the 2015-2016 Future Talents Cup International tournament. Match data was collected using a GPS device for physical performance measures across different positions, level of team success and during match congestion (MD1, MD 2 and MD3). The top ranked teams produced significantly higher total and low speed running distances compared to bottom ranked teams (p < .05). Players covered significantly more total distance and PlayerLoad TM on MD1 compared to MD2 and MD3 (p < .05). High speed distance output remained unaffected during this period of match congestion. Central defenders were found to have the lowest output across physical performance variables compared to all other positions (p < .05). Wide players (WD and WM) produced the greatest outputs at higher speed distances compared to other positions (p < .05). Therefore, the present study revealed that teams who had higher levels of success produced greater physical outputs compared to those of lower rankings. Match congestion resulted in a reduction in total and lower speed distances covered. Finally, differences in physical demands across playing positions was evident. Coaches should be aware of the implications of fatigue during periods of fixture congestion and the individual positional requirements for youth soccer players

Scattering theory for Klein-Gordon equations with non-positive energy

We study the scattering theory for charged Klein-Gordon equations: \{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. where: \epsilon^{2}(x, D_{x})= \sum_{1\leq j, k\leq n}(\p_{x_{j}} \i b_{j}(x))A^{jk}(x)(\p_{x_{k}} \i b_{k}(x))+ m^{2}(x), describing a Klein-Gordon field minimally coupled to an external electromagnetic field described by the electric potential $v(x)$ and magnetic potential $\vec{b}(x)$. The flow of the Klein-Gordon equation preserves the energy: h[f, f]:= \int_{\rr^{n}}\bar{f}_{1}(x) f_{1}(x)+ \bar{f}_{0}(x)\epsilon^{2}(x, D_{x})f_{0}(x) - \bar{f}_{0}(x) v^{2}(x) f_{0}(x) \d x. We consider the situation when the energy is not positive. In this case the flow cannot be written as a unitary group on a Hilbert space, and the Klein-Gordon equation may have complex eigenfrequencies. Using the theory of definitizable operators on Krein spaces and time-dependent methods, we prove the existence and completeness of wave operators, both in the short- and long-range cases. The range of the wave operators are characterized in terms of the spectral theory of the generator, as in the usual Hilbert space case

Regional spreading of paleo-gravel formations in north-western Croatia and their geomorphological importance for explantion of morphogenesis and neotectonical movements

U ovom se članku obrađuje regionalna distribucija kvartarnih šljunčanih naslaga u dijelu sjeverozapadne Hrvatske, kao i njihovovo geomorfološko značenje u tumačenju morfogeneze reljefa i kvartarnih neotektonskih pokreta.Regionally distributed Quaternary fluvial gravel layers in North-western Croatia, which were by neotectonic movements subsequently removed at different hypsometrical levels, are discussed in the paper

MOST light-curve analysis of the γ Doradus pulsator HR 8799, showing resonances and amplitude variations

Context. The central star of the HR 8799 system is a γ Doradus-type pulsator. The system harbours four planetary-mass companions detected by direct imaging, and is a good solar system analogue. The masses of the companions are not accurately known because the estimation depends greatly on the age of the system, which is also not known with sufficient accuracy. Asteroseismic studies of the star might help to better constrain the age of HR 8799. We organized an extensive photometric and multi-site spectroscopic observing campaign to study the pulsations of the central star. Aims: The aim of the present study is to investigate the pulsation properties of HR 8799 in detail via the ultra-precise 47 d nearly continuous photometry obtained with the Microvariability and Oscillations in STars (MOST) space telescope, and to find as many independent pulsation modes as possible, which is the prerequisite for an asteroseismic age determination. Methods: We carried out Fourier analysis of the wide-band photometric time series. Results: We find that resonance and sudden amplitude changes characterize the pulsation of HR 8799. The dominant frequency is always at f1 = 1.978 d-1.Many multiples of one-ninth of the dominant frequency appear in the Fourier spectrum of the MOST data: n/9 f1, where n = {1,2,3,4,5,6,7,8,9,10,13,14,17,18}. Our analysis also reveals that many of these peaks show strong amplitude decrease and phase variations even on the 47 d time scale. The dependencies between the pulsation frequencies of HR 8799 make the planned subsequent asteroseismic analysis rather difficult. We point out some resemblance between the light curve of HR 8799 and the modulated pulsation light curves of Blazhko RR Lyrae stars. Based on data from the MOST satellite, a Canadian Space Agency mission, jointly operated by Dynacon Inc., the University of Toronto Institute for Aerospace Studies and the University of British Columbia, with the assistance of the University of Vienna

Array algorithms for H^2 and H^∞ estimation

Currently, the preferred method for implementing H^2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Using our recent observation that H^∞ filtering coincides with Kalman filtering in Krein space, in this chapter we develop array algorithms for H^∞ filtering. These can be regarded as natural generalizations of their H^2 counterparts, and involve propagating the indefinite square roots of the quantities of interest. The H^∞ square-root and fast array algorithms both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H^∞ filters. These conditions are built into the algorithms themselves so that an H^∞ estimator of the desired level exists if, and only if, the algorithms can be executed. However, since H^∞ square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H^2 case, further investigation is needed to determine the numerical behavior of such algorithms

MOST light-curve analysis of the [gamma] Doradus pulsator HR8799, showing resonances and amplitude variations

Publisher's Version/PDFContext. The central star of the HR 8799 system is a &gamma; Doradus-type pulsator. The system harbours four planetary-mass companions detected by direct imaging, and is a good solar system analogue. The masses of the companions are not accurately known because the estimation depends greatly on the age of the system, which is also not known with sufficient accuracy. Asteroseismic studies of the star might help to better constrain the age of HR 8799. We organized an extensive photometric and multi-site spectroscopic observing campaign to study the pulsations of the central star. Aims. The aim of the present study is to investigate the pulsation properties of HR 8799 in detail via the ultra-precise 47 d nearly continuous photometry obtained with the Microvariability and Oscillations in STars (MOST) space telescope, and to find as many independent pulsation modes as possible, which is the prerequisite for an asteroseismic age determination. Methods. We carried out Fourier analysis of the wide-band photometric time series. Results. We find that resonance and sudden amplitude changes characterize the pulsation of HR 8799. The dominant frequency is always at f1 = 1.978 d&minus;1. Many multiples of one-ninth of the dominant frequency appear in the Fourier spectrum of the MOST data: n/9 f1, where n = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 14, 17, 18}. Our analysis also reveals that many of these peaks show strong amplitude decrease and phase variations even on the 47 d time scale. The dependencies between the pulsation frequencies of HR 8799 make the planned subsequent asteroseismic analysis rather difficult. We point out some resemblance between the light curve of HR 8799 and the modulated pulsation light curves of Blazhko RR Lyrae star