Helly dimension of algebraic groups

It is shown that for a linear algebraic group G over a field of characteristic zero, there is a natural number \kappa(G) such that if a system of Zariski closed cosets in G has empty intersection, then there is a subsystem consisting of at most \kappa(G) cosets with empty intersection. This is applied to the study of algebraic group actions on product varieties.Comment: 18 page

The Blazhko effect and additional excited modes in RR Lyrae stars

Recent photometric space missions, such as CoRoT and Kepler revealed that many RR Lyrae stars pulsate -- beyond their main radial pulsation mode -- in low amplitude modes. Space data seem to indicate a clear trend, namely overtone (RRc) stars and modulated fundamental (RRab) RR Lyrae stars ubiquitously show additional modes, while non-Blazhko RRab stars never do. Two Kepler stars (V350 Lyr and KIC 7021124), however, apparently seemed to break this rule: they were classified as non-Blazhko RRab stars showing additional modes. We processed Kepler pixel photometric data of these stars. We detected small amplitude, but significant Blazhko effect for both stars by using the resulted light curves and O$-$C diagrams. This finding strengthens the apparent connection between the Blazhko effect and the excitation of additional modes. In addition, it yields a potential tool for detecting Blazhko stars through the additional frequency patterns even if we have only short but accurate time series observations. V350 Lyr shows the smallest amplitude multiperiodic Blazhko effect ever detected.Comment: 6 pages, 4 figures and 2 tables. Accepted for publication in ApJ Letter

Blood Vessel Tortuosity Selects against Evolution of Agressive Tumor Cells in Confined Tissue Environments: a Modeling Approach

Cancer is a disease of cellular regulation, often initiated by genetic mutation within cells, and leading to a heterogeneous cell population within tissues. In the competition for nutrients and growth space within the tumors the phenotype of each cell determines its success. Selection in this process is imposed by both the microenvironment (neighboring cells, extracellular matrix, and diffusing substances), and the whole of the organism through for example the blood supply. In this view, the development of tumor cells is in close interaction with their increasingly changing environment: the more cells can change, the more their environment will change. Furthermore, instabilities are also introduced on the organism level: blood supply can be blocked by increased tissue pressure or the tortuosity of the tumor-neovascular vessels. This coupling between cell, microenvironment, and organism results in behavior that is hard to predict. Here we introduce a cell-based computational model to study the effect of blood flow obstruction on the micro-evolution of cells within a cancerous tissue. We demonstrate that stages of tumor development emerge naturally, without the need for sequential mutation of specific genes. Secondly, we show that instabilities in blood supply can impact the overall development of tumors and lead to the extinction of the dominant aggressive phenotype, showing a clear distinction between the fitness at the cell level and survival of the population. This provides new insights into potential side effects of recent tumor vasculature renormalization approaches

Pushing the limits: K2 observations of the trans-Neptunian objects 2002 GV31 and (278361) 2007 JJ43

We present the first photometric observations of trans-Neptunian objects (TNOs) taken with the Kepler space telescope, obtained in the course of the K2 ecliptic survey. Two faint objects have been monitored in specifically designed pixel masks that were centered on the stationary points of the objects, when their daily motion was the slowest. In the design of the experiment, only the apparent path of these objects were retrieved from the detectors, i.e. the costs in terms of Kepler pixels were minimized. Because of the faintness of the targets we employ specific reduction techniques and co-added images. We measure rotational periods and amplitudes in the unfiltered Kepler band as follows: for (278361) 2007 JJ43 and 2002 GV31 we get P_rot=12.097 h and P_rot=29.2 h while 0.10 and 0.35 mag for the total amplitudes, respectively. Future space missions, like TESS and PLATO are not well suited to this kind of observations. Therefore, we encourage to include the brightest TNOs around their stationary points in each observing campaign to exploit this unique capability of the K2 Mission -- and therefore to provide unbiased rotational, shape and albedo characteristics of many objects.Comment: Accepted for publication in ApJ Letters, 5.2 pages in emulateapj style, misspelled 2007 JJ43 designation correcte

Frozen to death? -- Detection of comet Hale-Bopp at 30.7 AU

Comet Hale--Bopp (C/1995 O1) has been the single most significant comet encountered by modern astronomy, still having displayed significant activity at 25.7 AU solar distance in late 2007. It is a puzzling question when and where this activity will finally cease. Here we present new observations with the ESO 2.2m telescope at La Silla to check the activity of Hale--Bopp at 30.7 AU solar distance. On 2010-12-04, 26 CCD images were taken with 180 s exposure times for photometry and morphology. The comet was detected in R and had a total brightness of 23.3+-0.2 mag, referring to an absolute brightness of R(1,1,0)=8.3. The profile of the coma was star-like at a seeing of 1.9", without any evidence of a coma or tail extending farther than 2.5" (=55,000 km in projection) and exceeding 26.5 mag/arcs^2 surface brightness. The measured total brightness corresponds to a relative total reflecting surface, a_RC, of 485 km^2, nine times less than three years before. The calculated a_RC value would imply a nucleus with 60--65 km radius assuming 4% albedo. This size estimate is in significant contradiction with the previous results scattering around 35 km. Therefore we suggest that the comet may still be in a low-level activity, despite the lack of a prominent coma. Alternatively, if the nucleus is already dormant, the albedo should be as high as 13%, assuming a radius of 35 km. With this observation, Hale--Bopp has been the most distant comet ever observed, far beyond the orbit of Neptune.Comment: 4 pages, accepted by A&

Particle-based simulation of ellipse-shaped particle aggregation as a model for vascular network formation

Computational modelling is helpful for elucidating the cellular mechanisms driving biological morphogenesis. Previous simulation studies of blood vessel growth based on the Cellular Potts model (CPM) proposed that elongated, adhesive or mutually attractive endothelial cells suffice for the formation of blood vessel sprouts and vascular networks. Because each mathematical representation of a model introduces potential artifacts, it is important that model results are reproduced using alternative modelling paradigms. Here, we present a lattice-free, particle-based simulation of the cell elongation model of vasculogenesis. The new, particle-based simulations confirm the results obtained from the previous Cellular Potts simulations. Furthermore, our current findings suggest that the emergence of order is possible with the application of a high enough attractive force or, alternatively, a longer attraction radius. The methodology will be applicable to a range of problems in morphogenesis and noisy particle aggregation in which cell shape is a key determining factor.Comment: 9 pages, 11 figures, 2 supplementary videos (on Youtube), submitted to Computational Particle Mechanics, special issue: Jos\'e-Manuel Garcia Aznar (Ed.) Particle-based simulations on cell and biomolecular mechanic

Kepler RR Lyrae stars: beyond period doubling

We examined the complete short cadence sample of Kepler RR Lyrae stars to further investigate the recently discovered dynamical effects such as period doubling and additional modes. Here we present the findings on four stars. V450 Lyr may be a non-classical double-mode RR Lyrae star pulsating in the fundamental mode and the second overtone. In three cases we observe the interaction of three different modes. Since the period ratios are close to resonant values, we observe quasi-repetiting patterns in the pulsation cycles in the stars. These findings support the mode-resonance explanations of the Blazhko effect.Comment: 2 pages, 1 figure. Proceedings of the 301st IAU Symposium, Precision Asteroseismology, August 2013, Wroc{\l}aw. V2: small corrections to the wordin