Scalar field breathers on anti-de Sitter background

We study spatially localized, time-periodic solutions (breathers) of scalar field theories with various self-interacting potentials on Anti-de Sitter (AdS) spacetimes in $D$ dimensions. A detailed numerical study of spherically symmetric configurations in $D=3$ dimensions is carried out, revealing a rich and complex structure of the phase-space (bifurcations, resonances). Scalar breather solutions form one-parameter families parametrized by their amplitude, $\varepsilon$, while their frequency, $\omega=\omega(\varepsilon)$, is a function of the amplitude. The scalar breathers on AdS we find have a small amplitude limit, tending to the eigenfunctions of the linear Klein-Gordon operator on AdS. Importantly most of these breathers appear to be generically stable under time evolution.Comment: 30 pages, 22 figure

Self-gravitating scalar breathers with negative cosmological constant

Breather-type (time-periodic and spatially localized) solutions with spherical symmetry are investigated in a massless scalar field theory coupled to Einstein's gravity with cosmological constant in $d$ spatial dimensions imposing anti de Sitter (AdS) asymptotics on space-time. Using a code constructed with the Kadath library that enables the use of spectral methods, the phase space of breather solutions is explored in detail for $d=3$ and $d=4$. It is found that there are discrete families of solutions indexed by an integer and by their frequency. Using a time evolution code these AdS breathers are found to be stable for up to a critical central density, in analogy to boson stars. Using an analytical perturbative expansion small amplitude breathers are worked out for arbitrary dimensions $d$.Comment: 24 pages, 13 figures, one figure and references added, version accepted for Phys. Rev.

A humán és a patkány húgyhólyag purinerg és kolinerg jelátviteli útvonalainak szerepe a hólyagkontrakció szabályozásában = Cholinergic and purinergic signalisation of the regulation of micturition in human and rat urinary bladders

Összefoglalva elmondhatjuk, hogy az atropin jobban gátolja mind a spontán hólyagkontrakciókat, mind a téringerléssel kiváltott választ idősebb patkányok húgyhólyagjában. Ráadásul a hólyagcsúcs atropinérzékenysége fokozottabban csökken az életkor előrehaladásakor. Ezzel párhuzamosan a carbachol stimuláló hatása hasonló életkor és hólyagterület függést mutat. Az alfa-beta-metil ATP hatásának életkorfüggése alternál az előzőekkel, ami a purinerg jelátvitel jelentőségének fokozódását mutatja az idősebb állatokban. A bemutatott kísérletek klinikai jelentősége kettős. Egyrészt az adatok alapján úgy tűnik, hogy a húgyhólyag telődés és ürülés szabályozásának klasszikus leírását felül kell vizsgálnunk. Másrészt a 2-3 hetes patkány húgyhólyag az un. „túlstimulált” hólyag (overactive bladder) kórképét mutatja. Ennek következtében a patkány hólyag szabályozási folyamatainak feltérképezése, mint állatmodell, alapvető jelentőségű lehet az emberekben kialakuló „túlstimulált” hólyag mechanizmusának megismerésében és terápiájának továbbfejlesztésében. | In summary, we can say that the atropine has more inhibitory effect both spontaneous and evoked bladder contractions in aged rats. The atropine sensitivity of the urinary bladder’s dome is greater decreases in aged animals. In parallel, the stimulatory effect of carbachol shows similar age and bladder area dependence. The age dependence of the alpha-beta-methylene ATP’s effect shows opposite tendency, which means that the purinergic signaling more significant in the older animals. The clinical significance of the presented experiments is double. First, based on the presented data the classic description of the regulation of filling and emptying of the bladder should be re-examined. On the other hand, the 2-3 weeks old rat urinary bladder shows the picture of overactive bladder. As a result, the mapping of rat bladder regulatory processes, such as animal model, may be essential for us to understand the mechanism of “overactive"" bladder and for the further development of therapy

Two-colorings with many monochromatic cliques in both colors

Color the edges of the n-vertex complete graph in red and blue, and suppose that red k-cliques are fewer than blue k-cliques. We show that the number of red k-cliques is always less than cknk, where ck∈(0, 1) is the unique root of the equation zk=(1-z)k+kz(1-z)k-1. On the other hand, we construct a coloring in which there are at least cknk-O(nk-1) red k-cliques and at least the same number of blue k-cliques. © 2013 Elsevier Inc

Radiation of scalar oscillons in 2 and 3 dimensions

The radiation loss of small-amplitude radially symmetric oscillons (long-living, spatially localized, time-dependent solutions) in two- and three-dimensional scalar field theories is computed analytically in the small-amplitude expansion. The amplitude of the radiation is beyond all orders in perturbation theory and it is determined using matched asymptotic series expansions and Borel summation. The general results are illustrated on the case of the two- and three-dimensional sine-Gordon theory and a two-dimensional $\phi^6$ model. The analytic predictions are found to be in good agreement with the results of numerical simulations of oscillons.Comment: 7 pages, 3 figure

SIS epidemic propagation on hypergraphs

Mathematical modeling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infection pressure on the number of infected neighbours. The exact master equations of the propagation process are derived for an arbitrary hypergraph given by its incidence matrix. Based on these, moment closure approximation and mean-field models are introduced and compared to individual-based stochastic simulations. The simulation algorithm, developed for networks, is extended to hypergraphs. The effects of hypergraph structure and the model parameters are investigated via individual-based simulation results