We have investigated spreading of postmitotic PtK2 cells and the behavior of actin filaments in this system by time-lapse microscopy and photoactivation of fluorescence. During mitosis PtK2 cells round up and at cytokinesis the daughter cells spread back to regain their interphase morphology. Normal spreading edges are quite homogenous and are not comprised of two distinct areas (lamellae and l...

Soon after the discovery of x-rays by Roentgen, radioactivity by Becquerel, and radium by the Curies, it was concluded that x-rays could not only be used for diagnostic purposes but also for therapy [1,2]. In the early years of radiation therapy, physicians had little understanding or knowledge of the physical nature and biological effects of radiation, the delivered doses were not certain, the...

Let shape P be any simply-connected set in the plane, bounded by a Jordan curve, that is not a circular disk. We say that a set of points I on the boundary of P immobilize the shape if any rigid motion of P in the plane causes at least one point of I to penetrate the interior of P. We prove that four points always suffice to immobilize any shape. For a large class of shapes, which includes poly...

We consider undirected non-regular connected graphs without loops and multiple edges (other than complete bipartite graphs) which have exactly three distinct eigenvalues (such graphs are called non-standard graphs). The interest in these graphs is motivated by the questions posed by W. Haemers during the 15th British Combinatorial Conference (Stirling, July 1995); the main question concerned th...

dark and deep, but the shallow, sunlit edges are where most of the cichlids live. Brown or green Eretmodus algae scrapers, covered with blue spots, thrive among the breaking waves; the turbulent water pushes their rounded backs onto the rock surfaces instead of pulling them off. These fish nip algae off the rocks with their chisel-like teeth. Their neighbors the Tanganicodus insect pickers also...

Round robin tournaments are used in a wide variety of competition settings and especially in recreational sports leagues. The outcomes of such tournaments can be modelled by an orientation of the edges of a complete graph, where each vertex corresponds to a unique competitor. A score sequence is an nondecreasing sequence of the out-degrees of such a graph. In this paper we analyze two previousl...

The d-ary back-to-back tree of height k, BBT k d , consists of two complete d-ary trees of height k the leaves of which are identiied. For a proper coloring of the edges of BBT k d with c d + 1 colors, we consider periodic gossiping, i.e. full-duplex all-to-all broadcasting in the 1-port model where communication is made on a link of color i at any time (round) i mod c. We present a coloring fo...

Last year, during the. rainy season, many cases of painful ulcer, round in shape, covered with dirty sloughs and undermined edges, were admitted in the District Hospital, Unao. They went on spreading and often several ulcers existed on one leg, but all of them were situated on the legs. All of them came to the hospital after about a fortnight or a month when they had tried all other treatment o...

In an Achlioptas process two random pairs of {1, . . . , n} arrive in each round and the player has to choose one of them. We study the very restrictive version where player’s decisions cannot depend on the previous history and only one vertex from the two random edges is revealed. We prove that the player can create a giant component in (2 √ 5 − 4 + o(1))n = (0.4721 . . . + o(1))n rounds and t...