number of systems, such as the World Wide Web (www) [3–5], Internet [6], social networks [7] or a cell [8], display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected by even unrealistically high failure rates. However,

regular fashion. These arise regularly in connection with extremal structures: such structures often have an unexpected degree of regularity and, because of this, often give rise to an association scheme. This in turn leads to a semisimple commutative algebra and the representation theory of this algebra

Abstract. The gastrointestinal tract is lined with a monolayer of cells that undergo perpetual and rapid renewal. Four principal, terminally differentiated cell types populate the monolayer, enterocytes, goblet cells, Paneth cells, and enteroendocrine cells. This epithelium exhibits complex patterns of regional differentiation, both from crypt-to-villus and from duodenumto-colon. The "liver " fatty acid binding protein (L-FABP) gene represents a useful model for analyzing the molecular basis for intestinal epithelial differentiation since it exhibits cell-specific, regionspecific, as well as developmental stage specific expression. We have previously linked portions of the 5' nontranscribed domain of the rat L-FABP gene to the human growth hormone (hGH) gene and analyzed expression

ones. PEAS operations are based on individual node's observation of the local environment and do not require any node to maintain per neighbor node state. PEAS performance possesses a high degree of robustness in the presence of both node power depletions and unexpected failures. Our simulations

energy exchange schedules that decrease the peak electricity demand and reduce the cost to consumers. The resulting charging and discharging schedules are assigned to tens of thousands of vehicles instantly as they plug into the grid and are robust to unexpected events in driving patterns. We give

In the last six years, several combinatorics problems have been solved in an unexpected way using high degree polynomials. The most well-known of these problems is the distinct distance problem in the plane. In [Erdős46], Erdős asked what is the smallest number of distinct distances determined

≥ 0, the least degrees α such that the Hilbert functions are positive (and hence to determining the classes of all effective divisors on blow ups of P d at r generic points). We also use this point of view for d = 2 to show that the following conjecture is, surprisingly, equivalent to the standard

.B.S.) Haldane, who entered the same institution (New College, Oxford) exactly one hundred years before him. Destined to become one of the foremost evolutionary biologists, he began with a mathematics scholarship, and then switched to ‘Greats ’ (Latin and ancient Greek), gaining a first-class degree under

Abstract. Let S(n) be the set of all polynomials of degree n with all roots in the unit disk, and define d(P) to be the maximum of the distances from each of the roots of a polynomial P to that root’s nearest critical point. In this notation, Sendov’s conjecture asserts that d(P) ≤ 1 for every P

regarding nematode neurobiology. Despite differences in size and habitat, C. elegans and A. suum share a surprisingly similar neuroanatomy. Here, we examined species across several clades in the phylum Nematoda and show that there is a surprising degree of neuroanatomical variation both within and among