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812
Error and attack tolerance of complex networks
, 2000
"... Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network [1]. C ..."
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Cited by 1013 (7 self)
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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,
Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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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
Mapping enteroendocrine cell populations in transgenic mice reveals an unexpected degree of complexity in cellular differentiation within the gastrointestinal tract
 J. Cell
, 1990
"... 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 ..."
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Cited by 13 (4 self)
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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 crypttovillus and from duodenumtocolon. The "liver " fatty acid binding protein (LFABP) gene represents a useful model for analyzing the molecular basis for intestinal epithelial differentiation since it exhibits cellspecific, regionspecific, as well as developmental stage specific expression. We have previously linked portions of the 5' nontranscribed domain of the rat LFABP gene to the human growth hormone (hGH) gene and analyzed expression
PEAS: A Robust Energy Conserving Protocol for Longlived Sensor Networks
, 2003
"... In this paper we present PEAS, a robust energyconserving protocol that can build longlived, resilient sensor networks using a very large number of small sensors with short battery lifetime. PEAS extends the network lifetime by maintaining a necessary set of working nodes and turning o redundant one ..."
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Cited by 349 (5 self)
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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
FOR THE DEGREE OF
"... Over the few next decades, the personal vehicle may evolve into a device distinct from what exists today. This thesis considers energy and communication systems among vehicles that utilize two developing technologies: batterypowered drive trains and accurate sensors. We use linear optimization to c ..."
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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
UNEXPECTED APPLICATIONS OF POLYNOMIALS IN COMBINATORICS
"... In the last six years, several combinatorics problems have been solved in an unexpected way using high degree polynomials. The most wellknown of these problems is the distinct distance problem in the plane. In [Erdős46], Erdős asked what is the smallest number of distinct distances determined by ..."
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Cited by 1 (0 self)
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In the last six years, several combinatorics problems have been solved in an unexpected way using high degree polynomials. The most wellknown of these problems is the distinct distance problem in the plane. In [Erdős46], Erdős asked what is the smallest number of distinct distances determined
The (unexpected) importance of knowing α
, 2008
"... and for providing such a pleasant environment for discussing mathematics, and the NSA for its support of his research. We show that the determination, for all r ≥ 0, of the Hilbert functions of all fat point subschemes of P d with support at r generic points is equivalent to determining, for all r ≥ ..."
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Cited by 1 (0 self)
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≥ 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
COMMENT The unexpected always happens
"... Last October my son went off to University. Always a wrench, these life transitions, and they seem to happen so fast. One moment fighting in the bath with plastic dinosaurs, and the next moment leaving home, to do battle with the lecture, the launderette and the bank account. He has followed not in ..."
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.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 firstclass degree under
Unexpected local extrema for the Sendov conjecture
"... 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 ∈ ..."
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Cited by 2 (0 self)
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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
Unexpected Variation in Neuroanatomy among Diverse
, 2015
"... Nematodes are considered excellent models for understanding fundamental aspects of neuron function. However, nematodes are less frequently used as models for examining the evolution of nervous systems. While the habitats and behaviors of nematodes are diverse, the neuroanatomy of nematodes is often ..."
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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
Results 1  10
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812