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Homological coverings of graphs
 Journal of London Mathematical Society II
, 1984
"... The homology group of a graph, with any coefficient ring, can be used to construct covering graphs. The properties of the covering graphs are studied, and it, is proved that they admit groups of automorphisms related to the group of the base graph. In the case of cubic graphs the construction throws ..."
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Cited by 11 (0 self)
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The homology group of a graph, with any coefficient ring, can be used to construct covering graphs. The properties of the covering graphs are studied, and it, is proved that they admit groups of automorphisms related to the group of the base graph. In the case of cubic graphs the construction
Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual CalabiYau manifolds V, W of dimension n (not necessarily equal to 3) one has dim H p (V, Ω q) = dim H n−p (W, Ω q). Physicists conjectured that conformal field theories associated with mirror varieties are equivalent. Mathematically, MS is considered now as a relation between numbers of rational curves on such a manifold and Taylor coefficients of periods of Hodge structures considered as functions on the moduli space of complex structures on a mirror manifold. Recently it has been realized that one can make predictions for numbers of curves of positive genera and also on CalabiYau manifolds of arbitrary dimensions. We will not describe here the complicated history of the subject and will not mention many beautiful contsructions, examples and conjectures motivated
The SWISSMODEL Workspace: A webbased environment for protein structure homology modelling
 BIOINFORMATICS
, 2005
"... Motivation: Homology models of proteins are of great interest for planning and analyzing biological experiments when no experimental threedimensional structures are available. Building homology models requires specialized programs and uptodate sequence and structural databases. Integrating all re ..."
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Cited by 555 (5 self)
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Motivation: Homology models of proteins are of great interest for planning and analyzing biological experiments when no experimental threedimensional structures are available. Building homology models requires specialized programs and uptodate sequence and structural databases. Integrating all
SWISSMODEL: an automated protein homologymodeling server
 Nucleic Acids Research
, 2003
"... SWISSMODEL ..."
Minimum Cuts and Shortest NonSeparating Cycles via Homology Covers
 SYMPOSIUM ON DISCRETE ALGORITHMS
, 2011
"... Let G be a directed graph with weighted edges, embedded on a surface of genus g with b boundaries. We describe an algorithm to compute the shortest directed cycle in G in any given � 2homology class in 2 O(g+b) n log n time; this problem is NPhard even for undirected graphs. We also present two ap ..."
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Cited by 18 (5 self)
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surface graphs in 2 O(g) n log n time, improving an algorithm of Chambers et al. [SOCG 2009] for all positive g. Unlike earlier algorithms for surface graphs that construct and search finite portions of the universal cover, our algorithms use another canonical covering space, called the Z 2homology cover.
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning
Rho GTPases and the actin cytoskeleton
 Science
, 1998
"... The actin cytoskeleton mediates a variety of essential biological functions in all eukaryotic cells. In addition to providing a structural framework around which cell shape and polarity are defined, its dynamic properties provide the driving force for cells to move and to divide. Understanding the b ..."
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Cited by 589 (4 self)
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The actin cytoskeleton mediates a variety of essential biological functions in all eukaryotic cells. In addition to providing a structural framework around which cell shape and polarity are defined, its dynamic properties provide the driving force for cells to move and to divide. Understanding the biochemical mechanisms that control the organization of actin is thus a major goal of contemporary cell biology, with implications for health and disease. Members of the Rho family of small guanosine triphosphatases have emerged as key regulators of the actin cytoskeleton, and furthermore, through their interaction with multiple target proteins, they ensure coordinated control of other cellular activities such as gene transcription and adhesion. The story begins back in the early 1990s with the analysis of Rho, then a newly described member of the Ras superfamily of small guanosine triphosphatases (GTPases). In Swiss 3T3 fibroblasts, it was shown that Rho can be activated by the addition of extracellular ligands [for example, lysophosphatidic acid] and that Rho activation leads to the assembly of contractile actinmyosin filaments (stress fibers) and of associated focal adhesion complexes (Fig. 1, C and D) (1). It was concluded that Rho acts as a molecular switch to control a signal transduction pathway that links membrane receptors to the cytoskeleton. Rac, the next member of the Rho family to be analyzed, could be activated by a distinct set of agonists (for example, plateletderived growth factor or insulin), leading to the assembly of a meshwork of actin filaments at the cell periphery to produce lamellipodia and membrane ruffles (Fig. 1E) (2). More recently, activation of Cdc42, a third member of the Rho subfamily, was shown to induce actinrich surface protrusions called filopodia (Fig. 1G) (3, 4). As with Rho, the cytoskeletal changes induced by Rac and Cdc42 are also associated with distinct, integrinbased adhesion complexes (Fig. 1, F and H) (3). Moreover, there is significant crosstalk between GTPases of the Ras and
Premotor cortex and the recognition of motor actions
 Cognitive Brain Research
, 1996
"... In area F5 of the monkey premotor cortex there are neurons that discharge both when the monkey performs an action and when he observes a similar action made by another monkey or by the experimenter. We report here some of the properties of these 'mirror' neurons and we propose that their a ..."
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Cited by 702 (44 self)
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In area F5 of the monkey premotor cortex there are neurons that discharge both when the monkey performs an action and when he observes a similar action made by another monkey or by the experimenter. We report here some of the properties of these 'mirror' neurons and we propose that their activity 'represents ' the observed action. We posit, then, that this motor epresentation is at the basis of the understanding of motor events. Finally, on the basis of some recent data showing that, in man, the observation of motor actions activate the posterior part of inferior frontal gyrus, we suggest that the development of the lateral verbal communication system in man derives from a more ancient communication system based on recognition of hand and face gestures.
Accurate whole human genome sequencing using reversible terminator chemistry. Nature 456: 53–59
, 2008
"... ..."
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