TY - JOUR AB - Although nuclear envelope (NE) assembly is known to require the GTPase Ran, the membrane fusion machinery involved is uncharacterized. NE assembly involves formation of a reticular network on chromatin, fusion of this network into a closed NE and subsequent expansion. Here we show that p97, an AAA-ATPase previously implicated in fusion of Golgi and transitional endoplasmic reticulum (ER) membranes together with the adaptor p47, has two discrete functions in NE assembly. Formation of a closed NE requires the p97–Ufd1–Npl4 complex, not previously implicated in membrane fusion. Subsequent NE growth involves a p97–p47 complex. This study provides the first insights into the molecular mechanisms and specificity of fusion events involved in NE formation. AU - HETZER, Martin W AU - Meyer, Hemmo H. AU - Walther, Tobias C. AU - Bilbao-Cortes, Daniel AU - Warren, Graham AU - Mattaj, Iain W. ID - 11125 IS - 12 JF - Nature Cell Biology KW - Cell Biology SN - 1465-7392 TI - Distinct AAA-ATPase p97 complexes function in discrete steps of nuclear assembly VL - 3 ER - TY - JOUR AB - We present the first fully dynamic algorithm for maintaining a minimum spanning forest in time 𝑜(𝑛√) per operation. To be precise, the algorithm uses O(n1/3 log n) amortized time per update operation. The algorithm is fairly simple and deterministic. An immediate consequence is the first fully dynamic deterministic algorithm for maintaining connectivity and bipartiteness in amortized time O(n1/3 log n) per update, with O(1) worst case time per query. AU - Henzinger, Monika H AU - King, Valerie ID - 11892 IS - 2 JF - SIAM Journal on Computing SN - 0097-5397 TI - Maintaining minimum spanning forests in dynamic graphs VL - 31 ER - TY - CONF AB - Previous studies of the Web graph structure have focused on the graph structure at the level of individual pages. In actuality the Web is a hierarchically nested graph, with domains, hosts and Web sites introducing intermediate levels of affiliation and administrative control. To better understand the growth of the Web we need to understand its macro-structure, in terms of the linkage between Web sites. We approximate this by studying the graph of the linkage between hosts on the Web. This was done based on snapshots of the Web taken by Google in Oct 1999, Aug 2000 and Jun 2001. The connectivity between hosts is represented by a directed graph, with hosts as nodes and weighted edges representing the count of hyperlinks between pages on the corresponding hosts. We demonstrate how such a "hostgraph" can be used to study connectivity properties of hosts and domains over time, and discuss a modified "copy model" to explain observed link weight distributions as a function of subgraph size. We discuss changes in the Web over time in the size and connectivity of Web sites and country domains. We also describe a data mining application of the hostgraph: a related host finding algorithm which achieves a precision of 0.65 at rank 3. AU - Bharat, K. AU - Chang, Bay-Wei AU - Henzinger, Monika H AU - Ruhl, M. ID - 11914 SN - 15504786 T2 - 1st IEEE International Conference on Data Mining TI - Who links to whom: Mining linkage between Web sites ER - TY - GEN AB - A molecular classification method is based on a space filling description of a molecule. The three dimensional body corresponding to the space filling molecular structure is divided into Voronoi regions to provide a basis for efficiently processing local structural information. A Delaunay triangulation provides a basis for systematically processing information relating to the Voronoi regions into shape descriptors in the form of topological elements. Preferably, additional shape and/or property descriptors are included in the classification method. The classification methods generally are used to identify similarities between molecules that can be used as property predictors for a variety of applications. Generally, the property predictions are the basis for selection of compounds for incorporation into efficacy evaluations. AU - Liang, Jie AU - Edelsbrunner, Herbert ID - 3507 TI - Molecular classification for property prediction ER - TY - BOOK AB - The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The original motivation for these topics was the difficulty faced (both conceptually and in the technical execution) in any attempt to combine elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains recent breakthrough solutions to meshing that fit into this category.The book should be an ideal graduate text for courses on mesh generation. The specific material is selected giving preference to topics that are elementary, attractive, lend themselves to teaching, useful, and interesting. AU - Edelsbrunner, Herbert ID - 3586 SN - 0-521-79309-2 TI - Geometry and Topology for Mesh Generation VL - 7 ER - TY - CONF AU - Krishnendu Chatterjee AU - Dasgupta, Pallab AU - Chakrabarti, Partha P ID - 3447 TI - Weighted quantified computation tree logic ER - TY - JOUR AB - For diffeomorphisms of smooth compact manifolds, we consider the problem of how fast the number of periodic points with period $n$grows as a function of $n$. In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily fast growth is possible; in fact, the first author has shown that arbitrarily fast growth is topologically (Baire) generic for $C^2$ or smoother diffeomorphisms. In the present work we show that, by contrast, for a measure-theoretic notion of genericity we call ``prevalence'', the growth is not much faster than exponential. Specifically, we show that for each $\delta > 0$, there is a prevalent set of ( $C^{1+\rho}$ or smoother) diffeomorphisms for which the number of period $n$ points is bounded above by $\operatorname{exp}(C n^{1+\delta})$ for some $C$ independent of $n$. We also obtain a related bound on the decay of the hyperbolicity of the periodic points as a function of $n$. The contrast between topologically generic and measure-theoretically generic behavior for the growth of the number of periodic points and the decay of their hyperbolicity shows this to be a subtle and complex phenomenon, reminiscent of KAM theory. AU - Kaloshin, Vadim AU - Hunt, Brian R. ID - 8522 IS - 4 JF - Electronic Research Announcements of the American Mathematical Society KW - General Mathematics SN - 1079-6762 TI - A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms I VL - 7 ER - TY - JOUR AB - We continue the previous article's discussion of bounds, for prevalent diffeomorphisms of smooth compact manifolds, on the growth of the number of periodic points and the decay of their hyperbolicity as a function of their period $n$. In that article we reduced the main results to a problem, for certain families of diffeomorphisms, of bounding the measure of parameter values for which the diffeomorphism has (for a given period $n$) an almost periodic point that is almost nonhyperbolic. We also formulated our results for $1$-dimensional endomorphisms on a compact interval. In this article we describe some of the main techniques involved and outline the rest of the proof. To simplify notation, we concentrate primarily on the $1$-dimensional case. AU - Kaloshin, Vadim AU - Hunt, Brian R. ID - 8521 IS - 5 JF - Electronic Research Announcements of the American Mathematical Society KW - General Mathematics SN - 1079-6762 TI - A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms II VL - 7 ER - TY - JOUR AB - A number α∈R is diophantine if it is not well approximable by rationals, i.e. for some C,ε>0 and any relatively prime p,q∈Z we have |αq−p|>Cq−1−ε. It is well-known and is easy to prove that almost every α in R is diophantine. In this paper we address a noncommutative version of the diophantine properties. Consider a pair A,B∈SO(3) and for each n∈Z+ take all possible words in A, A -1, B, and B - 1 of length n, i.e. for a multiindex I=(i1,i1,…,im,jm) define |I|=∑mk=1(|ik|+|jk|)=n and \( W_n(A,B ) = \{W_{\cal I}(A,B) = A^{i_1} B^{j_1} \dots A^{i_m} B^{j_m}\}_{|{\cal I|}=n \).¶Gamburd—Jakobson—Sarnak [GJS] raised the problem: prove that for Haar almost every pair A,B∈SO(3) the closest distance of words of length n to the identity, i.e. sA,B(n)=min|I|=n∥WI(A,B)−E∥, is bounded from below by an exponential function in n. This is the analog of the diophantine property for elements of SO(3). In this paper we prove that s A,B (n) is bounded from below by an exponential function in n 2. We also exhibit obstructions to a “simple” proof of the exponential estimate in n. AU - Kaloshin, Vadim AU - Rodnianski, I. ID - 8524 IS - 5 JF - Geometric And Functional Analysis SN - 1016-443X TI - Diophantine properties of elements of SO(3) VL - 11 ER - TY - JOUR AB - Epigenetic silenced alleles of the Arabidopsis SUPERMANlocus (the clark kent alleles) are associated with dense hypermethylation at noncanonical cytosines (CpXpG and asymmetric sites, where X = A, T, C, or G). A genetic screen for suppressors of a hypermethylated clark kent mutant identified nine loss-of-function alleles of CHROMOMETHYLASE3(CMT3), a novel cytosine methyltransferase homolog. These cmt3 mutants display a wild-type morphology but exhibit decreased CpXpG methylation of the SUP gene and of other sequences throughout the genome. They also show reactivated expression of endogenous retrotransposon sequences. These results show that a non-CpG DNA methyltransferase is responsible for maintaining epigenetic gene silencing. AU - Lindroth, A. M. AU - Cao, Xiaofeng AU - Jackson, James P. AU - Zilberman, Daniel AU - McCallum, Claire M. AU - Henikoff, Steven AU - Jacobsen, Steven E. ID - 9444 IS - 5524 JF - Science KW - Multidisciplinary SN - 0036-8075 TI - Requirement of CHROMOMETHYLASE3 for maintenance of CpXpG methylation VL - 292 ER -