102,700 research outputs found
Limit groups and groups acting freely on R^n-trees
We give a simple proof of the finite presentation of Sela's limit groups by
using free actions on R^n-trees. We first prove that Sela's limit groups do
have a free action on an R^n-tree. We then prove that a finitely generated
group having a free action on an R^n-tree can be obtained from free abelian
groups and surface groups by a finite sequence of free products and
amalgamations over cyclic groups. As a corollary, such a group is finitely
presented, has a finite classifying space, its abelian subgroups are finitely
generated and contains only finitely many conjugacy classes of non-cyclic
maximal abelian subgroups.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol8/paper39.abs.htm
The fully residually F quotients of F*<x,y>
We describe the fully residually F; or limit groups relative to F; (where F
is a free group) that arise from systems of equations in two variables over F
that have coefficients in F.Comment: 64 pages, 2 figures. Following recommendations from a referee, the
paper has been completely reorganized and many small mistakes have been
corrected. There were also a few gaps in the earlier version of the paper
that have been fixed. In particular much of the content of Section 8 in the
previous version had to be replaced. This paper is to appear in Groups. Geom.
Dy
A proteomic atlas of senescence-associated secretomes for aging biomarker development.
The senescence-associated secretory phenotype (SASP) has recently emerged as a driver of and promising therapeutic target for multiple age-related conditions, ranging from neurodegeneration to cancer. The complexity of the SASP, typically assessed by a few dozen secreted proteins, has been greatly underestimated, and a small set of factors cannot explain the diverse phenotypes it produces in vivo. Here, we present the "SASP Atlas," a comprehensive proteomic database of soluble proteins and exosomal cargo SASP factors originating from multiple senescence inducers and cell types. Each profile consists of hundreds of largely distinct proteins but also includes a subset of proteins elevated in all SASPs. Our analyses identify several candidate biomarkers of cellular senescence that overlap with aging markers in human plasma, including Growth/differentiation factor 15 (GDF15), stanniocalcin 1 (STC1), and serine protease inhibitors (SERPINs), which significantly correlated with age in plasma from a human cohort, the Baltimore Longitudinal Study of Aging (BLSA). Our findings will facilitate the identification of proteins characteristic of senescence-associated phenotypes and catalog potential senescence biomarkers to assess the burden, originating stimulus, and tissue of origin of senescent cells in vivo
Some Examples of Free actions on Products of Spheres
If and are finite groups with periodic Tate cohomology, then
acts freely and smoothly on some product .Comment: 17 pages. Final version: to appear in Topolog
Inductive-data-type Systems
In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the last
two authors presented a combined language made of a (strongly normalizing)
algebraic rewrite system and a typed lambda-calculus enriched by
pattern-matching definitions following a certain format, called the "General
Schema", which generalizes the usual recursor definitions for natural numbers
and similar "basic inductive types". This combined language was shown to be
strongly normalizing. The purpose of this paper is to reformulate and extend
the General Schema in order to make it easily extensible, to capture a more
general class of inductive types, called "strictly positive", and to ease the
strong normalization proof of the resulting system. This result provides a
computation model for the combination of an algebraic specification language
based on abstract data types and of a strongly typed functional language with
strictly positive inductive types.Comment: Theoretical Computer Science (2002
Theory of Interface: Category Theory, Directed Networks and Evolution of Biological Networks
Biological networks have two modes. The first mode is static: a network is a
passage on which something flows. The second mode is dynamic: a network is a
pattern constructed by gluing functions of entities constituting the network.
In this paper, first we discuss that these two modes can be associated with the
category theoretic duality (adjunction) and derive a natural network structure
(a path notion) for each mode by appealing to the category theoretic
universality. The path notion corresponding to the static mode is just the
usual directed path. The path notion for the dynamic mode is called lateral
path which is the alternating path considered on the set of arcs. Their general
functionalities in a network are transport and coherence, respectively. Second,
we introduce a betweenness centrality of arcs for each mode and see how the two
modes are embedded in various real biological network data. We find that there
is a trade-off relationship between the two centralities: if the value of one
is large then the value of the other is small. This can be seen as a kind of
division of labor in a network into transport on the network and coherence of
the network. Finally, we propose an optimization model of networks based on a
quality function involving intensities of the two modes in order to see how
networks with the above trade-off relationship can emerge through evolution. We
show that the trade-off relationship can be observed in the evolved networks
only when the dynamic mode is dominant in the quality function by numerical
simulations. We also show that the evolved networks have features qualitatively
similar to real biological networks by standard complex network analysis.Comment: 59 pages, minor corrections from v
Tits Geometry and Positive Curvature
There is a well known link between (maximal) polar representations and
isotropy representations of symmetric spaces provided by Dadok. Moreover, the
theory by Tits and Burns-Spatzier provides a link between irreducible symmetric
spaces of non-compact type of rank at least three and irreducible topological
spherical buildings of rank at least three.
We discover and exploit a rich structure of a (connected) chamber system of
finite (Coxeter) type M associated with any polar action of cohomogeneity at
least two on any simply connected closed positively curved manifold. Although
this chamber system is typically not a Tits geometry of type M, we prove that
in all cases but two that its universal Tits cover indeed is a building. We
construct a topology on this universal cover making it into a compact spherical
building in the sense of Burns and Spatzier. Using this structure we classify
up to equivariant diffeomorphism all polar actions on (simply connected)
positively curved manifolds of cohomogeneity at least two.Comment: 43 pages, to appear in Acta Mathematic
On the construction problem for Hodge numbers
For any symmetric collection of natural numbers h^{p,q} with p+q=k, we
construct a smooth complex projective variety whose weight k Hodge structure
has these Hodge numbers; if k=2m is even, then we have to impose that h^{m,m}
is bigger than some quadratic bound in m. Combining these results for different
weights, we solve the construction problem for the truncated Hodge diamond
under two additional assumptions. Our results lead to a complete classification
of all nontrivial dominations among Hodge numbers of Kaehler manifolds.Comment: 34 pages; final version, to appear in Geometry & Topolog
- …