1,049 research outputs found
Tachyon Condensation on the Elliptic Curve
We use the framework of matrix factorizations to study topological B-type
D-branes on the cubic curve. Specifically, we elucidate how the brane RR
charges are encoded in the matrix factors, by analyzing their structure in
terms of sections of vector bundles in conjunction with equivariant R-symmetry.
One particular advantage of matrix factorizations is that explicit moduli
dependence is built in, thus giving us full control over the open-string moduli
space. It allows one to study phenomena like discontinuous jumps of the
cohomology over the moduli space, as well as formation of bound states at
threshold. One interesting aspect is that certain gauge symmetries inherent to
the matrix formulation lead to a non-trivial global structure of the moduli
space. We also investigate topological tachyon condensation, which enables us
to construct, in a systematic fashion, higher-dimensional matrix factorizations
out of smaller ones; this amounts to obtaining branes with higher RR charges as
composites of ones with minimal charges. As an application, we explicitly
construct all rank-two matrix factorizations.Comment: 69p, 6 figs, harvmac; v2: minor change
Examples of integrable sub-Riemannian geodesic flows
Motivated by a paper of Bolsinov and Taimanov DG/9911193 we consider
non-holonomic situation and exhibit examples of sub-Riemannian metrics with
integrable geodesic flows and positive topological entropy. Moreover the
Riemannian examples are obtained as "holonomization" of sub-Riemannian ones. A
feature of non-holonomic situation is non-compactness of the phase space.
We also exhibit a Liouvulle-integrable Hamiltonian system with topological
entropy of all integrals positive.Comment: 21 pages; Answer to the self-posed question is added: Is it possible
to construct Liouville-integrable Hamiltonian system with positive
topological entropies of all integrals? Yes and we present an exampl
A Network Coding Approach to Loss Tomography
Network tomography aims at inferring internal network characteristics based
on measurements at the edge of the network. In loss tomography, in particular,
the characteristic of interest is the loss rate of individual links and
multicast and/or unicast end-to-end probes are typically used. Independently,
recent advances in network coding have shown that there are advantages from
allowing intermediate nodes to process and combine, in addition to just
forward, packets. In this paper, we study the problem of loss tomography in
networks with network coding capabilities. We design a framework for estimating
link loss rates, which leverages network coding capabilities, and we show that
it improves several aspects of tomography including the identifiability of
links, the trade-off between estimation accuracy and bandwidth efficiency, and
the complexity of probe path selection. We discuss the cases of inferring link
loss rates in a tree topology and in a general topology. In the latter case,
the benefits of our approach are even more pronounced compared to standard
techniques, but we also face novel challenges, such as dealing with cycles and
multiple paths between sources and receivers. Overall, this work makes the
connection between active network tomography and network coding
- …