768 research outputs found
High energy limits of Laplace-type and Dirac-type eigenfunctions and frame flows
We relate high-energy limits of Laplace-type and Dirac-type operators to
frame flows on the corresponding manifolds, and show that the ergodicity of
frame flows implies quantum ergodicity in an appropriate sense for those
operators. Observables for the corresponding quantum systems are matrix-valued
pseudodifferential operators and therefore the system remains non-commutative
in the high-energy limit. We discuss to what extent the space of stationary
high-energy states behaves classically.Comment: 26 pages, latex2
The Algebra of Strand Splitting. I. A Braided Version of Thompson's Group V
We construct a braided version of Thompson's group V.Comment: 27 page
PageRank in scale-free random graphs
We analyze the distribution of PageRank on a directed configuration model and
show that as the size of the graph grows to infinity it can be closely
approximated by the PageRank of the root node of an appropriately constructed
tree. This tree approximation is in turn related to the solution of a linear
stochastic fixed point equation that has been thoroughly studied in the recent
literature
The chameleon groups of Richard J. Thompson: automorphisms and dynamics
The automorphism groups of several of Thompson's countable groups of
piecewise linear homeomorphisms of the line and circle are computed and it is
shown that the outer automorphism groups of these groups are relatively small.
These results can be interpreted as stability results for certain structures of
PL functions on the circle. Machinery is developed to relate the structures on
the circle to corresponding structures on the line
Smoluchowski-Kramers approximation in the case of variable friction
We consider the small mass asymptotics (Smoluchowski-Kramers approximation)
for the Langevin equation with a variable friction coefficient. The limit of
the solution in the classical sense does not exist in this case. We study a
modification of the Smoluchowski-Kramers approximation. Some applications of
the Smoluchowski-Kramers approximation to problems with fast oscillating or
discontinuous coefficients are considered.Comment: already publishe
Isomorphisms of Brin-Higman-Thompson groups
Let be positive integers with . Let
denote the ring that is universal with an invertible matrix. Let
denote the ring of matrices over the tensor
product of copies of . In a natural way, is a
partially ordered ring with involution. Let denote the
group of positive unitary elements. We show that is
isomorphic to the Brin-Higman-Thompson group ; the case was
found by Pardo, that is, is isomorphic to the Higman-Thompson group
. We survey arguments of Abrams, \'Anh, Bleak, Brin, Higman, Lanoue,
Pardo, and Thompson that prove that if and only
if , and (if and only if
and are isomorphic as
partially ordered rings with involution).Comment: 24 page
Distributed Generation and Resilience in Power Grids
We study the effects of the allocation of distributed generation on the
resilience of power grids. We find that an unconstrained allocation and growth
of the distributed generation can drive a power grid beyond its design
parameters. In order to overcome such a problem, we propose a topological
algorithm derived from the field of Complex Networks to allocate distributed
generation sources in an existing power grid.Comment: proceedings of Critis 2012 http://critis12.hig.no
Elementary amenable subgroups of R. Thompson's group F
The subgroup structure of Thompson's group F is not yet fully understood. The
group F is a subgroup of the group PL(I) of orientation preserving, piecewise
linear self homeomorphisms of the unit interval and this larger group thus also
has a poorly understood subgroup structure. It is reasonable to guess that F is
the "only" subgroup of PL(I) that is not elementary amenable. In this paper, we
explore the complexity of the elementary amenable subgroups of F in an attempt
to understand the boundary between the elementary amenable subgroups and the
non-elementary amenable. We construct an example of an elementary amenable
subgroup up to class (height) omega squared, where omega is the first infinite
ordinal.Comment: 20 page
You can't see what you can't see: Experimental evidence for how much relevant information may be missed due to Google's Web search personalisation
The influence of Web search personalisation on professional knowledge work is
an understudied area. Here we investigate how public sector officials
self-assess their dependency on the Google Web search engine, whether they are
aware of the potential impact of algorithmic biases on their ability to
retrieve all relevant information, and how much relevant information may
actually be missed due to Web search personalisation. We find that the majority
of participants in our experimental study are neither aware that there is a
potential problem nor do they have a strategy to mitigate the risk of missing
relevant information when performing online searches. Most significantly, we
provide empirical evidence that up to 20% of relevant information may be missed
due to Web search personalisation. This work has significant implications for
Web research by public sector professionals, who should be provided with
training about the potential algorithmic biases that may affect their judgments
and decision making, as well as clear guidelines how to minimise the risk of
missing relevant information.Comment: paper submitted to the 11th Intl. Conf. on Social Informatics;
revision corrects error in interpretation of parameter Psi/p in RBO resulting
from discrepancy between the documentation of the implementation in R
(https://rdrr.io/bioc/gespeR/man/rbo.html) and the original definition
(https://dl.acm.org/citation.cfm?id=1852106) as per 20/05/201
Multifractal properties of return time statistics
Fluctuations in the return time statistics of a dynamical system can be
described by a new spectrum of dimensions. Comparison with the usual
multifractal analysis of measures is presented, and difference between the two
corresponding sets of dimensions is established. Theoretical analysis and
numerical examples of dynamical systems in the class of Iterated Functions are
presented.Comment: 4 pages, 3 figure
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