130 research outputs found
Packing dimensions of the divergence points of self-similar measures with the open set condition
Let be the self-similar measure supported on the self-similar set
with open set condition. In this article, we discuss the packing dimension of
the set for
, where denotes the
set of accumulation points of \frac{\log\mu(B(x,r))}{\log r}r\searrow0$.
Our main result solves the conjecture about packing dimension posed by Olsen
and Winter \cite{OlsWin} and generalizes the result in \cite{BaeOlsSni}.Comment: 13 page
Multifractal Analysis of Ergodic Averages in Some Nonuniformly Hyperbolic Systems
This article is devoted to the study of the multifractal analysis of ergodic
averages in some nonuniformly hyperbolic systems. In particular, our results
hold for the robust classes of multidimensional nonuniformly expanding local
diffeomorphisms and Viana maps.Comment: 15 page
Multifractal analysis for historic set in topological dynamical systems
In this article, the historic set is divided into different level sets and we
use topological pressure to describe the size of these level sets. We give an
application of these results to dimension theory. Especially, we use
topological pressure to describe the relative multifractal spectrum of ergodic
averages and give a positive answer to the conjecture posed by L. Olsen (J.
Math. Pures Appl. {\bf 82} (2003)).Comment: 30 page
The variational principle of local pressure for actions of sofic group
This study establishes the variational principle for local pressure in the
sofic context.Comment: 13 page
The Bowen's topological entropy of the Cartesian product sets
This article is devoted to showing the product theorem for Bowen's
topological entropy.Comment: 11 pages. arXiv admin note: text overlap with arXiv:1012.1103 by
other author
The Historic Set of Ergodic Averages in Some Nonuniformly Hyperbolic Systems
This article is devoted to the study of the historic set of ergodic averages
in some nonuniformly hyperbolic systems. In particular, our results hold for
the robust classes of multidimensional nonuniformly expanding local
diffeomorphisms and Viana maps.Comment: 18 pages. Comments are welcome. arXiv admin note: text overlap with
arXiv:1310.234
Topological pressure, mistake functions and average metric
In this paper, we showed that the Pesin pressure of any subset under a
mistake function is equal to the classical Pesin pressure of the subset in
dynamical systems. Our result extended the result of [1] in additive case,
which proved the topological pressure of the whole system is self adaptable
under a mistake function. As an application, we showed that the Pesin pressure
defined by average metric is equal to the classical Pesin pressure.Comment: 7 page
Shadowing and mixing on systems of countable group actions
Let be a dynamical system, where is compact Hausdorff space,
and is a countable discrete group. We investigate shadowing property and
mixing between subshifts and general dynamical systems. For the shadowing
property, fix some finite subset . We prove that if is totally
disconnected, then has -shadowing property if and only if
is conjugate to an inverse limit of a sequence of shifts of finite
type which satisfies Mittag-Leffler condition. Also, suppose that is metric
space (may be not totally disconnected), we prove that if has
-shadowing property, then is a factor of an inverse limit of a
sequence of shifts of finite type by a factor map which almost lifts
pseudo-orbit for .
On the other hand, let property be one of the following property:
transitivity, minimal, totally transitivity, weakly mixing, mixing, and
specification property. We prove that if is totally disconnected, then
has property if and only if is conjugate to an inverse
limit of an inverse system that consists of subshifts with property which
satisfies Mittag-Leffler condition. Also, for the case of metric space (may be
not totally disconnected), if property is not minimal or specification
property, we prove that has property if and only if is
a factor of an inverse limit of a sequence of subshifts with property which
satisfies Mittag-Leffler condition.Comment: 23 page
Entropy and Emergence of Topological Dynamical Systems
A topological dynamical system induces two natural systems, one is on
the probability measure spaces and other one is on the hyperspace.
We introduce a concept for these two spaces, which is called entropy order,
and prove that it coincides with topological entropy of . We also
consider the entropy order of an invariant measure and a variational principle
is established.Comment: Any comments are welcom
AXNet: ApproXimate computing using an end-to-end trainable neural network
Neural network based approximate computing is a universal architecture
promising to gain tremendous energy-efficiency for many error resilient
applications. To guarantee the approximation quality, existing works deploy two
neural networks (NNs), e.g., an approximator and a predictor. The approximator
provides the approximate results, while the predictor predicts whether the
input data is safe to approximate with the given quality requirement. However,
it is non-trivial and time-consuming to make these two neural network
coordinate---they have different optimization objectives---by training them
separately. This paper proposes a novel neural network structure---AXNet---to
fuse two NNs to a holistic end-to-end trainable NN. Leveraging the philosophy
of multi-task learning, AXNet can tremendously improve the invocation
(proportion of safe-to-approximate samples) and reduce the approximation error.
The training effort also decrease significantly. Experiment results show 50.7%
more invocation and substantial cuts of training time when compared to existing
neural network based approximate computing framework.Comment: Accepted by ICCAD 201
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