5,124 research outputs found
Almost isomorphism for countable state Markov shifts
Countable state Markov shifts are a natural generalization of the well-known
subshifts of finite type. They are the subject of current research both for
their own sake and as models for smooth dynamical systems. In this paper, we
investigate their almost isomorphism and entropy conjugacy and obtain a
complete classification for the especially important class of strongly positive
recurrent Markov shifts. This gives a complete classification up to entropy
conjugacy of the natural extensions of smooth entropy expanding maps, including
all smooth interval maps with non-zero topological entropy
An Efficient Data Structure for Dynamic Two-Dimensional Reconfiguration
In the presence of dynamic insertions and deletions into a partially
reconfigurable FPGA, fragmentation is unavoidable. This poses the challenge of
developing efficient approaches to dynamic defragmentation and reallocation.
One key aspect is to develop efficient algorithms and data structures that
exploit the two-dimensional geometry of a chip, instead of just one. We propose
a new method for this task, based on the fractal structure of a quadtree, which
allows dynamic segmentation of the chip area, along with dynamically adjusting
the necessary communication infrastructure. We describe a number of algorithmic
aspects, and present different solutions. We also provide a number of basic
simulations that indicate that the theoretical worst-case bound may be
pessimistic.Comment: 11 pages, 12 figures; full version of extended abstract that appeared
in ARCS 201
Recovering metric from full ordinal information
Given a geodesic space (E, d), we show that full ordinal knowledge on the
metric d-i.e. knowledge of the function D d : (w, x, y, z) 1
d(w,x)d(y,z) , determines uniquely-up to a constant factor-the metric d.
For a subspace En of n points of E, converging in Hausdorff distance to E, we
construct a metric dn on En, based only on the knowledge of D d on En and
establish a sharp upper bound of the Gromov-Hausdorff distance between (En, dn)
and (E, d)
Characterization for entropy of shifts of finite type on Cayley trees
The notion of tree-shifts constitutes an intermediate class in between
one-sided shift spaces and multidimensional ones. This paper proposes an
algorithm for computing of the entropy of a tree-shift of finite type.
Meanwhile, the entropy of a tree-shift of finite type is for some , where is a Perron number. This
extends Lind's work on one-dimensional shifts of finite type. As an
application, the entropy minimality problem is investigated, and we obtain the
necessary and sufficient condition for a tree-shift of finite type being
entropy minimal with some additional conditions
Fast optimization of parametrized quantum optical circuits
Parametrized quantum optical circuits are a class of quantum circuits in
which the carriers of quantum information are photons and the gates are optical
transformations. Classically optimizing these circuits is challenging due to
the infinite dimensionality of the photon number vector space that is
associated to each optical mode. Truncating the space dimension is unavoidable,
and it can lead to incorrect results if the gates populate photon number states
beyond the cutoff. To tackle this issue, we present an algorithm that is orders
of magnitude faster than the current state of the art, to recursively compute
the exact matrix elements of Gaussian operators and their gradient with respect
to a parametrization. These operators, when augmented with a non-Gaussian
transformation such as the Kerr gate, achieve universal quantum computation.
Our approach brings two advantages: first, by computing the matrix elements of
Gaussian operators directly, we don't need to construct them by combining
several other operators; second, we can use any variant of the gradient descent
algorithm by plugging our gradients into an automatic differentiation framework
such as TensorFlow or PyTorch. Our results will find applications in quantum
optical hardware research, quantum machine learning, optical data processing,
device discovery and device design.Comment: 21 pages, 10 figure
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