3,410 research outputs found
Abstractions of Stochastic Hybrid Systems
In this paper we define a stochastic bisimulation concept for a very general class of stochastic hybrid systems, which subsumes most classes of stochastic hybrid systems. The definition of this bisimulation builds on the concept of zigzag morphism defined for strong Markov processes.
The main result is that this stochastic bisimulation is indeed an equivalence relation. The secondary result is that this bisimulation relation for the stochastic hybrid system models used in this paper implies the same
kind of bisimulation for their continuous parts and respectively for their jumping structures
Generative Model with Coordinate Metric Learning for Object Recognition Based on 3D Models
Given large amount of real photos for training, Convolutional neural network
shows excellent performance on object recognition tasks. However, the process
of collecting data is so tedious and the background are also limited which
makes it hard to establish a perfect database. In this paper, our generative
model trained with synthetic images rendered from 3D models reduces the
workload of data collection and limitation of conditions. Our structure is
composed of two sub-networks: semantic foreground object reconstruction network
based on Bayesian inference and classification network based on multi-triplet
cost function for avoiding over-fitting problem on monotone surface and fully
utilizing pose information by establishing sphere-like distribution of
descriptors in each category which is helpful for recognition on regular photos
according to poses, lighting condition, background and category information of
rendered images. Firstly, our conjugate structure called generative model with
metric learning utilizing additional foreground object channels generated from
Bayesian rendering as the joint of two sub-networks. Multi-triplet cost
function based on poses for object recognition are used for metric learning
which makes it possible training a category classifier purely based on
synthetic data. Secondly, we design a coordinate training strategy with the
help of adaptive noises acting as corruption on input images to help both
sub-networks benefit from each other and avoid inharmonious parameter tuning
due to different convergence speed of two sub-networks. Our structure achieves
the state of the art accuracy of over 50\% on ShapeNet database with data
migration obstacle from synthetic images to real photos. This pipeline makes it
applicable to do recognition on real images only based on 3D models.Comment: 14 page
Semipullbacks of labelled Markov processes
A labelled Markov process (LMP) consists of a measurable space together
with an indexed family of Markov kernels from to itself. This structure has
been used to model probabilistic computations in Computer Science, and one of
the main problems in the area is to define and decide whether two LMP and
"behave the same". There are two natural categorical definitions of
sameness of behavior: and are bisimilar if there exist an LMP and
measure preserving maps forming a diagram of the shape ; and they are behaviorally equivalent if there exist some
and maps forming a dual diagram .
These two notions differ for general measurable spaces but Doberkat
(extending a result by Edalat) proved that they coincide for analytic Borel
spaces, showing that from every diagram one
can obtain a bisimilarity diagram as above. Moreover, the resulting square of
measure preserving maps is commutative (a "semipullback").
In this paper, we extend the previous result to measurable spaces
isomorphic to a universally measurable subset of a Polish space with the trace
of the Borel -algebra, using a version of Strassen's theorem on common
extensions of finitely additive measures.Comment: 10 pages; v2: missing attribution to Doberka
The wall of the cave
In this article old and new relations between gauge fields and strings are
discussed. We add new arguments that the Yang Mills theories must be described
by the non-critical strings in the five dimensional curved space. The physical
meaning of the fifth dimension is that of the renormalization scale represented
by the Liouville field. We analyze the meaning of the zigzag symmetry and show
that it is likely to be present if there is a minimal supersymmetry on the
world sheet. We also present the new string backgrounds which may be relevant
for the description of the ordinary bosonic Yang-Mills theories. The article is
written on the occasion of the 40-th anniversary of the IHES.Comment: 18 pages, Late
A Geometric Perspective on Sparse Filtrations
We present a geometric perspective on sparse filtrations used in topological
data analysis. This new perspective leads to much simpler proofs, while also
being more general, applying equally to Rips filtrations and Cech filtrations
for any convex metric. We also give an algorithm for finding the simplices in
such a filtration and prove that the vertex removal can be implemented as a
sequence of elementary edge collapses
Essential spectra of difference operators on \sZ^n-periodic graphs
Let (\cX, \rho) be a discrete metric space. We suppose that the group
\sZ^n acts freely on and that the number of orbits of with respect to
this action is finite. Then we call a \sZ^n-periodic discrete metric
space. We examine the Fredholm property and essential spectra of band-dominated
operators on where is a \sZ^n-periodic discrete metric space.
Our approach is based on the theory of band-dominated operators on \sZ^n and
their limit operators.
In case is the set of vertices of a combinatorial graph, the graph
structure defines a Schr\"{o}dinger operator on in a natural way. We
illustrate our approach by determining the essential spectra of Schr\"{o}dinger
operators with slowly oscillating potential both on zig-zag and on hexagonal
graphs, the latter being related to nano-structures
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