Random Finite Noncommutative Geometries and Topological Recursion
June 21, 2019
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Physics
Mathematics
Mathematical Physics
High Energy Physics - Theory
Mathematical Physics
Quantum Algebra
In this paper we investigate a model for quantum gravity on finite
noncommutative spaces using the theory of blobbed topological recursion. The
model is based on a particular class of random finite real spectral triples
${(\mathcal{A}, \mat...
Asymmetric Distributed Trust
June 21, 2019
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Computer Science
Distributed, Parallel, and Cluster Computing
Cryptography and Security
Quorum systems are a key abstraction in distributed fault-tolerant computing
for capturing trust assumptions. They can be found at the core of many
algorithms for implementing reliable broadcasts, shared memory, consensus and
other problems...
Frobenius objects in the category of relations
June 20, 2019
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Mathematics
Physics
Category Theory
Mathematical Physics
Mathematical Physics
We give a characterization, in terms of simplicial sets, of Frobenius objects
in the category of relations. This result generalizes a result of Heunen,
Contreras, and Cattaneo showing that special dagger Frobenius objects in the
category of...
Derivation of the Variational Bayes Equations
June 20, 2019
Computer Science
Quantitative Biology
Neural and Evolutionary Computing
Neurons and Cognition
The derivation of key equations for the variational Bayes approach is
well-known in certain circles. However, translating the fundamental derivations
(e.g., as found in Beal's work) to Friston's notation is somewhat delicate.
Further, the n...
Bayesian Modelling in Practice: Using Uncertainty to Improve
Trustworthiness in Medical Applications
June 20, 2019
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Computer Science
Statistics
Machine Learning
Artificial Intelligence
Machine Learning
The Intensive Care Unit (ICU) is a hospital department where machine learning
has the potential to provide valuable assistance in clinical decision making.
Classical machine learning models usually only provide point-estimates and no
uncert...
Octonions, Albert vectors and the group E6(F)
June 20, 2019
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Mathematics
Group Theory
Representation Theory
We present a uniform approach to the construction of the groups of type
E6 over arbitrary fields without using Lie theory. This gives a
simple description of the group generators and some of the subgroup structure.
In the finite...
ENCORE: Ensemble Learning using Convolution Neural Machine Translation
for Automatic Program Repair
June 20, 2019
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Computer Science
Software Engineering
Machine Learning
Automated generate-and-validate (G&V) program repair techniques typically
rely on hard-coded rules, only fix bugs following specific patterns, and are
hard to adapt to different programming languages. We propose ENCORE, a new G&V
technique,...
Steinhaus Filtration and Stable Paths in the Mapper
June 19, 2019
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Computer Science
Mathematics
Machine Learning
Computational Geometry
Algebraic Topology
Machine Learning
Computational Geometry
Algebraic Topology
We define a new filtration called the Steinhaus filtration built from a
single cover based on a generalized Steinhaus distance, a generalization of
Jaccard distance. The homology persistence module of a Steinhaus filtration
with infinitely ...
First-order methods almost always avoid saddle points: the case of
vanishing step-sizes
June 18, 2019
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Mathematics
Optimization and Control
Optimization and Control
In a series of papers \cite{LSJR16, PP17, LPP}, it was established that some
of the most commonly used first order methods almost surely (under random
initializations) and with step-size being small enough, avoid strict saddle
points, as lo...
Phase transition and asymptotic behaviour of flocking Cucker-Smale model
June 18, 2019
Mathematics
Analysis of PDEs
In this paper, we study a continuous ocking Cucker-Smale model with noise,
which has isotropic and polarized stationary solutions depending on the
intensity of the noise. The first result establishes the threshold value of the
noise paramet...