Lattice theory of torsion classes: Beyond τ-tilting theory
November 6, 2017
| | | |
Mathematics
Representation Theory
Combinatorics
Rings and Algebras
The aim of this paper is to establish a lattice theoretical framework to
study the partially ordered set torsA of torsion
classes over a finite-dimensional algebra A. We show that
$\operatorname{\mathsf{tors}} A...
Optimal actuator design based on shape calculus
November 3, 2017
| |
Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
Optimization and Control
An approach to optimal actuator design based on shape and topology
optimisation techniques is presented. For linear diffusion equations, two
scenarios are considered. For the first one, best actuators are determined
depending on a given ini...
A Comprehensive Low and High-level Feature Analysis for Early Rumor
Detection on Twitter
November 2, 2017
Computer Science
Social and Information Networks
Machine Learning
Recent work have done a good job in modeling rumors and detecting them over
microblog streams. However, the performance of their automatic approaches are
not relatively high when looking early in the diffusion. A first intuition is
that, at...
Approximating quantum channels by completely positive maps with small
Kraus rank
November 2, 2017
|
Physics
Mathematics
Quantum Physics
Functional Analysis
Probability
We study the problem of approximating a quantum channel by one with as few
Kraus operators as possible (in the sense that, for any input state, the output
states of the two channels should be close to one another). Our main result is
that a...
On Ordinal Invariants in Well Quasi Orders and Finite Antichain Orders
November 1, 2017
| |
Mathematics
Logic
Combinatorics
We investigate the ordinal invariants height, length, and width of well quasi
orders (WQO), with particular emphasis on width, an invariant of interest for
the larger class of orders with finite antichain condition (FAC). We show that
the w...
Sophisticated and small versus simple and sizeable: When does it pay off
to introduce drifting coefficients in Bayesian VARs?
November 1, 2017
| | |
Statistics
Economics
Methodology
Econometrics
Applications
Computation
We assess the relationship between model size and complexity in the
time-varying parameter VAR framework via thorough predictive exercises for the
Euro Area, the United Kingdom and the United States. It turns out that
sophisticated dynamics...
Cosmological constant as quantum error correction from generalised gauge
invariance in double field theory
October 29, 2017
Physics
High Energy Physics - Theory
The holographic principle and its realisation as the AdS/CFT correspondence
leads to the existence of the so called precursor operators. These are boundary
operators that carry non-local information regarding events occurring deep
inside th...
Paley--Wiener theorems on the Siegel upper half-space
October 27, 2017
| | |
Mathematics
Complex Variables
In this paper we study spaces of holomorphic functions on the Siegel upper
half-space U and prove Paley-Wiener type theorems for such spaces.
The boundary of U can be identified with the Heisenberg group
Hn....
The Implicit Bias of Gradient Descent on Separable Data
October 27, 2017
| | | |
Statistics
Computer Science
Machine Learning
Machine Learning
We examine gradient descent on unregularized logistic regression problems,
with homogeneous linear predictors on linearly separable datasets. We show the
predictor converges to the direction of the max-margin (hard margin SVM)
solution. The...
The cohomology of projective unitary groups
October 25, 2017
Mathematics
Algebraic Topology
The projective unitary group PU(n) is the quotient of the unitary group U(n)
by its center. We compute the integral cohomology ring of PU(n) using explicit
constructed generators....