D-critical locus structure on the Hilbert schemes of some local toric
Calabi-Yau threefolds
September 11, 2020
|
Mathematics
Algebraic Geometry
The notion of a d-critical locus is an ingredient in the definition of
motivic Donaldson-Thomas invariants by [BJM19]. In this paper we show that
there is a d-critical locus structure on the Hilbert scheme of dimension zero
subschemes on so...
Reforms meet fairness concerns in school and college admissions
September 11, 2020
|
Economics
Theoretical Economics
Recently, many matching systems around the world have been reformed. These
reforms responded to objections that the matching mechanisms in use were unfair
and manipulable. Surprisingly, the mechanisms remained unfair even after the
reforms:...
General measurements with limited resources and their application to
quantum unambiguous state discrimination
September 11, 2020
|
Physics
Quantum Physics
In this report, we present a framework for implementing an arbitrary
n-outcome generalized quantum measurement (POVM) on an m-qubit register as
a sequence of two-outcome measurements requiring only single ancillary qubit.
Our procedure ...
Inflationary Dynamics and Particle Production in a Toroidal
Bose-Einstein Condensate
September 11, 2020
| |
Physics
Quantum Gases
General Relativity and Quantum Cosmology
We present a theoretical study of the dynamics of a Bose-Einstein condensate
(BEC) trapped inside an expanding toroid that can realize an analogue
inflationary universe. As the system expands, we find that phonons in the BEC
undergo redshif...
Autoregressive Transformer Neural Network for Simulating Open Quantum
Systems via a Probabilistic Formulation
September 11, 2020
| | |
Physics
Strongly Correlated Electrons
Disordered Systems and Neural Networks
Computational Physics
Quantum Physics
The theory of open quantum systems lays the foundations for a substantial
part of modern research in quantum science and engineering. Rooted in the
dimensionality of their extended Hilbert spaces, the high computational
complexity of simula...
Topological Structures of Large Scale Interacting Systems via Uniform
Functions and Forms
September 10, 2020
| |
Mathematics
Probability
Algebraic Geometry
Algebraic Topology
Combinatorics
In this article, we investigate the topological structure of large scale
interacting systems on infinite graphs, by constructing a suitable cohomology
which we call the uniform cohomology. The central idea for the construction is
the introd...
Finding Groups of Cross-Correlated Features in Bi-View Data
September 10, 2020
| | | |
Statistics
Computer Science
Methodology
Machine Learning
Machine Learning
Datasets in which measurements of two (or more) types are obtained from a
common set of samples arise in many scientific applications. A common problem
in the exploratory analysis of such data is to identify groups of features of
different ...
The relatively perfect Greenberg transform and cycle class maps
September 10, 2020
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Mathematics
Number Theory
Algebraic Geometry
Given a scheme over a complete discrete valuation ring of mixed
characteristic with perfect residue field, the Greenberg transform produces a
new scheme over the residue field thicker than the special fiber. In this
paper, we will generaliz...
Convex co-compact representations of 3-manifold groups
September 10, 2020
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Mathematics
Geometric Topology
Differential Geometry
A representation of a finitely generated group into the projective general
linear group is called convex co-compact if it has finite kernel and its image
acts convex co-compactly on a properly convex domain in real projective space.
We prov...
KNN-DBSCAN: a DBSCAN in high dimensions
September 9, 2020
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Computer Science
Distributed, Parallel, and Cluster Computing
Clustering is a fundamental task in machine learning. One of the most
successful and broadly used algorithms is DBSCAN, a density-based clustering
algorithm. DBSCAN requires ϵ-nearest neighbor graphs of the input
dataset, which are...