Non-commutative manifolds, the free square root and symmetric functions
in two non-commuting variables
August 30, 2018
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Mathematics
Complex Variables
The richly developed theory of complex manifolds plays important roles in our
understanding of holomorphic functions in several complex variables. It is
natural to consider manifolds that will play similar roles in the theory of
holomorphic...
Hard Non-Monotonic Attention for Character-Level Transduction
August 29, 2018
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Computer Science
Computation and Language
Character-level string-to-string transduction is an important component of
various NLP tasks. The goal is to map an input string to an output string,
where the strings may be of different lengths and have characters taken from
different alp...
The Weyl law for algebraic tori
August 29, 2018
Mathematics
Representation Theory
Number Theory
We give an asymptotic evaluation for the number of automorphic characters of
an algebraic torus T with bounded analytic conductor. The analytic conductor
which we use is defined via the local Langlands correspondence for tori by
choosing ...
The Undirected Optical Indices of Trees
August 28, 2018
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Mathematics
Combinatorics
Combinatorics
For a connected graph G, an instance I is a set of pairs of vertices and
a corresponding routing R is a set of paths specified for all vertex-pairs in
I. Let RI be the collection of all routings with respect to
I. Th...
A Discriminative Latent-Variable Model for Bilingual Lexicon Induction
August 28, 2018
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Computer Science
Statistics
Computation and Language
Machine Learning
Machine Learning
We introduce a novel discriminative latent variable model for bilingual
lexicon induction. Our model combines the bipartite matching dictionary prior
of Haghighi et al. (2008) with a representation-based approach (Artetxe et al.,
2017). To ...
Combinatorics of Borel Ideals
August 27, 2018
Mathematics
Logic
In this work, I investigate several combinatorial properties of Borel (or
co-analytic) ideals on countable sets. I extend a theorem presented in M.
Hru\v{s}\'{a}k, D. Meza-Alc\'antara, E. Th\"ummel, and C. Uzc\'ategui,
\emph{Ramsey Type Pro...
A Dichotomous Analysis of Unemployment Benefits
August 26, 2018
Quantitative Finance
General Finance
Using equal employment opportunity as a fairness hypothesis, real-time
balanced-budget rule as a constraint, and policy stability as an objective, we
derive a scientific formula for taxation policy and formulate a fair allocation
for unempl...
The Gauss--skizze decomposition is a Goresky-MacPherson stratification
August 25, 2018
Mathematics
Algebraic Geometry
We consider a new stratification of the space of configurations of n marked
points on the complex plane. Recall that this space can be differently
interpreted as the space DPoln of degree n>1 complex, monic
polynomials...
Spatial heterogeneity can explain the stable coexistence of savanna and
forest in South America
August 24, 2018
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Mathematics
Probability
Probability
In work with a variety of co-authors, Staver and Levin have argued that
savanna and forest coexist as alternative stable states with discontinuous
changes in density of trees at the boundary. Here we formulate a nonhomogeneous
spatial model...
Continuous bulk and interface description of topological insulators
August 23, 2018
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Physics
Mathematics
Mathematical Physics
Mathematical Physics
Mathematical Physics
Mathematical Physics
We analyze continuous partial differential models of topological insulators
in the form of systems of Dirac equations. We describe the bulk and interface
topological properties of the materials by means of indices of Fredholm
operators cons...