Ramsey expansions of metrically homogeneous graphs
July 9, 2017
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Mathematics
Computer Science
Combinatorics
Discrete Mathematics
Logic
We investigate Ramsey expansions, the coherent extension property for partial
isometries (EPPA), and the existence of a stationary independence relation for
all classes of metrically homogeneous graphs from Cherlin's catalogue. We show
that...
Facilitated exclusion process
July 6, 2017
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Mathematics
Physics
Probability
Statistical Mechanics
Mathematical Physics
Mathematical Physics
Probability
Statistical Mechanics
Mathematical Physics
Mathematical Physics
We study the Facilitated TASEP, an interacting particle system on the one
dimensional integer lattice. We prove that starting from step initial
condition, the position of the rightmost particle has Tracy Widom GSE
statistics on a cube root ...
Anomaly cancellation by generalised cohomology
July 4, 2017
Physics
High Energy Physics - Theory
Supersymmetric states in M-theory are mapped after compactification to
perturbatively non-supersymmetric states in type IIA string theory, with the
supersymmetric parts being encoded in the non-perturbative section of the
string theory. An ...
Utility maximization in constrained and unbounded financial markets:
Applications to indifference valuation, regime switching, consumption and
Epstein-Zin recursive utility
July 1, 2017
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Mathematics
Quantitative Finance
Probability
Mathematical Finance
This memoir presents a systematic study of utility maximization problems for
an investor in constrained and unbounded financial markets. Building upon the
foundational work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a
bound...
Schubert puzzles and integrability I: invariant trilinear forms
June 30, 2017
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Mathematics
Physics
Combinatorics
Mathematical Physics
Algebraic Geometry
Mathematical Physics
The puzzle rules for computing Schubert calculus on d-step flag manifolds,
proven in [Knutson Tao 2003] for 1-step, in [Buch Kresch Purbhoo Tamvakis
2016] for 2-step, and conjectured in [Coskun Vakil 2009] for 3-step, lead
to vector...
Decomposing Network Influence: Social Influence Regression
June 27, 2017
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Statistics
Physics
Applications
Physics and Society
Methodology
Understanding network influence and its determinants are key challenges in
political science and network analysis. Traditional latent variable models
position actors within a social space based on network dependencies but often
do not eluci...
Hybrid Localized Spectral Decomposition for multiscale problems
June 27, 2017
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Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
We consider a finite element method for elliptic equation with heterogeneous
and possibly high-contrast coefficients based on primal hybrid formulation. A
space decomposition as in FETI and BDCC allows a sequential computations of the
unkno...
A progress on the binary Goldbach conjecture
June 26, 2017
Mathematics
Number Theory
In this paper we develop the method of circle of partitions and associated
statistics. As an application we prove conditionally the binary Goldbach
conjecture. We develop series of steps to prove the binary Goldbach conjecture
in full. We e...
An algorithm to find maximum area polygons circumscribed about a convex
polygon
June 25, 2017
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Mathematics
Metric Geometry
Combinatorics
A convex polygon Q is circumscribed about a convex polygon P if every vertex
of P lies on at least one side of Q. We present an algorithm for finding a
maximum area convex polygon circumscribed about any given convex n-gon in
O(n^3) time. A...
The coarse index class with support
June 21, 2017
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Mathematics
Differential Geometry
K-Theory and Homology
We construct the coarse index class with support condition (as an element of
coarse K-homology) of an equivariant Dirac operator on a complete Riemannian
manifold endowed with a proper, isometric action of a group. We further show a
coars...