We provide a self contained proof of a result of Dudley [Dud64]} which shows
that a bounded convex-body in ℜd can be ε-approximated, by the
intersection of Od(ε−(d−1)/2) halfspaces, where
Od hi...
Fair Division with Bounded Sharing: Binary and Non-Degenerate Valuations
December 1, 2019
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Computer Science
Economics
Computer Science and Game Theory
Theoretical Economics
A set of objects is to be divided fairly among agents with different tastes,
modeled by additive utility-functions. An agent is allowed to share a bounded
number of objects between two or more agents in order to attain fairness.
The paper...
Beyond classical Hamilton's Rule. State distribution asymmetry and the
dynamics of altruism
December 1, 2019
|
Quantitative Biology
Physics
Populations and Evolution
Adaptation and Self-Organizing Systems
This paper analyzes relationships between demographic and state-based
evolutionary game framework and inclusive fitness and Hamilton's rule. It is
shown that the classical Hamilton's rule (counterfactual method) combined with
demographic pa...
The Ooguri-Vafa space as a moduli space of framed wild harmonic bundles
November 30, 2019
Mathematics
Differential Geometry
The Ooguri-Vafa space is a 4-dimensional incomplete hyperk\"{a}hler manifold,
defined on the total space of a singular torus fibration with one singular
nodal fiber. It has been proposed that the Ooguri-Vafa hyperk\"ahler metric
should be p...
Barcodes as Summary of Loss Function Topology
November 29, 2019
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Computer Science
Mathematics
Statistics
Machine Learning
Algebraic Topology
Dynamical Systems
Optimization and Control
Machine Learning
Machine Learning
Algebraic Topology
Dynamical Systems
Optimization and Control
Machine Learning
We propose to study neural networks' loss surfaces by methods of topological
data analysis. We suggest to apply barcodes of Morse complexes to explore
topology of loss surfaces. An algorithm for calculations of the loss function's
barcodes ...
Discrete-time approximation for backward stochastic differential
equations driven by G-Brownian motion
November 29, 2019
|
Mathematics
Computer Science
Numerical Analysis
Numerical Analysis
In this paper, we study the discrete-time approximation schemes for a class
of backward stochastic differential equations driven by G-Brownian motion
(G-BSDEs) which corresponds to the hedging pricing of European contingent
claims. By i...
Morse theory for group presentations
November 29, 2019
Mathematics
Algebraic Topology
Geometric Topology
We introduce a novel combinatorial method to study Q∗∗-transformations
of group presentations or, equivalently, 3-deformations of CW-complexes of
dimension 2. Our procedure is based on a refinement of discrete Morse theory
that gives a...
Clique and cycle frequencies in a sparse random graph model with
overlapping communities
November 28, 2019
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Mathematics
Computer Science
Statistics
Probability
Social and Information Networks
Statistics Theory
Statistics Theory
Probability
Social and Information Networks
Statistics Theory
Statistics Theory
A statistical network model with overlapping communities can be generated as
a superposition of mutually independent random graphs of varying size. The
model is parameterized by the number of nodes, the number of communities, and
the joint ...
Closure properties of knapsack semilinear groups
November 28, 2019
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Mathematics
Group Theory
Group Theory
We show that the following group constructions preserve the semilinearity of
the solution sets for knapsack equations (equations of the form g1x1⋯gkxk=g in a group G, where the variables x1,…,xk
take values...
Pricing and hedging short-maturity Asian options in local volatility
models
November 28, 2019
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Quantitative Finance
Mathematical Finance
This paper discusses the short-maturity behavior of Asian option prices and
hedging portfolios. We consider the risk-neutral valuation and the delta value
of the Asian option having a H\"older continuous payoff function in a local
volatilit...