Refining Fuchs' Theorem: Ensuring Uniqueness through No-Resummation
Constraints
March 5, 2018
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Mathematics
Classical Analysis and ODEs
Classical Analysis and ODEs
This paper revisits Fuchs' theorem to address a critical limitation in its
framework: the implicit assumption that power series expansions remain
invariant under term rearrangement. We propose a \textit{No-Resummation
Constraint} that ensur...
On the index of minimal 2-tori in the 4-sphere
March 5, 2018
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Mathematics
Differential Geometry
In this note we prove that any minimal 2-torus in S4 has Morse index at
least 6, with equality if and only if it is congruent to the Clifford torus
in some great S3⊂S4.For a minimal 2-torus in Sn with vanishing
Hopf d...
Perpertual Coupled Simulated Annealing for Continuous Optimization
March 2, 2018
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Mathematics
Optimization and Control
Optimization and Control
Global optimization heuristics are popular to optimize hard non-convex
problems. Despite their irrefutably large cost-to-solution, in the lack of
other working greedy or convex approaches, global optimization algorithms
remain the no-braine...
Rough Path Renormalization from Stratonovich to It\^o for Fractional
Brownian Motion
March 1, 2018
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Mathematics
Probability
This paper develops an It\^o-type fractional pathwise integration theory for
fractional Brownian motion with Hurst parameters H∈(31,21], using the Lyons' rough path framework. This approach is
designed to fill g...
Boyer-Lindquist space-times and beyond: Meta-material analogues
February 27, 2018
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Physics
General Relativity and Quantum Cosmology
Analogue space-times (and in particular metamaterial analogue space-times)
have a long varied and complex history. Much of the previous related work has
focused on spherically symmetric models; however, axial symmetry is much more
relevant ...
Approximation Algorithms for D-optimal Design
February 22, 2018
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Statistics
Computer Science
Machine Learning
Data Structures and Algorithms
Machine Learning
Data Structures and Algorithms
Experimental design is a classical statistics problem and its aim is to
estimate an unknown m-dimensional vector β from linear measurements
where a Gaussian noise is introduced in each measurement. For the combinatorial
experimental...
Higher Hochschild homology and exponential functors
February 21, 2018
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Mathematics
Algebraic Topology
Algebraic Topology
We study higher Hochschild homology evaluated on wedges of circles, viewed as
a functor on the category of free groups. The main results use coefficients
arising from square-zero extensions; this is motivated by work of Turchin and
Willwach...
A Note on Coherent States for Virasoro Orbits
February 21, 2018
Physics
High Energy Physics - Theory
There are two sets of orbits of the Virasoro group which admit a K\"ahler
structure. We consider the construction of coherent states for the orbit
diffS1/SL(2,R) which furnishes unitary
representations of t...
The Malicious Use of Artificial Intelligence: Forecasting, Prevention,
and Mitigation
February 20, 2018
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Computer Science
Artificial Intelligence
Cryptography and Security
Computers and Society
Artificial Intelligence
Cryptography and Security
Computers and Society
This report surveys the landscape of potential security threats from
malicious uses of AI, and proposes ways to better forecast, prevent, and
mitigate these threats. After analyzing the ways in which AI may influence the
threat landscape in...
Causal Perturbative QFT and Space-time Geometry
February 19, 2018
Physics
Mathematics
Mathematical Physics
Mathematical Physics
This work is devoted to the causal perturbative Quantum Field Theory (QFT)
due to Bogoliubov, including QED and other realistic QFT. The white noise
analysis and the Hida operators as the creation and annihilation operators for
free fields ...