At the Mercy of the Common Noise: Blow-ups in a Conditional
McKean--Vlasov Problem
July 13, 2018
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Mathematics
Quantitative Finance
Probability
Analysis of PDEs
Mathematical Finance
We extend a model of positive feedback and contagion in large mean-field
systems, by introducing a common source of noise driven by Brownian motion.
Although the driving dynamics are continuous, the positive feedback effect can
lead to `blo...
Representation-theoretic properties of balanced big Cohen-Macaulay
modules
July 12, 2018
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Mathematics
Commutative Algebra
Commutative Algebra
Let (R, \m, k) be a complete Cohen-Macaulay local ring. In this paper, we
assign a numerical invariant, for any balanced big Cohen-Macaulay module,
called \uh-length. Among other results, it is proved that, for a given
balanced big Cohe...
Sharp bounds on the number of squares in recurrence sequences and
solutions of X2−(a2+b)Y4=−b
July 11, 2018
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Mathematics
Number Theory
Number Theory
We obtain best possible results for the number of coprime positive integer
solutions of the equation in the title when a is a positive integer,
b=pm, 2pm or 4pm, where m is a non-negative integer, p is
prime, a2+b ...
NNNLO pressure of cold quark matter: leading logarithm
July 11, 2018
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Physics
High Energy Physics - Phenomenology
High Energy Astrophysical Phenomena
Nuclear Theory
At high baryon chemical potential μB, the equation of state of QCD
allows a weak-coupling expansion in the QCD coupling αs. The result is
currently known up to and including the full next-to-next-to-leading order
(NNLO) $\alpha...
Large gaps of CUE and GUE
July 5, 2018
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Mathematics
Probability
In this article, we study the largest gaps of the classical random matrices
of CUE and GUE, and show that after rescaling, the limiting densities are given
by the Gumbel distributions....
Polynomial time algorithm for optimal stopping with fixed accuracy
July 5, 2018
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Mathematics
Computer Science
Quantitative Finance
Probability
Data Structures and Algorithms
Optimization and Control
Computational Finance
Mathematical Finance
The problem of high-dimensional path-dependent optimal stopping (OS) is
important to multiple academic communities and applications. Modern OS tasks
often have a large number of decision epochs, and complicated non-Markovian
dynamics, makin...
Deep Learning Based Sphere Decoding
July 5, 2018
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Electrical Engineering and Systems Science
Computer Science
Signal Processing
Machine Learning
In this paper, a deep learning (DL)-based sphere decoding algorithm is
proposed, where the radius of the decoding hypersphere is learned by a deep
neural network (DNN). The performance achieved by the proposed algorithm is
very close to the...
In search of higher Bochner theorem
July 4, 2018
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Physics
Mathematics
Mathematical Physics
High Energy Physics - Theory
Classical Analysis and ODEs
Mathematical Physics
We initiate the study of a natural generalisation of the classical
Bochner-Krall problem asking which linear ordinary differential operators
possess sequences of eigenpolynomials satisfying linear recurrence relations of
finite length; the ...
Determination of lattice functions and 2nd-order transfer matrix for
High Power Cyclotron
July 3, 2018
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Physics
Accelerator Physics
Accelerator Physics
This paper describes the development of beam dynamic simulation code for
cyclotron. Starting from a description of beam dynamics in the cyclotron,
lattice functions were determined and the solutions for the 2nd-order nonlinear
Hamiltonian w...
7x±1: Close Relative of Collatz Problem
July 2, 2018
Mathematics
Number Theory
We show an iterated function of which iterates oscillate wildly and grow at a
dizzying pace. We conjecture that the orbit of arbitrary positive integer
always returns to 1, as in the case of Collatz function. The conjecture is
supported by ...