Some paradoxes in the Tilman model, how to avoid or accept them
January 18, 2021
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Quantitative Biology
Populations and Evolution
In making models for biological systems one expects to grasp the biology and
be able to use ones intuition to predict the outcome. This paper is about the
discrepancy between what is expected and what is the outcome of the analysis of
the m...
Upper, down, two-sided Lorenz attractor, collisions, merging and
switching
January 18, 2021
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Mathematics
Dynamical Systems
We present a slightly modified version of the well known "geometric Lorenz
attractor". It consists in a C1 open set O of vector fields in R3 having an
attracting region U containing: (1) a unique singular saddle point sigma; (2) a
unique at...
Some Examples of Family Floer Mirrors
January 18, 2021
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Mathematics
Symplectic Geometry
Algebraic Geometry
In this article, we give explicit calculations for the family Floer mirrors
of some non-compact Calabi-Yau surfaces. We compare it with the mirror
construction of Gross-Hacking-Keel for suitably chosen log Calabi-Yau pairs and
the rank two ...
Improved Asymptotic Formulae for Statistical Interpretation Based on
Likelihood Ratio Tests
January 18, 2021
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Physics
High Energy Physics - Experiment
Data Analysis, Statistics and Probability
In this work, we try to improve the classic asymptotic formulae to describe
the probability distribution of likelihood-ratio statistical tests. The idea is
to split the probability distribution function into two parts. One part is
universal...
The Lerch Φ Analytic Continuation
January 17, 2021
Mathematics
Number Theory
We demonstrate how to extend formulae for the Lerch transcendent function,
Φ(ez,k,b), and the polylogarithm, Lik(ez), that only
hold at the positive integers to the right half of the complex k-plane, that
is, $\Re{(...
Minimal Gaussian Curvature Surface
January 17, 2021
Mathematics
Differential Geometry
This paper deals with finding surfaces in R3 which are as close
as possible to being flat and span a given contour such that the contour is a
geodesic on the sought surface. We look for a surface which minimizes the total
Gaussi...
Higher Order Automatic Differentiation of Higher Order Functions
January 17, 2021
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Computer Science
Programming Languages
Logic in Computer Science
We present semantic correctness proofs of automatic differentiation (AD). We
consider a forward-mode AD method on a higher order language with algebraic
data types, and we characterise it as the unique structure preserving macro
given a cho...
Quantum traces for SLn(C): The case n=3
January 17, 2021
Mathematics
Geometric Topology
Quantum Algebra
We generalize Bonahon-Wong's SL2(C)-quantum trace map to
the setting of SL3(C). More precisely, given a non-zero
complex parameter q=e2πiℏ, we associate to each isotopy class of
framed...
Extremal Numbers of Hypergraph Suspensions of Even Cycles
January 17, 2021
Mathematics
Combinatorics
For fixed k≥2, determining the order of magnitude of the number of edges
in an n-vertex bipartite graph not containing C2k, the cycle of length
2k, is a long-standing open problem. We consider an extension of this problem
to t...
Bloch sphere analog of qudits using Heisenberg-Weyl Operators
January 16, 2021
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Physics
Quantum Physics
We study an analogous Bloch sphere representation of higher-level quantum
systems using the Heisenberg-Weyl operator basis. We introduce a
parametrization method that will allow us to identify a real-valued Bloch
vector for an arbitrary den...