Arithmetic D-modules on locally noetherian formal schemes
January 5, 2017
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Mathematics
Algebraic Geometry
Algebraic Geometry
We extend Berthelot's theory of arithmetic D-modules to a class of morphisms
that are not necessarily of finite type. As an application we give a new
construction of the category of convergent isocrystals on a separated scheme of
finite typ...
Tunnel number one knots satisfy the Berge Conjecture
January 5, 2017
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Mathematics
Geometric Topology
Let K be a tunnel number one knot in M with irreducible knot exterior,
where M is either S3, or a connected sum of S2×S1 with any lens
space. (In particular, this includes M=S2×S1.) We prove that if a
non-triv...
Abstract Wiener measure using abelian Yang-Mills action on
R4
January 5, 2017
Mathematics
Physics
Probability
Mathematical Physics
Functional Analysis
Mathematical Physics
Let g be the Lie algebra of a compact Lie group. For a
g-valued 1-form A, consider the Yang-Mills action
\begin{equation} S_{{\rm YM}}(A) = \int_{\mathbb{R}^4} \left|dA + A \wedge A
\right|^2\ d\omega \nonumber \...
Measurement-to-Track Association and Finite-Set Statistics
January 5, 2017
Statistics
Methodology
This is a shortened, clarified, and mathematically more rigorous version of
the original arXiv version. Its first four findings remain unchanged from the
original: 1) measurement-to-track associations (MTAs) in multitarget tracking
(MTT) ar...
Local index theorem for orbifold Riemann surfaces
January 3, 2017
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Mathematics
Algebraic Geometry
We derive a local index theorem in Quillen's form for families of
Cauchy-Riemann operators on orbifold Riemann surfaces (or Riemann orbisurfaces)
that are quotients of the hyperbolic plane by the action of cofinite finitely
generated Fuchsi...
Diosi-Penrose criterion for solids and electrical components in quantum
superpositions and application to a single-photon detector
January 2, 2017
Physics
Quantum Physics
The Diosi-Penrose criterion is applied to solids in quantum superpositions
that are slightly displaced against each other or have different expansions in
the superposed states. The calculations take the microscopic mass distribution
of the ...
Phase transition in one-dimensional excitable media with variable
interaction range
January 2, 2017
| |
Mathematics
Probability
We investigate two discrete models of excitable media on a one-dimensional
integer lattice Z: the κ-color Cyclic Cellular Automaton
(CCA) and the κ-color Firefly Cellular Automaton (FCA). In both models,
sites are a...
Spatial best linear unbiased prediction: A computational mathematics
approach for high dimensional massive datasets
January 1, 2017
Statistics
Computation
Machine Learning
With the advent of massive data sets much of the computational science and
engineering community has moved toward data-intensive approaches in regression
and classification. However, these present significant challenges due to
increasing si...
First Families of Regular Polygons and their Mutations
December 29, 2016
Mathematics
Dynamical Systems
Every regular N-gon defines a canonical family of regular polygons which are
conforming to the bounds of the 'star polygons' determined by N. These star
polygons are formed from truncated extended edges of the N-gon and the
intersection poi...
Selection originating from protein stability/foldability: Relationships
between protein folding free energy, sequence ensemble, and fitness
December 29, 2016
Quantitative Biology
Populations and Evolution
Biomolecules
Assuming that mutation and fixation processes are reversible Markov
processes, we prove that the equilibrium ensemble of sequences obeys a
Boltzmann distribution with exp(4Nem(1−1/(2N))), where m is Malthusian
fitness and Ne and...