Google employs PageRank to rank web pages, determining the order in which
search results are presented to users based on their queries. PageRank is
primarily utilized for directed networks, although there are instances where it
is also appl...
Revisiting virtual difference ideals
August 30, 2016
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Mathematics
Logic
The main idea of [4] was that structures built from periodic prime ideals
have better properties from the usual ones built from invariant ideals; but
unable to work with periodic ideals alone, we had to generalise further to a
somewhat ephe...
Garoufalidis-Levine's finite type invariants for
Zπ-homology equivalences from 3-manifolds to the 3-torus
August 30, 2016
Mathematics
Geometric Topology
Algebraic Topology
Garoufalidis and Levine defined a filtration for 3-manifolds equipped with
some degree 1 map (Zπ-homology equivalence) to a fixed 3-manifold
N and showed that there is a natural surjection from a space of
π=π1N-decorat...
A Proof of Onsager's Conjecture
August 29, 2016
Mathematics
Physics
Analysis of PDEs
Mathematical Physics
Mathematical Physics
Fluid Dynamics
For any α<1/3, we construct weak solutions to the 3D
incompressible Euler equations in the class CtCxα that have nonempty,
compact support in time on R×T3 and therefore
fail to conserve the...
Non-Euclidean Triangle Centers
August 29, 2016
Mathematics
Metric Geometry
Non-Euclidean triangle centers can be described using homogeneous coordinates
that are proportional to the generalized sines of the directed distances of a
given center from the edges of the reference triangle. Identical homogeneous
coordin...
Human Action Recognition without Human
August 28, 2016
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Computer Science
Computer Vision and Pattern Recognition
Multimedia
The objective of this paper is to evaluate "human action recognition without
human". Motion representation is frequently discussed in human action
recognition. We have examined several sophisticated options, such as dense
trajectories (DT) ...
The homotopy type of the PL cobordism category. I
August 22, 2016
Mathematics
Geometric Topology
Algebraic Topology
In this paper, we introduce a bordism category CdPL whose
objects are bundles of closed (d−1)-dimensional piecewise linear manifolds
and whose morphisms are bundles of d-dimensional piecewise linear cobordisms.
In the ma...
Semantics, Specification Logic, and Hoare Logic of Exact Real
Computation
August 20, 2016
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Computer Science
Numerical Analysis
Logic in Computer Science
We propose a simple imperative programming language, ERC, that features
arbitrary real numbers as primitive data type, exactly. Equipped with a
denotational semantics, ERC provides a formal programming language-theoretic
foundation to the a...
Introduction to Cluster Algebras. Chapters 1-3
August 19, 2016
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Mathematics
Combinatorics
Rings and Algebras
Representation Theory
Combinatorics
Rings and Algebras
Representation Theory
This is a preliminary draft of Chapters 1-3 of our forthcoming textbook
"Introduction to Cluster Algebras." This installment contains:
Chapter 1. Total positivity
Chapter 2. Mutations of quivers and matrices
Chapter 3. Clusters and se...
Nonexistence of time-periodic solutions of the Dirac equation in
nonextreme Kerr-Newman-AdS spacetime
August 18, 2016
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Physics
Mathematics
General Relativity and Quantum Cosmology
Classical Analysis and ODEs
In non-extreme Kerr-Newman-AdS spacetime, we prove that there is no
nontrivial Dirac particle which is Lp for 0<p≤34 with
arbitrary eigenvalue λ, and for 34<p≤3−2q4,
0<q<23 with eig...