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...
Linear-time logics -- a coalgebraic perspective
December 22, 2016
Computer Science
Logic in Computer Science
We describe a general approach to deriving linear-time logics for a wide
variety of state-based, quantitative systems, by modelling the latter as
coalgebras whose type incorporates both branching and linear behaviour.
Concretely, we define ...
GuStL - An Experimental Guarded States Language
December 20, 2016
Computer Science
Distributed, Parallel, and Cluster Computing
Programming Languages
Programming a parallel computing system that consists of several thousands or
even up to a million message passing processing units may ask for a language
that supports waiting for and sending messages over hardware channels. As
programs ar...
Monte Carlo goodness-of-fit tests for degree corrected and related
stochastic blockmodels
December 18, 2016
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Statistics
Mathematics
Statistics Theory
Statistics Theory
Methodology
We construct Bayesian and frequentist finite-sample goodness-of-fit tests for
three different variants of the stochastic blockmodel for network data. Since
all of the stochastic blockmodel variants are log-linear in form when block
assignme...
Metabolic allometric scaling of unicellular organisms as a product of
selection and optimization of nutrient distribution in food chains
December 14, 2016
Quantitative Biology
Other Quantitative Biology
One of the major characteristics of living organisms is metabolic rate -
amount of energy produced per unit time. When the size of organisms increases,
the metabolic rate also increases in a certain regular way. This regularity,
whose cause...
Metabolic allometric scaling of multicellular organisms as a product of
evolutionary development and optimization of food chains
November 30, 2016
Quantitative Biology
Other Quantitative Biology
Production of energy is a foundation of life. Metabolic rate of organisms
(amount of energy produced per unit time) generally increases slower than
organisms' mass. This phenomenon, when considered across different taxa, is
called interspec...
A generalization of Marstrand's theorem and some geometric applications
November 29, 2016
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Mathematics
Metric Geometry
In this paper we prove using quite elementary methods, with a combinatorial
nature, two general results related to Marstrand's projection theorem in a
quite general formulation over metric spaces under a suitable transversality
condition (t...
The q−Onsager algebra and multivariable q−special functions
November 28, 2016
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Physics
Mathematics
Exactly Solvable and Integrable Systems
Quantum Algebra
Mathematical Physics
Mathematical Physics
Two sets of mutually commuting q−difference operators xi and yj,
i,j=1,...,N such that xi and yi generate a homomorphic image of the
q−Onsager algebra for each i are introduced. The common polynomial
eigenfunctions of e...
Evolution of networks with multiple junctions
November 24, 2016
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Mathematics
Differential Geometry
We consider the motion by curvature of a network of curves in the plane and
we discuss existence, uniqueness, singularity formation and asymptotic behavior
of the flow....