300,327 research outputs found
A Tutorial on Independent Component Analysis
Independent component analysis (ICA) has become a standard data analysis
technique applied to an array of problems in signal processing and machine
learning. This tutorial provides an introduction to ICA based on linear algebra
formulating an intuition for ICA from first principles. The goal of this
tutorial is to provide a solid foundation on this advanced topic so that one
might learn the motivation behind ICA, learn why and when to apply this
technique and in the process gain an introduction to this exciting field of
active research
Construction and Verification of Performance and Reliability Models
Over the last two decades formal methods have been extended towards performance and reliability evaluation. This paper tries to provide a rather intuitive explanation of the basic concepts and features in this area.
Instead of striving for mathematical rigour, the intention is to give an illustrative introduction to the basics of stochastic models, to stochastic modelling using process algebra, and to model checking as a technique to analyse stochastic models
On Products and Duality of Binary, Quadratic, Regular Operads
Since its introduction by Loday in 1995 with motivation from algebraic
K-theory, dendriform dialgebras have been studied quite extensively with
connections to several areas in mathematics and physics. A few more similar
structures have been found recently, such as the tri-, quadri-, ennea- and
octo-algebras, with increasing complexity in their constructions and
properties. We consider these constructions as operads and their products and
duals, in terms of generators and relations, with the goal to clarify and
simplify the process of obtaining new algebra structures from known structures
and from linear operators.Comment: 22 page
Lambda Models From Chern-Simons Theories
In this paper we refine and extend the results of arXiv:1701.04138, where a
connection between the superstring lambda model on
and a double Chern-Simons (CS) theory on based on the
Lie superalgebra was suggested, after introduction of
the spectral parameter . The relation between both theories mimics the
well-known CS/WZW symplectic reduction equivalence but is non-chiral in nature.
All the statements are now valid in the strong sense, i.e. valid on the whole
phase space, making the connection between both theories precise. By
constructing a -dependent gauge field in the 2+1 Hamiltonian CS theory it is
shown that: i) by performing a symplectic reduction of the CS theory the
Maillet algebra satisfied by the extended Lax connection of the lambda model
emerges as a boundary current algebra and ii) the Poisson algebra of the
supertraces of -dependent Wilson loops in the CS theory obey some sort of
spectral parameter generalization of the Goldman bracket. The latter algebra is
interpreted as the precursor of the (ambiguous) lambda model monodromy matrix
Poisson algebra prior to the symplectic reduction. As a consequence, the
problematic non-ultralocality of lambda models is avoided (for any value of the
deformation parameter ), showing how the lambda model
classical integrable structure can be understood as a byproduct of the
symplectic reduction process of the -dependent CS theory.Comment: Published version+Erratum (of typos), 57 page
A stochastic Lagrangian representation of the 3-dimensional incompressible Navier-Stokes equations
In this paper we derive a representation of the deterministic 3-dimensional
Navier-Stokes equations based on stochastic Lagrangian paths. The particle
trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber
formula for the Euler equations of ideal fluids is used to recover the velocity
field. This method admits a self-contained proof of local existence for the
nonlinear stochastic system, and can be extended to formulate stochastic
representations of related hydrodynamic-type equations, including viscous
Burgers equations and LANS-alpha models.Comment: v4: Minor corrections to bibliography, and final version that will
apear in CPAM. v3: Minor corrections to the algebra in the last section. v2:
Minor changes to introduction and refferences. 14 pages, 0 figure
Nonequilibrium Dynamics in Low Dimensional Systems
In these lectures we give an overview of nonequilibrium stochastic systems.
In particular we discuss in detail two models, the asymmetric exclusion process
and a ballistic reaction model, that illustrate many general features of
nonequilibrium dynamics: for example coarsening dynamics and nonequilibrium
phase transitions. As a secondary theme we shall show how a common mathematical
structure, the q-deformed harmonic oscillator algebra, serves to furnish exact
results for both systems. Thus the lectures also serve as a gentle introduction
to things q-deformed.Comment: 48 pages LaTeX2e with 9 figures and using elsart.cls (included);
Lectures at the International Summer School on Fundamental Problems in
Statistical Physics X, August-September 2001, Altenberg, Germany. v2 corrects
some errors and includes further discussion/reference
Categorial L\'evy Processes
We generalize Franz' independence in tensor categories with inclusions from
two morphisms (which represent generalized random variables) to arbitrary
ordered families of morphisms. We will see that this only works consistently if
the unit object is an initial object, in which case the inclusions can be
defined starting from the tensor category alone. The obtained independence for
morphisms is called categorial independence. We define categorial L\'evy
processes on every tensor category with initial unit object and present a
construction generalizing the reconstruction of a L\'evy process from its
convolution semigroup via the Daniell-Kolmogorov theorem. Finally, we discuss
examples showing that many known independences from algebra as well as from
(noncommutative) probability are special cases of categorial independence.Comment: Changes in v2: Abstract and introduction extended. Background on
tensor functors moved to Section 2. Example section extended and reorganized.
References updated. Acknowledgements updated. (Some Enrivonment numbers have
changed!
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