59,680 research outputs found
FITTING TRAFFIC TRACES WITH DISCRETE CANONICAL PHASE TYPE DISTRIBUTIONS AND MARKOV ARRIVAL PROCESSES
Recent developments of matrix analytic methods make phase type distributions (PHs) and Markov Arrival Processes (MAPs) promising stochastic model candidates for capturing traffic trace behaviour and for efficient usage in queueing analysis. After introducing basics of these sets of stochastic models, the paper discusses the following subjects in detail: (i) PHs and MAPs have different representations. For efficient use of these models, sparse (defined by a minimal number of parameters) and unique representations of discrete time PHs and MAPs are needed, which are commonly referred to as canonical representations. The paper presents new results on the canonical representation of discrete PHs and MAPs. (ii) The canonical representation allows a direct mapping between experimental moments and the stochastic models, referred to as moment matching. Explicit procedures are provided for this mapping. (iii) Moment matching is not always the best way to model the behavior of traffic traces. Model fitting based on appropriately chosen distance measures might result in better performing stochastic models. We also demonstrate the efficiency of fitting procedures with experimental result
Wigner distributions and quantum mechanics on Lie groups: the case of the regular representation
We consider the problem of setting up the Wigner distribution for states of a
quantum system whose configuration space is a Lie group. The basic properties
of Wigner distributions in the familiar Cartesian case are systematically
generalised to accommodate new features which arise when the configuration
space changes from -dimensional Euclidean space to a Lie group
. The notion of canonical momentum is carefully analysed, and the meanings
of marginal probability distributions and their recovery from the Wigner
distribution are clarified. For the case of compact an explicit definition
of the Wigner distribution is proposed, possessing all the required properties.
Geodesic curves in which help introduce a notion of the `mid point' of two
group elements play a central role in the construction.Comment: Latex, 54 pages, Section VII enlarged, new references adde
Self Duality and Quantization
Quantum theory of the free Maxwell field in Minkowski space is constructed
using a representation in which the self dual connection is diagonal. Quantum
states are now holomorphic functionals of self dual connections and a
decomposition of fields into positive and negative frequency parts is
unnecessary. The construction requires the introduction of new mathematical
techniques involving ``holomorphic distributions''. The method extends also to
linear gravitons in Minkowski space. The fact that one can recover the entire
Fock space --with particles of both helicities-- from self dual connections
alone provides independent support for a non-perturbative, canonical
quantization program for full general relativity based on self dual variables.Comment: 14 page
The Grow-Shrink strategy for learning Markov network structures constrained by context-specific independences
Markov networks are models for compactly representing complex probability
distributions. They are composed by a structure and a set of numerical weights.
The structure qualitatively describes independences in the distribution, which
can be exploited to factorize the distribution into a set of compact functions.
A key application for learning structures from data is to automatically
discover knowledge. In practice, structure learning algorithms focused on
"knowledge discovery" present a limitation: they use a coarse-grained
representation of the structure. As a result, this representation cannot
describe context-specific independences. Very recently, an algorithm called
CSPC was designed to overcome this limitation, but it has a high computational
complexity. This work tries to mitigate this downside presenting CSGS, an
algorithm that uses the Grow-Shrink strategy for reducing unnecessary
computations. On an empirical evaluation, the structures learned by CSGS
achieve competitive accuracies and lower computational complexity with respect
to those obtained by CSPC.Comment: 12 pages, and 8 figures. This works was presented in IBERAMIA 201
Linear canonical transformations and quantum phase:a unified canonical and algebraic approach
The algebra of generalized linear quantum canonical transformations is
examined in the prespective of Schwinger's unitary-canonical basis. Formulation
of the quantum phase problem within the theory of quantum canonical
transformations and in particular with the generalized quantum action-angle
phase space formalism is established and it is shown that the conceptual
foundation of the quantum phase problem lies within the algebraic properties of
the quantum canonical transformations in the quantum phase space. The
representations of the Wigner function in the generalized action-angle unitary
operator pair for certain Hamiltonian systems with the dynamical symmetry are
examined. This generalized canonical formalism is applied to the quantum
harmonic oscillator to examine the properties of the unitary quantum phase
operator as well as the action-angle Wigner function.Comment: 19 pages, no figure
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