482 research outputs found
Many-server diffusion limits for queues
This paper studies many-server limits for multi-server queues that have a
phase-type service time distribution and allow for customer abandonment. The
first set of limit theorems is for critically loaded queues, where
the patience times are independent and identically distributed following a
general distribution. The next limit theorem is for overloaded
queues, where the patience time distribution is restricted to be exponential.
We prove that a pair of diffusion-scaled total-customer-count and
server-allocation processes, properly centered, converges in distribution to a
continuous Markov process as the number of servers goes to infinity. In the
overloaded case, the limit is a multi-dimensional diffusion process, and in the
critically loaded case, the limit is a simple transformation of a diffusion
process. When the queues are critically loaded, our diffusion limit generalizes
the result by Puhalskii and Reiman (2000) for queues without customer
abandonment. When the queues are overloaded, the diffusion limit provides a
refinement to a fluid limit and it generalizes a result by Whitt (2004) for
queues with an exponential service time distribution. The proof
techniques employed in this paper are innovative. First, a perturbed system is
shown to be equivalent to the original system. Next, two maps are employed in
both fluid and diffusion scalings. These maps allow one to prove the limit
theorems by applying the standard continuous-mapping theorem and the standard
random-time-change theorem.Comment: Published in at http://dx.doi.org/10.1214/09-AAP674 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Non-extensive study of Rigid and Non-rigid Rotators
The isotropic rigid and non-rigid rotators in the framework of Tsallis
statistics are studied in the high and low temperature limits. The generalized
partition functions, internal energies and heat capacities are calculated. It
has been found that results are in well agreement with the classical
Boltzmann-Gibbs statistics in the limiting Tsallis index. It has also been
observed that nonextensivity parameter q behaves like a scale parameter in the
low temperature regime.Comment: 11 Pages, 3 Figures, Late
Locating bugs without looking back
Bug localisation is a core program comprehension task in software maintenance: given the observation of a bug, e.g. via a bug report, where is it located in the source code? Information retrieval (IR) approaches see the bug report as the query, and the source code files as the documents to be retrieved, ranked by relevance. Such approaches have the advantage of not requiring expensive static or dynamic analysis of the code. However, current state-of-the-art IR approaches rely on project history, in particular previously fixed bugs or previous versions of the source code. We present a novel approach that directly scores each current file against the given report, thus not requiring past code and reports. The scoring method is based on heuristics identified through manual inspection of a small sample of bug reports. We compare our approach to eight others, using their own five metrics on their own six open source projects. Out of 30 performance indicators, we improve 27 and equal 2. Over the projects analysed, on average we find one or more affected files in the top 10 ranked files for 76% of the bug reports. These results show the applicability of our approach to software projects without history
Exact solution of Schrodinger equation for modified Kratzer's molecular potential with the position-dependent mass
Exact solutions of Schrodinger equation are obtained for the modified Kratzer
and the corrected Morse potentials with the position-dependent effective mass.
The bound state energy eigenvalues and the corresponding eigenfunctions are
calculated for any angular momentum for target potentials. Various forms of
point canonical transformations are applied. PACS numbers: 03.65.-w; 03.65.Ge;
12.39.Fd Keywords: Morse potential, Kratzer potential, Position-dependent mass,
Point canonical transformation, Effective mass Schr\"{o}dinger equation.Comment: 9 page
Effective Mass Dirac-Morse Problem with any kappa-value
The Dirac-Morse problem are investigated within the framework of an
approximation to the term proportional to in the view of the
position-dependent mass formalism. The energy eigenvalues and corresponding
wave functions are obtained by using the parametric generalization of the
Nikiforov-Uvarov method for any -value. It is also studied the
approximate energy eigenvalues, and corresponding wave functions in the case of
the constant-mass for pseudospin, and spin cases, respectively.Comment: 12 page
Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics
Using the NU method [A.F.Nikiforov, V.B.Uvarov, Special Functions of
Mathematical Physics, Birkhauser,Basel,1988], we investigated the real
eigenvalues of the complex and/or - symmetric, non-Hermitian and the
exponential type systems, such as Poschl-Teller and Morse potentials.Comment: 14 pages, Late
Modelling the Distribution of 3D Brain MRI using a 2D Slice VAE
Probabilistic modelling has been an essential tool in medical image analysis,
especially for analyzing brain Magnetic Resonance Images (MRI). Recent deep
learning techniques for estimating high-dimensional distributions, in
particular Variational Autoencoders (VAEs), opened up new avenues for
probabilistic modeling. Modelling of volumetric data has remained a challenge,
however, because constraints on available computation and training data make it
difficult effectively leverage VAEs, which are well-developed for 2D images. We
propose a method to model 3D MR brain volumes distribution by combining a 2D
slice VAE with a Gaussian model that captures the relationships between slices.
We do so by estimating the sample mean and covariance in the latent space of
the 2D model over the slice direction. This combined model lets us sample new
coherent stacks of latent variables to decode into slices of a volume. We also
introduce a novel evaluation method for generated volumes that quantifies how
well their segmentations match those of true brain anatomy. We demonstrate that
our proposed model is competitive in generating high quality volumes at high
resolutions according to both traditional metrics and our proposed evaluation.Comment: accepted for publication at MICCAI 2020. Code available
https://github.com/voanna/slices-to-3d-brain-vae
Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential
The energy eigenvalues and the corresponding eigenfunctions of the
one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential
are analytically obtained within the position-dependent mass formalism. The
parametric generalization of the Nikiforov-Uvarov method is used in the
calculations by choosing a mass distribution.Comment: 10 page
A new approach to the exact solutions of the effective mass Schrodinger equation
Effective mass Schrodinger equation is solved exactly for a given potential.
Nikiforov-Uvarov method is used to obtain energy eigenvalues and the
corresponding wave functions. A free parameter is used in the transformation of
the wave function. The effective mass Schrodinger equation is also solved for
the Morse potential transforming to the constant mass Schr\"{o}dinger equation
for a potential. One can also get solution of the effective mass Schrodinger
equation starting from the constant mass Schrodinger equation.Comment: 14 page
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