4,305 research outputs found
A Bayesian - Deep Learning model for estimating Covid-19 evolution in Spain
This work proposes a semi-parametric approach to estimate Covid-19
(SARS-CoV-2) evolution in Spain. Considering the sequences of 14 days
cumulative incidence of all Spanish regions, it combines modern Deep Learning
(DL) techniques for analyzing sequences with the usual Bayesian Poisson-Gamma
model for counts. DL model provides a suitable description of observed
sequences but no reliable uncertainty quantification around it can be obtained.
To overcome this we use the prediction from DL as an expert elicitation of the
expected number of counts along with their uncertainty and thus obtaining the
posterior predictive distribution of counts in an orthodox Bayesian analysis
using the well known Poisson-Gamma model. The overall resulting model allows us
to either predict the future evolution of the sequences on all regions, as well
as, estimating the consequences of eventual scenarios.Comment: Related to: https://github.com/scabras/covid19-bayes-d
Auxetic two-dimensional lattice with Poisson's Ratio arbitrarily close to -1
In this paper we propose a new lattice structure having macroscopic Poisson's
ratio arbitrarily close to the stability limit -1. We tested experimentally the
effective Poisson's ratio of the micro-structured medium; the uniaxial test has
been performed on a thermoplastic lattice produced with a 3d printing
technology. A theoretical analysis of the effective properties has been
performed and the expression of the macroscopic constitutive properties is
given in full analytical form as a function of the constitutive properties of
the elements of the lattice and on the geometry of the microstructure. The
analysis has been performed on three micro-geometry leading to an isotropic
behaviour for the cases of three-fold and six-fold symmetry and to a cubic
behaviour for the case of four-fold symmetry.Comment: 26 pages, 12 figures (26 subfigures
A class of auxetic three-dimensional lattices
We propose a class of auxetic three-dimensional lattice structures. The
elastic microstructure can be designed in order to have omni-directional
Poisson's ratio arbitrarily close to the stability limit -1. The cubic behavior
of the periodic system has been fully characterized; the minumum and maximum
Poisson's ratio and the associated principal directions are given as a function
of the microstructural parameters. The initial microstructure is then modified
into a body centered-cubic system that can achieve a Poisson's ratio lower than
-1 and that can also behave as an isotropic three-dimensional auxetic
structure.Comment: 24 pages, 16 Figures (33 subfigures
Functorial prolongations of some functional bundles
We discuss two kinds of functorial prolongations of the functional bundle of
all smooth maps between the fibers over the same base point of two fibered
manifolds over the same base. We study the prolongation of vector fields in
both cases and we prove that the bracket is preserved. Our proof is based on
several new results concerning the finite dimensional Weil bundles
Rotational inertia interface in a dynamic lattice of flexural beams
The paper presents a novel analysis of a transmission problem for a network
of flexural beams incorporating conventional Euler-Bernoulli beams as well as
Rayleigh beams with the enhanced rotational inertia. Although, in the
low-frequency regime, these beams have a similar dynamic response, we have
demonstrated novel features which occur in the transmission at higher
frequencies across the layer of the Rayleigh beams.Comment: 20 page
Free and forced wave propagation in a Rayleigh-beam grid: flat bands, Dirac cones, and vibration localization vs isotropization
In-plane wave propagation in a periodic rectangular grid beam structure,
which includes rotational inertia (so-called 'Rayleigh beams'), is analyzed
both with a Floquet-Bloch exact formulation for free oscillations and with a
numerical treatment (developed with PML absorbing boundary conditions) for
forced vibrations (including Fourier representation and energy flux
evaluations), induced by a concentrated force or moment. A complex interplay is
observed between axial and flexural vibrations (not found in the common
idealization of out-of-plane motion), giving rise to several forms of vibration
localization: 'X-', 'cross-' and 'star-' shaped, and channel propagation. These
localizations are triggered by several factors, including rotational inertia
and slenderness of the beams and the type of forcing source (concentrated force
or moment). Although the considered grid of beams introduces an orthotropy in
the mechanical response, a surprising 'isotropization' of the vibration is
observed at special frequencies. Moreover, rotational inertia is shown to
'sharpen' degeneracies related to Dirac cones (which become more pronounced
when the aspect ratio of the grid is increased), while the slenderness can be
tuned to achieve a perfectly flat band in the dispersion diagram. The obtained
results can be exploited in the realization of metamaterials designed to
control wave propagation.Comment: 25 pages, 20 figure
Approximate Bayesian Computation by Modelling Summary Statistics in a Quasi-likelihood Framework
Approximate Bayesian Computation (ABC) is a useful class of methods for
Bayesian inference when the likelihood function is computationally intractable.
In practice, the basic ABC algorithm may be inefficient in the presence of
discrepancy between prior and posterior. Therefore, more elaborate methods,
such as ABC with the Markov chain Monte Carlo algorithm (ABC-MCMC), should be
used. However, the elaboration of a proposal density for MCMC is a sensitive
issue and very difficult in the ABC setting, where the likelihood is
intractable. We discuss an automatic proposal distribution useful for ABC-MCMC
algorithms. This proposal is inspired by the theory of quasi-likelihood (QL)
functions and is obtained by modelling the distribution of the summary
statistics as a function of the parameters. Essentially, given a real-valued
vector of summary statistics, we reparametrize the model by means of a
regression function of the statistics on parameters, obtained by sampling from
the original model in a pilot-run simulation study. The QL theory is well
established for a scalar parameter, and it is shown that when the conditional
variance of the summary statistic is assumed constant, the QL has a closed-form
normal density. This idea of constructing proposal distributions is extended to
non constant variance and to real-valued parameter vectors. The method is
illustrated by several examples and by an application to a real problem in
population genetics.Comment: Published at http://dx.doi.org/10.1214/14-BA921 in the Bayesian
Analysis (http://projecteuclid.org/euclid.ba) by the International Society of
Bayesian Analysis (http://bayesian.org/
Prestress tuning of negative refraction and wave channeling from flexural sources
The quest for wave channeling and manipulation has driven a strong research
effort on topological and architected materials, capable of propagating
localized electromagnetical or mechanical signals. With reference to an elastic
structural grid, which elements can sustain both axial and flexural
deformations, it is shown that material interfaces can be created with
structural properties tuned by prestress states to achieve total reflection,
negative refraction, and strongly localized signal channeling. The achievement
of a flat lens and topologically localized modes is demonstrated and tunability
of the system allows these properties to hold for a broad range of wavelengths.
An ingredient to obtain these effects is the use, suggested here and never
attempted before, of concentrated pulsating moments. The important aspect of
the proposed method is that states of prestress can be easily removed or
changed to tune with continuity the propagational characteristics of the
medium, so that a new use of vibration channeling and manipulation is envisaged
for elastic materials.Comment: 10 pages, 5 figure
- …