14,844 research outputs found
Bayesian inference and non-linear extensions of the CIRCE method for quantifying the uncertainty of closure relationships integrated into thermal-hydraulic system codes
Uncertainty Quantification of closure relationships integrated into
thermal-hydraulic system codes is a critical prerequisite in applying the
Best-Estimate Plus Uncertainty (BEPU) methodology for nuclear safety and
licensing processes.The purpose of the CIRCE method is to estimate the
(log)-Gaussian probability distribution of a multiplicative factor applied to a
reference closure relationship in order to assess its uncertainty. Even though
this method has been implemented with success in numerous physical scenarios,
it can still suffer from substantial limitations such as the linearity
assumption and the difficulty of properly taking into account the inherent
statistical uncertainty. In the paper, we will extend the CIRCE method in two
aspects. On the one hand, we adopt the Bayesian setting putting prior
probability distributions on the parameters of the (log)-Gaussian distribution.
The posterior distribution of the parameters is then computed with respect to
an experimental database by means of Markov Chain Monte Carlo (MCMC)
algorithms. On the other hand, we tackle the more general setting where the
simulations do not move linearly against the multiplicative factor(s). MCMC
algorithms then become time-prohibitive when the thermal-hydraulic simulations
exceed a few minutes. This handicap is overcome by using Gaussian process (GP)
emulators which can yield both reliable and fast predictions of the
simulations. The GP-based MCMC algorithms will be applied to quantify the
uncertainty of two condensation closure relationships at a safety injection
with respect to a database of experimental tests. The thermal-hydraulic
simulations will be run with the CATHARE 2 computer code.Comment: 37 pages, 5 figure
A framework for Thinking about Distributed Cognition
As is often the case when scientific or engineering fields emerge, new concepts are forged or old ones are adapted. When this happens, various arguments rage over what ultimately turns out to be conceptual misunderstandings. At that critical time, there is a need for an explicit reflection on the meaning of the concepts that define the field. In this position paper, we aim to provide a reasoned framework in which to think about various issues in the field of distributed cognition. We argue that both relevant concepts, distribution and cognition, must be understood as continuous. As it is used in the context of distributed cognition, the concept of distribution is essentially fuzzy, and we will link it to the notion of emergence of system-level properties. The concept of cognition must also be seen as fuzzy, but for different a reason: due its origin as an anthropocentric concept, no one has a clear handle on its meaning in a distributed setting. As the proposed framework forms a space, we then explore its geography and (re)visit famous landmarks
Majority voting with stochastic preferences : The whims of a committee are smaller than the whims of its members.
We study the volatility of the policy chosen by a committee whose members have volatile preferences. It is smaller than if it was chosen by a single member, smaller the larger the size of the committee, and smaller the volatility of members' preferences.Committee, majority voting, uncertainty, volatility.
The Making of International Environmental Agreements
We examine in this paper the formation and the stability of international environmental agreements when cooperation means to commit to a minimum abatement level. Each country decides whether to ratify the agreement and this latter enters into force only if it is ratified by a number of countries at least equal to some ratification threshold. We analyze the role played by ratification threshold rules and provide conditions for international environmental agreements to enter into force. We show that a large typology of agreements can enter into force among the one constituted by the grand coalition.International Environmental Agreement,
Global well-posedness of a conservative relaxed cross diffusion system
We prove global existence in time of solutions to relaxed conservative cross
diffusion systems governed by nonlinear operators of the form where the represent
density-functions, is a spatially regularized form of
and the nonlinearities are merely assumed to be
continuous and bounded from below. Existence of global weak solutions is
obtained in any space dimension. Solutions are proved to be regular and unique
when the are locally Lipschitz continuous
New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized
The definitional equality of an intensional type theory is its test of type
compatibility. Today's systems rely on ordinary evaluation semantics to compare
expressions in types, frustrating users with type errors arising when
evaluation fails to identify two `obviously' equal terms. If only the machine
could decide a richer theory! We propose a way to decide theories which
supplement evaluation with `-rules', rearranging the neutral parts of
normal forms, and report a successful initial experiment.
We study a simple -calculus with primitive fold, map and append operations on
lists and develop in Agda a sound and complete decision procedure for an
equational theory enriched with monoid, functor and fusion laws
Splitting methods with variable metric for KL functions
We study the convergence of general abstract descent methods applied to a
lower semicontinuous nonconvex function f that satisfies the
Kurdyka-Lojasiewicz inequality in a Hilbert space. We prove that any precompact
sequence converges to a critical point of f and obtain new convergence rates
both for the values and the iterates. The analysis covers alternating versions
of the forward-backward method with variable metric and relative errors. As an
example, a nonsmooth and nonconvex version of the Levenberg-Marquardt algorithm
is detailled
Accretion Dynamics on Wet Granular Materials
Wet granular aggregates are common precursors of construction materials,
food, and health care products. The physical mechanisms involved in the mixing
of dry grains with a wet substrate are not well understood and difficult to
control. Here, we study experimentally the accretion of dry grains on a wet
granular substrate by measuring the growth dynamics of the wet aggregate. We
show that this aggregate is fully saturated and its cohesion is ensured by the
capillary depression at the air-liquid interface. The growth dynamics is
controlled by the liquid fraction at the surface of the aggregate and exhibits
two regimes. In the viscous regime, the growth dynamics is limited by the
capillary-driven flow of liquid through the granular packing to the surface of
the aggregate. In the capture regime, the capture probability depends on the
availability of the liquid at the saturated interface, which is controlled by
the hydrostatic depression in the material. We propose a model that
rationalizes our observations and captures both dynamics based on the evolution
of the capture probability with the hydrostatic depression
Geodesics for a class of distances in the space of probability measures
In this paper, we study the characterization of geodesics for a class of
distances between probability measures introduced by Dolbeault, Nazaret and
Savar e. We first prove the existence of a potential function and then give
necessary and suffi cient optimality conditions that take the form of a coupled
system of PDEs somehow similar to the Mean-Field-Games system of Lasry and
Lions. We also consider an equivalent formulation posed in a set of probability
measures over curves
A Bayesian alternative to mutual information for the hierarchical clustering of dependent random variables
The use of mutual information as a similarity measure in agglomerative
hierarchical clustering (AHC) raises an important issue: some correction needs
to be applied for the dimensionality of variables. In this work, we formulate
the decision of merging dependent multivariate normal variables in an AHC
procedure as a Bayesian model comparison. We found that the Bayesian
formulation naturally shrinks the empirical covariance matrix towards a matrix
set a priori (e.g., the identity), provides an automated stopping rule, and
corrects for dimensionality using a term that scales up the measure as a
function of the dimensionality of the variables. Also, the resulting log Bayes
factor is asymptotically proportional to the plug-in estimate of mutual
information, with an additive correction for dimensionality in agreement with
the Bayesian information criterion. We investigated the behavior of these
Bayesian alternatives (in exact and asymptotic forms) to mutual information on
simulated and real data. An encouraging result was first derived on
simulations: the hierarchical clustering based on the log Bayes factor
outperformed off-the-shelf clustering techniques as well as raw and normalized
mutual information in terms of classification accuracy. On a toy example, we
found that the Bayesian approaches led to results that were similar to those of
mutual information clustering techniques, with the advantage of an automated
thresholding. On real functional magnetic resonance imaging (fMRI) datasets
measuring brain activity, it identified clusters consistent with the
established outcome of standard procedures. On this application, normalized
mutual information had a highly atypical behavior, in the sense that it
systematically favored very large clusters. These initial experiments suggest
that the proposed Bayesian alternatives to mutual information are a useful new
tool for hierarchical clustering
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