223 research outputs found
Full metastable asymptotic of the Fisher information
We establish an expansion by Gamma-convergence of the Fisher information
relative to the reference measure exp(-beta V), where V is a generic multiwell
potential and beta goes to infinity. The expansion reveals a hierarchy of
multiple scales reflecting the metastable behavior of the underlying overdamped
Langevin dynamics: distinct scales emerge and become relevant depending on
whether one considers probability measures concentrated on local minima of V,
probability measures concentrated on critical points of V, or generic
probability measures on R^d. We thus fully describe the asymptotic behavior of
minima of the Fisher information over regular sets of probabilities. The
analysis mostly relies on spectral properties of diffusion operators and the
related semiclassical Witten Laplacian and covers also the case of a compact
smooth manifold as underlying space.Comment: 24 pages. Typos correcte
Spectral Analysis of Discrete Metastable Diffusions
We consider a discrete Schr\"odinger operator on , where is a small parameter and the potential
is defined in terms of a multiwell energy landscape on
. This operator can be seen as a discrete analog of the
semiclassical Witten Laplacian of . It is unitarily equivalent to
the generator of a diffusion on , satisfying the
detailed balance condition with respect to the Boltzmann weight
. These type of diffusions exhibit metastable behaviour
and arise in the context of disordered mean field models in Statistical
Mechanics. We analyze the bottom of the spectrum of in the
semiclassical regime and show that there is a one-to-one
correspondence between exponentially small eigenvalues and local minima of .
Then we analyze in more detail the bistable case and compute the precise
asymptotic splitting between the two exponentially small eigenvalues. Through
this purely spectral-theoretical analysis of the discrete Witten Laplacian we
recover in a self-contained way the Eyring-Kramers formula for the metastable
tunneling time of the underlying stochastic process
An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension two
We study spectral Galerkin approximations of an Allen--Cahn equation over the
two-dimensional torus perturbed by weak space-time white noise of strength
. We introduce a Wick renormalisation of the equation in
order to have a system that is well-defined as the regularisation is removed.
We show sharp upper and lower bounds on the transition times from a
neighbourhood of the stable configuration to the stable configuration
in the asymptotic regime . These estimates are uniform in
the discretisation parameter , suggesting an Eyring-Kramers formula for the
limiting renormalised stochastic PDE. The effect of the "infinite
renormalisation" is to modify the prefactor and to replace the ratio of
determinants in the finite-dimensional Eyring-Kramers law by a renormalised
Carleman-Fredholm determinant.Comment: 28 pages, 1 Figure. Revised version with expanded discussio
Jump Markov models and transition state theory: the Quasi-Stationary Distribution approach
We are interested in the connection between a metastable continuous state
space Markov process (satisfying e.g. the Langevin or overdamped Langevin
equation) and a jump Markov process in a discrete state space. More precisely,
we use the notion of quasi-stationary distribution within a metastable state
for the continuous state space Markov process to parametrize the exit event
from the state. This approach is useful to analyze and justify methods which
use the jump Markov process underlying a metastable dynamics as a support to
efficiently sample the state-to-state dynamics (accelerated dynamics
techniques). Moreover, it is possible by this approach to quantify the error on
the exit event when the parametrization of the jump Markov model is based on
the Eyring-Kramers formula. This therefore provides a mathematical framework to
justify the use of transition state theory and the Eyring-Kramers formula to
build kinetic Monte Carlo or Markov state models.Comment: 14 page
Best Translation Practices of Medical Language Terms in the Works of Galdós: the Example of Fortunata y Jacinta
In this paper, through the study of some terms present in the novel Fortunata y Jacinta by Galdós that refer to the medical and pharmaceutical field, we want to carry out a reflection on some ‘best practices’ that the translator can use in his rewriting work, considered as the result of a cognitive operation, a complex intrigue of acquisition, categorization, reflective observation, elaboration, experimentation and creation of emotional-motivational dynamics which has, as its ultimate product, the recreation of the metatext. These 'best practices' fall to all intents and purposes in the topics to be treated within a teaching of translation with a neurolinguistic slant.In quest’articolo, attraverso lo studio di alcuni termini presenti nel romanzo Fortunata y Jacinta di Galdós che si riferiscono all’ambito medico e farmaceutico, si desidera portare avanti una riflessione su alcune “buone prassi” che il traduttore può impiegare nel suo lavoro di riscrittura, considerate come il frutto di un’operazione cognitiva, complesso intrigo di acquisizione, categorizzazione, osservazione riflessiva, elaborazione, sperimentazione e di creazione di dinamiche emotivo-motivazionali che hanno come prodotto ultimo la ricreazione del metatesto. Tali “buone prassi” rientrano a tutti gli effetti negli argomenti da trattare all’interno di una didattica della traduzione dal taglio neurolinguistico
L'"OSTINATO RIGORE" DEL TRADUTTORE
The reflection on the role of the translator, on his way of approaching a prototext, on the responsibility of constructing a metatext can only be described in the Leonardian terms of an "Ostinato Rigore", or in terms of method and will. The rigor, therefore, the method can be seen as the sum of the skills, abilities and competences that allow the translator to manage the translation process. It is in the actual translation in which the "rigor" becomes "obstinate", that is, the method merges with the desire to seek the most adequate rendering in the target text and it is in this cognitive operation that psychophysiological components come into play such as memory and emotional-motivational dynamics
Simboli religiosi e libertà religiosa. Profili costituzionali
The essay analyzes some aspects of the freedom of religion enshrined in the Italian Constitution in relation to the principle of secularism as supreme principle of the Italian Republic, according to the definition of the italian Constitutional Court; and the extension of religious symbols and, in particular, the crucifix. First of all, the essay analyzes the question of «Italian» secularism, verifying the disparities and similarities among the various declinations of this principle, reconstructing the debate in the constituent assembly and the main jurisprudential approaches of the Italian Constitutional Court in this matter. Secondly, the essay analyzes the issue of religious symbols in public spaces and, in particular, a leading case concerning the exhibition of the crucifix in the classrooms, both at the jurisprudence level (Administrative Judge, Constitutional Court, EDU Court), and at doctrinal one. The essay, then, notes the cd. Bavarian solution, adopted by the Government of the homonymous German region, in search of a reconciliation between the religious freedom of each person and the quantitative factor per single religion. There is also an excursus on the main case law of the European Court of Human Rights about secularity, religious freedom and religious symbols
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