Search results for "convergence"
showing 10 items of 655 documents
Gamma-convergence of Gaussian fractional perimeter
2021
Abstract We prove the Γ-convergence of the renormalised Gaussian fractional s-perimeter to the Gaussian perimeter as s → 1 - {s\to 1^{-}} . Our definition of fractional perimeter comes from that of the fractional powers of Ornstein–Uhlenbeck operator given via Bochner subordination formula. As a typical feature of the Gaussian setting, the constant appearing in front of the Γ-limit does not depend on the dimension.
Derivation of Models for Thin Sprays from a Multiphase Boltzmann Model
2017
We shall review the validation of a class of models for thin sprays where a Vlasov type equation is coupled to an hydrodynamic equation of Navier–Stokes or Stokes type. We present a formal derivation of these models from a multiphase Boltzmann system for a binary mixture: under suitable assumptions on the collision kernels and in appropriate asymptotics (resp. for the two different limit models), we prove the convergence of solutions to the multiphase Boltzmann model to distributional solutions to the Vlasov–Navier–Stokes or Vlasov–Stokes system. The proofs are based on the procedure followed in Bardos et al. (J Stat Phys 63:323–344 (1991), [2]) and explicit evaluations of the coupling term…
The Division of Labour Within Households: Men’s Increased Participation?
2018
Unequal division of domestic labor has been seen as a one of the most commonly documented feature on gender inequality in the western countries. The relevance of studying the division of labour in the household has actualized as female participation rates in paid labour have increased and changes in employment systems have taken place. Division of labor refers to the amount and share of time men and women spend in paid and unpaid work. Unpaid work includes domestic chores such as cleaning, repairs, preparing meals, but also caring for children. Unpaid work is usually divided in three subgroups: core household tasks i.e. housework, repairs and household upkeep and child care. Paid and unpaid…
Parameter identification for heterogeneous materials by optimal control approach with flux cost functionals
2021
The paper deals with the identification of material parameters characterizing components in heterogeneous geocomposites provided that the interfaces separating different materials are known. We use the optimal control approach with flux type cost functionals. Since solutions to the respective state problems are not regular, in general, the original cost functionals are expressed in terms of integrals over the computational domain using the Green formula. We prove the existence of solutions to the optimal control problem and establish convergence results for appropriately defined discretizations. The rest of the paper is devoted to computational aspects, in particular how to handle high sens…
Circular law for sparse random regular digraphs
2020
Fix a constant $C\geq 1$ and let $d=d(n)$ satisfy $d\leq \ln^{C} n$ for every large integer $n$. Denote by $A_n$ the adjacency matrix of a uniform random directed $d$-regular graph on $n$ vertices. We show that, as long as $d\to\infty$ with $n$, the empirical spectral distribution of appropriately rescaled matrix $A_n$ converges weakly in probability to the circular law. This result, together with an earlier work of Cook, completely settles the problem of weak convergence of the empirical distribution in directed $d$-regular setting with the degree tending to infinity. As a crucial element of our proof, we develop a technique of bounding intermediate singular values of $A_n$ based on studyi…
Interpretable Option Discovery Using Deep Q-Learning and Variational Autoencoders
2021
Deep Reinforcement Learning (RL) is unquestionably a robust framework to train autonomous agents in a wide variety of disciplines. However, traditional deep and shallow model-free RL algorithms suffer from low sample efficiency and inadequate generalization for sparse state spaces. The options framework with temporal abstractions [18] is perhaps the most promising method to solve these problems, but it still has noticeable shortcomings. It only guarantees local convergence, and it is challenging to automate initiation and termination conditions, which in practice are commonly hand-crafted.
On the Parameterization of Cartesian Genetic Programming
2020
In this work, we present a detailed analysis of Cartesian Genetic Programming (CGP) parametrization of the selection scheme ($\mu+\lambda$), and the levels back parameter l. We also investigate CGP’s mutation operator by decomposing it into a self-recombination, node function mutation, and inactive gene randomization operators. We perform experiments in the Boolean and symbolic regression domains with which we contribute to the knowledge about efficient parametrization of two essential parameters of CGP and the mutation operator.
Exploratory spatial data analysis of the distribution of regional per capita GDP in Europe, 1980-1995
2000
The aim of this paper is to study the dynamics of European regional per capita product over time and space. This purpose is achieved by using the recently developed methods of Exploratory Spatial Data Analysis. Using a sample of European regions over the 1980-1995 period, we find strong evidence of global and local spatial autocorrelation in per capita GDP throughout the period. The detection of clusters of high and low per capita products during the period is an indication of the persistence of spatial disparities between European regions. This analysis is finally refined by the investigation of the spatial pattern of regional growth. Key words:exploratory spatial data analysis; distributi…
Institutions and Geography: Empirical tests of Spatial Growth Models for the regions of Europe
2010
This article provides an empirical assessment of the growth experiences of European regions, during the period 1991–2004, by taking into account the spatial effects due to both institutions and geography. These effects have been modelled by means of specific controls and by using a non-conventional spatial weight matrix. Results favour a model dealing with substantive spatial externalities. Within this framework, the country-specific institutions are strongly and positively related to the regional productivity's growth rate. In addition, the geo-institutional proximity increases the spatial dependence of the regional output per worker and raises the speed of convergence. By contrast, the pu…
La forma del rilievo terrestre e il problema della convergenza morfologica
2018
Argomento della presente relazione è la forma del ri-lievo terrestre. Il rilievo terrestre può essere raffigurato come un grande mosaico le cui tessere sono i versanti. Un versante può es-sere: o una superficie piana caratterizzata da una determinata espo-sizione e da una specifica inclinazione; oppure una superficie curva di tipo concavo o convesso. Ogni singolo versante è inoltre identificabile con una forma del rilievo ben definita, la cui genesi è riconducibile ad un processo morfogenetico peculiare. Ogni cambiamento nell’esposizione, nell’inclinazione o nella curvatura di un versante segna pertanto il passaggio a forme del rilievo di-verse. Complessivamente, tutti i processi morfogenet…