Numerical Bifurcation Analysis of PDEs From Lattice Boltzmann Model Simulations: a Parsimonious Machine Learning Approach

We address a three-tier data-driven approach for the numerical solution of the inverse problem in Partial Differential Equations (PDEs) and for their numerical bifurcation analysis from spatio-temporal data produced by Lattice Boltzmann model simulations using machine learning. In the first step, we exploit manifold learning and in particular parsimonious Diffusion Maps using leave-one-out cross-validation (LOOCV) to both identify the intrinsic dimension of the manifold where the emergent dynamics evolve and for feature selection over the parameter space. In the second step, based on the selected features, we learn the right-hand-side of the effective PDEs using two machine learning schemes, namely shallow Feedforward Neural Networks (FNNs) with two hidden layers and single-layer Random Projection Networks (RPNNs), which basis functions are constructed using an appropriate random sampling approach. Finally, based on the learned black-box PDE model, we construct the corresponding bifurcation diagram, thus exploiting the numerical bifurcation analysis toolkit. For our illustrations, we implemented the proposed method to perform numerical bifurcation analysis of the 1D FitzHugh-Nagumo PDEs from data generated by D1Q3 Lattice Boltzmann simulations. The proposed method was quite effective in terms of numerical accuracy regarding the construction of the coarse-scale bifurcation diagram. Furthermore, the proposed RPNN scheme was ∼ 20 to 30 times less costly regarding the training phase than the traditional shallow FNNs, thus arising as a promising alternative to deep learning for the data-driven numerical solution of the inverse problem for high-dimensional PDEs

The Pricing Behaviour of Firms in the Euro Area: New Survey Evidence

This study investigates the pricing behaviour of firms in the euro area on the basis of surveys conducted by nine Eurosystem national central banks. Overall, more than 11,000 firms participated in the survey. The results are very robust across countries. Firms operate in monopolistically competitive markets, where prices are mostly set following mark-up rules and where price discrimination is a common practice. Our evidence suggests that both time- and state-dependent pricing strategies are applied by firms in the euro area: around one-third of the companies follow mainly time-dependent pricing rules while two-thirds use pricing rules with some element of state-dependence. Although the majority of firms take into account a wide range of information, including past and expected economic developments, about one-third adopts a purely backward-looking behaviour. The pattern of results lends support to the recent wave of estimations of hybrid versions of the New Keynesian Phillips Curve. Price stickiness arises both at the stage when firms review their prices and again when they actually change prices. The most relevant factors underlying price rigidity are customer relationships – as expressed in the theories about explicit and implicit contracts – and thus, are mainly found at the price changing (second) stage of the price adjustment process. Finally, we provide evidence that firms adjust prices asymmetrically in response to shocks, depending on the direction of the adjustment and the source of the shock: while cost shocks have a greater impact when prices have to be raised than when they have to be reduced, reductions in demand are more likely to induce a price change than increases in demand.

The pricing behaviour of firms in the euro area : new survey evidence

This study investigates the pricing behaviour of firms in the euro area on the basis of surveys conducted by nine Eurosystem national central banks. Overall, more than 11,000 firms participated in the survey. The results are very robust across countries. Firms operate in monopolistically competitive markets, where prices are mostly set following mark-up rules and where price discrimination is a common practice. Our evidence suggests that both time- and state-dependent pricing strategies are applied by firms in the euro area: around one-third of the companies follow mainly time-dependent pricing rules while two-thirds use pricing rules with some element of state-dependence. Although the majority of firms take into account a wide range of information, including past and expected economic developments, about one-third adopts a purely backward-looking behaviour. The pattern of results lends support to the recent wave of estimations of hybrid versions of the New Keynesian Phillips Curve. Price stickiness arises both at the stage when firms review their prices and again when they actually change prices. The most relevant factors underlying price rigidity are customer relationships - as expressed in the theories about explicit and implicit contracts - and thus, are mainly found at the price changing (second) stage of the price adjustment process. Finally, we provide evidence that firms adjust prices asymmetrically in response to shocks, depending on the direction of the adjustment and the source of the shock: while cost shocks have a greater impact when prices have to be raised than when they have to be reduced, reductions in demand are more likely to induce a price change than increases in demand.price setting, nominal rigidity, real rigidity, inflation persistence, survey data.

Dynamical density functional theory for the drying and stratification of binary colloidal dispersions

We develop a dynamical density functional theory based model for the drying of colloidal films on planar surfaces. We consider mixtures of two different sizes of hard-sphere colloids. Depending on the solvent evaporation rate and the initial concentrations of the two species, we observe varying degrees of stratification in the final dried films. Our model predicts the various structures described in the literature previously from experiments and computer simulations, in particular the small-on-top stratified films. Our model also includes the influence of adsorption of particles to the interfaces.Comment: 13 pages, 12 figures, published in Langmui

Epidemiology of intensive care unit-acquired sepsis in Italy: results of the SPIN-UTI network

BACKGROUND: Sepsis is the major cause of mortality from any infectious disease worldwide. Sepsis may be the result of a healthcare associated infection (HAI): the most frequent adverse events during care delivery especially in Intensive Care Units (ICUs). The main aim of the present study was to describe the epidemiology of ICU-acquired sepsis and related outcomes among patients enrolled in the framework of the Italian Nosocomial Infections Surveillance in ICUs - SPIN-UTI project. STUDY DESIGN: Prospective multicenter study. METHODS: The SPIN-UTI network adopted the European protocols for patient-based HAI surveillance. RESULTS: During the five editions of the SPIN-UTI project, from 2008 to 2017, 47.0% of HAIs has led to sepsis in 832 patients. Overall, 57.0% episodes were classified as sepsis, 20.5% as severe sepsis and 22.5% as septic shock. The most common isolated microorganisms from sepsis episodes were Acinetobacter baumannii, Klebsiella pneumoniae and Pseudomonas aeruginosa. The case fatality rate increased with the severity of sepsis and the mean length of ICU-stay was significantly higher in patients with ICU-acquired sepsis than in patients without. CONCLUSION: Our study provides evidence that ICU-acquired sepsis occurs frequently in Italian ICU patients and is associated with a high case fatality rate and increased length of stay. However, in order to explain these findings further analyses are needed in this population of ICU patient

The diet of Weddell seals (Leptonychotes weddellii) in Terra Nova Bay using stable isotope analysis

Stable isotope analyses were used to investigate the diet of Weddell seals in Terra Nova Bay (Ross Sea) and the potential variation of their foraging behaviour with age, sex and body mass. For this purpose, skin samples were collected from adult breeding seals and pups, together with muscle samples of their potential prey. Our results showed variation in foraging behavior between age classes, with pups reporting lower δ13C values than adults, while no significant differences in δ15N were recorded. In addition, contrary to expectations, a mixing model analysis showed that adult seals foraged mainly on shallow benthic prey, such as Trematomus spp. (34.1%) and Dissostichus mawsoni (21.1%), rather than on pelagic fish, such as Pleuragramma antarcticum (9.8%). Overall, with this paper we provide novel diet information on a seal colony not previously sampled, adding new insight into the feeding ecology of a top Antarctic predator

MAPPA cores: an interdisciplinary approach

In the urban and periurban area of Pisa, 18 cores ranging in depth between 7 and 15 m were performed and analysed through an interdisciplinary approach, which led to an improved stratigraphic log representation. The acquired data also improved our knowledge about the palaeoenvironmental and human settlement evolution of Pisa area over the past 6000 years, evidencing the mutual interaction existing between landscape and human activities