Kolmogorov equations on spaces of measures associated to nonlinear filtering processes

We introduce and study some backward Kolmogorov equations associated to stochastic filtering problems. Measure-valued processed arise naturally in the context of stochastic filtering and one can formulate two stochastic differential equations, called Zakai and Kushner-Stratonovitch equation, that are satisfied by a positive measure and a probability measure-valued process respectively. The associated Kolmogorov equations have been intensively studied, mainly assuming that the measure-valued processes admit a density and then by exploiting stochastic calculus techniques in Hilbert spaces. Our approach differs from this since we do not assume the existence of a density and we work directly in the context of measures. We first formulate two Kolmogorov equations of parabolic type, one on a space of positive measures and one on a space of probability measures, and then we prove existence and uniqueness of classical solutions. In order to do that, we prove some intermediate results of independent interest. In particular, we prove It\^o formulas for the composition of measure-valued filtering processes and real-valued functions. Moreover we study the regularity of the solution to the filtering equations with respect to the initial datum. In order to achieve these results, proper notions of derivatives on space of positive measures have been introduced and discussed

On smooth approximations in the Wasserstein space

In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are able to construct a sequence of infinitely differentiable functions having the same Lipschitz constant as the original function. This solves an open problem raised in [11]. For (resp. twice) continuously differentiable function, we show that our approximation also holds for the first-order derivative (resp. second-order derivatives), therefore solving another open problem raised in [11]

A Novel T6 Rapid Heat Treatment for AlSi10Mg Alloy Produced by Laser-Based Powder Bed Fusion: Comparison with T5 and Conventional T6 Heat Treatments

AlSi10Mg is the most widely studied Al alloy used to produce components by laser-basedpowder bed fusion (LPBF), also known as selective laser melting. Several papers have alreadyinvestigated the effects of conventional heat treatment on the microstructure and mechanicalbehavior of the LPBF AlSi10Mg alloy, overlooking, however, the particular microstructureinduced by rapid solidification. This paper reports on the effects of a T5 heat treatment and anovel T6 heat treatment on microstructure and mechanical behavior of the LPBF AlSi10Mgalloy, consisting of rapid solution (10 minutes at 510°C) followed by artificial aging (6 hours at160°C). The short solution soaking time reduced the typical porosity growth occurring at thehigh temperature and led to a homogeneous distribution of fine globular Si particles in the Almatrix. In addition, it limited the diffusion processes, increasing the amount of Mg and Si insolid solution available for precipitation hardening and avoiding the microstructuralcoarsening. As a result, the strength-ductility balance was improved by increasing both yieldstrength and elongation to failure, respectively of about 14 and 7 pct compared with the bestsolution among those reported in the literature for conventional T6 heat treatment of LPBFAlSi10Mg alloy

Stochastic Control of Inertial Sea Wave Energy Converter

The ISWEC (inertial sea wave energy converter) is presented, its control problems are stated, and an optimal control strategy is introduced. As the aim of the device is energy conversion, the mean absorbed power by ISWEC is calculated for a plane 2D irregular sea state. The response of the WEC (wave energy converter) is driven by the sea-surface elevation, which is modeled by a stationary and homogeneous zero mean Gaussian stochastic process. System equations are linearized thus simplifying the numerical model of the device. The resulting response is obtained as the output of the coupled mechanic-hydrodynamic model of the device. A stochastic suboptimal controller, derived from optimal control theory, is defined and applied to ISWEC. Results of this approach have been compared with the ones obtained with a linear spring-damper controller, highlighting the capability to obtain a higher value of mean extracted power despite higher power peaks

Evolution of infectious bronchitis virus in the field after homologous vaccination introduction

International audienceAbstractDespite the fact that vaccine resistance has been typically considered a rare phenomenon, some episodes of vaccine failure have been reported with increasing frequency in intensively-raised livestock. Infectious bronchitis virus (IBV) is a widespread avian coronavirus, whose control relies mainly on extensive vaccine administration. Unfortunately, the continuous emergence of new vaccine-immunity escaping variants prompts the development of new vaccines. In the present work, a molecular epidemiology study was performed to evaluate the potential role of homologous vaccination in driving IBV evolution. This was undertaken by assessing IBV viral RNA sequences from the ORF encoding the S1 portion of viral surface glycoprotein (S) before and after the introduction of a new live vaccine on broiler farms in northern-Italy. The results of several biostatistics analyses consistently demonstrate the presence of a higher pressure in the post-vaccination period. Natural selection was detected essentially on sites located on the protein surface, within or nearby domains involved in viral attachment or related functions. This evidence strongly supports the action of vaccine-induced immunity in conditioning viral evolution, potentially leading to the emergence of new vaccine-escape variants. The great plasticity of rapidly-evolving RNA-viruses in response to human intervention, which extends beyond the poultry industry, is demonstrated, claiming further attention due to their relevance for animal and especially human health

Evaluation of Bacillus thuringiensis subsp. Israelensis and Bacillus sphaericus combination against Culex pipiens in highly vegetated ditches

9openInternationalItalian coauthor/editorAmong the few mosquito larvicides available in the market, Bacillus thuringiensis subsp. israelensis (Bti) and B. sphaericus (Bs) represent the most environmentally safe alternatives. The combination of the 2 products is known to overcome their specific limitations by producing a synergistic effect. The aim of the study was to assess the effect and persistence of a single treatment with a granular Bti + Bs formulation on highly vegetated ditches in northeastern Italy that represents the primary rural larval sites for Culex pipiens, the primary vector of the West Nile virus in Europe. The analysis takes into account the nonlinear temporal effects on the population dynamics of larvae and pupae. The results showed a dramatic reduction in mosquito larval abundance 24 h posttreatment (93%) and was effective against larvae up to 22 days (100%). The residual effect after 28 days was 99.5%, and a limited residual effect was observed after 39 days (31.2%). A reduction in pupal density was observed after 4 days (70%) and was >98% from days 14 to 28 posttreatment, persisting for up to 39 days (84% after 39 days). The results demonstrate the effective use of the Bti + Bs formulation against Cx. pipiens in vegetated ditches in rural areas. Our modeling framework provides a flexible statistical approach to predict the residual effect of the product over time, in order to plan a seasonal intervention scheme.openVirgillito, Chiara; Manica, Mattia; Marini, Giovanni; Rosà, Roberto; Della Torre, Alessandra; Martini, Simone; Drago, Andrea; Baseggio, Alberto; Caputo, BeniaminoVirgillito, C.; Manica, M.; Marini, G.; Rosà, R.; Della Torre, A.; Martini, S.; Drago, A.; Baseggio, A.; Caputo, B

avian metapneumovirus circulation in italian broiler farms

Abstract With increasing frequency, avian Metapneumovirus (aMPV) is reported to induce respiratory signs in chickens. An adequate knowledge of current aMPV prevalence among Italian broilers is lacking, with little information available on its economical and health impact on the poultry industry. In order to collect preliminary data on the epidemiological context of aMPV in broiler flocks, a survey was performed in areas of Northern Italy with high poultry density from 2014 to 2016. Upper respiratory tract swabs were collected and processed by A and B subtype-specific multiplex real-time reverse transcription PCR (RT-PCR). Samples were also screened for infectious bronchitis virus (IBV) by generic RT-PCR and sequencing. Productive data and respiratory signs were detailed where possible. The high prevalence of aMPV was confirmed in broilers older than 26 d and also attested in IBV-negative farms. All aMPV detections belonged to subtype B. Italian strain genetic variability was evaluated by the partial attachment (G) gene sequencing of selected strains and compared with contemporary turkey strains and previously published aMPV references, revealing no host specificity and the progressive evolution of this virus in Italy

Where do Chip and Dale come from? Origins of invasive populations of the Siberian chipmunk in Europe

Among invasive squirrels in Europe, the Siberian chipmunk Eutamias sibiricus, native to North-East Asia, shows the highest number of free-ranging populations in European countries, due to the intense pet trade it underwent between the 1960s and the 1980s. We describe 628-bp cytochrome b sequences from the Netherlands (N = 3), Belgium (N = 4) and Switzerland (N = 1), and through phylogenetic analysis show that they belong to the Korean subspecies. This confirms previous findings that the Korean subspecies (Eutamias sibiricus barberi) has been the most commonly introduced to Europe. Another subspecies (the Northern subspecies, Eutamias sibiricus sibiricus) has only been reported previously in an Italian free-living population. If the splitting of the Korean taxon as a proper species (Eutamias barberi) will be confirmed by analysis of nuclear markers, a revision of the European Regulation 1143/2014 should be conducted to explicitly ban the trade of newly identified taxa.Support to MM for this research (grant LCF/BQ/DR20/11790020) was provided by ‘La Caixa’ Foundation (ID 100010434)