On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity

We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local (in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedeness result is shown for all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying to a strong angular singularity, except in the special case of Maxwell molecules. Our proof relies on the ideas of Tanaka: we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to couple two such processes started with two different initial conditions, in such a way that they almost surely remain close to each other

Results and recommendations from an intercomparison of six Hygroscopicity-TDMA systems

The performance of six custom-built Hygrocopicity-Tandem Differential Mobility Analyser (H-TDMA) systems was investigated in the frame of an international calibration and intercomparison workshop held in Leipzig, February 2006. The goal of the workshop was to harmonise H-TDMA measurements and develop recommendations for atmospheric measurements and their data evaluation. The H-TDMA systems were compared in terms of the sizing of dry particles, relative humidity (RH) uncertainty, and consistency in determination of number fractions of different hygroscopic particle groups. The experiments were performed in an air-conditioned laboratory using ammonium sulphate particles or an external mixture of ammonium sulphate and soot particles. The sizing of dry particles of the six H-TDMA systems was within 0.2 to 4.2% of the selected particle diameter depending on investigated size and individual system. Measurements of ammonium sulphate aerosol found deviations equivalent to 4.5% RH from the set point of 90% RH compared to results from previous experiments in the literature. Evaluation of the number fraction of particles within the clearly separated growth factor modes of a laboratory generated externally mixed aerosol was done. The data from the H-TDMAs was analysed with a single fitting routine to investigate differences caused by the different data evaluation procedures used for each H-TDMA. The differences between the H-TDMAs were reduced from +12/-13% to +8/-6% when the same analysis routine was applied. We conclude that a common data evaluation procedure to determine number fractions of externally mixed aerosols will improve the comparability of H-TDMA measurements. It is recommended to ensure proper calibration of all flow, temperature and RH sensors in the systems. It is most important to thermally insulate the aerosol humidification unit and the second DMA and to monitor these temperatures to an accuracy of 0.2 degrees C. For the correct determination of external mixtures, it is necessary to take into account size-dependent losses due to diffusion in the plumbing between the DMAs and in the aerosol humidification unit.Peer reviewe

Derivation of the particle dynamics from kinetic equations

We consider the microscopic solutions of the Boltzmann-Enskog equation discovered by Bogolyubov. The fact that the time-irreversible kinetic equation has time-reversible microscopic solutions is rather surprising. We analyze this paradox and show that the reversibility or irreversibility property of the Boltzmann-Enskog equation depends on the considered class of solutions. If the considered solutions have the form of sums of delta-functions, then the equation is reversible. If the considered solutions belong to the class of continuously differentiable functions, then the equation is irreversible. Also, we construct the so called approximate microscopic solutions. These solutions are continuously differentiable and they are reversible on bounded time intervals. This analysis suggests a way to reconcile the time-irreversible kinetic equations with the time-reversible particle dynamics. Usually one tries to derive the kinetic equations from the particle dynamics. On the contrary, we postulate the Boltzmann-Enskog equation or another kinetic equation and treat their microscopic solutions as the particle dynamics. So, instead of the derivation of the kinetic equations from the microdynamics we suggest a kind of derivation of the microdynamics from the kinetic equations.Comment: 18 pages; some misprints have been corrected, some references have been adde

Measurement and classification of human characteristics and capabilities during interaction tasks

In this paperwe address the need to design adaptive interacting systems for advanced industrial production machines. Modern production systems have become highly complex and include many subsidiary functionalities, thus making it difficult for least skilled human operators interact with them. In this regard, adapting the behavior of the machine and of the operator interface to the characteristics of the user allows a more effective interaction process, with a positive impact on manufacturing efficiency and user's satisfaction. To this end, it is crucial to understandwhich are the user's capabilities that influence the interaction and, hence, should be measured to provide the correct amount of adaptation.Moving along these lines, in this paper we identify groups of users that, despite having different individual capabilities and features, have common needs and response to the interaction with complex production systems. As a consequence,we define clusters of users that have the same need for adaptation. Then, adaptation rules can be defined by considering such users' clusters, rather than addressing specific individual user's needs

Consideration of nutritional value and food labels are associated with food intake in adults with depression

Background/Aims: Individuals with depression are more likely to consume poor diets and as a result are at increased risk of poor cardiometabolic health. Healthy diet may reduce depressive symptoms, however better understanding is needed of factors that support healthy eating in this population. There is limited evidence about how much consideration of the nutritional value of foods may be associated with food choices. The aim of this study was to investigate associations between food intake and consideration of nutritional value of foods in adults with depression. Methods: Adults (n = 161) with depression completed a semi-quantitative food frequency questionnaire and shopping and budgeting questionnaire. Associations between consideration of nutritional value and nutrition label use with vegetable, wholegrain, legume, snack food and soft drink intake were evaluated using linear regression, adjusting for age, gender and education. Results: In adjusted models, more consideration of the nutrition value of foods was positively associated with vegetable intake (β = 0.188; p = 0.025), wholegrain intake (β = 0.213; p = 0.015) and negatively associated with snack food intake (β = -0.236, p = 0.006). More frequent reading of nutrition labels was positively associated with legume intake (β = 0.185; p = 0.036). Better understanding of nutrition labels was positively associated with vegetable intake (β = 0.780; p = 0.035), wholegrain intake (β = 0.233; p = 0.008), and legume intake (β = 0.254; p = 0.004). There were no associations between soft drink intake and nutrition value consideration or nutrition label use. Conclusions: These findings suggest that increasing consideration of the nutrition value of foods and nutrition label use may support healthy eating in adults with depression

Fast Optimal Transport Averaging of Neuroimaging Data

Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a voxel grid or a triangulation remains a challenge. Data are large, the geometry of the brain is complex and the between subjects variability leads to spatially or temporally non-overlapping effects of interest. To address the problem of variability, data are commonly smoothed before group linear averaging. In this work we build on ideas originally introduced by Kantorovich to propose a new algorithm that can average efficiently non-normalized data defined over arbitrary discrete domains using transportation metrics. We show how Kantorovich means can be linked to Wasserstein barycenters in order to take advantage of an entropic smoothing approach. It leads to a smooth convex optimization problem and an algorithm with strong convergence guarantees. We illustrate the versatility of this tool and its empirical behavior on functional neuroimaging data, functional MRI and magnetoencephalography (MEG) source estimates, defined on voxel grids and triangulations of the folded cortical surface.Comment: Information Processing in Medical Imaging (IPMI), Jun 2015, Isle of Skye, United Kingdom. Springer, 201

Lung segmentation and characterization in covid-19 patients for assessing pulmonary thromboembolism: An approach based on deep learning and radiomics

The COVID-19 pandemic is inevitably changing the world in a dramatic way, and the role of computed tomography (CT) scans can be pivotal for the prognosis of COVID-19 patients. Since the start of the pandemic, great care has been given to the relationship between interstitial pneumonia caused by the infection and the onset of thromboembolic phenomena. In this preliminary study, we collected n = 20 CT scans from the Polyclinic of Bari, all from patients positive with COVID-19, nine of which developed pulmonary thromboembolism (PTE). For eight CT scans, we obtained masks of the lesions caused by the infection, annotated by expert radiologists; whereas for the other four CT scans, we obtained masks of the lungs (including both healthy parenchyma and lesions). We developed a deep learning-based segmentation model that utilizes convolutional neural networks (CNNs) in order to accurately segment the lung and lesions. By considering the images from publicly available datasets, we also realized a training set composed of 32 CT scans and a validation set of 10 CT scans. The results obtained from the segmentation task are promising, allowing to reach a Dice coefficient higher than 97%, posing the basis for analysis concerning the assessment of PTE onset. We characterized the segmented region in order to individuate radiomic features that can be useful for the prognosis of PTE. Out of 919 extracted radiomic features, we found that 109 present different distributions according to the Mann–Whitney U test with corrected p-values less than 0.01. Lastly, nine uncorrelated features were retained that can be exploited to realize a prognostic signature