Nonlinear microscale interactions in the kinetic theory of active particles

Benfenati, Alessandro; Coscia, Vincenzo

doi:10.1016/j.aml.2013.04.007

Cited by 14 publications

(11 citation statements)

References 14 publications

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“…The random walker (RW) method (see [51]) is a segmentation method based on a "path distance". It belongs to the classes of probabilistic methods, that allow to address several scientific tasks, such as optimization problems via Consensus-Based Optimization [62], Opinion Formation [63] or Particle Swarm Optimization [64]. More precisely, the RW method works as follows: in each image there are subregions of pixels which are marked with labels.…”

Section: The Random Walker Methodsmentioning

confidence: 99%

A Semi-Supervised Reduced-Space Method for Hyperspectral Imaging Segmentation

2021

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The development of the hyperspectral remote sensor technology allows the acquisition of images with a very detailed spectral information for each pixel. Because of this, hyperspectral images (HSI) potentially possess larger capabilities in solving many scientific and practical problems in agriculture, biomedical, ecological, geological, hydrological studies. However, their analysis requires developing specialized and fast algorithms for data processing, due the high dimensionality of the data. In this work, we propose a new semi-supervised method for multilabel segmentation of HSI that combines a suitable linear discriminant analysis, a similarity index to compare different spectra, and a random walk based model with a direct label assignment. The user-marked regions are used for the projection of the original high-dimensional feature space to a lower dimensional space, such that the class separation is maximized. This allows to retain in an automatic way the most informative features, lightening the successive computational burden. The part of the random walk is related to a combinatorial Dirichlet problem involving a weighted graph, where the nodes are the projected pixel of the original HSI, and the positive weights depend on the distances between these nodes. We then assign to each pixel of the original image a probability quantifying the likelihood that the pixel (node) belongs to some subregion. The computation of the spectral distance involves both the coordinates in a features space of a pixel and of its neighbors. The final segmentation process is therefore reduced to a suitable optimization problem coupling the probabilities from the random walker computation, and the similarity with respect the initially labeled pixels. We discuss the properties of the new method with experimental results carried on benchmark images.

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Section: The Random Walker Methodsmentioning

confidence: 99%

A Semi-Supervised Reduced-Space Method for Hyperspectral Imaging Segmentation

2021

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“…Therefore N is the total number of tweets posted during the day 1 + 3( − 1) and N = L =1 N = 699 450 is the sample size. Inside each cluster the sentiment associated to each message is driven by a reinforcement mechanism, that can be modelled by means of a GRP urn: the probability to have a tweet with positive sentiment is increasing with the number of past tweets with positive sentiment and the reinforcement is mostly driven by the most recent tweets, in the sense explained in Section 2 (conversely, a particle interacting approach to study opinion formation may be found in [8,10,11]). In Fig.…”

Section: Covid-19 Epidemic Twitter Analysismentioning

confidence: 99%

Generalized Rescaled Pólya urn and its statistical application

Aletti¹,

Crimaldi²

2022

Electron. J. Statist.

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We introduce the Generalized Rescaled Pólya (GRP) urn, that provides a generative model for a chi-squared test of goodness of fit for the long-term probabilities of clustered data, with independence between clusters and correlation, due to a reinforcement mechanism, inside each cluster. We apply the proposed test to a data set of Twitter posts about COVID-19 pandemic: in a few words, for a classical chi-squared test the data result strongly significant for the rejection of the null hypothesis (the daily long-run sentiment rate remains constant), but, taking into account the correlation among data, the introduced test leads to a different conclusion. Beside the statistical application, we point out that the GRP urn is a simple variant of the standard Eggenberger-Pólya urn, that, with suitable choices of the parameters, shows "local" reinforcement, almost sure convergence of the empirical mean to a deterministic limit and different asymptotic behaviours of the predictive mean. Moreover, the study of this model provides the opportunity to analyze stochastic approximation dynamics, that are unusual in the related literature.

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“…Some important examples include biophysics, where these techniques are involved in the observation of molecular level motion of kinesin in microtubules and of motion of myosin on actin [52], in the study of the infection path of a virus [49] or in the investigation of cytoskeletal filaments [1]; another topic involving particles tracking problem regards the observation of protein motion in cell membranes [37] or intracellular transport [32]. Other interesting areas of application include statistical mechanics [5,6], fluid dynamics and mechanics, in particular rheology [34], where the thermal motion of Brownian particles has been tracked to study local rheological properties [20], complex fluids [2,47] and microrheology in medicine [23]. Colloidal works have benefited from developments in particle tracking procedures in measuring biofluids such as mucus [48] and vitreous humor [50].…”

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confidence: 99%

Efficient Position Estimation of 3D Fluorescent Spherical Beads in Confocal Microscopy via Poisson Denoising

Benfenati¹,

Bonacci²,

Bourouina

et al. 2020

J Math Imaging Vis

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Particle estimation is a classical problem arising in many science fields, such as biophysics, fluid mechanics and biomedical imaging. Many interesting applications in these areas involve 3D imaging data: This work presents a technique to estimate the 3D coordinates of the center of spherical particles. This procedure has its core in the processing of the images of the scanned volume: It firstly applies denoising techniques to each frame of the scanned volume and then provides an estimation of both the center and the profile of the 2D intersections of the particles with the frames, by coupling the usage of Total Variation functional and of a regularized weighted Least Squares fit. Then, the 2D information is used to retrieve the 3D coordinates using geometrical properties. The experiments provide evidence that image denoising has a large impact on the performance of the particle tracking procedures, since they strongly depend on the quality of the initial acquisition. This work shows that the choice of tailored image denoising technique for Poisson noise leads to a better estimation of the particle positions.

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Nonlinear microscale interactions in the kinetic theory of active particles

Cited by 14 publications

References 14 publications

A Semi-Supervised Reduced-Space Method for Hyperspectral Imaging Segmentation

A Semi-Supervised Reduced-Space Method for Hyperspectral Imaging Segmentation

Generalized Rescaled Pólya urn and its statistical application

Efficient Position Estimation of 3D Fluorescent Spherical Beads in Confocal Microscopy via Poisson Denoising

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