Grain Dynamics in a Two-dimensional Granular Flow

We have used particle tracking methods to study the dynamics of individual balls comprising a granular flow in a small-angle two-dimensional funnel. We statistically analyze many ball trajectories to examine the mechanisms of shock propagation. In particular, we study the creation of, and interactions between, shock waves. We also investigate the role of granular temperature and draw parallels to traffic flow dynamics.Comment: 17 pages, 24 figures. To appear in Phys.Rev.E. High res./color figures etc. on http://www.nbi.dk/CATS/Granular/GrainDyn.htm

Shock waves in two-dimensional granular flow: effects of rough walls and polydispersity

We have studied the two-dimensional flow of balls in a small angle funnel, when either the side walls are rough or the balls are polydisperse. As in earlier work on monodisperse flows in smooth funnels, we observe the formation of kinematic shock waves/density waves. We find that for rough walls the flows are more disordered than for smooth walls and that shock waves generally propagate more slowly. For rough wall funnel flow, we show that the shock velocity and frequency obey simple scaling laws. These scaling laws are consistent with those found for smooth wall flow, but here they are cleaner since there are fewer packing-site effects and we study a wider range of parameters. For pipe flow (parallel side walls), rough walls support many shock waves, while smooth walls exhibit fewer or no shock waves. For funnel flows of balls with varying sizes, we find that flows with weak polydispersity behave qualitatively similar to monodisperse flows. For strong polydispersity, scaling breaks down and the shock waves consist of extended areas where the funnel is blocked completely.Comment: 11 pages, 15 figures; accepted for PR

Second-order Democratic Aggregation

Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets

Nonlinear dynamics and chaos in an optomechanical beam

[EN] Optical nonlinearities, such as thermo-optic mechanisms and free-carrier dispersion, are often considered unwelcome effects in silicon-based resonators and, more specifically, optomechanical cavities, since they affect, for instance, the relative detuning between an optical resonance and the excitation laser. Here, we exploit these nonlinearities and their intercoupling with the mechanical degrees of freedom of a silicon optomechanical nanobeam to unveil a rich set of fundamentally different complex dynamics. By smoothly changing the parameters of the excitation laser we demonstrate accurate control to activate two-and four-dimensional limit cycles, a period-doubling route and a six-dimensional chaos. In addition, by scanning the laser parameters in opposite senses we demonstrate bistability and hysteresis between two-and four-dimensional limit cycles, between different coherent mechanical states and between four-dimensional limit cycles and chaos. Our findings open new routes towards exploiting silicon-based optomechanical photonic crystals as a versatile building block to be used in neurocomputational networks and for chaos-based applications.This work was supported by the European Comission project PHENOMEN (H2020-EU-713450), the Spanish Severo Ochoa Excellence program and the MINECO project PHENTOM (FIS2015-70862-P). DNU, PDG and MFC gratefully acknowledge the support of a Ramon y Cajal postdoctoral fellowship (RYC-2014-15392), a Beatriu de Pinos postdoctoral fellowship (BP-DGR 2015 (B) and a Severo Ochoa studentship, respectively. We would like to acknowledge Jose C. Sabina de Lis, J.M. Plata Suarez, A. Trifonova and C. Masoller for fruitful discussions.Navarro-Urrios, D.; Capuj, NE.; Colombano, MF.; García, PD.; Sledzinska, M.; Alzina, F.; Griol Barres, A.... (2017). Nonlinear dynamics and chaos in an optomechanical beam. Nature Communications. 8. https://doi.org/10.1038/ncomms14965S8Strogatz, S. H. 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Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping

The problem of defining appropriate distances between shapes or images and modeling the variability of natural images by group transformations is at the heart of modern image analysis. A current trend is the study of probabilistic and statistical aspects of deformation models, and the development of consistent statistical procedure for the estimation of template images. In this paper, we consider a set of images randomly warped from a mean template which has to be recovered. For this, we define an appropriate statistical parametric model to generate random diffeomorphic deformations in two-dimensions. Then, we focus on the problem of estimating the mean pattern when the images are observed with noise. This problem is challenging both from a theoretical and a practical point of view. M-estimation theory enables us to build an estimator defined as a minimizer of a well-tailored empirical criterion. We prove the convergence of this estimator and propose a gradient descent algorithm to compute this M-estimator in practice. Simulations of template extraction and an application to image clustering and classification are also provided

Statistical Computing on Non-Linear Spaces for Computational Anatomy

International audienceComputational anatomy is an emerging discipline that aims at analyzing and modeling the individual anatomy of organs and their biological variability across a population. However, understanding and modeling the shape of organs is made difficult by the absence of physical models for comparing different subjects, the complexity of shapes, and the high number of degrees of freedom implied. Moreover, the geometric nature of the anatomical features usually extracted raises the need for statistics on objects like curves, surfaces and deformations that do not belong to standard Euclidean spaces. We explain in this chapter how the Riemannian structure can provide a powerful framework to build generic statistical computing tools. We show that few computational tools derive for each Riemannian metric can be used in practice as the basic atoms to build more complex generic algorithms such as interpolation, filtering and anisotropic diffusion on fields of geometric features. This computational framework is illustrated with the analysis of the shape of the scoliotic spine and the modeling of the brain variability from sulcal lines where the results suggest new anatomical findings

Probing the structure of a massive filament: ArTéMiS 350 and 450 μm mapping of the integral-shaped filament in Orion A

Context. The Orion molecular cloud is the closest region of high-mass star formation. It is an ideal target for investigating the detailed structure of massive star-forming filaments at high resolution and the relevance of the filament paradigm for the earliest stages of intermediate- to high-mass star formation. Aims. Within the Orion A molecular cloud, the integral-shaped filament (ISF) is a prominent, degree-long structure of dense gas and dust with clear signs of recent and ongoing high-mass star formation. Our aim is to characterise the structure of this massive filament at moderately high angular resolution (8′′ or ~0.016 pc) in order to measure the intrinsic width of the main filament, down to scales well below 0.1 pc, which has been identified as the characteristic width of filaments. Methods. We used the ArTéMiS bolometer camera at APEX to map a ~0.6 × 0.2 deg2 region covering OMC-1, OMC-2, and OMC-3 at 350 and 450 μm. We combined these data with Herschel-SPIRE maps to recover extended emission. The combined Herschel-ArTéMiS maps provide details on the distribution of dense cold material, with a high spatial dynamic range, from our 8′′ resolution up to the transverse angular size of the map, ~10-15′. By combining Herschel and ArTéMiS data at 160, 250, 350, and 450 μm, we constructed high-resolution temperature and H2 column density maps. We extracted radial intensity profiles from the column density map in several representative portions of the ISF, which we fitted with Gaussian and Plummer models to derive their intrinsic widths. We also compared the distribution of material traced by ArTéMiS with that seen in the higher-density tracer N2H+(1-0) that was recently observed with the ALMA interferometer. Results. All the radial profiles that we extracted show a clear deviation from a Gaussian, with evidence for an inner plateau that had not previously been seen clearly using Herschel-only data. We measure intrinsic half-power widths in the range 0.06-0.11 pc. This is significantly larger than the Gaussian widths measured for fibres seen in N2H+, which probably only traces the dense innermost regions of the large-scale filament. These half-power widths are within a factor of two of the value of ~0.1 pc found for a large sample of nearby filaments in various low-mass star-forming regions, which tends to indicate that the physical conditions governing the fragmentation of pre-stellar cores within transcritical or supercritical filaments are the same over a large range of masses per unit length. © F. Schuller et al. 2021

A Feature-Driven Active Framework for Ultrasound-Based Brain Shift Compensation

A reliable Ultrasound (US)-to-US registration method to compensate for brain shift would substantially improve Image-Guided Neurological Surgery. Developing such a registration method is very challenging, due to factors such as missing correspondence in images, the complexity of brain pathology and the demand for fast computation. We propose a novel feature-driven active framework. Here, landmarks and their displacement are first estimated from a pair of US images using corresponding local image features. Subsequently, a Gaussian Process (GP) model is used to interpolate a dense deformation field from the sparse landmarks. Kernels of the GP are estimated by using variograms and a discrete grid search method. If necessary, the user can actively add new landmarks based on the image context and visualization of the uncertainty measure provided by the GP to further improve the result. We retrospectively demonstrate our registration framework as a robust and accurate brain shift compensation solution on clinical data acquired during neurosurgery

Simulation of Ground-Truth Validation Data Via Physically- and Statistically-Based Warps

Abstract. The problem of scarcity of ground-truth expert delineations of medi-cal image data is a serious one that impedes the training and validation of medi-cal image analysis techniques. We develop an algorithm for the automatic generation of large databases of annotated images from a single reference data-set. We provide a web-based interface through which the users can upload a reference data set (an image and its corresponding segmentation and landmark points), provide custom setting of parameters, and, following server-side com-putations, generate and download an arbitrary number of novel ground-truth data, including segmentations, displacement vector fields, intensity non-uniformity maps, and point correspondences. To produce realistic simulated data, we use variational (statistically-based) and vibrational (physically-based) spatial deformations, nonlinear radiometric warps mimicking imaging non-homogeneity, and additive random noise with different underlying distributions. We outline the algorithmic details, present sample results, and provide the web address to readers for immediate evaluation and usage

Learning low-dimensional representations of shape data sets with diffeomorphic autoencoders

Auteur collectif : Alzheimer’s Disease Neuroimaging InitiativeInternational audienceContemporary deformation-based morphometry offers parametric classes of diffeomorphisms that can be searched to compute the optimal transformation that warps a shape into another, thus defining a similarity metric for shape objects. Extending such classes to capture the geometrical variability in always more varied statistical situations represents an active research topic. This quest for genericity however leads to computationally-intensive estimation problems. Instead, we propose in this work to learn the best-adapted class of diffeomorphisms along with its parametrization, for a shape data set of interest. Optimization is carried out with an auto-encoding variational inference approach, offering in turn a coherent model-estimator pair that we name diffeomorphic auto-encoder. The main contributions are: (i) an original network-based method to construct diffeomorphisms, (ii) a current-splatting layer that allows neural network architectures to process meshes, (iii) illustrations on simulated and real data sets that show differences in the learned statistical distributions of shapes when compared to a standard approach