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Various results concerning homogenisation of nematic liquid crystals
Get PDFIn this thesis we present various results concerning homogenisation of nematic liquid crystals: two of them are in perforated domains, while the other one concerns rates of convergence for boundary homogenisation. The first work described in this thesis is a -convergence result for the Landau-de Gennes model in domains with connected perforations. The goal of the analysis is to find new terms in the energy functional that are independent of the gradient. The second result is an error estimate for a D toy model used to describe rugosity effects in nematic liquid crystals via homogenisation problems, using once again the Landau-de Gennes model. The last problem is a local -convergence result for a homogenisation problem in with isolated perforations. Here we use the Oseen-Frank model, with the goal of finding new gradient-dependent terms in the energy functional.
We start, in Chapter 1, with a brief introduction to nematic liquid crystals. We introduce two major variational models used to describe nematic liquid crystals: Landau-de Gennes (LdG) and Oseen-Frank (OF). For LdG theory, which uses -tensors as the order parameter, we present typical choices for each type of energy contribution (bulk, elastic and surface). For OF theory based on the order parameter we discuss the elastic energy, that depends on the director and its gradient. We then present a short summary of the main mathematical results obtained for LdG and OF.
In Chapter 2, we analyse a homogenisation problem in using the Landau-de Gennes model in which the perforations form a cubic microlattice. We assume a dillute regime, that is the volume of the cubic microlattice tends to as its characteristic length scale tends to . The goal of this problem is to show that, given this geometrical setting, by choosing various types of surface energies one can obtain a new material in the limit of vanishing characteristic size of the microlattice. This material also behaves like a nematic liquid crystal, but now with different bulk coefficients. At the end of this chapter, we discuss a rate of convergence of the approximating surface energies to a homogenised term.
In Chapter 3, we concentrate on achieving and improving error estimates in homogenisation problems, since they can give us crucial information for manufacturing processes. Here, we consider a simplified D model in which we highlight how one could replace a rugose boundary with the imposed homeotropic alignment by a flat boundary with an effective alignment depending on the initial geometry of the rugosity. We are able to improve an error estimate for a class of linear nonhomogeneous Robin problems.
In Chapter 4, we consider a general elastic energy in a D case for the Oseen-Frank model in domains with isolated perforations. The goal of this study is to analyse how one could obtain a nematic liquid crystal with novel elastic properties via homogenisation procedures. Under suitable conditions we can analyse the -valued homogenisation problem via a scalar problem obtained through the lifting procedure. We also prove a local convergence result
Development of machine learning system for airway prediction from facial image with mobile device
Get PDFGoals: A reliable prognostic tool for a difficult airway (DA) may enhance patients’ safety during orotracheal intubation by decreasing
unanticipated DAs. We aim to examine the applicability of an Artificial Intelligence-Deep Learning (AI-DL) algorithm to measure airway’s anatomy, and to predict DA based on published models.
Materials and methods: Observational prospective cohort study with n=503 patients recruited at Galdakao-Usansolo and Basurto University Hospitals (Biscay, Spain) between 2018 and 2020. Two pre-operative photos for each patient were collected: a frontal view, in which patients were instructed to open their mouth completely; and a lateral view, with head in vertical ex tension.
Smartphones with general-purpose cameras were used, and a cue card was added to the scene as reference. Patients’ medical records were logged. After intubation, HAN score and IDS-ASA criteria for intubation difficulty [1] were collected.
Our anaesthesiology team defined a set of relevant orofacial landmarks, whereas our data-science team developed an AI-DL algorithm, trained to identify locate them automatically within the images. In a previous evaluation, the system achieved an accuracy comparable to the consensus of two human annotators [2]. Landmark positions output by the AI-DL method were subsequently used by the system to ex tract two anatomical measurements: thyromental distance and interincisor gap. Finally, these two were integrated into a published model for DA prognosis: Naguib et al. 2006 [3], which also employed patients’ height and Mallampati score.
Results and discussion: The estimated incidence of DA was 6.36% (32 out of 503 patients) according to the IDS-ASA criteria. Naguib’s
model, when used in combination with our automatic AI-DL based measurements, achieved 53.12% sensitivity and 79.83% specificity; compared to clinicians’ subjective assessment, who obtained 25.00% sensitivity and 93.63% specificity.
Conclusion(s): In this work, we evaluated an AI-DL method to predict DA for intubation, with two pre-operative photos and Naguib’s model. Our results complemented expert judgements’ predictive ability in terms of sensitivity, substantially lowering false negatives; at the expense of a restrained loss in specificity (false positives). Thus, our proposal may provide anaesthesiologists with an automatic, objective and accessible decision support tool for the prognosis of DAs
Recurrent, nonequilibrium systems and the Markov blanket assumption
No full textMarkov blankets - statistical independences between system and environment - have become popular to describe the boundaries of living systems under Bayesian views of cognition. The intuition behind Markov blankets originates from considering acyclic, atemporal networks. In contrast, living systems display recurrent, nonequilibrium interactions that generate pervasive couplings between system and environment, making Markov blankets highly unusual and restricted to particular cases
Machining-induced characteristics of microstructure-supported LPBF-IN718 curved thin walls
Get PDFThe microstructure-supported design of engineering components is recently gaining attention due to their high strength-to-weight and high stiffness-to-weight properties. The present study investigates the hybrid manufacturing of Inconel 718 curved thin walls with internal microstructural supports fabricated by laser powder bed fusion (LPBF). Printed walls contain a fixed curvature and thickness, whereas the internal microstructures were varied at different inclination angles. In this research, a finish milling operation has been performed at different milling parameters. Machining-induced damages on the internal microstructures have been studied and correlated with geometrical deviation and surface integrity features on the outer thin wall surfaces
Technology-Agnostic Assessment of Wave Energy System Capabilities
Get PDFDeveloping new wave energy technologies is risky, costly and time-consuming. The large diversity of concepts, components and evaluation criteria creates a vast design space of potentially feasible solutions. This paper aims to introduce a novel methodology for the holistic assessment of wave energy capabilities in various market applications based on sound Systems Engineering methods. The methodology provides a consistent hierarchy of performance metrics relevant to the given system of reference, design activity and development stage under consideration as a means to scrutinise wave energy requirements. Full traceability of system requirements and performance metrics is then facilitated by multi-criteria decision tools and aggregation logic, respectively. The qualitative assessment in the case studies has resulted in very different rankings of System Drivers and Stakeholders for the two market applications considered. However, the Stakeholder Requirements and Functional Requirements present a small variation in the weights for the two application markets which results in a quantitative assessment with very similar Global Merit. Finally, the performance benchmark using the Commercial Attractiveness and Technical Achievability concepts enables a more objective comparison in the utility-scale and remote generation markets and a way to concentrate innovation efforts before proceeding to the next development stage
Ad-Hoc Explanation for Time Series Classification
Get PDFIn this work, a perturbation-based model-agnostic explanation method for time series classification is presented. One of the main novelties of the proposed method is that the considered perturbations are interpretable and specific for time series. In real-world time series, variations in the speed or the scale of a particular action, for instance, may determine the class, so modifying this type of characteristic leads to ad-hoc explanations for time series. To this end, four perturbations or transformations are proposed: warp, scale, noise, and slice. Given a transformation, an interval of a series is considered relevant for the prediction of a classifier if a transformation in this interval changes the prediction. Another novelty is that the method provides a two-level explanation: a high-level explanation, where the robustness of the prediction with respect to a particular transformation is measured, and a low-level explanation, where the relevance of each region of the time series in the prediction is visualized. In order to analyze and validate our proposal, first some illustrative examples are provided, and then a thorough quantitative evaluation is carried out using a specifically designed evaluation procedure.PID2019-104966GB-I00
3KIA-KK2020/004
Aeroacoustic Analysis of a Subsonic Jet using the Discontinuous Galerkin Method
Get PDFIn this work, the open-source spectral/hp element framework Nektar++ (www.nektar.info) is coupled with the Antares library (www.cerfacs.fr/antares/) to predict noise from a subsonic jet. Nektar++ uses the high-order discontinuous Galerkin method to solve the compressible Navier-Stokes equations on unstructured grids. Unresolved turbulent scales are modeled using an implicit Large Eddy Simulation approach. In this approach, the favourable dissipation properties of the discontinuous Galerkin method are used to remove the highest resolved wavenumbers from the solution. For time-integration, an implicit, matrix-free, Newton-Krylov method is used. To compute the far-field noise, Antares solves the Ffowcs Williams-Hawkings equation for a permeable integration surface in the time-domain using a source-time dominant algorithm. The simulation results are validated against experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton
Kato–Ponce estimates for fractional sublaplacians in the Heisenberg group
Get PDFWe give a proof of commutator estimates for fractional powers of the sublaplacian
on the Heisenberg group. Our approach is based on pointwise and estimates involving square
fractional integrals and Littlewood--Paley square functionsBERC 2022-2025
RYC2018-025477-I
Ikerbasque
PID2021-123034NB-I00
IT1615-2
Geometry of spiking patterns in early visual cortex: A topological data analytic approach
Get PDFIn the brain, spiking patterns live in a high-dimensional space of neurons and time. Thus, determining the intrinsic structure of this space presents a theoretical and experimental challenge. To address this challenge, we introduce a new framework for applying topological data analysis (TDA) to spike train data and use it to determine the geometry of spiking patterns in the visual cortex. Key to our approach is a parametrized family of distances based on the timing of spikes that quantifies the dissimilarity between neuronal responses. We applied TDA to visually driven single-unit and multiple single-unit spiking activity in macaque V1 and V2. TDA across timescales reveals a common geometry for spiking patterns in V1 and V2 which, among simple models, is most similar to that of a low-dimensional space endowed with Euclidean or hyperbolic geometry with modest curvature. Remarkably, the inferred geometry depends on timescale and is clearest for the timescales that are important for encoding contrast, orientation and spatial correlations.NIH grants number EY09314 and EY07977 from the National Eye Institute of the NIH.
NIH grants no. EY034150 from the National Eye Institute and NS111019 from the National Institute of Neurological Disorders and Stroke.
Ikerbasque.
Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation.
Inria Associated Team "NeuroTransSF"
Rank aggregation for non-stationary data streams
Get PDFThe problem of learning over non-stationary ranking streams arises naturally, particularly in recommender systems. The rankings represent the preferences of a population, and the non-stationarity means that the distribution of preferences changes over time. We propose an algorithm that learns the current distribution of ranking in an online manner. The bottleneck of this process is a
rank aggregation problem.
We propose a generalization of the Borda algorithm for non-stationary ranking streams. As a main result, we bound the minimum number of samples required to output the ground truth with high probability. Besides, we show how the optimal parameters are set. Then, we generalize the whole family of weighted voting rules (the family to which Borda belongs) to situations in which some rankings are more reliable than others. We show that, under mild assumptions, this generalization can solve the problem of rank aggregation over non-stationary data streams