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The yield stress and shear thinning properties of mucus are identified as critical for ciliary coordination and mucus transport in human airways. We use here numerical simulations to explore the hydrodynamic coupling of cilia and mucus with these two properties using the Herschel--Bulkley model, in a lattice Boltzmann solver for the fluid flow. Three mucus flow regimes, i.e. a poorly organized regime, a swirly regime, and a fully unidirectional regime, are observed and analysed by parametric studies. We systematically investigate the effects of ciliary density, interaction length, Bingham number and flow index on the mucus flow regime formation. The underlying mechanism of the regime formation is analysed in detail by examining the variation of two physical quantities (polarization and integral length) and the evolution of the flow velocity, viscosity and shear-rate fields. Mucus viscosity is found to be the dominant parameter influencing the regime formation when enhancing the yield stress and shear thinning properties. The present model is able to reproduce the solid body rotation observed in experiments (Loiseau et al. , Nat. Phys. , vol. 16, 2020, pp. 1158--1164). A more precise prediction can be achieved by incorporating non-Newtonian properties into the modelling of mucus as proposed by Gsell et al. ( Sci. Rep. , vol. 10, 2020, 8405).

Spontaneous mechanical self-assembly of monodisperse bubbles generally leads to disordered foams at low density: producing crystalline structures such as Kelvin foams has proven to be challenging experimentally, despite them being a minimum of energy. Here we show how bubbling in different fiber arrays controls foam architectures through a guided mechanical self-assembly. Analyzing X-ray tomography scans of solidified polymer foams using Steinhardt's parameters highlights clear signatures of Kelvin and hexagonal close packing crystalline foams, opening a novel route towards ordered hierarchical materials., Comment: 6 pages, 4 figures

We present a substantial extension of our Human-Aware Task Planning framework, tailored for scenarios with intermittent shared execution experiences and significant belief divergence between humans and robots, particularly due to the uncontrollable nature of humans. Our objective is to build a robot policy that accounts for uncontrollable human behaviors, thus enabling the anticipation of possible advancements achieved by the robot when the execution is not shared, e.g. when humans are briefly absent from the shared environment to complete a subtask. But, this anticipation is considered from the perspective of humans who have access to an estimated model for the robot. To this end, we propose a novel planning framework and build a solver based on AND-OR search, which integrates knowledge reasoning, including situation assessment by perspective taking. Our approach dynamically models and manages the expansion and contraction of potential advances while precisely keeping track of when (and when not) agents share the task execution experience. The planner systematically assesses the situation and ignores worlds that it has reason to think are impossible for humans. Overall, our new solver can estimate the distinct beliefs of the human and the robot along potential courses of action, enabling the synthesis of plans where the robot selects the right moment for communication, i.e. informing, or replying to an inquiry, or defers ontic actions until the execution experiences can be shared. Preliminary experiments in two domains, one novel and one adapted, demonstrate the effectiveness of the framework., Comment: 15 pages, 4 figures, 1 table

The pipeline of a fair ML practitioner is generally divided into three phases: 1) Selecting a fairness measure. 2) Choosing a model that minimizes this measure. 3) Maximizing the model's performance on the data. In the context of group fairness, this approach often obscures implicit assumptions about how bias is introduced into the data. For instance, in binary classification, it is often assumed that the best model, with equal fairness, is the one with better performance. However, this belief already imposes specific properties on the process that introduced bias. More precisely, we are already assuming that the biasing process is a monotonic function of the fair scores, dependent solely on the sensitive attribute. We formally prove this claim regarding several implicit fairness assumptions. This leads, in our view, to two possible conclusions: either the behavior of the biasing process is more complex than mere monotonicity, which means we need to identify and reject our implicit assumptions in order to develop models capable of tackling more complex situations; or the bias introduced in the data behaves predictably, implying that many of the developed models are superfluous.

Fair cake-cutting is a mathematical subfield that studies the problem of fairly dividing a resource among a number of participants. The so-called ``cake,'' as an object, represents any resource that can be distributed among players. This concept is connected to supervised multi-label classification: any dataset can be thought of as a cake that needs to be distributed, where each label is a player that receives its share of the dataset. In particular, any efficient cake-cutting solution for the dataset is equivalent to an optimal decision function. Although we are not the first to demonstrate this connection, the important ramifications of this parallel seem to have been partially forgotten. We revisit these classical results and demonstrate how this connection can be prolifically used for fairness in machine learning problems. Understanding the set of achievable fair decisions is a fundamental step in finding optimal fair solutions and satisfying fairness requirements. By employing the tools of cake-cutting theory, we have been able to describe the behavior of optimal fair decisions, which, counterintuitively, often exhibit quite unfair properties. Specifically, in order to satisfy fairness constraints, it is sometimes preferable, in the name of optimality, to purposefully make mistakes and deny giving the positive label to deserving individuals in a community in favor of less worthy individuals within the same community. This practice is known in the literature as cherry-picking and has been described as ``blatantly unfair.''

We study uniqueness of best approximation in Orlicz spaces L$\Phi$, for different types of convex functions $\Phi$ and for some finite dimensional approximation classes of functions, where Tchebycheff spaces, and more general approximation ones, are involved, Comment: 15 pages

It is widely accepted that biased data leads to biased and thus potentially unfair models. Therefore, several measures for bias in data and model predictions have been proposed, as well as bias mitigation techniques whose aim is to learn models that are fair by design. Despite the myriad of mitigation techniques developed in the past decade, however, it is still poorly understood under what circumstances which methods work. Recently, Wick et al. showed, with experiments on synthetic data, that there exist situations in which bias mitigation techniques lead to more accurate models when measured on unbiased data. Nevertheless, in the absence of a thorough mathematical analysis, it remains unclear which techniques are effective under what circumstances. We propose to address this problem by establishing relationships between the type of bias and the effectiveness of a mitigation technique, where we categorize the mitigation techniques by the bias measure they optimize. In this paper we illustrate this principle for label and selection bias on the one hand, and demographic parity and ``We're All Equal'' on the other hand. Our theoretical analysis allows to explain the results of Wick et al. and we also show that there are situations where minimizing fairness measures does not result in the fairest possible distribution.

In this paper, we consider the best multivalued polynomial approximation operator for functions in an Orlicz Space $L^{\varphi}(\Omega)$. We obtain its characterization involving $\psi^-$ and $\psi^+$, which are the left and right derivatives functions of $\varphi$. And then, we extend the operator to $L^{\psi^+}(\Omega)$. We also get pointwise convergence of this extension, where the Calder\'on-Zygmund class $t_m^p (x)$ adapted to $L^{\psi^+}(\Omega)$ plays an important role.

We consider inertial waves propagating in a fluid contained in a non-axisymmetric three-dimensional rotating cavity. We focus on the particular case of a fluid enclosed inside a truncated cone or frustum, which is the volume that lies between two horizontal parallel planes cutting an upright cone. While this geometry has been studied in the past, we generalise it by breaking its axisymmetry and consider the case of a truncated elliptical cone for which the horizontal sections are elliptical instead of circular. The problem is first tackled using ray tracing where local wave packets are geometrically propagated and reflected within the closed volume without attenuation. We complement these results with a local asymptotic analysis and numerical simulations of the original linear viscous problem. We show that the attractors, well-known in two dimensional or axisymmetric domains, can be trapped in a particular plane in three-dimension provided that the axisymmetry of the domain is broken. Contrary to previous examples of attractors in three-dimensional domains, all rays converge towards the same limit cycle regardless of initial conditions, and it is localised in the bulk of the fluid., Comment: 22 pages, 11 figures

We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) of either sign, and two states composed of many similar SVs. Of the latter, the first is a dense vortex gas where all SVs have the same sign and diffuse across the domain. The second is a hexagonal vortex crystal forming from this gas when the instability is sufficiently weak. These solutions coexist stably over a wide parameter range. The late-time evolution of the system from small-amplitude initial conditions is nearly self-similar, involving three phases: initial inverse cascade, random nucleation of SVs from turbulence and, once a critical number of vortices is reached, a phase of explosive nucleation of SVs, leading to a statistically stationary state. The vortex gas is continued in the forcing parameter, revealing a sharp transition towards the crystal state as the forcing strength decreases. This transition is analysed in terms of the diffusion of individual vortices and tools from statistical physics. The crystal can also decay via an inverse cascade resulting from the breakdown of shielding or insufficient nonlinear damping acting on SVs. Our study highlights the importance of the forcing details in two-dimensional turbulence and reveals the presence of nontrivial SV states in this system, specifically the emergence and melting of a vortex crystal.

Following our previous work on periodic ray paths (He et al, 2022), we study asymptotically and numerically the structure of internal shear layers for very small Ekman numbers in a three-dimensional (3D) spherical shell and in a two-dimensional (2D) cylindrical annulus when the rays converge towards an attractor. We first show that the asymptotic solution obtained by propagating the self-similar solution generated at the critical latitude on the librating inner core describes the main features of the numerical solution. The internal shear layer structure and the scaling for its width and velocity amplitude in $E^{1/3}$ and $E^{1/12}$ respectively are recovered. The amplitude of the asymptotic solution is shown to decrease to $E^{1/6}$ when it reaches the attractor, as it is also observed numerically. However, some discrepancies are observed close to the particular attractors along which the phase of the wave beam remains constant. Another asymptotic solution close to those attractors is then constructed using the model of Ogilvie (2005). The solution obtained for the velocity has an $O(E^{1/6})$ amplitude, but a different self-similar structure than the critical-latitude solution. It also depends on the Ekman pumping at the contact points of the attractor with the boundaries. We demonstrate that it reproduces correctly the numerical solution. Surprisingly, the solution close to an attractor with phase shift (that is an attractor that touches the axis in 3D or in 2D with a symmetric forcing) is found to be much weaker., Comment: 31 pages, 13 figures

Circular Rydberg atoms (CRAs), i.e., Rydberg atoms with maximal orbital momentum, are highly promising for quantum computation, simulation and sensing. They combine long natural lifetimes with strong inter-atomic interactions and coupling to electromagnetic fields. Trapping individual CRAs is essential to harness these unique features. We report the first demonstration of CRAs laser-trapping in a programmable array of optical bottle beams. We observe the decay of a trapped Rubidium circular level over 5ms using a novel optical detection method. This first optical detection of alkali CRAs is both spatially- and level selective. We finally observe the mechanical oscillations of the CRAs in the traps. This work opens the route to the use of circular levels in quantum devices. It is also promising for quantum simulation and information processing using the full extent of Rydberg manifolds.

The heat transport by rapidly-rotating Rayleigh-B\'enard convection is of fundamental importance to many geophysical flows. Laboratory measurements are impeded by robust wall modes which develop along vertical walls, significantly perturbing the heat flux. We show that narrow horizontal fins along the vertical walls efficiently suppress wall modes ensuring that their contribution to the global heat flux is negligible compared with bulk convection in the geostrophic regime, thereby paving the way for new experimental studies of geophysically relevant regimes of rotating convection., Comment: 6 pages, 6 figures

We experimentally investigate the behaviour of instantaneous localised releases of heavy particles falling as turbulent clouds in quiescent water, both with and without background rotation. We present the results of 514 systematic experiments for no rotation and for three rotation rates $\Omega = 5,10,20$rpm, and for the size of particles in the range $5\mu m$ to $1mm$, exploring four decades of the Rouse number $\mathcal{R} \in [6\times 10^{-4},4]$ which quantifies the inertia of particles. In the canonical framework of turbulent thermals described by Morton \textit{et al.}, [Proc. R. Soc. A: Math. Phys. Sci. \textbf{234}, 1 (1956)], we compare particle clouds with salt-water thermals to highlight specificities due to the particulate nature of the turbulence forcing. In the absence of rotation, particle clouds initially behave as salty thermals with a modulation of their entrainment capacity, which is optimally enhanced for a finite inertia $\mathcal{R}\simeq 0.3$ due to particulate effects. However this regime of turbulence is limited in time due to the inertial decoupling between turbulent eddies and particles. For the three values of $\Omega$ explored here, the particulate enhancement of entrainment is inhibited. Moreover the cloud's expansion is interrupted when the Coriolis force overcomes its inertia, forcing the cloud to transform into vortical columnar flows which considerably increase the residence time of particles.

Current approaches in human-aware or social robot navigation address the humans that are visible to the robot. However, it is also important to address the possible emergences of humans to avoid shocks or surprises to humans and erratic behavior of the robot planner. In this paper, we propose a novel approach to detect and address these human emergences called `invisible humans'. We determine the places from which a human, currently not visible to the robot, can appear suddenly and then adapt the path and speed of the robot with the anticipation of potential collisions. This is done while still considering and adapting humans present in the robot's field of view. We also show how this detection can be exploited to identify and address the doorways or narrow passages. Finally, the effectiveness of the proposed methodology is shown through several simulated and real-world experiments.

We consider the human-aware task planning problem where a human-robot team is given a shared task with a known objective to achieve. Recent approaches tackle it by modeling it as a team of independent, rational agents, where the robot plans for both agents' (shared) tasks. However, the robot knows that humans cannot be administered like artificial agents, so it emulates and predicts the human's decisions, actions, and reactions. Based on earlier approaches, we describe a novel approach to solve such problems, which models and uses execution-time observability conventions. Abstractly, this modeling is based on situation assessment, which helps our approach capture the evolution of individual agents' beliefs and anticipate belief divergences that arise in practice. It decides if and when belief alignment is needed and achieves it with communication. These changes improve the solver's performance: (a) communication is effectively used, and (b) robust for more realistic and challenging problems., Comment: 10 pages, 2 figures, 1 table, AI-HRI AAAI 2022 Fall Symposium Series

Four series of PLA based composite films containing horizontally aligned few layer graphene (FLG) flakes of high aspect ratio and adsorbed albumin are prepared. The mechanical and thermal properties vary with percentage, dispersion degree and size of FLG flakes. Great improvement up to 290 and 360% of tensile modulus and strength respectively was obtained for the composite containing high lateral size of FLG at 0.17% wt., and up to 60 and 80% for the composite with very well dispersed 0.02% wt. FLG. The composites of PLA and PEG-PLLA containing very well dispersed FLG flakes at 0.07 % wt. are ductile showing enhancement of elongation at break up to respectively 80 and 88%. Relatively high electrical conductivity, 5 x 10-3 S/cm, is measured for PLA film charged with 3% of FLG.