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Unlike crystalline solids or ideal gases, transport properties remain difficult to describe from a microscopic point of view in liquids, whose dynamics result from complex energetic and entropic contributions at the atomic scale. Two scenarios are generally proposed: one represents the dynamics in a fluid as a series of energy barrier crossings, leading to Arrhenius-like laws, while the other assumes that atoms rearrange themselves by collisions, as exemplified by the free volume model. To assess the validity of these two views, we computed, using molecular dynamics simulations, the transport properties of the Lennard-Jones fluid and tested to what extent the Arrhenius equation and the free volume model describe the temperature dependence of the viscosity and of the diffusion coefficient at fixed pressure. Although both models reproduce the simulation results over a wide range of pressure and temperature covering the liquid and supercritical states of the Lennard-Jones fluid, we found that the parameters of the free volume model can be estimated directly from local structural parameters, also obtained in the simulations. This consistency of the results gives more credibility to the free volume description of transport properties in liquids., Comment: 6 pages, 4 figures

The aim of this work is to study the controllability of the Schr\"odinger equation \begin{equation}\label{eq_abstract} i\partial_t u(t)=-\Delta u(t)~~~~~\text{ on }\Omega(t) \tag{$\ast$} \end{equation} with Dirichlet boundary conditions, where $\Omega(t)\subset\mathbb{R}^N$ is a time-varying domain. We prove the global approximate controllability of \eqref{eq_abstract} in $L^2(\Omega)$, via an adiabatic deformation $\Omega(t)\subset\mathbb{R}$ ($t\in[0,T]$) such that $\Omega(0)=\Omega(T)=\Omega$. This control is strongly based on the Hamiltonian structure of \eqref{eq_abstract} provided by [18], which enables the use of adiabatic motions. We also discuss several explicit interesting controls that we perform in the specific framework of rectangular domains.

This paper presents a novel data augmentation technique for text-to-speech (TTS), that allows to generate new (text, audio) training examples without requiring any additional data. Our goal is to increase diversity of text conditionings available during training. This helps to reduce overfitting, especially in low-resource settings. Our method relies on substituting text and audio fragments in a way that preserves syntactical correctness. We take additional measures to ensure that synthesized speech does not contain artifacts caused by combining inconsistent audio samples. The perceptual evaluations show that our method improves speech quality over a number of datasets, speakers, and TTS architectures. We also demonstrate that it greatly improves robustness of attention-based TTS models., Comment: ICASSP 2022: camera-ready

In modern classification tasks, the number of labels is getting larger and larger, as is the size of the datasets encountered in practice. As the number of classes increases, class ambiguity and class imbalance become more and more problematic to achieve high top-1 accuracy. Meanwhile, Top-K metrics (metrics allowing K guesses) have become popular, especially for performance reporting. Yet, proposing top-K losses tailored for deep learning remains a challenge, both theoretically and practically. In this paper we introduce a stochastic top-K hinge loss inspired by recent developments on top-K calibrated losses. Our proposal is based on the smoothing of the top-K operator building on the flexible "perturbed optimizer" framework. We show that our loss function performs very well in the case of balanced datasets, while benefiting from a significantly lower computational time than the state-of-the-art top-K loss function. In addition, we propose a simple variant of our loss for the imbalanced case. Experiments on a heavy-tailed dataset show that our loss function significantly outperforms other baseline loss functions.

Quantum effects of fields on curved spacetimes may be studied in the laboratory thanks to quantum fluids. Here we use a polariton fluid to study the Hawking effect, the correlated emission from the quantum vacuum at the acoustic horizon. We show how out-of-equilibrium physics affects the dispersion relation, and hence the emission and propagation of correlated waves: the fluid properties on either side of the horizon are critical to observing the Hawking effect. We find that emission may be optimised by supporting the phase and density of the fluid upstream of the horizon in a regime of optical bistability. This opens new avenues for the observation of the Hawking effect in out-of-equilibrium systems as well as for the study of new phenomenology of fields on curved spacetimes., Comment: 16 pages + appendix, 6 figures, comments are welcome. arXiv admin note: substantial text overlap with arXiv:2110.14452

When many labels are possible, choosing a single one can lead to low precision. A common alternative, referred to as top-$K$ classification, is to choose some number $K$ (commonly around 5) and to return the $K$ labels with the highest scores. Unfortunately, for unambiguous cases, $K>1$ is too many and, for very ambiguous cases, $K \leq 5$ (for example) can be too small. An alternative sensible strategy is to use an adaptive approach in which the number of labels returned varies as a function of the computed ambiguity, but must average to some particular $K$ over all the samples. We denote this alternative average-$K$ classification. This paper formally characterizes the ambiguity profile when average-$K$ classification can achieve a lower error rate than a fixed top-$K$ classification. Moreover, it provides natural estimation procedures for both the fixed-size and the adaptive classifier and proves their consistency. Finally, it reports experiments on real-world image data sets revealing the benefit of average-$K$ classification over top-$K$ in practice. Overall, when the ambiguity is known precisely, average-$K$ is never worse than top-$K$, and, in our experiments, when it is estimated, this also holds., Comment: 53 pages, 21 figures

Among all fluids, water has always been of special concern for scientists from a broad variety of research fields due to its rich behavior. In particular, some questions remain unanswered nowadays concerning the temperature dependence of bulk and interfacial transport properties of supercooled and liquid water, e.g. regarding the fundamentals of the violation of the Stokes-Einstein relation in the supercooled regime or the subtle relation between structure and dynamical properties. Here we investigated the temperature dependence of the bulk transport properties from ab initio molecular dynamics based on density functional theory, down to the supercooled regime. We determined from a selection of functionals, that SCAN better describes the experimental viscosity and self-diffusion coefficient, although we found disagreements at the lowest temperatures. For a limited set of temperatures, we also explored the role of nuclear quantum effects on water dynamics using ab initio molecular dynamics that has been accelerated via a recently introduced machine learning approach. We then investigated the molecular mechanisms underlying the different functionals performance and assessed the validity of the Stokes-Einstein relation. We also explored the connection between structural properties and the transport coefficients, verifying the validity of the excess entropy scaling relations for all the functionals. These results pave the way to predict the transport coefficients from the radial distribution function, helping to develop better functionals. On this line, they indicate the importance of describing the long-range features of the radial distribution function., Comment: 10 pages, 5 figures

In this article, the main goal is to give a dynamical point of view of Floer homology barcodes for Hamiltonian homeomorphisms of surfaces. More specifically, we describe a way to construct barcodes for Hamiltonian homeomorphisms of surfaces from graphs. We will define graphes associated to maximal isotopies of a Hamiltonian homeomorphism using Le Calvez's positively transverse foliation theory and to those graphs we will associate barcodes. In particular, we will prove that for the simplest cases, our constructions coincide with the Floer Homology barcodes.

Electro-osmosis (EO) is a powerful tool to manipulate liquids in micro and nanofluidic systems. While EO has been studied extensively at liquid-solid interfaces, the case of liquid-vapor interfaces, found e.g. in foam films and bubbles, remains to be explored. Here we perform molecular dynamics (MD) simulations of EO in a film of aqueous electrolyte covered with fluid layers of ionic surfactants and surrounded by gas. Following the experimental procedure, we compute the zeta potential from the EO velocity, defined as the velocity difference between the middle of the liquid film and the surrounding gas. We show that the zeta potential can be smaller or larger than existing predictions depending on the surfactant coverage. We explain the failure of previous descriptions by the fact that surfactants and bound ions move as rigid bodies and do not transmit the electric driving force to the liquid locally. Considering the reciprocal streaming current effect, we then develop an extended model, which can be used to predict the experimental zeta potential of surfactant-laden liquid-gas interfaces., Comment: 11 pages, 10 figures; accepted version

Vacuum quantum fluctuations near horizons are known to yield correlated emission by the Hawking effect. We use a driven-dissipative quantum fluid of microcavity polaritons as an analog model of a quantum field theory on a black-hole spacetime and numerically calculate correlated emission. We show that, in addition to the Hawking effect at the sonic horizon, quantum fluctuations may result in a sizeable stationary excitation of a quasi-normal mode of the field theory. Observable signatures of the excitation of the quasi-normal mode are found in the spatial density fluctuations as well as in the spectrum of Hawking emission. This suggests an intrinsic fluctuation-driven mechanism leading to the quantum excitation of quasi-normal modes on black hole spacetimes., Comment: Version accepted for publication

In this paper we present the practical benefits of a new random forest algorithm to deal withmissing values in the sample. The purpose of this work is to compare the different solutionsto deal with missing values with random forests and describe our new algorithm performanceas well as its algorithmic complexity. A variety of missing value mechanisms (such as MCAR,MAR, MNAR) are considered and simulated. We study the quadratic errors and the bias ofour algorithm and compare it to the most popular missing values random forests algorithms inthe literature. In particular, we compare those techniques for both a regression and predictionpurpose. This work follows a first paper Gomez-Mendez and Joly (2020) on the consistency ofthis new algorithm.

This paper is concerned with the time-dependent Maxwell's equations for a plane interface between a negative material described by the Drude model and the vacuum, which fill, respectively, two complementary half-spaces. In a first paper, we have constructed a generalized Fourier transform which diagonalizes the Hamiltonian that represents the propagation of transverse electric waves. In this second paper, we use this transform to prove the limiting absorption and limiting amplitude principles, which concern, respectively, the behavior of the resolvent near the continuous spectrum and the long time response of the medium to a time-harmonic source of prescribed frequency. This paper also underlines the existence of an interface resonance which occurs when there exists a particular frequency characterized by a ratio of permittivities and permeabilities equal to $-1$ across the interface. At this frequency, the response of the system to a harmonic forcing term blows up linearly in time. Such a resonance is unusual for wave problem in unbounded domains and corresponds to a non-zero embedded eigenvalue of infinite multiplicity of the underlying operator. This is the time counterpart of the ill-posdness of the corresponding harmonic problem., Comment: 64 pages, 4 figures

Detection of the energy conversion pathways, between photons, charge carriers, and the lattice is of fundamental importance to understand fundamental physics and to advance materials and devices. Yet, such insight remains incomplete due to experimental challenges in disentangling the various signatures on overlapping time scales. Here, we show that attosecond core-level X-ray spectroscopy can identify these interactions with attosecond precision and across a picosecond range. We demonstrate this methodology on graphite since its investigation is complicated by a variety of mechanisms occurring across a wide range of temporal scales. Our methodology reveals, through the simultaneous real-time detection of electrons and holes, the different dephasing mechanisms for each carrier type dependent on excitation with few-cycle-duration light fields. These results demonstrate the general ability of our methodology to detect and distinguish the various dynamic contributions to the flow of energy inside materials on their native time scales.

Inferring functional relationships within complex networks from static snapshots of a subset of variables is a ubiquitous problem in science. For example, a key challenge of systems biology is to translate cellular heterogeneity data obtained from single-cell sequencing or flow-cytometry experiments into regulatory dynamics. We show how static population snapshots of co-variability can be exploited to rigorously infer properties of gene expression dynamics when gene expression reporters probe their upstream dynamics on separate time-scales. This can be experimentally exploited in dual-reporter experiments with fluorescent proteins of unequal maturation times, thus turning an experimental bug into an analysis feature. We derive correlation conditions that detect the presence of closed-loop feedback regulation in gene regulatory networks. Furthermore, we show how genes with cell-cycle dependent transcription rates can be identified from the variability of co-regulated fluorescent proteins. Similar correlation constraints might prove useful in other areas of science in which static correlation snapshots are used to infer causal connections between dynamically interacting components.

Osmotic transport in nanoconfined aqueous electrolytes provides new venues for water desalination and "blue energy" harvesting; the osmotic response of nanofluidic systems is controlled by the interfacial structure of water and electrolyte solutions in the so-called electrical double layer (EDL), but a molecular-level picture of the EDL is to a large extent still lacking. Particularly, the role of the electronic structure has not been considered in the description of electrolyte/surface interactions. Here, we report enhanced sampling simulations based on ab initio molecular dynamics, aiming at unravelling the free energy of prototypical ions adsorbed at the aqueous graphene and hBN interfaces, and its consequences on nanofluidic osmotic transport. Specifically, we predicted the zeta potential, the diffusio-osmotic mobility and the diffusio-osmotic conductivity for a wide range of salt concentrations from the ab initio water and ion spatial distributions through an analytical framework based on Stokes equation and a modified Poisson-Boltzmann equation. We observed concentration-dependent scaling laws, together with dramatic differences in osmotic transport between the two interfaces, including diffusio-osmotic flow and current reversal on hBN, but not on graphene. We could rationalize the results for the three osmotic responses with a simple model based on characteristic length scales for ion and water adsorption at the surface, which are quite different on graphene and on hBN. Our work provides first principles insights into the structure and osmotic transport of aqueous electrolytes on two-dimensional materials and explores new pathways for efficient water desalination and osmotic energy conversion., Comment: 19 pages, 3 figures

We propose a platform that combines the fields of cavity optomagnonics and levitated optomechanics in order to control and probe the coupled spin-mechanics of magnetic dielectric particles. We theoretically study the dynamics of a levitated Faraday-active dielectric microsphere serving as an optomagnonic cavity, placed in an external magnetic field and driven by an external laser. We find that the optically driven magnetization dynamics induces angular oscillations of the particle with low associated damping. Further, we show that the magnetization and angular motion dynamics can be probed via the power spectrum of the outgoing light. Namely, the characteristic frequencies attributed to the angular oscillations and the spin dynamics are imprinted in the light spectrum by two main resonance peaks. Additionally, we demonstrate that a ferromagnetic resonance setup with an oscillatory perpendicular magnetic field can enhance the resonance peak corresponding to the spin oscillations and induce fast rotations of the particle around its anisotropy axis., Comment: 22 pages, 13 figures

In more and more application areas, we are witnessing the emergence of complex workflows that combine computing, analytics and learning. They often require a hybrid execution infrastructure with IoT devices interconnected to cloud/HPC systems (aka Computing Continuum). Such workflows are subject to complex constraints and requirements in terms of performance, resource usage, energy consumption and financial costs. This makes it challenging to optimize their configuration and deployment. We propose a methodology to support the optimization of real-life applications on the Edge-to-Cloud Continuum. We implement it as an extension of E2Clab, a previously proposed framework supporting the complete experimental cycle across the Edge-to-Cloud Continuum. Our approach relies on a rigorous analysis of possible configurations in a controlled testbed environment to understand their behaviour and related performance trade-offs. We illustrate our methodology by optimizing Pl@ntNet, a world-wide plant identification application. Our methodology can be generalized to other applications in the Edge-to-Cloud Continuum.

Nanofluids; dispersions of nanometer-sized particles in a liquid medium; have been proposed for a wide variety of thermal management applications. It is known that a solid-like nanolayer of liquid of typical thickness 0.5-1 nm surrounding the colloidal nanoparticles can act as a thermal bridge between the nanoparticle and the bulk liquid. Yet, its effect on the nanofluid viscosity has not been elucidated so far. In this article, we compute the local viscosity of the nanolayer using equilibrium molecular dynamics based on the Green-Kubo formula. We first assess the validity of the method to predict the viscosity locally. We apply this methodology to the calculation of the local viscosity in the immediate vicinity of a metallic nanoparticle for a wide range of solid-liquid interaction strength, where a nanolayer of thickness 1 nm is observed as a result of the interaction with the nanoparticle. The viscosity of the nanolayer, which is found to be higher than its corresponding bulk value, is directly dependent on the solid-liquid interaction strength. We discuss the origin of this viscosity enhancement and show that the liquid density increment alone cannot explain the values of the viscosity observed. Rather, we suggest that the solid-like structure of the distribution of the liquid atoms in the vicinity of the nanoparticle contributes to the nanolayer viscosity enhancement. Finally, we observe a failure of the Stokes-Einstein relation between viscosity and diffusion close to the wall, depending on the liquid-solid interaction strength, which we rationalize in terms of hydrodynamic slip.

Nanofluidics shows great promise for energy conversion and desalination applications. The performance of nanofluidic devices is controlled by liquid-solid friction, quantified by the Navier friction coefficient (FC). Despite decades of research, there is no well-established generic framework to determine the frequency dependent Navier FC from atomistic simulations. Here, we have derived analytical expressions to connect the Navier FC to the random force autocorrelation on the confining wall, from the observation that the random force autocorrelation can be related to the hydrodynamic boundary condition, where the Navier FC appears. The analytical framework is generic in the sense that it explicitly includes the system size dependence and also the frequency dependence of the FC, which enabled us to address (i) the long-standing plateau issue in the evaluation of the FC and (ii) the non-Markovian behavior of liquid-solid friction of a Lennard-Jones liquid and of water on various walls and at various temperatures, including the supercooled regime. This new framework opens the way to explore the frequency dependent FC for a wide range of complex liquids., Comment: 5 pages, 3 figures

We present the use of linearly down-tapered gas-filled hollow-core photonic crystal fiber in a single-stage, pumped with pulses from a compact infrared laser source, to generate a supercontinuum carrying significant spectral power in the deep ultraviolet (200 - 300 nm). The generated supercontinuum extends from the near infrared down to around 213 nm with up to 0.83 mW/nm in the deep ultraviolet., Comment: 4 pages (+1 page for full reference list), 3 figures

We propose a novel Multi-Scale Spectrogram (MSS) modelling approach to synthesise speech with an improved coarse and fine-grained prosody. We present a generic multi-scale spectrogram prediction mechanism where the system first predicts coarser scale mel-spectrograms that capture the suprasegmental information in speech, and later uses these coarser scale mel-spectrograms to predict finer scale mel-spectrograms capturing fine-grained prosody. We present details for two specific versions of MSS called Word-level MSS and Sentence-level MSS where the scales in our system are motivated by the linguistic units. The Word-level MSS models word, phoneme, and frame-level spectrograms while Sentence-level MSS models sentence-level spectrogram in addition. Subjective evaluations show that Word-level MSS performs statistically significantly better compared to the baseline on two voices., Comment: Accepted for the 11th ISCA Speech Synthesis Workshop (SSW11)

Tunable biphotons are highly important for a wide range of quantum applications. For some applications, especially interesting are cases where two photons of a pair are far apart in frequency. Here, we report a tunable biphoton source based on a xenon-filled hollow-core photonic crystal fiber. Tunability is achieved by adjusting the pressure of the gas inside the fiber. This allows us to tailor the dispersion landscape of the fiber, overcoming the principal limitations of solid-core fiber-based biphoton sources. We report a maximum tunability of 120 THz for a pressure range of 4 bar with a continuous shift of 30 THz/bar. At 21 bar, the photons of a pair are separated by more than one octave. Despite the large separation, both photons have large bandwidths. At 17 bar, they form a very broad (110 THz) band around the frequency of the pump., Comment: 5 pages, 4 figures

Many factors influence speech yielding different renditions of a given sentence. Generative models, such as variational autoencoders (VAEs), capture this variability and allow multiple renditions of the same sentence via sampling. The degree of prosodic variability depends heavily on the prior that is used when sampling. In this paper, we propose a novel method to compute an informative prior for the VAE latent space of a neural text-to-speech (TTS) system. By doing so, we aim to sample with more prosodic variability, while gaining controllability over the latent space's structure. By using as prior the posterior distribution of a secondary VAE, which we condition on a speaker vector, we can sample from the primary VAE taking explicitly the conditioning into account and resulting in samples from a specific region of the latent space for each condition (i.e. speaker). A formal preference test demonstrates significant preference of the proposed approach over standard Conditional VAE. We also provide visualisations of the latent space where well-separated condition-specific clusters appear, as well as ablation studies to better understand the behaviour of the system., Comment: in Proceedings of Interspeech 2021

The Poisson-Boltzmann (PB) equation provides a mean-field theory of electrolyte solutions at interfaces and in confinement, describing how ions reorganize close to charged surfaces to form the so-called electrical double layer (EDL), with numerous applications ranging from colloid science to biology. This formulary focuses on situations of interest for micro and nanofluidics, and gathers important formulas for the PB description of a Z:Z electrolyte solution inside slit and cylindrical channels. Different approximated solutions (thin EDLs, no co-ion, Debye-H\"uckel, and homogeneous/parabolic potential limits) and their range of validity are discussed, together with the full solution for the slit channel. Common boundary conditions are presented, the thermodynamics of the EDL is introduced, and an overview of the application of the PB framework to the description of electrokinetic effects is given. Finally, the limits of the PB framework are briefly discussed, and Python scripts to solve the PB equation numerically are provided., Comment: 24 pages, 6 figures

In this article, we study the Calabi invariant on the unit disk usually defined on compactly supported Hamiltonian diffeomorphisms of the open disk. In particular we extend the Calabi invariant to the group of $C^1$ diffeomorphisms of the closed disk which preserves the standard symplectic form. We also compute the Calabi invariant for some diffeomorphisms of the disk which satisfies some rigidity hypothesis., Comment: 30 pages. Comments are welcome

Deep learning models have become increasingly useful in many different industries. On the domain of image classification, convolutional neural networks proved the ability to learn robust features for the closed set problem, as shown in many different datasets, such as MNIST FASHIONMNIST, CIFAR10, CIFAR100, and IMAGENET. These approaches use deep neural networks with dense layers with softmax activation functions in order to learn features that can separate classes in a latent space. However, this traditional approach is not useful for identifying classes unseen on the training set, known as the open set problem. A similar problem occurs in scenarios involving learning on small data. To tackle both problems, few-shot learning has been proposed. In particular, metric learning learns features that obey constraints of a metric distance in the latent space in order to perform classification. However, while this approach proves to be useful for the open set problem, current implementation requires pair-wise training, where both positive and negative examples of similar images are presented during the training phase, which limits the applicability of these approaches in large data or large class scenarios given the combinatorial nature of the possible inputs.In this paper, we present a constraint-based approach applied to the representations in the latent space under the normalized softmax loss, proposed by[18]. We experimentally validate the proposed approach for the classification of unseen classes on different datasets using both metric learning and the normalized softmax loss, on disjoint and joint scenarios. Our results show that not only our proposed strategy can be efficiently trained on larger set of classes, as it does not require pairwise learning, but also present better classification results than the metric learning strategies surpassing its accuracy by a significant margin., Comment: 9 pages with 10 figures and 6 tables. Not currently published