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This study addresses the challenge of analyzing the growth kinetics of carbon nanotubes using in-situ homodyne polarization microscopy (HPM) by developing an automated deep learning (DL) approach. A Mask-RCNN architecture, enhanced with a ResNet-50 backbone, was employed to recognize and track individual nanotubes in microscopy videos, significantly improving the efficiency and reproducibility of kinetic data extraction. The method involves a series of video processing steps to enhance contrast and used differential treatment techniques to manage low signal and fast kinetics. The DL model demonstrates consistency with manual measurements and increased throughput, laying the foundation for statistical studies of nanotube growth. The approach can be adapted for other types of in-situ microscopy studies, emphasizing the importance of automation in high-throughput data acquisition for research on individual nano-objects., Comment: 13 pages, 5 Figures, No supporting information included

Motivated by the study of the propagation of convexity by semi-groups of stochastic differential equations and convex comparison between the distributions of solutions of two such equations, we study the comparison for the convex order between a Gaussian distribution and a Gaussian mixture. We give and discuss intrinsic necessary and sufficient conditions for convex ordering. On the examples that we have worked out, the two conditions appear to be closely related.

We show the existence and uniqueness of a continuous solution to a path-dependent volatility model introduced by Guyon and Lekeufack (2023) to model the price of an equity index and its spot volatility. The considered model for the trend and activity features can be written as a Stochastic Volterra Equation (SVE) with non-convolutional and non-bounded kernels as well as non-Lipschitz coefficients. We first prove the existence and uniqueness of a solution to the SVE under integrability and regularity assumptions on the two kernels and under a condition on the second kernel weighting the past squared returns which ensures that the activity feature is bounded from below by a positive constant. Then, assuming in addition that the kernel weighting the past returns is of exponential type and that an inequality relating the logarithmic derivatives of the two kernels with respect to their second variables is satisfied, we show the positivity of the volatility process which is obtained as a non-linear function of the SVE's solution. We show numerically that the choice of an exponential kernel for the kernel weighting the past returns has little impact on the quality of model calibration compared to other choices and the inequality involving the logarithmic derivatives is satisfied by the calibrated kernels. These results extend those of Nutz and Valdevenito (2023).

We are interested in the discretization of stable driven SDEs with additive noise for $\alpha$ $\in$ (1, 2) and Lq -- Lp drift under the Serrin type condition $\alpha$/q + d/p < $\alpha$ -- 1. We show weak existence and uniqueness as well as heat kernel estimates for the SDE and obtain a convergence rate of order (1/$\alpha$)*($\alpha$ -- 1 -- $\alpha$/q - d/p) for the difference of the densities for the Euler scheme approximation involving suitably cutoffed and time randomized drifts.

Pavement rutting poses a significant challenge in flexible pavements, necessitating costly asphalt resurfacing. To address this issue comprehensively, we propose an advanced Bayesian hierarchical framework of latent Gaussian models with spatial components. Our model provides a thorough diagnostic analysis, pinpointing areas exhibiting unexpectedly high rutting rates. Incorporating spatial and random components, and important explanatory variables like annual average daily traffic (traffic intensity), asphalt type, rut depth and lane width, our proposed models account for and estimate the influence of these variables on rutting. This approach not only quantifies uncertainties and discerns locations at the highest risk of requiring maintenance, but also uncover spatial dependencies in rutting (millimetre/year). We apply our models to a data set spanning eleven years (2010-2020). Our findings emphasise the systematic unexplained spatial rutting effect, where some of the rutting variability is accounted for by spatial components, asphalt type, in conjunction with traffic intensity, is also found to be the primary driver of rutting. Furthermore, the spatial dependencies uncovered reveal road sections experiencing more than 1 millimeter of rutting beyond annual expectations. This leads to a halving of the expected pavement lifespan in these areas. Our study offers valuable insights, presenting maps indicating expected rutting, and identifying locations with accelerated rutting rates, resulting in a reduction in pavement life expectancy of at least 10 years., Comment: 29 pages, 5 figures and 3 tables in main text, 2 tables and 4 figures in appendix 4 figures; and 3 tables in supplementary

We propose a new model for the coherent forecasting of both the implied volatility surfaces and the underlying asset returns.In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility indices (e.g. the VIX) on the paths of the associated equity indices (e.g. the S&P 500), we first study how implied volatility can be predicted using the past trajectory of the underlying asset price. Our empirical study reveals that a large part of the movements of the at-the-money-forward implied volatility for up to two years maturities can be explained using the past returns and their squares. Moreover, we show that up to four years of the past evolution of the underlying price should be used for the prediction and that this feedback effect gets weaker when the maturity increases. Building on this new stylized fact, we fit to historical data a parsimonious version of the SSVI parameterization (Gatheral and Jacquier, 2014) of the implied volatility surface relying on only four parameters and show that the two parameters ruling the at-the-money-forward implied volatility as a function of the maturity exhibit a path-dependent behavior with respect to the underlying asset price. Finally, we propose a model for the joint dynamics of the implied volatility surface and the underlying asset price. The latter is modelled using a variant of the path-dependent volatility model of Guyon and Lekeufack and the former is obtained by adding a feedback effect of the underlying asset price onto the two parameters ruling the at-the-money-forward implied volatility in the parsimonious SSVI parameterization and by specifying a hidden semi-Markov diffusion model for the residuals of these two parameters and the two other parameters. Thanks to this model, we are able to simulate highly realistic paths of implied volatility surfaces that are arbitrage-free.

In this paper, we are interested in the propagation of convexity by the strong solution to a one-dimensional Brownian stochastic differential equation with coefficients Lipschitz in the spatial variable uniformly in the time variable and in the convex ordering between the solutions of two such equations. We prove that while these properties hold without further assumptions for convex functions of the processes at one instant only, an assumption almost amounting to spatial convexity of the diffusion coefficient is needed for the extension to convex functions at two instants. Under this spatial convexity of the diffusion coefficients, the two properties even hold for convex functionals of the whole path. For directionally convex functionals, the spatial convexity of the diffusion coefficient is no longer needed. Our method of proof consists in first establishing the results for time discretization schemes of Euler type and then transferring them to their limiting Brownian diffusions. We thus exhibit approximations which avoid {\em convexity arbitrages} by preserving convexity propagation and comparison and can be computed by Monte Carlo simulation.

In this note, we complete the analysis of the Martingale Wasserstein Inequality started in arXiv:2011.11599 by checking that this inequality fails in dimension $d\ge 2$ when the integrability parameter $\rho$ belongs to $[1,2)$ while a stronger Maximal Martingale Wasserstein Inequality holds whatever the dimension $d$ when $\rho\ge 2$., Comment: 7 pages

Despite several decades of development, microfluidics lacks a sealing material that can be readily fabricated, leak-tight under high liquid water pressure, stable over a long time, and vacuum compatible. In this paper, we report the performances of a micro-scale processable sealing material for nanofluidic/microfluidics chip fabrication, which enables us to achieve all these requirements. We observed that micrometric walls made of SU-8 photoresist, whose thickness can be as low as 35 $\mu$m, exhibit water pressure leak-tightness from 1.5 bar up to 5.5 bar, no water porosity even after 2 months of aging, and are able to sustain under $10^{-5}$ mbar vacuum. This sealing material is therefore reliable and versatile for building microchips, part of which must be isolated from liquid water under pressure or vacuum. Moreover, the fabrication process we propose does not require the use of aggressive chemicals or high-temperature or high-energy plasma treatment. It thus opens a new perspective to seal microchips where delicate surfaces such as nanomaterials are present.

The question of the origin of the hard X-ray/soft gamma-ray emission in Centaurus A (Cen A) persists despite decades of observations. Results from X-ray instruments suggest a jet origin since the implied electron temperature (kT_e) would cause pair production runaway in the corona. In contrast, instruments sensitive to soft gamma-rays report electron temperatures indicating a corona origin may be possible. In this context, we analyzed archival INTEGRAL/IBIS-ISGRI and SPI data and observations from a 2022 Cen A monitoring program. Our analysis did not find any spectral variability. Thus we combined all observations for long-term average spectra, which were fit with a NuSTAR observation to study the 3.5 keV - 2.2 MeV spectrum. Spectral fits using a CompTT model found kT_e ~ 550 keV, near pair-production runaway. The spectrum was also well described by a log-parabola to model synchrotron self-Compton emission from the jet. Additionally, a spectral fit with the 12-year catalog Fermi/LAT spectrum using a log-parabola can explain the data up to ~ 3 GeV. Above ~ 3 GeV, a power-law excess is present, which has been previously reported in LAT/H.E.S.S. analysis. However, including a corona spectral component can also describe the data well. In this scenario, the hard X-rays/soft gamma-rays are due the corona and the MeV to GeV emission is due to the jet., Comment: 20 pages, 4 figures. Accepted by ApJ

The stratified resampling mechanism is one of the resampling schemes commonly used in the resampling steps of particle filters. In the present paper, we prove a central limit theorem for this mechanism under the assumption that the initial positions are independent and identically distributed and the weights proportional to a positive function of the positions such that the image of their common distribution by this function has a non zero component absolutely continuous with respect to the Lebesgue measure. This result relies on the convergence in distribution of the fractional part of partial sums of the normalized weights to some random variable uniformly distributed on $[0,1]$, which is established in the companion paper \cite{CLTfract} by overcoming the difficulty raised by the coupling through the normalization. Under the conjecture that a similar convergence in distribution remains valid at the next steps of a particle filter which alternates selections according to the stratified resampling mechanism and mutations according to Markov kernels, we provide an inductive formula for the asymptotic variance of the resampled population after $n$ steps. We perform numerical experiments which support the validity of this formula.

In this work, we prove the joint convergence in distribution of $q$ variables modulo one obtained as partial sums of a sequence of i.i.d. square integrable random variables multiplied by a common factor given by some function of an empirical mean of the same sequence. The limit is uniformy distributed over $[0,1]^q$. To deal with the coupling introduced by the common factor, we assume that the joint distribution of the random variables has a non zero component absolutely continuous with respect to the Lebesgue measure, so that the convergence in the central limit theorem for this sequence holds in total variation distance. While our result provides a generalization of Benford's law to a data adapted mantissa, our main motivation is the derivation of a central limit theorem for the stratified resampling mechanism, which is performed in the companion paper \cite{echant}.

In recent experiments, unprecedentedly large values for the conductivity of electrolytes through carbon nanotubes (CNTs) have been measured, possibly owing to flow slip and a high pore surface charge density whose origin is still unknown. By accounting for the coupling between the {quantum} CNT and the {classical} electrolyte-filled pore capacitances, we study the case where a gate voltage is applied to the CNT. The computed surface charge and conductivity dependence on reservoir salt concentration and gate voltage are intimately connected to the CNT electronic density of states. This approach provides key insight into why metallic CNTs have larger conductivities than semi-conducting ones.

For many examples of couples $(\mu,\nu)$ of probability measures on the real line in the convex order, we observe numerically that the Hobson and Neuberger martingale coupling, which maximizes for $\rho=1$ the integral of $|y-x|^\rho$ with respect to any martingale coupling between $\mu$ and $\nu$, is still a maximizer for $\rho\in(0,2)$ and a minimizer for $\rho>2$. We investigate the theoretical validity of this numerical observation and give rather restrictive sufficient conditions for the property to hold. We also exhibit couples $(\mu,\nu)$ such that it does not hold. The support of the Hobson and Neuberger coupling is known to satisfy some monotonicity property which we call non-decreasing. We check that the non-decreasing property is preserved for maximizers when $\rho\in(0,1]$. In general, there exist distinct non-decreasing martingale couplings, and we find some decomposition of $\nu$ which is in one-to-one correspondence with martingale couplings non-decreasing in a generalized sense., Comment: 41 pages, 1 figure

While many questions in robust finance can be posed in the martingale optimal transport framework or its weak extension, others like the subreplication price of VIX futures, the robust pricing of American options or the construction of shadow couplings necessitate additional information to be incorporated into the optimization problem beyond that of the underlying asset. In the present paper, we take into account this extra information by introducing an additional parameter to the weak martingale optimal transport problem. We prove the stability of the resulting problem with respect to the risk neutral marginal distributions of the underlying asset, thus extending the results in \cite{BeJoMaPa21b}. A key step is the generalization of the main result in \cite{BJMP22} to include the extra parameter into the setting. This result establishes that any martingale coupling can be approximated by a sequence of martingale couplings with specified marginals, provided that the marginals of this sequence converge to those of the original coupling. Finally, we deduce stability of the three previously mentioned motivating examples.

Recent direct measurements of the growth kinetics of individual carbon nanotubes revealed abrupt changes in the growth rate of nanotubes maintaining the same crystal structure. These stochastic switches call into question the possibility of chirality selection based on growth kinetics. Here, we show that a similar average ratio between fast and slow rates of around 1.7 is observed largely independent of the catalyst and growth conditions. A simple model, supported by computer simulations, shows that these switches are caused by tilts of the growing nanotube edge between two main orientations, close-armchair or close-zigzag, inducing different growth mechanisms. The rate ratio of around 1.7 then simply results from an averaging of the number of growth sites and edge configurations in each orientation. Beyond providing new insights on nanotube growth based on classical crystal growth theory, these results point to ways to control the dynamics of nanotube edges, a key requirement for stabilizing growth kinetics and producing arrays of long structurally-selected nanotubes.

On 2 September 2017 MAXI J1535-571 went into outburst and peaked at ~5 Crab in the 2-20 keV energy range. Early in the flare INTEGRAL performed Target of Opportunity pointings and monitored the source as it transitioned from the hard state to the soft state. Using quasi-simultaneous observations from MAXI/GSC and INTEGRAL/SPI, we studied the temporal and spectral evolution of MAXI J1535-571 in the 2-500 keV range. Early spectra show a Comptonized spectrum and a high-energy component dominant above ~150 keV. CompTT fits to the SPI data found electron temperatures (kTe) evolves from ~31 keV to 18 keV with a tied optical depth (tau ~ 0.85) or tau evolving from ~1.2-0.65 with a tied kTe (~24 keV). To investigate the nature of the high-energy component, we performed a spectral decomposition of the 100-400 keV energy band. The CompTT flux varies significantly during the hard state while the high-energy component flux is consistent with a constant flux. This result suggests that the two components originate from different locations, which favors a jet origin interpretation for the high-energy component over a hybrid corona interpretation. Lastly, two short rebrightenings during the hard-to-soft transition are compared to similar events reported in MAXI J1820+070.

In this paper, we are interested in comparing solutions to stochastic Volterra equations for the convex order on the space of continuous $\R^d$-valued paths and for the monotonic convex order when $d=1$. Even if in general these solutions are neither semi-martingales nor Markov processes, we are able to exhibit conditions on their coefficients enabling the comparison. Our approach consists in first comparing their Euler schemes and then taking the limit as the time step vanishes. We consider two types of Euler schemes depending on the way the Volterra kernels are discretized. The conditions ensuring the comparison are slightly weaker for the first scheme than for the second one and this is the other way round for convergence. Moreover, we extend the integrability needed on the starting values in the existence and convergence results in the literature to be able to only assume finite first order moments, which is the natural framework for convex ordering.

New Target-Ion Source Systems combining a target and a catcher material are developed in the radioactive beam community, in particular at GANIL, in order to maximise the yield of very short lived atoms by minimizing the atom-to-ion transformation time. The aim of this study is to characterize the release properties of 81Rb collected on two graphite catchers and two carbon nanotube catchers. The release fractions were measured at various catcher-heating temperatures and then compared to the analytical expressions relevant to each catcher. This comparison led to the extraction of the pre-exponential factor (D0) and the activation energy (Eact) involved in the diffusion coefficient of Rb for three carbon microstructures. All these data allowed to define an ideal catcher which could be made of aligned carbon nanotubes of small diameter and oriented in order to collect all the 81Rb atoms produced by the target but also to release them efficiently.

Wasserstein projections in the convex order were first considered in the framework of weak optimal transport, and found application in various problems such as concentration inequalities and martingale optimal transport. In dimension one, it is well-known that the set of probability measures with a given mean is a lattice w.r.t. the convex order. Our main result is that, contrary to the minimum and maximum in the convex order, the Wasserstein projections are Lipschitz continuity w.r.t. the Wasserstein distance in dimension one. Moreover, we provide examples that show sharpness of the obtained bounds for the 1-Wasserstein distance.

Motivated by insurance applications, we propose a new approach for the validation of real-world economic scenarios. This approach is based on the statistical test developed by Chevyrev and Oberhauser (2022) and relies on the notions of signature and maximum mean distance. This test allows to check whether two samples of stochastic processes paths come from the same distribution. Our contribution is to apply this test to a variety of stochastic processes exhibiting different pathwise properties (H{\"o}lder regularity, autocorrelation, regime switches) and which are relevant for the modelling of stock prices and stock volatility as well as of inflation in view of actuarial applications.

We present measurements of the polarization of X-rays in the $2-8 \thinspace \mathrm{keV}$ band from the nucleus of the radio galaxy Centaurus A (Cen A), using a 100ks observation from the Imaging X-ray Polarimetry Explorer (IXPE). Nearly simultaneous observations of Cen A were also taken with the Swift, NuSTAR, and INTEGRAL observatories. No statistically significant degree of polarization is detected with IXPE. These observations have a minimum detectable polarization at $99 \%$ percent confidence (MDP$_{99}$) of $6.5 \%$ using a weighted, spectral model-independent calculation in the $2-8 \thinspace \mathrm{keV}$ band. The polarization angle $\psi$ is consequently unconstrained. Spectral fitting across three orders of magnitude in X-ray energy ($0.3-400 \thinspace \mathrm{keV}$) demonstrates that the SED of Cen A is well described by a simple power law with moderate intrinsic absorption ($N_H \sim 10^{23} \thinspace \mathrm{cm}^{-2}$) and a Fe K$\alpha$ emission line, although a second unabsorbed power law is required to account for the observed spectrum at energies below $2 \thinspace \mathrm{keV}$. This spectrum suggests that the reprocessing material responsible for this emission line is optically thin and distant from the central black hole. Our upper limits on the X-ray polarization are consistent with the predictions of Compton scattering, although the specific seed photon population responsible for production of the X-rays cannot be identified. The low polarization degree, variability in the core emission, and the relative lack of variability in the Fe K$\alpha$ emission line support a picture where electrons are accelerated in a region of highly disordered magnetic fields surrounding the innermost jet., Comment: Accepted for Publication in ApJ, 15 pages