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For the 2D Oberbeck-Boussinesq system in an annulus we are looking for the critical Rayleigh number for which the (nonzero) basic flow loses stability. For this we consider the corresponding Euler-Lagrange equations and construct a precise functional analytical frame for the Laplace- and the Stokes problem as well as the Bilaplacian operator in this domain. With this frame and the right set of basis functions it is then possible to construct and apply a numerical scheme providing the critical Rayleigh number.

Contactless fingerprint recognition systems offer a hygienic, user-friendly, and efficient alternative to traditional contact-based methods. However, their accuracy heavily relies on precise fingertip detection and segmentation, particularly under challenging background conditions. This paper introduces TipSegNet, a novel deep learning model that achieves state-of-the-art performance in segmenting fingertips directly from grayscale hand images. TipSegNet leverages a ResNeXt-101 backbone for robust feature extraction, combined with a Feature Pyramid Network (FPN) for multi-scale representation, enabling accurate segmentation across varying finger poses and image qualities. Furthermore, we employ an extensive data augmentation strategy to enhance the model's generalizability and robustness. TipSegNet outperforms existing methods, achieving a mean Intersection over Union (mIoU) of 0.987 and an accuracy of 0.999, representing a significant advancement in contactless fingerprint segmentation. This enhanced accuracy has the potential to substantially improve the reliability and effectiveness of contactless biometric systems in real-world applications.

Fingerprint mosaicking, which is the process of combining multiple fingerprint images into a single master fingerprint, is an essential process in modern biometric systems. However, it is prone to errors that can significantly degrade fingerprint image quality. This paper proposes a novel deep learning-based approach to detect and score mosaicking artifacts in fingerprint images. Our method leverages a self-supervised learning framework to train a model on large-scale unlabeled fingerprint data, eliminating the need for manual artifact annotation. The proposed model effectively identifies mosaicking errors, achieving high accuracy on various fingerprint modalities, including contactless, rolled, and pressed fingerprints and furthermore proves to be robust to different data sources. Additionally, we introduce a novel mosaicking artifact score to quantify the severity of errors, enabling automated evaluation of fingerprint images. By addressing the challenges of mosaicking artifact detection, our work contributes to improving the accuracy and reliability of fingerprint-based biometric systems.

In this paper, we derive quasi-optimal $\textit{a priori}$ error estimates for the kinematic pressure for a Finite Element (FE) approximation of steady systems of $p$-Navier-Stokes type in the case of shear-thickening, $\textit{i.e.}$, in the case $p>2$, imposing a new mild Muckenhoupt regularity condition., Comment: 20 pages, 3 figures, 6 tables. arXiv admin note: substantial text overlap with arXiv:2402.03056

On-board processing of hyperspectral data with machine learning models would enable unprecedented amount of autonomy for a wide range of tasks, for example methane detection or mineral identification. This can enable early warning system and could allow new capabilities such as automated scheduling across constellations of satellites. Classical methods suffer from high false positive rates and previous deep learning models exhibit prohibitive computational requirements. We propose fast and accurate machine learning architectures which support end-to-end training with data of high spectral dimension without relying on hand-crafted products or spectral band compression preprocessing. We evaluate our models on two tasks related to hyperspectral data processing. With our proposed general architectures, we improve the F1 score of the previous methane detection state-of-the-art models by 27% on a newly created synthetic dataset and by 13% on the previously released large benchmark dataset. We also demonstrate that training models on the synthetic dataset improves performance of models finetuned on the dataset of real events by 6.9% in F1 score in contrast with training from scratch. On a newly created dataset for mineral identification, our models provide 3.5% improvement in the F1 score in contrast to the default versions of the models. With our proposed models we improve the inference speed by 85% in contrast to previous classical and deep learning approaches by removing the dependency on classically computed features. With our architecture, one capture from the EMIT sensor can be processed within 30 seconds on realistic proxy of the ION-SCV 004 satellite., Comment: 13 pages, This work has been submitted to the IEEE for possible publication

The high-performance computing (HPC) community has recently seen a substantial diversification of hardware platforms and their associated programming models. From traditional multicore processors to highly specialized accelerators, vendors and tool developers back up the relentless progress of those architectures. In the context of scientific programming, it is fundamental to consider performance portability frameworks, i.e., software tools that allow programmers to write code once and run it on different computer architectures without sacrificing performance. We report here on the benefits and challenges of performance portability using a field-line tracing simulation and a particle-in-cell code, two relevant applications in computational plasma physics with applications to magnetically-confined nuclear-fusion energy research. For these applications we report performance results obtained on four HPC platforms with server-class CPUs from Intel (Xeon) and AMD (EPYC), and high-end GPUs from Nvidia and AMD, including the latest Nvidia H100 GPU and the novel AMD Instinct MI300A APU. Our results show that both Kokkos and OpenMP are powerful tools to achieve performance portability and decent "out-of-the-box" performance, even for the very latest hardware platforms. For our applications, Kokkos provided performance portability to the broadest range of hardware architectures from different vendors., Comment: 15 pages, 8 figures, this is a pre-print to be published in the Latin America High Performance Computing Conference (CARLA) 2024 proceedings

Gellan gum has gained significant attention due to its versatility in multiple applications in the form of hydrogels and microgels. A thorough understanding of the rheological behaviour of these systems is crucial both for fundamental research and to optimize the manufacturing needs. To this aim, here we extensively characterize the rheological behaviour of gellan based hydrogels and microgels recently used for efficient paper cleaning for restoration interventions. In particular, we study their viscoelastic properties, also during hydrogel and microgel formation, assessing the role of temperature, gellan concentration, and, importantly, the presence of different cations, which plays a crucial role in the gelation process. We find the interesting result that, in the conditions where they are efficient for cleaning, gellan hydrogels exhibit a double yielding behavior. In addition, we provide a detailed description of gellan microgels preparation, ensuring high control and reproducibility of the samples. Altogether our study sheds light on the mechanical stability, network structure, and overall functionality of the gellan-based gels, providing valuable insights into optimizing conditions for desired applications in paper cleaning.

We investigate sufficient H\"older continuity conditions on Leray-Hopf (weak) solutions to the in unsteady Navier-Stokes equations in three dimensions guaranteeing energy conservation. Our focus is on the half-space case with homogeneous Dirichlet boundary conditions. This problem is more technically challenging, if compared to the Cauchy or periodic cases, and has not been previously addressed. At present are known a few sub-optimal results obtained through Morrey embedding results based on conditions for the gradient of the velocity in Sobolev spaces. Moreover, the results in this paper are obtained without any additional assumption neither on the pressure nor the flux of the velocity, near to the boundary., Comment: 23 pages

High-momentum two-particle correlations are a useful tool for studying jet-quenching effects in the quark-gluon plasma. Angular correlations between neutral-pion triggers and charged hadrons with transverse momenta in the range 4--12~GeV/$c$ and 0.5--7~GeV/$c$, respectively, have been measured by the PHENIX experiment in 2014 for Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$~GeV. Suppression is observed in the yield of high-momentum jet fragments opposite the trigger particle, which indicates jet suppression stemming from in-medium partonic energy loss, while enhancement is observed for low-momentum particles. The ratio and differences between the yield in Au$+$Au collisions and $p$$+$$p$ collisions, $I_{AA}$ and $\Delta_{AA}$, as a function of the trigger-hadron azimuthal separation, $\Delta\phi$, are measured for the first time at the Relativistic Heavy Ion Collider. These results better quantify how the yield of low-$p_T$ associated hadrons is enhanced at wide angle, which is crucial for studying energy loss as well as medium-response effects., Comment: 535 authors from 84 institutions, 12 pages, 8 figures. v2 is version accepted for publication in Physical Review C. HEPdata tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html

In this paper, we derive quasi-optimal a priori error estimates for the kinematic pressure for a Local Discontinuous Galerkin (LDG) approximation of steady systems of $p$-Navier-Stokes type in the case of shear-thickening, i.e., in the case $p>2$, imposing a new mild Muckenhoupt regularity condition., Comment: 26 pages, 3 figures, 5 tables

The classical arguments employed when obtaining error estimates of Finite Element (FE) discretisations of elliptic problems lead to more restrictive assumptions on the regularity of the exact solution when applied to non-conforming methods. The so-called minimal regularity estimates available in the literature relax some of these assumptions, but are not truly of -minimal regularity-, since a data oscillation term appears in the error estimate. Employing an approach based on a smoothing operator, we derive for the first time error estimates for Discontinuous Galerkin (DG) type discretisations of non-linear problems with $(p,\delta)$-structure that only assume the natural $W^{1,p}$-regularity of the exact solution, and which do not contain any oscillation terms.

Fingerprints have long been recognized as a unique and reliable means of personal identification. Central to the analysis and enhancement of fingerprints is the concept of the fingerprint core. Although the location of the core is used in many applications, to the best of our knowledge, this study is the first to investigate the empirical distribution of the core over a large, combined dataset of rolled, as well as plain fingerprint recordings. We identify and investigate the extent of incomplete rolling during the rolled fingerprint acquisition and investigate the centrality of the core. After correcting for the incomplete rolling, we find that the core deviates from the fingerprint center by 5.7% $\pm$ 5.2% to 7.6% $\pm$ 6.9%, depending on the finger. Additionally, we find that the assumption of normal distribution of the core position of plain fingerprint recordings cannot be rejected, but for rolled ones it can. Therefore, we use a multi-step process to find the distribution of the rolled fingerprint recordings. The process consists of an Anderson-Darling normality test, the Bayesian Information Criterion to reduce the number of possible candidate distributions and finally a Generalized Monte Carlo goodness-of-fit procedure to find the best fitting distribution. We find the non-central Fischer distribution best describes the cores' horizontal positions. Finally, we investigate the correlation between mean core position offset and the NFIQ 2 score and find that the NFIQ 2 prefers rolled fingerprint recordings where the core sits slightly below the fingerprint center.

The occurrence of non-equilibrium transitions between arrested states has recently emerged as an intriguing issue in the field of soft glassy materials. The existence of one such transition has been suggested for aging colloidal clays (Laponite$^{\circledR}$ suspensions) at weight concentration 3.0%, although further experimental evidences are necessary to validate this scenario. Here, we test the occurrence of this transition for spontaneously aged (non-rejuvenated) samples, by exploiting the rheological tools of Dynamical Mechanical Analysis. On imposing consecutive compression cycles to differently aged clay suspensions, we find that a quite abrupt change of rheological parameters occurs for ages around three days. For the Young and elastic moduli, the change with the waiting time is essentially independent from the deformation rate, whereas other "fluid-like" properties, such as the loss modulus, do clearly display some rate dependence. We also show that the crossover identified by rheology coincides with deviations of the relaxation time (obtained through X-Ray Photon Correlation Spectroscopy) from its expected monotonic increase with aging. Thus, our results robustly support the existence of a glass-glass transition in aging colloidal clays, highlighting characteristic features of of their viscoelastic behaviour., Comment: 10 pages, 7 figures

The microscopic dynamics of spontaneously aged and rejuvenated glassy Laponite is investigated through X-ray photon correlation spectroscopy. Two different behaviours of the intensity autocorrelation functions are observed depending on the history of the sample: stretched for spontaneously aged samples and samples rejuvenated from a Wigner glass and compressed, typical of anomalous dynamics, for samples rejuvenated from a DHOC glass. The relaxation time behaviour in the three cases indicates a non-diffusive dynamics of the particles. The present system offers therefore an overview of various dynamical behaviours previously observed individually in several systems and the possibility to pass from one to the other choosing ad hoc the time parameter., Comment: 5 pages, 4 figures

The localization length r_{loc} associated with a fast secondary relaxation in glassy Laponite is determined by X-ray photon correlation spectroscopy (XPCS) through a Debye-Waller fit of the non-ergodicity parameter. Quantitative differences are observed between the time dependence (aging) of r_{loc} in spontaneously aged and rejuvenated samples. This behavior is also reflected in the calculated shear modulus which matches well with data obtained by rheological measurements., Comment: 6 pages, 5 figures

The aging dynamics of a colloidal glass has been studied by multiangle Dynamic Light Scattering, Neutron Spin Echo, X-ray Photon Correlation Spectroscopy and Molecular Dynamics simulations. The two relaxation processes, microscopic (fast) and structural (slow), have been investigated in an unprecedentedly wide range of time and length scales covering both ergodic and nonergodic regimes. The microscopic relaxation time remains diffusive at all length scales across the glass transition scaling with wavevector Q as Q^{-2}. The length-scale dependence of structural relaxation time changes from diffusive, characterized by a Q^{-2}-dependence in the early stages of aging, to Q^{-1}- dependence in the full aging regime which marks a discontinuous hopping dynamics. Both regimes are associated with a stretched behaviour of the correlation functions. We expect these findings to provide a general description of both relaxations across the glass transition., Comment: 6 pages, 4 figures

An unexpected dichotomic long time aging behaviour is observed in a glassy colloidal clay suspension investigated by X-Ray Photon Correlation Spectroscopy and Dynamic Light Scattering. In the long time aging regime the intensity autocorrelations are non-exponential, following the Kohlrausch-Williams-Watts functional form with exponent bQ. We show that for spontaneously aged samples a stretched behaviour (\beta_Q < 1) is always found. Surprisingly a compressed exponent (\beta_Q > 1) appears only when the system is rejuvenated by application of a shear field. In both cases the relaxation times scale as Q^{-1}. These observations shed light on the origin of compressed exponential behaviour and helps in classifying previous results in the literature on anomalous dynamics., Comment: 5 pages, 5 figures

Artificial intelligence onboard satellites has the potential to reduce data transmission requirements, enable real-time decision-making and collaboration within constellations. This study deploys a lightweight foundational model called RaVAEn on D-Orbit's ION SCV004 satellite. RaVAEn is a variational auto-encoder (VAE) that generates compressed latent vectors from small image tiles, enabling several downstream tasks. In this work we demonstrate the reliable use of RaVAEn onboard a satellite, achieving an encoding time of 0.110s for tiles of a 4.8x4.8 km$^2$ area. In addition, we showcase fast few-shot training onboard a satellite using the latent representation of data. We compare the deployment of the model on the on-board CPU and on the available Myriad vision processing unit (VPU) accelerator. To our knowledge, this work shows for the first time the deployment of a multi-task model on-board a CubeSat and the on-board training of a machine learning model., Comment: 4 pages, 4 figures, International Geoscience and Remote Sensing Symposium (IGARSS) 2023

Dynamic Light Scattering (DLS) and Small-Angle Neutron Scattering (SANS) are two key tools with which to probe the dynamic and static structure factor, respectively, in soft matter. Usually DLS and SANS measurements are performed separately, in different laboratories, on different samples and at different times. However, this methodology has particular disadvantages for a large variety of soft materials which exhibit high sensitivity to small changes in fundamental parameters such as waiting times, concentration, pH, ionic strength, etc. Here we report on a new portable DLS-SANS apparatus that allows one to simultaneously measure both the microscopic dynamics (through DLS) and the static structure (through SANS) on the same sample. The apparatus has been constructed as a collaboration between two laboratories, each an expert in one of the scattering methods, and was commissioned on the \textit{LOQ} and \textit{ZOOM} SANS instruments at the ISIS Pulsed Neutron \& Muon Source, U.K.

We consider the question of existence of weak solutions for the fully inhomogeneous, stationary generalized Navier-Stokes equations for homogeneous, shear-thinning fluids. For a shear rate exponent $p \in \big(\tfrac{2d}{d+1}, 2\big)$, previous results require either smallness of the norm or vanishing of the normal component of the boundary data. In this work, combining previous methods, we propose a new, more general smallness condition.

We propose MCLFIQ: Mobile Contactless Fingerprint Image Quality, the first quality assessment algorithm for mobile contactless fingerprint samples. To this end, we re-trained the NIST Fingerprint Image Quality (NFIQ) 2 method, which was originally designed for contact-based fingerprints, with a synthetic contactless fingerprint database. We evaluate the predictive performance of the resulting MCLFIQ model in terms of Error-vs.-Discard Characteristic (EDC) curves on three real-world contactless fingerprint databases using three recognition algorithms. In experiments, the MCLFIQ method is compared against the original NFIQ 2.2 method, a sharpness-based quality assessment algorithm developed for contactless fingerprint images \rev{and the general purpose image quality assessment method BRISQUE. Furthermore, benchmarks on four contact-based fingerprint datasets are also conducted.} Obtained results show that the fine-tuning of NFIQ 2 on synthetic contactless fingerprints is a viable alternative to training on real databases. Moreover, the evaluation shows that our MCLFIQ method works more accurate and robust compared to all baseline methods on contactless fingerprints. We suggest considering the proposed MCLFIQ method as a \rev{starting point for the development of} a new standard algorithm for contactless fingerprint quality assessment.

In this paper, we consider a fully-discrete approximation of an abstract evolution equation deploying a non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of the discrete solutions to a weak solution of the continuous problem. Therefore, the result can be interpreted either as a justification of the numerical method or as an alternative way of constructing weak solutions. We formulate the problem in the very general and abstract setting of so-called non-conforming Bochner pseudo-monotone operators, which allows for a unified treatment of several evolution problems. Our abstract results for non-conforming Bochner pseudo-monotone operators allow to establish (weak) convergence just by verifying a few natural assumptions on the operators time-by-time and on the discretization spaces. Hence, applications and extensions to several other evolution problems can be performed easily. We exemplify the applicability of our approach on several DG schemes for the unsteady $p$-Navier-Stokes problem. The results of some numerical experiments are reported in the final section., Comment: 31 pages, 5 tables

The accurate characterization of the severity of the wildfire event strongly contributes to the characterization of the fuel conditions in fire-prone areas, and provides valuable information for disaster response. The aim of this study is to develop an autonomous system built on top of high-resolution multispectral satellite imagery, with an advanced deep learning method for detecting burned area change. This work proposes an initial exploration of using an unsupervised model for feature extraction in wildfire scenarios. It is based on the contrastive learning technique SimCLR, which is trained to minimize the cosine distance between augmentations of images. The distance between encoded images can also be used for change detection. We propose changes to this method that allows it to be used for unsupervised burned area detection and following downstream tasks. We show that our proposed method outperforms the tested baseline approaches., Comment: 5 pages (+3 in appendix), 3 figures (+2 in appendix). Artificial Intelligence for Humanitarian Assistance and Disaster Response Workshop (AI+HADR 2022), 36th Conference on Neural Information Processing Systems (NeurIPS 2022)

In the present paper, we prove convergence rates for the pressure of the Local Discontinuous Galerkin (LDG) approximation, proposed in Part I of the paper, of systems of $p$-Navier-Stokes type and $p$-Stokes type with $p\in (2,\infty)$. The results are supported by numerical experiments., Comment: 18 pages, 0 figures, 1 table, this article is the third part of arXiv:2208.04106 and strongly refers to the second part arXiv:2208.04107

This report explains, implements and extends the works presented in "Tighter Variational Bounds are Not Necessarily Better" (T Rainforth et al., 2018). We provide theoretical and empirical evidence that increasing the number of importance samples $K$ in the importance weighted autoencoder (IWAE) (Burda et al., 2016) degrades the signal-to-noise ratio (SNR) of the gradient estimator in the inference network and thereby affecting the full learning process. In other words, even though increasing $K$ decreases the standard deviation of the gradients, it also reduces the magnitude of the true gradient faster, thereby increasing the relative variance of the gradient updates. Extensive experiments are performed to understand the importance of $K$. These experiments suggest that tighter variational bounds are beneficial for the generative network, whereas looser bounds are preferable for the inference network. With these insights, three methods are implemented and studied: the partially importance weighted autoencoder (PIWAE), the multiply importance weighted autoencoder (MIWAE) and the combination importance weighted autoencoder (CIWAE). Each of these three methods entails IWAE as a special case but employs the importance weights in different ways to ensure a higher SNR of the gradient estimators. In our research study and analysis, the efficacy of these algorithms is tested on multiple datasets such as MNIST and Omniglot. Finally, we demonstrate that the three presented IWAE variations are able to generate approximate posterior distributions that are much closer to the true posterior distribution than for the IWAE, while matching the performance of the IWAE generative network or potentially outperforming it in the case of PIWAE.

In the present paper, we prove convergence rates for the Local Discontinuous Galerkin (LDG) approximation, proposed in Part I of the paper, for systems of $p$-Navier-Stokes type and $p$-Stokes type with $p\in (2,\infty)$. The convergence rates are optimal for linear ansatz functions. The results are supported by numerical experiments., Comment: 21 pages, 3 tables, this article is the second part of arXiv:2208.04106

In the present paper, we propose a Local Discontinuous Galerkin (LDG) approximation for fully non-homogeneous systems of $p$-Navier-Stokes type. On the basis of the primal formulation, we prove well-posedness, stability (a priori estimates), and weak convergence of the method. To this end, we propose a new DG discretization of the convective term and develop an abstract non-conforming theory of pseudo-monotonicity, which is applied to our problem. We also use our approach to treat the $p$-Stokes problem., Comment: 26 pages, 4 tables

Microgel particles composed of Interpenetrated Polymer Networks (IPN) of poly(N-isopropylacrylamide) (PNIPAM) and poly(acrylic acid) (PAAc) dispersed in water have been investigated through dynamic light scattering. The study of the temperature, concentration and pH dependence of the relaxation time has highlighted the existence of a thermoreversible transition corresponding to the swollen-shrunken volume phase transition. The presence of PAAc introduces an additional pH-sensitivity with respect to the temperature-sensitivity due to PNIPAM and leads to interesting differences in the transition process at acid and neutral pH.

In this paper, we investigate a Local Discontinuous Galerkin (LDG) approximation for systems with balanced Orlicz-structure. We propose a new numerical flux, which yields optimal convergence rates for linear ansatz functions. In particular, our approach yields a unified treatment for problems with $(p,\delta)$-structure for arbitrary $p \in (1,\infty)$ and $\delta\ge 0$., Comment: 27 pages, 3 figures, 3 tables

The challenge of dynamic traffic demand in mobile networks is tackled by moving cells based on unmanned aerial vehicles. Considering the tremendous potential of unmanned aerial vehicles in the future, we propose a new heuristic algorithm for coverage optimization. The proposed algorithm is implemented based on a conditional generative adversarial neural network, with a unique multilayer sum-pooling loss function. To assess the performance of the proposed approach, we compare it with the optimal core-set algorithm and quasi-optimal spiral algorithm. Simulation results show that the proposed approach converges to the quasi-optimal solution with a negligible difference from the global optimum while maintaining a quadratic complexity regardless of the number of users., Comment: International Journal of Distributed Sensor Networks. 2022

Poly(N-isopropylacrylamide) (PNIPAM) is a synthetic polymer that is widely studied for its thermoresponsive character. However, recent works also reported evidence of a low temperature (protein-like) dynamical transition around 225 K in concentrated PNIPAM suspensions, independently of the polymer architecture, i.e., both for linear chains and for microgels. In this work, we investigate water-polymer interactions by extensive differential scanning calorimetry (DSC) measurements of both systems, in order to understand the effect of the different topological structures on the solution behaviour, in particular regarding crystallization and melting processes. In addition, we compare protiated and deuterated microgels, in both water and deuterated water. The DSC results are complemented by dynamic light scattering experiments, which confirm that the selective isotopic substitution differently affects the solution behaviour. Our findings highlight the important role played by the polymer architecture on the solution behaviour: indeed, microgels turn out to be more efficient confining agents, able to avoid water crystallization in a wider concentration range with respect to linear chains. Altogether, the present data will be valuable to interpret future low-temperature investigations of PNIPAM dispersions, particularly by neutron scattering experiments., Comment: 33 pages, 10 figures

The phase behaviour of soft colloids has attracted great attention due to the large variety of new phenomenologies emerging from their ability to pack at very high volume fractions. Here we report rheological measurements on interpenetrated polymer network microgels composed of poly(Nisopropylacrylamide) (PNIPAM) and polyacrylic acid (PAAc) at fixed PAAc content as a function of weight concentration. We found three different rheological regimes characteristic of three different states: a Newtonian shear-thinning fluid, an attractive glass characterized by a yield stress, and a jamming state. We discuss the possible molecular mechanisms driving the formation of these states.

Interpenetrated polymer network microgels, composed of crosslinked networks of poly(N-isopropylacrylamide) and polyacrylic acid (PAAc), have been investigated through rheological measurements at four different amounts of polyacrylic acid. Both PAAc content and crosslinking degree modify particle dimensions, mass and softness, thereby strongly affecting the volume fraction and the system viscosity. Here the volume fraction is derived from the flow curves at low concentrations by fitting the zero-shear viscosity with the Einstein-Batchelor equation which provides a parameter k to shift weight concentration to volume fraction. We find that particles with higher PAAc content and crosslinker are characterized by a greater value of k and therefore by larger volume fractions when compared to softer particles. The packing fractions obtained from rheological measurements are compared with those from static light scattering for two PAAc contents revealing a good agreement. Moreover, the behaviour of the viscosity as a function of packing fraction, at room temperature, has highlighted an Arrhenius dependence for microgels synthesized with low PAAc content and a Vogel-Fulcher-Tammann dependence for the highest investigated PAAc concentration. A comparison with the hard spheres behaviour indicates a steepest increase of the viscosity with decreasing particles softness. Finally, the volume fraction dependence of the viscosity at a fixed PAAc and at two different temperatures, below and above the volume phase transition, shows a quantitative agreement with the structural relaxation time measured through dynamic light scattering indicating that IPN microgels softness can be tuned with PAAc and temperature and that, depending on particle softness, two different routes are followed.

In this paper we consider nonlinear problems with an operator depending only on the deformation tensor. We consider the class of operators derived from a potential and with $(p,\delta)$ structure, for $1

In this paper, we study the existence of weak solutions to a steady system that describes the motion of a micropolar electrorheological fluid. The constitutive relations for the stress tensors belong to the class of generalized Newtonian fluids. The analysis of this particular problem leads naturally to weighted variable exponent Sobolev spaces. We establish the existence of solutions for a material function $\hat p$ that is $\log$--H\"older continuous and an electric field $\mathbf{E}$ for that $\vert\mathbf{E}\vert^2$ is bounded and smooth. Note that these conditions do not imply that the variable shear exponent $p=\hat p\circ\vert \mathbf{E}\vert^2$ is globally $\log$--H\"older continuous., Comment: 24 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2112.06512

In this paper we study the existence of solutions to a steady system that describes the motion of a micropolar electrorheological fluid. The constitutive relations for the stress tensors belong to the class of generalized Newtonian fluids. The analysis of this particular problem leads naturally to weighted Sobolev spaces. By deploying the Lipschitz truncation technique, we establish the existence of solutions without additional assumptions on the electric field., Comment: 24 pages

We study photoexcitations in small Hubbard clusters of up to 12 sites, some of which show an increase of the double occupation after the electric field pulse through impact ionization. Here, the time-dependent electromagnetic field is introduced through a Peierls substitution and the time evolution is calculated by exact diagonalization with commutator-free Magnus integrators. As a tool to better analyze the out-of-equilibrium dynamics, we generalize the Loschmidt amplitude. This way, we are able to resolve which many-body energy eigenstates are responsible for impact ionization and which show pronounced changes in the double occupation and spin energy. This analysis reveals that the loss of spin energy is of little importance for impact ionization. We further demonstrate that, for one-dimensional chains, the optical conductivity has a characteristic peak structure originating solely from vertex corrections., Comment: 21 pages, 16 figures

The PHENIX collaboration presents a systematic study of $\pi^0$ production from $p$$+$$p$, $p$$+$Al, $p$$+$Au, $d$$+$Au, and $^{3}$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. Measurements were performed with different centrality selections as well as the total inelastic, 0%--100%, selection for all collision systems. For 0%--100% collisions, the nuclear modification factors, $R_{xA}$, are consistent with unity for $p_T$ above 8 GeV/$c$, but exhibit an enhancement in peripheral collisions and a suppression in central collisions. The enhancement and suppression characteristics are similar for all systems for the same centrality class. It is shown that for high-$p_T$-$\pi^0$ production, the nucleons in the $d$ and $^3$He interact mostly independently with the Au nucleus and that the counter intuitive centrality dependence is likely due to a physical correlation between multiplicity and the presence of a hard scattering process. These observations disfavor models where parton energy loss has a significant contribution to nuclear modifications in small systems. Nuclear modifications at lower $p_T$ resemble the Cronin effect -- an increase followed by a peak in central or inelastic collisions and a plateau in peripheral collisions. The peak height has a characteristic ordering by system size as $p$$+$Au $>$ $d$$+$Au $>$ $^{3}$He$+$Au $>$ $p$$+$Al. For collisions with Au ions, current calculations based on initial state cold nuclear matter effects result in the opposite order, suggesting the presence of other contributions to nuclear modifications, in particular at lower $p_T$., Comment: 554 authors from 81 institutions, 21 pages, 13 figures, and 3 tables. Data from 2008, 2014, and 2015. v2 is version accepted for publication in Physical Review C. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html

In this paper, we introduce RaVAEn, a lightweight, unsupervised approach for change detection in satellite data based on Variational Auto-Encoders (VAEs) with the specific purpose of on-board deployment. Applications such as disaster management enormously benefit from the rapid availability of satellite observations. Traditionally, data analysis is performed on the ground after all data is transferred - downlinked - to a ground station. Constraint on the downlink capabilities therefore affects any downstream application. In contrast, RaVAEn pre-processes the sampled data directly on the satellite and flags changed areas to prioritise for downlink, shortening the response time. We verified the efficacy of our system on a dataset composed of time series of catastrophic events - which we plan to release alongside this publication - demonstrating that RaVAEn outperforms pixel-wise baselines. Finally we tested our approach on resource-limited hardware for assessing computational and memory limitations., Comment: 5 pages (+2 in appendix), 5 figures (+1 in appendix), 2 tables (+3 in appendix), NeurIPS Workshop on Artificial Intelligence for Humanitarian Assistance and Disaster Response Workshop (AI+HADR), 2021

In this paper we consider parabolic problems with stress tensor depending only on the symmetric gradient. By developing a new approximation method (which allows to use energy-type methods typical for linear problems) we provide an approach to obtain global regularity results valid for general potential operators with $(p,\delta)$-structure, for all $p>1$ and for all $\delta>0$. In this way we prove ``natural'' second order spatial regularity -- up to the boundary -- in the case of homogeneous Dirichlet boundary conditions. The regularity results, are presented with full details for the parabolic setting in the case $p>2$. However, the same method also yields regularity in the elliptic case and for $1

In this paper, we investigate mathematical content representations suitable for the automated classification of and the similarity search in STEM documents using standard machine learning algorithms: the Latent Dirichlet Allocation (LDA) and the Latent Semantic Indexing (LSI). The methods are evaluated on a subset of arXiv.org papers with the Mathematics Subject Classification (MSC) as a reference classification and using the standard precision/recall/F1-measure metrics. The results give insight into how different math representations may influence the performance of the classification and similarity search tasks in STEM repositories. Non-surprisingly, machine learning methods are able to grab distributional semantics from textual tokens. A proper selection of weighted tokens representing math may improve the quality of the results slightly. A structured math representation that imitates successful text-processing techniques with math is shown to yield better results than flat TeX tokens.

In this paper we show that the rotational Smagorinsky model for turbulent flows, can be put, for a wide range of parameters in the setting of Bochner pseudo-monotone evolution equations. This allows to prove existence of weak solutions a) identifying a proper functional setting in weighted spaces and b) checking some easily verifiable assumptions, at fixed time. We also will discuss the critical role of the exponents present in the model (power of the distance function and power of the curl) for what concerns the application of the theory of pseudo-monotone operators.

Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semiclassical models with mode selective losses, and minimal quantum systems, and the meteoric research on them has mainly focused on the wide range of novel functionalities they demonstrate. Here, we address the following questions: Does anything remain constant in the dynamics of such open systems? What are the consequences of such conserved quantities? Through spectral-decomposition method and explicit, recursive procedure, we obtain all conserved observables for general $\mathcal{PT}$-symmetric systems. We then generalize the analysis to Hamiltonians with other antilinear symmetries, and discuss the consequences of conservation laws for open systems. We illustrate our findings with several physically motivated examples., Comment: 13 pages, 1 figure, for vPHHQP Proceedings in the Journal of Physics: Conference Series

We present a method for automatised detection and analysis of quasi-periodic lineament structures from images at pixel-precision. The method exploits properties of the images' frequency domain found by using the Fourier transform. We developed this method with the goal of detecting lineament structures in an image of the Hathor cliff of comet 67P/Churyumov-Gerasimenko, which are caused by layerings and furrows in the nucleus material. Using our method, we determined the orientation and wavelength-range of these structures. The detected layering edges have similar orientations, spatial separations of 9-20 m, and are ubiquitous throughout the image. We suggest that the layerings are a global feature of the comet nucleus that provide information about formation and evolution of comet 67P. The furrows are non-uniformly distributed throughout the image. Their orientation is broadly parallel to the direction of the local gravity vector at the Hathor cliff, with spacings similar to that of the layering structures. The furrows are interpreted as signatures of local down-slope movement of cliff material. We demonstrate that the developed method is broadly applicable to the detection and analysis of various kinds of quasi-periodic structures like geological layering, folding and faulting, and texture analysis in general. In order to facilitate the application of our method, this paper is accompanied by a demo program written in Matlab.

Non-Hermitian systems with parity-time ($\mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such systems have been extensively explored in the classical domain, where second or higher order EPs have been proposed or realized. In contrast, quantum information studies of $\mathcal{PT}$-symmetric systems have been confined to systems with a two-dimensional Hilbert space. Here by using a single-photon interferometry setup, we simulate quantum dynamics of a four-dimensional $\mathcal{PT}$-symmetric system across a fourth-order exceptional point. By tracking the coherent, non-unitary evolution of the density matrix of the system in $\mathcal{PT}$-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire system, and the gain and loss subsystems. Our setup is scalable to the higher-dimensional $\mathcal{PT}$-symmetric systems, and our results point towards the rich dynamics and critical properties., Comment: 7 pages, 5 figures

In this paper we prove optimal error estimates for {solutions with natural regularity} of the equations describing the unsteady motion of incompressible shear-thinning fluids. We consider a full space-time semi-implicit scheme for the discretization. The main novelty, with respect to previous results, is that we obtain the estimates directly without introducing intermediate semi-discrete problems, which enables the treatment of homogeneous Dirichlet boundary conditions., Comment: arXiv admin note: text overlap with arXiv:2001.09888

We introduce function spaces for the treatment of non-linear parabolic equations with variable $\log$-H\"older continuous exponents, which only incorporate information of the symmetric part of a gradient. As an analogue of Korn's inequality for these functions spaces is not available, the construction of an appropriate smoothing method proves itself to be difficult. To this end, we prove a point-wise Poincar\'e inequality near the boundary of a bounded Lipschitz domain involving only the symmetric gradient. Using this inequality, we construct a smoothing operator with convenient properties. In particular, this smoothing operator leads to several density results, and therefore to a generalized formula of integration by parts with respect to time. Using this formula and the theory of maximal monotone operators, we prove an abstract existence result.

We investigate active learning in the context of deep neural network models for change detection and map updating. Active learning is a natural choice for a number of remote sensing tasks, including the detection of local surface changes: changes are on the one hand rare and on the other hand their appearance is varied and diffuse, making it hard to collect a representative training set in advance. In the active learning setting, one starts from a minimal set of training examples and progressively chooses informative samples that are annotated by a user and added to the training set. Hence, a core component of an active learning system is a mechanism to estimate model uncertainty, which is then used to pick uncertain, informative samples. We study different mechanisms to capture and quantify this uncertainty when working with deep networks, based on the variance or entropy across explicit or implicit model ensembles. We show that active learning successfully finds highly informative samples and automatically balances the training distribution, and reaches the same performance as a model supervised with a large, pre-annotated training set, with $\approx$99% fewer annotated samples., Comment: 10 pages, 5 figures, ECML/PKDD Workshop on Machine Learning for Earth Observation, 2020

In this paper we consider fully discrete approximations of abstract evolution equations, by means of a quasi non-conforming spatial approximation and finite differences in time (Rothe-Galerkin method). The main result is the convergence of the discrete solutions to a weak solution of the continuous problem. Hence, the result can be interpreted either as a justification of the numerical method, or as an alternative way of constructing weak solutions. We set the problem in the very general and abstract setting of pseudo-monotone operators, which allows for a unified treatment of several evolution problems. The examples -- which fit into our setting and which motivated our research -- are problems describing the motion of incompressible fluids, since the quasi non-conforming approximation allows to handle problems with prescribed divergence. Our abstract results for pseudo-monotone operators allow to show convergence just by verifying a few natural assumptions on the operator time-by-time and on the discretization spaces. Hence, applications and extensions to several other evolution problems can be easily performed. The results of some numerical periments are reported in the final section.

We prove existence of weak solutions for the fully inhomogeneous, stationary generalized Navier-Stokes equations for shear-thinning fluids. Our proof is based on the theory of pseudomonotone operators and the Lipschitz truncation method, whose application is presented as a general result. Our approach requires a smallness and a regularity assumption on the data; we show that this is inevitable in the framework of pseudomonotone operators.