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The famous Erlangen Programme was coined by Felix Klein in 1872 as an algebraic approach allowing to incorporate fixed symmetry groups as the core ingredient for geometric analysis, seeing the chosen symmetries as intrinsic invariance of all objects and tools. This idea was broadened essentially by Elie Cartan in the beginning of the last century, and we may consider (curved) geometries as modelled over certain (flat) Klein's models. The aim of this short survey is to explain carefully the basic concepts and algebraic tools built over several recent decades. We focus on the direct link between the jets of sections of homogeneous bundles and the associated induced modules, allowing us to understand the overall structure of invariant linear differential operators in purely algebraic terms. This allows us to extend essential parts of the concepts and procedures to the curved cases., Comment: 24 pages

The Penrose transform was used to construct a complex starting with the Dirac operator in $k$ Clifford variables in dimension $2n$ in the stable range $n\geq k.$ In the paper, we consider the same Penrose transform in the special case of dimension $4$ and for any number of variables (i.e., in the nonstable range). In this case, we describe explicitely the corresponding relative BGG complex and its direct image for cohomology with values in a suitable line bundle (in singular infinitesimal character). We show that how to construct then a complex starting with the Dirac operator in any number of variables.

We address the task of generating temporally consistent and physically plausible images of actions and object state transformations. Given an input image and a text prompt describing the targeted transformation, our generated images preserve the environment and transform objects in the initial image. Our contributions are threefold. First, we leverage a large body of instructional videos and automatically mine a dataset of triplets of consecutive frames corresponding to initial object states, actions, and resulting object transformations. Second, equipped with this data, we develop and train a conditioned diffusion model dubbed GenHowTo. Third, we evaluate GenHowTo on a variety of objects and actions and show superior performance compared to existing methods. In particular, we introduce a quantitative evaluation where GenHowTo achieves 88% and 74% on seen and unseen interaction categories, respectively, outperforming prior work by a large margin., Comment: CVPR 2024

Energetic plasma is everywhere in the Universe. The terrestrial Magnetospheric System is a key case where direct measures of plasma energization and energy transport can be made in situ at high resolution. Despite the large amount of available observations, we still do not fully understand how plasma energization and energy transport work. Key physical processes driving much plasma energization and energy transport occur where plasma on fluid scales couple to the smaller ion kinetic scales. These scales (1 RE) are strongly related to the larger mesoscales (several RE) at which large-scale plasma energization and energy transport structures form. All these scales and processes need to be resolved experimentally, however existing multi-point in situ observations do not have a sufficient number of measurement points. New multiscale observations simultaneously covering scales from mesoscales to ion kinetic scales are needed. The implementation of these observations requires a strong international collaboration in the coming years between the major space agencies. The Plasma Observatory is a mission concept tailored to resolve scale coupling in plasma energization and energy transport at fluid and ion scales. It targets the two ESA-led Medium Mission themes Magnetospheric Systems and Plasma Cross-scale Coupling of the ESA Voyage 2050 report and is currently under evaluation as a candidate for the ESA M7 mission. MagCon (Magnetospheric Constellation) is a mission concept being studied by NASA aiming at studying the flow of mass, momentum, and energy through the Earth magnetosphere at mesoscales. Coordination between Plasma Observatory and MagCon missions would allow us for the first time to simultaneously cover from mesoscales to ion kinetic scales leading to a paradigm shift in the understanding of the Earth Magnetospheric System., Comment: A White Paper submitted for the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033

Main topic of the paper is a study of properties of massless fields of spin 3/2 in its Euclidean version. A lot of information is available already for massless fields in dimension 4. Here, we concentrate on dimension 6 and we are using the fact that the group SL(4,C) is isomorphic with the group Spin(6,C). It makes it possible to use tensor formalism for massless fields. Main problems treated in the paper are a description of fields which need to be considered in the spin 3/2 case, a suitable choice of equations they should satisfy, irreducibility of homogeneous solutions of massless field equations, the Fischer decomposition and the Howe duality for such fields., Comment: 37 pages

In the 1980s, Enright, Howe and Wallach [EHW] and independently Jakobsen [J] gave a complete classification of the unitary highest weight modules. In this paper we give a more direct and elementary proof of the same result for the (universal covers of the) Lie groups $Sp(2n, \mathbb{R}), SO^{*}(2n)$ and $SU(p, q)$. We also show how to describe the set of unitary highest weight modules with a given infinitesimal character., Comment: 31 pages

We aim to learn to temporally localize object state changes and the corresponding state-modifying actions by observing people interacting with objects in long uncurated web videos. We introduce three principal contributions. First, we explore alternative multi-task network architectures and identify a model that enables efficient joint learning of multiple object states and actions such as pouring water and pouring coffee. Second, we design a multi-task self-supervised learning procedure that exploits different types of constraints between objects and state-modifying actions enabling end-to-end training of a model for temporal localization of object states and actions in videos from only noisy video-level supervision. Third, we report results on the large-scale ChangeIt and COIN datasets containing tens of thousands of long (un)curated web videos depicting various interactions such as hole drilling, cream whisking, or paper plane folding. We show that our multi-task model achieves a relative improvement of 40% over the prior single-task methods and significantly outperforms both image-based and video-based zero-shot models for this problem. We also test our method on long egocentric videos of the EPIC-KITCHENS and the Ego4D datasets in a zero-shot setup demonstrating the robustness of our learned model.

Let $G$ be a connected simply connected noncompact exceptional simple Lie group of Hermitian type. In this paper, we work with the Dirac inequality which is a very useful tool for the classification of unitary highest weight modules., Comment: 26 pages

The Athena X-ray Integral Unit (X-IFU) is the high resolution X-ray spectrometer, studied since 2015 for flying in the mid-30s on the Athena space X-ray Observatory, a versatile observatory designed to address the Hot and Energetic Universe science theme, selected in November 2013 by the Survey Science Committee. Based on a large format array of Transition Edge Sensors (TES), it aims to provide spatially resolved X-ray spectroscopy, with a spectral resolution of 2.5 eV (up to 7 keV) over an hexagonal field of view of 5 arc minutes (equivalent diameter). The X-IFU entered its System Requirement Review (SRR) in June 2022, at about the same time when ESA called for an overall X-IFU redesign (including the X-IFU cryostat and the cooling chain), due to an unanticipated cost overrun of Athena. In this paper, after illustrating the breakthrough capabilities of the X-IFU, we describe the instrument as presented at its SRR, browsing through all the subsystems and associated requirements. We then show the instrument budgets, with a particular emphasis on the anticipated budgets of some of its key performance parameters. Finally we briefly discuss on the ongoing key technology demonstration activities, the calibration and the activities foreseen in the X-IFU Instrument Science Center, and touch on communication and outreach activities, the consortium organisation, and finally on the life cycle assessment of X-IFU aiming at minimising the environmental footprint, associated with the development of the instrument. Thanks to the studies conducted so far on X-IFU, it is expected that along the design-to-cost exercise requested by ESA, the X-IFU will maintain flagship capabilities in spatially resolved high resolution X-ray spectroscopy, enabling most of the original X-IFU related scientific objectives of the Athena mission to be retained. (abridged)., Comment: 48 pages, 29 figures, Accepted for publication in Experimental Astronomy with minor editing

Human actions often induce changes of object states such as "cutting an apple", "cleaning shoes" or "pouring coffee". In this paper, we seek to temporally localize object states (e.g. "empty" and "full" cup) together with the corresponding state-modifying actions ("pouring coffee") in long uncurated videos with minimal supervision. The contributions of this work are threefold. First, we develop a self-supervised model for jointly learning state-modifying actions together with the corresponding object states from an uncurated set of videos from the Internet. The model is self-supervised by the causal ordering signal, i.e. initial object state $\rightarrow$ manipulating action $\rightarrow$ end state. Second, to cope with noisy uncurated training data, our model incorporates a noise adaptive weighting module supervised by a small number of annotated still images, that allows to efficiently filter out irrelevant videos during training. Third, we collect a new dataset with more than 2600 hours of video and 34 thousand changes of object states, and manually annotate a part of this data to validate our approach. Our results demonstrate substantial improvements over prior work in both action and object state-recognition in video., Comment: To be published in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2022

We study the interaction of upstream ultra-low frequency (ULF) waves with collisionless shocks by analyzing the outputs of eleven 2D local hybrid simulation runs. Our simulated shocks have Alfv\'enic Mach numbers between 4.29-7.42 and their $\theta_{BN}$ angles are 15$^\circ$, 30$^\circ$, 45$^\circ$ and 50$^\circ$. The ULF wave foreshocks develop upstream of all of them. The wavelength and the amplitude of the upstream waves exhibit a complex dependence on the shock's M$_A$ and $\theta_{BN}$. The wavelength positively correlates with both parameters, with the dependence on $\theta_{BN}$ being much stronger. The amplitude of the ULF waves is proportional to the product of the reflected beam velocity and density, which also depend on M$_A$ and $\theta_{BN}$. The interaction of the ULF waves with the shock causes large-scale (several tens of upstream ion inertial lengths) shock rippling. The properties of the shock ripples are related to the ULF wave properties, namely thier wavelength and amplitude. In turn, the ripples have a large impact on the ULF wave transmission across the shock because they change local shock properties ($\theta_{BN}$, strength), so that different sections of the same ULF wave front encounter shock with different characteristics. Downstream fluctuations do not resemble the upstream waves in terms the wavefront extension, orientation or their wavelength. However some features are conserved in the Fourier spectra of downstream compressive waves that present a bump or flattening at wavelengths approximately corresponding to those of the upstream ULF waves. In the transverse downstream spectra these features are weaker.

While nitrogen-vacancy (NV-) centers have been extensively investigated in the context of spin-based quantum technologies, the spin-state readout is conventionally performed optically, which may limit miniaturization and scalability. Here, we report photoelectric readout of ground-state cross-relaxation features, which serves as a method for measuring electron spin resonance spectra of nanoscale electronic environments and also for microwave-free sensing. As a proof of concept, by systematically tuning NV centers into resonance with the target electronic system, we extracted the spectra for the P1 electronic spin bath in diamond. Such detection may enable probing optically inactive defects and the dynamics of local spin environment. We also demonstrate a magnetometer based on photoelectric detection of the ground-state level anticrossings (GSLAC), which exhibits a favorable detection efficiency as well as magnetic sensitivity. This approach may offer potential solutions for determining spin densities and characterizing local environment.

The goal of our study is to detect and characterize the electromagnetic waves that can modify the electron distribution functions, with a special attention to whistler waves. We analyse in details the electric and magnetic field fluctuations observed by the Solar Orbiter spacecraft during its first orbit around the Sun between 0.5 and 1 AU. Using data of the Search Coil Magnetometer and electric antenna, both parts of the Radio and Plasma Waves (RPW) instrumental suite, we detect the electromagnetic waves with frequencies above 3 Hz and determine the statistical distribution of their amplitudes, frequencies, polarization and k-vector as a function of distance. We also discuss relevant instrumental issues regarding the phase between the electric and magnetic measurements and the effective length of the electric antenna. An overwhelming majority of the observed waves are right hand circularly polarized in the solar wind frame and identified as outward propagating and quasi parallel whistler waves. Their occurrence rate increases by a least a factor two from 1 AU to 0.5 AU. These results are consistent with the regulation of the heat flux by the whistler heat flux instability. Near 0.5 AU, whistler waves are found to be more field-aligned and to have smaller normalized frequency ($f/f_{ce}$), larger amplitude, and larger bandwidth than at 1 AU., Comment: accepted in A&A

In order to allow for a comparison with the measurements from other antenna systems, the voltage power spectral density measured by the Radio and Plasma waves receiver (RPW) on board Solar Orbiter needs to be converted into physical quantities that depend on the intrinsic properties of the radiation itself.The main goal of this study is to perform a calibration of the RPW dipole antenna system that allows for the conversion of the voltage power spectral density measured at the receiver's input into the incoming flux density. We used space observations from the Thermal Noise Receiver (TNR) and the High Frequency Receiver (HFR) to perform the calibration of the RPW dipole antenna system. Observations of type III bursts by the Wind spacecraft are used to obtain a reference radio flux density for cross-calibrating the RPW dipole antennas. The analysis of a large sample of HFR observations (over about ten months), carried out jointly with an analysis of TNR-HFR data and prior to the antennas' deployment, allowed us to estimate the reference system noise of the TNR-HFR receivers. We obtained the effective length of the RPW dipoles and the reference system noise of TNR-HFR in space, where the antennas and pre-amplifiers are embedded in the solar wind plasma. The obtained $l_{eff}$ values are in agreement with the simulation and measurements performed on the ground. By investigating the radio flux intensities of 35 type III bursts simultaneously observed by Solar Orbiter and Wind, we found that while the scaling of the decay time as a function of the frequency is the same for the Waves and RPW instruments, their median values are higher for the former. This provides the first observational evidence that Type III radio waves still undergo density scattering, even when they propagate from the source, in a medium with a plasma frequency that is well below their own emission frequency.

Within the theory of interacting continua, we develop a model for a heat conducting mixture of two interacting fluids described in terms of the densities and the velocities for each fluid and the temperature field for the mixture as a whole. We use a general thermodynamic framework that determines the response of the material from the knowledge of two pieces of information, namely how the material stores the energy and how the entropy is produced. This information is expressed in the form of the constitutive equations for two scalars: the Helmholtz free energy and the entropy production. Additionally, we follow the goal to determine the response of a mixture from a small (minimal) set of material parameters, including shear viscosity, bulk viscosity and heat conductivity associated with the mixture as a whole and the drag coefficient connected with the interaction force between the constituents. The same thermodynamic approach is used to obtain the model when the mixture as a whole responses as an incompressible material. For both the compressible and incompressible mixtures, we investigate three variants stemming from different definitions of the (averaged) velocity associated with the mixture as a whole. We also address the issue of identification of boundary conditions for the individual constituents from the standard boundary conditions formulated in terms of the quantities associated with the mixture as a whole.

The recently released spacecraft potential measured by the RPW instrument on-board Solar Orbiter has been used to estimate the solar wind electron density in the inner heliosphere. Solar-wind electron density measured during June 2020 has been analysed to obtain a thorough characterization of the turbulence and intermittency properties of the fluctuations. Magnetic field data have been used to describe the presence of ion-scale waves. Selected intervals have been extracted to study and quantify the properties of turbulence. The Empirical Mode Decomposition has been used to obtain the generalized marginal Hilbert spectrum, equivalent to the structure functions analysis, and additionally reducing issues typical of non-stationary, short time series. The presence of waves was quantitatively determined introducing a parameter describing the time-dependent, frequency-filtered wave power. A well defined inertial range with power-law scaling has been found almost everywhere. However, the Kolmogorov scaling and the typical intermittency effects are only present in part of the samples. Other intervals have shallower spectra and more irregular intermittency, not described by models of turbulence. These are observed predominantly during intervals of enhanced ion frequency wave activity. Comparisons with compressible magnetic field intermittency (from the MAG instrument) and with an estimate of the solar wind velocity (using electric and magnetic field) are also provided to give general context and help determine the cause for the anomalous fluctuations.

Impacts of dust grains on spacecraft are known to produce typical impulsive signals in the voltage waveform recorded at the terminals of electric antennas. Such signals are routinely detected by the Time Domain Sampler (TDS) system of the Radio and Plasma Waves (RPW) instrument aboard Solar Orbiter. We investigate the capabilities of RPW in terms of interplanetary dust studies and present the first analysis of dust impacts recorded by this instrument. We discuss previously developed models of voltage pulses generation after a dust impact onto a spacecraft and present the relevant technical parameters for Solar Orbiter RPW as a dust detector. Then we present the statistical analysis of the dust impacts recorded by RPW/TDS from April 20th, 2020 to February 27th, 2021 between 0.5 AU and 1 AU. The study shows that the dust population studied presents a radial velocity component directed outward from the Sun, the order of magnitude of which can be roughly estimated as $v_{r, dust} \simeq 50$ km.$s^{-1}$. This is consistent with the flux of impactors being dominated by $\beta$-meteoroids. We estimate the cumulative flux of these grains at 1 AU to be roughly $F_\beta \simeq 8\times 10^{-5} $ m$^{-2}$s$^{-1}$, for particles of radius $r \gtrsim 100$ nm. The power law index $\delta$ of the cumulative mass flux of the impactors is evaluated by two differents methods (direct observations of voltage pulses and indirect effect on the impact rate dependency on the impact speed). Both methods give a result $\delta \simeq 0.3-0.4$. Solar Orbiter RPW proves to be a suitable instrument for interplanetary dust studies. These first results are promising for the continuation of the mission, in particular for the in-situ study of the dust cloud outside the ecliptic plane, which Solar Orbiter will be the first spacecraft to explore., Comment: 13 pages, 8 figures

Solar Orbiter was launched on February 10, 2020 with the purpose of investigating solar and heliospheric physics using a payload of instruments designed for both remote and in-situ sensing. Similar to the recently launched Parker Solar Probe, and unlike earlier missions, Solar Orbiter carries instruments designed to measure the low frequency DC electric fields. In this paper we assess the quality of the low-frequency DC electric field measured by the Radio and Plasma Waves instrument (RPW) on Solar Orbiter. In particular we investigate the possibility of using Solar Orbiter's DC electric and magnetic field data to estimate the solar wind speed. We use deHoffmann-Teller (HT) analysis based on measurements of the electric and magnetic fields to find the velocity of solar wind current sheets which minimizes a single component of the electric field. By comparing the HT velocity to proton velocity measured by the Proton and Alpha particle Sensor (PAS) we develop a simple model for the effective antenna length, $L_\text{eff}$ of the E-field probes. We then use the HT method to estimate the speed of the solar wind. Using the HT method, we find that the observed variations in $E_y$ are often in excellent agreement with the variations in the magnetic field. The magnitude of $E_y$, however, is uncertain due to the fact that the $L_\text{eff}$ depends on the plasma environment. We derive an empirical model relating $L_\text{eff}$ to the Debye length, which we can use to improve the estimate of $E_y$ and consequently the estimated solar wind speed. The low frequency electric field provided by RPW is of high quality. Using deHoffmann-Teller analysis, Solar Orbiter's magnetic and electric field measurements can be used to estimate the solar wind speed when plasma data is unavailable., Comment: 7 pages, 4 figures

Electric field measurements of the Time Domain Sampler (TDS) receiver, part of the Radio and Plasma Waves (RPW) instrument on board Solar Orbiter, often exhibit very intense broadband wave emissions at frequencies below 20~kHz in the spacecraft frame. In this paper, we present a year-long study of electrostatic fluctuations observed in the solar wind at an interval of heliocentric distances from 0.5 to 1~AU. The RPW/TDS observations provide a nearly continuous data set for a statistical study of intense waves below the local plasma frequency. The on-board and continuously collected and processed properties of waveform snapshots allow for the mapping plasma waves at frequencies between 200~Hz and 20~kHz. We used the triggered waveform snapshots and a Doppler-shifted solution of the dispersion relation for wave mode identification in order to carry out a detailed spectral and polarization analysis. Electrostatic ion-acoustic waves are the common wave emissions observed between the local electron and proton plasma frequency in the soler wind. The occurrence rate of ion-acoustic waves peaks around perihelion at distances of 0.5~AU and decreases with increasing distances, with only a few waves detected per day at 0.9~AU. Waves are more likely to be observed when the local proton moments and magnetic field are highly variable. A more detailed analysis of more than 10000 triggered waveform snapshots shows the mean wave frequency at about 3 kHz and wave amplitude about 2.5 mV/m. The wave amplitude varies as 1/R^(1.38) with the heliocentric distance. The relative phase distribution between two components of the E-field shows a mostly linear wave polarization. Electric field fluctuations are closely aligned with the directions of the ambient field lines. Only a small number (3%) of ion-acoustic waves are observed at larger magnetic discontinuities., Comment: 9 pages, 8 figures

A variety of kinetic waves develop in the solar wind. The relationship between these waves and larger-scale structures, such as current sheets and ongoing turbulence remain a topic of investigation. Similarly, the instabilities producing ion-acoustic waves in the solar wind remains an open question. The goals of this paper are to investigate kinetic electrostatic Langmuir and ion-acoustic waves in the solar wind at 0.5 AU and determine whether current sheets and associated streaming instabilities can produce the observed waves. The relationship between these waves and currents is investigated statistically. Solar Orbiter's Radio and Plasma Waves instrument suite provides high-resolution snapshots of the fluctuating electric field. The Low Frequency Receiver resolves the waveforms of ion-acoustic waves and the Time Domain Sampler resolves the waveforms of both ion-acoustic and Langmuir waves. Using these waveform data we determine when these waves are observed in relation to current structures in the solar wind, estimated from the background magnetic field. Langmuir and ion-acoustic waves are frequently observed in the solar wind. Ion-acoustic waves are observed about 1% of the time at 0.5 AU. The waves are more likely to be observed in regions of enhanced currents. However, the waves typically do not occur at current structures themselves. The observed currents in the solar wind are too small to drive instability by the relative drift between single ion and electron populations. When multi-component ion and/or electron distributions are present the observed currents may be sufficient for instability. Ion beams are the most plausible source of ion-acoustic waves. The spacecraft potential is confirmed to be a reliable probe of the background electron density by comparing the peak frequencies of Langmuir waves with the plasma frequency calculated from the spacecraft potential., Comment: 13 pages, 12 figures

We use the plasma density based on measurements of the probe-to-spacecraft potential in combination with magnetic field measurements by MAG to study fields and density fluctuations in the solar wind observed by Solar Orbiter during the first perihelion encounter ($\sim$0.5~AU away from the Sun). In particular we use the polarization of the wave magnetic field, the phase between the compressible magnetic field and density fluctuations and the compressibility ratio (the ratio of the normalized density fluctuations to the normalized compressible fluctuations of B) to characterize the observed waves and turbulence. We find that the density fluctuations are out-of-phase with the compressible component of magnetic fluctuations for intervals of turbulence, while they are in phase for the circular-polarized waves around the proton cyclotron frequency. We analyze in detail two specific events with simultaneous presence of left- and right-handed waves at different frequencies. We compare observed wave properties to a prediction of the three-fluid (electrons, protons and alphas) model. We find a limit on the observed wavenumbers, $10^{-6} < k < 7 \times 10^{-6}$~m$^{-1}$, which corresponds to wavelength $7 \times 10^6 >\lambda > 10^6$~m. We conclude that most likely both the left- and right-handed waves correspond to the low-wavenumber part (close to the cut-off at $\Omega_{c\mathrm{He}++}$) proton-band electromagnetic ion cyclotron (left-handed wave in the plasma frame confined to the frequency range $\Omega_{c\mathrm{He}++} < \omega < \Omega_{c\mathrm{H}+}$) waves propagating in the outwards and inwards directions respectively. The fact that both wave polarizations are observed at the same time and the identified wave mode has a low group velocity suggests that the double-banded events occur in the source regions of the waves., Comment: 13 pages, 9 figures

In this paper, we investigate the phenomenon of particle rebound in a viscous incompressible fluid environment. We focus on the important case of no-slip boundary conditions, for which it is by now classical that, under certain assumptions, collisions cannot occur in finite time. Motivated by the desire to understand this fascinating yet counterintuitive fluid-structure interaction, we introduce a reduced model which we study both analytically and numerically. In this simplified framework, we provide conditions which allow to prove that rebound is possible even in the absence of a topological contact. Our results lead to conjecture that a qualitative change in the shape of the solid is necessary for obtaining a physically meaningful rebound. We support the conjecture by also comparing numerical simulations performed for the reduced model with the finite element solutions obtained for the corresponding well-established PDE system.