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We present a sensor-agnostic spectral transformer as the basis for spectral foundation models. To that end, we introduce a Universal Spectral Representation (USR) that leverages sensor meta-data, such as sensing kernel specifications and sensing wavelengths, to encode spectra obtained from any spectral instrument into a common representation, such that a single model can ingest data from any sensor. Furthermore, we develop a methodology for pre-training such models in a self-supervised manner using a novel random sensor-augmentation and reconstruction pipeline to learn spectral features independent of the sensing paradigm. We demonstrate that our architecture can learn sensor independent spectral features that generalize effectively to sensors not seen during training. This work sets the stage for training foundation models that can both leverage and be effective for the growing diversity of spectral data.

In this paper we study the isometric rigidity of certain classes of metric spaces with respect to the $p$-Wasserstein space. We prove that spaces that split a separable Hilbert space are not isometrically rigid with respect to $\mathbb{P}_2$. We then prove that infinite rays are isometrically rigid with respect to $\mathbb{P}_p$ for any $p\geq 1$, whereas taking infinite half-cylinders (i.e.\ product spaces of the form $X\times [0,\infty)$) over compact non-branching geodesic spaces preserves isometric rigidity with respect to $\mathbb{P}_p$, for $p>1$. Finally, we prove that spherical suspensions over compact spaces with diameter less than $\pi/2$ are isometrically rigid with respect to $\mathbb{P}_p$, for $p>1$.

The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnostic capabilities for studying the Sun, providing complementary insights through high spatial and temporal resolution at millimeter wavelengths. ALMA acts as a linear thermometer for atmospheric gas, aiding in understanding the solar atmosphere's structure, dynamics, and energy balance. Given the Sun's complex emission patterns and rapid evolution, high-cadence imaging is essential for solar observations. Snapshot imaging is required, though it limits available visibility data, making full exploitation of ALMA's capabilities non-trivial. Challenges in processing solar ALMA data highlight the need for revising and enhancing the solar observing mode. The ALMA development study High-Cadence Imaging of the Sun demonstrated the potential benefits of high cadence observations through a forward modelling approach. The resulting report provides initial recommendations for improved post-processing solar ALMA data and explores increasing the observing cadence to sub-second intervals to improve image reliability., Comment: ALMA Memo 628 summarising the results of the ESO-funded ALMA development study "High-cadence Imaging of the Sun", concluded in 2023 (74 pages, 53 figures)

We study $\mathsf{RCD}$-spaces $(X,d,\mathfrak{m})$ with group actions by isometries preserving the reference measure $\mathfrak{m}$ and whose orbit space has dimension one, i.e. cohomogeneity one actions. To this end we prove a Slice Theorem asserting that each slice at a point is homeomorphic to a non-negatively curved $\mathsf{RCD}$-space. Under the assumption that $X$ is non-collapsed we further show that the slices are homeomorphic to metric cones over homogeneous spaces with $\mathrm{Ric} \geq 0$. As a consequence we obtain complete topological structural results and a principal orbit representation theorem. Conversely, we show how to construct new $\mathsf{RCD}$-spaces from a cohomogeneity one group diagram, giving a complete description of $\mathsf{RCD}$-spaces of cohomogeneity one. As an application of these results we obtain the classification of cohomogeneity one, non-collapsed $\mathsf{RCD}$-spaces of essential dimension at most $4$., Comment: 57 pages, changes to sections 3 and 4

This article provides a comprehensive overview of recent research in the area of Child-Computer Interaction (CCI). The main contributions of the present article are two-fold. First, we present a novel longitudinal CCI database named ChildCIdbLong, which comprises over 600 children aged 18 months to 8 years old, acquired continuously over 4 academic years (2019-2023). As a result, ChildCIdbLong comprises over 12K test acquisitions over a tablet device. Different tests are considered in ChildCIdbLong, requiring different touch and stylus gestures, enabling the evaluation of praxical and cognitive skills such as attentional, visuo-spatial, and executive, among others. In addition to the ChildCIdbLong database, we propose a novel quantitative metric called Test Quality (Q), designed to measure the motor and cognitive development of children through their interaction with a tablet device. In order to provide a better comprehension of the proposed Q metric, popular percentile-based growth representations are introduced for each test, providing a two-dimensional space to compare children's development with respect to the typical age skills of the population. The results achieved in the present article highlight the potential of the novel ChildCIdbLong database in conjunction with the proposed Q metric to measure the motor and cognitive development of children as they grow up. The proposed framework could be very useful as an automatic tool to support child experts (e.g., paediatricians, educators, or neurologists) for early detection of potential physical/cognitive impairments during children's development., Comment: 13 pages, 5 figures, 7 tables, 46 references

This article proposes a novel Children-Computer Interaction (CCI) approach for the task of age group detection. This approach focuses on the automatic analysis of the time series generated from the interaction of the children with mobile devices. In particular, we extract a set of 25 time series related to spatial, pressure, and kinematic information of the children interaction while colouring a tree through a pen stylus tablet, a specific test from the large-scale public ChildCIdb database. A complete analysis of the proposed approach is carried out using different time series selection techniques to choose the most discriminative ones for the age group detection task: i) a statistical analysis, and ii) an automatic algorithm called Sequential Forward Search (SFS). In addition, different classification algorithms such as Dynamic Time Warping Barycenter Averaging (DBA) and Hidden Markov Models (HMM) are studied. Accuracy results over 85% are achieved, outperforming previous approaches in the literature and in more challenging age group conditions. Finally, the approach presented in this study can benefit many children-related applications, for example, towards an age-appropriate environment with the technology., Comment: 10 pages, 6 figures, 6 tables, 32 references

Determination of solar magnetic fields with a spatial resolution set by the diffraction limit of a telescope is difficult because the time required to measure the Stokes vector with sufficient signal-to-noise is long compared to the solar evolution timescale. This difficulty gets worse with increasing telescope size as the photon flux per diffraction-limited resolution element remains constant but the evolution timescale decreases linearly with the diffraction-limited resolution. We aim to improve magnetic field reconstruction at the diffraction limit without averaging the observations in time or space, and without applying noise filtering. The magnetic field vector tends to evolve slower than the temperature, velocity and microturbulence. We exploit this by adding temporal regularisation terms for the magnetic field to the linear least-squares fitting used in the weak-field approximation, as well as to the Levenberg-Marquardt algorithm used in inversions. The other model parameters are allowed to change in time without constraints. We infer the chromospheric magnetic field from Ca II 854.2 nm observations using the weak field approximation and the photospheric magnetic field from Fe I 617.3 nm observations using Milne-Eddington inversions, both with and without temporal regularisation. Temporal regularisation reduce the noise in the reconstructed maps of the magnetic field and provides a better coherency in time in both the weak-field approximation and Milne-Eddington inversions. Temporal regularisation markedly improves magnetic field determination from spatially and temporally resolved observations., Comment: 8 pages, 7 figures, accepted for publication in Astronomy & Astrophysics

Spectropolarimetric observations used to infer the solar magnetic fields are obtained with a limited spatial resolution. The effects of this limited resolution on the inference of the open flux over the observed region have not been extensively studied. We aim to characterize the biases that arise in the inference of the mean flux density by performing an end-to-end study that involves the generation of synthetic data, its interpretation (inversion), and a comparison of the results with the original model. We synthesized polarized spectra of the two magnetically sensitive lines of neutral iron around 630\,nm from a state-of-the-art numerical simulation of the solar photosphere. We then performed data degradation to simulate the effect of the telescope with a limited angular resolution and interpreted (inverted) the data using a Milne-Eddington spectropolarimetric inversion code. We then studied the dependence of the inferred parameters on the telescope resolution. The results show a significant decrease in the mean magnetic flux density -- related to the open flux observed at the disk center -- with decreasing telescope resolution. The original net magnetic field flux is fully resolved by a 1m telescope, but a 20\,cm aperture telescope yields a 30\% smaller value. Even in the fully resolved case, the result is still biased due to the corrugation of the photospheric surface. Even the spatially averaged quantities, such as the open magnetic flux in the observed region, are underestimated when the magnetic structures are unresolved. The reason for this is the presence of nonlinearities in the magnetic field inference process. This effect might have implications for the modeling of large-scale solar magnetic fields; for example, those corresponding to the coronal holes, or the polar magnetic fields, which are relevant to our understanding of the solar cycle., Comment: To be published in A&A

We investigate the thermal, kinematic and magnetic structure of small-scale heating events in an emerging flux region (EFR). We use high-resolution multi-line observations (including Ca II 8542~\AA, Ca II K, and Fe I 6301~\AA line pair) of an EFR located close to the disk center from the CRISP and CHROMIS instruments at the Swedish 1-m Solar Telescope. We perform non-LTE inversions of multiple spectral lines to infer the temperature, velocity, and magnetic field structure of the heating events. Additionally, we use the data-driven Coronal Global Evolutionary Model to simulate the evolution of the 3D magnetic field configuration above the events and understand their dynamics. Furthermore, we analyze the differential emission measure to gain insights into the heating of the coronal plasma in the EFR. Our analysis reveals the presence of numerous small-scale heating events in the EFR, primarily located at polarity inversion lines of bipolar structures. These events not only heat the lower atmosphere but also significantly heat the corona. The data-driven simulations, along with the observed enhancement of currents and Poynting flux, suggest that magnetic reconnection in the lower atmosphere is likely responsible for the observed heating at these sites., Comment: 20 pages, 15 figures, accepted for publication in the ApJ

We extend the Margulis Lemma for manifolds with lower Ricci curvature bounds to the $\text{RCD}(K,N)$ setting. As one of our main tools, we obtain improved regularity estimates for Regular Langrangian flows on these spaces., Comment: 51 pages

Neural-symbolic approaches to machine learning incorporate the advantages from both connectionist and symbolic methods. Typically, these models employ a first module based on a neural architecture to extract features from complex data. Then, these features are processed as symbols by a symbolic engine that provides reasoning, concept structures, composability, better generalization and out-of-distribution learning among other possibilities. However, neural approaches to the grounding of symbols in sensory data, albeit powerful, still require heavy training and tedious labeling for the most part. This paper presents a new symbolic-only method for the generation of hierarchical concept structures from complex spatial sensory data. The approach is based on Bateson's notion of difference as the key to the genesis of an idea or a concept. Following his suggestion, the model extracts atomic features from raw data by computing elemental sequential comparisons in a stream of multivariate numerical values. Higher-level constructs are built from these features by subjecting them to further comparisons in a recursive process. At any stage in the recursion, a concept structure may be obtained from these constructs and features by means of Formal Concept Analysis. Results show that the model is able to produce fairly rich yet human-readable conceptual representations without training. Additionally, the concept structures obtained through the model (i) present high composability, which potentially enables the generation of 'unseen' concepts, (ii) allow formal reasoning, and (iii) have inherent abilities for generalization and out-of-distribution learning. Consequently, this method may offer an interesting angle to current neural-symbolic research. Future work is required to develop a training methodology so that the model can be tested against a larger dataset.

We study the reach (in the sense of Federer) of the natural isometric embedding $X\hookrightarrow W_p(X)$ of $X$ inside its $p$-Wasserstein space, where $(X,\operatorname{dist})$ is a geodesic metric space. We prove that if a point $x\in X$ can be joined to another point $y\in X$ by two minimizing geodesics, then $\operatorname{reach}(x, X\subset W_p(X)) = 0$. This includes the cases where $X$ is a compact manifold or a non-simply connected one. On the other hand, we show that $\operatorname{reach}(X\subset W_p(X)) = \infty$ when $X$ is a CAT(0) space. The infinite reach enables us to examine the regularity of the projection map. Furthermore, we replicate these findings by considering the isometric embedding $X\hookrightarrow W_\vartheta(X)$ into an Orlicz--Wasserstein space, a generalization by Sturm of the classical Wasserstein space. Lastly, we establish the nullity of the reach for the isometric embedding of $X$ into $\operatorname{Dgm}_\infty$, the space of persistence diagrams equipped with the bottleneck distance.

Heat pumps are an energy-efficient and increasingly cost-effective solution for reducing greenhouse gas emissions in the building sector. However, other clean energy technologies such as rooftop solar are less likely to be adopted in underserved communities, and thus policies incentivizing their adoption may funnel tax dollars to well-resourced communities. Unlike previously-studied technologies, the effects of heat pumps on household energy bills may be positive or negative depending on local climate, fuel availability and costs, and other factors. Here we propose a framework for assessing heat pump inequities across the U.S. We find that households in communities of color and with higher percentages of renters are less likely to use heat pumps across the board. Moreover, communities of color are least likely to use heat pumps in regions where they are most likely to reduce energy bills. Public policies must address these inequities to advance beneficial electrification and energy justice., Comment: Figure 2 modified; included additional variables in Figure 3 (no change in main findings); SI updated with newer data and additional robustness results (no change in main findings); references added

Intermediate stages between pores and sunspots are a rare phenomenon and can manifest with the formation of transient photospheric penumbral-like filaments. Although the magnetic field changes rapidly during the evolution of such filaments, they have not been shown to be connected to magnetic reconnection events yet. We analyzed observations of a pore in NOAA AR 12739 from the Swedish Solar Telescope including spectropolarimetric data of the Fe I 6173 {\AA} and the Ca II 8542 {\AA} line and spectroscopic data of the Ca II K 3934 {\AA} line. The VFISV Milne-Eddington inversion code and the multi-line Non-LTE inversion code STiC were utilized to obtain atmospheric parameters in the photosphere and the chromosphere. Multiple filamentary structures of inclined magnetic fields are found in photospheric inclination maps at the boundary of the pore, although the pore never developed a penumbra. One of the filaments shows a clear counterpart in continuum intensity maps in addition to photospheric blueshifts. During its decay, a brightening in the blue wing of the Ca II 8542 {\AA} line is observed. The Ca II K 3934 {\AA} and the Ca II 8542 {\AA} lines show complex spectral profiles in this region. Depth-dependent STiC inversion results using data from all available lines yield a temperature increase (roughly 1000 Kelvin) and bidirectional flows (magnitudes up to 8 km/s) at log tau=-3.5. The temporal and spatial correlation of the decaying filament (observed in the photosphere) to the temperature increase and the bidirectional flows in the high photosphere/low chromosphere suggests that they are connected. We propose scenarios in which magnetic reconnection happens at the edge of a rising magnetic flux tube in the photosphere. This leads to both the decay of the filament in the photosphere and the observed temperature increase and the bidirectional flows in the high photosphere/low chromosphere., Comment: Paper accepted by "Astronomy & Astrophysics" on 02/03/2023

We investigated the diagnostic potential of the Stokes $V$ profile of the H$\alpha$ line to probe the chromospheric line-of-sight (LOS) magnetic field ($B_{\mathrm{LOS}}$) by comparing the $B_{\mathrm{LOS}}$ inferred from the weak field approximation (WFA) with that of inferred from the multi-line inversions of the Ca II 8542 {\AA}, Si I 8536 {\AA} and Fe I 8538 {\AA} lines using the STiC inversion code. Simultaneous spectropolarimetric observations of a pore in the Ca II 8542 {\AA} and H$\alpha$ spectral lines obtained from the SPINOR at the Dunn Solar Telescope on the 4th of December, 2008 are used in this study. The WFA was applied on the Stokes $I$ and $V$ profiles of H$\alpha$ line over three wavelength ranges viz.: around line core ($\Delta\lambda=\pm0.35$ {\AA}), line wings ($\Delta\lambda=[-1.5, -0.6]$ and $[+0.6, +1.5]$ {\AA}) and full spectral range of the line ($\Delta\lambda=\pm1.5$ {\AA}) to derive the $B_{\mathrm{LOS}}$. We found the maximum $B_{\mathrm{LOS}}$ strengths of $\sim+800$ and $\sim+600$ G at $\log\tau_{\mathrm{500}}$ = $-$1 and $-$4.5, respectively in the pore. The morphological map of the $B_{\mathrm{LOS}}$ inferred from the H$\alpha$ line core is similar to the $B_{\mathrm{LOS}}$ map at $\log\tau_{\mathrm{500}}$ = $-$4.5 inferred from multi-line inversions. The $B_{\mathrm{LOS}}$ map inferred from the H$\alpha$ line wings and full spectral range have a similar morphological structure to the $B_{\mathrm{LOS}}$ map inferred at $\log\tau_{\mathrm{500}}$ = $-$1. The $B_{\mathrm{LOS}}$ estimated from H$\alpha$ using WFA is weaker by a factor of $\approx 0.53$ than that of inferred from the multi-line inversions., Comment: Accepted to be published in the ApJ on 25th February, 2023

The heating of the chromosphere in internetwork regions remains one of the foremost open questions in solar physics. In the present study we tackle this old problem by using a very high spatial-resolution simulation of quiet-Sun conditions performed with radiative MHD numerical models and IRIS observations. We have expanded a previously existing 3D radiative MHD numerical model of the solar atmosphere, which included self-consistently locally driven magnetic amplification in the chromosphere, by adding ambipolar diffusion and time-dependent non-equilibrium hydrogen ionization to the model. The energy of the magnetic field is dissipated in the upper chromosphere, providing a large temperature increase due to ambipolar diffusion and the non-equilibrium ionization (NEQI). At the same time, we find that adding the ambipolar diffusion and NEQI in the simulation has a minor impact on the local growth of the magnetic field in the lower chromosphere and its dynamics. Our comparison between synthesized Mg II profiles from these high spatial resolution models, with and without ambipolar diffusion and NEQI, and quiet Sun and coronal hole observations from IRIS now reveal a better correspondence. The intensity of profiles is increased and the line cores are slightly broader when ambipolar diffusion and NEQI effects are included. Therefore, the Mg II profiles are closer to those observed than in previous models, but some differences still remain., Comment: submitted to ApJL, 3 figures

Fibrils in the solar chromosphere carry transverse oscillations as determined from non-spectroscopic imaging data. They are estimated to carry an energy flux of several $\mathrm{kW~m}^{-2}$, which is a significant fraction of the average chromospheric radiative energy losses. We aim to determine oscillation properties of fibrils not only in the plane-of-the-sky (horizontal) direction, but also along the line-of-sight (vertical) direction. We obtained imaging-spectroscopy data in $\mathrm{Fe~I}$, $\mathrm{Ca~II~IR}$, and $\mathrm{Ca~II~K}$ with the Swedish 1-m Solar Telescope. We created a sample of 605 bright $\mathrm{Ca~II~K}$ fibrils and measured their horizontal motions. Their vertical motion was determined through non-LTE inversion of the observed spectra. We determined the periods and velocity amplitudes of the fibril oscillations, as well as phase differences between vertical and horizontal oscillations in the fibrils. The bright $\mathrm{Ca~II~K}$ fibrils carry transverse waves with a mean period of $2.1\times10^2~$s, and a horizontal velocity amplitude of 1$~\mathrm{km~s}^{-1}$, consistent with earlier results. The mean vertical velocity amplitude is 1.1$~\mathrm{km~s}^{-1}$. We find that 77% of the fibrils carry waves in both the vertical and horizontal directions, and 80% of this subsample exhibits oscillations with similar periods in both horizontal and vertical directions. For the latter, we find that all phase differences between $0$ and $2\pi$ occur, with a mild but significant preference for linearly polarized waves (phase difference of $0$ or $\pi$). The results are consistent with the scenario where transverse waves are excited by granular buffeting at the photospheric footpoints of the fibrils. Estimates of transverse wave flux based only on imaging data are too low because they ignore the contribution of the vertical velocity., Comment: 12 pages, 12 figures

The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnostic possibilities that complement other commonly used diagnostics for the study of our Sun. In particular, ALMA's ability to serve as an essentially linear thermometer of the chromospheric gas at unprecedented spatial resolution at millimetre wavelengths and future polarisation measurements have great diagnostic potential. Solar ALMA observations are therefore expected to contribute significantly to answering long-standing questions about the structure, dynamics and energy balance of the outer layers of the solar atmosphere. In this regard, current and future ALMA data are also important for constraining and further developing numerical models of the solar atmosphere, which in turn are often vital for the interpretation of observations. The latter is particularly important given the Sun's highly intermittent and dynamic nature that involves a plethora of processes occurring over extended ranges in spatial and temporal scales. Realistic forward modelling of the Sun therefore requires time-dependent three-dimensional radiation magnetohydrodynamics that account for non-equilibrium effects and, typically as a separate step, detailed radiative transfer calculations, resulting in synthetic observables that can be compared to observations. Such artificial observations sometimes also account for instrumental and seeing effects, which, in addition to aiding the interpretation of observations, provide instructive tools for designing and optimising ALMA's solar observing modes. In the other direction, ALMA data in combination with other simultaneous observations enables the reconstruction of the solar atmospheric structure via data inversion techniques. This article highlights central aspects of the impact of ALMA for numerical modelling for the Sun, their potential and challenges, together with selected examples., Comment: 32 pages, 7 figures. Accepted for publication in Frontiers in Astronomy and Space Sciences (Stellar and Solar Physics)

We obtain results about fundamental groups of $RCD^{\ast}(K,N)$ spaces previously known under additional conditions such as smoothness or lower sectional curvature bounds. For fixed $K \in \mathbb{R}$, $N \in [1,\infty )$, $D > 0 $, we show the following, $\bullet$ There is $C>0$ such that for each $RCD^{\ast}(K,N)$ space $X$ of diameter $\leq D$, its fundamental group $\pi_1(X)$ is generated by at most $C$ elements. $\bullet$ There is $\tilde{D}>0$ such that for each $RCD^{\ast}(K,N)$ space $X$ of diameter $\leq D$ with compact universal cover $\tilde{X}$, one has diam$(\tilde{X})\leq \tilde{D}$. $\bullet$ If a sequence of $RCD^{\ast}(0,N)$ spaces $X_i$ of diameter $\leq D$ and rectifiable dimension $n$ is such that their universal covers $\tilde{X}_i$ converge in the pointed Gromov--Hausdorff sense to a space $X$ of rectifiable dimension $n$, then there is $C>0$ such that for each $i$, the fundamental group $\pi_1(X_i)$ contains an abelian subgroup of index $\leq C$. $\bullet$ If a sequence of $RCD^{\ast}(K,N)$ spaces $X_i$ of diameter $\leq D$ and rectifiable dimension $n$ is such that their universal covers $\tilde{X}_i$ are compact and converge in the pointed Gromov--Hausdorff sense to a space $X$ of rectifiable dimension $n$, then there is $C>0$ such that for each $i$, the fundamental group $\pi_1(X_i)$ contains an abelian subgroup of index $\leq C$. $\bullet$ If a sequence of $RCD^{\ast}(K,N)$ spaces $X_i$ with first Betti number $\geq r$ and rectifiable dimension $ n$ converges in the Gromov--Hausdorff sense to a compact space $X$ of rectifiable dimension $m$, then the first Betti number of $X$ is at least $r + m - n$. The main tools are the splitting theorem by Gigli, the splitting blow-up property by Mondino--Naber, the semi-locally-simple-connectedness of $RCD^{\ast}(K,N)$ spaces by Wang, and the isometry group structure by Guijarro and the first author.

This article presents a comprehensive analysis of the different tests proposed in the recent ChildCI framework, proving its potential for generating a better understanding of children's neuromotor and cognitive development along time, as well as their possible application in other research areas such as e-Health and e-Learning. In particular, we propose a set of over 100 global features related to motor and cognitive aspects of the children interaction with mobile devices, some of them collected and adapted from the literature. Furthermore, we analyse the robustness and discriminative power of the proposed feature set including experimental results for the task of children age group detection based on their motor and cognitive behaviours. Two different scenarios are considered in this study: i) single-test scenario, and ii) multiple-test scenario. Results over 93% accuracy are achieved using the publicly available ChildCIdb_v1 database (over 400 children from 18 months to 8 years old), proving the high correlation of children's age with the way they interact with mobile devices., Comment: 12 pages, 3 figures, 7 tables

Scattering polarization tends to dominate the linear polarization signals of the Ca II 8542 A line in weakly magnetized areas ($B \lesssim 100$ G), especially when the observing geometry is close to the limb. In this paper we evaluate the degree of applicability of existing non-LTE spectral line inversion codes (which assume that the spectral line polarization is due to the Zeeman effect only) at inferring the magnetic field vector and, particularly, its transverse component. To this end, we use the inversion code STiC to extract the strength and orientation of the magnetic field from synthetic spectropolarimetric data generated with the Hanle-RT code. The latter accounts for the generation of polarization through scattering processes as well as the joint actions of the Hanle and the Zeeman effects. We find that, when the transverse component of the field is stronger than $\sim$80 G, the inversion code is able to retrieve accurate estimates of the transverse field strength as well as its azimuth in the plane of the sky. Below this threshold, the scattering polarization signatures become the major contributors to the linear polarization signals and often mislead the inversion code into severely over- or under-estimating the field strength. Since the line-of-sight component of the field is derived from the circular polarization signal, which is not affected by atomic alignment, the corresponding inferences are always good., Comment: Accepted for publication in ApJ

Let $(X,d,\mathfrak{m})$ be a metric measure space. The study of the Wasserstein space $(\mathbb{P}_p(X),\mathbb{W}_p)$ associated to $X$ has proved useful in describing several geometrical properties of $X.$ In this paper we focus on the study of isometries of $\mathbb{P}_p(X)$ for $p \in (1,\infty)$ under the assumption that there is some characterization of optimal maps between measures, the so called Good transport behaviour $GTB_p$. Our first result states that the set of Dirac deltas is invariant under isometries of the Wasserstein space. Additionally we obtain that the isometry groups of the base Riemannian manifold $M$ coincides with the one of the Wasserstein space $\mathbb{P}_p(M)$ under assumptions on the manifold; namely, for $p=2$ that the sectional curvature is strictly positive and for general $p\in (1,\infty)$ that $M$ is a Compact Rank One Symmetric Space., Comment: 16 pages, all comments are welcome

This article provides an overview of recent research in Child-Computer Interaction with mobile devices and describe our framework ChildCI intended for: i) overcoming the lack of large-scale publicly available databases in the area, ii) generating a better understanding of the cognitive and neuromotor development of children along time, contrary to most previous studies in the literature focused on a single-session acquisition, and iii) enabling new applications in e-Learning and e-Health through the acquisition of additional information such as the school grades and children's disorders, among others. Our framework includes a new mobile application, specific data acquisition protocols, and a first release of the ChildCI dataset (ChildCIdb v1), which is planned to be extended yearly to enable longitudinal studies. In our framework children interact with a tablet device, using both a pen stylus and the finger, performing different tasks that require different levels of neuromotor and cognitive skills. ChildCIdb is the first database in the literature that comprises more than 400 children from 18 months to 8 years old, considering therefore the first three development stages of the Piaget's theory. In addition, and as a demonstration of the potential of the ChildCI framework, we include experimental results for one of the many applications enabled by ChildCIdb: children age detection based on device interaction.