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In this paper, an analysis of hourly air temperatures in four groups of 32 stations of the UK highland (five stations), UK lowland (four stations), Italian highland (eleven stations), and Italian lowland (twelve stations) at various altitudes was conducted over the period from 2002 to 2021. The study aimed to examine the trends of each hour of the day in that period, over different averaging time windows (-10 day, -30 day, and -60 day). The trends were computed using the Mann-Kendall trend test and Sen's slope estimator. The similarity of trends within and across the groups of stations was assessed using the hierarchical clustering with dynamic time warping technique. An additional analysis was conducted to show the correlation of trends among the group of stations using the correlation distance matrix. Hierarchical clustering and distance correlation analysis show trend similarities and correlations, also indicating dissimilarities among different groups. Using 30 day averages, significant warming trends in specific months at the Italian stations are evident, especially in February, July, August, and December. The UK highland stations did not show statistically significant trends, but clear pattern similarities were found within the groups, especially in certain months. The ultimate goal of this paper is to provide insights into temperature dynamics and climate change characteristics on regional and diurnal scales.

We present a coil system designed to generate a highly uniform magnetic field for the n2EDM experiment at the Paul Scherrer Institute. It consists of a main $B_0$ coil and a set of auxiliary coils mounted on a cubic structure with a side length of 273 cm, inside a large magnetically shielded room (MSR). We have assembled this system and characerized its performances with a mapping robot. The apparatus is able to generate a 1 $\mu$ T vertical field with a relative root mean square deviation $\sigma$ ($B_z$)/$B_z$ = 3 $\times$ $10^{-5}$ over the volume of interest, a cylinder of radius 40 cm and height 30 cm. This level of uniformity overcomes the n2EDM requirements, allowing a measurement of the neutron Electric Dipole Moment with a sensitivity better than 1 $\times$ $10^{-27}$ ecm., Comment: 20 pages, 13 figures

This paper presents a statistical analysis of air temperature data from 32 stations in Italy and the UK up to 2000 m above sea level, from 2002 to 2021. The data came from both highland and lowland areas, in order to evaluate both the differences due to location, and elevation. The analysis focused on detecting trends at annual and monthly time scales, employing both ordinary least squares, robust S-estimator regression, and Mann-Kendall and Sen's slope methods. Then hierarchical clustering using Dynamic Time Warping (DTW) was applied to the monthly data to analyze the intra-annual pattern similarity of trends within and across the groups. Two different regions of Europe were chosen because of the different climate and temperature trends, namely the Northern UK (smaller trends) and the North-West Italian Alps (larger trends). The main novelty of the work is to show that stations having similar locations and altitudes have similar monthly slopes by quantifying them using DTW and clustering. These results reveal the nonrandomness of different trends along the year and among different parts of Europe, with a modest influence of altitude in wintertime. The findings revealed that group average trends were close to the NOAA values for the areas in Italy and the UK, confirming the validity of analyzing a small number of stations. More interestingly, intra-annual patterns were detected commonly at the stations of each of the groups, and clearly different between them Hierarchical clustering in combination with DTW showed consistent similarity between monthly patterns of means and trends within the group of stations and inconsistent similarity between patterns across groups. Distance correlation matrices also contributes to what is the main result of the paper, which is to clearly show the different temporal patterns in relation to location and (in some months) altitude., Comment: The final version of this paper is in press on International journal of Climatology

Groundwater resources are one of the most relevant elements in the water cycle, therefore developing models to accurately predict them is a pivotal task in the sustainable resources management framework. Deep Learning (DL) models have been revealed very effective in hydrology, especially by feeding spatially distributed data (e.g. raster data). In many regions, hydrological measurements are difficult to obtain regularly or periodically in time, and in some cases, last available data are not up to date. Reversely, weather data, which significantly impacts water resources, are usually more available and with higher quality. More specifically, we have proposed two different DL models to predict the water table depth in the Grana-Maira catchment (Piemonte, IT) using only exogenous weather image time series. To deal with the image time series, both models are made of a first Time Distributed Convolutional Neural Network (TDC) which encodes the image available at each time step into a vectorial representation. The first model, TDC-LSTM uses then a Sequential Module based on an LSTM layer to learn temporal relations and output the predictions. The second model, TDC-UnPWaveNet uses instead a new version of the WaveNet architecture, adapted here to output a sequence shorter and completely shifted in the future with respect to the input one. To this aim, and to deal with the different sequence lengths in the UnPWaveNet, we have designed a new Channel Distributed layer, that acts like a Time Distributed one but on the channel dimension, i.e. applying the same set of operations to each channel of the input. TDC-LSTM and TDC-UnPWaveNet have shown both remarkable results. However, the two models have focused on different learnable information: TDC-LSTM has focused more on lowering the bias, while the TDC-UnPWaveNet has focused more on the temporal dynamics maximising correlation and KGE.

As the demand for lithium-ion batteries rapidly increases there is a need to design these cells in a safe manner to mitigate thermal runaway. Thermal runaway in batteries leads to an uncontrollable temperature rise and potentially fires, which is a major safety concern. Typically, when modelling the chemical kinetics of thermal runaway calorimetry data ( e.g. Accelerating Rate Calorimetry (ARC)) is needed to determine the temperature-driven decomposition kinetics. Conventional methods of fitting Arrhenius Ordinary Differential Equation (ODE) thermal runaway models to Accelerated Rate Calorimetry (ARC) data make several assumptions that reduce the fidelity and generalizability of the obtained model. In this paper, Chemical Reaction Neural Networks (CRNNs) are trained to fit the kinetic parameters of N-equation Arrhenius ODEs to ARC data obtained from a Molicel 21700 P45B. The models are found to be better approximations of the experimental data. The flexibility of the method is demonstrated by experimenting with two-equation and four-equation models. Thermal runaway simulations are conducted in 3D using the obtained kinetic parameters, showing the applicability of the obtained thermal runaway models to large-scale simulations.

The modelling of the occurrence of rainfall dry and wet spells (ds and ws, respectively) can be jointly conveyed using the inter-arrival times (it). While the modelling of it has the advantage of requiring a single fitting for the description of all rainfall time characteristics (including wet and dry chains, an extension of the concept of spells), the assumption on the independence and identical distribution of the renewal times it implicitly imposes a memoryless property on the derived ws, which may not be true in some cases. In this study, two different methods for the modelling of rainfall time characteristics at station scale have been applied: i) a direct method (DM) that fits the discrete Lerch distribution to it records, and then derives ws and ds (as well as the corresponding chains) from the it distribution; and ii) an indirect method (IM) that fits the Lerch distribution to the ws and ds records separately, relaxing the assumptions of the renewal process. The results of this application over six stations in Europe, characterized by a wide range of rainfall regimes, highlight how the geometric distribution does not always reasonably reproduce the ws frequencies, even when it are modelled by the Lerch distribution well. Improved performances are obtained with the IM, thanks to the relaxation of the assumption on the independence and identical distribution of the renewal times. A further improvement on the fittings is obtained when the datasets are separated into two periods, suggesting that the inferences may benefit for accounting for the local seasonality., Comment: 28 pages, 11 figures

We review Holst formalism and we discuss dynamical equivalence with standard GR (in dimension 4). Holst formalism is written for a spin coframe field $e^I_\mu$ and a $Spin(3,1)$-connection $\omega^{IJ}_\mu$ on spacetime $M$ and it depends on the Holst parameter $\gamma\in \mathbb{R}-\{0\}$. We show the model is dynamically equivalent to standard GR, in the sense that up to a pointwise $Spin(3,1)$-gauge transformation acting on frame indices, solutions of the two models are in one-to-one correspondence. Hence the two models are classically equivalent. One can also introduce new variables by splitting the spin connection into a pair of a $Spin(3)$-connection $A^i_\mu$ and a $Spin(3)$-valued 1-form $k^i_\mu$. The construction of these new variables relies on a particular algebraic structure, called a reductive splitting. A reductive splitting is a weaker structure than requiring that the gauge group splits as the products of two sub-groups, as it happens in Euclidean signature in the selfdual formulation originally introduced in this context by Ashtekar, and it still allows to deal with the Lorentzian signature without resorting to complexifications. The reductive splitting of $SL(2, \mathbb{C})$ is not unique and it is parameterized by a real parameter $\beta$, called the Immirzi parameter. The splitting is here done on spacetime, not on space, to obtain a $Spin(3)$-connection $A^i_\mu$, which is called the Barbero-Immirzi connection on spacetime. One obtains a covariant model depending on the fields $(e^I_\mu, A^i_\mu, k^i_\mu)$ which is again dynamically equivalent to standard GR (as well as the Holst action). Usually, in the literature one sets $\beta=\gamma$ for the sake of simplicity. Here we keep the Holst and Immirzi parameters distinct to show that eventually, only $\beta$ will survive in boundary field equations., Comment: 19 pages

Over the past two decades, magnetic resonance spectroscopy with two-shot difference editing has been widely employed to characterize altered levels of GABA, the primary inhibitory neurotransmitter in the brain, in various neuropsychiatric disorders. This conventional technique detects the GABA H4 resonance, making it unsuitable for investigating GABA metabolism. It also suffers from subtraction artifacts, signal loss, and significant contamination by macromolecules. Here, we introduce a single-shot method for detecting GABA H2, effectively overcoming these difficulties. Since GABA turnover initiates at its protonated C2 and unprotonated C1 positions, we demonstrate, for the first time, noninvasive real-time monitoring of GABA metabolism in the human brain, utilizing GABA H2 as a highly sensitive reporter for GABA C2. This new method not only enhances the quantitative measurement of GABA levels but also opens up a new avenue to probe the metabolic processes underlying alterations in GABA levels in patients.

A covariant, global, variational framework for perturbations in field theories is presented. Perturbations are obtained as vertical vector fields on the configuration bundle and they drag, exactly, solution into solutions. The flow of a perturbation drags solutions into solutions and the dragged perturbed solutions can be expanded in a series with respect to the flow parameter, hence it contains perturbations at any order. Mechanics is included as a special case. As a simple application, we recover the well-known discussion about stability of geodesics on a sphere $S_2$., Comment: 14 pages

We extend to three dimensions the proposal of a completely relativistic positioning system (rPS). The system does not rely on approximations, in fact, it works at a few Schwarzschild radii from a black hole, and it does not rely on Newtonian physics or special relativity. Since general relativity (GR) claims to be our fundamental framework to describe classical physics, it must provide tools to bootstrap physics within the theory itself, without relying on previous approximated frameworks. The rPS is able to self-diagnose, that is, it detects deviations from assumptions about the gravitational field and consequently stops operations; in addition it is robust, i.e., it is able to autonomously restore operations when assumptions are restored. From a more general viewpoint, the rPS is equivalent to geodesy in spacetime, which establishes a (conventional) coordinate system on a surface by means of measurements within the surface itself, as well as allowing it to extract information about the intrinsic geometry of the same surface. In other words, the positioning system is potentially able to extract information about the gravitational field (which in fact is identified with the geometry of spacetime) in addition to the gravitational theory, which describes its dynamics. Thus, it becomes a framework within which one can operationally distinguish different theories of gravitation., Comment: 29 pages, 8 figures

Accurate 3D tracking of hand and fingers movements poses significant challenges in computer vision. The potential applications span across multiple domains, including human-computer interaction, virtual reality, industry, and medicine. While gesture recognition has achieved remarkable accuracy, quantifying fine movements remains a hurdle, particularly in clinical applications where the assessment of hand dysfunctions and rehabilitation training outcomes necessitate precise measurements. Several novel and lightweight frameworks based on Deep Learning have emerged to address this issue; however, their performance in accurately and reliably measuring fingers movements requires validation against well-established gold standard systems. In this paper, the aim is to validate the handtracking framework implemented by Google MediaPipe Hand (GMH) and an innovative enhanced version, GMH-D, that exploits the depth estimation of an RGB-Depth camera to achieve more accurate tracking of 3D movements. Three dynamic exercises commonly administered by clinicians to assess hand dysfunctions, namely Hand Opening-Closing, Single Finger Tapping and Multiple Finger Tapping are considered. Results demonstrate high temporal and spectral consistency of both frameworks with the gold standard. However, the enhanced GMH-D framework exhibits superior accuracy in spatial measurements compared to the baseline GMH, for both slow and fast movements. Overall, our study contributes to the advancement of hand tracking technology, the establishment of a validation procedure as a good-practice to prove efficacy of deep-learning-based hand-tracking, and proves the effectiveness of GMH-D as a reliable framework for assessing 3D hand movements in clinical applications.

We present a novel Active Magnetic Shield (AMS), designed and implemented for the n2EDM experiment at the Paul Scherrer Institute. The experiment will perform a high-sensitivity search for the electric dipole moment of the neutron. Magnetic-field stability and control is of key importance for n2EDM. A large, cubic, 5m side length, magnetically shielded room (MSR) provides a passive, quasi-static shielding-factor of about 10^5 for its inner sensitive volume. The AMS consists of a system of eight complex, feedback-controlled compensation coils constructed on an irregular grid spanned on a volume of less than 1000m^3 around the MSR. The AMS is designed to provide a stable and uniform magnetic-field environment around the MSR, while being reasonably compact. The system can compensate static and variable magnetic fields up to +-50muT (homogeneous components) and +-5muT (first-order gradients), suppressing them to a few muT in the sub-Hertz frequency range. The presented design concept and implementation of the AMS fulfills the requirements of the n2EDM experiment and can be useful for other applications, where magnetically silent environments are important and spatial constraints inhibit simpler geometrical solutions.

We study the $T {-} {\mu}$ phase diagram of quark matter under the influence of a strong uniform magnetic field in the framework of a nonlocal extension of the Polyakov Nambu Jona Lasinio model (PNJL). The existence of a critical end point (CEP) is found for the whole considered range of the magnetic field (up to 1 $GeV^{2}$). We analyze the location of this CEP as a function of the external field and discuss the presence of inverse magnetic catalysis for nonzero chemical potentials. Our results show that the temperature of the CEP decreases with the magnetic field, in contrast to the behavior observed in local NJL/PNJL models.

We study the phase diagram in the $T-\mu$ plane for quark matter under the influence of a strong uniform magnetic field $\vec{B}$, in the framework of a non-local extension of the two-flavor Polyakov Nambu-Jona-Lasinio model. We analyze the deconfinement and chiral symmetry restoration transitions in the mean field approximation. For the considered parameterization, it is found that there is always a critical end point (CEP) in the $T-\mu$ plane that separates a first-order transition line from a smooth crossover. The location of the CEP is studied as a function of the magnetic field., Comment: 5 pages, 3 figures

Let G(k,n) be the Grassmannian of oriented subspaces of dimension k of R^n with its canonical Riemannian metric. We study the energy of maps assigning to each P \in G(k,n) a unit vector normal to P. They are sections of a sphere bundle E_{k,n}^1 over G(k,n). The octonionic double and triple cross products induce in a natural way such sections for k=2, n=7 and k=3, n=8, respectively. We prove that they are harmonic maps into E_{k,n}^1 endowed with the Sasaki metric. This, together with the well-known result that Hopf vector fields on odd dimensional spheres are harmonic maps into their unit tangent bundles, allows us to conclude that all unit normal sections of the Grassmannians associated with cross products are harmonic. In a second instance we analyze the energy of maps assigning an orthogonal complex structure J(P) on P^{\bot} to each P\in G(2,8). We prove that the one induced by the octonionic triple product is a harmonic map into a suitable sphere bundle over G(2,8). This generalizes the harmonicity of the canonical almost complex structure of S^6.

Joint registration of a stack of 2D histological sections to recover 3D structure (``3D histology reconstruction'') finds application in areas such as atlas building and validation of \emph{in vivo} imaging. Straightforward pairwise registration of neighbouring sections yields smooth reconstructions but has well-known problems such as ``banana effect'' (straightening of curved structures) and ``z-shift'' (drift). While these problems can be alleviated with an external, linearly aligned reference (e.g., Magnetic Resonance (MR) images), registration is often inaccurate due to contrast differences and the strong nonlinear distortion of the tissue, including artefacts such as folds and tears. In this paper, we present a probabilistic model of spatial deformation that yields reconstructions for multiple histological stains that that are jointly smooth, robust to outliers, and follow the reference shape. The model relies on a spanning tree of latent transforms connecting all the sections and slices of the reference volume, and assumes that the registration between any pair of images can be see as a noisy version of the composition of (possibly inverted) latent transforms connecting the two images. Bayesian inference is used to compute the most likely latent transforms given a set of pairwise registrations between image pairs within and across modalities. The framework is used for accurate 3D reconstruction of two stains (Nissl and parvalbumin) from the Allen human brain atlas, showing its benefits on real data with severe distortions. Moreover, we also provide the registration of the reconstructed volume to MNI space, bridging the gaps between two of the most widely used atlases in histology and MRI. The 3D reconstructed volumes and atlas registration can be downloaded from https://openneuro.org/datasets/ds003590. The code is freely available at https://github.com/acasamitjana/3dhirest., Comment: Medical Image Analysis (Accepted on 07/10/2021). 22 pages, 11 figures

Experiments dedicated to the measurement of the electric dipole moment of the neutron require outstanding control of the magnetic field uniformity. The neutron electric dipole moment (nEDM) experiment at the Paul Scherrer Institute uses a 199Hg co-magnetometer to precisely monitor magnetic field variations. This co-magnetometer, in the presence of field non-uniformity, is responsible for the largest systematic effect of this measurement. To evaluate and correct that effect, offline measurements of the field non-uniformity were performed during mapping campaigns in 2013, 2014 and 2017. We present the results of these campaigns, and the improvement the correction of this effect brings to the neutron electric dipole moment measurement.

We study the behavior of two-flavor dense quark matter under the influence of an external magnetic field in the framework of a nonlocal chiral quark model with separable interactions. The nonlocality is incorporated in the model by using a Gaussian form factor. It is found that for low and moderate values of magnetic field there is a decrease of the critical chiral restoration chemical potential $\mu_c$, i.e. an inverse magnetic catalysis effect is observed. For larger values of $eB$ the behavior of $\mu_c$ becomes more or less flat, depending on the parametrization. Within the considered parametrization range we do not find a significant growth of the critical chemical potential for large magnetic fields, as occurs in the case of the local NJL model.

We present the design of a next-generation experiment, n2EDM, currently under construction at the ultracold neutron source at the Paul Scherrer Institute (PSI) with the aim of carrying out a high-precision search for an electric dipole moment of the neutron. The project builds on experience gained with the previous apparatus operated at PSI until 2017, and is expected to deliver an order of magnitude better sensitivity with provision for further substantial improvements. An overview is given of the experimental method and setup, the sensitivity requirements for the apparatus are derived, and its technical design is described.