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In the presence of a magnetic field, axions can convert into photons and viceversa. The phenomenology of the conversion is captured by a system of two coupled Klein-Gordon equations, which, assuming that the axion is relativistic, is usually recast into a pair of first order Schr\"odinger-like equations. In such a limit, focusing on a constant magnetic field and plasma frequency, the equations admit an exact analytic solution. The relativistic limit significantly simplifies the calculations; therefore, it is widely used in phenomenological applications. In this work, we discuss how to evaluate the axion-photon system evolution without relying on such relativistic approximation. In particular, we give an exact analytical solution, valid for any axion energy, in the case that both the magnetic field and plasma frequency are constant. Moreover, we devise an analytic perturbative expansion that allows for tracking the conversion probability in a slightly inhomogeneous magnetic field or plasma frequency, whose characteristic scale of variation is much larger than the typical axion-photon oscillation length. Finally, we discuss a case of resonant axion-photon conversion giving useful simplified formulae that might be directly applied to dark matter axions converting in neutron star magnetospheres., Comment: 9 Pages, 5 Figures. Comments welcome!

Since the advent of the internet, communication paradigms have continuously evolved, resulting in a present-day landscape where the dynamics of information dissemination have undergone a complete transformation compared to the past. In this study, we challenge the conventional two-step flow model of communication, a long-standing paradigm in the field. Our approach introduces a more intricate multi-step and multi-actor model that effectively captures the complexities of modern information spread. We test our hypothesis by examining the spread of information on the Twitter platform. Our findings support the multi-step and multi-actor model hypothesis. In this framework, influencers (individuals with a significant presence in social media) emerges as new central figures and partially take on the role previously attributed to opinion leaders. However, this does not apply to opinion leaders who adapt and reaffirm their influential position on social media, here defined as opinion-leading influencers. Additionally, we note a substantial number of adopters directly accessing information sources, suggesting a potentialdecline if influence in both opinion leaders and influencers. Finally, we found distinctions in the diffusion patterns of left- and right-leaning groups, indicating variations in the underlying structure of information dissemination across different ideologies., Comment: 24 pages, 6 figures, 4 tables

Diffusion-weighted MRI is increasingly used to study the normal and abnormal development of fetal brain in-utero. Recent studies have shown that dMRI can offer invaluable insights into the neurodevelopmental processes in the fetal stage. However, because of the low data quality and rapid brain development, reliable analysis of fetal dMRI data requires dedicated computational methods that are currently unavailable. The lack of automated methods for fast, accurate, and reproducible data analysis has seriously limited our ability to tap the potential of fetal brain dMRI for medical and scientific applications. In this work, we developed and validated a unified computational framework to (1) segment the brain tissue into white matter, cortical/subcortical gray matter, and cerebrospinal fluid, (2) segment 31 distinct white matter tracts, and (3) parcellate the brain's cortex and delineate the deep gray nuclei and white matter structures into 96 anatomically meaningful regions. We utilized a set of manual, semi-automatic, and automatic approaches to annotate 97 fetal brains. Using these labels, we developed and validated a multi-task deep learning method to perform the three computations. Our evaluations show that the new method can accurately carry out all three tasks, achieving a mean Dice similarity coefficient of 0.865 on tissue segmentation, 0.825 on white matter tract segmentation, and 0.819 on parcellation. The proposed method can greatly advance the field of fetal neuroimaging as it can lead to substantial improvements in fetal brain tractography, tract-specific analysis, and structural connectivity assessment.

Time series forecasting is an important task in many fields ranging from supply chain management to weather forecasting. Recently, Transformer neural network architectures have shown promising results in forecasting on common time series benchmark datasets. However, application to supply chain demand forecasting, which can have challenging characteristics such as sparsity and cross-series effects, has been limited. In this work, we explore the application of Transformer-based models to supply chain demand forecasting. In particular, we develop a new Transformer-based forecasting approach using a shared, multi-task per-time series network with an initial component applying attention across time series, to capture interactions and help address sparsity. We provide a case study applying our approach to successfully improve demand prediction for a medical device manufacturing company. To further validate our approach, we also apply it to public demand forecasting datasets as well and demonstrate competitive to superior performance compared to a variety of baseline and state-of-the-art forecast methods across the private and public datasets.

We study weighted basic parallel processes (WBPP), a nonlinear recursive generalisation of weighted finite automata inspired from process algebra and Petri net theory. Our main result is an algorithm of 2-EXPSPACE complexity for the WBPP equivalence problem. While (unweighted) BPP language equivalence is undecidable, we can use this algorithm to decide multiplicity equivalence of BPP and language equivalence of unambiguous BPP, with the same complexity. These are long-standing open problems for the related model of weighted context-free grammars. Our second contribution is a connection between WBPP, power series solutions of systems of polynomial differential equations, and combinatorial enumeration. To this end we consider constructible differentially finite power series (CDF), a class of multivariate differentially algebraic series introduced by Bergeron and Reutenauer in order to provide a combinatorial interpretation to differential equations. CDF series generalise rational, algebraic, and a large class of D-finite (holonomic) series, for which decidability of equivalence was an open problem. We show that CDF series correspond to commutative WBPP series. As a consequence of our result on WBPP and commutativity, we show that equivalence of CDF power series can be decided with 2-EXPTIME complexity. The complexity analysis is based on effective bounds from algebraic geometry, namely on the length of chains of polynomial ideals constructed by repeated application of finitely many, not necessarily commuting derivations of a multivariate polynomial ring. This is obtained by generalising a result of Novikov and Yakovenko in the case of a single derivation, which is noteworthy since generic bounds on ideal chains are non-primitive recursive in general. On the way, we develop the theory of \WBPP~series and \CDF~power series, exposing several of their appealing properties., Comment: Full version of a paper accepted at CONCUR'24

White dwarfs are the remnants of stars not massive enough to become supernovae. This review explores the concept of strange dwarfs, a unique class of white dwarfs which contain cores of strange quark matter. Strange dwarfs have different sizes, masses, and evolutionary paths with respect to white dwarfs. They might form through the accumulation of normal matter on strange quark stars or by capture of strangelets. The stability of strange dwarfs has been debated, with initial studies suggesting stability, while later analyses indicated potential instability. This review revisits these discussions, focusing on the critical role of boundary conditions between nuclear and quark matter in determining stability. It also offers insights into their formation, structure, and possible detection in the universe.

This paper deals with the problem of clustering data returned by a radar sensor network that monitors a region where multiple moving targets are present. The network is formed by nodes with limited functionalities that transmit the estimates of target positions (after a detection) to a fusion center without any association between measurements and targets. To solve the problem at hand, we resort to model-based learning algorithms and instead of applying the plain maximum likelihood approach, due to the related computational requirements, we exploit the latent variable model coupled with the expectation-maximization algorithm. The devised estimation procedure returns posterior probabilities that are used to cluster the huge amount of data collected by the fusion center. Remarkably, we also consider challenging scenarios with an unknown number of targets and estimate it by means of the model order selection rules. The clustering performance of the proposed strategy is compared to that of conventional data-driven methods over synthetic data. The numerical examples point out that the herein proposed solutions can provide reliable clustering performance overcoming the considered competitors., Comment: 12 pages 14 figures

Millisecond pulsars are extremely precise celestial clocks: as they rotate, the beamed radio waves emitted along the axis of their magnetic field can be detected with radio telescopes, which allows for tracking subtle changes in the pulsars' rotation periods. A possible effect on the period of a pulsar is given by a potential coupling to dark matter, in cases where it is modeled with an "ultralight" scalar field. In this paper, we consider a universal conformal coupling of the dark matter scalar to gravity, which in turn mediates an effective coupling between pulsars and dark matter. If the dark matter scalar field is changing in time, as expected in the Milky Way, this effective coupling produces a periodic modulation of the pulsar rotational frequency. By studying the time series of observed radio pulses collected by the European Pulsar Timing Array experiment, we present constraints on the coupling of dark matter, improving on existing bounds. These bounds can also be regarded as constraints on the parameters of scalar-tensor theories of the Fierz-Jordan-Brans-Dicke and Damour-Esposito-Far\`{e}se types in the presence of a (light) mass potential term., Comment: 17 pages, 5 figures, Updated plots, matching published version

A pseudo Nambu-Goldstone boson (PNGB) coupled to a confining gauge group via an anomalous term is characterised, during the confining phase transition, by a temperature dependent mass $m^2(T) \propto T^{-n}$. For $n>2$, a non-relativistic population of such particles dominating the cosmological energy density would act as dark energy (DE), accelerating the expansion. We study the possibility that a PNGB $\varphi_b$ coupled to a hidden gauge group that is presently undergoing confinement could realise this scenario. To obtain the observed amount of DE, the number density of $\varphi_b$ must be boosted by some mechanism. Assuming that the QCD axion $\varphi_a$ constitutes the dark matter (DM), a non-adiabatic level crossing between $\varphi_a$ and $\varphi_b$ shortly before matter-DE equality can convert a small fraction of DM into DE, providing such mechanism and explaining the coincidence puzzle., Comment: 6 pages, 2 figures

We simulate $N_f=2+1$ QCD at the physical point combining open and periodic boundary conditions in a parallel tempering framework, following the original proposal by M. Hasenbusch for $2d$ $\mathrm{CP}^{N-1}$ models, which has been recently implemented and widely employed in $4d$ $\mathrm{SU}(N)$ pure Yang-Mills theories too. We show that using this algorithm it is possible to achieve a sizable reduction of the auto-correlation time of the topological charge in dynamical fermions simulations both at zero and finite temperature, allowing to avoid topology freezing down to lattice spacings as fine as $a \sim 0.02$ fm. Therefore, this implementation of the Parallel Tempering on Boundary Conditions algorithm has the potential to substantially push forward the investigation of the QCD vacuum properties by means of lattice simulations., Comment: 26 pages, 7 figures. v2: expanded discussion about PTBC improvement over standard RHMC, improved estimate of tau_int(Q^2) with standard RHMC at finest lattice spacing, final results and conclusions unchanged, matches accepted version on JHEP

Forty years ago, Witten suggested that dark matter could be composed of macroscopic clusters of strange quark matter. This idea was very popular for several years, but it dropped out of fashion once lattice QCD calculations indicated that the confinement/deconfinement transition, at small baryonic chemical potential, is not first order, which seemed to be a crucial requirement in order to produce large clusters of quarks. Here we revisit both the conditions under which strangelets can be produced in the Early Universe and the many phenomenological implications of their existence. Most of the paper discusses the limits on their mass distribution and a possible and simple scheme for their production. Finally, we discuss the most promising techniques to detect this type of objects., Comment: 13 pages, 13 figures. In this version, subsection 3.3 has been significantly revised and expanded

The monitoring of diver health during emergency events is crucial to ensuring the safety of personnel. A non-invasive system continuously providing a measure of the respiration rate of individual divers is exceedingly beneficial in this context. The paper reports on the application of short-range radar to record the respiration rate of divers within hyperbaric lifeboat environments. Results demonstrate that the respiratory motion can be extracted from the radar return signal applying routine signal processing. Further, evidence is provided that the radar-based approach yields a more accurate measure of respiration rate than an audio signal from a headset microphone. The system promotes an improvement in evacuation protocols under critical operational scenarios., Comment: Presented at IEEE OCEANS 2021 San Diego, Porto

The paper centres on an assessment of the modelling approaches for the processing of signals in CW and FMCW radar-based systems for the detection of vital signs. It is shown that the use of the widely adopted phase extraction method, which relies on the approximation of the target as a single point scatterer, has limitations in respect of the simultaneous estimation of both respiratory and heart rates. A method based on a velocity spectrum is proposed as an alternative with the ability to treat a wider range of application scenarios., Comment: Presented at 2020 14th European Conference on Antennas and Propagation (EuCAP)

Deep learning techniques are subject to increasing adoption for a wide range of micro-Doppler applications, where predictions need to be made based on time-frequency signal representations. Most, if not all, of the reported applications focus on translating an existing deep learning framework to this new domain with no adjustment made to the objective function. This practice results in a missed opportunity to encourage the model to prioritize features that are particularly relevant for micro-Doppler applications. Thus the paper introduces a micro-Doppler coherence loss, minimized when the normalized power of micro-Doppler oscillatory components between input and output is matched. The experiments conducted on real data show that the application of the introduced loss results in models more resilient to noise., Comment: Presented at 2021 18th European Radar Conference (EuRAD)

The treatment of interfering motion contributions remains one of the key challenges in the domain of radar-based vital sign monitoring. Removal of the interference to extract the vital sign contributions is demanding due to overlapping Doppler bands, the complex structure of the interference motions and significant variations in the power levels of their contributions. A novel approach to the removal of interference through the use of a probabilistic deep learning model is presented. Results show that a convolutional encoder-decoder neural network with a variational objective is capable of learning a meaningful representation space of vital sign Doppler-time distribution facilitating their extraction from a mixture signal. The approach is tested on semi-experimental data containing real vital sign signatures and simulated returns from interfering body motions. The application of the proposed network enhances the extraction of the micro-Doppler frequency corresponding to the respiration rate is demonstrated., Comment: Presented at 2021 IEEE Radar Conference (RadarConf21)

Convolutional neural networks have often been proposed for processing radar Micro-Doppler signatures, most commonly with the goal of classifying the signals. The majority of works tend to disregard phase information from the complex time-frequency representation. Here, the utility of the phase information, as well as the optimal format of the Doppler-time input for a convolutional neural network, is analysed. It is found that the performance achieved by convolutional neural network classifiers is heavily influenced by the type of input representation, even across formats with equivalent information. Furthermore, it is demonstrated that the phase component of the Doppler-time representation contains rich information useful for classification and that unwrapping the phase in the temporal dimension can improve the results compared to a magnitude-only solution, improving accuracy from 0.920 to 0.938 on the tested human activity dataset. Further improvement of 0.947 is achieved by training a linear classifier on embeddings from multiple-formats., Comment: Presented at International Conference on Radar Systems (RADAR 2022)

Nowadays human interactions largely take place on social networks, with online users' behavior often falling into a few general typologies or "social roles". Among these, opinion leaders are of crucial importance as they have the ability to spread an idea or opinion on a large scale across the network, with possible tangible consequences in the real world. In this work we extract and characterize the different social roles of users within the Reddit WallStreetBets community, around the time of the GameStop short squeeze of January 2021 -- when a handful of committed users led the whole community to engage in a large and risky financial operation. We identify the profiles of both average users and of relevant outliers, including opinion leaders, using an iterative, semi-supervised classification algorithm, which allows us to discern the characteristics needed to play a particular social role. The key features of opinion leaders are large risky investments and constant updates on a single stock, which allowed them to attract a large following and, in the case of GameStop, ignite the interest of the community. Finally, we observe a substantial change in the behavior and attitude of users after the short squeeze event: no new opinion leaders are found and the community becomes less focused on investments. Overall, this work sheds light on the users' roles and dynamics that led to the GameStop short squeeze, while also suggesting why WallStreetBets no longer wielded such large influence on financial markets, in the aftermath of this event., Comment: main text: 15 pages, 4 figures. supplementary materials: 15 pages, 12 figures

We propose a superconducting diode device comprising a central superconducting film flanked by two wires carrying an applied DC bias, suitably chosen so as to generate different asymmetric field profiles. Through numerical simulations of the coupled Ginzburg-Landau and heat-diffusion equations, we show that this design is capable of efficiently breaking the reciprocity of the critical current in the central superconductor, thus promoting the diode effect in response to an applied AC current. By adjusting the DC bias in the wires, we find the optimum inhomogeneous field profile that facilitates the entrance of vortices and antivortices in a given polarity of the applied AC current and impede their entrance in the other polarity. This way, the system behaves as an ideal superconducting half-wave rectifier, with diode efficiencies surpassing 70%. Furthermore, we detail the behavior and diode efficiency of the system under different experimental conditions, such as the substrate heat transfer coefficient and the sweep rate of the external current., Comment: 13 pages, 14 figures

The demand for unprecedented performance in the upcoming 6G wireless networks is fomenting the research on THz communications empowered by Reconfigurable Inteligent Surfaces (RISs). A wide range of use cases have been proposed, most of them, assuming high-level RIS models that overlook some of the hardware impairments that this technology faces. The expectation is that the emergent reconfigurable THz technologies will eventually overcome its current limitations. This disassociation from the hardware may mask nonphysical assumptions, perceived as hardware limitations. In this paper, a top-down approach bounded by physical constraints is presented, distilling from system-level specifications, hardware requirements, and upper bounds for the RIS-aided system performance. We consider D-band indoor and outdoor scenarios where a more realistic assessment of the state-of-the-art solution can be made. The goal is to highlight the intricacies of the design procedure based on sound assumptions for the RIS performance. For a given signal range and angular coverage, we quantify the required RIS size, number of switching elements, and maximum achievable bandwidth and capacity., Comment: 6 pages, 6 figures, submitted for a conference presentation

With the great capabilities of deep classifiers for radar data processing come the risks of learning dataset-specific features that do not generalize well. In this work, the robustness of two deep convolutional architectures, trained and tested on the same data, is evaluated. When standard training practice is followed, both classifiers exhibit sensitivity to subtle temporal shifts of the input representation, an augmentation that carries minimal semantic content. Furthermore, the models are extremely susceptible to adversarial examples. Both small temporal shifts and adversarial examples are a result of a model overfitting on features that do not generalize well. As a remedy, it is shown that training on adversarial examples and temporally augmented samples can reduce this effect and lead to models that generalise better. Finally, models operating on cadence-velocity diagram representation rather than Doppler-time are demonstrated to be naturally more immune to adversarial examples.

Temporal Networks, and more specifically, Markovian Temporal Networks, present a unique challenge regarding the community discovery task. The inherent dynamism of these systems requires an intricate understanding of memory effects and structural heterogeneity, which are often key drivers of network evolution. In this study, we address these aspects by introducing an innovative approach to community detection, centered around a novel modularity function. We focus on demonstrating the improvements our new approach brings to a fundamental aspect of community detection: the detectability threshold problem. We show that by associating memory directly with nodes' memberships and considering it in the expression of the modularity, the detectability threshold can be lowered with respect to cases where memory is not considered, thereby enhancing the quality of the communities discovered. To validate our approach, we carry out extensive numerical simulations, assessing the effectiveness of our method in a controlled setting. Furthermore, we apply our method to real-world data to underscore its practicality and robustness. This application not only demonstrates the method's effectiveness but also reveals its capacity to indirectly tackle additional challenges, such as determining the optimal time window for aggregating data in dynamic graphs. This illustrates the method's versatility in addressing complex aspects of temporal network analysis.

In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the point of differential geometry in infinite dimensions. In this second part we use the tools of Gaussian analysis in infinite dimensional spaces introduced in the first part to describe rigorously the procedures of geometric quantization in the space of Cauchy data of a scalar theory. This leads us to discuss and establish relations between different pictures of QFT. We also apply these tools to describe the geometrization of the space of pure states of quantum field theory as a Kh\"aler manifold. We use this to derive an evolution equation that preserves the geometric structure and avoids norm losses in the evolution. This leads us to a modification of the Schr\"odinger equation via a quantum connection that we discuss and exemplify in a simple case., Comment: 60 pages no figures. Changes in section 3.4, section 6 and 7.2.1

The supporting vectors of a matrix A are the solutions of max || x ||_2 =1 {||Ax||_2^2}. The generalized supporting vectors of matrices A_1 , . . . , A_k are the solutions of max || x ||_2 =1 {||A_1x||_2^2 + ||A_2x||_2^2 + ... + ||A_kx||_2^2}. Notice that the previous optimization problem is also a boundary element problem since the maximum is attained on the unit sphere. Many problems in Physics, Statistics and Engineering can be modeled by using generalized supporting vectors. In this manuscript we first raise the generalized supporting vectors to the infinite dimensional case by solving the optimization problem max || x || =1 sum_{i=1}^\infty ||T i (x )||^2 where (T i )_i is a sequence ofbounded linear operators between Hilbert spaces H and K of any dimension. Observe that the previous optimization problem generalizes the first two. Then a unified MATLAB code is presented for computing generalized supporting vectors of a finite number of matrices. Some particular cases are considered and three novel examples are provided to which our technique applies: optimized observable magnitudes by a pure state in a quantum mechanical system, a TMS optimized coil and an optimal location problem using statistics multivariate analysis. These three examples show the wide applicability of our theoretical and computational model.

In this manuscript we provide an exact solution to the maxmin problem max ||Ax|| subject to ||Bx||<= 1, where A and B are real matrices. This problem comes from a remodeling of max ||Ax|| subject to min ||Bx||, because the latter problem has no solution. Our mathematical method comes from the Abstract Operator Theory, whose strong machinery allows us to reduce the first problem to max parallel to Cx parallel to subject to parallel to x parallel to <= 1, which can be solved exactly by relying on supporting vectors. Finally, as appendices, we provide two applications of our solution: first, we construct a truly optimal minimum stored-energy Transcranian Magnetic Stimulation (TMS) coil, and second, we find an optimal geolocation involving statistical variables

Wireless communications in the THz frequency band is an envisioned revolutionary technology for sixth Generation (6G) networks. However, such frequencies impose certain coverage and device design challenges that need to be efficiently overcome. To this end, the development of cost- and energy-efficient approaches for scaling these networks to realistic scenarios constitute a necessity. Among the recent research trends contributing to these objectives belongs the technology of Reconfigurable Intelligent Surfaces (RISs). In fact, several high-level descriptions of THz systems based on RISs have been populating the literature. Nevertheless, hardware implementations of those systems are still very scarce, and not at the scale intended for most envisioned THz scenarios. In this paper, we overview some of the most significant hardware design and signal processing challenges with THz RISs, and present a preliminary analysis of their impact on the overall link budget and system performance, conducted in the framework of the ongoing TERRAMETA project., Comment: 5 pages, 7 figures, EuCAP 2024