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Individuals with bipolar disorder tend to cycle through disease states such as depression and mania. The heterogeneous nature of disease across states complicates the evaluation of interventions for bipolar disorder patients, as varied interventional success is observed within and across individuals. In fact, we hypothesize that disease state acts as an effect modifier for the causal effect of a given intervention on health outcomes. To address this dilemma, we propose an N-of-1 approach using an adapted autoregressive hidden Markov model, applied to longitudinal mobile health data collected from individuals with bipolar disorder. This method allows us to identify a latent variable from mobile health data to be treated as an effect modifier between the exposure and outcome of interest while allowing for missing data in the outcome. A counterfactual approach is employed for causal inference and to obtain a g-formula estimator to recover said effect. The performance of the proposed method is compared with a naive approach across extensive simulations and application to a multi-year smartphone study of bipolar patients, evaluating the individual effect of digital social activity on sleep duration across different latent disease states.

The orbital parameter space of wide, weakly bound binary stars has been shaped by the still poorly known circumstances of their formation, as well as by subsequent dynamical evolution in parent clusters and in the field. The advance of the Gaia mission astrometry takes statistical studies of wide stellar systems to an unprecedented level of precision and scope. On the theoretical side of the problem, the old approach proposed by Jeans and developed by Ambartsumian is revisited here. It is shown how certain simplifying assumptions about the phase density of binary systems in the framework of general copula distributions can lead to a family of analytical representations for the marginal distribution of orbital eccentricity, including accommodating and flexible power-law models. We further demonstrate the application of these models in forward Monte Carlo simulations of the measured motion angles between the relative velocity and separation vectors on the example of 170K listed Gaia binary systems, providing inference in the intrinsic distribution of orbital eccentricity., Comment: Accepted for publication in AJ

The Kapitza-Dirac effect is the diffraction of quantum particles by a standing wave of light. We here report an analogous phenomenon in pilot-wave hydrodynamics, wherein droplets walking across the surface of a vibrating liquid bath are deflected by a standing Faraday wave. We show that, in certain parameter regimes, the statistical distribution of the droplet deflection angles reveals a diffraction pattern reminiscent of that observed in the Kapitza-Dirac effect. Through experiments and simulations, we show that the diffraction pattern results from the complex interactions of the droplets with the standing wave. Our study highlights non-resonant effects associated with the detuning of the droplet bouncing and the bath vibration, which are shown to lead to drop speed variations and droplet sorting according to the droplet's phase of impact. We discuss the similarities and differences between our hydrodynamic system and the discrete and continuum interpretations of the Kapitza-Dirac effect, and introduce the notion of ponderomotive effects in pilot-wave hydrodynamics.

In this study, we demonstrate the possibility to protect, with Quantum Key Distribution (QKD), a critical infrastructure as the fiber-based one used for time and frequency (TF) dissemination service. The proposed technique allows to disseminate secure and precise TF signals between two fiber-opticconnected locations, on a critical infrastructure, using both QKD and White Rabbit technique. This secure exchange allows the secret sharing of time information between two parties for the synchronization of distant clocks with the highest stability and traceable to the Italian time scale. When encrypted, time signals would reveal to a third party no useful information about the synchronization status, providing a time stability two orders of magnitude worsened.

Not accounting for competing events in survival analysis can lead to biased estimates, as individuals who die from other causes do not have the opportunity to develop the event of interest. Formal definitions and considerations for causal effects in the presence of competing risks have been published, but not for the mediation analysis setting. We propose, for the first time, an approach based on the path-specific effects framework to account for competing risks in longitudinal mediation analysis with time-to-event outcomes. We do so by considering the pathway through the competing event as another mediator, which is nested within our longitudinal mediator of interest. We provide a theoretical formulation and related definitions of the effects of interest based on the mediational g-formula, as well as a detailed description of the algorithm. We also present an application of our algorithm to data from the Strong Heart Study, a prospective cohort of American Indian adults. In this application, we evaluated the mediating role of the blood pressure trajectory (measured during three visits) on the association between arsenic and cadmium, in separate models, with time to cardiovascular disease, accounting for competing risks by death. Identifying the effects through different paths enables us to evaluate the impact of metals on the outcome of interest, as well as through competing risks, more transparently.

Use real word data to evaluate the performance of the electrocardiographic markers of GEH as features in a machine learning model with Standard ECG features and Risk Factors in Predicting Outcome of patients in a population referred to a tertiary cardiology hospital. Patients forwarded to specific evaluation in a cardiology specialized hospital performed an ECG and a risk factor anamnesis. A series of follow up attendances occurred in periods of 6 months, 12 months and 15 months to check for cardiovascular related events (mortality or new nonfatal cardiovascular events (Stroke, MI, PCI, CS), as identified during 1-year phone follow-ups. The first attendance ECG was measured by a specialist and processed in order to obtain the global electric heterogeneity (GEH) using the Kors Matriz. The ECG measurements, GEH parameters and risk factors were combined for training multiple instances of XGBoost decision trees models. Each instance were optmized for the AUCPR and the instance with higher AUC is chosen as representative to the model. The importance of each parameter for the winner tree model was compared to better understand the improvement from using GEH parameters. The GEH parameters turned out to have statistical significance for this population specially the QRST angle and the SVG. The combined model with the tree parameters class had the best performance. The findings suggest that using VCG features can facilitate more accurate identification of patients who require tertiary care, thereby optimizing resource allocation and improving patient outcomes. Moreover, the decision tree model's transparency and ability to pinpoint critical features make it a valuable tool for clinical decision-making and align well with existing clinical practices.

In this paper we study local Hamiltonian operators for multi-component evolutionary differential-difference equations. We address two main problems: the first one is the classification of low order operators for the two-component case. On the one hand, this extends the previously known results in the scalar case; on the other hand, our results include the degenerate cases, going beyond the foundational investigation conducted by Dubrovin. The second problem is the study and the computation of the Poisson cohomology for a two-component (-1,1)-order Hamiltonian operator with degenerate leading term appearing in many integrable differential-difference systems, notably the Toda lattice. The study of its Poisson cohomology sheds light on its deformation theory and the structure of the bi-Hamiltonian pairs where it is included in, as we demonstrate in a series of examples., Comment: v1: 36 pages. Comments are welcome

LLMs demand significant computational resources for both pre-training and fine-tuning, requiring distributed computing capabilities due to their large model sizes \cite{sastry2024computing}. Their complex architecture poses challenges throughout the entire AI lifecycle, from data collection to deployment and monitoring \cite{OECD_AIlifecycle}. Addressing critical AI system challenges, such as explainability, corrigibility, interpretability, and hallucination, necessitates a systematic methodology and rigorous benchmarking \cite{guldimann2024complai}. To effectively improve AI systems, we must precisely identify systemic vulnerabilities through quantitative evaluation, bolstering system trustworthiness. The enactment of the EU AI Act \cite{EUAIAct} by the European Parliament on March 13, 2024, establishing the first comprehensive EU-wide requirements for the development, deployment, and use of AI systems, further underscores the importance of tools and methodologies such as Z-Inspection. It highlights the need to enrich this methodology with practical benchmarks to effectively address the technical challenges posed by AI systems. To this end, we have launched a project that is part of the AI Safety Bulgaria initiatives \cite{AI_Safety_Bulgaria}, aimed at collecting and categorizing AI benchmarks. This will enable practitioners to identify and utilize these benchmarks throughout the AI system lifecycle., Comment: November 2024 v1.0

Published analyses of very long baseline interferometry (VLBI) data for the sources included in the third International Celestial Reference Frame (ICRF3) catalog have revealed object-specific, excess astrometric variability and quasi-coherent trajectories as functions of time. A fraction of these sources show markedly elongated distributions of positions on the sky measured with diurnal observations. Here we apply a novel statistical and data-processing method to the diurnal position measurements stretching over 40 years to quantify the degree of elongation and its position angle, for each source with more than 200 data points. We find that 49\% of the examined sources have distribution elongations in excess of 1.3. Robust uncertainties of the directions of maximal astrometric dispersion are computed by the bootstrapping method, and the results are compared with a larger catalog of radio jet directions by Plavin et al. 2022. Nearly one-half of the sources with smaller position angle uncertainties are found to have astrometric position excursions from their mean positions aligned with the radio jet structures within $\pm 30\degr$., Comment: To be published in ApJL

Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions describing regular black holes. Its reduced action depends on a function of one of the basic curvature invariants of the corresponding metric. In this paper we study a generalization of this model to the case when this function depends on all the basic curvature invariants. We show that the metrics which are solutions of such a model possess a universal scaling property. We demonstrate that there exists a special class of such models for which the "master" equation basic curvature invariant is a linear second order ordinary differential equation. We specify a domain in the space of parameters of the model for which the corresponding solutions describe regular static spherically symmetric black holes and study their properties., Comment: 17 pages, 10 figures

Interactions have strong effects in systems with flat bands. We examine the role of Coulomb interactions in two dimensional chiral anisotropic quasiparticles that disperse linearly in one direction and have relatively flat bands near the neutrality point in the other direction, dispersing with an arbitrary positive even power law $2n\geq 2$. As in the conventional semi-Dirac case ($n = 1$), we show using renormalization group that strong logarithmic divergences in the self-energy of generalized semi-Dirac fermions resum and lead to a restoration of the linearity of the spectrum for arbitrary n over a sizable energy window in the perturbative regime. We discuss those results in light of previous non-perturbative large $N_f$ results and address the implications for physical observables., Comment: 11 pages, 6 figures

We study spinoptics equations in the Schwarzschild spacetime. We demonstrate that using the explicit and hidden symmetries of this metric one can explicitly solve the equations for complex null tetrad associated with null rays representing photon's and graviton's motion. This allows one to integrate the spinoptics equations both for the electromagnetic and gravitational waves. It is shown that the main effect of the interaction of the spin of these fields with the spacetime curvature is the tilt of the asymptotic planes of the massless particle orbit. The corresponding tilting angle is calculated. It is shown that this angle grows when a null ray passes in the vicinity of the circular null orbit located at $r=3M$., Comment: 8 pages, 3 figures

The distribution of period ratios for 580 known two-planet systems is apparently nonuniform, with several sharp peaks and troughs. In particular, the vicinity of the 2:1 commensurability seems to have a deficit of systems. Using Monte Carlo simulations and an empirically inferred population distribution of period ratios, we prove that this apparent dearth of near-resonant systems is not statistically significant. The excess of systems with period ratios in the wider vicinity of the 2:1 resonance is significant, however. Long-term WHFast integrations of a synthetic two-planet system on a grid period ratios from 1.87 through 2.12 reveal that the eccentricity and inclination exchange mechanism between non-resonant planets represents the orbital evolution very well in all cases, except at the exact 2:1 mean motion resonance. This resonance destroys the orderly exchange of eccentricity, while the exchange of inclination still takes place. Additional simulations of the Kepler-113 system on a grid of initial inclinations show that the secular periods of eccentricity and inclination variations are well fitted by a simple hyperbolic cosine function of the initial mutual inclination. We further investigate the six known two-planet systems with period ratios within 2\% of the exact 2:1 resonance (TOI-216, KIC 5437945, Kepler-384, HD 82943, HD 73526, HD 155358) on a grid of initial inclinations and for two different initial periastron longitudes corresponding to the aligned and anti-aligned states. All these systems are found to be long-term stable except HD 73526, which is likely a false positive. The periodic orbital momentum exchange is still at work in some of these systems, albeit with much shorter cycling periods of a few years.

Using the light curve time series data for more than 11.7 million variable sources published in the Gaia Data Release 3, the average magnitudes, colors, and variability parameters have been computed for 0.836 million Gaia CRF objects, which are mostly quasars and active galactic nuclei (AGNs). To mitigate the effects of occasional flukes in the data, robust statistical measures have been employed, namely, the median, median absolute deviation, and Spearman correlation. We find that the majority of the CRF sources have moderate amplitudes of variability in the Gaia $G$ band just below 0.1 mag. The heavy-tailed distribution of variability amplitudes (quantified as robust standard deviations) does not find a single analytical form, but is closer to Maxwell distribution with a scale of 0.078 mag. The majority of CRF sources have positive correlations between $G$ magnitude and $G_{\rm BP}-G_{\rm RP}$ colors, meaning that these quasars and AGNs become bluer when they are brighter. The variations in the BP and RP bands are also mostly positively correlated. Dependencies of all variability parameters with cosmological redshift are fairly flat for the more accurate estimates above redshift 0.7, while the median color shows strong systematic variations with redshift. Using a robust normalized score of magnitude deviations, a sample of 5000 most variable quasars is selected and published. The intersection of this sample with the ICRF3 catalog shows a much higher rate of strongly variable quasars (mostly, blazars) in ICRF3., Comment: Accepted for publication

Recent advances in manipulating droplet emissions from a thin vibrating fluid using submerged cavities, have introduced an innovative platform for generating hydrodynamic analogs of quantum and optical systems. This platform unlocks unique features not found in traditional pilot-wave hydrodynamics, inviting further exploration across varied physical settings to fully unravel its potential and limitations as a quantum analog. In this study, we explore how the recently reported phenomenon of hydrodynamic superradiance is affected when a single hydrodynamic cavity is taken to interact with a submerged reflective barrier. Our experimental findings reveal that the presence of a barrier near a cavity enhances its droplet emission rate, emulating the effect of a second cavity positioned at twice the distance. Moreover, the system exhibits a sinusoidal modulation of the emission rate as a function of the distance between the cavity and its mirror image, echoing the characteristic superradiance signature observed in optical systems. These findings broaden our understanding of wave-particle duality in hydrodynamic quantum analogs and suggest new pathways for replicating quantum behaviors in macroscopic systems.

Using very long baseline interferometry data for the sources that comprise the third International Celestial Reference Frame (ICRF3), we examine the quality of the formal source position uncertainties of ICRF3 by determining the excess astrometric variability (unexplained variance) for each source as a function of time. We also quantify multiple qualitatively distinct aspects of astrometric variability seen in the data, using a variety of metrics. Average position offsets, statistical dispersion measures, and coherent trends over time as explored by smoothing the data are combined to characterize the most and least positionally stable ICRF3 sources. We find a notable dependence of the excess variance and statistical variability measures on declination, as is expected for unmodeled ionospheric delay errors and the northern hemisphere dominated network geometries of most astrometric and geodetic observing campaigns., Comment: Accepted for publication in ApJS. 22 pages, 14 figures

We investigate whether large language models (LLMs) can successfully perform financial statement analysis in a way similar to a professional human analyst. We provide standardized and anonymous financial statements to GPT4 and instruct the model to analyze them to determine the direction of firms' future earnings. Even without narrative or industry-specific information, the LLM outperforms financial analysts in its ability to predict earnings changes directionally. The LLM exhibits a relative advantage over human analysts in situations when the analysts tend to struggle. Furthermore, we find that the prediction accuracy of the LLM is on par with a narrowly trained state-of-the-art ML model. LLM prediction does not stem from its training memory. Instead, we find that the LLM generates useful narrative insights about a company's future performance. Lastly, our trading strategies based on GPT's predictions yield a higher Sharpe ratio and alphas than strategies based on other models. Our results suggest that LLMs may take a central role in analysis and decision-making., Comment: Previously posted on SSRN (May 21, 2024). See http://papers.ssrn.com/sol3/papers.cfm?abstract_id=4835311

Mobile technology (mobile phones and wearable devices) generates continuous data streams encompassing outcomes, exposures and covariates, presented as intensive longitudinal or multivariate time series data. The high frequency of measurements enables granular and dynamic evaluation of treatment effect, revealing their persistence and accumulation over time. Existing methods predominantly focus on the contemporaneous effect, temporal-average, or population-average effects, assuming stationarity or invariance of treatment effects over time, which are inadequate both conceptually and statistically to capture dynamic treatment effects in personalized mobile health data. We here propose new causal estimands for multivariate time series in N-of-1 studies. These estimands summarize how time-varying exposures impact outcomes in both short- and long-term. We propose identifiability assumptions and a g-formula estimator that accounts for exposure-outcome and outcome-covariate feedback. The g-formula employs a state space model framework innovatively to accommodate time-varying behavior of treatment effects in non-stationary time series. We apply the proposed method to a multi-year smartphone observational study of bipolar patients and estimate the dynamic effect of phone-based communication on mood of patients with bipolar disorder in an N-of-1 setting. Our approach reveals substantial heterogeneity in treatment effects over time and across individuals. A simulation-based strategy is also proposed for the development of a short-term, dynamic, and personalized treatment recommendation based on patient's past information, in combination with a novel positivity diagnostics plot, validating proper causal inference in time series data.

In this paper we consider a rotating black hole with electric and magnetic monopole charges that moves in a static homogeneous electromagnetic field. We assume that both the charges and the fields are weak, so that they have no effect on the spacetime geometry, which is described by the Kerr metric. We present exact solutions to Maxwell's equations describing the field of a charged rotating black hole moving in an external field background. We use these solutions to calculate the energy, momentum, and angular momentum fluxes of the electromagnetic field into the black hole. Using these results, we obtain expressions for the torque and force acting on the moving charged rotating black hole arising as a result of its interaction with the external electromagnetic field. We calculate these quantities both in the frame comoving with the black hole and in the frame of the external background field. We use this result to derive the equations that govern the change in the black hole's mass and spin, as well as the motion of the black hole. We provide exact solutions for specific cases which illustrate the role of charge and spin on the motion of the black hole., Comment: 12 pages

In this paper we discuss propagation of the weak high-frequency gravitational waves in a curved spacetime background. We develop a so-called spinoptics approximation which takes into account interaction of the spin of the field with the curvature of the background metric. This is achieved by modifying the standard geometric optics approximation by including the helicity sensitive terms of the order $1/\omega$ in the eikonal equation. The novelty of the approach developed in this paper is that instead of study of the high-frequency expansion of the equations for the gravitational field perturbations we construct the effective action for the gravitational spinoptics. The gravitational spinoptics equations derived by variation of the effective action correctly reproduce the earlier obtained results. However, the proposed effective action approach is technically more simple and transparent. It allows one to reduce the study of the high-frequency gravitational waves to study classical dynamics of massless particles with internal discrete degree of freedom (helicity). The formalism is covariant and it can be applied for arbitrary vacuum space-time background., Comment: 9 pages

Limited access to corrective eyewear remains a significant medical, societal, and economic challenge, even in the 21st century. More than 1 billion people suffer from uncorrected vision impairment, with the vast majority residing in developing countries. Decades of philanthropic efforts failed to supply even a small fraction of the demand, whereas local manufacturing using standard machining technologies remains out of reach due to inadequate resources. We here show that the Fluidic Shaping approach can be utilized to create a new manufacturing modality for high-quality ophthalmic lenses that entirely eliminates the need for machining, and instead uses surface tension to shape liquid polymer volumes into prescription lenses. We present a compact device wherein a liquid photopolymer is injected into an elliptical frame submerged within an immersion liquid of equal density, resulting in two liquid surfaces whose minimum-energy states correspond to two lens surfaces. After several minutes of curing, a complete solid lens is obtained, requiring no post-processing. We provide an analytical model and experimental validation, showing that all spherical and cylindrical corrections can be attained by simply controlling the volume of the polymer and the frame's eccentricity. We demonstrate the fabrication of complete eyeglasses that meet and exceed industry standards, relying solely on a 1 gallon water container integrated with an array of low-power LEDs.

Measurement error can often be harmful when estimating causal effects. Two scenarios in which this is the case are in the estimation of (a) the average treatment effect when confounders are measured with error and (b) the natural indirect effect when the exposure and/or confounders are measured with error. Methods adjusting for measurement error typically require external data or knowledge about the measurement error distribution. Here, we propose methodology not requiring any such information. Instead, we show that when the outcome regression is linear in the error-prone variables, consistent estimation of these causal effects can be recovered using constructed instrumental variables under certain conditions. These variables, which are functions of only the observed data, behave like instrumental variables for the error-prone variables. Using data from a study of the effects of prenatal exposure to heavy metals on growth and neurodevelopment in Bangladeshi mother-infant pairs, we apply our methodology to estimate (a) the effect of lead exposure on birth length while controlling for maternal protein intake, and (b) lead exposure's role in mediating the effect of maternal protein intake on birth length. Protein intake is calculated from food journal entries, and is suspected to be highly prone to measurement error., Comment: 72 pages, 4 figures

Astronomical time series often have non-uniform sampling in time, or irregular cadences, with long gaps separating clusters of observations. Some of these data sets are also explicitly non-Gaussian with respect to the expected model fit, or the simple mean. The standard Lomb-Scargle periodogram is based on the least squares solution for a set of test periods and, therefore, is easily corrupted by a subset of statistical outliers or an intrinsically non-Gaussian population. It can produce completely misleading results for heavy-tailed distribution of residuals. We propose a robust 1-norm periodogram technique, which is based on the principles of robust statistical estimation. This technique can be implemented in weighted or unweighted options. The method is described in detail and compared with the classical least squares periodogram on a set of astrometric VLBI measurements of the ICRF quasar IERS B0642+449. It is uniformly applied to a collection of 259 ICRF3 quasars each with more than 200 epoch VLBI measurements, resulting in a list of 49 objects with quasi-periodic position changes above the $3\sigma$ level, which warrant further investigation., Comment: accepted for publication in PASP

A large number of candidate binary stars with apparent acceleration on the sky has emerged from analysis of astrometric data collected by the Hipparcos, Tycho-2, and Gaia space missions. Although the apparent acceleration can serve as a relatively reliable indicator of binarity, it provides scarce information about the orbital and physical parameters of the components. With an emphasis on the search for stellar-mass black holes and neutron stars hidden in binary systems, we start a broader effort to characterize the most promising candidates using follow-up ground-based observations. Accurate quantification of orbital and physical parameters of systems with dim or invisible companions requires combination of Hipparcos, Gaia, and precision spectroscopic measurements. In this paper, we review the necessary steps in this implementation and describe the improved Hipparcos-Gaia sample of long-term astrometric accelerations which includes correction of sky-correlated systematic errors using the vector spherical decomposition method. As an example, we study one Hipparcos star with a large acceleration, HIP 44842, where the companion is revealed to be a normal main sequence star., Comment: Accepted for publication in AJ

In this paper we study propagation of the high frequency electromagnetic waves in a curved spacetime. We discuss a so call spinoptics approach which generalizes a well known geometric optics approximation and allows one to take into account spin-dependent corrections. A new element proposed in this work is the use of effective action which allows one to derive spinoptics equations. This method is simpler and more transparent than the earlier proposed methods. It is explicitly covariant and can be applied to an arbitrary spacetime background. We also demonstrate how the initial value problem for the high frequency electromagnetiv wave can be soled in the developed spinoptics approximation., Comment: 7 pages, a couple of misprints are corrected

Brillouin light scattering (BLS) spectroscopy is a powerful tool for detecting spin waves in magnetic thin films and nanostructures. Despite comprehensive access to spin-wave properties, BLS spectroscopy suffers from the limited wavenumber of detectable spin waves and the typically relatively low sensitivity. In this work, we present the results of numerical simulations based on the recently developed analytical model describing plasmon-enhanced BLS. The effective susceptibility is defined for a single plasmonic nanoparticle in the shape of an ellipsoid of rotation, for the sandwiched plasmonic nanoparticles separated by a dielectric spacer, as well as for the array of plasmonic resonators on the surface of a magnetic film. It is shown that the eccentricity of the metal nanoparticles, which describes their shape, plays a key role in the enhancement of the BLS signal. The optimal conditions for BLS enhancement are numerically defined for gold and silver plasmon systems for photons of different energies. The presented results define the roadmap for the experimental realization of plasmon-enhanced BLS spectroscopy., Comment: 29 pages, 23 formulas, 17 figures

Brillouin light scattering (BLS) spectroscopy is an effective method for detecting spin waves in magnetic thin films and nanostructures. While it provides extensive insight into the properties of spin waves, BLS spectroscopy is impeded in many practical cases by the limited range of detectable spin wave wavenumbers and its low sensitivity. Here, we present a generalized theoretical model describing plasmon-enhanced BLS spectroscopy. Three types of plasmonic nanoparticles in the shape of an ellipsoid of rotation are considered: a single plasmon resonator, a sandwiched plasmonic structure in which two nanoparticles are separated by a dielectric spacer, and an ensemble of metallic nanoparticles on the surface of a magnetic film. The effective susceptibilities for the plasmonic systems at the surface of the magnetic film are calculated using the electrodynamic Green functions method, and the enhancement coefficient is defined. It is analytically shown that the ratio of the plasmon resonator height to its radius plays the key role in the development of plasmon-enhanced BLS spectroscopy. The developed model serves as a basis for numerical engineering of the optimized plasmon nanoparticle morphology for BLS enhancement., Comment: 23 pages, 43 formulas, 4 figures

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave background in the test case of Euclidean $E_1$ topology (the 3-torus) with a cubic fundamental domain of a size scale significantly smaller than the diameter of the last scattering surface. This is the first step toward developing a machine learning approach to classification of cosmic topology and likelihood-free inference of topological parameters. Different machine learning approaches are capable of classifying the harmonic-space realizations with accuracy greater than 99% if the topology scale is half of the diameter of the last-scattering surface and orientation of the topology is known. For distinguishing random rotations of these sky realizations from realizations of the covering space, the extreme gradient boosting classifier algorithm performs best with an accuracy of 88%. Slightly lower accuracies of 83% to 87% are obtained with the random forest classifier along with one- and two-dimensional convolutional neural networks. The techniques presented here can also accurately classify non-rotated cubic $E_1$ topology realizations with a topology scale slightly larger than the diameter of the last-scattering surface, if enough training data are provided. While information compressing methods like most machine learning approaches cannot exceed the statistical power of a likelihood-based approach that captures all available information, they potentially offer a computationally cheaper alternative. A principle challenge appears to be accounting for arbitrary orientations of a given topology, although this is also a significant hurdle for likelihood-based approaches., Comment: 34 pages, 12 figures, 4 tables

Mediation analysis aims to decipher the underlying causal mechanisms between an exposure, an outcome, and intermediate variables called mediators. Initially developed for fixed-time mediator and outcome, it has been extended to the framework of longitudinal data by discretizing the assessment times of mediator and outcome. Yet, processes in play in longitudinal studies are usually defined in continuous time and measured at irregular and subject-specific visits. This is the case in dementia research when cerebral and cognitive changes measured at planned visits in cohorts are of interest. We thus propose a methodology to estimate the causal mechanisms between a time-fixed exposure ($X$), a mediator process ($\mathcal{M}_t$) and an outcome process ($\mathcal{Y}_t$) both measured repeatedly over time in the presence of a time-dependent confounding process ($\mathcal{L}_t$). We consider three types of causal estimands, the natural effects, path-specific effects and randomized interventional analogues to natural effects, and provide identifiability assumptions. We employ a dynamic multivariate model based on differential equations for their estimation. The performance of the methods are explored in simulations, and we illustrate the method in two real-world examples motivated by the 3C cerebral aging study to assess: (1) the effect of educational level on functional dependency through depressive symptomatology and cognitive functioning, and (2) the effect of a genetic factor on cognitive functioning potentially mediated by vascular brain lesions and confounded by neurodegeneration.

Automated hand gesture recognition has long been a focal point in the AI community. Traditionally, research in this field has predominantly focused on scenarios with access to a continuous flow of hand's images. This focus has been driven by the widespread use of cameras and the abundant availability of image data. However, there is an increasing demand for gesture recognition technologies that operate on low-power sensor devices. This is due to the rising concerns for data leakage and end-user privacy, as well as the limited battery capacity and the computing power in low-cost devices. Moreover, the challenge in data collection for individually designed hardware also hinders the generalisation of a gesture recognition model. In this study, we unveil a novel methodology for pattern recognition systems using adaptive and agile error correction, designed to enhance the performance of legacy gesture recognition models on devices with limited battery capacity and computing power. This system comprises a compact Support Vector Machine as the base model for live gesture recognition. Additionally, it features an adaptive agile error corrector that employs few-shot learning within the feature space induced by high-dimensional kernel mappings. The error corrector can be customised for each user, allowing for dynamic adjustments to the gesture prediction based on their movement patterns while maintaining the agile performance of its base model on a low-cost and low-power micro-controller. This proposed system is distinguished by its compact size, rapid processing speed, and low power consumption, making it ideal for a wide range of embedded systems.

In this paper we consider the motion of a rotating black hole through a static, homogeneous, massless scalar field. In the general case, a constant vector of the field gradient can be timelike, spacelike or null. We consider and compare all of these cases. We demonstrate that as a result of the interaction of the black hole with the scalar field, its mass, spin and relative velocity with respect to the field can change. We obtain the equations describing the evolution of these parameters and present solutions of the obtained equations for some simple cases., Comment: 11 pages, 2 figures

In the present paper, we consider a rotating black hole moving in a static homogeneous electromagnetic field. We assume that the field is weak and neglect its backreaction on the geometry, so that the metric at far distance from the black hole is practically flat. We present an exact solution for a stationary electromagnetic field in the presence of the black hole for this problem and use it to calculate fluxes of the energy, momentum and angular momentum into the black hole. Using these results we derive the equations of motion of the rotating black hole in the electromagnetic field and discuss some of the interesting solutions of these equations. In particular, we demonstrate how the interaction of the spin of the black hole with the external magnetic field changes its trajectory., Comment: 8 pagees

The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation protocols. Within this context, Bayesian estimation offers a complete framework for optimal quantum metrology techniques, such as adaptive protocols. However, the use of the Bayesian approach requires extensive computational resources, especially in the multiparameter estimations that represent the typical operational scenario for quantum sensors. Hence, the requirement to characterize protocols implementing Bayesian estimations can become a significant challenge. This work focuses on the crucial task of robustly benchmarking the performances of these protocols in both single and multiple-parameter scenarios. By comparing different figures of merits, evidence is provided in favor of using the median of the quadratic error in the estimations in order to mitigate spurious effects due to the numerical discretization of the parameter space, the presence of limited data, and numerical instabilities. These results, providing a robust and reliable characterization of Bayesian protocols, find natural applications to practical problems within the quantum estimation framework.

The paper considers methods of particle cooling mostly concentrating on cooling of high energy heavy particles in the high energy colliders. Presently, there are two major methods of the cooling the electron cooling and stochastic cooling. The latter can be additionally separated on the microwave stochastic cooling, the optical stochastic cooling (OSC) and the coherent electron cooling (CEC). OSC and CEC are essentially extensions of microwave stochastic cooling operating in 1-10 GHz frequency range to the optical frequencies corresponding to 30-300 THz frequency range. The OSC uses undulators as a pickup and a kicker, and an optical amplifier for signal amplification, while the CEC uses an electron beam for all these functions.

(Abridged) Planets are surrounded by fractal surfaces (traditionally called Hill spheres), separating the inner zones of long-term stable orbital motion of their satellites from the outer space where the gravitational pull from the Sun takes over. Through this surface, external minor bodies in trajectories loosely co-orbital to a planet can be stochastically captured by the planet without any assistance from external perturbative forces, and can become moons chaotically orbiting the planet for extended periods of time. Using state-of-the-art orbital integrators, we simulate such capture events for Venus, resulting in long-term attachment phases by reversing the forward integration of a moon initially attached to the planet and escaping it after an extended period of time. Although the probability of a long-term chaotic capture from a single encounter is generally low, the high density of co-orbital bodies in the primordial protoplanetary disk makes this outcome possible, if not probable. The early Venus was surrounded by a dusty gaseous disk of its own, which, coupled with the tidal dissipation of the kinetic energy in the moon and the planet, could shrink the initial orbit and stabilize the captured body within the Hill surface. The tidal torque from the moon, for which we use the historical name Neith, gradually brakes the prograde rotation of Venus, and then reverses it, while the orbit continues to decay. Neith eventually reaches the Roche radius and disintegrates, probably depositing most of its material on Venus' surface. Our calculations show that surface density values of about 0.06 kg m$^{-2}$ for the debris disk may be sufficient to stabilize the initial chaotic orbit of Neith and to bring it down within several radii of Venus, where tidal dissipation becomes more efficient., Comment: Published in Universe, 2024, 10, 15

For systems of evolutionary partial differential equations the tau-structure is an important notion which originated from the deep relation between integrable systems and quantum field theories. We show that, under a certain non-degeneracy condition, existence of a tau-structure implies integrability. As an example, we apply this principle to provide a new proof of the integrability of the Drinfeld--Sokolov hierarchy associated to an arbitrary Kac--Moody algebra and a choice of a vertex of its Dynkin diagram., Comment: v2: minor editing and corrections. 25 pages