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A tensor space is a vector space equipped with a finite collection of multilinear forms. The length of a tensor space is its length as a representation of its symmetry group. Infinite dimension tensor spaces of finite length are special, highly symmetrical objects. We classify the (universal) biquadratic spaces of length two; there are seven families of them. As a corollary, we establish some cases of the linear analog of the Ryll-Nardzewski theorem. We view this work as a first attempt to classify highly symmetrical tensor spaces., Comment: 26 pages

We investigate gas transfer processes occurring at the air-water interface of progressive water waves using high-fidelity numerical simulations. Waves with varying initial steepness, including regular wave patterns, mild spilling and intense plunging breakers are examined. A multiphase solver is employed to model gas flux and diffusion processes enabling precise estimation of the air-water interface area and gas transfer velocity, achieving an accuracy unattainable in experiments. We reveal that the volume of gas transferred across the air-water interface increases significantly with the amount of air entrained due to wave breaking, peak values in the gas transfer velocity being concurrent with peaks in energy dissipation rate and air entrainment. Furthermore, the gas transfer velocity is observed to scale approximately as the one-fourth power of the energy dissipation rate, consistent with previous theoretical predictions. We anticipate that the present findings can help reduce the substantial uncertainty associated with parameterizing fundamental natural processes, such as CO2 absorption by the oceans.

In table grape cultivation, harvesting depends on accurately assessing fruit quality. While some characteristics, like color, are visible, others, such as Soluble Solid Content (SSC), or sugar content measured in degrees Brix ({\deg}Brix), require specific tools. SSC is a key quality factor that correlates with ripeness, but lacks a direct causal relationship with color. Hyperspectral cameras can estimate SSC with high accuracy under controlled laboratory conditions, but their practicality in field environments is limited. This study investigates the potential of simple RGB sensors under uncontrolled lighting to estimate SSC and color, enabling cost-effective, robot-assisted harvesting. Over the 2021 and 2022 summer seasons, we collected grape images with corresponding SSC and color labels to evaluate algorithmic solutions for SSC estimation on embedded devices commonly used in robotics and smartphones. Our results demonstrate that SSC can be estimated from visual appearance with human-like performance. We propose computationally efficient histogram-based methods for resource-constrained robots and deep learning approaches for more complex applications.

We prove precise conditional estimates for the third moment of the logarithm of the Riemann zeta function, refining what is implied by the Selberg central limit theorem, both for the real and imaginary parts. These estimates match predictions made in work of Keating and Snaith. We require the Riemann Hypothesis, a conjecture for the triple correlation of Riemann zeros and another ``twisted'' pair correlation conjecture which explains the interaction of a prime power with Montgomery's pair correlation function. We believe this to be of independent interest, and devote substantial effort to its justification. Namely, we prove this conjecture on a certain range unconditionally, and on a larger range under the assumption of a variant of the Hardy-Littlewood conjecture with good uniformity.

The increasing demand for mental health services has highlighted the need for innovative solutions, particularly in the realm of psychological conversational AI, where the availability of sensitive data is scarce. In this work, we explored the development of a system tailored for mental health support with a novel approach to psychological assessment based on explainable emotional profiles in combination with empathetic conversational models, offering a promising tool for augmenting traditional care, particularly where immediate expertise is unavailable. Our work can be divided into two main parts, intrinsecaly connected to each other. First, we present RACLETTE, a conversational system that demonstrates superior emotional accuracy compared to state-of-the-art benchmarks in both understanding users' emotional states and generating empathetic responses during conversations, while progressively building an emotional profile of the user through their interactions. Second, we show how the emotional profiles of a user can be used as interpretable markers for mental health assessment. These profiles can be compared with characteristic emotional patterns associated with different mental disorders, providing a novel approach to preliminary screening and support.

One of the most challenging and fascinating issues in mathematical and theoretical physics concerns identifying the common logic, if any, which underlies the physical world. More precisely, this involves the search of the possibly-unique axiomatic logical proposition calculus to apply simultaneously both to classical and quantum realms of physics and to be consistent with the corresponding mathematical and filosophysical setups. Based on the recent establishment of quantum logic, which has been shown to apply both to Quantum Mechanics and Quantum Gravity, the crucial remaining step involves the identification of the appropriate axiomatic logical proposition calculus to be associated with Classical Mechanics. In this paper the issue is posed for a fundamental example of Classical Mechanics, which is represented by the so-called Boltzmann-Sinai dynamical system. This is realized by the ensemble of classical smooth hard-spheres, which is set at the basis of Classical Statistical Mechanics and is also commonly regarded as a possible realization of Classical Newtonian Cosmology. Depending on the initial conditions which are prescribed for such a system, its classical state is shown to obey the propositional calculus of non-classical logic. In particular, the latter is expressed by the 3-way Principle of Non-Contradiction, namely the same logical principle that holds for quantum logic. The result therefore permits to question on a mathematical basis the principles of deterministic classical logic and the validity of their character within the domain of Classical Physics. Such a conclusion represents a potential notable innovation in the logical dicotomy true/false, a crucial topic which has crossed millennia through philosophy, logic, mathematics and physics.

We propose a lattice formulation of four dimensional super Yang-Mills model with a twisted N=4 supersymmetry in a manifestly gauge covariant manner. The formulation we employ here is a four dimensional extension of the manifestly gauge covariant method which was developed in our proposals of Dirac-Kahler twisted N=D=2 and N=4 D=3 super Yang-Mills on a lattice. Twisted N=4 supersymmetry algebra is geometrically realized on a four dimensional lattice with link supercharges and the use of link (anti-)commutators. Employing Grassmann parameters with link nature, we explicitly show that the resulting super Yang-Mills action is invariant under all the supercharges on a lattice without chiral fermion problems. As a group and algebraic interpretation of the link approach, we show that promoting bosonic supercovariant derivatives to their exponentials consistently with the lattice Leibniz rule naturally gives rise to the notion of gauge covariant link (anti-)commutators. This can be regarded as a fermionic decomposition of a Lie group element, which may provide a new methodology in super Lie group and super Lie algebra. We also provide a five dimensional lift-up of the formulation with exact N=4 SUSY invariance on a five dimensional lattice., Comment: 70 pages, 2 figures

A novel least-squares model-reference direct adaptive control (LS-MRAC) algorithm for multivariable (MIMO) plants is presented. The controller parameters are directly updated based on the output tracking error. The control law is crucially modified to reduce the relative degree of the error model to zero. A complete Lyapunov-based stability analysis as well as a tracking error convergence characterization is provided demonstrating that the LS-MRAC can achieve arbitrarily fast tracking while maintaining satisfactory parameter convergence for appropriate adaptation gains. Simulation results show a significant improvement in tracking performance compared to previous methods., Comment: 8 pages, 8 figures

The growing complexity of radar signals demands responsive and accurate detection systems that can operate efficiently on resource-constrained edge devices. Existing models, while effective, often rely on substantial computational resources and large datasets, making them impractical for edge deployment. In this work, we propose an ultralight hybrid neural network optimized for edge applications, delivering robust performance across unfavorable signal-to-noise ratios (mean accuracy of 96.3% at 0 dB) using less than 100 samples per class, and significantly reducing computational overhead., Comment: 8 pages, 8 figures

In recent years, there has been a significant surge of interest in Mars exploration, driven by the planet's potential for human settlement and its proximity to Earth. In this paper, we explore the performance of the LoRaWAN technology on Mars, to study whether commercial off-the-shelf IoT products, designed and developed on Earth, can be deployed on the Martian surface. We use the ns-3 simulator to model various environmental conditions, primarily focusing on the Free Space Path Loss (FSPL) and the impact of Martian dust storms. Simulation results are given with respect to Earth, as a function of the distance, packet size, offered traffic, and the impact of Mars' atmospheric perturbations. We show that LoRaWAN can be a viable communication solution on Mars, although the performance is heavily affected by the extreme Martian environment over long distances., Comment: This paper has been accepted for presentation at the 2025 International Conference on Computing, Networking and Communications (ICNC)

We study orientability in spaces with Ricci curvature bounded below. Building on the theory developed by Honda, we establish equivalent characterizations of orientability for Ricci limit and RCD spaces in terms of the orientability of their manifold part. We prove a new stability theorem and, as a corollary, we deduce that four-manifolds with Ricci curvature bounded below and volume non-collapsing are uniformly locally orientable. As a global counterpart of the latter, we show that four-manifolds with nonnegative Ricci curvature and Euclidean volume growth are orientable.

Effective String Theory (EST) is a powerful tool used to study confinement in pure gauge theories by modeling the confining flux tube connecting a static quark-anti-quark pair as a thin vibrating string. Recently, flow-based samplers have been applied as an efficient numerical method to study EST regularized on the lattice, opening the route to study observables previously inaccessible to standard analytical methods. Flow-based samplers are a class of algorithms based on Normalizing Flows (NFs), deep generative models recently proposed as a promising alternative to traditional Markov Chain Monte Carlo methods in lattice field theory calculations. By combining NF layers with out-of-equilibrium stochastic updates, we obtain Stochastic Normalizing Flows (SNFs), a scalable class of machine learning algorithms that can be explained in terms of stochastic thermodynamics. In this contribution, we outline EST and SNFs, and report some numerical results for the shape of the flux tube., Comment: 1+ 10 pages, 2 figures, contribution for the 41st International Symposium on Lattice Field Theory (Lattice 2024), 28 July - 3 August 2024, Liverpool, UK; v2: 1+ 10 pages, 2 figures, reference added

We develop a neurogeometric model for the arm area of motor cortex, which encodes complex motor primitives, ranging from simple movement features like movement direction, to short hand trajectories, termed fragments, and ultimately to more complex patterns known as neural states (Georgopoulos, Hatsopoulos, Kadmon-Harpaz et al). Based on the sub-riemannian framework introduced in 2023, we model the space of fragments as a set of short curves defined by kinematic parameters. We then introduce a geometric kernel that serves as a model for cortical connectivity and use it in a differential equation to describe cortical activity. By applying a grouping algorithm to this cortical activity model, we successfully recover the neural states observed in Kadmon-Harpaz et al, which were based on measured cortical activity. This confirms that the choice of kinematic variables and the distance metric used here are sufficient to explain the phenomena of neural state formation. The modularity of our model reflects the brain's hierarchical structure, where initial groupings in the kinematic space $\mathcal{M}$ lead to more abstract representations. This approach mimics how the brain processes stimuli at different scales, extracting both local and global properties.

We investigate the behaviour of a flexible stem completely submerged under a surface gravity wave of finite amplitude using fully resolved direct numerical simulations. By varying the rigidity of the stem over ten orders of magnitude, we explore its motion in the drag-dominated regime with realistic air and water properties. Our findings reveal two distinct structural responses of the stem depending on the ratio between its natural frequency (f_nat) and the wave frequency (f_wave). For f_nat/f_wave >> 1, the stem maintains on average a straight configuration and exhibits streamwise oscillations in phase-opposition with the wave, moving symmetrically with respect to the vertical direction. Conversely, for f_nat/f_wave << 1, the stem reconfigures under the influence of the Stokes drift, bending forward and breaking the symmetry, and exhibits oscillations that are more coherent with the surrounding flow field. Resonance is observed when f_nat is approximatively f_wave. These results provide new insights into the dynamics of slender vegetation and man-made structures in wave fields, offering valuable implications for marine biology and engineering., Comment: 12 pages, 7 figures

Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive Elastic-Net estimator for ergodic diffusion processes observed under high-frequency sampling schemes. Our method combines the least squares approximation of the quasi-likelihood with adaptive $\ell_1$ and $\ell_2$ regularization. This approach allows to enhance prediction accuracy and interpretability while effectively recovering the sparse underlying structure of the model. In the spirit of analyzing high-dimensional scenarios, we provide finite-sample guarantees for the (block-diagonal) estimator's performance by deriving high-probability non-asymptotic bounds for the $\ell_2$ estimation error. These results complement the established oracle properties in the high-frequency asymptotic regime with mixed convergence rates, ensuring consistent selection of the relevant interactions and achieving optimal rates of convergence. Furthermore, we utilize our results to analyze one-step-ahead predictions, offering non-asymptotic control over the $\ell_1$ prediction error. The performance of our method is evaluated through simulations and real data applications, demonstrating its effectiveness, particularly in scenarios with strongly correlated variables.

In this thesis we explore S. Klainerman's proof on the global existence of small amplitude solutions to nonlinear Klein-Gordon equations in four space-time dimensions, as established in his paper from 1985. We consider initial data with small amplitude and compact support and aim prove the global existence and uniform decay of smooth solutions. We establish that solutions exist globally if the initial data satisfy a suitable smallness condition. Key analytical tools include generalized Sobolev norms and uniform decay estimates for the associated linear problem. The solutions exhibit a decay rate of $t^{-5/4}$, uniform in time and space. This result is achieved by combining the energy method, perturbed Klein-Gordon techniques, and Sobolev inequalities.

We establish a linear $L^p$ rate of convergence, $1

We report on the complete computation of the mixed QCD-electroweak corrections to the neutral-current Drell-Yan process. Our calculation holds in the entire range of dilepton invariant masses. We present phenomenological results for several kinematical distributions in the case of bare muons both in the resonant region and for high invariant masses. We also consider the forward-backward asymmetry, which is a key observable to measure the weak mixing angle. We finally extend our calculation to dressed leptons and compare our results in the massless limit to those available in the literature., Comment: 27 pages, 7 Figures, and 2 Tables

We consider a spinning test particle around a rotating black hole and compare the Mathisson-Papapetrou-Dixon (MPD) formalism under the Tulczyjew-Dixon spin supplementary condition to the test-mass limit of the effective-one-body (EOB) Hamiltonian of [Phys. Rev. D.90, 044018(2014)], with enhanced spin-orbit sector. We focus on circular equatorial orbits: we first compare the constants of motion at their linear in secondary spin approximation and then we compute the gravitational-wave (GW) fluxes using a frequency domain Teukolsky equation solver. We find no difference between the EOB and MPD fluxes when the background spacetime is Schwarzschild, while the difference for a Kerr background is maximum for large, positive spins. Our work could be considered as a first step to improve the radiation reaction of the EOB model, in view of the needs of the next-generation of GW detectors., Comment: 16 pages, 9 figures

We propose a method to perform an exact calculation of one-loop quantum corrections to black hole entropy in terms of Virasoro semiclassical blocks. We analyse in detail four-dimensional Kerr black hole and show that in the near-extremal limit a branch of long-lived modes arises. We prove that the contribution of these modes accounts for a $(s-1/2)\log T_{\text{Hawking}}$ correction to the entropy for massless particles of spin $s=1,2$. We show that in the full calculation performed in the exact Kerr background the leading contribution actually is sourced by the near-horizon region only, and as such has a universal validity for any asymptotic behavior at infinity., Comment: 7+3 pages. Comments welcome

Recent measurements of the galaxy 4-Point Correlation Function (4PCF) have seemingly detected non-zero parity-odd modes at high significance. Since gravity, the primary driver of galaxy formation and evolution is parity-even, any parity violation, if genuine, is likely to have been produced by some new parity-violating mechanism in the early Universe. Here we investigate an inflationary model with a Chern-Simons interaction between an axion and a $U(1)$ gauge field, where the axion itself is the inflaton field. Evaluating the trispectrum (Fourier-space analog of the 4PCF) of the primordial curvature perturbations is an involved calculation with very high-dimensional loop integrals. We demonstrate how to simplify these integrals and perform all angular integrations analytically by reducing the integrals to convolutions and exploiting the Convolution Theorem. This leaves us with low-dimensional radial integrals that are much more amenable to efficient numerical evaluation. This paper is the first in a series in which we will use these results to compute the full late-time 4PCF for axion inflation, thence enabling constraints from upcoming 3D spectroscopic surveys such as Dark Energy Spectroscopic Instrument (DESI), Euclid, or Roman., Comment: 60 pages, 14 figures, submitted

We present a quantitative model for tracking dangerous AI capabilities over time. Our goal is to help the policy and research community visualise how dangerous capability testing can give us an early warning about approaching AI risks. We first use the model to provide a novel introduction to dangerous capability testing and how this testing can directly inform policy. Decision makers in AI labs and government often set policy that is sensitive to the estimated danger of AI systems, and may wish to set policies that condition on the crossing of a set threshold for danger. The model helps us to reason about these policy choices. We then run simulations to illustrate how we might fail to test for dangerous capabilities. To summarise, failures in dangerous capability testing may manifest in two ways: higher bias in our estimates of AI danger, or larger lags in threshold monitoring. We highlight two drivers of these failure modes: uncertainty around dynamics in AI capabilities and competition between frontier AI labs. Effective AI policy demands that we address these failure modes and their drivers. Even if the optimal targeting of resources is challenging, we show how delays in testing can harm AI policy. We offer preliminary recommendations for building an effective testing ecosystem for dangerous capabilities and advise on a research agenda., Comment: 26 pages, 15 figures

Let $M_i$, for $i=1,2$, be a K\"ahler manifold, and let $G$ be a Lie group acting on $M_i$ by K\"ahler isometries. Suppose that the action admits a momentum map $\mu_i$ and let $N_i:=\mu_i^{-1}(0)$ be a regular level set. When the action of $G$ on $N_i$ is proper and free, the Meyer--Marsden--Weinstein quotient $P_i:=N_i/G$ is a K\"ahler manifold and $\pi_i:N_i\to P_i$ is a principal fiber bundle with base $P_i$ and characteristic fiber $G$. In this paper, we define an almost complex structure for the manifold $N_1\times N_2$ and give necessary and sufficient conditions for its integrability. In the integrable case, we find explicit holomorphic charts for $N_1\times N_2$. As applications, we consider a non integrable almost-complex structure on the product of two complex Stiefel manifolds and the infinite Calabi-Eckmann manifolds $\mathbb S^{2n+1}\times S(\mathcal{H})$, for $n\geq 1$, where $S(\mathcal{H})$ denotes the unit sphere of an infinite dimensional Hilbert space $\mathcal{H}$, Comment: 7 pages

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024, building on the initial discussions during the inaugural workshop held at CERN in March 2023. Like the summary of the first workshop, this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions., Comment: Summary of the second Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at Imperial College London: https://indico.cern.ch/event/1369392/

We propose a revised formulation of General Relativity for cosmological contexts, in which the Einstein constant varies with the energy density of the Universe. We demonstrate that this modification has no direct phenomenological impact on the Universe's dynamics or on particle motion within the expanding cosmos. Assuming a state close to vacuum, here defined by the vanishing product of the Einstein coupling constant and the Universe's energy density, we perform a Taylor expansion of the theory. In this framework, the vacuum energy problem is addressed, and an additional constant pressure term, which induces a Chaplygin-like contribution to the dark energy equation of state, arises in the late-time dynamics. The correction to the late-time Hubble parameter is investigated by comparing theoretical predictions with the late Universe observational data. Our findings indicate that the current value of the vacuum energy is consistent with zero. Alternatively, the expansion used in our formulation would no longer be valid if the current state significantly deviates from the assumed near-vacuum condition. Implications of the modified $\Lambda$CDM model with respect to the Hubble tension are also discussed., Comment: 17 pages, 3 figures

Merger events are thought to be an important phase in the assembly of massive galaxies. At the same time, Active Galactic Nuclei (AGN) play a fundamental role in the evolution of their star formation histories. Both phenomena can be observed at work in NGC 6240, a local prototypical merger, classified as an UltraLuminous InfraRed Galaxy (ULIRG) thanks to its elevated infrared luminosity. Interestingly, NGC 6240 hosts two AGN separated by 1.5''(~ 735 pc), detected in both X-ray and radio band. Taking advantage of the unprecedented sensitivity and wavelength coverage provided by the Integral Field Unit (IFU) of the NIRSpec instrument onboard JWST, we observed the nuclear region of NGC 6240 in a FoV of 3.7'' x 3.7''(1.9 x 1.9 kpc^2), to investigate gas kinematics and InterStellar Medium (ISM) properties with a high spatial resolution of ~ 0.1'' (or ~ 50 pc). We separated the different gas kinematic components through multi-Gaussian fitting and studied the excitation properties of the ISM from the NIR diagnostic diagram based on the H_2 1-0 S(1)/BrGamma and [Fe II]1.257micron/PaBeta lines ratios. We isolated the ionization cones of the two nuclei, and detected coronal lines emission from both of them. Using H_2 line ratios, we found that the molecular hydrogen gas is excited mostly by thermal processes. We computed a hot molecular gas mass of 1.3 x 10^5 M_sun and an ionized gas mass in the range of 10^5 - 10^7 M_sun. We studied with unprecedented spatial resolution and sensitivity the kinematics of the molecular and ionized gas phases. We revealed the complex structure of the molecular gas and found a blueshifted outflow near the Southern nucleus, together with filaments connecting a highly redshifted H_2 cloud with the two nuclei. We speculate on the possible nature of this H_2 cloud and propose two possible scenarios: either outflowing gas, or a tidal cloud falling onto the nuclei., Comment: 27 pages, 25 figures. Accepted for publication in A&A on 03/01/2025

InAs on Insulator (InAsOI) has recently been demonstrated as a promising platform to develop hybrid semiconducting-superconducting electronics, which features an InAs epilayer grown onto a cryogenic insulating InAlAs metamorphic buffer. The miniaturization of Si microchips has progressed significantly due to the integration of high permittivity (high-k) gate insulators, compared to the conventional thermally-growth SiO2. Here, we investigate the gate-tunable electrical properties of InAsOI-based Josephson Field Effect Transistors (JoFETs) featuring different high-k gate insulators, namely, HfO2 and Al2O3. With both dielectrics, the JoFETs can entirely suppress the switching current and increase the normal state resistance by 10-20 times using negative gate voltages. The HfO2-JoFETs exhibit improved gate-tunable electrical performance compared to those achieved with Al2O3-JoFETs, which is related to the higher permittivity of the insulator. Gate-dependent electrical properties of InAsOI-based JoFETs were evaluated in the temperature range from 50 mK to 1 K. Moreover, under the influence of an out-of-plane magnetic field, JoFETs exhibited an unconventional Fraunhofer diffraction pattern., Comment: 16 pages, 4 figures, supporting information at the end of the paper

We revisit the long-only trend-following strategy presented in A Century of Profitable Industry Trends by Zarattini and Antonacci, which achieved exceptional historical performance with an 18.2% annualized return and a Sharpe Ratio of 1.39. While the results outperformed benchmarks, practical implementation raises concerns about robustness and evolving market conditions. This study explores modifications addressing reliance on T-bills, alternative fallback allocations, and industry exclusions. Despite attempts to enhance adaptability through momentum signals, parameter optimization, and Walk-Forward Analysis, results reveal persistent challenges. The results highlight challenges in adapting historical strategies to modern markets and offer insights for future trend-following frameworks.

In analog neuromorphic chips, designers can embed computing primitives in the intrinsic physical properties of devices and circuits, heavily reducing device count and energy consumption, and enabling high parallelism, because all devices are computing simultaneously. Neural network parameters can be stored in local analog non-volatile memories (NVMs), saving the energy required to move data between memory and logic. However, the main drawback of analog sub-threshold electronic circuits is their dramatic temperature sensitivity. In this paper, we demonstrate that a temperature compensation mechanism can be devised to solve this problem. We have designed and fabricated a chip implementing a two-layer analog neural network trained to classify low-resolution images of handwritten digits with a low-cost single-poly complementary metal-oxide-semiconductor (CMOS) process, using unconventional analog NVMs for weight storage. We demonstrate a temperature-resilient analog neuromorphic chip for image recognition operating between 10$^{\circ}$C and 60$^{\circ}$C without loss of classification accuracy, within 2\% of the corresponding software-based neural network in the whole temperature range., Comment: 12 pages, 8 figures

We characterize the Leray--Hopf solutions of the 2D inhomogeneous Navier--Stokes system that become strong for positive times. This characterization relies on the strong energy inequality and the regularity properties of the pressure. As an application, we establish a weak-strong uniqueness result and provide a unified framework for several recent advances in the field.

Modelling the progression of Degenerative Diseases (DD) is essential for detection, prevention, and treatment, yet it remains challenging due to the heterogeneity in disease trajectories among individuals. Factors such as demographics, genetic conditions, and lifestyle contribute to diverse phenotypical manifestations, necessitating patient stratification based on these variations. Recent methods like Subtype and Stage Inference (SuStaIn) have advanced unsupervised stratification of disease trajectories, but they face potential limitations in robustness, interpretability, and temporal granularity. To address these challenges, we introduce Disease Progression Modelling and Stratification (DP-MoSt), a novel probabilistic method that optimises clusters of continuous trajectories over a long-term disease time-axis while estimating the confidence of trajectory sub-types for each biomarker. We validate DP-MoSt using both synthetic and real-world data from the Parkinson's Progression Markers Initiative (PPMI). Our results demonstrate that DP-MoSt effectively identifies both sub-trajectories and subpopulations, and is a promising alternative to current state-of-the-art models., Comment: Longitudinal Disease Tracking and Modelling with Medical Images and Data, Oct 2024, Marrachech, Morocco

In general, there is a mismatch between a finite element model of a structure and its real behaviour. In aeronautics, this mismatch must be small because finite element models are a fundamental part of the development of an aircraft and of increasing importance with the trend to more flexible wings in modern designs. Finite element model updating can be computationally expensive for complex structures and surrogate models can be employed to reduce the computational burden. A novel approach for finite element model updating, namely assembly-like, is proposed and validated using real experimental data. The assembly-like model updating framework implies that the model is updated as parts are assembled. Benchmarking against the classical global, or one-shot, approach demonstrates that the proposed method is more computationally efficient since it takes 20% fewer iterations to obtain convergence, also using fewer parameters for the model evaluations. Despite the increase in computational performance, the new approach retains the fidelity of the global approach.

One of the main obstacles in exoplanet detection when using the radial velocity (RV) technique is the presence of stellar activity signal induced by magnetic regions. In this context, a realistic simulated dataset that can provide photometry and spectroscopic outputs is needed for method development. The goal of this paper is to describe two realistic simulations of solar activity obtained from SOAP-GPU and to compare them with real data obtained from the HARPS-N solar telescope. We describe two different methods of modeling solar activity using SOAP-GPU. The first models the evolution of active regions based on the spot number as a function of time. The second method relies on the extraction of active regions from the Solar Dynamics Observatory (SDO) data. The simulated spectral time series generated with the first method shows a long-term RV behavior similar to that seen in the HARPS-N solar observations. The effect of stellar activity induced by stellar rotation is also well modeled with prominent periodicities at the stellar rotation period and its first harmonic. The comparison between the simulated spectral time series generated using SDO images and the HARPS-N solar spectra shows that SOAP-GPU can precisely model the RV time series of the Sun to a precision better than 0.9 m/s. By studying the width and depth variations of each spectral line in the HARPS-N solar and SOAP-GPU data, we find a strong correlation between the observation and the simulation for strong spectral lines, therefore supporting the modeling of the stellar activity effect at the spectral level. These simulated solar spectral time series serve as a useful test bed for evaluating spectral-level stellar activity mitigation techniques., Comment: Accepted for publication in A&A

We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional dynamical systems. The Galerkin residual method is employed to find an approximate solution to the invariance equation using a Newton iteration on the coefficients of a monomial basis expansion of the solution. These solutions to the invariance equations can then be used to construct reduced-order models. We assess the ability of the method to solve the invariance PDE system as well as to achieve moment matching and recover a system's steady-state behaviour for linear and nonlinear signal generators with system dynamics up to $n=1000$ dimensions., Comment: 26 pages, 3 figures, submitted to SIAM Journal on Scientific Computing

Open stop-band (OSB) mitigation techniques are commonly used to improve the far-field radiating properties of leakywave antennas based on periodic structures. Recently, leaky waves have been proposed to focus energy in the near field through Bessel beams. However, the focusing character of Bessel beams is notably limited to a maximum distance known as the nondiffractive range. In this work, an OSB mitigation technique is originally exploited to significantly extend the nondiffractive range of a Bessel beam generated by a leaky-wave launcher in the microwave/millimeter-wave range. A comprehensive analysis of this device is presented, comparing the performance of the proposed launcher with the typical structure of a leaky-wave Bessel-beam launcher where the OSB is not suppressed. Theoretical results corroborated by full-wave simulations demonstrate that the proposed device, designed around 30 GHz, achieves an impressive nondiffractive range of approximately 25 m, which corresponds to 2500 vacuum wavelengths and to 50 times its aperture diameter of 50 cm. These results look particularly attractive for, e.g., near-field communications and wireless power transfer applications, where focusing energy in narrow spots and over large distances is a key factor., Comment: 5 pages, 4 figures, letter format

Classically simulating circuits with bosonic codes is a challenging task due to the prohibitive cost of simulating quantum systems with many, possibly infinite, energy levels. We propose an algorithm to simulate circuits with encoded Gottesman-Kitaev-Preskill states, specifically for odd-dimensional encoded qudits. Our approach is tailored to be especially effective in the most challenging but practically relevant regime, where the codeword states exhibit high (but finite) squeezing. Our algorithm leverages the Zak-Gross Wigner function introduced by J. Davis et al. [arXiv:2407.18394], which represents infinitely squeezed encoded stabilizer states positively. The runtime of the algorithm scales with the amount of negativity of this Wigner function, enabling fast simulation of certain large-scale circuits with a high degree of squeezing., Comment: 22 pages, 2 figures

We propose powering a quantum clock with the non-thermal resources offered by the stationary state of an integrable quantum spin chain, driven out of equilibrium by a quench in a parameter of our choice. Analyzing the bias conditions of the clock, we establish a direct connection with the negativity of the steady-state response function. Using experimentally relevant examples of quantum spin chains, we suggest crossing a phase transition point is crucial for optimal performance. The coupling takes place through a global observable and, even in this case, the battery lifespan is found to be extensive in its size.

Stars are unique bodies of the Universe where self-gravity compress matter to such high temperature and density that several nuclear fusion reactions ignite, providing enough feedback against further compression for a time that can be even larger than the age of the universe. The main property of a star is its mass because it determines its structure, evolutionary history, age, and ultimate fate. Depending on this quantity, stars are broadly classified as low-mass stars, like our Sun, intermediate mass stars as the variable star Delta Cephei, and massive stars as Betelgeuse, a red supergiant star in Orion constellation. Here we will introduce the basic notions useful to understand stellar evolution of low- and intermediate- mass stars. This mass range (0.1 M$_{\odot}$ - 10.0 M$_{\odot}$) deserves special attention, as it contains most of the stars in the universe. This chapter will focus on how these stars form, the processes that drive their evolution, and key details regarding their structure. Finally, we will discuss the death of such stars, emphasizing the unique fates associated with low- and intermediate-mass stars., Comment: This is a pre-print of a chapter for the Encyclopedia of Astrophysics (edited by I. Mandel, section editor F.R.N. Schneider) to be published by Elsevier as a Reference Module

Early detection of illnesses and pest infestations in fruit cultivation is critical for maintaining yield quality and plant health. Computer vision and robotics are increasingly employed for the automatic detection of such issues, particularly using data-driven solutions. However, the rarity of these problems makes acquiring and processing the necessary data to train such algorithms a significant obstacle. One solution to this scarcity is the generation of synthetic high-quality anomalous samples. While numerous methods exist for this task, most require highly trained individuals for setup. This work addresses the challenge of generating synthetic anomalies in an automatic fashion that requires only an initial collection of normal and anomalous samples from the user - a task that is straightforward for farmers. We demonstrate the approach in the context of table grape cultivation. Specifically, based on the observation that normal berries present relatively smooth surfaces, while defects result in more complex textures, we introduce a Dual-Canny Edge Detection (DCED) filter. This filter emphasizes the additional texture indicative of diseases, pest infestations, or other defects. Using segmentation masks provided by the Segment Anything Model, we then select and seamlessly blend anomalous berries onto normal ones. We show that the proposed dataset augmentation technique improves the accuracy of an anomaly classifier for table grapes and that the approach can be generalized to other fruit types.

Physics Playground is an immersive Virtual Reality (VR) application designed for educational purposes, featuring a virtual laboratory where users interact with various physics phenomena through guided experiments. This study aims to evaluate the application's design and educational content to facilitate its integration into classroom settings. A quantitative data collection investigated learning outcomes, related confidence, user experience, and perceived cognitive load, through a 2x2 within-between subjects setup, with participants divided into two conditions (VR vs. slideshow) and knowledge levels assessed twice (pre- and post-tests). A qualitative approach included interviews and a focus group to explore education experts' opinions on the overall experience and didactic content. Results showed an improvement in physics knowledge and confidence after the learning experience compared to baseline, regardless of the condition. Despite comparable perceived cognitive load, slideshow learning was slightly more effective in enhancing physics knowledge. However, both qualitative and quantitative results highlighted the immersive advantage of VR in enhancing user satisfaction. This approach pointed out limitations and advantages of VR-based learning, but more research is needed to understand how it can be implemented into broader teaching strategies., Comment: Presented at Intelligent Human Computer Interaction (IHCI) 2024

We study the effective bosonic string that describes confining flux tubes in three-dimensional SU(N) Yang--Mills theories. Although the low-energy properties are universal and well described by the Nambu--Got\=o action, the subtle dependence on the gauge group is embedded in a series of corrections, which remain undetermined, appearing in the expansion around the limit of an infinitely long string. We extract the first two of these corrections from a set of high-precision Monte Carlo simulations of Polyakov loop correlators at finite temperatures close to the deconfinement transition. We present and compare the results of new lattice simulations for theories with N=3 and N=6 color charges, along with an improved estimate for the N=2 case, discussing the approach to the large-N limit. We show that our results are compatible with analytical bounds derived from the S-matrix bootstrap approach. Additionally, we present a new test of the Svetitsky--Yaffe conjecture for the SU(3) theory in three dimensions, showing that our results for the correlator of Polyakov loops perfectly agree with the predictions obtained using a conformal perturbation approach to the two-dimensional three-state Potts model, Comment: arXiv admin note: substantial text overlap with arXiv:2407.10678

AI control protocols are plans for usefully deploying AI systems in a way that is safe, even if the AI intends to subvert the protocol. Previous work evaluated protocols by subverting them with a human-AI red team, where an AI follows the human-written strategy. This paper investigates how well AI systems can generate and act on strategies for subverting control protocols whilst operating without private memory. Usually, decision-makers only need the ability to generate optimal plans. However, to subvert a protocol, an AI system must be able to reliably generate optimal plans in each context; coordinate plans with other instances of itself without communicating; and take actions with well-calibrated probabilities. We develop evaluations for a model's ability to generate subversion strategies and develop affordance experiments that help isolate component capabilities. Our initial evaluations with Claude-3.5-sonnet highlight reasons why statelessly strategizing to subvert control protocols might be hard. We hope that our work can serve as a starting point for evaluations aimed at assessing whether a model is capable of strategizing to subvert control protocols., Comment: Accepted at AAAI datasafe workshop

We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle. Unlike conventional time-stepping approaches, our scheme computes the entire state trajectory over a finite time window by minimizing a physically motivated loss function that enforces the Schr\"odinger's equation. The variational state is parametrized with a Galerkin-inspired ansatz based on a time-dependent linear combination of time-independent Neural Quantum States. This structure effectively captures the relevant dynamical frequencies in the time evolution and is particularly well-suited for exploring long-time dynamics. We showcase the method's effectiveness by simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D. By extracting the asymptotic long-time evolution, we uncover signatures of ergodicity breaking and absence of thermalization in two dimensions. Overall, the method presented here shows competitive performance compared to state-of-the-art time-dependent variational approaches and highlight the potential to explore previously inaccessible dynamical regimes of strongly interacting quantum systems., Comment: 6 + 5 pages, 5 figures

In this paper, we present a novel framework to synthesize robust strategies for discrete-time nonlinear systems with random disturbances that are unknown, against temporal logic specifications. The proposed framework is data-driven and abstraction-based: leveraging observations of the system, our approach learns a high-confidence abstraction of the system in the form of an uncertain Markov decision process (UMDP). The uncertainty in the resulting UMDP is used to formally account for both the error in abstracting the system and for the uncertainty coming from the data. Critically, we show that for any given state-action pair in the resulting UMDP, the uncertainty in the transition probabilities can be represented as a convex polytope obtained by a two-layer state discretization and concentration inequalities. This allows us to obtain tighter uncertainty estimates compared to existing approaches, and guarantees efficiency, as we tailor a synthesis algorithm exploiting the structure of this UMDP. We empirically validate our approach on several case studies, showing substantially improved performance compared to the state-of-the-art.

The aim of inverse reinforcement learning (IRL) is to infer an agent's preferences from observing their behaviour. Usually, preferences are modelled as a reward function, $R$, and behaviour is modelled as a policy, $\pi$. One of the central difficulties in IRL is that multiple preferences may lead to the same observed behaviour. That is, $R$ is typically underdetermined by $\pi$, which means that $R$ is only partially identifiable. Recent work has characterised the extent of this partial identifiability for different types of agents, including optimal and Boltzmann-rational agents. However, work so far has only considered agents that discount future reward exponentially: this is a serious limitation, especially given that extensive work in the behavioural sciences suggests that humans are better modelled as discounting hyperbolically. In this work, we newly characterise partial identifiability in IRL for agents with non-exponential discounting: our results are in particular relevant for hyperbolical discounting, but they also more generally apply to agents that use other types of (non-exponential) discounting. We significantly show that generally IRL is unable to infer enough information about $R$ to identify the correct optimal policy, which entails that IRL alone can be insufficient to adequately characterise the preferences of such agents.

Probe Requests are Wi-Fi management frames periodically sent by devices during network discovery. Tracking Probe Requests over time offers insights into movement patterns, traffic flows, and behavior trends, which are keys in applications such as urban planning, human mobility analysis, and retail analytics. To protect user privacy, techniques such as MAC address randomization are employed, periodically altering device MAC addresses to limit tracking. However, research has shown that these privacy measures can be circumvented. By analyzing the Information Elements (IE) within the Probe Request body, it is possible to fingerprint devices and track users over time. This paper presents a machine learning-based approach for fingerprinting Wi-Fi Probe Requests in a compact fashion. We utilize Asymmetric Pairwise Boosting to learn discriminating filters which are then used to process specific bit sequences in Probe Request frames, and quantize the results into a compact binary format. Extensive evaluation on public datasets demonstrates a two-order-of-magnitude storage reduction compared to existing methods while maintaining robust fingerprinting performance., Comment: Pre-print

A challenge in high-dimensional inverse problems is developing iterative solvers to find the accurate solution of regularized optimization problems with low computational cost. An important example is computed tomography (CT) where both image and data sizes are large and therefore the forward model is costly to evaluate. Since several years algorithms from stochastic optimization are used for tomographic image reconstruction with great success by subsampling the data. Here we propose a novel way how stochastic optimization can be used to speed up image reconstruction by means of image domain sketching such that at each iteration an image of different resolution is being used. Hence, we coin this algorithm ImaSk. By considering an associated saddle-point problem, we can formulate ImaSk as a gradient-based algorithm where the gradient is approximated in the same spirit as the stochastic average gradient am\'elior\'e (SAGA) and uses at each iteration one of these multiresolution operators at random. We prove that ImaSk is linearly converging for linear forward models with strongly convex regularization functions. Numerical simulations on CT show that ImaSk is effective and increasing the number of multiresolution operators reduces the computational time to reach the modeled solution., Comment: 26 pages, 11 figures, submitted to SIAM Journal on Imaging Sciences

It is known that the same physical system can be described by different effective theories depending on the scale at which it is observed. In this work, we formulate a prescription for finding the unitary that best approximates the large scale dynamics of a quantum system evolving discretely in time, as it is the case for digital quantum simulators. We consider the situation in which the degrees of freedom of the system can be divided between an IR part that we can observe, and a UV part that we cannot observe. Following a principle of minimal dissipation, our goal is to find the unitary dynamics that best approximates the (generally non unitary) time evolution of the IR degrees of freedom. We first prove that when the IR and UV degrees of freedom are weakly coupled, the unitary that maximises the fidelity is given by a mean-field dynamics and the error is given by a sum of energy variances. We then apply our results to a one dimensional quantum walk, which is known to reproduce the Dirac equation in the small mass and momenta limit. We find that in this limit the effective IR dynamics is obtained by a mass redefinition., Comment: 9 pages, 2 figures

Two-stage stochastic programs become computationally challenging when the number of scenarios representing parameter uncertainties grows. Motivated by this, we propose the TULIP-algorithm ("Two-step warm start method Used for solving Large-scale stochastic mixed-Integer Problems"), a two-step approach for solving two-stage stochastic (mixed) integer linear programs with an exponential number of constraints. In this approach, we first generate a reduced set of representative scenarios and solve the root node of the corresponding integer linear program using a cutting-plane method. The generated constraints are then used to accelerate solving the original problem with the full scenario set in the second phase. We demonstrate the generic effectiveness of TULIP on two benchmark problems: the Stochastic Capacitated Vehicle Routing Problem and the Two-Stage Stochastic Steiner Forest Problem. The results of our extensive numerical experiments show that TULIP yields significant computational gains compared to solving the problem directly with branch-and-cut.

Systems with pronounced spin anisotropy play a pivotal role in advancing magnetization switching and spin-wave generation mechanisms, which are fundamental for spintronic technologies. Quasi-van der Waals ferromagnets, particularly Cr$_{1+\delta}$Te$_2$ compounds, represent seminal materials in this field, renowned for their delicate balance between frustrated layered geometries and magnetism. Despite extensive investigation, the precise nature of their magnetic ground state, typically described as a canted ferromagnet, remains contested, as does the mechanism governing spin reorientation under external magnetic fields and varying temperatures. In this work, we leverage a multimodal approach, integrating complementary techniques, to reveal that Cr$_{1+\delta}$Te$_2$ ($\delta = 0.25 - 0.50$) hosts a previously overlooked magnetic phase, which we term orthogonal-ferromagnetism. This single phase consists of alternating atomically sharp single layers of in-plane and out-of-plane ferromagnetic blocks, coupled via exchange interactions and as such, it differs significantly from crossed magnetism, which can be achieved exclusively by stacking multiple heterostructural elements together. Contrary to earlier reports suggesting a gradual spin reorientation in CrTe$_2$-based systems, we present definitive evidence of abrupt spin-flop-like transitions. This discovery, likely due to the improved crystallinity and lower defect density in our samples, repositions Cr$_{1+\delta}$Te$_2$ compounds as promising candidates for spintronic and orbitronic applications, opening new pathways for device engineering.