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The codling moth pest poses a significant threat to global crop production, with potential losses of up to 80% in apple orchards. Special camera-based sensor nodes are deployed in the field to record and transmit images of trapped insects to monitor the presence of the pest. This paper investigates the embedding of computer vision algorithms in the sensor node using a novel State-of-the-Art Microcontroller Unit (MCU), the GreenWaves Technologies' GAP9 System-on-Chip, which combines 10 RISC-V general purposes cores with a convolution hardware accelerator. We compare the performance of a lightweight Viola-Jones detector algorithm with a Convolutional Neural Network (CNN), MobileNetV3-SSDLite, trained for the pest detection task. On two datasets that differentiate for the distance between the camera sensor and the pest targets, the CNN generalizes better than the other method and achieves a detection accuracy between 83% and 72%. Thanks to the GAP9's CNN accelerator, the CNN inference task takes only 147 ms to process a 320$\times$240 image. Compared to the GAP8 MCU, which only relies on general-purpose cores for processing, we achieved 9.5$\times$ faster inference speed. When running on a 1000 mAh battery at 3.7 V, the estimated lifetime is approximately 199 days, processing an image every 30 seconds. Our study demonstrates that the novel heterogeneous MCU can perform end-to-end CNN inference with an energy consumption of just 4.85 mJ, matching the efficiency of the simpler Viola-Jones algorithm and offering power consumption up to 15$\times$ lower than previous methods. Code at: https://github.com/Bomps4/TAFE_Pest_Detection, Comment: 11 pages, 7 figures, 4 tables

This research introduces an innovative method for the early screening of cardiorespiratory diseases based on an acquisition protocol, which leverages commodity smartphone's Inertial Measurement Units (IMUs) and deep learning techniques. We collected, in a clinical setting, a dataset featuring recordings of breathing kinematics obtained by accelerometer and gyroscope readings from five distinct body regions. We propose an end-to-end deep learning pipeline for early cardiorespiratory disease screening, incorporating a preprocessing step segmenting the data into individual breathing cycles, and a recurrent bidirectional module capturing features from diverse body regions. We employed Leave-one-out-cross-validation with Bayesian optimization for hyperparameter tuning and model selection. The experimental results consistently demonstrated the superior performance of a bidirectional Long-Short Term Memory (Bi-LSTM) as a feature encoder architecture, yielding an average sensitivity of $0.81 \pm 0.02$, specificity of $0.82 \pm 0.05$, F1 score of $0.81 \pm 0.02$, and accuracy of $80.2\% \pm 3.9$ across diverse seed variations. We also assessed generalization capabilities on a skewed distribution, comprising exclusively healthy patients not used in training, revealing a true negative rate of $74.8 \% \pm 4.5$. The sustained accuracy of predictions over time during breathing cycles within a single patient underscores the efficacy of the preprocessing strategy, highlighting the model's ability to discern significant patterns throughout distinct phases of the respiratory cycle. This investigation underscores the potential usefulness of widely available smartphones as devices for timely cardiorespiratory disease screening in the general population, in at-home settings, offering crucial assistance to public health efforts (especially during a pandemic outbreaks, such as the recent COVID-19).

With the rise of Embodied Foundation Models (EFMs), most notably Small Language Models (SLMs), adapting Transformers for edge applications has become a very active field of research. However, achieving end-to-end deployment of SLMs on microcontroller (MCU)-class chips without high-bandwidth off-chip main memory access is still an open challenge. In this paper, we demonstrate high-efficiency end-to-end SLM deployment on a multicore RISC-V (RV32) MCU augmented with ML instruction extensions and a hardware neural processing unit (NPU). To automate the exploration of the constrained, multi-dimensional memory vs. computation tradeoffs involved in aggressive SLM deployment on heterogeneous (multicore+NPU) resources, we introduce Deeploy, a novel Deep Neural Network (DNN) compiler, which generates highly-optimized C code requiring minimal runtime support. We demonstrate that Deeploy generates end-to-end code for executing SLMs, fully exploiting the RV32 cores' instruction extensions and the NPU: We achieve leading-edge energy and throughput of \SI{490}{\micro\joule \per Token}, at \SI{340}{Token \per \second} for an SLM trained on the TinyStories dataset, running for the first time on an MCU-class device without external memory., Comment: Accepted for publication at ESWEEK - CASES 2024

AI-generated synthetic media, also called Deepfakes, have significantly influenced so many domains, from entertainment to cybersecurity. Generative Adversarial Networks (GANs) and Diffusion Models (DMs) are the main frameworks used to create Deepfakes, producing highly realistic yet fabricated content. While these technologies open up new creative possibilities, they also bring substantial ethical and security risks due to their potential misuse. The rise of such advanced media has led to the development of a cognitive bias known as Impostor Bias, where individuals doubt the authenticity of multimedia due to the awareness of AI's capabilities. As a result, Deepfake detection has become a vital area of research, focusing on identifying subtle inconsistencies and artifacts with machine learning techniques, especially Convolutional Neural Networks (CNNs). Research in forensic Deepfake technology encompasses five main areas: detection, attribution and recognition, passive authentication, detection in realistic scenarios, and active authentication. This paper reviews the primary algorithms that address these challenges, examining their advantages, limitations, and future prospects.

Understanding and accurately predicting hydrogen diffusion in materials is challenging due to the complex interactions between hydrogen defects and the crystal lattice. These interactions span large length and time scales, making them difficult to address with standard ab initio techniques. This work addresses this challenge by employing accelerated machine learning (ML) molecular dynamics simulations through active learning. We conduct a comparative study of different ML-based interatomic potential schemes, including VASP, MACE, and CHGNet, utilizing various training strategies such as on-the-fly learning, pre-trained universal models, and fine-tuning. We obtain an optimal hydrogen diffusion coefficient value of \(2.1 \cdot 10^{-8}\) m\(^2\)/s at 673 K in MgH\(_{0.06}\), which aligns exceptionally well with experimental results, underlining the efficacy and accuracy of ML-assisted methodologies in the context of diffusive dynamics. Particularly, our procedure significantly reduces the computational effort associated with traditional transition state calculations or ad-hoc designed interatomic potentials. The results highlight the limitations of pre-trained universal solutions for defective materials and how they can be improved by fine-tuning. Specifically, fine-tuning the models on a database produced during on-the-fly training of VASP ML force field allows the retrieving of DFT-level accuracy at a fraction of the computational cost.

Symmetric Multi-Processing (SMP) based on cache coherency is crucial for high-end embedded systems like automotive applications. RISC-V is gaining traction, and open-source hardware (OSH) platforms offer solutions to issues such as IP costs and vendor dependency. Existing multi-core cache-coherent RISC-V platforms are complex and not efficient for small embedded core clusters. We propose an open-source SystemVerilog implementation of a lightweight snoop-based cache-coherent cluster of Linux-capable CVA6 cores. Our design uses the MOESI protocol via the Arm's AMBA ACE protocol. Evaluated with Splash-3 benchmarks, our solution shows up to 32.87% faster performance in a dual-core setup and an average improvement of 15.8% over OpenPiton. Synthesized using GF 22nm FDSOI technology, the Cache Coherency Unit occupies only 1.6% of the system area., Comment: 4 pages, 4 figures, DSD2024 and SEAA2024 Works in Progress Session AUG 2024; Updated the acknowledgments

Methyl cyanide is one of the simplest interstellar complex organic molecules, widely detected in young solar analogues, shocked regions, protoplanetary disks and comets. CH3CN can be considered a key species to explore the chemical connections between planet forming disks and comets. For such comparison to be meaningful kinetics data for the reactions leading to CH3CN formation and destruction must be updated. We focus on the destruction of methyl cyanide through collisions with He+. A combined experimental and theoretical methodology is employed to obtain cross sections (CSs) and branching ratios (BRs) as a function of collision energy, from which reaction rate coefficients $k(T)$ are calculated in the temperature range from 10 to 300 K. CSs and BRs are measured using a guided ion beam set-up. A theoretical treatment based on an analytical formulation of the potential energy surfaces (PESs) for the charge exchange process is developed. The method employs a Landau Zener model to obtain reaction probabilities at crossings between the entrance and exit PESs, and an adiabatic centrifugal sudden approximation to calculate CSs and k(T). Rates and BRs differ from those predicted from widely-used capture models. In particular, the rate coefficient at 10 K is estimated to be almost one order of magnitude smaller than what reported in the KIDA database. As for BRs, the charge exchange is completely dissociative and the most abundant fragments are HCCN+/CCNH+, HCNH+ and CH2+. Our results, combined with a revised chemical network for formation of CH3CN, support the hypothesis that methyl cyanide in protoplanetary disks could be mostly the product of gas-phase processes rather than grain chemistry, as currently proposed. These findings are expected to have implications in the comparison of the abundance ratios of N-bearing molecules observed in disks with cometary abundance ratios, Comment: 19 pages, 7 figures, full article

The Son Of X-Shooter (SOXS) will be the specialized facility to observe any transient event with a flexible scheduler at the ESO New Technology Telescope (NTT) at La Silla, Chile. SOXS is a single object spectrograph offering simultaneous spectral coverage in UV-VIS (350-850 nm) and NIR (800-2000 nm) wavelength regimes with an average of R~4500 for a 1arcsec slit. SOXS also has imaging capabilities in the visible wavelength regime. Currently, SOXS is being integrated at the INAF-Astronomical Observatory of Padova. Subsystem- and system-level tests and verification are ongoing to ensure and confirm that every requirement and performance are met. In this paper, we report on the integration and verification of SOXS as the team and the instrument prepare for the Preliminary Acceptance Europe (PAE).

We present Crab X-ray polarization measurements using IXPE data with a total exposure of 300ks, three times more than the initial 2022 discovery paper. Polarization is detected in three times more pulsar phase bins, revealing an S-shaped $+40^\circ$ polarization angle sweep in the main pulse and ${>}1\sigma$ departures from the OPTIMA optical polarization in both pulses, suggesting different radiation mechanisms or sites for the polarized emission at the two wavebands. Our polarization map of the inner nebula reveals a toroidal magnetic field, as seen in prior IXPE analyses. Along the southern jet, the magnetic field orientation relative to the jet axis changes from perpendicular to parallel and the polarization degree decreases by ${\sim}6\%$. These observations may be explained by kink instabilities along the jet or a collision with a dense, jet-deflecting medium at the tip. Using spectropolarimetric analysis, we find asymmetric polarization in the four quadrants of the inner nebula, as expected for a toroidal field geometry, and a spatial correlation between polarization degree and photon index., Comment: 14 pages, 7 figures, 3 tables. Accepted by The Astrophysical Journal

We present multiwavelength polarization measurements of the luminous blazar Mrk~501 over a 14-month period. The 2--8 keV X-ray polarization was measured with the Imaging X-ray Polarimetry Explorer (IXPE) with six 100-ks observations spanning from 2022 March to 2023 April. Each IXPE observation was accompanied by simultaneous X-ray data from NuSTAR, Swift/XRT, and/or XMM-Newton. Complementary optical-infrared polarization measurements were also available in the B, V, R, I, and J bands, as were radio polarization measurements from 4.85 GHz to 225.5 GHz. Among the first five IXPE observations, we did not find significant variability in the X-ray polarization degree and angle with IXPE. However, the most recent sixth observation found an elevated polarization degree at $>3\sigma$ above the average of the other five observations. The optical and radio measurements show no apparent correlations with the X-ray polarization properties. Throughout the six IXPE observations, the X-ray polarization degree remained higher than, or similar to, the R-band optical polarization degree, which remained higher than the radio value. This is consistent with the energy-stratified shock scenario proposed to explain the first two IXPE observations, in which the polarized X-ray, optical, and radio emission arises from different regions., Comment: Accepted for publication in ApJ

The discovery of pulsations in (at least) six ultraluminous X-ray sources (ULXs) has shown that neutron stars can accrete at (highly) super-Eddington rates, challenging the standard accretion theories. M51 ULX-7, with a spin signal of $P\simeq2.8$ s, is the pulsating ULX (PULX) with the shortest known orbital period ($P_\mathrm{orb}\simeq2$ d) and has been observed multiple times by XMM-Newton, Chandra, and NuSTAR. We report on the timing and spectral analyses of three XMM-Newton observations of M51 ULX-7 performed between the end of 2021 and the beginning of 2022, together with a timing re-analysis of XMM-Newton, Chandra, and NuSTAR archival observations. We investigated the spin signal by applying accelerated search techniques and studied the power spectrum through the fast Fourier transform, looking for (a)periodic variability in the source flux. We analysed the energy spectra of the 2021-2022 observations and compared them to the older ones. We report the discovery of a recurrent, significant ($>$3$\sigma$) broad complex at mHz frequencies in the power spectra of M51 ULX-7. We did not detect the spin signal, setting a 3$\sigma$ upper limit on the pulsed fraction of $\lesssim10\%$ for the single observation. The complex is significantly detected also in five Chandra observations performed in 2012. M51 ULX-7 represents the second PULX for which we have a significant detection of mHz-QPOs at super-Eddington luminosities. These findings suggest that one should avoid using the observed QPO frequency to infer the mass of the accretor in a ULX. The absence of spin pulsations when the broad complex is detected suggests that the mechanism responsible for the aperiodic modulation also dampens the spin signal's pulsed fraction. If true, this represents an additional obstacle in the detection of new PULXs, suggesting an even larger occurrence of PULXs among ULXs., Comment: 14 pages (12 main text + Appendix), 5 figures. Accepted for publication on A&A

Diffusion-based recommender systems have recently proven to outperform traditional generative recommendation approaches, such as variational autoencoders and generative adversarial networks. Nevertheless, the machine learning literature has raised several concerns regarding the possibility that diffusion models, while learning the distribution of data samples, may inadvertently carry information bias and lead to unfair outcomes. In light of this aspect, and considering the relevance that fairness has held in recommendations over the last few decades, we conduct one of the first fairness investigations in the literature on DiffRec, a pioneer approach in diffusion-based recommendation. First, we propose an experimental setting involving DiffRec (and its variant L-DiffRec) along with nine state-of-the-art recommendation models, two popular recommendation datasets from the fairness-aware literature, and six metrics accounting for accuracy and consumer/provider fairness. Then, we perform a twofold analysis, one assessing models' performance under accuracy and recommendation fairness separately, and the other identifying if and to what extent such metrics can strike a performance trade-off. Experimental results from both studies confirm the initial unfairness warnings but pave the way for how to address them in future research directions.

{The paper studies classical, type-free theories of truth and determinateness. Recently, Volker Halbach and Kentaro Fujimoto proposed a novel approach to classical determinate truth, in which determinateness is axiomatized by a primitive predicate. In the paper we propose a different strategy to develop theories of classical determinate truth in Halbach and Fujimoto's sense featuring a \emph{defined} determinateness predicate. This puts our theories of classical determinate truth in continuity with a standard approach to determinateness by authors such as Feferman and Reinhardt. The theories entail all principles of Fujimoto and Halbach's theories, and are proof-theoretically equivalent to Halbach and Fujimoto's CD+. They will be shown to be logically equivalent to a class of natural theories of truth, the \emph{classical closures of Kripke-Feferman truth}. The analysis of the proposed theories will also provide new insights on Fujimoto and Halbach's theories: we show that the latter cannot prove most of the axioms of the classical closures of Kripke-Feferman truth. This entails that, unlike what happens in our theories of truth and determinateness, Fujimoto and Halbach's \emph{inner theories} -- the sentences living under two layers of truth -- cannot be closed under standard logical rules of inference.}

We present a novel approach for evaluating Wannier functions, offering a new perspective on their role in many-body systems. Unlike traditional methods, such as the maximally localized Wannier functions approach, which focuses on minimizing the function tails, our approach emphasizes these tails. Using perturbative analytical approximations and extensive numerical simulations on an exactly solvable model, we address nonstandard Hubbard terms and demonstrate their critical influence on many-body dynamics. Specifically, we study tunneling dynamics in arbitrary double-well potentials, moving beyond the standard Hubbard model to include nonstandard terms such as density-induced tunneling and pair tunneling. Our results reveal that these terms significantly modify the dynamics predicted by the standard Hubbard model: density-induced tunneling modifies the single-particle tunneling parameter $\Omega_0$, while pair tunneling enables coherent propagation not captured by the standard model. We show that the discrepancies between the standard and nonstandard Hubbard models grow with increasing interaction strength, potentially leading to novel transport behaviors. However, at lower interaction strengths, both models converge, as nonstandard terms become negligible. These findings have important implications for phenomena like superconductivity in twisted bilayer graphene and metal-insulator transitions. Our model aligns well with numerical simulations of lowest-band parameters and is strongly supported by experimental observations of second-order atom tunneling in optical double-well potentials. This strong agreement with experimental data highlights the accuracy and potential of our approach in providing a more comprehensive framework for describing complex many-body systems than the standard Hubbard model., Comment: 29 pages, 16 figures

If ultralight boson fields exist, then vacuum misalignment populates them with nonzero relic abundance. For a broad range of particle mass $m$ the field condenses into fuzzy cores in massive galaxies. We use numerical simulations to test this idea, extending previous work (Blum and Teodori 2021) and focusing on ultralight dark matter (ULDM) that makes-up a subdominant fraction of the total dark matter density, consistent with observational constraints. Our simulations mimic galactic halos and explore different initial conditions and levels of sophistication in the modeling of the halo potential. For $m\sim10^{-25}$ eV ULDM cores act as approximate internal mass sheets in strong gravitational lensing, and could first be detected as an $H_0$ bias in cosmography: a scenario we dub AxionH0graphy. The mass sheet degeneracy is broken by finite core radius and by the dynamical displacement of cores from the halo center of mass, which introduce imaging distortions and restrict the $H_0$ bias limit of AxionH0graphy to $m\lesssim5\times10^{-25}$ eV. Cosmological simulations are called for to sharpen the predicted connection between the amplitude of ULDM galactic cores and the ULDM cosmological fraction., Comment: 15 pages, comments welcome!

The physics case for quarkonium-production studies accessible at the US Electron Ion Collider is described., Comment: Latex, 84 pages. Review prepared for Progress in Particle and Nuclear Physics

It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free algebras which is known to be undecidable. As a by-product, a description of the pseudocomplemented distributive lattices that can be embedded into the free algebra is also obtained.

The solar wind is highly turbulent, and intermittency effects are observed for fluctuations within the inertial range. By analyzing magnetic field spectra and fourth-order moments, we perform a comparative study of intermittency in different types of solar wind measured during periods of solar minima and a maximum. Using eight fast solar wind intervals measured during solar minima between 0.3 au and 3.16 au, we found a clear signature of two inertial sub-ranges with $f^{-3/2}$ and $f^{-5/3}$ power laws in the magnetic power spectra. The intermittency, measured through the scaling law of the kurtosis of magnetic field fluctuations, further confirms the existence of two different power laws separated by a clear break. A systematic study on the evolution of the said sub-ranges as a function of heliospheric distance shows correlation of the break scale with both the turbulence outer scale and the typical ion scales. During solar maximum, we analyzed five intervals for each of Alfv\'enic fast, Alfv\'enic slow and non-Alfv\'enic slow solar wind. Unlike the case during the solar minima, the two sub-ranges are no longer prominent and the Alfv\'enic slow wind is found to be in an intermediate state of turbulence compared to that of the fast wind and the usual non-Alfv\'enic slow wind., Comment: 16 pages, 11 figures, submitted to ApJ

Quantum one-dimensional systems in their ordered phase admit kinks as elementary excitations above their symmetry-broken vacua. While the scattering properties of the kinks resemble those of quasiparticles, they have distinct locality features that are manifest in their entanglement content. In this work, we study the entanglement entropy of kink excitations. We first present detailed calculations for specific states of a spin-1/2 chain to highlight the salient features of these excitations. Second, we provide a field-theoretic framework based on the algebraic relations between the twist fields and the semilocal fields associated with the excitations, and we compute the R\'enyi entropies in this framework. We obtain universal predictions for the entropy difference between the excited states with a finite number of kinks and the symmetry-broken ground states, which do not depend on the microscopic details of the model in the limit of large regions. Finally, we discuss some consequences of the Kramers-Wannier duality, which relates the ordered and disordered phases of the Ising model, and we explain why, counterintuitively, no explicit relations between those phases are found at the level of entanglement., Comment: 32 pages, 3 figures

We prove that the singular set of an $m$-dimensional integral current $T$ in $\mathbb{R}^{n + m}$, semicalibrated by a $C^{2, \kappa_0}$ $m$-form $\omega$ is countably $(m - 2)$-rectifiable. Furthermore, we show that there is a unique tangent cone at $\mathcal{H}^{m - 2}$-a.e. point in the interior singular set of $T$. Our proof adapts techniques that were recently developed in [DLS23a, DLS23b, DLMS23] for area-minimizing currents to this setting.

We analyse divergences of the scalar curvature $R$ of the vector multiplet moduli space of type IIA string theory compactified on a Calabi--Yau $X$, along infinite-distance large volume limits. Extending previous results, we classify the origin of the divergence along trajectories which implement decompactifications to F-theory on $X$ and/or emergent heterotic string limits. In all cases, the curvature divergence can be traced back to a 4d rigid field theory that decouples from gravity along the limit. This can be quantified via the asymptotic relation $R \sim (\Lambda_{\rm WGC}/\Lambda_{\rm sp})^{2\nu}$, with $\Lambda_{\rm WGC} \equiv g_{\rm rigid} M_{\rm P}$ and $\Lambda_{\rm sp}$ the species scale. In the UV, the 4d rigid field theory becomes a higher-dimensional, strongly-coupled rigid theory that also decouples from gravity. The nature of this UV theory is encoded in the exponent $\nu$, and it either corresponds to a 5d SCFT, 6d SCFT or a Little String Theory., Comment: 56 pages, 5 figures, 2 tables

This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\"odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating Functionals (HDAF) to MPS, a highly accurate pseudospectral method for approximating functions of derivatives. Integrating HDAF into an MPS finite precision algebra, we test four types of quantum-inspired algorithms for time evolution: explicit Runge-Kutta methods, Crank-Nicolson method, explicitly restarted Arnoli iteration and split-step. The benchmark problem is the expansion of a particle in a quantum quench, characterized by a rapid increase in space requirements, where HDAF surpasses traditional finite difference methods in accuracy with a comparable cost. Moreover, the efficient HDAF approximation to the free propagator avoids the need for Fourier transforms in split-step methods, significantly enhancing their performance with an improved balance in cost and accuracy. Both approaches exhibit similar error scaling and run times compared to FFT vector methods; however, MPS offer an exponential advantage in memory, overcoming vector limitations to enable larger discretizations and expansions. Finally, the MPS HDAF split-step method successfully reproduces the physical behavior of a particle expansion in a double-well potential, demonstrating viability for actual research scenarios.

A critical step in the digital surface models(DSM) generation is feature matching. Off-track (or multi-date) satellite stereo images, in particular, can challenge the performance of feature matching due to spectral distortions between images, long baseline, and wide intersection angles. Feature matching methods have evolved over the years from handcrafted methods (e.g., SIFT) to learning-based methods (e.g., SuperPoint and SuperGlue). In this paper, we compare the performance of different features, also known as feature extraction and matching methods, applied to satellite imagery. A wide range of stereo pairs(~500) covering two separate study sites are used. SIFT, as a widely used classic feature extraction and matching algorithm, is compared with seven deep-learning matching methods: SuperGlue, LightGlue, LoFTR, ASpanFormer, DKM, GIM-LightGlue, and GIM-DKM. Results demonstrate that traditional matching methods are still competitive in this age of deep learning, although for particular scenarios learning-based methods are very promising., Comment: ECCV2024 Workshop - TradiCV

Information retrieval methods often rely on a single embedding model trained on large, general-domain datasets like MSMARCO. While this approach can produce a retriever with reasonable overall performance, models trained on domain-specific data often yield better results within their respective domains. While prior work in information retrieval has tackled this through multi-task training, the topic of combining multiple domain-specific expert retrievers remains unexplored, despite its popularity in language model generation. In this work, we introduce RouterRetriever, a retrieval model that leverages multiple domain-specific experts along with a routing mechanism to select the most appropriate expert for each query. It is lightweight and allows easy addition or removal of experts without additional training. Evaluation on the BEIR benchmark demonstrates that RouterRetriever outperforms both MSMARCO-trained (+2.1 absolute nDCG@10) and multi-task trained (+3.2) models. This is achieved by employing our routing mechanism, which surpasses other routing techniques (+1.8 on average) commonly used in language modeling. Furthermore, the benefit generalizes well to other datasets, even in the absence of a specific expert on the dataset. To our knowledge, RouterRetriever is the first work to demonstrate the advantages of using multiple domain-specific expert embedding models with effective routing over a single, general-purpose embedding model in retrieval tasks.

In his book 'A Beautiful Question', physicist Frank Wilczek argues that symmetry is 'nature's deep design,' governing the behavior of the universe, from the smallest particles to the largest structures. While symmetry is a cornerstone of physics, it has not yet been found widespread applicability to describe biological systems, particularly the human brain. In this context, we study the human brain network engaged in language and explore the relationship between the structural connectivity (connectome or structural network) and the emergent synchronization of the mesoscopic regions of interest (functional network). We explain this relationship through a different kind of symmetry than physical symmetry, derived from the categorical notion of Grothendieck fibrations. This introduces a new understanding of the human brain by proposing a local symmetry theory of the connectome, which accounts for how the structure of the brain's network determines its coherent activity. Among the allowed patterns of structural connectivity, synchronization elicits different symmetry subsets according to the functional engagement of the brain. We show that the resting state is a particular realization of the cerebral synchronization pattern characterized by a fibration symmetry that is broken in the transition from rest to language. Our findings suggest that the brain's network symmetry at the local level determines its coherent function, and we can understand this relationship from theoretical principles., Comment: 43 pages, 9 figures

Detecting monotonic changes in heart rate (HR) is crucial for early identification of cardiac conditions and health management. This is particularly important for dementia patients, where HR trends can signal stress or agitation. Developing wearable technologies that can perform always-on monitoring of HRs is essential to effectively detect slow changes over extended periods of time. However, designing compact electronic circuits that can monitor and process bio-signals continuously, and that can operate in a low-power regime to ensure long-lasting performance, is still an open challenge. Neuromorphic technology offers an energy-efficient solution for real-time health monitoring. We propose a neuromorphic implementation of a Neural State Machine (NSM) network to encode different health states and switch between them based on the input stimuli. Our focus is on detecting monotonic state switches in electrocardiogram data to identify progressive HR increases. This innovative approach promises significant advancements in continuous health monitoring and management.

In this paper, we investigate the presence of additive bias in Large Language Models (LLMs), drawing a parallel to the cognitive bias observed in humans where individuals tend to favor additive over subtractive changes. Using a series of controlled experiments, we tested various LLMs, including GPT-3.5 Turbo, Claude 3.5 Sonnet, Mistral, Math$\Sigma$tral, and Llama 3.1, on tasks designed to measure their propensity for additive versus subtractive modifications. Our findings demonstrate a significant preference for additive changes across all tested models. For example, in a palindrome creation task, Llama 3.1 favored adding letters 97.85% of the time over removing them. Similarly, in a Lego tower balancing task, GPT-3.5 Turbo chose to add a brick 76.38% of the time rather than remove one. In a text summarization task, Mistral 7B produced longer summaries in 59.40% to 75.10% of cases when asked to improve its own or others' writing. These results indicate that, similar to humans, LLMs exhibit a marked additive bias, which might have implications when LLMs are used on a large scale. Addittive bias might increase resource use and environmental impact, leading to higher economic costs due to overconsumption and waste. This bias should be considered in the development and application of LLMs to ensure balanced and efficient problem-solving approaches., Comment: 25 pages, 8 figures

Although currently one of the most popular instant messaging apps worldwide, Telegram has been largely understudied in the past years. In this paper, we aim to address this gap by presenting an analysis of publicly accessible groups covering discussions encompassing different topics, as diverse as Education, Erotic, Politics, and Cryptocurrencies. We engineer and offer an open-source tool to automate the collection of messages from Telegram groups, a non-straightforward problem. We use it to collect more than 50 million messages from 669 groups. Here, we present a first-of-its-kind, per-topic analysis, contrasting the characteristics of the messages sent on the platform from different angles -- the language, the presence of bots, the type and volume of shared media content. Our results confirm some anecdotal evidence, e.g., clues that Telegram is used to share possibly illicit content, and unveil some unexpected findings, e.g., the different sharing patterns of video and stickers in groups of different topics. While preliminary, we hope that our work paves the road for several avenues of future research on the understudied Telegram platform.

We introduce OLMoE, a fully open, state-of-the-art language model leveraging sparse Mixture-of-Experts (MoE). OLMoE-1B-7B has 7 billion (B) parameters but uses only 1B per input token. We pretrain it on 5 trillion tokens and further adapt it to create OLMoE-1B-7B-Instruct. Our models outperform all available models with similar active parameters, even surpassing larger ones like Llama2-13B-Chat and DeepSeekMoE-16B. We present various experiments on MoE training, analyze routing in our model showing high specialization, and open-source all aspects of our work: model weights, training data, code, and logs., Comment: 61 pages (24 main), 36 figures, 14 tables

We present the first comprehensive analysis of the internal dynamics of multiple stellar populations (MPs) in 28 Galactic Globular Clusters (GCs) across a wide field of view, extending from the innermost regions to the clusters' outskirts. Using astro-photometric catalogs from ground-based observations, Gaia, and the Hubble Space Telescope (HST), we identify first- (1P) and second-population (2P) stars, and study the internal dynamics of MPs using high-precision Gaia DR3 and HST proper motions. Our results reveal that while the 1P transitions from isotropy to slight tangential anisotropy toward the outer regions, 2P stars become increasingly radially anisotropic beyond the half-light radius. We also explore the connection between the dynamics of MPs and the clusters' structural and dynamical properties, finding statistically significant differences in the anisotropy profiles of dynamically young and non-relaxed clusters, particularly beyond the 1-2 half-light radii. In these regions, 1P stars transition from isotropic to slightly tangentially anisotropic motion, while 2P stars become more radially anisotropic. In contrast, dynamically older clusters, with mixed MPs, exhibit weaker relative differences. Furthermore, clusters with orbits closer to the Galactic center exhibit larger dynamical differences between 1P and 2P stars than those with larger peri-Galactic radii. These findings are consistent with a scenario where 2P stars form in a more centrally concentrated environment, where the interaction with the Milky Way tidal field plays a crucial role in the dynamical evolution of MPs, especially of 1P., Comment: 19 pages, 13 figures (4 pages and 9 figures will be online supplementary material). Submitted to MNRAS, comments welcome

Geometrical frustration and long-range couplings are key contributors to create quantum phases with different properties throughout physics. We propose a scheme where both ingredients naturally emerge in a Raman induced subwavelength lattice. We first demonstrate that Raman-coupled multicomponent quantum gases can realize a highly versatile frustrated Hubbard Hamiltonian with long-range interactions. The deeply subwavelength lattice period leads to strong long-range interparticle repulsion with tunable range and decay. We numerically demonstrate that the combination of frustration and long-range couplings generates many-body phases of bosons, including a range of density-wave and superfluid phases with broken translational and time reversal symmetries, respectively. Our results thus represent a powerful approach for efficiently combining long-range interactions and frustration in quantum simulations., Comment: 17 pages, 10 figures

Using exact enumeration, the Casimir amplitude and the Casimir force are calculated for the square lattice Ising model with quenched surface disorder on one surface in cylinder geometry at criticality. The system shape is characterized by the aspect ratio $\rho=L/M$, where the cylinder length $L$ can take arbitrary values, while the circumference $M$ is varied from $M=4$ to $M=54$, resulting in up to $2^{54}$ numerically exact free energy calculations. A careful $M\to\infty$ extrapolation shows that quenched surface disorder is irrelevant in two dimensions, but gives rise to logarithmic corrections., Comment: 18 pages, 4 figures

Let $E_{\lambda}$ be the Legendre family of elliptic curves with equation $Y^2=X(X-1)(X-\lambda)$. Given a curve $\mathcal{C}$, satisfying a condition on the degrees of some of its coordinates and parametrizing $m$ points $P_1, \ldots, P_m \in E_{\lambda}$ and $n$ points $Q_1, \ldots, Q_n \in E_{\mu}$ and assuming that those points are generically linearly independent over the generic endomorphism ring, we prove that there are at most finitely many points $\mathbf{c}_0$ on $\mathcal{C}$, such that there exists an isogeny $\phi: E_{\mu(\mathbf{c}_0)} \rightarrow E_{\lambda(\mathbf{c}_0)}$ and the $m+n$ points $P_1(\mathbf{c}_0), \ldots, P_m(\mathbf{c}_0), \phi(Q_1(\mathbf{c}_0)), \ldots, \phi(Q_n(\mathbf{c}_0)) \in E_{\lambda(\mathbf{c}_0)}$ are linearly dependent over $\mathrm{End}(E_{\lambda(\mathbf{c}_0)})$., Comment: 17 pages. Comments are welcome!

In the current Noisy Intermediate Scale Quantum (NISQ) era, the presence of noise deteriorates the performance of quantum computing algorithms. Quantum Reservoir Computing (QRC) is a type of Quantum Machine Learning algorithm, which, however, can benefit from different types of tuned noise. In this paper, we analyse the effect that finite-sampling noise has on the chaotic time-series prediction capabilities of QRC and Recurrence-free Quantum Reservoir Computing (RF-QRC). First, we show that, even without a recurrent loop, RF-QRC contains temporal information about previous reservoir states using leaky integrated neurons. This makes RF-QRC different from Quantum Extreme Learning Machines (QELM). Second, we show that finite sampling noise degrades the prediction capabilities of both QRC and RF-QRC while affecting QRC more due to the propagation of noise. Third, we optimize the training of the finite-sampled quantum reservoir computing framework using two methods: (a) Singular Value Decomposition (SVD) applied to the data matrix containing noisy reservoir activation states; and (b) data-filtering techniques to remove the high-frequencies from the noisy reservoir activation states. We show that denoising reservoir activation states improve the signal-to-noise ratios with smaller training loss. Finally, we demonstrate that the training and denoising of the noisy reservoir activation signals in RF-QRC are highly parallelizable on multiple Quantum Processing Units (QPUs) as compared to the QRC architecture with recurrent connections. The analyses are numerically showcased on prototypical chaotic dynamical systems with relevance to turbulence. This work opens opportunities for using quantum reservoir computing with finite samples for time-series forecasting on near-term quantum hardware., Comment: 11 pages, 14 figures

Exciton plasmon polaritons have gained increasing interests over recent years due to their versatile properties emerging by the underlying light-matter coupling and making them potential candidates for new photonic applications. We have advanced this concept by studying thin films of laterally aligned J-type aggregates of self-assembled tetra-bay phenoxy-dendronized perylene bisimide (PBI) molecules, arranged in a helical manner of three strains on a silver surface. As a result of the interaction between the uniformly aligned dipole moments and the surface plasmons of a thin silver layer underneath, the excitonic state at 1.94 eV evolves into dispersions in absorption and emission, both characterized by a distinct anisotropy. The coupling constant defined by the scalar product of the transition dipole moment $\vec{\mu}$ and the surface plasmon wavevector $\vec{k}_x$ shows a pronounced two-fold rotational symmetry with values between almost 0 to 28 meV. Complementary TD-DFT calculations of the angular dependent absorption and photoluminescence provide insights in the coherent energy exchange between the excitonic and plasmonic sub-systems. Additionally, power dependent PL studies yield first evidence that the diffusion length of the coupled exciton-plasmon polaritons exceeds that of the mere Frenkel state in neat PBI by at least one order of magnitude. Our results not only demonstrate the possibility to control the photo-physical properties of strongly coupled states by their spatially anisotropic light-matter interaction but also reveal innovative strategies to influence opto-electronic device operation by the directional transport of hybrid state energy., Comment: 26 pages, 7 figures, 2 tables, Supporting Information

Colloidal Solids (COLIS) is a state-of-the-art light scattering setup developed for experiments onboard the International Space Station (ISS). COLIS allows for probing the structure and dynamics of soft matter systems on a wide range of length scales, from a few nm to tens of microns, and on time scales from 100 ns to tens of hours. In addition to conventional static and dynamic light scattering, COLIS includes depolarized dynamic light scattering, a small-angle camera, photon correlation imaging, and optical manipulation of thermosensitive samples through an auxiliary near-infrared laser beam, thereby providing a unique platform for probing soft matter systems. We demonstrate COLIS through ground tests on standard Brownian suspensions, and on protein, colloidal glasses, and gel systems similar to those to be used in future ISS experiments.

We study the conformation and topological properties of cyclical star polymers with $f$ ring arms, each made of $n$ beads. We find that the conformational properties of unlinked cyclical star polymers are compatible to those of linear star polymers with $2f$ arms made of $n/2$ beads each. This compatibility vanishes when the topology of the star, measured as the degree of linking between arms, changes. In fact, when links are allowed we notice that the gyration radius decreases as a function of the absolute linking number $\vert Lk \vert$ of the arms, regardless of the protocol that is employed to introduce said links. Furthermore, the internal structure of the macromolecules, as highlighted by the radial density function, changes qualitatively for large values of $\vert Lk \vert$., Comment: 11 pages, 11 figures

Ptychography is a scanning coherent diffraction imaging technique successfully applied in the electron, visible and x-ray regimes. One of the distinct features of ptychography with respect to other coherent diffraction techniques is its capability of dealing with partial spatial and temporal coherence via the reconstruction algorithm. Here we focus on the temporal and clarify the constraints which affect the energy resolution limits of the ptychographic algorithms. Based on this, we design and perform simulations for a broadband ptychography in the hard x-ray regime, which enables an energy resolution down to 1 eV. We benchmark the simulations against experimental ptychographic data of an NMC battery cathode material, attaining an energy resolution of 5 eV. We review the results, discuss the limitations, and provide guidelines for future broadband ptychography experiments, its prospective application for single acquisition x-ray absorption near edge structure imaging, magnetic dichroism imaging, and potential impact on achieving diffraction limited resolutions.

Data from fluid flow measurements are typically sparse, noisy, and heterogeneous, often from mixed pressure and velocity measurements, resulting in incomplete datasets. In this paper, we develop a physics-constrained convolutional neural network, which is a deterministic tool, to reconstruct the full flow field from incomplete data. We explore three loss functions, both from machine learning literature and newly proposed: (i) the softly-constrained loss, which allows the prediction to take any value; (ii) the snapshot-enforced loss, which constrains the prediction at the sensor locations; and (iii) the mean-enforced loss, which constrains the mean of the prediction at the sensor locations. The proposed methods do not require the full flow field during training, making it suitable for reconstruction from incomplete data. We apply the method to reconstruct a laminar wake of a bluff body and a turbulent Kolmogorov flow. First, we assume that measurements are not noisy and reconstruct both the laminar wake and the Kolmogorov flow from sensors located at fewer than 1% of all grid points. The snapshot-enforced loss reduces the reconstruction error of the Kolmogorov flow by approximately 25% compared to the softly-constrained loss. Second, we assume that measurements are noisy and propose the mean-enforced loss to reconstruct the laminar wake and the Kolmogorov flow at three different signal-to-noise ratios. We find that, across the ratios tested, the loss functions with harder constraints are more robust to both the random initialization of the networks and the noise levels in the measurements. At high noise levels, the mean-enforced loss can recover the instantaneous snapshots accurately, making it the suitable choice when reconstructing flows from data corrupted with an unknown amount of noise. The proposed method opens opportunities for physical flow reconstruction from sparse, noisy data.

Robotic-assisted surgery (RAS) relies on accurate depth estimation for 3D reconstruction and visualization. While foundation models like Depth Anything Models (DAM) show promise, directly applying them to surgery often yields suboptimal results. Fully fine-tuning on limited surgical data can cause overfitting and catastrophic forgetting, compromising model robustness and generalization. Although Low-Rank Adaptation (LoRA) addresses some adaptation issues, its uniform parameter distribution neglects the inherent feature hierarchy, where earlier layers, learning more general features, require more parameters than later ones. To tackle this issue, we introduce Depth Anything in Robotic Endoscopic Surgery (DARES), a novel approach that employs a new adaptation technique, Vector Low-Rank Adaptation (Vector-LoRA) on the DAM V2 to perform self-supervised monocular depth estimation in RAS scenes. To enhance learning efficiency, we introduce Vector-LoRA by integrating more parameters in earlier layers and gradually decreasing parameters in later layers. We also design a reprojection loss based on the multi-scale SSIM error to enhance depth perception by better tailoring the foundation model to the specific requirements of the surgical environment. The proposed method is validated on the SCARED dataset and demonstrates superior performance over recent state-of-the-art self-supervised monocular depth estimation techniques, achieving an improvement of 13.3% in the absolute relative error metric. The code and pre-trained weights are available at https://github.com/mobarakol/DARES., Comment: 11 pages

We consider function spaces defined by self-attention networks without normalization, and theoretically analyze their geometry. Since these networks are polynomial, we rely on tools from algebraic geometry. In particular, we study the identifiability of deep attention by providing a description of the generic fibers of the parametrization for an arbitrary number of layers and, as a consequence, compute the dimension of the function space. Additionally, for a single-layer model, we characterize the singular and boundary points. Finally, we formulate a conjectural extension of our results to normalized self-attention networks, prove it for a single layer, and numerically verify it in the deep case.

Context: Software Quality Assurance (SQA) is a fundamental part of software engineering to ensure stakeholders that software products work as expected after release in operation. Machine Learning (ML) has proven to be able to boost SQA activities and contribute to the development of quality software systems. In this context, Causal Reasoning is gaining increasing interest as a methodology to solve some of the current ML limitations. It aims to go beyond a purely data-driven approach by exploiting the use of causality for more effective SQA strategies. Objective: Provide a broad and detailed overview of the use of causal reasoning for SQA activities, in order to support researchers to access this research field, identifying room for application, main challenges and research opportunities. Methods: A systematic literature review of causal reasoning in the SQA research area. Scientific papers have been searched, classified, and analyzed according to established guidelines for software engineering secondary studies. Results: Results highlight the primary areas within SQA where causal reasoning has been applied, the predominant methodologies used, and the level of maturity of the proposed solutions. Fault localization is the activity where causal reasoning is more exploited, especially in the web services/microservices domain, but other tasks like testing are rapidly gaining popularity. Both causal inference and causal discovery are exploited, with the Pearl's graphical formulation of causality being preferred, likely due to its intuitiveness. Tools to favour their application are appearing at a fast pace - most of them after 2021. Conclusions: The findings show that causal reasoning is a valuable means for SQA tasks with respect to multiple quality attributes, especially during V&V, evolution and maintenance to ensure reliability, while it is not yet fully exploited for phases like ..., Comment: Preprint Journal Information and Software Technology

In recent years, significant advancements have been made in computational methods for analyzing masonry structures. Within the Finite Element Method, two primary approaches have gained traction: Micro and Macro Scale modeling, and their subsequent integration via Multi-scale methods based on homogenization theory and the representative volume element concept. While Micro and Multi-scale approaches offer high fidelity, they often come with a substantial computational burden. On the other hand, calibrating homogenized material parameters in Macro-scale approaches presents challenges for practical engineering problems. Machine learning techniques have emerged as powerful tools for training models using vast datasets from various domains. In this context, we propose leveraging Machine Learning methods to develop a novel homogenization strategy for the in-plane analysis of masonry structures. This strategy involves automatically calibrating a continuum nonlinear damage constitutive law and an appropriate yield criteria using relevant data derived from Micro-scale analysis. The optimization process not only enhances material parameters but also refines yield criteria and damage evolution laws to better align with existing data. To achieve this, a virtual laboratory is created to conduct micro-model simulations that account for the individual behaviors of constituent materials. Subsequently, a data isotropization process is employed to reconcile the results with typical isotropic constitutive models. Next, an optimization algorithm that minimizes the difference of internal dissipated work between the micro and macro scales is executed. We apply this technique to the in-plane homogenization of a Flemish bond masonry wall. Evaluation examples, including simulations of shear and compression tests, demonstrate the method's accuracy compared to micro modeling of the entire structure., Comment: Submitted to Computers and Structures

Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution also exhibits numerical quasiseparability. This property enables us to develop two efficient Riccati solvers. The first solver is applicable to the general quasiseparable case, while the second is tailored to the particular case of banded coefficients. Numerical experiments confirm the effectiveness of the proposed algorithms on both synthetic examples and case studies from the control of partial differential equations and agent-based models.

Fractional flow reserve (FFR) is the gold standard for diagnosing coronary artery disease (CAD). FFRCT uses computational fluid dynamics (CFD) to evaluate FFR non-invasively by simulating coronary flow in geometries reconstructed from computed tomography (CT). However, it faces challenges related to the cost of computing and uncertainties in defining patient-specific boundary conditions (BCs). We investigated using time-averaged steady BCs instead of pulsatile ones to reduce computational time and deployed a self-adjusting method for tuning BCs to patient clinical data. 133 coronary arteries were reconstructed from CT images of CAD patients. For each vessel, invasive FFR was measured. Steady BCs for CFD were defined in two steps: i) rest BCs were extrapolated from clinical and image-derived data; ii) hyperemic BCs were computed from resting conditions. Flow rate was iteratively adjusted during the simulation until patient aortic pressure was matched. Pulsatile BCs were defined using the convergence values of steady BCs. Lesion-specific hemodynamic indexes were computed and compared between groups of patients indicated for surgery and those not. The whole pipeline was implemented as a straightforward, fully automated process. Steady and pulsatile FFRCT showed a strong correlation (r=0.988) and correlated with invasive FFR (r=0.797). The per-point difference between the pressure and FFRCT field predicted by the two methods was below 0.01 and 0.02, respectively. Both approaches exhibited good diagnostic performance: accuracy was 0.860 and 0.864, with AUCs of 0.923 and 0.912, for steady and pulsatile cases, respectively. Computational time for steady BCs CFD was approximately 30-fold lower than for the pulsatile case. This work demonstrates the feasibility of using steady BCs CFD for computing FFRCT in coronary arteries and its performance in a fully automated pipeline.

In the last few years the literature has witnessed a remarkable surge of interest for chaotic maps implemented by discrete-time (DT) memristor circuits. This paper investigates on the reasons underlying this type of chaotic behavior. To this end, the papers considers the map implemented by the simplest memristor circuit given by a capacitor and an ideal flux-controlled memristor or an inductor and an ideal charge-controlled memristor. In particular, the manuscript uses the DT flux-charge analysis method (FCAM) introduced in a recent paper to ensure that the first integrals and foliation in invariant manifolds of continuous-time (CT) memristor circuits are preserved exactly in the discretization for any step size. DT-FCAM yields a two-dimensional map in the voltage-current domain (VCD) and a manifold-dependent one-dimensional map in the flux-charge domain (FCD), i.e., a one-dimensional map on each invariant manifold. One main result is that, for suitable choices of the circuit parameters and memristor nonlinearities, both DT circuits can exactly embed two classic chaotic maps, i.e., the logistic map and the tent map. Moreover, due to the property of extreme multistability, the DT circuits can simultaneously embed in the manifolds all the dynamics displayed by varying one parameter in the logistic and tent map. The paper then considers a DT memristor Murali-Lakshmanan-Chua circuit and its dual. Via DT-FCAM these circuits implement a three-dimensional map in the VCD and a two-dimensional map on each invariant manifold in the FCD. It is shown that both circuits can simultaneously embed in the manifolds all the dynamics displayed by two other classic chaotic maps, i.e., the Henon map and the Lozi map, when varying one parameter in such maps. In essence, these results provide an explanation of why it is not surprising to observe complex dynamics even in simple DT memristor circuits.

Stereoelectroencephalography (SEEG) is an invasive surgical procedure to record the electrical activities in cortical brain regions, aiming at identifying the Epileptogenic Zone (EZ) in patients with drug-resistant epilepsy. To improve the accuracy of the EZ definition, SEEG analysis can be supported by computational tools, among which the Epileptogenic Index (EI) represents the most common solution. However, the scientific community has still not found an agreement on which quantitative biomarkers can characterize the cortical sites within the EZ. In this work, we design a new algorithm, named Desynchronization Index (DI), to assist neurophysiologists in SEEG interpretation. Our algorithm estimates the effective connectivity between cortical sites and hypothesizes that the EZ is identified by those sites getting abnormally desynchronized from the network during the seizure generation. We test the proposed method over a SEEG dataset of 10 seizures, comparing its accuracy in terms of EZ definition against the EI algorithm and clinical ground truth. Our results indicate that the DI algorithm underscores specific connectivity dynamics that can hardly be identified with a pure visual analysis, increasing sensitivity in detecting epileptogenic cortical sites.

Cosmic strings, theoretical one-dimensional topological defects from the early universe, provide a valuable opportunity for exploring dark matter (DM) production and gravitational wave (GW) emission. Our study investigates the production of gauge bosons and GW emission from cosmic string decay, considering the constraints imposed by cosmological observations. We specifically examine how gauge bosons radiated from strings contribute to DM and dark radiation, with limits set by the observed DM abundance and cosmic microwave background data, respectively. Additionally, we analyze the gravitational wave spectrum of this model across both low and high frequencies. Notably, the spectrum typically follows a $f^{-1/3}$ pattern at high frequencies, beyond the pivot frequency $f_*$. We derive an analytical expression for the frequency $f_*$ and confirm its accuracy through numerical verification. Furthermore, we compare the GW spectrum of this model with the forecasted capabilities of future GW observatories, such as the Einstein Telescope, the Laser Interferometer Space Antenna, the Big Bang Observer, and $\mu$Ares. Finally, we discuss how these considerations impact the model parameters, specifically the gauge boson mass and the energy scale of U(1) symmetry breaking, providing insights into how cosmic strings could enhance our understanding of DM and GW astronomy., Comment: 12 pages, 4 figure. COST Actions CA21106 and CA21136

The purpose of the paper is threefold: first, we prove optimal regularity results for the distance from $C^k$ submanifolds of general rank-varying sub-Riemannian structures. Then, we study the asymptotics of the volume of tubular neighbourhoods around such submanifolds. Finally, for the case of curves in the Heisenberg groups, we prove a Weyl's invariance result: the volume of small tubes around a curve does not depend on the way the curve is isometrically embedded, but only on its Reeb angle. The proof does not need the computation of the actual volume of the tube, and it is new even for the three-dimensional Heisenberg group., Comment: 25 pages, 1 figure