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Breakthroughs in ultra-low-power chip technology are transforming biomedical wearables, making it possible to monitor patients in real time with devices operating on mere {\mu}W. Although many studies have examined the power performance of commercial microcontrollers, it remains unclear which ones perform best across diverse application profiles and which hardware features are most crucial for minimizing energy consumption under varying computational loads. Identifying these features for typical wearable applications and understanding their effects on performance and energy efficiency are essential for optimizing deployment strategies and informing future hardware designs. In this work, we conduct an in-depth study of state-of-the-art (SoA) micro-controller units(MCUs) in terms of processing capability and energy efficiency using representative end-to-end SoA wearable applications. We systematically benchmark each platform across three primary application phases: idle, data acquisition, and processing, allowing a holistic assessment of the platform processing capability and overall energy efficiency across varying patient-monitoring application profiles. Our detailed analysis of performance and energy discrepancies across different platforms reveals key strengths and limitations of the current low-power hardware design and pinpoints the strengths and weaknesses of SoA MCUs. We conclude with actionable insights for wearable application designers and hardware engineers, aiming to inform future hardware design improvements and support optimal platform selection for energy-constrained biomedical applications., Comment: 21 pages, 6 Figures, 6 Tables, Submitted to ACM TECS journal

We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with variable-length memory. Each chain describes the activity of a single neuron, indicating whether it spikes at a given time. One neuron's influence on another can be either excitatory or inhibitory. To identify the existence and nature of an interaction between a neuron and its postsynaptic counterpart, we propose a model selection procedure based on the observation of the spike activity of a finite set of neurons over a finite time. The proposed procedure is also based on the maximum likelihood estimator for the synaptic weight matrix of the network neuronal model. In this sense, we prove the consistency of the maximum likelihood estimator followed by a proof of the consistency of the neighborhood interaction estimation procedure. The effectiveness of the proposed model selection procedure is demonstrated using simulated data, which validates the underlying theory. The method is also applied to analyze spike train data recorded from hippocampal neurons in rats during a visual attention task, where a computational model reconstructs the spiking activity and the results reveal interesting and biologically relevant information., Comment: 29 pages, 2 figures

We prove that the transitive permutation group 17T7, isomorphic to a split extension of $C_2$ by $\mathrm{PSL}_2(\mathbb{F}_{16})$, is a Galois group over the rationals. The group arises from the field of definition of the 2-torsion on an abelian fourfold with real multiplication defined over a real quadratic field. We find such fourfolds using Hilbert modular forms. Finally, building upon work of Demb\'el\'e, we show how to conjecturally reconstruct a period matrix for an abelian variety attached to a Hilbert modular form; we then use this to exhibit an explicit degree 17 polynomial with Galois group 17T7., Comment: 23 pages, comments welcome

Imaging atmospheric Cherenkov telescopes (IACTs) are used to observe very high-energy photons from the ground. Gamma rays are indirectly detected through the Cherenkov light emitted by the air showers they induce. The new generation of experiments, in particular the Cherenkov Telescope Array Observatory (CTAO), sets ambitious goals for discoveries of new gamma-ray sources and precise measurements of the already discovered ones. To achieve these goals, both hardware and data analysis must employ cutting-edge techniques. This also applies to the LST-1, the first IACT built for the CTAO, which is currently taking data on the Canary island of La Palma. This paper introduces a new event reconstruction technique for IACT data, aiming to improve the image reconstruction quality and the discrimination between the signal and the background from misidentified hadrons and electrons. The technique models the development of the extensive air shower signal, recorded as a waveform per pixel, seen by CTAO telescopes' cameras. Model parameters are subsequently passed to random forest regressors and classifiers to extract information on the primary particle. The new reconstruction was applied to simulated data and to data from observations of the Crab Nebula performed by the LST-1. The event reconstruction method presented here shows promising performance improvements. The angular and energy resolution, and the sensitivity, are improved by 10 to 20% over most of the energy range. At low energy, improvements reach up to 22%, 47%, and 50%, respectively. A future extension of the method to stereoscopic analysis for telescope arrays will be the next important step., Comment: Accepted in A&A

We establish global bounds for solutions to stationary and time-dependent Schr\"odinger equations associated with the sublaplacian $\mathcal L$ on the Heisenberg group, as well as its pure fractional power $\mathcal L^s$ and conformally invariant fractional power $\mathcal L_s$. The main ingredient is a new abstract uniform weighted resolvent estimate which is proved by using the method of weakly conjugate operators -- a variant of Mourre's commutator method -- and Hardy's type inequalities on the Heisenberg group. As applications, we show Kato-type smoothing effects for the time-dependent Schr\"odinger equation, and spectral stability of the sublaplacian perturbed by complex-valued decaying potentials satisfying an explicit subordination condition. In the local case $s=1$, we obtain uniform estimates without any symmetry or derivative loss, which improve previous results., Comment: 28 pages

A database of abstract groups has been added to the L-functions and Modular Forms Database (LMFDB), available at https://www.lmfdb.org/Groups/Abstract/. We discuss the functionality of the database and what makes it distinct from other available databases of abstract groups. We describe solutions to mathematical problems we encountered while creating the database, as well as connections between the abstract groups database and other collections of objects in the LMFDB.

Wearable systems provide continuous health monitoring and can lead to early detection of potential health issues. However, the lifecycle of wearable systems faces several challenges. First, effective model training for new wearable devices requires substantial labeled data from various subjects collected directly by the wearable. Second, subsequent model updates require further extensive labeled data for retraining. Finally, frequent model updating on the wearable device can decrease the battery life in long-term data monitoring. Addressing these challenges, in this paper, we propose MetaWearS, a meta-learning method to reduce the amount of initial data collection required. Moreover, our approach incorporates a prototypical updating mechanism, simplifying the update process by modifying the class prototype rather than retraining the entire model. We explore the performance of MetaWearS in two case studies, namely, the detection of epileptic seizures and the detection of atrial fibrillation. We show that by fine-tuning with just a few samples, we achieve 70% and 82% AUC for the detection of epileptic seizures and the detection of atrial fibrillation, respectively. Compared to a conventional approach, our proposed method performs better with up to 45% AUC. Furthermore, updating the model with only 16 minutes of additional labeled data increases the AUC by up to 5.3%. Finally, MetaWearS reduces the energy consumption for model updates by 456x and 418x for epileptic seizure and AF detection, respectively.

We investigate the Hubble constant tension within $f(R)$ modified gravity in the Jordan frame, focusing on its application to the dynamics of an isotropic Universe. A scalar field, non-minimally coupled to the metric, provides an extra degree of freedom compared to General Relativity. We analyze the impact of such a scalar field on the cosmic expansion, leading to an effective Hubble constant $H_{0}^{\text{eff}}(z)$, dependent on redshift $z$. We show that our $f(R)$ model might mimic dark energy and provide an apparent variation of the Hubble constant. Our results align with recent cosmological data analysis in redshift bins, indicating a decreasing trend of the Hubble constant. The redshift dependence of $H_{0}^{\text{eff}}(z)$ might potentially reconcile measurements of the Hubble constant from probes at different redshifts., Comment: 6 pages, 1 figure, contribution to IFAE 2024, Florence (Italy), 3-5 April 2024

Context: There are currently three pulsars firmly detected by imaging atmospheric Cherenkov telescopes (IACTs), two of them reaching TeV energies, challenging models of very-high-energy (VHE) emission in pulsars. More precise observations are needed to better characterize pulsar emission at these energies. The LST-1 is the prototype of the Large-Sized Telescope, that will be part of the Cherenkov Telescope Array Observatory (CTAO). Its improved performance over previous IACTs makes it well suited for studying pulsars. Aims: To study the Crab pulsar emission with the LST-1, improving and complementing the results from other telescopes. These observations can also be used to characterize the potential of the LST-1 to study other pulsars and detect new ones. Methods: We analyzed a total of $\sim$103 hours of gamma-ray observations of the Crab pulsar conducted with the LST-1 in the period from September 2020 to January 2023. The observations were carried out at zenith angles less than 50 degrees. A new analysis of the Fermi-LAT data was also performed, including $\sim$14 years of observations. Results: The Crab pulsar phaseogram, long-term light-curve, and phase-resolved spectra are reconstructed with the LST-1 from 20 GeV to 450 GeV for P1 and up to 700 GeV for P2. The pulsed emission is detected with a significance of 15.2$\sigma$. The two characteristic emission peaks of the Crab pulsar are clearly detected (>10$\sigma$), as well as the so-called bridge emission (5.7$\sigma$). We find that both peaks are well described by power laws, with spectral indices of $\sim$3.44 and $\sim$3.03 respectively. The joint analysis of Fermi-LAT and LST-1 data shows a good agreement between both instruments in the overlapping energy range. The detailed results obtained in the first observations of the Crab pulsar with LST-1 show the potential that CTAO will have to study this type of sources., Comment: Accepted by A&A

The widespread adoption of data-centric algorithms, particularly Artificial Intelligence (AI) and Machine Learning (ML), has exposed the limitations of centralized processing infrastructures, driving a shift towards edge computing. This necessitates stringent constraints on energy efficiency, which traditional von Neumann architectures struggle to meet. The Compute-In-Memory (CIM) paradigm has emerged as a superior candidate due to its efficient exploitation of available memory bandwidth. However, existing CIM solutions require high implementation effort and lack flexibility from a software integration standpoint. This work proposes a novel, software-friendly, general-purpose, and low-integration-effort Near-Memory Computing (NMC) approach, paving the way for the adoption of CIM-based systems in the next generation of edge computing nodes. Two architectural variants, NM-Caesar and NM-Carus, are proposed and characterized to target different trade-offs in area efficiency, performance, and flexibility, covering a wide range of embedded microcontrollers. Post-layout simulations show up to $25.8\times$ and $50.0\times$ lower execution time and $23.2\times$ and $33.1\times$ higher energy efficiency at the system level, respectively, compared to executing the same tasks on a state-of-the-art RISC-V CPU (RV32IMC). NM-Carus achieves a peak energy efficiency of $306.7$ GOPS/W in 8-bit matrix multiplications, surpassing recent state-of-the-art in- and near-memory circuits., Comment: 14 pages, 12 figures, submitted to IEEE Transactions on Emerging Topics in Computing

The design of low-power wearables for the biomedical domain has received a lot of attention in recent decades, as technological advances in chip manufacturing have allowed real-time monitoring of patients using low-complexity ML within the mW range. Despite advances in application and hardware design research, the domain lacks a systematic approach to hardware evaluation. In this work, we propose BiomedBench, a new benchmark suite composed of complete end-to-end TinyML biomedical applications for real-time monitoring of patients using wearable devices. Each application presents different requirements during typical signal acquisition and processing phases, including varying computational workloads and relations between active and idle times. Furthermore, our evaluation of five state-of-the-art low-power platforms in terms of energy efficiency shows that modern platforms cannot effectively target all types of biomedical applications. BiomedBench is released as an open-source suite to standardize hardware evaluation and guide hardware and application design in the TinyML wearable domain., Comment: 7 pages, 5 figures. Accepted for publication to Design & Test Special Issue TinyML

Foundation models contain a wealth of information from their vast number of training samples. However, most prior arts fail to extract this information in a precise and efficient way for small sample sizes. In this work, we propose a framework utilizing reinforcement learning as a control for foundation models, allowing for the granular generation of small, focused synthetic support sets to augment the performance of neural network models on real data classification tasks. We first allow a reinforcement learning agent access to a novel context based dictionary; the agent then uses this dictionary with a novel prompt structure to form and optimize prompts as inputs to generative models, receiving feedback based on a reward function combining the change in validation accuracy and entropy. A support set is formed this way over several exploration steps. Our framework produced excellent results, increasing classification accuracy by significant margins for no additional labelling or data cost., Comment: 4 pages, 2 figures. Code available at: https://github.com/mesophil/deeprl

Reconfigurable computing offers a good balance between flexibility and energy efficiency. When combined with software-programmable devices such as CPUs, it is possible to obtain higher performance by spatially distributing the parallelizable sections of an application throughout the reconfigurable device while the CPU is in charge of control-intensive sections. This work introduces an elastic Coarse-Grained Reconfigurable Architecture (CGRA) integrated into an energy-efficient RISC-V-based SoC designed for the embedded domain. The microarchitecture of CGRA supports conditionals and irregular loops, making it adaptable to domain-specific applications. Additionally, we propose specific mapping strategies that enable the efficient utilization of the CGRA for both simple applications, where the fabric is only reconfigured once (one-shot kernel), and more complex ones, where it is necessary to reconfigure the CGRA multiple times to complete them (multi-shot kernels). Large kernels also benefit from the independent memory nodes incorporated to streamline data accesses. Due to the integration of CGRA as an accelerator of the RISC-V processor enables a versatile and efficient framework, providing adaptability, processing capacity, and overall performance across various applications. The design has been implemented in TSMC 65 nm, achieving a maximum frequency of 250 MHz. It achieves a peak performance of 1.22 GOPs computing one-shot kernels and 1.17 GOPs computing multi-shot kernels. The best energy efficiency is 72.68 MOPs/mW for one-shot kernels and 115.96 MOPs/mW for multi-shot kernels. The design integrates power and clock-gating techniques to tailor the architecture to the embedded domain while maintaining performance. The best speed-ups are 17.63x and 18.61x for one-shot and multi-shot kernels. The best energy savings in the SoC are 9.05x and 11.10x for one-shot and multi-shot kernels., Comment: 14 pages, 11 figures

Monochromatic gamma-ray signals constitute a potential smoking gun signature for annihilating or decaying dark matter particles that could relatively easily be distinguished from astrophysical or instrumental backgrounds. We provide an updated assessment of the sensitivity of the Cherenkov Telescope Array (CTA) to such signals, based on observations of the Galactic centre region as well as of selected dwarf spheroidal galaxies. We find that current limits and detection prospects for dark matter masses above 300 GeV will be significantly improved, by up to an order of magnitude in the multi-TeV range. This demonstrates that CTA will set a new standard for gamma-ray astronomy also in this respect, as the world's largest and most sensitive high-energy gamma-ray observatory, in particular due to its exquisite energy resolution at TeV energies and the adopted observational strategy focussing on regions with large dark matter densities. Throughout our analysis, we use up-to-date instrument response functions, and we thoroughly model the effect of instrumental systematic uncertainties in our statistical treatment. We further present results for other potential signatures with sharp spectral features, e.g.~box-shaped spectra, that would likewise very clearly point to a particle dark matter origin., Comment: 44 pages JCAP style (excluding author list and references), 19 figures; minor changes to match published version

Recently, efficiently deploying deep learning solutions on the edge has received increasing attention. New platforms are emerging to support the increasing demand for flexibility and high performance. In this work, we explore the efficient mapping of convolutional layers on an open-hardware, low-power Coarse-Grain Reconfigurable Array (CGRA), namely OpenEdgeCGRA. We explore both direct implementations of convolution and solutions that transform it into a matrix multiplication through an Im2col transformation, and experiment with various tensor parallelism axes. We show that for this hardware target, direct convolution, coupled with weight parallelism reaches the best latency and energy efficiency, outperforming a CPU implementation by 3.4x and 9.9x in terms of energy and latency, respectively.

We analyze the performance of enhanced spread spectrum Aloha (E-SSA) in the framework of unsourced multiple access (UMAC). The asynchronous, unframed transmission of E-SSA is modified to enable a direct comparison with framed UMAC schemes and with Polyanskiy's achievability bound. The design of E-SSA is tailored to the UMAC setting, resorting to short polar codes and the use of a timing channel to improve the energy efficiency of the protocol. We assess the impact of the preamble length and of the spreading factor on the system efficiency. The resulting scheme exhibits simplicity at the transmitter and linear complexity with respect to the number of active users at the receiver, approaching the UMAC achievability bound in close competition with the best known UMAC schemes., Comment: Pre-print version of the IEEE Communications Letter

In this article we give explicit formulas for the equations of a generic genus $4$ curve in terms of its theta constants. The method uses the Prym construction and the beautiful classical geometry around it.

We carry on the approach used in [Sch] to provide a solution for the inverse problem of the calculus of variations for Maxwell equations in vacuum and we provide an abstract theory including all implicit differential equations that can be formulated in terms of vector fields over pre-symplectic manifolds.

The field of edge computing has witnessed remarkable growth owing to the increasing demand for real-time processing of data in applications. However, challenges persist due to limitations in performance and power consumption. To overcome these challenges, heterogeneous architectures have emerged that combine host processors with specialized accelerators tailored to specific applications, leading to improved performance and reduced power consumption. However, most of the existing platforms lack the necessary configurability and extendability options for integrating custom accelerators. To overcome these limitations, we introduce in this paper the eXtendible Heterogeneous Energy-Efficient Platform (X-HEEP). X-HEEP is an open-source platform designed to natively support the integration of ultra-low-power edge accelerators. It provides customization options to match specific application requirements by exploring various core types, bus topologies, addressing modes, memory sizes, and peripherals. Moreover, the platform prioritizes energy efficiency by implementing low-power strategies, such as clock-gating and power-gating. We demonstrate the real-world applicability of X-HEEP by providing an integration example tailored for healthcare applications that includes a coarse-grained reconfigurable array (CGRA) and in-memory computing (IMC) accelerators. The resulting design, called HEEPocrates, has been implemented both in field programmable gate array (FPGA) on the Xilinx Zynq-7020 chip and in silicon with TSMC 65nm low-power CMOS technology. We run a set of healthcare applications and measure their energy consumption to demonstrate the alignment of our chip with other state-of-the-art microcontrollers commonly adopted in this domain. Moreover, we present the energy benefits of 4.9x and 4.8x gained by exploiting the integrated CGRA and IMC accelerators compared to running on the host CPU.

We present the coisotropic embedding theorem as a tool to provide a solution for the inverse problem of the calculus of variations for a particular class of implicit differential equations, namely the equations of motion of free Electrodynamics.

We prove uniform resolvent estimates in weighted $L^2$-spaces for radial solutions of the sublaplacian $\mathcal{L}$ on the Heisenberg group $\mathbb{H}^d$. The proofs are based on the multipliers methods, and strongly rely on the use of suitable multipliers and of the associated Hardy inequalities. The constants in our inequalities are explicit and depend only on the dimension $d$. As application of the method, we obtain some suitable smallness and repulsivity conditions on a complex radial potential $V$ on $\mathbb{H}^d$ such that $\mathcal{L}+V$ has no radial eigenfunctions., Comment: 28 pages. Minor typos corrected. arXiv admin note: substantial text overlap with arXiv:2203.07296

Active Learning (AL) and Few Shot Learning (FSL) are two label-efficient methods which have achieved excellent results recently. However, most prior arts in both learning paradigms fail to explore the wealth of the vast unlabelled data. In this study, we address this issue in the scenario where the annotation budget is very limited, yet a large amount of unlabelled data for the target task is available. We frame this work in the context of histopathology where labelling is prohibitively expensive. To this end, we introduce an active few shot learning framework, Myriad Active Learning (MAL), including a contrastive-learning encoder, pseudo-label generation, and novel query sample selection in the loop. Specifically, we propose to massage unlabelled data in a self-supervised manner, where the obtained data representations and clustering knowledge form the basis to activate the AL loop. With feedback from the oracle in each AL cycle, the pseudo-labels of the unlabelled data are refined by optimizing a shallow task-specific net on top of the encoder. These updated pseudo-labels serve to inform and improve the active learning query selection process. Furthermore, we introduce a novel recipe to combine existing uncertainty measures and utilize the entire uncertainty list to reduce sample redundancy in AL. Extensive experiments on two public histopathology datasets show that MAL has superior test accuracy, macro F1-score, and label efficiency compared to prior works, and can achieve a comparable test accuracy to a fully supervised algorithm while labelling only 5% of the dataset., Comment: Accepted to IEEE CAI 2024. 8 pages, 2 figures. Code available at: https://github.com/mesophil/MyriadAL

The stock market presents a challenging environment for accurately predicting future stock prices due to its intricate and ever-changing nature. However, the utilization of advanced methodologies can significantly enhance the precision of stock price predictions. One such method is Hidden Markov Models (HMMs). HMMs are statistical models that can be used to model the behavior of a partially observable system, making them suitable for modeling stock prices based on historical data. Accurate stock price predictions can help traders make better investment decisions, leading to increased profits. In this article, we trained and tested a Hidden Markov Model for the purpose of predicting a stock closing price based on its opening price and the preceding day's prices. The model's performance has been evaluated using two indicators: Mean Average Prediction Error (MAPE), which specifies the average accuracy of our model, and Directional Prediction Accuracy (DPA), a newly introduced indicator that accounts for the number of fractional change predictions that are correct in sign.

Starting from a recently proposed framework for the evaluation of the cosmological averages, we evaluate the higher-order moments for the distribution of a given observable. Then, we explicitly discuss the case of the Hubble-Lema\^itre diagram and evaluate its skewness at the leading order in the cosmological perturbative expansion of the gravitational potential. In particular, we focus on perturbations of the luminosity distance due to gravitational lensing. Finally, we discuss our findings in view of recent numerical relativistic simulations, confirming that the skewness in the Hubble-Lema\^itre diagram primarily originates from the late-time matter bispectrum, with other line-of-sight projection effects being sub-dominant., Comment: 32 pages, 4 figures, references added, discussions improved, conclusions unchanged

Binary neural networks (BNNs) are an attractive solution for developing and deploying deep neural network (DNN)-based applications in resource constrained devices. Despite their success, BNNs still suffer from a fixed and limited compression factor that may be explained by the fact that existing pruning methods for full-precision DNNs cannot be directly applied to BNNs. In fact, weight pruning of BNNs leads to performance degradation, which suggests that the standard binarization domain of BNNs is not well adapted for the task. This work proposes a novel more general binary domain that extends the standard binary one that is more robust to pruning techniques, thus guaranteeing improved compression and avoiding severe performance losses. We demonstrate a closed-form solution for quantizing the weights of a full-precision network into the proposed binary domain. Finally, we show the flexibility of our method, which can be combined with other pruning strategies. Experiments over CIFAR-10 and CIFAR-100 demonstrate that the novel approach is able to generate efficient sparse networks with reduced memory usage and run-time latency, while maintaining performance., Comment: Accepted as conference paper at ECML PKDD 2023