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We study minimal left ideals in Steinberg algebras of Hausdorff groupoids. We establish a relationship between minimal left ideals in the algebra and open singletons in the unit space of the groupoid. We apply this to obtain results about the socle of Steinberg algebras under certain hypotheses. This encompasses known results about Leavitt path algebras and improves on Kumjian-Pask algebra results to include higher-rank graphs that are not row-finite., Comment: 13 pages

Binarity in massive stars has proven to be an important aspect in the their evolution. For Be stars, it might be the cause of their spin up, and thus part of the mechanism behind the formation of their viscous decretion disks. Detecting companions in systems with Be stars is challenging, making it difficult to obtain observational constraints on their binary fraction. We explore the effects of a binary companion in a system with a Be star, from disk formation to quasi steady-state using smoothed particle hydrodynamics (SPH) simulations of coplanar, circular binary systems. High spatial resolution is achieved by adopting particle splitting in the SPH code, as well as a more realistic description of the secondary star and the disk viscosity. The tidal forces considerably affect the Be disk, forming distinct regions in the system, with observational consequences that can be used to infer the presence of a otherwise undetectable companion. With the upgraded code, we can probe a region approximately 4 times larger than previously possible. We describe the configuration and kinematics of each part of the system, and provide a summary of their expected observational signals. Material that enters the Roche lobe of the companion is partially captured by it, forming a rotationally supported, disk-like structure. Material not accreted escapes and forms a circumbinary disk around the system. This is the first work to describe the region beyond the truncation region of the Be disk and its observational consequences with detail. We argue that observational features of previously unclear origin, such as the intermittent shell features and emission features of HR 2142 and HD 55606, originate in areas beyond the truncation region. This new understanding of the behavior of disks in Be binaries will allow not just for better interpretation of existing data, but also for the planning of future observations.

This work presents FreeSVC, a promising multilingual singing voice conversion approach that leverages an enhanced VITS model with Speaker-invariant Clustering (SPIN) for better content representation and the State-of-the-Art (SOTA) speaker encoder ECAPA2. FreeSVC incorporates trainable language embeddings to handle multiple languages and employs an advanced speaker encoder to disentangle speaker characteristics from linguistic content. Designed for zero-shot learning, FreeSVC enables cross-lingual singing voice conversion without extensive language-specific training. We demonstrate that a multilingual content extractor is crucial for optimal cross-language conversion. Our source code and models are publicly available.

The presence or absence of topologically-produced edge states of a crystal are robust to disorder; their stability in the presence of decay is less clear. For topologically nontrivial bosonic systems with finite particle lifetimes, such as photonic, phononic, or magnonic structures, a natural hypothesis suggests that if the linewidth from particle decay exceeds the gap between neighboring bands, then topological features such as Berry phases or edge states will lose their protection. Here we show that topological properties are significantly more robust than this, by assessing the properties of a one-dimensional magnonic crystal as the damping is increased. Even when the damping greatly exceeds the gap between neighboring bands the Zak phase of those bands is nearly unchanged, and the edge states remain clearly visible in micromagnetic simulations of microwave transmission. These results clarify the understanding of robust topological properties and bulk-boundary correspondence., Comment: 5 Pages, 4 Figures

We discuss how the two existing approximate N$^3$LO (aN$^3$LO) sets of parton distributions (PDFs) from the MSHT20 and NNPDF4.0 series can be combined for LHC phenomenology, both in the pure QCD case and for the QCD$\otimes$QED sets that include the photon PDF. Using the resulting combinations, we present predictions for the total inclusive cross-section for Higgs production in gluon fusion, vector boson fusion, and associated production at the LHC Run-3. For the gluon fusion and vector boson fusion channels, the corrections that arise when using correctly matched aN$^3$LO PDFs with N$^3$LO cross section calculations, compared to using NNLO PDFs, are significant, in many cases larger than the PDF uncertainty, and generally larger than the differences between the two aN$^3$LO PDF sets entering the combination. The combined aN$^3$LO PDF sets, MSHT20xNNPDF40_an3lo and MSHT20xNNPDF40_an3lo_qed, are made publicly available in the LHAPDF format and can be readily used for LHC phenomenology., Comment: 22 pages, 11 figures, LHAPDF grids available from https://zenodo.org/records/13843626

Fabrication of quantum processors in advanced 300 mm wafer-scale complementary metal-oxide-semiconductor (CMOS) foundries provides a unique scaling pathway towards commercially viable quantum computing with potentially millions of qubits on a single chip. Here, we show precise qubit operation of a silicon two-qubit device made in a 300 mm semiconductor processing line. The key metrics including single- and two-qubit control fidelities exceed 99% and state preparation and measurement fidelity exceeds 99.9%, as evidenced by gate set tomography (GST). We report coherence and lifetimes up to $T_\mathrm{2}^{\mathrm{*}} = 30.4$ $\mu$s, $T_\mathrm{2}^{\mathrm{Hahn}} = 803$ $\mu$s, and $T_1 = 6.3$ s. Crucially, the dominant operational errors originate from residual nuclear spin carrying isotopes, solvable with further isotopic purification, rather than charge noise arising from the dielectric environment. Our results answer the longstanding question whether the favourable properties including high-fidelity operation and long coherence times can be preserved when transitioning from a tailored academic to an industrial semiconductor fabrication technology., Comment: 10 pages, 4 figures, 4 extended data figures

Calibration of quantum devices is fundamental to successfully deploy quantum algorithms on current available quantum hardware. We present Qibocal, an open-source software library to perform calibration and characterization of superconducting quantum devices within the Qibo framework. Qibocal completes the Qibo middleware framework by providing all necessary tools to easily (re)calibrate self-hosted quantum platforms. After presenting the layout and the features of the library, we give an overview on some of the protocols implemented to perform single and two-qubit gates calibration. Finally, we present applications involving recalibration and monitoring of superconducting platforms., Comment: 12 pages, 9 figures, code available at https://github.com/qiboteam/qibocal

We developed a jitted compiler for training Artificial Neural Networks using C++, LLVM and Cuda. It features object-oriented characteristics, strong typing, parallel workers for data pre-processing, pythonic syntax for expressions, PyTorch like model declaration and Automatic Differentiation. We implement the mechanisms of cache and pooling in order to manage VRAM, cuBLAS for high performance matrix multiplication and cuDNN for convolutional layers. Our experiments with Residual Convolutional Neural Networks on ImageNet, we reach similar speed but degraded performance. Also, the GRU network experiments show similar accuracy, but our compiler have degraded speed in that task. However, our compiler demonstrates promising results at the CIFAR-10 benchmark, in which we reach the same performance and about the same speed as PyTorch. We make the code publicly available at: https://github.com/NoSavedDATA/NoSavedKaleidoscope, Comment: 12 pages, 3 figures and 3 tables

Using Ostaszewski's $\clubsuit$-principle, we construct a non-metrizable, locally compact, scattered space $L$ in which the operators on the Banach space $C_0(L \times L)$ exhibit a remarkably simple structure. We provide a detailed analysis and, through a series of decomposition steps, offer an explicit characterization of all operators on $C_0(L \times L)$.

We present a freely available spontaneous speech corpus for the Brazilian Portuguese language and report preliminary automatic speech recognition (ASR) results, using both the Wav2Vec2-XLSR-53 and Distil-Whisper models fine-tuned and trained on our corpus. The NURC-SP Audio Corpus comprises 401 different speakers (204 females, 197 males) with a total of 239.30 hours of transcribed audio recordings. To the best of our knowledge, this is the first large Paulistano accented spontaneous speech corpus dedicated to the ASR task in Portuguese. We first present the design and development procedures of the NURC-SP Audio Corpus, and then describe four ASR experiments in detail. The experiments demonstrated promising results for the applicability of the corpus for ASR. Specifically, we fine-tuned two versions of Wav2Vec2-XLSR-53 model, trained a Distil-Whisper model using our dataset with labels determined by Whisper Large-V3 model, and fine-tuned this Distil-Whisper model with our corpus. Our best results were the Distil-Whisper fine-tuned over NURC-SP Audio Corpus with a WER of 24.22% followed by a fine-tuned versions of Wav2Vec2-XLSR-53 model with a WER of 33.73%, that is almost 10% point worse than Distil-Whisper's. To enable experiment reproducibility, we share the NURC-SP Audio Corpus dataset, pre-trained models, and training recipes in Hugging-Face and Github repositories.

This study presents the design, simulation, and experimental characterization of a superconducting transmon qubit circuit prototype for potential applications in dark matter detection experiments. We describe a planar circuit design featuring two non-interacting transmon qubits, one with fixed frequency and the other flux tunable. Finite-element simulations were employed to extract key Hamiltonian parameters and optimize component geometries. The qubit was fabricated and then characterized at $20$ mK, allowing for a comparison between simulated and measured qubit parameters. Good agreement was found for transition frequencies and anharmonicities (within 1\% and 10\% respectively) while coupling strengths exhibited larger discrepancies (30\%). We discuss potential causes for measured coherence times falling below expectations ($T_1\sim\,$1-2 \textmu s) and propose strategies for future design improvements. Notably, we demonstrate the application of a hybrid 3D-2D simulation approach for energy participation ratio evaluation, yielding a more accurate estimation of dielectric losses. This work represents an important first step in developing planar Quantum Non-Demolition (QND) single-photon counters for dark matter searches, particularly for axion and dark photon detection schemes.

Advancing Machine Learning (ML)-based perception models for autonomous systems necessitates addressing weak spots within the models, particularly in challenging Operational Design Domains (ODDs). These are environmental operating conditions of an autonomous vehicle which can contain difficult conditions, e.g., lens flare at night or objects reflected in a wet street. This report introduces a novel methodology for training with augmentations to enhance model robustness and performance in such conditions. The proposed approach leverages customized physics-based augmentation functions, to generate realistic training data that simulates diverse ODD scenarios. We present a comprehensive framework that includes identifying weak spots in ML models, selecting suitable augmentations, and devising effective training strategies. The methodology integrates hyperparameter optimization and latent space optimization to fine-tune augmentation parameters, ensuring they maximally improve the ML models' performance. Experimental results demonstrate improvements in model performance, as measured by commonly used metrics such as mean Average Precision (mAP) and mean Intersection over Union (mIoU) on open-source object detection and semantic segmentation models and datasets. Our findings emphasize that optimal training strategies are model- and data-specific and highlight the benefits of integrating augmentations into the training pipeline. By incorporating augmentations, we observe enhanced robustness of ML-based perception models, making them more resilient to edge cases encountered in real-world ODDs. This work underlines the importance of customized augmentations and offers an effective solution for improving the safety and reliability of autonomous driving functions.

The FitzHugh-Nagumo system is a $4$-parameter family of $3$D vector field used for modeling neural excitation and nerve impulse propagation. The origin represents a Hopf-zero equilibrium in the FitzHugh-Nagumo system for two classes of parameters. In this paper, we employ recent techniques in averaging theory to investigate, besides periodic solutions, the bifurcation of invariant tori within the aforementioned families. We provide explicit generic conditions for the existence of these tori and analyze their stability properties. Furthermore, we employ the backward differentiation formula to solve the stiff differential equations and provide numerical simulations for each of the mentioned results.

We present a new prescription to account for heavy quark mass effects in the determination of parton distribution functions (PDFs) based on the FONLL scheme. Our prescription makes explicit use of the freedom to choose the number of active flavors at a given scale and, thus, use coexisting PDFs with different active flavor number. This new prescription is perturbatively equivalent to the former but improves the implementation in two ways. First, it can be naturally generalized to account simultaneously for multiple heavy quark effects, such as charm and bottom effects, which can both be relevant at the same scale due to the small mass difference. Second, it can be trivially generalized to use at any fixed-order or collinear resummed accuracy, while previous prescriptions required ad-hoc expansions of the DGLAP evolution kernels for each coefficient. We supplement the paper with codes for the computation of deep inelastic scattering observables in this new prescription., Comment: 17 pages, 4 figures. Version as published in JHEP. Various clarifications added. A new appendix (now App. A) added. Code documentation available from https://pineko.readthedocs.io/en/latest/theory/fonll.html

The development of quantum computers needs reliable quantum hardware and tailored software for controlling electronics specific to various quantum platforms. Middleware is a type of computer software program that aims to provide standardized software tools across the entire pipeline, from high level execution of quantum computing algorithms to low level driver instructions tailored to specific experimental setups, including instruments. This paper presents updates to Qibolab, a software library that leverages Qibo capabilities to execute quantum algorithms on self hosted quantum hardware platforms. Qibolab offers an application programming interface (API) for instrument control through arbitrary pulses and driver operations including sweepers. This paper offers an overview of the new features implemented in Qibolab, including the redefined boundaries between platform and channel classes, the integration of an emulator for simulating quantum hardware behaviour, and it shows updated execution times benchmarks for superconducting single qubit calibration routines., Comment: 6 pages, 3 figures, proceedings for ACAT24, code available at https://github.com/qiboteam/qibolab

We contrast high effectiveness of state of the art deep learning architectures designed for general audio classification tasks, refined for respiratory insufficiency (RI) detection and blood oxygen saturation (SpO$_2$) estimation and classification through automated audio analysis. Recently, multiple deep learning architectures have been proposed to detect RI in COVID patients through audio analysis, achieving accuracy above 95% and F1-score above 0.93. RI is a condition associated with low SpO$_2$ levels, commonly defined as the threshold SpO$_2$ <92%. While SpO$_2$ serves as a crucial determinant of RI, a medical doctor's diagnosis typically relies on multiple factors. These include respiratory frequency, heart rate, SpO$_2$ levels, among others. Here we study pretrained audio neural networks (CNN6, CNN10 and CNN14) and the Masked Autoencoder (Audio-MAE) for RI detection, where these models achieve near perfect accuracy, surpassing previous results. Yet, for the regression task of estimating SpO$_2$ levels, the models achieve root mean square error values exceeding the accepted clinical range of 3.5% for finger oximeters. Additionally, Pearson correlation coefficients fail to surpass 0.3. As deep learning models perform better in classification than regression, we transform SpO$_2$-regression into a SpO$_2$-threshold binary classification problem, with a threshold of 92%. However, this task still yields an F1-score below 0.65. Thus, audio analysis offers valuable insights into a patient's RI status, but does not provide accurate information about actual SpO$_2$ levels, indicating a separation of domains in which voice and speech biomarkers may and may not be useful in medical diagnostics under current technologies., Comment: 23 pages, 4 figures, in review at Journal of Biomedical Signal Processing and Control

In this paper, we establish a connection between evolution algebras of dimension two and Hopf algebras, via the algebraic group of automorphisms of an evolution algebra. Initially, we describe the Hopf algebra associated with the automorphism group of a 2-dimensional evolution algebra. Subsequently, for a 2-dimensional evolution algebra $A$ over a field $K$, we detail the relation between the algebra associated with the (tight) universal associative and commutative representation of $A$, referred to as the (tight) $p$-algebra, and the corresponding Hopf algebra, $\mathcal{H}$, representing the affine group scheme $\text{Aut}(A)$. Our analysis involves the computation of the (tight) $p-$algebra associated with any 2-dimensional evolution algebra, whenever it exists. We find that $\text{Aut}(A)=1$ if and only if there is no faithful associative and commutative representation for $A$. Moreover, there is a faithful associative and commutative representation for $A$ if and only if $\mathcal{H}\not\cong K$ and $\text{char} (K)\neq 2$, or $\mathcal{H}\not\cong K(\epsilon)$ (the dual numbers algebra) and $\mathcal{H}\not\cong K$ in case of $\text{char} (K)= 2$. Furthermore, if $A$ is perfect and has a faithful tight $p$-algebra, then this $p$-algebra is isomorphic to $\mathcal{H}$ (as algebras). Finally, we derive implications for arbitrary finite-dimensional evolution algebras.

Large Language Models (LLMs) are increasingly bringing advances to Natural Language Processing. However, low-resource languages, those lacking extensive prominence in datasets for various NLP tasks, or where existing datasets are not as substantial, such as Portuguese, already obtain several benefits from LLMs, but not to the same extent. LLMs trained on multilingual datasets normally struggle to respond to prompts in Portuguese satisfactorily, presenting, for example, code switching in their responses. This work proposes a fine-tuned LLaMA 2-based model for Portuguese prompts named Bode in two versions: 7B and 13B. We evaluate the performance of this model in classification tasks using the zero-shot approach with in-context learning, and compare it with other LLMs. Our main contribution is to bring an LLM with satisfactory results in the Portuguese language, as well as to provide a model that is free for research or commercial purposes., Comment: 10 pages, 3 figures

We investigate the Shubnikov-de Haas (SdH) magneto-oscillations in the resistivity of two-dimensional topological insulators (TIs). Within the Bernevig-Hughes-Zhang (BHZ) model for TIs in the presence of a quantizing magnetic field, we obtain analytical expressions for the SdH oscillations by combining a semiclassical approach for the resistivity and a trace formula for the density of states. We show that when the non-trivial topology is produced by inverted bands with ''Mexican-hat'' shape, SdH oscillations show an anomalous beating pattern that is {\it solely} due to the non-trivial topology of the system. These beatings are robust against, and distinct from beatings originating from spin-orbit interactions. This provides a direct way to experimentally probe the non-trivial topology of 2D TIs entirely from a bulk measurement. Furthermore, the Fourier transform of the SdH oscillations as a function of the Fermi energy and quantum capacitance models allows for extracting both the topological gap and gap at zero momentum., Comment: 6 pages, 3 figures

We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a projectional skeleton, Banach spaces with a $w^*$-separable dual unit ball and locally separable complete metric spaces.

This work investigates Artificial Intelligence (AI) systems that detect respiratory insufficiency (RI) by analyzing speech audios, thus treating speech as a RI biomarker. Previous works collected RI data (P1) from COVID-19 patients during the first phase of the pandemic and trained modern AI models, such as CNNs and Transformers, which achieved $96.5\%$ accuracy, showing the feasibility of RI detection via AI. Here, we collect RI patient data (P2) with several causes besides COVID-19, aiming at extending AI-based RI detection. We also collected control data from hospital patients without RI. We show that the considered models, when trained on P1, do not generalize to P2, indicating that COVID-19 RI has features that may not be found in all RI types., Comment: 5 pages, 2 figures, 1 table. Published in Artificial Intelligence in Medicine (AIME) 2023

Dual topological insulators (DTIs) are simultaneously protected by time-reversal and crystal symmetries, representing advantageous alternatives to conventional topological insulators. By combining ab initio calculations and the $\mathbf{k}\cdot\mathbf{p}$ approach, here, we investigate the electronic band structure of a Na$_2$CdSn triatomic layer and derive a low-energy $4\times 4$ effective model consistent with all the symmetries of this material class. We obtain the effective Hamiltonian using the L\"owdin perturbation theory, the folding-down technique, and the theory of invariants and determine its parameters by fitting our analytical dispersion relations to those of ab initio calculations. We then calculate the bulk topological invariants of the system and show that the Na$_2$CdSn triatomic layer is a giant-gap (hundreds of millielectronvolts) quasi-two-dimensional DTI characterized by both spin and mirror Chern numbers $-2$. In agreement with the bulk-boundary correspondence theorem, we find that a finite-width strip of Na$_2$CdSn possesses two pairs of counterpropagating helical edge states per interface. We obtain analytical expressions for the edge state energy dispersions and wave functions, which are shown to agree with our numerical calculations. Our work opens an avenue for further studies of Na$_2$CdSn as a potential DTI candidate with room-temperature applications in areas of technological interest, such as nanoelectronics and spintronics.

Here, we calculate and study correlations of the Dicke model in the presence of qubit-qubit interaction. Whereas the analysis of correlations among its subsystems is essential for the understanding of corresponding critical phenomena and for performing quantum information tasks, the majority of correlation measures are restricted to bipartitions due to the inherent challenges associated with handling multiple partitions. To circunvent this we employ the calculation of Genuine Multipartite Correlations (GMC) based on the invariance of our model under particle permutation. We then quantify the correlations within each subpart of the system, as well as the percentage contribution of each GMC of order $k$, highlighting the many-body behaviors for different regimes of parameters. Additionally, we show that GMC signal both first- and second-order quantum phase transitions present in the model. Furthermore, as GMC encompasses both classical and quantum correlations, we employ Quantum Fisher Information (QFI) to detect genuine multipartite entanglement. Ultimately, we map the Dicke model with interacting qubits to spin in solids interacting with a quantum field of magnons, thus demonstrating a potential experimental realization of this model., Comment: 10 pages, 3 figures

The group scheme of ternary automorphisms of a perfect finite dimensional evolution algebra A is computed. The main advantage of using group schemes is that it allows to apply the Lie functor to determine the Lie algebra of ternary derivations of A. Using the generalised inverse of a matrix, we provide a precise classification of all ternary derivations of an arbitrary finite-dimensional evolution algebra A. The ternary derivations of all 2-dimensional evolution algebras are also computed.

Electronic correlation is a complex many-body effect and the correlation energy depends on the specific electronic structure and spatial distribution of electrons in each atom and molecule. Although the total correlation energy in an atom can be decomposed into different components such as inter-orbital and intra-orbital pair-correlation energies (PCE), it is generally believed that the PCEs in different atoms cannot be the same. In this work, we investigate the correlation energies of the atoms in the first three rows of the periodic table (He to Ar). It is found that when the correlation energy is defined as the difference between the exact ground-state energy and the unrestricted Hartree-Fock (UHF) energy, the inter- and intra-orbital PECs associated with the valence electrons of the atoms in the same row of the periodic table have the same values. These PCEs are not entangled and their values depend only on the electron orbitals. For two specific orbitals, the inter-orbital correlation energy is the same between two electrons of parallel spins or anti-parallel spins. We also show that the effects of orbital relaxation on the correlation energy are surprisingly small., Comment: 6 pages, 1 figure, and 2 tables

As the demand for Internet of Things (IoT) and Human-to-Machine Interaction (HMI) increases, modern System-on-Chips (SoCs) offering such solutions are becoming increasingly complex. This intricate design poses significant challenges for verification, particularly when time-to-market is a crucial factor for consumer electronics products. This paper presents a case study based on our work to verify a complex Radio Detection And Ranging (RADAR) based SoC that performs on-chip sensing of human motion with millimetre accuracy. We leverage both formal and simulation-based methods to complement each other and achieve verification sign-off with high confidence. While employing a requirements-driven flow approach, we demonstrate the use of different verification methods to cater to multiple requirements and highlight our know-how from the project. Additionally, we used Machine Learning (ML) based methods, specifically the Xcelium ML tool from Cadence, to improve verification throughput., Comment: Published in DVCon Europe 2023

The leitmotiv of this paper is linking algebraic properties of an evolution algebra with combinatorial properties of the (possibly several) graphs that one can associate to the algebra. We link nondegeneracy, zero annihilator, absorption property, von Neumann regularity, and primeness with suitable properties in the associated graph. In the presence of semiprimeness, the property of primeness is equivalent to any associated graph being downward directed. We also provide a description of the prime ideals in an evolution algebra and prove that certain algebraic properties, such as semiprimeness and perfection, can not be characterized in combinatorial terms. We describe the centroid of evolution algebras as constant functions along the connected components of its associated graph. The dimension of the centroid of a zero annihilator algebra $A$ agrees with the cardinal of the connected components of any possible graph associated to $A$. This is the combinatorial expression of an algebraic uniqueness property in the decomposition of $A$ as indecomposable algebras with $1$-dimensional centroid.

We discuss a Bayesian methodology for the solution of the inverse problem underlying the determination of parton distribution functions (PDFs). In our approach, Gaussian Processes (GPs) are used to model the PDF prior, while Bayes theorem is used in order to determine the posterior distribution of the PDFs given a set of data. We discuss the general formalism, the Bayesian inference at the level of both parameters and hyperparameters, and the simplifications which occur when the observable entering the analysis is linear in the PDF. We benchmark the new methodology in two simple examples for the determination of a single PDF flavor from a set of Deep Inelastic Scattering (DIS) data and from a set of equal-time correlators computed using lattice QCD. We discuss our results, showing how the proposed methodology allows for a well-defined statistical interpretation of the different sources of errors entering the PDF uncertainty, and how results can be validated a posteriori.

This work is motivated by the interest in determining the effect of the micro-anatomy of the spinal subarachnoid space on the cerebrospinal fluid flow and on the associated transport of solutes. To that aim, we focus on a canonical model problem in which a circular post of radius $a$, confined between two parallel plates separated by a distance $2h$, is subjected to an oscillatory flow. In particular, we are concerned with the steady, viscous, time-averaged flow that persists in the vicinity on the cylinder, when the stroke length of the oscillating flow, $U_{\infty}/\omega$ is smaller or comparable to the radius of the post, $a$, where $U_{\infty}$ and $\omega$ are the mean velocity amplitude and the corresponding angular frequency, respectively. First, we analyze the asymptotic limit of small values of the stroke length varying the aspect ratio of the post $\lambda$ and the Womersley number $M$. First-order steady-streaming corrections at leading order have been computed, together with associated Stokes-drift component, the sum of both yielding the mean Lagrangian velocity field. The confinement effect is seen to induce the three-dimensionality of flow. Moreover, in the mid plane the time-averaged steady flow exhibits a recirculating vortex attached to the wall of the post that decreases as $M$ increases for low values of $M$. However, for values of $M$ larger than a critical one, $M_{cr}(\lambda)$, a second, outer vortex is also formed. The dependence $M_{cr}(\lambda)$ has been quantified. The analysis has been corroborated experimentally for a fixed aspect ratio. Consideration of an anharmonic oscillating flow shows the fort-and-aft symmetry of the steady flow is broken. Finally, the analysis is experimentally extended to consider an array of equally spaced posts., Comment: 24 pages, 13 figures

In this paper, we analyze the effects of random sampling on adaptive diffusion networks. These networks consist in a collection of nodes that can measure and process data, and that can communicate with each other to pursue a common goal of estimating an unknown system. In particular, we consider in our theoretical analysis the diffusion least-mean-squares algorithm in a scenario in which the nodes are randomly sampled. Hence, each node may or may not adapt its local estimate at a certain iteration. Our model shows that, if the nodes cooperate, a reduction in the sampling probability leads to a slight decrease in the steady-state Network Mean-Square Deviation (NMSD), assuming that the environment is stationary and that all other parameters of the algorithm are kept fixed. Furthermore, under certain circumstances, this can also ensure the stability of the algorithm in situations in which it would otherwise be unstable. Although counter-intuitive, our findings are backed by simulation results, which match the theoretical curves well., Comment: Submitted to the IEEE Transactions on Signal Processing

We extend the existing leading (LO), next-to-leading (NLO), and next-to-next-to-leading order (NNLO) NNPDF4.0 sets of parton distribution functions (PDFs) to approximate next-to-next-to-next-to-leading order (aN$^3$LO). We construct an approximation to the N$^3$LO splitting functions that includes all available partial information from both fixed-order computations and from small and large $x$ resummation, and estimate the uncertainty on this approximation by varying the set of basis functions used to construct the approximation. We include known N$^3$LO corrections to deep-inelastic scattering structure functions and extend the FONLL general-mass scheme to $\mathcal{O}\left( \alpha_s^3\right)$ accuracy. We determine a set of aN$^3$LO PDFs by accounting both for the uncertainty on splitting functions due to the incomplete knowledge of N$^3$LO terms, and to the uncertainty related to missing higher corrections (MHOU), estimated by scale variation, through a theory covariance matrix formalism. We assess the perturbative stability of the resulting PDFs, we study the impact of MHOUs on them, and we compare our results to the aN$^3$LO PDFs from the MSHT group. We examine the phenomenological impact of aN$^3$LO corrections on parton luminosities at the LHC, and give a first assessment of the impact of aN$^3$LO PDFs on the Higgs and Drell-Yan total production cross-sections. We find that the aN$^3$LO NNPDF4.0 PDFs are consistent within uncertainties with their NNLO counterparts, that they improve the description of the global dataset and the perturbative convergence of Higgs and Drell-Yan cross-sections, and that MHOUs on PDFs decrease substantially with the increase of perturbative order., Comment: 63 pages, 41 figures. Final version, as published in EPJC. Various clarifications added. Fig 2.9 and Tab. 4.6, 5.1 and 5.2 added. In particular, comparison to approximate YR4 estimate of PDF uncertainties added (Tab 4.1, 4.2 and associate discussion in sect. 5)