Miracle-dz/UniFAR-FTUs huggingface dataset:
On the use of Hadamard expansions in hyperasymptotic evaluation. II Complex variables

This paper extends the method of hyperasymptotic evaluation using absolutely convergent Hadamard expansions, developed in the first part, to the confluent hypergeometric functions of complex argument z. It is shown that the representation of this class of functions involves an infinite number of Hadamard expansions associated with a decreasing sequence of subdominant exponential levels for large |z|. Numerical examples involving the Bessel functions are given to illustrate the attainable levels of accuracy.
Landau theory-based analysis of grain-size dependence of ferroelectric-to-paraelectric phase transition and its thermal hysteresis in barium titanate ceramics

Ferroelectric barium titanate ceramics with grain sizes in the range (0.5, 20) µm were used for a comparative study of grain-size influence on the ferro-para phase transition and its thermal hysteresis. The investigations were performed by recording the temperature dependence of the dielectric constant, heat capacity and pyrocharge. The experimental results have been analysed in the framework of Landau-Devonshire theory. The grain-size dependent Landau coefficients of the free energy have been derived from our experimental data and used to compute the grain-size dependence of the theoretical transition interval related to the thermal hysteresis. The good qualitative agreement between theory and experiment recommends the size dependent Landau coefficients as a way to improve the modelling of the size dependent ferro-para phase transition in ceramics.
A role for M -matrices in modelling population growth

Adopting a discrete-time cohort-type model to represent the dynamics of a population, the problem of achieving a desired total size of the population under a balanced growth (contraction) and the problem of maintaining the desired size, once achieved, are studied. Properties of positive-time systems and M-matrices are used to develop the results, which are illustrated using simple examples. The material is presented in a format that makes it appropriate as background material for interesting applications based modelling assignments on undergraduate programmes in the mathematical sciences, applied sciences, economics and technology. All relevant properties of both positive-time systems and M-matrices are presented and clarified at the outset.
Recent Advances on Federated Learning: A Systematic Survey

Federated learning has emerged as an effective paradigm to achieve privacy-preserving collaborative learning among different parties. Compared to traditional centralized learning that requires collecting data from each party, in federated learning, only the locally trained models or computed gradients are exchanged, without exposing any data information. As a result, it is able to protect privacy to some extent. In recent years, federated learning has become more and more prevalent and there have been many surveys for summarizing related methods in this hot research topic. However, most of them focus on a specific perspective or lack the latest research progress. In this paper, we provide a systematic survey on federated learning, aiming to review the recent advanced federated methods and applications from different aspects. Specifically, this paper includes four major contributions. First, we present a new taxonomy of federated learning in terms of the pipeline and challenges in federated scenarios. Second, we summarize federated learning methods into several categories and briefly introduce the state-of-the-art methods under these categories. Third, we overview some prevalent federated learning frameworks and introduce their features. Finally, some potential deficiencies of current methods and several future directions are discussed.
Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices

The study of non-equilibrium dynamics is one of the most important challenges of modern quantum many-body physics, in relationship with fundamental questions in quantum statistical mechanics, as well as with the fields of quantum simulation and computing. In this work we propose a Gaussian Ansatz for the study of the nonequilibrium dynamics of quantum spin systems. Within our approach, the quantum spins are mapped onto Holstein-Primakoff bosons, such that a coherent spin state - chosen as the initial state of the dynamics - represents the bosonic vacuum. The state of the system is then postulated to remain a bosonic Gaussian state at all times, an assumption which is exact when the bosonic Hamiltonian is quadratic; and which is justified in the case of a nonlinear Hamiltonian if the boson density remains moderate. We test the accuracy of such an Ansatz in the paradigmatic case of the S=1/2S=1/2 transverse-field Ising model, in one and two dimensions, initialized in a state aligned with the applied field. We show that the Gaussian Ansatz, when applied to the bosonic Hamiltonian with nonlinearities truncated to quartic order, is able to reproduce faithfully the evolution of the state, including its relaxation to the equilibrium regime, for fields larger than the critical field for the paramagnetic-ferromagnetic transition in the ground state. In particular the spatio-temporal pattern of correlations reconstructed via the Gaussian Ansatz reveals the dispersion relation of quasiparticle excitations, exhibiting the softening of the excitation gap upon approaching the critical field. Our results suggest that the Gaussian Ansatz correctly captures the essential effects of nonlinearities in quantum spin dynamics; and that it can be applied to the study of fundamental phenomena such as quantum thermalization and its breakdown.
Provably Fast and Space-Efficient Parallel Biconnectivity

Computing biconnected components (BCC) of a graph is a fundamental graph problem. The canonical parallel BCC algorithm is the Tarjan-Vishkin algorithm, which has O(n + m) optimal work and polylogarithmic span on a graph with n vertices and m edges. However, Tarjan-Vishkin is not widely used in practice. We believe the reason is the space-inefficiency (it uses O(m) extra space). In practice, existing parallel implementations are based on breath-first search (BFS). Since BFS has span proportional to the diameter of the graph, existing parallel BCC implementations suffer from poor performance on large-diameter graphs and can be slower than the sequential algorithm on many real-world graphs. We propose the first p arallel b iconnectivity algorithm (FAST-BCC) that has optimal work, polylogarithmic span, and is space-efficient. Our algorithm creates a skeleton graph based on any spanning tree of the input graph. Then we use the connectivity information of the skeleton to compute the biconnectivity of the original input. We carefully analyze the correctness of our algorithm, which is highly non-trivial. We implemented FAST-BCC and compared it with existing implementations, including GBBS, Slota and Madduri's algorithm, and the sequential Hopcroft-Tarjan algorithm. We tested them on a 96-core machine on 27 graphs with varying edge distributions. FAST-BCC is the fastest on all graphs. On average (geometric means), FAST-BCC is 3.1× faster than the best existing baseline on each graph.
Multi-Task System Identification of Similar Linear Time-Invariant Dynamical Systems

This paper presents a system identification framework - inspired by multi-task learning - to estimate the dynamics of a given number of linear time-invariant (LTI) systems jointly by leveraging structural similarities across the systems. In particular, we consider LTI systems that model networked systems with similar connectivity, or LTI systems with small differences in their matrices. The system identification task involves the minimization of the least-squares (LS) fit for individual systems, augmented with a regularization function that enforces structural similarities. The proposed method is particularly suitable for cases when the recorded trajectories for one or more LTI systems are not sufficiently rich, leading to ill-conditioning of LS methods. We analyze the performance of the proposed method when the matrices of the LTI systems feature a common sparsity pattern (i.e., similar connectivity), and provide simulations based on real data for the estimation of the brain dynamics. We show that the proposed method requires a significantly smaller number of fMRI scans to achieve similar error levels of the LS.
The e-posterior

We develop a representation of a decision maker’s uncertainty based on e-variables. Like the Bayesian posterior, this e-posterior allows for making predictions against arbitrary loss functions that may not be specified ex ante. Unlike the Bayesian posterior, it provides risk bounds that have frequentist validity irrespective of prior adequacy: if the e-collection (which plays a role analogous to the Bayesian prior) is chosen badly, the bounds get loose rather than wrong, making e-posterior minimax decision rules safer than Bayesian ones. The resulting quasi-conditional paradigm is illustrated by re-interpreting a previous influential partial Bayes-frequentist unification, Kiefer–Berger–Brown–Wolpert conditional frequentist tests, in terms of e-posteriors. This article is part of the theme issue ‘Bayesian inference: challenges, perspectives, and prospects’.
Non-singular actions of infinite-dimensional groups and polymorphisms

Let $Z$ be a probabilistic measure space with a measure $\zeta$, $\mathbb{R}^\times$ be the multiplicative group of positive reals, let $t$ be the coordinate on $\mathbb{R}^\times$. A polymorphism of $Z$ is a measure $\pi$ on $Z\times Z\times \mathbb{R}^\times$ such that for any measurable $A$, $B\subset Z$ we have $\pi(A\times Z\times \mathbb{R}^\times)=\zeta(A)$ and the integral $\int t\,d\pi(z,u,t)$ over $Z\times B\times \mathbb{R}^\times$ is $\zeta(B)$. The set of all polymorphisms has a natural semigroup structure, the group of all nonsingular transformations is dense in this semigroup. We discuss a problem of closure in polymorphisms for certain types of infinite dimensional ('large') groups and show that a non-singular action of an infinite-dimensional group generates a representation of its train (category of double cosets) by polymorphisms.
Modeling communication asymmetry and algorithmic personalization in online social networks

Modeling social interactions and their impact on opinion dynamics has attracted growing interest in recent decades, fuelled by the mounting popularity of online social networks (OSNs). On online social platforms, a few individuals, commonly referred to as inﬂuencers , produce the majority of content consumed by users. However, classic opinion models do not capture this communication asymmetry in OSNs. We develop an opinion model inspired by observations on leading social media platforms and tailored to the peculiarities of online interactions. Our work has two main objectives: ﬁrst, to describe the inherent communication asymmetry in OSNs, where a tiny group of inﬂuencers hegemonizes the landscape of social debate, and second, to model the personalization of content by the social media platform. We derive a Fokker-Planck equation for the temporal evolution of users’ opinion distribution and analytically characterize the stationary system behavior. Analytical results, conﬁrmed by Monte Carlo simulations, show how content personalization tends to radicalize user opinion and favor structurally advantaged inﬂuencers. These emerging behaviors suggest that algorithmic bias, inherently associated with platform ﬁltering, can lead to undesirable outcomes. As an example application, we apply our model to Facebook during the Italian government crisis in the summer of 2019. Our work provides a ﬂexible framework to assess the impact of algorithmic ﬁltering on the opinion formation process and a ﬁne-grained tool to study the complex interaction between inﬂuencers and social network users.
Identifying Personal Data Processing for Code Review

Code review is a critical step in the software development life cycle, which assesses and boosts the code's effectiveness and correctness, pinpoints security issues, and raises its quality by adhering to best practices. Due to the increased need for personal data protection motivated by legislation, code reviewers need to understand where personal data is located in software systems and how it is handled. Although most recent work on code review focuses on security vulnerabilities, privacy-related techniques are not easy for code reviewers to implement, making their inclusion in the code review process challenging. In this paper, we present ongoing work on a new approach to identifying personal data processing, enabling developers and code reviewers in drafting privacy analyses and complying with regulations such as the General Data Protection Regulation (GDPR).
Towards Explainable Land Cover Mapping: a Counterfactual-based Strategy

Counterfactual explanations are an emerging tool to enhance interpretability of deep learning models. Given a sample, these methods seek to find and display to the user similar samples across the decision boundary. In this paper, we propose a generative adversarial counterfactual approach for satellite image time series in a multi-class setting for the land cover classification task. One of the distinctive features of the proposed approach is the lack of prior assumption on the targeted class for a given counterfactual explanation. This inherent flexibility allows for the discovery of interesting information on the relationship between land cover classes. The other feature consists of encouraging the counterfactual to differ from the original sample only in a small and compact temporal segment. These time-contiguous perturbations allow for a much sparser and, thus, interpretable solution. Furthermore, plausibility/realism of the generated counterfactual explanations is enforced via the proposed adversarial learning strategy.
Influence of incompressible surfactant on drag in flow along an array of gas-filled grooves

Surfactants can have a detrimental effect on the drag reduction in shear flow over superhydrophobic surfaces in Cassie state. While surfactant-free gas-liquid interfaces are often well approximated as shear-free, surfactants can impede the flow by stacking up in front of obstacles. We study shear-flow along an array of narrow gas-filled grooves of finite length embedded in an otherwise planar surface, with the gas-liquid interface protruding slightly above or below the plane. Assuming immiscible surfactants forming an incompressible, inviscid surfactant phase at the gas-liquid interfaces we employ a recently proposed model [Baier and Hardt, J.Fluid Mech. , 949 (2022)] for addressing this situation. Using a domain perturbation technique together with the Lorentz reciprocal theorem we obtain the slip length characterizing the flow over such surfaces to second order in the maximal interface deflection as a small parameter. We find that within the range of moderate interface deflections studied, the slip length for flow over such surfaces is negative (positive) for surfaces protruding above (below) the surface and is much smaller than for flow over a corresponding surfactant-free interface. Thus, contrary to expectations of reduced drag in flow over superhydrophobic surfaces in Cassie state, surfactant covered interfaces can even be detrimental for drag reduction in the limit where surfactants act as an effectively incompressible surface-fluid. This has important implications for the appropriate design of superhydrophobic surfaces for reducing flow resistance.
Entropy dissipative higher order accurate positivity preserving time-implicit discretizations for nonlinear degenerate parabolic equations

We develop entropy dissipative higher order accurate local discontinuous Galerkin (LDG) discretizations coupled with Diagonally Implicit Runge-Kutta (DIRK) methods for nonlinear degenerate parabolic equations with a gradient flow structure. Using the simple alternating numerical flux, we construct DIRK-LDG discretizations that combine the advantages of higher order accuracy, entropy dissipation and proper long-time behavior. The implicit time-discrete methods greatly alleviate the time-step restrictions needed for the stability of the numerical discretizations. Also, the larger time step significantly improves computational efficiency. We theoretically prove the unconditional entropy dissipation of the implicit Euler-LDG discretization. Next, in order to ensure the positivity of the numerical solution, we use the Karush-Kuhn-Tucker (KKT) limiter, which couples the positivity inequality constraint with higher order accurate DIRK-LDG discretizations using Lagrange multipliers. In addition, mass conservation of the positivity-limited solution is ensured by imposing a mass conservation equality constraint to the KKT equations. The unique solvability and unconditional entropy dissipation for an implicit first order accurate in time, but higher order accurate in space, KKT-LDG discretizations are proved, which provides a first theoretical analysis of the KKT limiter. Finally, numerical results demonstrate the higher order accuracy and entropy dissipation of the KKT-DIRK-LDG discretizations for problems requiring a positivity limiter.
Unimodular approaches to the cosmological constant problem

We review selected aspects of unimodular gravity and we discuss its viability as a solution of the old cosmological constant problem. In unimodular gravity the cosmological constant is promoted to a global degree of freedom. We highlight the importance of correctly setting up its initial data in order to achieve a resolution of the cosmological constant problem on a semi-classical level. We review recent path integral analysis of quantum aspects of unimodular gravity to note that the semi-classical findings carry over to the quantum level as well. We point out that a resolution of the problem inherently relies on a global constraint on the space-time four-volume. This makes the theory closely related to the vacuum energy sequester, which operates in a similar way. We discuss possible avenues of extending unimodular gravity that preserve the resolution of the cosmological constant problem.
Spectral analysis and $k$-spine decomposition of inhomogeneous branching Brownian motions. Genealogies in fully pushed fronts

We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift $-\mu$ and killed upon reaching $0$. More precisely, the particles branch at rate $r(x)=(1+f(x))/2,$ where $f$ is a compactly supported and non-negative smooth function and the drift $\mu$ is chosen in such a way that the system is critical in some sense. This particle system can be seen as an analytically tractable model for fluctuating fronts, describing the internal mechanisms driving the invasion of a habitat by a cooperating population. Recent studies from Birzu, Hallatschek and Korolev suggest the existence of three classes of fluctuating fronts: pulled, semi pushed and fully pushed fronts. Here, we focus on the fully pushed regime. We establish a Yaglom law for this branching process and prove that the genealogy of the particles converges to a Brownian Coalescent Point Process using a method of moments. In practice, the genealogy of the BBM is seen as a random marked metric measure space and we use spinal decomposition to prove its convergence in the Gromov-weak topology. We also carry the spectral decomposition of a differential operator related to the BBM to determine the invariant measure of the spine as well as its mixing time.
Origin of Quasi-periodic Pulsation at the Base of a Kink-unstable Jet

We studied a blowout jet that occurred at the west limb of the Sun on 2014 August 29 using high-resolution imaging/spectroscopic observations provided by the Solar Dynamics Observatory/Atmospheric Imaging Assembly and the Interface Region Imaging Spectrograph. An inverse γ-shaped flux rope appeared before the jet–morphological indication of the onset of kink instability. The twisted field lines of the kink-unstable flux rope reconnected at its bright knot and launched the blowout jet at ≈06:30:43 UT with an average speed of 234 km s−1. Just after the launch, the northern leg of the flux rope erupted completely. The time–distance diagrams show multiple spikes or bright dots, which is the result of periodic fluctuations, i.e., quasi-periodic fluctuations (QPPs). The wavelet analysis confirms that QPPs have a dominant period of ≈3 minutes. IRIS spectra (Si iv, C ii, and Mg ii) may also indicate the occurrence of magnetic reconnection through the existence of broad and complex profiles and bidirectional flows in the jet. Further, we found that line broadening is periodic with a period of ≈3 minutes, and plasma upflow always occurs when the line width is high, i.e., multiple reconnection may produce periodic line broadening. The emission measure (EM) curves also show the same period of ≈3 minutes in different temperature bins. The images and EM show that this jet spire is mainly cool (chromospheric/transition region) rather than hot (coronal) material. Further, line broadening, intensity, and EM curves have a period of ≈3 minutes, which strongly supports the fact that multiple magnetic reconnection triggers QPPs in the blowout jet.
TRASH: Tandem Rover and Aerial Scrap Harvester

Addressing the challenge of roadside litter in the United States, which has traditionally relied on costly and ineffective manual cleanup methods, this paper presents an autonomous multi-robot system for highway litter monitoring and collection. Our solution integrates an aerial vehicle to scan and gather data across highway stretches with a terrestrial robot equipped with a Convolutional Neural Network (CNN) for litter detection and mapping. Upon detecting litter, the ground robot navigates to each pinpointed location, re-assesses the vicinity, and employs a"greedy pickup"approach to address potential mapping inaccuracies or litter misplacements. Through simulation studies and real-world robotic trials, this work highlights the potential of our proposed system for highway cleanliness and management in the context of Robotics, Automation, and Artificial Intelligence
Audio-Visual Efficient Conformer for Robust Speech Recognition

End-to-end Automatic Speech Recognition (ASR) systems based on neural networks have seen large improvements in recent years. The availability of large scale hand-labeled datasets and sufficient computing resources made it possible to train powerful deep neural networks, reaching very low Word Error Rate (WER) on academic benchmarks. However, despite impressive performance on clean audio samples, a drop of performance is often observed on noisy speech. In this work, we propose to improve the noise robustness of the recently proposed Efficient Conformer Connectionist Temporal Classification (CTC)-based architecture by processing both audio and visual modalities. We improve previous lip reading methods using an Efficient Conformer back-end on top of a ResNet-18 visual front-end and by adding intermediate CTC losses between blocks. We condition intermediate block features on early predictions using Inter CTC residual modules to relax the conditional independence assumption of CTC-based models. We also replace the Efficient Conformer grouped attention by a more efficient and simpler attention mechanism that we call patch attention. We experiment with publicly available Lip Reading Sentences 2 (LRS2) and Lip Reading Sentences 3 (LRS3) datasets. Our experiments show that using audio and visual modalities allows to better recognize speech in the presence of environmental noise and significantly accelerate training, reaching lower WER with 4 times less training steps. Our Audio-Visual Efficient Conformer (AVEC) model achieves state-of-the-art performance, reaching WER of 2.3% and 1.8% on LRS2 and LRS3 test sets. Code and pretrained models are available at https://github.com/burchim/AVEC.