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Binary search trees (BST) are a popular type of data structure when dealing with ordered data. Indeed, they enable one to access and modify data efficiently, with their height corresponding to the worst retrieval time. From a probabilistic point of view, binary search trees associated with data arriving in a uniform random order are well understood, but less is known when the input is a non-uniform random permutation. We consider here the case where the input comes from i.i.d. random points in the plane with law $\mu$, a model which we refer to as a permuton sample. Our results show that the asymptotic proportion of nodes in each subtree depends on the behavior of the measure $\mu$ at its left boundary, while the height of the BST has a universal asymptotic behavior for a large family of measures $\mu$. Our approach involves a mix of combinatorial and probabilistic tools, namely combinatorial properties of binary search trees, coupling arguments, and deviation estimates., Comment: 27 pages, 6 figures

Absorption of light is one of the main selection effects limiting our ability to detect celestial sources, and ultimately, appearance of the sky across most of the electromagnetic spectrum. Recent advances in quantity and quality of available observational data and analysis methods led to major improvements in resolution, depth and fidelity of 3D dust distribution and extinction maps. The Galactic plane remains, however, essentially ``terra incognita'' beyond distances of a few kilo-parsecs due to the strong absorption in optical and near-infrared bands. Here I attempt to address this issue and present a 3D-$N_{\rm H}$-tool to estimate line of sight reddening and X-ray absorption column combining state of the art optical extinction and dust emission maps, and the results of dispersion measure modeling based on radio pulsar observations. The resulting maps are calibrated using independent absorption tracers and are accessible to general community via a convenient web-interface and full data cube., Comment: submitted to A&A

It is well known that Newton's method, especially when applied to large problems such as the discretization of nonlinear partial differential equations (PDEs), can have trouble converging if the initial guess is too far from the solution. This work focuses on accelerating this convergence, in the context of the discretization of nonlinear elliptic PDEs. We first provide a quick review of existing methods, and justify our choice of learning an initial guess with a Fourier neural operator (FNO). This choice was motivated by the mesh-independence of such operators, whose training and evaluation can be performed on grids with different resolutions. The FNO is trained using a loss minimization over generated data, loss functions based on the PDE discretization. Numerical results, in one and two dimensions, show that the proposed initial guess accelerates the convergence of Newton's method by a large margin compared to a naive initial guess, especially for highly nonlinear or anisotropic problems.

We introduce $C^*$-algebras associated to directed graphs of groups. In particular, we associate a combinatorial $C^*$-algebra to each row-finite directed graph of groups with no sources, and show that this $C^*$-algebra is Morita equivalent to the crossed product coming from the corresponding group action on the boundary of a directed tree. Finally, we show that these $C^*$-algebras (and their Morita equivalent crossed products) contain the class of stable UCT Kirchberg algebras., Comment: 31 pages, comments welcome

An introduction to the emerging fusion of machine learning and causal inference. The book presents ideas from classical structural equation models (SEMs) and their modern AI equivalent, directed acyclical graphs (DAGs) and structural causal models (SCMs), and covers Double/Debiased Machine Learning methods to do inference in such models using modern predictive tools.

The production of a single charged Higgs boson pair by photon - photon interactions in $pp$ collisions at the LHC is investigated in this exploratory study. We focus on the exclusive production, which is characterized by intact protons and two - rapidity gaps in the final state, and assume the type - I two - Higgs - doublet model, which still allows a light charged Higgs. Assuming the leptonic $H^{\pm}\rightarrow [\tau\nu_{\tau}]$ decay mode, we derive predictions for the transverse momentum, rapidity and invariant mass distributions of the $\tau^+ \tau^-$ pair for different values of the charged Higgs mass. The contributions of different background processes are also estimated. Our results indicate that the contribution of the exclusive $H^+ H^-$ production for the $[\tau^{+}\nu_{\tau}][\tau^{-} \nu_{\tau}]$ final state is non - negligible and can, in principle, be used to searching for a light charged Higgs., Comment: 14 pages, 3 figures, 3 tables

The reduction in sea ice cover with Arctic warming facilitates the transit of ships through routes that are remarkably shorter than the traditional shipping routes. Automatic Identification System (AIS), ideally designed to avoid vessel collisions, transmits on vessel navigation information (currently 27 types of messages) such as name, position or speed, is a powerful data source to monitor the progress of Arctic shipping as the ice cover decreases. Based on the analysis of an online platform collecting shipping AIS data, we quantified the spatial distribution of shipping through the Arctic Ocean, its intensity and the temporal evolution, in relation to the area released by the sea ice area. Shipping through the Arctic Ocean is distributed spatially following a heavy-tailed distribution, implying heavy traffic through a limited Arctic area, with an exponent that depends on the vessel category. Fishing is the category with the largest spatial spread, with the width of shipping routes correlated with the proximal sea ice area. The time evolution of these routes is characterized by increasing extended periods of shipping activity through the year. AIS data offers valuable information on the activity of the international fleet worldwide. In the context of the new international agreements, it is a valuable source to monitor shipping, fishing and the potential impact in marine life among other aspects. Here we have focused on the Arctic shipping in recent years, which is rapidly growing, particularly around the Northeastern and Northwest Passage coastal routes, providing an opportunity for the design of shorter shipping routes and reduced greenhouse gas emissions from transport of goods, but at a risk of impacts on the Arctic ecosystem.

Supply chain optimization is key to a healthy and profitable business. Many companies use online procurement systems to agree contracts with suppliers. It is vital that the most competitive suppliers are invited to bid for such contracts. In this work, we propose a recommender system to assist with supplier discovery in road freight online procurement. Our system is able to provide personalized supplier recommendations, taking into account customer needs and preferences. This is a novel application of recommender systems, calling for design choices that fit the unique requirements of online procurement. Our preliminary results, using real-world data, are promising.

The classical P\'olya-Tchebotarev problem, commonly stated as a max-min logarithmic energy problem, asks for finding a compact of minimal capacity in the complex plane which connects a prescribed collection of fixed points. Variants of this problem have found ramifications and applications in the theory of non-hermitian orthogonal polynomials, random matrices, approximation theory, among others. Here we consider an extension of this classical problem, including a semiclassical external field, and enforcing finitely many prescribed collections of points to be connected, possibly also to infinity. Our method is based on Rakhmanov's approach to max-min problems in logarithmic potential theory, utilizes the developed machinery by Mart\'inez-Finkelshtein and Rakhmanov on critical measures, and extends the development of Kuijlaars and the second named author from the context of polynomial external fields to the semiclassical case considered here.

Let $G$ be a finite group, and let $\pi$ be a set of primes. The aim of this paper is to obtain some results concerning how much information about the $\pi$-structure of $G$ can be gathered from the knowledge of the lengths of conjugacy classes of its $\pi$-elements and of their multiplicities. Among other results, we prove that this multiset of class lengths determine whether $G$ has a hypercentral Hall $\pi$-subgroup.

We analyze the modifications that a dense nuclear medium induces in the $D_{s0}^\ast(2317)^\pm$ and $D_{s1}(2460)^\pm$. In the vacuum, we consider them as isoscalar $D^{(*)}K$ and $\overline{D}{}^{(*)}\overline{K}$ $S$-wave bound states, which are dynamically generated from effective interactions that lead to different Weinberg compositeness scenarios. Matter effects are incorporated through the two-meson loop functions, taking into account the self energies that the $D^{(*)}$, $\overline{D}{}^{(*)}$, $K$, and $\overline{K}$ develop when embedded in a nuclear medium. Although particle-antiparticle [$D^{(\ast)}_{s0,s1}(2317,2460)^+$ versus $D^{(\ast)}_{s0,s1}(2317,2460)^-$] lineshapes are the same in vacuum, we find extremely different density patterns in matter. This charge-conjugation asymmetry mainly stems from the very different kaon and antikaon interaction with the nucleons of the dense medium. We show that the in-medium lineshapes found for these resonances strongly depend on their $D^{(*)}K$/$\overline{D}{}^{(*)}\overline{K}$ molecular content, and discuss how this novel feature can be used to better determine/constrain the inner structure of these exotic states., Comment: 14 pages, 4 figures

The design of direct data-based controllers has become a fundamental part of control theory research in the last few years. In this paper, we consider three classes of data-based state feedback control problems for linear systems. These control problems are such that, besides stabilization, some additional performance requirements must be satisfied. First, we formulate and solve a trajectory-reference control problem, on which desired closed-loop trajectories are known and a controller that allows the system to closely follow those trajectories is computed. Then, in the area of data-based optimal control, we solve two different problems: the inverse problem of optimal control, and the solution of the LQR problem for continuous-time systems. Finally, we consider the case in which the precise position of the desired poles of the closed-loop system is known, and introduce a data-based variant of a robust pole-placement procedure. Although we focus on continuous-time systems, all of the presented methods can also be easily formulated for the discrete-time case. The applicability of the proposed methods is tested using numerical simulations., Comment: 16 pages, 1 figure

This paper focuses on the hypothesis of optimizing time series predictions using fractal interpolation techniques. In general, the accuracy of machine learning model predictions is closely related to the quality and quantitative aspects of the data used, following the principle of \textit{garbage-in, garbage-out}. In order to quantitatively and qualitatively augment datasets, one of the most prevalent concerns of data scientists is to generate synthetic data, which should follow as closely as possible the actual pattern of the original data. This study proposes three different data augmentation strategies based on fractal interpolation, namely the \textit{Closest Hurst Strategy}, \textit{Closest Values Strategy} and \textit{Formula Strategy}. To validate the strategies, we used four public datasets from the literature, as well as a private dataset obtained from meteorological records in the city of Brasov, Romania. The prediction results obtained with the LSTM model using the presented interpolation strategies showed a significant accuracy improvement compared to the raw datasets, thus providing a possible answer to practical problems in the field of remote sensing and sensor sensitivity. Moreover, our methodologies answer some optimization-related open questions for the fractal interpolation step using \textit{Optuna} framework.

Chimeric Antigen Receptor T (CAR-T) cell therapy has been proven to be successful against different leukaemias and lymphomas. This paper makes an analytical and numerical study of a mathematical model describing the competition of CAR-T, leukaemias tumor and B cells. Considering its significance in sustaining anti-CD19 CAR T-cell stimulation, we integrate a B-cell source term into the model. Through stability and bifurcation analyses, we reveal the potential for tumor eradication contingent on the continuous influx of B-cells, uncovering a transcritical bifurcation at a critical B-cell input. Additionally, we identify an almost heteroclinic cycle between equilibrium points, providing a theoretical basis for understanding disease relapse. Analyzing the oscillatory behavior of the system, we approximate the time-dependent dynamics of CAR T-cells and leukemic cells, shedding light on the impact of initial tumor burden on therapeutic outcomes. In conclusion, our study provides insights into CAR T-cell therapy dynamics for acute lymphoblastic leukemias, offering a theoretical foundation for clinical observations and suggesting avenues for future immunotherapy modeling research.

Cardiovascular diseases, including Heart Failure (HF), remain a leading global cause of mortality, often evading early detection. In this context, accessible and effective risk assessment is indispensable. Traditional approaches rely on resource-intensive diagnostic tests, typically administered after the onset of symptoms. The widespread availability of electrocardiogram (ECG) technology and the power of Machine Learning are emerging as viable alternatives within smart healthcare. In this paper, we propose several multi-modal approaches that combine 30-second ECG recordings and approximate long-term Heart Rate Variability (HRV) data to estimate the risk of HF hospitalization. We introduce two survival models: an XGBoost model with Accelerated Failure Time (AFT) incorporating comprehensive ECG features and a ResNet model that learns from the raw ECG. We extend these with our novel long-term HRVs extracted from the combination of ultra-short-term beat-to-beat measurements taken over the day. To capture their temporal dynamics, we propose a survival model comprising ResNet and Transformer architectures (TFM-ResNet). Our experiments demonstrate high model performance for HF risk assessment with a concordance index of 0.8537 compared to 14 survival models and competitive discrimination power on various external ECG datasets. After transferability tests with Apple Watch data, our approach implemented in the myHeartScore App offers cost-effective and highly accessible HF risk assessment, contributing to its prevention and management.

A new combined sub-filter scale turbulence and shock-capturing model is developed for high-order finite volume numerics, extending previous work to unstructured solvers. Block Spectral Stresses (BSS) method relies on the spectra of the velocity gradients to estimate the subfilter scale stresses, heat-flux, and pressure-work based on the resolved field. The method is able to capture shocks with numerical order up to 25 and in a shock-vortex interaction simulation is able to capture the shock and not interfere with the vortex structure. In turbulence calculations the new method is compared with Smagorinsky, dynamic Smagorinsky, and Vreman methods adapted to a block spectral code. In the simulations of homogeneous isotropic turbulence, the new model is worse than the others when on coarse meshes and better on finer ones. Instead, for supersonic and hypersonic channel flow the case is the opposite because as expected the sub-filter terms are mostly depend on the numerical order and not the mesh resolution., Comment: 18 pages, 10 figures

The vector autoregression (VAR) has been widely used in system identification, econometrics, natural science, and many other areas. However, when the state dimension becomes large the parameter dimension explodes. So rank reduced modelling is attractive and is well developed. But a fundamental requirement in almost all applications is stability of the fitted model. And this has not been addressed in the rank reduced case. Here, we develop, for the first time, a closed-form formula for an estimator of a rank reduced transition matrix which is guaranteed to be stable. We show that our estimator is consistent and asymptotically statistically efficient and illustrate it in comparative simulations., Comment: 17 pages, 6 figures

To describe the polar properties of the nanosized HfxZr1-xO2-y, we evolve the "effective" Landau-Ginzburg-Devonshire (LGD) model based on the parametrization of the Landau expansion coefficients for the polar and antipolar orderings. We have shown that the effective LGD model can predict the influence of screening conditions and size effects on phase diagrams, polarization reversal and structural properties of the nanosized HfxZr1-xO2-y of various shape and sizes. To verify the model, we use available experimental results for HfxZr1-xO2 thin films and oxygen-deficient HfO2-y nanoparticles prepared at different annealing conditions. X-ray diffraction, which was used to determine the phase composition of the HfO2-y nanoparticles, revealed the formation of the ferroelectric orthorhombic phase in them. Micro-Raman spectroscopy was used to explore the correlation of lattice dynamics and structural changes appearing in dependence on the oxygen vacancies concentration in the HfO2-y nanoparticles. Since our approach allows to determine the conditions (shape, sizes, Zr content and/or oxygen vacancies amount) for which the nanosized HfxZr1-xO2-y are ferroelectrics or antiferroelectrics, we hope that obtained results are useful for creation of next generation of Si-compatible ferroelectric gate oxide nanomaterials., Comment: 24 pages, 7 figures, 1 Appendix

We propose a model for the origin of the broad He II 4686A emission in the early spectrum of type II SN~2020jfo. The 4686A line is emitted presumably by dense fragments embedded into a hot gas of the forward shock wave. The fragments are produced as a result of a heavy braking of the dense low-mass shell at the ejecta boundary and a simultaneous Rayleigh-Taylor instability. The temperature of line-emitting fragments is $\approx$5$\times10^4$K. Calculations of ionization and excitation of helium and hydrogen account for the He II 4686A luminosity, the large flux ratio of He II 4686A/H$\alpha$, and a significant optical depth of the 4686A line. We demonstrate that fragments heating by hot electrons behind the forward shock compensates cooling via the HeII 304A emission., Comment: Astronomy Letters (accepted)

In this paper, we study the dynamical behavior of a linear control system on $\R^2$ when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative to the control range can have a strong interference in such dynamics if the matrix is not invertible. In the invertible case, we explicitly construct the unique control set with a nonempty interior.

Over the last decade, Unmanned Aerial Vehicles (UAVs) have been extensively used in many commercial applications due to their manageability and risk avoidance. One of the main problems considered is the Mission Planning for multiple UAVs, where a solution plan must be found satisfying the different constraints of the problem. This problem has multiple variables that must be optimized simultaneously, such as the makespan, the cost of the mission or the risk. Therefore, the problem has a lot of possible optimal solutions, and the operator must select the final solution to be executed among them. In order to reduce the workload of the operator in this decision process, a Decision Support System (DSS) becomes necessary. In this work, a DSS consisting of ranking and filtering systems, which order and reduce the optimal solutions, has been designed. With regard to the ranking system, a wide range of Multi-Criteria Decision Making (MCDM) methods, including some fuzzy MCDM, are compared on a multi-UAV mission planning scenario, in order to study which method could fit better in a multi-UAV decision support system. Expert operators have evaluated the solutions returned, and the results show, on the one hand, that fuzzy methods generally achieve better average scores, and on the other, that all of the tested methods perform better when the preferences of the operators are biased towards a specific variable, and worse when their preferences are balanced. For the filtering system, a similarity function based on the proximity of the solutions has been designed, and on top of that, a threshold is tuned empirically to decide how to filter solutions without losing much of the hypervolume of the space of solutions., Comment: Preprint submitted and acepted in Expert Systems with Applications

Foundation models are powerful technologies: how they are released publicly directly shapes their societal impact. In this position paper, we focus on open foundation models, defined here as those with broadly available model weights (e.g. Llama 2, Stable Diffusion XL). We identify five distinctive properties (e.g. greater customizability, poor monitoring) of open foundation models that lead to both their benefits and risks. Open foundation models present significant benefits, with some caveats, that span innovation, competition, the distribution of decision-making power, and transparency. To understand their risks of misuse, we design a risk assessment framework for analyzing their marginal risk. Across several misuse vectors (e.g. cyberattacks, bioweapons), we find that current research is insufficient to effectively characterize the marginal risk of open foundation models relative to pre-existing technologies. The framework helps explain why the marginal risk is low in some cases, clarifies disagreements about misuse risks by revealing that past work has focused on different subsets of the framework with different assumptions, and articulates a way forward for more constructive debate. Overall, our work helps support a more grounded assessment of the societal impact of open foundation models by outlining what research is needed to empirically validate their theoretical benefits and risks.

Cycling power measurement is an indispensable metric with profound implications for cyclists' performance and fitness levels. It empowers riders with real-time feedback, supports precise training regimen planning, mitigates injury risks, and enhances muscular development. Despite these advantages, the widespread adoption of cycling power meters has been hampered by their prohibitive cost and deployment complexity. This paper pioneers a groundbreaking approach to power measurement in cycling, prioritizing affordability and user-friendliness. To achieve this goal, we introduce a cutting-edge Internet of Things (IoT) device that seamlessly integrates force signals with inertial sensor data while leveraging the power of edge machine learning techniques. In-field experimental evaluations demonstrate that our prototype can estimate power with remarkable accuracy, boasting a Mean Absolute Error (MAE) of only 12.29 Watts (4.1\%). Notably, our design emphasizes energy efficiency, operating in a low-power mode that consumes a mere 50 milliwatts and offers an exceptional battery life of up to 25.8 hours in always-on active mode. With an ultra-low latency of 4.33 milliseconds for data processing and inference, our system ensures real-time power estimation during cycling activities. Incorporating IoT concepts and devices, this paper marks a significant milestone in developing cost-effective and accurate cycling power meters.

In this work, we address the challenge of efficiently modeling dynamical systems in process engineering. We use reduced-order model learning, specifically operator inference. This is a non-intrusive, data-driven method for learning dynamical systems from time-domain data. The application in our study is carbon dioxide methanation, an important reaction within the Power-to-X framework, to demonstrate its potential. The numerical results show the ability of the reduced-order models constructed with operator inference to provide a reduced yet accurate surrogate solution. This represents an important milestone towards the implementation of fast and reliable digital twin architectures., Comment: 10 pages, 3 figures

The $(m,b)$ Maker-Breaker percolation game on $(\mathbb{Z}^2)_p$, introduced by Day and Falgas-Ravry, is played in the following way. Before the game starts, each edge of $\mathbb{Z}^2$ is removed independently with probability $1-p$. After that, Maker chooses a vertex $v_0$ to protect. Then, in each round Maker and Breaker claim respectively $m$ and $b$ unclaimed edges of $G$. Breaker wins if after the removal of the edges claimed by him the component of $v_0$ becomes finite, and Maker wins if she can indefinitely prevent Breaker from winning. We show that for any $p < 1$, Breaker almost surely has a wining strategy for the $(1,1)$ game on $(\mathbb{Z}^2)_p$. This fully answers a question of Day and Falgas-Ravry, who showed that for $p = 1$ Maker has a winning strategy for the $(1,1)$ game. Further, we show that in the $(2,1)$ game on $(\mathbb{Z}^2)_p$ Maker almost surely has a winning strategy whenever $p > 0.9402$, while Breaker almost surely has a winning strategy whenever $p < 0.5278$. This shows that the threshold value of $p$ above which Maker has a winning strategy for the $(2,1)$ game on $\mathbb{Z}^2$ is non-trivial. In fact, we prove similar results in various settings, including other lattices and biases $(m,b)$. These results extend also to the most general case, which we introduce, where each edge is given to Maker with probability $\alpha$ and to Breaker with probability $\beta$ before the game starts., Comment: 34 pages, 6 figures

Broadband quantum light is a vital resource for quantum metrology and spectroscopy applications such as quantum optical coherence tomography or entangled two photon absorption. For entangled two photon absorption in particular, very high photon flux combined with high time-frequency entanglement is crucial for observing a signal. So far these conditions could be met by using high power lasers driving degenerate, type 0 bulk-crystal spontaneous parametric down conversion (SPDC) sources. This naturally limits the available wavelength ranges and precludes deterministic splitting of the generated output photons. In this work we demonstrate an integrated two-colour SPDC source utilising a group-velocity matched lithium niobate waveguide, reaching both exceptional brightness $1.52\cdot10^6\frac{\mathrm{pairs}}{\mathrm{s\,mW\,GHz}}$ and large bandwidth ($7.8\,$THz FWHM) while pumped with a few mW of continuous wave (CW) laser light. By converting a narrow band pump to broadband pulses the created photon pairs show correlation times of $\Delta \tau \approx 120\,\text{fs}$ while maintaining the narrow bandwidth $\Delta \omega_p \ll 1\,\text{MHz}$ of the CW pump light, yielding strong time-frequency entanglement. Furthermore our process can be adapted to a wide range of central wavelengths., Comment: 12 pages, 6 figures

A method for estimating the linearity of superconducting electronic devices is discussed. The method allows the obtaining of expected spurious-free dynamic range values based on the results of preliminary numerical modeling and solving optimization problems. A description of the method and an analysis of measurement errors are provided., Comment: v2: Incorrect reference [3] changed; subsection 4.3 added; Appedix A title added; typos corrected. No changes have been made based on the comments from any peer-review process

Deep Learning is the state-of-the-art technology for segmenting brain tumours. However, this requires a lot of high-quality data, which is difficult to obtain, especially in the medical field. Therefore, our solutions address this problem by using unconventional mechanisms for data augmentation. Generative adversarial networks and registration are used to massively increase the amount of available samples for training three different deep learning models for brain tumour segmentation, the first task of the BraTS2023 challenge. The first model is the standard nnU-Net, the second is the Swin UNETR and the third is the winning solution of the BraTS 2021 Challenge. The entire pipeline is built on the nnU-Net implementation, except for the generation of the synthetic data. The use of convolutional algorithms and transformers is able to fill each other's knowledge gaps. Using the new metric, our best solution achieves the dice results 0.9005, 0.8673, 0.8509 and HD95 14.940, 14.467, 17.699 (whole tumour, tumour core and enhancing tumour) in the validation set.

Audits are critical mechanisms for identifying the risks and limitations of deployed artificial intelligence (AI) systems. However, the effective execution of AI audits remains incredibly difficult. As a result, practitioners make use of various tools to support their efforts. Drawing on interviews with 35 AI audit practitioners and a landscape analysis of 390 tools, we map the current ecosystem of available AI audit tools. While there are many tools designed to assist practitioners with setting standards and evaluating AI systems, these tools often fell short of supporting the accountability goals of AI auditing in practice. We thus highlight areas for future tool development beyond evaluation -- from harms discovery to advocacy -- and outline challenges practitioners faced in their efforts to use AI audit tools. We conclude that resources are lacking to adequately support the full scope of needs for many AI audit practitioners and recommend that the field move beyond tools for just evaluation, towards more comprehensive infrastructure for AI accountability.

Accurate models of turbulent buoyant flows are essential for the design of nuclear reactors thermal hydraulics and passive safety systems. However, available models fail to fully capture the physics of turbulent mixing when buoyancy becomes predominant with respect to momentum. Therefore, high-fidelity experiments of well-controlled fundamental flows are needed to develop and validate more accurate models. We analyze experiments of positive and negative turbulent buoyant jets, both in uniform and stratified environments, with the aim of understanding the thermal hydraulics of turbulent mixing with variable density and providing high-fidelity data for the development and validation of turbulence models. Non-intrusive, simultaneous Particle Image Velocimetry and Laser Induced Fluorescence measurements were carried out to acquire instantaneous velocity and concentration fields on a vertical section parallel to the axis of a jet in the self-similar region. The Refractive Index Matching method was applied to measure high-resolution buoyant jets with up to 8.6% density difference. These data are free of the typical errors that characterize optical measurements of buoyancy driven flows (e.g., natural and mixed convection) where the refractive index of the fluid is inhomogeneous throughout the measurement domain. Turbulent statistics and entrainment of buoyant jets in uniform and stratified environments are presented. These data are compared with non-buoyant jets in uniform environment, as a reference to investigate the effects of buoyancy and stratification on turbulent mixing. The results will be used for the assessment of current turbulence models and as basis for the development of a new one that captures turbulent mixing.

KKL (Kazantzis-Kravaris/Luenberger) observers are based on the idea of immersing a given nonlinear system into a target system that is a linear stable filter of the measured output. In the present paper, we extend this theory by allowing this target system to be a nonlinear contracting filter of the output. We prove, under a differential observability condition, the existence of these new KKL observers. We motivate their introduction by showing numerically the possibility of combining convergence speed and robustness to noise, unlike what is known for linear filtering.

A three-dimensional model of polydisperse reactive sedimentation is developed by means of a multilayer shallow water approach. The model consists of a variety of solid particles of different sizes and densities, and substrates diluted in water, which produce biochemical reactions while the sedimentation process occurs. Based on the Masliyah-Lockett-Bassoon settling velocity, compressibility of the sediment and viscosity of the mixture, the system of governing equations is composed by non-homogeneous transport equations, coupled to a momentum equation describing the mass-average velocity. Besides, the free-surface depicted by the total height of the fluid column is incorporated and fully determined through the multilayer approach. A finite volume numerical scheme on Cartesian grids is proposed to approximate the model equations. Numerical simulations of the denitrification process exemplify the performance of the numerical scheme and model under different scenarios and bottom topographies., Comment: 23 pages, 6 figures

We prove that the Fibonacci Lie algebra and the related just infinite self-similar Lie algebra are not finitely presented.

The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps across mesh interfaces from the FEM stiffness bilinear form while maintaining the system's coercivity. Herein, we present two generalizations for SoftFEM that aim to improve the approximation accuracy and further reduce the discrete systems' stiffness. Firstly and most naturally, we generalize SoftFEM by adding a least-square term to the mass bilinear form. Superconvergent results of rates $h^6$ and $h^8$ for eigenvalues are established for linear uniform elements; $h^8$ is the highest order of convergence known in the literature. Secondly, we generalize SoftFEM by applying the blended Gaussian-type quadratures. We demonstrate further reductions in stiffness compared to traditional FEM and SoftFEM. The coercivity and analysis of the optimal error convergences follow the work of SoftFEM. Thus, this paper focuses on the numerical study of these generalizations. For linear and uniform elements, analytical eigenpairs, exact eigenvalue errors, and superconvergent error analysis are established. Various numerical examples demonstrate the potential of generalized SoftFEMs for spectral approximation, particularly in high-frequency regimes.

Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex to a tree. For example, it is shown that the number of generators of the sandpile group is at most one less than the number of leaves in the tree. For trees on a fixed number of vertices, the paths and stars are shown to provide extreme behavior, not only for the number of generators, but also for the number of spanning trees, and for Tutte polynomial evaluations that count the recurrent sandpile configurations by their numbers of chips., Comment: Version to appear in Research in the Mathematical Sciences

While ethical challenges are widely discussed in HCI, far less is reported about the ethical processes that researchers routinely navigate. We reflect on a multispecies project that negotiated an especially complex ethical approval process. Cat Royale was an artist-led exploration of creating an artwork to engage audiences in exploring trust in autonomous systems. The artwork took the form of a robot that played with three cats. Gaining ethical approval required an extensive dialogue with three Institutional Review Boards (IRBs) covering computer science, veterinary science and animal welfare, raising tensions around the welfare of the cats, perceived benefits and appropriate methods, and reputational risk to the University. To reveal these tensions we introduce beneficiary-epistemology space, that makes explicit who benefits from research (humans or animals) and underlying epistemologies. Positioning projects and IRBs in this space can help clarify tensions and highlight opportunities to recruit additional expertise., Comment: Proceedings of the CHI Conference on Human Factors in Computing Systems (CHI '24), May 11--16, 2024, Honolulu, HI, USA

We reflect on the design of a multispecies world centred around a bespoke enclosure in which three cats and a robot arm coexist for six hours a day during a twelve-day installation as part of an artist-led project. In this paper, we present the project's design process, encompassing various interconnected components, including the cats, the robot and its autonomous systems, the custom end-effectors and robot attachments, the diverse roles of the humans-in-the-loop, and the custom-designed enclosure. Subsequently, we provide a detailed account of key moments during the deployment and discuss the design implications for future multispecies systems. Specifically, we argue that designing the technology and its interactions is not sufficient, but that it is equally important to consider the design of the `world' in which the technology operates. Finally, we highlight the necessity of human involvement in areas such as breakdown recovery, animal welfare, and their role as audience., Comment: Proceedings of the CHI Conference on Human Factors in Computing Systems (CHI '24), May 11--16, 2024, Honolulu, HI, USA

We present the first detection in space of O-protonated carbonyl sulfide (\ch{HOCS+}), in the midst of an ultradeep molecular line survey toward the G+0.693-0.027 molecular cloud. From the observation of all $K$$_a$ = 0 transitions ranging from $J$$_{lo}$ = 2 to $J$$_{lo}$ = 13 of \ch{HOCS+} covered by our survey, we derive a column density of $N$ = (9 $\pm$ 2)$\times$10$^{12}$ cm$^{-2}$, translating into a fractional abundance relative to H$_2$ of $\sim$7$\times$10$^{-11}$. Conversely, the S-protonated \ch{HSCO+} isomer remains undetected, and we derive an upper limit to its abundance with respect to H$_2$ of $\leq$3$\times$10$^{-11}$, a factor of $\geq$2.3 less abundant than \ch{HOCS+}. We obtain a \ch{HOCS+}/OCS ratio of $\sim$2.5$\times$10$^{-3}$, in good agreement with the prediction of astrochemical models. These models show that one of the main chemical routes to the interstellar formation of \ch{HOCS+} is likely the protonation of OCS, which appears to be more efficient at the oxygen end. Also, we find that high values of cosmic-ray ionisation rates (10$^{-15}$-10$^{-14}$ s$^{-1}$) are needed to reproduce the observed abundance of \ch{HOCS+}. In addition, we compare the O/S ratio across different interstellar environments. G+0.693-0.027 appears as the source with the lowest O/S ratio. We find a \ch{HOCO+}/\ch{HOCS+} ratio of $\sim$31, in accordance with other O/S molecular pairs detected toward this region and also close to the O/S solar value ($\sim$37). This fact indicates that S is not significantly depleted within this cloud due to the action of large-scale shocks, unlike in other sources where S-bearing species remain trapped on icy dust grains., Comment: Forthcoming paper in The Astrophysical Journal (in press)

Given a smooth projective complex curve inside a smooth projective surface, one can ask how its Hodge structure varies when the curve moves inside the surface. In this paper we develop a general theory to study the infinitesimal version of this question in the case of ample curves. We can then apply the machinery to show that the infinitesimal variation of Hodge structure of a general deformation of an ample curve in $\mathbb{P}^1\times\mathbb{P}^1$ is an isomorphism., Comment: 30 pages. Comments Welcome!

In interactive systems, actions are often correlated, presenting an opportunity for more sample-efficient off-policy evaluation (OPE) and learning (OPL) in large action spaces. We introduce a unified Bayesian framework to capture these correlations through structured and informative priors. In this framework, we propose sDM, a generic Bayesian approach designed for OPE and OPL, grounded in both algorithmic and theoretical foundations. Notably, sDM leverages action correlations without compromising computational efficiency. Moreover, inspired by online Bayesian bandits, we introduce Bayesian metrics that assess the average performance of algorithms across multiple problem instances, deviating from the conventional worst-case assessments. We analyze sDM in OPE and OPL, highlighting the benefits of leveraging action correlations. Empirical evidence showcases the strong performance of sDM., Comment: 23 pages, 5 figures

Absolute Pose Regressors (APRs) directly estimate camera poses from monocular images, but their accuracy is unstable for different queries. Uncertainty-aware APRs provide uncertainty information on the estimated pose, alleviating the impact of these unreliable predictions. However, existing uncertainty modelling techniques are often coupled with a specific APR architecture, resulting in suboptimal performance compared to state-of-the-art (SOTA) APR methods. This work introduces a novel APR-agnostic framework, HR-APR, that formulates uncertainty estimation as cosine similarity estimation between the query and database features. It does not rely on or affect APR network architecture, which is flexible and computationally efficient. In addition, we take advantage of the uncertainty for pose refinement to enhance the performance of APR. The extensive experiments demonstrate the effectiveness of our framework, reducing 27.4\% and 15.2\% of computational overhead on the 7Scenes and Cambridge Landmarks datasets while maintaining the SOTA accuracy in single-image APRs., Comment: Accepted in in 2024 IEEE International Conference on Robotics and Automation (ICRA). Code: https://github.com/lck666666/HR-APR

Collisions of left- and right-polarized spatiotemporal optical solitons have been numerically simulated for a locally isotropic focusing Kerr medium with anomalous chromatic dispersion. The stable propagation of such ``light bullets'' in a moderate nonlinear regime is ensured by a transverse parabolic profile of the refraction index in a multimode waveguide. The transverse motion of centers of mass of wave packets in such systems occurs on classical trajectories of a harmonic oscillator, whereas the motion in the longitudinal direction is uniform. Therefore, collisions of two solitons can be not only head-on but also tangential. An inelastic collision of two solitons with opposite circular polarizations can result either in two binary light bullets combining the left and right polarization or in more complex bound systems. DOI: 10.1134/S0021364024600691, Comment: 7 pages, 15 figures, in English, to appear as [JETP Lett. 119(8), 585 (2024)]

The identification and characterization of various rock types is one of the fundamental activities for geology and related areas such as mining, petroleum, environment, industry and construction. Traditionally, a human specialist is responsible for analyzing and explaining details about the type, composition, texture, shape and other properties using rock samples collected in-situ or prepared in a laboratory. The results become subjective based on experience, in addition to consuming a large investment of time and effort. The present proposal uses artificial intelligence techniques combining computer vision and natural language processing to generate a textual and verbal description from a thin section image of rock. We build a dataset of images and their respective textual descriptions for the training of a model that associates the relevant features of the image extracted by EfficientNetB7 with the textual description generated by a Transformer network, reaching an accuracy value of 0.892 and a BLEU value of 0.71. This model can be a useful resource for research, professional and academic work, so it has been deployed through a Web application for public use., Comment: 21 pages, in Spanish language, 7 figures

Transferring the nanocrystals (NCs) from the laboratory environment toward practical applications has raised new challenges. In the case of NCs for display and lightning, the focus was on reduced Auger recombination and maintaining luminescence at high temperatures. When it comes to infrared sensing, narrow band gap materials are required and HgTe appears as the most spectrally tunable platform. Its low-temperature synthesis reduces the growth energy cost yet also favors sintering. As a result, once coupled to a read-out circuit, the Joule effect aggregates the particles leading to a poorly defined optical edge and dramatically large dark current. Here, we demonstrate that CdS shells bring the expected thermal stability (no redshift upon annealing, reduced tendency to form amalgams and preservation of photoconduction after an atomic layer deposition process). The peculiar electronic structure of these confined particles is unveiled using k.p self-consistent simulations showing a significant exciton biding energy at around 200 meV. After shelling, the material displays a p-type behavior that favors the generation of photoconductive gain. The latter is then used to increase the external quantum

This article conducts a large dimensional study of a simple yet quite versatile classification model, encompassing at once multi-task and semi-supervised learning, and taking into account uncertain labeling. Using tools from random matrix theory, we characterize the asymptotics of some key functionals, which allows us on the one hand to predict the performances of the algorithm, and on the other hand to reveal some counter-intuitive guidance on how to use it efficiently. The model, powerful enough to provide good performance guarantees, is also straightforward enough to provide strong insights into its behavior., Comment: 13 pages, 9 figures

In the realm of dialogue systems, user simulation techniques have emerged as a game-changer, redefining the evaluation and enhancement of task-oriented dialogue (TOD) systems. These methods are crucial for replicating real user interactions, enabling applications like synthetic data augmentation, error detection, and robust evaluation. However, existing approaches often rely on rigid rule-based methods or on annotated data. This paper introduces DAUS, a Domain-Aware User Simulator. Leveraging large language models, we fine-tune DAUS on real examples of task-oriented dialogues. Results on two relevant benchmarks showcase significant improvements in terms of user goal fulfillment. Notably, we have observed that fine-tuning enhances the simulator's coherence with user goals, effectively mitigating hallucinations -- a major source of inconsistencies in simulator responses.

Transformers demonstrate impressive performance on a range of reasoning benchmarks. To evaluate the degree to which these abilities are a result of actual reasoning, existing work has focused on developing sophisticated benchmarks for behavioral studies. However, these studies do not provide insights into the internal mechanisms driving the observed capabilities. To improve our understanding of the internal mechanisms of transformers, we present a comprehensive mechanistic analysis of a transformer trained on a synthetic reasoning task. We identify a set of interpretable mechanisms the model uses to solve the task, and validate our findings using correlational and causal evidence. Our results suggest that it implements a depth-bounded recurrent mechanisms that operates in parallel and stores intermediate results in selected token positions. We anticipate that the motifs we identified in our synthetic setting can provide valuable insights into the broader operating principles of transformers and thus provide a basis for understanding more complex models.

The automated program repair field has attracted substantial interest over the years, but despite significant research efforts, creating a system that works well for complex semantic bugs such as security vulnerabilities has proven difficult. A promising direction to solve this challenge is by leveraging large language models (LLMs), which are increasingly used to solve various programming tasks. In this paper, we investigate the effectiveness of LLMs for solving code-repair task. We show that the task is difficult as it requires the model to learn long-range code relationships, a task that inherently relies on extensive amounts of training data. At the same time, creating a large, clean dataset for complex program bugs and their corresponding fixes is non-trivial. We propose a technique to address these challenges with a new approach for querying and fine-tuning LLMs. The idea is to use program analysis to limit the LLM's attention mechanism on the portions of code needed to perform the fix, drastically reducing the amount of required training data. Concretely, for training and inference, rather than feeding the entire program to the LLM, we reduce its code to a much shorter snippet that contains the reported defect together with the necessary context - and use that instead. Our evaluation shows that this code reduction approach substantially improves available models such as GPT-4 using few-shot learning, as well as fine-tuning models. To train and evaluate our system, we created a comprehensive code fixing dataset by extensively labeling 156 bug patterns (including 40 security rules), requiring complex interprocedural dataflow to discover. Our best system with Mixtral-8x7B can remove more than 80% of the reported defects while exactly matching the human fix in between 10 and 50% of cases, outperforming baselines based on GPT-3.5 and GPT-4, or based on window-based models like TFix., Comment: 26 pages, 13 figures (v2, small fix in author affiliations)

In this work, we present a high-order finite volume framework for the numerical simulation of shallow water flows. The method is designed to accurately capture complex dynamics inherent in shallow water systems, particularly suited for applications such as tsunami simulations. The arbitrarily high-order framework ensures precise representation of flow behaviors, crucial for simulating phenomena characterized by rapid changes and fine-scale features. Thanks to an {\it ad-hoc} reformulation in terms of production-destruction terms, the time integration ensures positivity preservation without any time-step restrictions, a vital attribute for physical consistency, especially in scenarios where negative water depth reconstructions could lead to unrealistic results. In order to introduce the preservation of general steady equilibria dictated by the underlying balance law, the high-order reconstruction and numerical flux are blended in a convex fashion with a well-balanced approximation, which is able to provide exact preservation of both static and moving equilibria. Through numerical experiments, we demonstrate the effectiveness and robustness of the proposed approach in capturing the intricate dynamics of shallow water flows, while preserving key physical properties essential for flood simulations.

Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such as simulation, analysis, and design. Often, there's a need to maintain high accuracy within a specific time or frequency interval, while errors beyond this limit can be tolerated. This paper addresses time-limited and frequency-limited model order reduction scenarios for linear systems with quadratic outputs, by generalizing the recently introduced structure-preserving balanced truncation algorithm. To that end, limited interval system Gramians are defined, and the corresponding generalized Lyapunov equations governing their computation are derived. Additionally, low-rank solutions for these equations are investigated. Next, balanced truncation algorithms are proposed for time-limited and frequency-limited scenarios, each utilizing its corresponding limited-interval system Gramians. The proposed algorithms ensure accurate results within specified time and frequency intervals while preserving the quadratic-output structure. Two benchmark numerical examples are presented to demonstrate the effectiveness of the algorithms, showcasing their ability to achieve superior accuracy within the desired time or frequency interval.