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We propose a simple method to estimate the parameters of a continuously measured quantum system, by fitting correlation functions of the measured signal. We demonstrate the approach in simulation, both on toy examples and on a recent superconducting circuits experiment which proved particularly difficult to characterise using conventional methods. The idea is applicable to any system whose evolution is described by a jump or diffusive stochastic master equation. It allows the simultaneous estimation of many parameters, is practical for everyday use, is suitable for large Hilbert space dimensions, and takes into account experimental constraints such as detector imperfections and signal filtering and digitisation. Unlike existing methods, it also provides a direct way to understand how each parameter is estimated from the measured signal. This makes the approach interpretable, facilitates debugging, and enables validating the adequacy of a model with the observed data., Comment: 26 pages, 15 figures

We study zero-sum turn-based games on graphs. In this note, we show the existence of a game objective that is $\mathbf{\Pi}^0_3$-complete for the Borel hierarchy and that is positional, i.e., for which positional strategies suffice for the first player to win over arenas of arbitrary cardinality. To the best of our knowledge, this is the first known such objective; all previously known positional objectives are in $\mathbf{\Sigma}^0_3$. The objective in question is a qualitative variant of the well-studied total-payoff objective, where the goal is to maximise the sum of weights., Comment: 7 pages, 1 figure

Semiconductor quantum dot arrays are a promising platform to perform spin-based error-corrected quantum computation with large numbers of qubits. However, due to the diverging number of possible charge configurations combined with the limited sensitivity of large-footprint charge sensors, achieving single-spin occupancy in each dot in a growing quantum dot array is exceedingly complex. Therefore, to scale-up a spin-based architecture we must change how individual charges are readout and controlled. Here, we demonstrate single-spin occupancy of each dot in a foundry-fabricated array by combining two methods. 1/ Loading a finite number of electrons into the quantum dot array; simplifying electrostatic tuning by isolating the array from the reservoirs. 2/ Deploying multiplex gate-based reflectometry to dispersively probe charge tunneling and spin states without charge sensors or reservoirs. Our isolated arrays probed by embedded multiplex readout can be readily electrostatically tuned. They are thus a viable, scalable approach for spin-based quantum architectures., Comment: 15 pages 5 figures

We investigate the matter-antimatter properties of elementary systems, modeled as free quantum fields, within the global structure of de Sitter spacetime. By leveraging the distinctive causal and analytic properties of de Sitter spacetime, we propose that matter-antimatter asymmetry could emerge as an observer-dependent effect shaped by time orientation within a local causal patch, rather than as a fundamental property of de Sitter Universe itself. This kinematic perspective complements, rather than replaces, standard dynamical processes (such as baryon number violation, $\texttt{CP}$ violation, and nonequilibrium processes) that fulfill Sakharov's criteria. Within this framework, the limited presence of antimatter in our predominantly matter-filled Universe, specifically within the causal patch of de Sitter spacetime under consideration, may arise from these mechanisms, though through pathways distinct from conventional interpretations., Comment: 5 pages, 1 figure, version accepted for publication in Europhysics Letters (EPL)

We show that for every first-order logic (FO) formula $\varphi$, and every graph class $\mathcal{G}$ of bounded expansion, there exists a distributed (deterministic) algorithm that, for every $n$-node graph $G\in\mathcal{G}$ of diameter $D$, decides whether $G\models \varphi$ in $O(D+\log n)$ rounds under the standard CONGEST model. Graphs of bounded expansion encompass many classes of sparse graphs such as planar graphs, bounded-treedepth graphs, bounded-treewidth graphs, bounded-degree graphs, and graphs excluding a fixed graph $H$ as a minor or topological minor. Note that our algorithm is optimal up to a logarithmic additional term, as even a simple FO formula such as "there are two vertices of degree 3" already on trees requires $\Omega(D)$ rounds in CONGEST. Our result extends to solving optimization problems expressed in FO (e.g., $k$-vertex cover of minimum weight), as well as to counting the number of solutions of a problem expressible in a fragment of FO (e.g., counting triangles), still running in $O(D+\log n)$ rounds under the CONGEST model. This exemplifies the contrast between sparse graphs and general graphs as far as CONGEST algorithms are concerned. For instance, Drucker, Kuhn, and Oshman [PODC 2014] showed that the problem of deciding whether a general graph contains a 4-cycle requires $\Theta(\sqrt{n}/\log n)$ rounds in CONGEST. For counting triangles, the best known algorithm of Chang, Pettie, and Zhang [SODA 2019] takes $\tilde{O}(\sqrt{n})$ rounds. Finally, our result extends to distributed certification. We show that, for every FO formula~$\varphi$, and every graph class of bounded expansion, there exists a certification scheme for $\varphi$ using certificates on $O(\log n)$ bits. This significantly generalizes the recent result of Feuilloley, Bousquet, and Pierron [PODC 2022], which held solely for graphs of bounded treedepth.

We give the stabilisation of local orbital integrals and the trace formula over a global field for $SL(2)$ with proofs valid in any characteristic. New features appear in characteristic 2. We obtain, via the stabilisation, an asymptotic expansion near the identity of local orbital integrals which is equivalent, up to a Fourier transform, to the standard germ expansion due to Shalika when the characteristic is not 2 but it is new in characteristic 2. Similarly the fine expansion of the unipotent contribution to the trace formula cannot be obtained using Arthur's techniques and a pre-stabilisation is necessary., Comment: in French language

Axis-driven random walks were introduced by P. Andreoletti and P. Debs [AD23] to provide a rough description of the behaviour of a particle trapped in a localized force field. In contrast to their work, we examine the scenario where a repulsive force (controlled by a parameter $\alpha$) is applied along the axes, with the hypothesis that the walk remains diffusive within the cones. This force gradually pushes the particle away from the origin whenever it encounters an axis. We prove that even with a minimal force (i.e., a small $\alpha$), the walk exhibits transient, superdiffusive behaviour, and we derive the left and right tails of its distribution.

In this work, we propose a new way to (non-interactively, verifiably) demonstrate Quantum Advantage by solving the average-case $\mathsf{NP}$ search problem of finding a solution to a system of (underdetermined) multivariate quadratic equations over the finite field $\mathbb{F}_2$ drawn from a specified distribution. In particular, we design a distribution of degree-2 polynomials $\{p_i(x_1,\ldots,x_n)\}_{i\in [m]}$ for $m

In the dorsal horn, projection neurons play a significant role in pain processing by transmitting sensory stimuli to supraspinal centers during nociception. Following exposure to intense noxious stimuli, a sensitization process occurs to adapt the dorsal horn functional state. Notably, projection neurons can display a switch in firing pattern from tonic firing to plateau potentials with sustained afterdischarges. For afterdischarges to manifest after this switch, the neuron must develop bistability, which characterizes the ability to show resting or spiking at the same input current depending on the context. In numerous instances, neuronal bistability arises through voltage-gated calcium channels. However, computational studies have demonstrated a trade-off between bistability and the plausibility of its resting states if calcium channels are counterbalanced with voltage-gated potassium channels. Current knowledge leaves a gap in understanding the underlying mechanisms by which robust bistability, plateau potentials, and sustained afterdischarges emerge in neurons via calcium channels. In this study, we used a conductance-based model to explore the mechanisms by which L-type calcium (CaL) channels can achieve bistability when combined with either M-type potassium (KM) channels or inward-rectifying potassium (Kir) channels. Unlike KM channels, Kir channels enhance bistability. Combined with CaL channels, KM and Kir channels promote different types of bistability, with distinct robustness, and function. An analysis of their inward/outward properties revealed that their distinct steady-state currents explain this contrast. Altogether, the complementary of CaL and Kir channels creates a reliable possible pathway for central sensitization in the dorsal horn.

The spectroscopic study of mature giant planets and low mass planets (Neptune-like, Earth-like) requires instruments capable of achieving very high contrasts ($10^{-10}-10^{-11}$) at short angular separations. To achieve such high performance on a real instrument, many limitations must be overcome: complex component defects (coronagraph, deformable mirror), optical aberrations and scattering, mechanical vibrations and drifts, polarization effects, etc. To study the overall impact on a complete system representative of high contrast instruments, we have developed a test bench at Paris Observatory, called THD2. In this paper, we focus on the polarization effects that are present on the bench which creates differential aberrations between the two linear polarization states. We compare the recorded beam positions of the two polarization states with the predicted from the Goos-H\"anchen and Imbert-Fedorov effects, both of which cause spatial shifts and angular deviations of the beam, longitudinal and transverse respectively. Although these effects have already been studied in the literature from the optical and quantum mechanical points of view, their measurement and impact on a complete optical bench are rather rare, although they are crucial for high-contrast instruments. After describing the Goos-H\"anchen and Imbert-Fedorov effects and estimating their amplitude on the THD2 bench, we present the protocol we used to measure these effects of polarization on the light beam. We compare predictions and measurements and we conclude on the most limiting elements on our bench polarization-wise., Comment: 13 pages, SPIE Proceedings of the 13092 conference

MICADO, the European Extremely Large Telescope first light imager will feature a dedicated high contrast imaging mode specifically designed for observing and characterizing exoplanets and circumstellar disks. Its improved sensitivity and angular resolution, compared to existing instruments will significantly increase our knowledge on these planetary systems. MICADO will include three classical Lyot coronagraphs, one vector phase-apodized pupil plane (vAPP) and two sparse apertures. After rapidly describing the final design of MICADO high contrast mode, we will describe the current state of development of the coronographic components and the testing of the first Lyot coronagraph prototypes., Comment: 9 pages

We consider a one-dimensional system comprising of $N$ run-and-tumble particles confined in a harmonic trap interacting via a repulsive inverse-square power-law interaction. This is the ``active" version of the Calogero-Moser system where the particles are associated with telegraphic noise with two possible states $\pm v_0$. We numerically compute the global density profile in the steady state which shows interesting crossovers between three different regimes: as the activity increases, we observe a change from a density with sharp peaks characteristic of a crystal region to a smooth bell-shaped density profile, passing through the intermediate stage of a smooth Wigner semi-circle characteristic of a liquid phase. We also investigate analytically the crossover between the crystal and the liquid regions by computing the covariance of the positions of these particles in the steady state in the weak noise limit. It is achieved by using the method introduced in Touzo {\it et al.} [Phys. Rev. E {\bf 109}, 014136 (2024)] to study the active Dyson Brownian motion. Our analytical results are corroborated by thorough numerical simulations.

The Dean-Kawasaki (DK) equation, which is at the basis of stochastic density functional theory (SDFT), was proposed in the mid-nineties to describe the evolution of the density of interacting Brownian particles, which can represent a large number of systems such as colloidal suspensions, supercooled liquids, polymer melts, biological molecules, active or chemotactic particles, or ions in solution. This theoretical framework, which can be summarized as a mathematical reformulation of the coupled overdamped Langevin equations that govern the dynamics of the particles, has attracted a significant amount of attention during the past thirty years. In this review, I present the context in which this framework was introduced, and I recall the main assumptions and calculation techniques that are employed to derive the DK equation. Then, in the broader context of statistical mechanics, I show how SDFT is connected to other theories, such fluctuating hydrodynamics, macroscopic fluctuation theory, or mode-coupling theory. The mathematical questions that are raised by the DK equation are presented in a non-specialist language. In the last parts of the review, I show how the original result was extended in several directions, I present the different strategies and approximations that have been employed to solve the DK equation, both analytically and numerically. I finally list the different situations where SDFT was employed to describe the fluctuations of Brownian suspensions, from the physics of active matter to the description of charged particles and electrolytes., Comment: Review article

We report on an air-spaced virtually imaged phased array (VIPA) spectrometer that resolves the modes of a mid-infrared frequency comb with a repetition rate of 250 MHz, without an optical filter cavity. With a record spectral resolution of 94 MHz for VIPA, the spectrometer enables precision molecular spectroscopy with high resolution, broad spectral coverage and fast data acquisition. We demonstrate the capabilities of the spectrometer by measuring the absorption spectra of molecular species generated in plasmas. Using plasmas of a mixture of nitrogen, hydrogen, and methane at a low pressure of 1.5 mbar, we obtained high-resolution spectra of methane, around 3017 cm$^{-1}$, as well as hydrogen cyanide and ammonia, around 3240 cm$^{-1}$, demonstrating a wide spectral coverage over 290 cm$^{-1}$ (equivalent to 8.7 THz). The spectrometer performance in terms of Allan-Werle deviation and noise-equivalent absorption is discussed. The air-spaced VIPA concept offers a compact and practical spectrometer that harnesses the full potential of a stabilized frequency comb, making it suitable for a wide range of high-precision spectroscopic applications., Comment: 11 pages, 4 figures

We consider cylindrical algebraic decomposition (CAD) and the key concept of delineability which underpins CAD theory. We introduce the novel concept of projective delineability which is easier to guarantee computationally. We prove results about this which can allow reduced CAD computations., Comment: Accepted for publication in the Proceedings of the 26th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2024)

We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of $\mathbb{R}^n$. In this framework, a CAD $\mathscr{C}$ is adapted to a given set $S$ if $S$ is a union of cells of $\mathscr{C}$. Different algorithms computing an adapted CAD may produce different outputs, usually with redundant cell divisions. In this paper we analyse the possibility to remove the superfluous data. More precisely we consider the set CAD$(S)$ of CADs that are adapted to $S$, endowed with the refinement partial order and we study the existence of minimal and minimum elements in this poset. We show that for every semi-algebraic set $S$ of $\mathbb{R}^n$ and every CAD $\mathscr{C}$ adapted to $S$, there is a minimal CAD adapted to $S$ and smaller (i.e. coarser) than or equal to $\mathscr{C}$. Moreover, when $n=1$ or $n=2$, we strengthen this result by proving the existence of a minimum element in CAD$(S)$. Astonishingly for $n \geq 3$, there exist semi-algebraic sets whose associated poset of adapted CADs does not admit a minimum. We prove this result by providing explicit examples. We finally use a reduction relation on CAD$(S)$ to define an algorithm for the computation of minimal CADs. We conclude with a characterization of those semi-algebraic sets $S$ for which CAD$(S)$ has a minimum by means of confluence of the associated reduction system., Comment: International Symposium on Symbolic and Algebraic Computation (ISSAC '24), July 16-19, 2024, Raleigh, NC, USA

The Bethe-Salpeter equation has been extensively employed to compute the two-body electron-hole propagator and its poles which correspond to the neutral excitation energies of the system. Through a different time-ordering, the two-body Green's function can also describe the propagation of two electrons or two holes. The corresponding poles are the double ionization potentials and double electron affinities of the system. In this work, a Bethe-Salpeter equation for the two-body particle-particle propagator is derived within the linear-response formalism using a pairing field and anomalous propagators. This framework allows us to compute kernels corresponding to different self-energy approximations ($GW$, $T$-matrix, and second-Born) as in the usual electron-hole case. The performance of these various kernels is gauged for singlet and triplet valence double ionization potentials using a set of 23 small molecules. The description of double core hole states is also analyzed., Comment: 19 pages, 8 figures

We establish a central limit theorem for the sum of $\epsilon$-independent random variables, extending both the classical and free probability setting. Central to our approach is the use of graphon limits to characterize the limiting distribution, which depends on the asymptotic structure of the underlying graphs governing $\epsilon$-independence. This framework yields a range of exotic limit laws, interpolating between free and classical cases and allowing for mixtures such as free and classical convolutions of the semi-circle and Gaussian distributions. We provide a complete characterization of the limiting law, captured as the distribution of an operator on the full Fock space. We extend our main result to the multivariate setting as well as the non-identically distributed case. The proof provides insights into the combinatorial structure of $\epsilon$-independence, shedding light on a natural connection between the graph of crossings of the partitions involved and the graphon limit of the graphs of $\epsilon$-independence.

The shortage of doctors is creating a critical squeeze in access to medical expertise. While conversational Artificial Intelligence (AI) holds promise in addressing this problem, its safe deployment in patient-facing roles remains largely unexplored in real-world medical settings. We present the first large-scale evaluation of a physician-supervised LLM-based conversational agent in a real-world medical setting. Our agent, Mo, was integrated into an existing medical advice chat service. Over a three-week period, we conducted a randomized controlled experiment with 926 cases to evaluate patient experience and satisfaction. Among these, Mo handled 298 complete patient interactions, for which we report physician-assessed measures of safety and medical accuracy. Patients reported higher clarity of information (3.73 vs 3.62 out of 4, p < 0.05) and overall satisfaction (4.58 vs 4.42 out of 5, p < 0.05) with AI-assisted conversations compared to standard care, while showing equivalent levels of trust and perceived empathy. The high opt-in rate (81% among respondents) exceeded previous benchmarks for AI acceptance in healthcare. Physician oversight ensured safety, with 95% of conversations rated as "good" or "excellent" by general practitioners experienced in operating a medical advice chat service. Our findings demonstrate that carefully implemented AI medical assistants can enhance patient experience while maintaining safety standards through physician supervision. This work provides empirical evidence for the feasibility of AI deployment in healthcare communication and insights into the requirements for successful integration into existing healthcare services., Comment: 14 pages, 7 figures, 3 tables

In the last years, Regev's reduction has been used as a quantum algorithmic tool for providing a quantum advantage for variants of the decoding problem. Following this line of work, the authors of [JSW+24] have recently come up with a quantum algorithm called Decoded Quantum Interferometry that is able to solve in polynomial time several optimization problems. They study in particular the Optimal Polynomial Interpolation (OPI) problem, which can be seen as a decoding problem on Reed-Solomon codes. In this work, we provide strong improvements for some instantiations of the OPI problem. The most notable improvements are for the $ISIS_{\infty}$ problem (originating from lattice-based cryptography) on Reed-Solomon codes but we also study different constraints for OPI. Our results provide natural and convincing decoding problems for which we believe to have a quantum advantage. Our proof techniques involve the use of a soft decoder for Reed-Solomon codes, namely the decoding algorithm from Koetter and Vardy [KV03]. In order to be able to use this decoder in the setting of Regev's reduction, we provide a novel generic reduction from a syndrome decoding problem to a coset sampling problem, providing a powerful and simple to use theorem, which generalizes previous work and is of independent interest. We also provide an extensive study of OPI using the Koetter and Vardy algorithm., Comment: v1, 33 pages

Building pluralistic AI requires designing models that are able to be shaped to represent a wide range of value systems and cultures. Achieving this requires first being able to evaluate the degree to which a given model is capable of reflecting various personas. To this end, we propose a benchmark for evaluating the steerability of model personas as a function of prompting. Our design is based on a formal definition of prompt steerability, which analyzes the degree to which a model's joint behavioral distribution can be shifted from its baseline behavior. By defining steerability indices and inspecting how these indices change as a function of steering effort, we can estimate the steerability of a model across various persona dimensions and directions. Our benchmark reveals that the steerability of many current models is limited -- due to both a skew in their baseline behavior and an asymmetry in their steerability across many persona dimensions. We release an implementation of our benchmark at https://github.com/IBM/prompt-steering.

AI workloads, particularly those driven by deep learning, are introducing novel usage patterns to high-performance computing (HPC) systems that are not comprehensively captured by standard HPC benchmarks. As one of the largest academic research centers dedicated to deep learning, Mila identified the need to develop a custom benchmarking suite to address the diverse requirements of its community, which consists of over 1,000 researchers. This report introduces Milabench, the resulting benchmarking suite. Its design was informed by an extensive literature review encompassing 867 papers, as well as surveys conducted with Mila researchers. This rigorous process led to the selection of 26 primary benchmarks tailored for procurement evaluations, alongside 16 optional benchmarks for in-depth analysis. We detail the design methodology, the structure of the benchmarking suite, and provide performance evaluations using GPUs from NVIDIA, AMD, and Intel. The Milabench suite is open source and can be accessed at github.com/mila-iqia/milabench.

Brillouin Light Scattering (BLS) spectroscopy is a non-invasive, non-contact, label-free optical technique that can provide information on the mechanical properties of a material on the sub-micron scale. Over the last decade it has seen increased applications in the life sciences, driven by the observed significance of mechanical properties in biological processes, the realization of more sensitive BLS spectrometers and its extension to an imaging modality. As with other spectroscopic techniques, BLS measurements not only detect signals characteristic of the investigated sample, but also of the experimental apparatus, and can be significantly affected by measurement conditions. The aim of this consensus statement is to improve the comparability of BLS studies by providing reporting recommendations for the measured parameters and detailing common artifacts. Given that most BLS studies of biological matter are still at proof-of-concept stages and use different--often self-built--spectrometers, a consensus statement is particularly timely to assure unified advancement., Comment: Main Text & Supplementary Text: 56 pages, 3 Figures, 2 Supplementary Figures, 1 Supplementary Table

The formation of condensates is now considered as a major organization principle of eukaryotic cells. Several studies have recently shown that the properties of these condensates are affected by enzymatic reactions. We propose here a simple generic model to study the interplay between two enzyme populations and a two-state protein. In one state, the protein forms condensed droplets through attractive interactions, while in the other state, the proteins remain dispersed. Each enzyme catalyzes the production of one of these two protein states only when reactants are in its vicinity. A key feature of our model is the explicit representation of enzyme trajectories, capturing the fluctuations in their local concentrations. The spatially dependent growth rate of droplets naturally arises from the stochastic motion of these explicitly modeled enzymes. Using two complementary numerical methods, (1) Brownian Dynamics simulations, and (2) a hybrid method combining Cahn-Hilliard-Cook diffusion equations with Brownian Dynamics for the enzymes, we investigate how enzyme concentration and dynamics influence the evolution with time, and the steady-state number and size of droplets. Our results show that the concentration and diffusion coefficient of enzymes govern the formation and size-selection of biocondensates., Comment: 14 pages, 9 figures

$p$-adic geometric pro-\'etale cohomology of smooth partially proper rigid analytic varieties over $p$-adic fields can be represented by solid quasi-coherent sheaves on the Fargues-Fontaine curve. We prove that these sheaves satisfy a Poincar\'e duality. This is done by passing, via comparison theorems, to analogous sheaves representing syntomic cohomology and then reducing to Poincar\'e duality for ${\mathbf B}^+_{\rm st}$-twisted Hyodo-Kato and filtered ${\mathbf B}^+_{\rm dR}$-cohomologies that, in turn, reduce to Serre duality for smooth Stein varieties -- a classical result. A similar computation yields a K\"unneth formula., Comment: First draft. Comments welcome !

An analytical derivation of the buoyancy-induced initial acceleration of a spherical gas bubble in a host liquid is presented. The theory makes no assumptions further than applying the two-phase incompressible Navier-Stokes equations, showing that neither the classical approach using potential theory nor other simplifying assumptions are needed. The result for the initial bubble acceleration as a function of the gas and liquid densities, classically built on potential theory, is retained. The result is reproduced by detailed numerical simulations. The accelerated, although stagnant state of the bubble induces a pressure distribution on the bubble surface which is different from the result related to the Archimedean principle, emphasizing the importance of the non-equilibrium state for the force acting on the bubble.

Since cosmic shear was first observed in 2000, it has become a key cosmological probe and promises to deliver exquisite dark energy constraints. However, shear is inferred from coherent distortions of galaxy shapes, and the relation between galaxy ellipticities and gravitational shear is a serious potential source of bias. To address this, we are developing a shear estimation method that makes no assumption on galaxy shapes, in order to avoid the shortcomings of a simulation-based shear calibration. Our method relies on the estimation of second moments on the image, and the evaluation of how second moments respond to a shear applied to the coordinate system, without altering the image itself, at variance with the Metacalibration method. We also evaluate analytically the noise bias due to the non-linearity of the estimator, and confront it with the bias derived from noisy image simulations, which allows a fast and precise noise bias correction.

Close to a saddle-node bifurcation, when two invariant solutions collide and disappear, the behavior of a dynamical system can closely resemble that of a solution which is no longer present at the chosen parameter value. For bifurcating equilibria in low-dimensional ODEs, the influence of such 'ghosts' on the temporal behavior of the system, namely delayed transitions, has been studied previously. We consider spatio-temporal PDEs and characterize the phenomenon of ghosts by defining representative state-space structures, which we term 'ghost states,' as minima of appropriately chosen cost functions. Using recently developed variational methods, we can compute and parametrically continue ghost states of equilibria, periodic orbits, and other invariant solutions. We demonstrate the relevance of ghost states to the observed dynamics in various nonlinear systems including chaotic maps, the Lorenz ODE system, the spatio-temporally chaotic Kuramoto-Sivashinsky PDE, the buckling of an elastic arc, and 3D Rayleigh-B\'enard convection.

We report the discovery of a rare isolated group of five dwarf galaxies located at z = 0.0086 ($D$ = 36 Mpc). All member galaxies are star-forming, blue, and gas-rich with $g-r$ indices ranging from 0.2 to 0.6 mag, and two of them show signs of ongoing mutual interaction. The most massive member of the group has a stellar mass that is half of the Small Magellanic Cloud stellar mass, and the median stellar mass of the group members is 7.87 $\times$ 10$^{7}$ M$_{\odot}$. The derived total dynamical mass of the group is $M_{\rm dyn}$ = 6.02$\times$10$^{10}$ M$_{\odot}$, whereas its total baryonic mass (stellar + HI) is 2.6$\times$10$^{9}$ M$_{\odot}$, which gives us the dynamical to baryonic mass ratio of 23. Interestingly, all galaxies found in the group are aligned along a straight line in the plane of the sky. The observed spatial extent of the member galaxies is 154 kpc, and their relative line-of-sight velocity span is within 75 km s$^{-1}$. Using the spatially resolved optical spectra provided by DESI EDR, we find that three group members share a common rotational direction. With these unique properties of the group and its member galaxies, we discuss the possible importance of such a system in the formation and evolution of dwarf galaxy groups and in testing the theory of large-scale structure formation., Comment: Accepted for publication in ApJL

Accurate modeling of terrestrial carbon and water exchange requires robust ecological parameters that capture vegetation responses and adaptations to the local environment. The current generation of land models use Plant Functional Types (PFTs) to discretize vegetation functional diversity, but these coarse categorizations often overlook fine-scale variations shaped by local climate, soil, and forest age factors. The lack of governing equations for plant adaptation demands a paradigm shift in how we integrate diverse Earth observations to uncover ecological functional dependence on changing environments. To address this challenge, we developed DifferLand, a differentiable, hybrid physics and machine learning model that infers the spatial distributions of ecological parameters and their relationships with environmental factors constrained by satellite and in-situ observations. Our model unifies top-down and bottom-up observational constraints with process-based knowledge to generate a global analysis of ecological functions and their adaptation to environmental gradients. We found PFTs account for less than half of the explainable spatial parameter variations controlling carbon fluxes and vegetation states. The remaining parameter variability is largely driven by local climate and forest demography factors, and the learned environment-parameter relationships lead to enhanced spatial generalization at unseen locations. DifferLand identified growing season length, leaf economics, and agricultural intensity as the three orthogonal spatial gradients underlying parameter variations. Our novel framework can lead to new insights on global carbon cycling by learning directly from data and expanding our understanding of local responses of ecosystems to environmental drivers.

Importance sampling and independent Metropolis-Hastings (IMH) are among the fundamental building blocks of Monte Carlo methods. Both require a proposal distribution that globally approximates the target distribution. The Radon-Nikodym derivative of the target distribution relative to the proposal is called the weight function. Under the weak assumption that the weight is unbounded but has a number of finite moments under the proposal distribution, we obtain new results on the approximation error of importance sampling and of the particle independent Metropolis-Hastings algorithm (PIMH), which includes IMH as a special case. For IMH and PIMH, we show that the common random numbers coupling is maximal. Using that coupling we derive bounds on the total variation distance of a PIMH chain to the target distribution. The bounds are sharp with respect to the number of particles and the number of iterations. Our results allow a formal comparison of the finite-time biases of importance sampling and IMH. We further consider bias removal techniques using couplings of PIMH, and provide conditions under which the resulting unbiased estimators have finite moments. We compare the asymptotic efficiency of regular and unbiased importance sampling estimators as the number of particles goes to infinity., Comment: 35 pages including the proofs in appendices

This review presents recent developments in the study of inhomogeneous XX spin chains, highlighting results on perfect state transfer, out-of-equilibrium stationary dynamics in open systems, and entanglement and correlations in ground states. We discuss the conditions on couplings that enable perfect state transfer, examine how heat currents scale when the chains are coupled to thermal baths, explore the role of tridiagonal matrices in approximating the entanglement Hamiltonian and investigate bulk and boundary entanglement negativity and correlation decay. These findings underscore some of the distinctive physical behavior of inhomogeneous spin chains and their potential applications in quantum information and thermal transport., Comment: 21 pages. This paper is based on talks given by Luc Vinet at the 33/35 International Colloquium on Group Theoretical Methods in Physics, Cotonou, B\'enin, July 2024 and at the Conference Quantissima in the Serenissima V, Venice, Italy, August 2024

Quantifying the correlations between the position of a tagged tracer and the density of surrounding bath particles is key to understanding tracer diffusion in interacting particle systems. We address this problem analytically for both hard-core and soft-core interactions, using minimal yet paradigmatic models in $d$ spatial dimensions. In both cases, we derive analytical expressions for the spatial correlation profiles in the reference frame of the tracer. We reveal unexpected universal features in their large-distance behavior, characterized by power-law tails with exponents that depend solely on the spatial dimensionality of the system. Beyond these simple models, we demonstrate the robustness of our results across different regimes using particle-based numerical simulations., Comment: 6 pages, 3 figures + 17 pages SM

Lattice Boltzmann models are briefly introduced together with references to methods used to predict their ability for simulations of systems described by partial differential equations that are first order in time and low order in space derivatives. Several previous works have been devoted to analyzing the accuracy of these models with special emphasis on deviations from pure Newtonian viscous behaviour, related to higher order space derivatives of even order. The presentcontribution concentrates on possible inaccuracies of the advection behaviour linked to space derivatives of odd order. Detailed properties of advection-diffusion and athermal fluids are presented for two-dimensional situations allowing to propose situations that are accurate to third order in space derivatives. Simulations of the advection of a gaussian dot or vortex are presented. Similar results are discussed in appendices for three-dimensional advection-diffusion.

The Douglas' majorization and factorization theorem characterizes the inclusion of operator ranges in Hilbert spaces. Notably, it reinforces the well-established connections between the inclusion of kernels of operators in Hilbert spaces and the (inverse) inclusion of the closures of the ranges of their adjoints. This note aims to present a ''mixed'' version of these concepts for operators with a codomain in a product space. Additionally, an application in control theory of coupled systems of linear partial differential equations is presented.

This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution $f_N(t)$ is governed by the Liouville equation. Our primary objective is to analyze the system's behavior over extended time intervals, focusing on stability, potential chaotic dynamics and the impact of singularities. In particular, we aim to derive reduced models in the regime where $N \gg 1$, exploring both the mean-field approximation and configurations far from chaos, where the mean-field approximation no longer holds. These reduced models do not always emerge but in these cases it is possible to derive uniform bounds in $ L^2 $, both over time and with respect to the number of particles, on the marginals $ \left(f_{k,N}\right)_{1\leq k \leq N}$, irrespective of the initial state's chaotic nature. Furthermore, we extend previous results by considering a wide range of singular interaction kernels surpassing the traditional $L^d$ regularity barriers, $K \in W^{\frac{-2}{d+2},d+2}(\mathbb{T}^d)$, where $\mathbb{T}$ denotes the $1$-torus and $d\geq2$ is the dimension. Finally, we address the highly singular case of $K \in H^{-1}(\mathbb{T}^d)$ within high-temperature regimes, offering new insights into the behavior of such systems.

We propose a low-dimensional modeling approach to simulate the dynamics, acoustic emissions and interactions of cavitation bubbles, based on a quasi-acoustic assumption. This quasi-acoustic assumption accounts for the compressibility of the medium surrounding the bubble and its finite speed of sound, whereby the potential of the acoustic wave emitted by the bubble propagates along outgoing characteristics. With these ingredients, a consistent set of equations describing the radial bubble dynamics as well as the resulting acoustic emissions and bubble-bubble interactions is obtained, which is accurate to the first order of the Mach number. This model is tested by considering several representative test cases, including the resonance behavior of multiple interacting bubbles and the response of dense mono- and polydisperse bubble clusters to a change in ambient pressure. The results are shown to be in excellent agreement with results reported in the literature. The differences associated with the finite propagation speed of the acoustic waves are observed to be most pronounced for the pressure-driven bubble dynamics in dense bubble clusters and the onset of cavitation in response to a change in ambient pressure., Comment: This article has been accepted for publication in Physics of Fluids

We discuss some consistent issues on how RepNet has been evaluated in various papers. As a way to mitigate these issues, we report RepNet performance results on different datasets, and release evaluation code and the RepNet checkpoint to obtain these results. Code URL: https://github.com/google-research/google-research/blob/master/repnet/

A recent study of the distribution of dwarf galaxies in the MATLAS sample in galaxy groups revealed an excess of flattened satellite structures, reminiscent of the co-rotating planes of dwarf galaxies discovered in the local Universe. If confirmed, this lends credence to the plane-of-satellite problem and further challenges the standard model of hierarchical structure formation. However, with only photometric data and no confirmation of the satellite membership, the study could not address the plane-of-satellite problem in full detail. Here we present spectroscopic follow-up observations of one of the most promising planes-of-satellites candidates in the MATLAS survey, the satellite system of NGC 474. Employing MUSE at the VLT and full spectrum fitting, we studied 13 dwarf galaxy candidates and confirmed nine to be members of the field around NGC 474. Measuring the stellar populations of all observed galaxies, we find that the MATLAS dwarfs have lower metallicities than the Local Group dwarfs at given luminosity. Two dwarf galaxies may form a pair of satellites based on their close projection and common velocity. Within the virial radius, we do not find a significant plane-of-satellites, however, there is a sub-population of six dwarf galaxies which seem to be anti-correlated in phase-space. Due to the low number of dwarf galaxies, this signal may arise by chance. With over 2000 dwarf galaxy candidates found in the MATLAS survey, this remains an intriguing data set to study the plane-of-satellites problem in a statistical fashion once more follow-up observations have been conducted., Comment: 9 pages, 8 figures, 2 tables. Accepted for publication in Astronomy & Astrophysics (A&A)

Image watermarking methods are not tailored to handle small watermarked areas. This restricts applications in real-world scenarios where parts of the image may come from different sources or have been edited. We introduce a deep-learning model for localized image watermarking, dubbed the Watermark Anything Model (WAM). The WAM embedder imperceptibly modifies the input image, while the extractor segments the received image into watermarked and non-watermarked areas and recovers one or several hidden messages from the areas found to be watermarked. The models are jointly trained at low resolution and without perceptual constraints, then post-trained for imperceptibility and multiple watermarks. Experiments show that WAM is competitive with state-of-the art methods in terms of imperceptibility and robustness, especially against inpainting and splicing, even on high-resolution images. Moreover, it offers new capabilities: WAM can locate watermarked areas in spliced images and extract distinct 32-bit messages with less than 1 bit error from multiple small regions - no larger than 10% of the image surface - even for small $256\times 256$ images., Comment: Under review. Code at https://github.com/facebookresearch/watermark-anything

In this paper, we introduce TreeCoders, a novel family of transformer trees. We moved away from traditional linear transformers to complete k-ary trees. Transformer blocks serve as nodes, and generic classifiers learn to select the best child and route the sequence of tokens to a specific leaf. The selectors, moved outside the transformer blocks, allow for the use of a variety of architecture without further modifications. Furthermore, our proposed architecture supports sparse node activation due to the logarithmic complexity of a tree search. We validate our idea by testing a series of decoder-only tree transformers, achieving competitive results across a diverse range of language datasets. Our study demonstrates that the proposed tree transformer model outperforms a size-equivalent linear transformer model 76\% of the time over a wide range of tree architectures. Furthermore, our proposed model naturally lends itself to distributed implementation.

We experimentally investigate a solid-state quantum emitter - a B center in hexagonal boron nitride (hBN) - that has lifetime-limited coherence at short times, and experiences inhomogeneous broadening due to spectral diffusion at longer times. By making use of power broadening in resonant laser excitation, we explore the crossover between the inhomogeneous and the homogeneous broadening regimes. With the support of numerical simulations, we show that the lineshape, count rate, second-order correlations and long-time photon statistics evolve from a regime where they are dictated by spectral diffusion to a regime where they are simply given by the homogeneous response of the emitter, yielding restored Lorentzian shape and Poissonian photon statistics. Saturation of the count rate and line broadening occur not at the onset of the Rabi oscillations, but when the power-broadened homogeneous response becomes comparable with the inhomogeneous linewidth. Moreover, we identify specific signatures in both the second-order correlations and long-time photon statistics that are well explained by a microscopic spectral diffusion model based on discrete jumps at timescales of micro- to milliseconds. Our work provides an extensive description of the photophysics of B-centers under resonant excitation, and can be readily extended to a wide variety of solid-state quantum emitters.

This paper investigates the use of the ASTD language for ensemble anomaly detection in data logs. It uses a sliding window technique for continuous learning in data streams, coupled with updating learning models upon the completion of each window to maintain accurate detection and align with current data trends. It proposes ASTD patterns for combining learning models, especially in the context of unsupervised learning, which is commonly used for data streams. To facilitate this, a new ASTD operator is proposed, the Quantified Flow, which enables the seamless combination of learning models while ensuring that the specification remains concise. Our contribution is a specification pattern, highlighting the capacity of ASTDs to abstract and modularize anomaly detection systems. The ASTD language provides a unique approach to develop data flow anomaly detection systems, grounded in the combination of processes through the graphical representation of the language operators. This simplifies the design task for developers, who can focus primarily on defining the functional operations that constitute the system.

The simulation of detector response is a vital aspect of data analysis in particle physics, but current Monte Carlo methods are computationally expensive. Machine learning methods, which learn a mapping from incident particle to detector response, are much faster but require a model for every detector element with unique geometry. Complex geometries may require many models, each with their own training samples and hyperparameter tuning tasks. A promising approach is the use of geometry-aware models, which condition the response on the geometry, but current efforts typically require cumbersome full geometry specification. We present a geometry-aware model that takes advantage of the regularity of detector segments, requiring only the definition of cell sizes across regular segments. This model outperforms the current state of the art by over 70% across several key metrics including the Wasserstein distance metric.

This paper synthesizes prior studies to develop a comprehensive three-dimensional description of reattached flow over an airfoil controlled by finite-span SJA arrays. When applied to a longer-span wing, the flow field exhibits three distinct regions: a directly controlled region, an unaffected region, and a transitional zone between them. Through the integration of multiple visualizations and measurements from both discrete and slot-style SJAs, this work provides insights into the shear layer behavior. The analysis of reattached mean flow provides insight into the interactions between controlled and surrounding flows, demonstrating broad applicability across different SJA configurations, Comment: 9 pages, 6 figures

We investigate the study of the symplectic manifolds equipped with a symplectic connection whose geodesic symmetries are (local) symplectomorphisms. We call "S-type" these affine symplectic manifolds.

HeH$^+$ was the first heteronuclear molecule to form in the metal-free Universe after the Big Bang. The molecule gained significant attention following its first circumstellar detection in the young and dense planetary nebula NGC 7027. We target some hydride ions associated with the noble gases (HeH$^+$, ArH$^+$, and NeH$^+$) to investigate their formation in a harsh environment like the novae outburst region. We use a photoionization modeling (based on the earlier published best-fitted physical parameters) of the moderately fast ONe type nova: QU Vulpeculae 1984 and CO type novae: RS Ophiuchi and V1716 Scorpii. Our steady-state modeling reveals a convincing amount of HeH$^+$, especially in the dense clump of RS Ophiuchi and V1716 Scorpii. The calculated upper limit of the surface brightness of HeH$^+$ transitions suggests that the James Webb Space Telescope (JWST) could detect some of them, particularly in sources like RS Ophiuchi and V1716 Scorpii with similar physical and chemical conditions and evolution. It is to be clearly noted that the sources studied are used as templates, not as targets for observations. The detection of these lines could be useful for determining physical conditions in similar types of systems and validating our predictions based on new electron-impact rovibrational collisional data at temperatures up to 20,000 K., Comment: 15 pages, 12 figures, accepted for publication in Astronomy & Astrophysics (A&A) Journal

Recent advances in large language models (LLMs) have led to significant progress in robotics, enabling embodied agents to better understand and execute open-ended tasks. However, existing approaches using LLMs face limitations in grounding their outputs within the physical environment and aligning with the capabilities of the robot. This challenge becomes even more pronounced with smaller language models, which are more computationally efficient but less robust in task planning and execution. In this paper, we present a novel modular architecture designed to enhance the robustness of LLM-driven robotics by addressing these grounding and alignment issues. We formalize the task planning problem within a goal-conditioned POMDP framework, identify key failure modes in LLM-driven planning, and propose targeted design principles to mitigate these issues. Our architecture introduces an ``expected outcomes'' module to prevent mischaracterization of subgoals and a feedback mechanism to enable real-time error recovery. Experimental results, both in simulation and on physical robots, demonstrate that our approach significantly improves task success rates for pick-and-place and manipulation tasks compared to both larger LLMs and standard baselines. Through hardware experiments, we also demonstrate how our architecture can be run efficiently and locally. This work highlights the potential of smaller, locally-executable LLMs in robotics and provides a scalable, efficient solution for robust task execution., Comment: Submitted to ICRA 2025

The topics of Artificial intelligence (AI) and especially Machine Learning (ML) are increasingly making their way into educational curricula. To facilitate the access for students, a variety of platforms, visual tools, and digital games are already being used to introduce ML concepts and strengthen the understanding of how AI works. We take a look at didactic principles that are employed for teaching computer science, define criteria, and, based on those, evaluate a selection of prominent existing platforms, tools, and games. Additionally, we criticize the approach of portraying ML mostly as a black-box and the resulting missing focus on creating an understanding of data, algorithms, and models that come with it. To tackle this issue, we present a concept that covers intermodal transfer, computational and explanatory thinking, ICE-T, as an extension of known didactic principles. With our multi-faceted concept, we believe that planners of learning units, creators of learning platforms and educators can improve on teaching ML., Comment: Accepted and presented at the 17th International Conference on Informatics in Schools (ISSEP 2024)

We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the problem arising in demography of estimating the covariance matrix of the total fertility rate (TFR) of 195 different countries when only 11 observations are available. We construct an estimator for high-dimensional covariance matrices by exploiting information about pairwise covariates, such as whether pairs of variables belong to the same cluster, or spatial structure of the variables, and interactions between the covariates. We reformulate the problem in terms of a mixed effects model. This requires the estimation of only a small number of parameters, which are easy to interpret and which can be selected using standard procedures. The estimator is consistent under general conditions, and asymptotically normal. It works if the mean and variance structure of the data is already specified or if some of the data are missing. We assess its performance under our model assumptions, as well as under model misspecification, using simulations. We find that it outperforms several popular alternatives. We apply it to the TFR dataset and draw some conclusions., Comment: 23 pages, 5 figures, submitted to the Annals of Applied Statistics