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Quantum collision describe open quantum systems through repeated interactions with a coarse-grained environment. However, a complete certification of these models is lacking, as no complete error bounds on the simulation of system observables have been established. Here, we show that Markovian and non-Markovian collision models can be recovered analytically from chain mapping techniques starting from a general microscopic Hamiltonian. This derivation reveals a previously unidentified source of error -- induced by an unfaithful sampling of the environment -- in dynamics obtained with collision models that can become dominant for small but finite time-steps. With the complete characterization of this error, all collision models errors are now identified and quantified, which enables the promotion of collision models to the class of numerically exact methods. To confirm the predictions of our equivalence results, we implemented a non-Markovian collision model of the Spin Boson Model, and identified, as predicted, a regime in which the collision model is fundamentally inaccurate., Comment: 17 pages, 4 figures

We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a submodular function break submodularity. Say that $F$ is $\varepsilon$-approximately submodular if there exists a submodular function $f$ such that $(1-\varepsilon)f(S) \leq F(S)\leq (1+\varepsilon)f(S)$ for all subsets $S$. We are interested in characterizing the query-complexity of maximizing $F$ subject to a cardinality constraint $k$ as a function of the error level $\varepsilon>0$. We provide both lower and upper bounds: for $\varepsilon>n^{-1/2}$ we show an exponential query-complexity lower bound. In contrast, when $\varepsilon< {1}/{k}$ or under a stronger bounded curvature assumption, we give constant approximation algorithms., Comment: 12 pages

We prove that, for a spherical Fano threefold not in the Mori-Mukai family 2-29, and a weight function associated with the action of the connected center of a Levi subgroup of its automorphism group, weighted K-polystability is equivalent to vanishing of the weighted Futaki invariant. This is surprising since unlike the case of toric Fano manifold, there exist non-product, special, equivariant test configurations. For the K\"ahler-Einstein Fano threefold 2-29, and for well-chosen torus action on the three dimensional quadric, we show that this property is false and exhibit explicit examples of weighted optimal degenerations. We then generalize this to higher-dimensional quadrics and blowups of quadrics along a codimension 2 subquadric., Comment: 17 pages

We prove level-by-level upper and lower bounds on the strength of determinacy for finite differences of sets in the hyperarithmetical hierarchy in terms of subsystems of finite-and transfinite-order arithmetic, extending the Montalb\'an-Shore theorem to each of the levels of the Borel hierarchy beyond the one they treated. We also prove equivalences between reflection principles for higher-order arithmetic and quantified determinacy axioms, answering two questions of Pacheco and Yokoyama.

This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

The decarbonisation of the energy system is crucial for achieving climate goals and is inherently linked to the decarbonisation of industry. Despite this, few studies explore the simultaneous impacts of decarbonising both sectors. This paper aims to examine how industrial decarbonisation in Europe affects the energy system and vice versa. To address this, an industry model incorporating key heavy industry sectors across six European countries is combined with an energy system model for electricity and hydrogen covering fifteen European regions, refered to as the EU-15, divided into eleven zones. The study evaluates various policy scenarios under different conditions.The results demonstrate that industrial decarbonisation leads to a significant increase in electricity and hydrogen demand. This additional demand for electricity is largely met through renewable energy sources, while hydrogen supply is predominantly addressed by blue hydrogen production when fossil fuels are authorized and the system lacks renewable energy. This increased demand results in higher prices with considerable regional disparities. Furthermore, the findings reveal that, regardless of the scenario, the electricity mix in the EU-15 remains predominantly renewable, exceeding 85%.A reduction in carbon taxes lowers the prices of electricity and hydrogen, but does not increase consumption, as the lower carbon tax makes the continued use of fossil fuels more attractive to industry. In scenarios that enforce a phase-out of fossil fuels, electricity prices rise, leading to a greater reliance on imports of low-carbon hydrogen and methanol. Results also suggest that domestic hydrogen production benefits from synergies between electrolytic hydrogen and blue hydrogen, helping to maintain competitive prices.

It has been claimed that graphite hosts superconductivity at room temperature, although all efforts to isolate it have been vain. Here we report a separation method that uses magnetic field gradients to sort the superconducting from normal grains out of industrial graphite powders. We have obtained a concentrate of above room temperature superconducting particles. Electrical resistance measurements on agglomerates of sorted grains of three types of graphite show transition temperatures up to T$_{c{_{onset}}} \sim$ 700K with zero resistance up to $\sim$ 500K. Magnetization measurements confirm these values through jumps at \textit{T$_c$} in the zero field cooled curves, and by the occurrence diamagnetic hysteretic cycles shrinking with temperature. Our results open the door towards the study of above room temperature superconducting ill-stacked graphite phases., Comment: 21 pages, 9 figures

We explore an optimal impulse control problem wherein an electronic device owner strategically calibrates protection levels against cyber attacks. Utilizing epidemiological compartment models, we qualitatively characterize the dynamics of cyber attacks within the network. We determine the optimal protective measures against effective hacking by formulating and solving a stochastic control problem with optimal switching. We demonstrate that the value function for the cluster owner constitutes a viscosity solution to a system of coupled variational inequalities associated with a fully coupled reflected backward stochastic differential equation (BSDE). Furthermore, we devise a comprehensive algorithm alongside a verification procedure to ascertain the optimal timing for network protection across various cyber attack scenarios. Our findings are illustrated through numerical approximations employing deep Galerkin methods for partial differential equations (PDEs). We visualize the optimal protection strategies in the context of two distinct attack scenarios: (1) a constant cyber attack, (2) an exogenous cyber attack strategy modeled with a Poisson process.

We introduce a new family of oriented manifolds with boundaries called the forest biassociahedra and forest bimultiplihedra, generalizing the standard biassociahedra. They are defined as moduli spaces of ascending-descending biforests and are expected to act as parameter spaces for operations defined on Morse and Floer chains in the context of compact Lie group actions. We study the structure of their boundary, and derive some algebraic notions of ``$f$-bialgebras'', as well as related notions of bimodules, morphisms and categories. This allows us to state some conjectures describing compact Lie group actions on Morse and Floer chains, and on Fukaya categories., Comment: 40 pages, 18 figures, comments are welcome

We are considering the problem of optimal portfolio delegation between an investor and a portfolio manager under a random default time. We focus on a novel variation of the Principal-Agent problem adapted to this framework. We address the challenge of an uncertain investment horizon caused by an exogenous random default time, after which neither the agent nor the principal can access the market. This uncertainty introduces significant complexities in analyzing the problem, requiring distinct mathematical approaches for two cases: when the random default time falls within the initial time frame [0,T] and when it extends beyond this period. We develop a theoretical framework to model the stochastic dynamics of the investment process, incorporating the random default time. We then analyze the portfolio manager's investment decisions and compensation mechanisms for both scenarios. In the first case, where the default time could be unbounded, we apply traditional results from Backward Stochastic Differential Equations (BSDEs) and control theory to address the agent problem. In the second case, where the default time is within the interval [0,T], the problem becomes more intricate due to the degeneracy of the BSDE's driver. For both scenarios, we demonstrate that the contracting problem can be resolved by examining the existence of solutions to integro-partial Hamilton-Jacobi-Bellman (HJB) equations in both situations. We develop a deep-learning algorithm to solve the problem in high-dimension with no access to the optimizer of the Hamiltonian function.

Soft particulate glasses are dense suspensions of jammed particles that flow like liquids under external shear and recover their solid-like properties almost instantly upon flow cessation. Here, we consider a dense suspension of core-shell attractive particles whose polymer brush allows for a delayed recovery that we monitor by time-resolved mechanical spectroscopy. Viscoelastic spectra recorded upon flow cessation show a striking power-law behavior and can be rescaled onto a master curve that hints at a time-connectivity superposition principle. Additionally, the non-linear response of this soft glass, measured at various aging times, shows a ductile-to-brittle transition, which suggests that the interactions between the particles display a progressive repulsive-to-attractive transition. These results depict an original scenario for the delayed recovery involving a time-dependent interaction potential in which attractive hydrophobic forces are only activated when neighboring particles deform their polymer shell and come in close contact., Comment: 6 pages, 5 figures

We measure the growth of cosmic density fluctuations on large scales and across the redshift range $0.3

In the context of the GRAVITY+ upgrade, the adaptive optics (AO) systems of the GRAVITY interferometer are undergoing a major lifting. The current CILAS deformable mirrors (DM, 90 actuators) will be replaced by ALPAO kilo-DMs (43x43, 1432 actuators). On top of the already existing 9x9 Shack-Hartmann wavefront sensors (SH-WFS) for infrared (IR) natural guide star (NGS), new 40x40 SH-WFSs for visible (VIS) NGS will be deployed. Lasers will also be installed on the four units of the Very Large Telescope to provide a laser guide star (LGS) option with 30x30 SH-WFSs and with the choice to either use the 9x9 IR-WFSs or 2x2 VIS-WFSs for low order sensing. Thus, four modes will be available for the GRAVITY+ AO system (GPAO): IR-NGS, IR-LGS, VIS-NGS and VIS-LGS. To prepare the instrument commissioning and help the observers to plan their observations, a tool is needed to predict the performances of the different modes and for different observing conditions (NGS magnitude, science object magnitude, turbulence conditions...) We developed models based on a Mar{\'e}chal approximation to predict the Strehl ratio of the four GPAO modes in order to feed the already existing tool that simulates the GRAVITY performances. Waiting for commissioning data, our model was validated and calibrated using the TIPTOP toolbox, a Point Spread Function simulator based on the computation of Power Spectrum Densities. In this work, we present our models of the NGS modes of GPAO and their calibration with TIPTOP.

Air ducts are integral to modern buildings but are challenging to access for inspection. Small quadrotor drones offer a potential solution, as they can navigate both horizontal and vertical sections and smoothly fly over debris. However, hovering inside air ducts is problematic due to the airflow generated by the rotors, which recirculates inside the duct and destabilizes the drone, whereas hovering is a key feature for many inspection missions. In this article, we map the aerodynamic forces that affect a hovering drone in a duct using a robotic setup and a force/torque sensor. Based on the collected aerodynamic data, we identify a recommended position for stable flight, which corresponds to the bottom third for a circular duct. We then develop a neural network-based positioning system that leverages low-cost time-of-flight sensors. By combining these aerodynamic insights and the data-driven positioning system, we show that a small quadrotor drone (here, 180 mm) can hover and fly inside small air ducts, starting with a diameter of 350 mm. These results open a new and promising application domain for drones., Comment: Video: https://youtu.be/BLQqoa7Zolw

As large language models (LLMs) are increasingly used across various applications, there is a growing need to control text generation to satisfy specific constraints or requirements. This raises a crucial question: Is it possible to guarantee strict constraint satisfaction in generated outputs while preserving the distribution of the original model as much as possible? We first define the ideal distribution - the one closest to the original model, which also always satisfies the expressed constraint - as the ultimate goal of guaranteed generation. We then state a fundamental limitation, namely that it is impossible to reach that goal through autoregressive training alone. This motivates the necessity of combining training-time and inference-time methods to enforce such guarantees. Based on this insight, we propose GUARD, a simple yet effective approach that combines an autoregressive proposal distribution with rejection sampling. Through GUARD's theoretical properties, we show how controlling the KL divergence between a specific proposal and the target ideal distribution simultaneously optimizes inference speed and distributional closeness. To validate these theoretical concepts, we conduct extensive experiments on two text generation settings with hard-to-satisfy constraints: a lexical constraint scenario and a sentiment reversal scenario. These experiments show that GUARD achieves perfect constraint satisfaction while almost preserving the ideal distribution with highly improved inference efficiency. GUARD provides a principled approach to enforcing strict guarantees for LLMs without compromising their generative capabilities., Comment: 22 pages, 11 figures

Performances of an adaptive optics (AO) system are directly linked with the quality of its alignment. During the instrument calibration, having open loop fast tools with a large capture range are necessary to quickly assess the system misalignment and to drive it towards a state allowing to close the AO loop. During operation, complex systems are prone to misalignments (mechanical flexions, rotation of optical elements, etc.) that potentially degrade the AO performances, creating a need for a monitoring tool to tackle their driftage. In this work, we first present an improved perturbative method to quickly assess large lateral errors in open loop. It uses the spatial correlation of the measured interaction matrix of a limited number of 2D spatial modes with a synthetic model. Then, we introduce a novel solution to finely measure and correct these lateral errors via the closed loop telemetry. Non-perturbative, this method consequently does not impact the science output of the instrument. It is based on the temporal correlation of 2D spatial frequencies in the deformable mirror commands. It is model-free (no need of an interaction matrix model) and sparse in the Fourier space, making it fast and easily scalable to complex systems such as future extremely large telescopes. Finally, we present some results obtained on the development bench of the GRAVITY+ extreme AO system (Cartesian grid, 1432 actuators). In addition, we show with on-sky results gathered with CHARA and GRAVITY/CIAO that the method is adaptable to non-conventional AO geometries (hexagonal grids, 60 actuators).

We introduce Pixtral-12B, a 12--billion-parameter multimodal language model. Pixtral-12B is trained to understand both natural images and documents, achieving leading performance on various multimodal benchmarks, surpassing a number of larger models. Unlike many open-source models, Pixtral is also a cutting-edge text model for its size, and does not compromise on natural language performance to excel in multimodal tasks. Pixtral uses a new vision encoder trained from scratch, which allows it to ingest images at their natural resolution and aspect ratio. This gives users flexibility on the number of tokens used to process an image. Pixtral is also able to process any number of images in its long context window of 128K tokens. Pixtral 12B substanially outperforms other open models of similar sizes (Llama-3.2 11B \& Qwen-2-VL 7B). It also outperforms much larger open models like Llama-3.2 90B while being 7x smaller. We further contribute an open-source benchmark, MM-MT-Bench, for evaluating vision-language models in practical scenarios, and provide detailed analysis and code for standardized evaluation protocols for multimodal LLMs. Pixtral-12B is released under Apache 2.0 license.

We resolve the multiple images of the binary-lens microlensing event ASASSN-22av using the GRAVITY instrument of the Very Large Telescope Interferometer (VLTI). The light curves show weak binary perturbations, complicating the analysis, but the joint modeling with the VLTI data breaks several degeneracies, arriving at a strongly favored solution. Thanks to precise measurements of angular Einstein radius \theta_E = 0.724 +/- 0.002 mas and microlens parallax, we determine that the lens system consists of two M dwarfs with masses of M_1 = 0.258 +/- 0.008 M_sun and M_2 = 0.130 +/- 0.007 M_sun, a projected separation of r_\perp = 6.83 +/- 0.31 AU and a distance of D_L = 2.29 +/- 0.08 kpc. The successful VLTI observations of ASASSN-22av open up a new path for studying intermediate-separation (i.e., a few AUs) stellar-mass binaries, including those containing dark compact objects such as neutron stars and stellar-mass black holes., Comment: Accepted by ApJ. See the ancillary file for animation associated with Fig. 8

Studying the orbital motion of stars around Sagittarius A* in the Galactic Center provides a unique opportunity to probe the gravitational potential near the supermassive black hole at the heart of our Galaxy. Interferometric data obtained with the GRAVITY instrument at the Very Large Telescope Interferometer (VLTI) since 2016 has allowed us to achieve unprecedented precision in tracking the orbits of these stars. GRAVITY data have been key to detecting the in-plane, prograde Schwarzschild precession of the orbit of the star S2, as predicted by General Relativity. By combining astrometric and spectroscopic data from multiple stars, including S2, S29, S38, and S55 - for which we have data around their time of pericenter passage with GRAVITY - we can now strengthen the significance of this detection to an approximately $10 \sigma$ confidence level. The prograde precession of S2's orbit provides valuable insights into the potential presence of an extended mass distribution surrounding Sagittarius A*, which could consist of a dynamically relaxed stellar cusp comprised of old stars and stellar remnants, along with a possible dark matter spike. Our analysis, based on two plausible density profiles - a power-law and a Plummer profile - constrains the enclosed mass within the orbit of S2 to be consistent with zero, establishing an upper limit of approximately $1200 \, M_\odot$ with a $1 \sigma$ confidence level. This significantly improves our constraints on the mass distribution in the Galactic Center. Our upper limit is very close to the expected value from numerical simulations for a stellar cusp in the Galactic Center, leaving little room for a significant enhancement of dark matter density near Sagittarius A*., Comment: Submitted to A&A on September 17, 2024

The present work emphasizes the relevance of low-field NMR relaxometry to investigate colloid-polymer hydrogels by probing water dynamics across a wide range of formulations between $\rm 10^{\circ}C$ and $\rm 80^{\circ}C$. By examining the temperature dependence of the transverse relaxation time $T_2$, we demonstrate a clear link between the NMR response and the rheological behavior of the hydrogels. In particular, we show that NMR relaxometry targeting the solvent provides reliable insights into the hydrogel microstructure and allows the detection of phase transitions and aging processes. Our findings suggest that this solvent-focused technique could greatly benefit the soft matter community, complementing other experimental methods in the study of gels., Comment: 6 pages, 4 figures

Contrary to fermions and bosons, anyons are quasiparticles that keep a robust memory of particle exchanges via a braiding phase factor. This provides them with unique dynamical properties so far unexplored. When an anyon excitation is emitted toward a quantum point contact (QPC) in a fractional quantum Hall (FQH) fluid, this memory translates into tunneling events that may occur long after the anyon excitation has exited the QPC. Here, we use triggered anyon pulses incident on a QPC in a $\nu= 1/3$ FQH fluid to investigate anyon tunneling in the time domain. We observe that braiding increases the tunneling timescale, which is set by the temperature and the anyon scaling dimension that characterizes the edge state dynamics. This contrasts with the electron behavior where braiding is absent and the tunneling timescale is set by the temporal width of the generated electron pulses. Our experiment introduces time-domain measurements for characterizing the braiding phase and scaling dimension of anyons.

We propose a source of purely electronic energy-entangled states implemented in a solid-state system with potential applications in quantum information protocols based on electron flying qubits. The proposed device relies on the standard tools of Electron Quantum Optics (EQO) and exploits entanglement of the Cooper pairs of a BCS superconductor. The latter is coupled via an adjustable quantum point contact to two opposite spin polarized electron wave-guides, which are driven by trains of Lorentzian pulses. This specific choice for the drive is crucial to inject purely electronic entangled-states devoid of spurious electron-hole pairs. In the Andreev regime, a perturbative calculation in the tunnel coupling confirms that entangled electrons states (EES) are generated at the output of the normal side. We introduce a quantity related to charge current cross-correlations which allows one to verify experimentally the entangled nature of the emitted state., Comment: 18 pages, 5 figures, comments are welcomed !

Being able to study the dynamics of quantum systems interacting with several environments is important in many settings ranging from quantum chemistry to quantum thermodynamics, through out-of-equilibrium systems. For such problems tensor network-based methods are state-of-the-art approaches to perform numerically exact simulations. However, to be used efficiently in this multi-environment non-perturbative context, these methods require a clever choice of the topology of the wave-function Ans\"atze. This is often done by analysing cross-correlations between different system and environment degrees of freedom. We show for canonical model Hamiltonians that simple orderings of bosonic environmental modes, which enable to write the joint {System + Environments} state as a matrix product state, reduce considerably the bond dimension required for convergence. These results suggest that complex correlation analyses in order to tweak tensor networks topology (e.g. entanglement renormalization) are usually not necessary and that tree tensor network states are sub-optimal compared to simple matrix product states in several applications., Comment: All comments welcome. 11 pages and 9 figures

Driving condensed matter systems with periodic electromagnetic fields can result in exotic states not found in equilibrium. Termed Floquet engineering, such periodic driving applied to electronic systems can tailor quantum effects to induce topological band structures and control spin interactions. However, Floquet engineering of magnon band structures in magnetic systems has proven challenging so far. Here, we present a class of Floquet states in a magnetic vortex that arise from nonlinear interactions between the vortex core and microwave magnons. Floquet bands emerge through the periodic oscillation of the core, which can be initiated by either driving the core directly or pumping azimuthal magnon modes. For the latter, the azimuthal modes induce core gyration through nonlinear interactions, which in turn renormalizes the magnon band structure. This represents a self-induced mechanism for Floquet band engineering and offers new avenues to study and control nonlinear magnon dynamics.

Phenotyping consists in applying algorithms to identify individuals associated with a specific, potentially complex, trait or condition, typically out of a collection of Electronic Health Records (EHRs). Because a lot of the clinical information of EHRs are lying in texts, phenotyping from text takes an important role in studies that rely on the secondary use of EHRs. However, the heterogeneity and highly specialized aspect of both the content and form of clinical texts makes this task particularly tedious, and is the source of time and cost constraints in observational studies. To facilitate the development, evaluation and reproductibility of phenotyping pipelines, we developed an open-source Python library named medkit. It enables composing data processing pipelines made of easy-to-reuse software bricks, named medkit operations. In addition to the core of the library, we share the operations and pipelines we already developed and invite the phenotyping community for their reuse and enrichment. medkit is available at https://github.com/medkit-lib/medkit

Tree ensembles, including boosting methods, are highly effective and widely used for tabular data. However, large ensembles lack interpretability and require longer inference times. We introduce a method to prune a tree ensemble into a reduced version that is "functionally identical" to the original model. In other words, our method guarantees that the prediction function stays unchanged for any possible input. As a consequence, this pruning algorithm is lossless for any aggregated metric. We formalize the problem of functionally identical pruning on ensembles, introduce an exact optimization model, and provide a fast yet highly effective method to prune large ensembles. Our algorithm iteratively prunes considering a finite set of points, which is incrementally augmented using an adversarial model. In multiple computational experiments, we show that our approach is a "free lunch", significantly reducing the ensemble size without altering the model's behavior. Thus, we can preserve state-of-the-art performance at a fraction of the original model's size.

Cell and nucleus segmentation are fundamental tasks for quantitative bioimage analysis. Despite progress in recent years, biologists and other domain experts still require novel algorithms to handle increasingly large and complex real-world datasets. These algorithms must not only achieve state-of-the-art accuracy, but also be optimized for efficiency, portability and user-friendliness. Here, we introduce InstanSeg: a novel embedding-based instance segmentation pipeline designed to identify cells and nuclei in microscopy images. Using six public cell segmentation datasets, we demonstrate that InstanSeg can significantly improve accuracy when compared to the most widely used alternative methods, while reducing the processing time by at least 60%. Furthermore, InstanSeg is designed to be fully serializable as TorchScript and supports GPU acceleration on a range of hardware. We provide an open-source implementation of InstanSeg in Python, in addition to a user-friendly, interactive QuPath extension for inference written in Java. Our code and pre-trained models are available at https://github.com/instanseg/instanseg ., Comment: 12 pages,6 figures

This four-pages note is an invitation to explore explicit K-stability for arbitrary K\"ahler classes of low dimension and low rank spherical varieties. We apply our simple combinatorial criterion of K-stability of rank one spherical varieties to the example of the blowup of the product of two copies of the projective planes along the diagonal, and obtain strong indication that it admits cscK metrics in every K\"ahler classes., Comment: 4 pages note

This paper presents a novel image reconstruction pipeline for three-gamma (3-{\gamma}) positron emission tomography (PET) aimed at improving spatial resolution and reducing noise in nuclear medicine. The proposed Direct3{\gamma} pipeline addresses the inherent challenges in 3-{\gamma} PET systems, such as detector imperfections and uncertainty in photon interaction points. A key feature of the pipeline is its ability to to determine the order of the detected photons to construct Compton cones, which intersect with the line of response (LOR) to provide an estimation of the emission point. The pipeline processes 3-{\gamma} PET raw data, reconstructs histo-images by propagating energy and spatial uncertainties along the LOR, and applies a 3-D convolutional neural network (CNN) to refine these intermediate images into high-quality reconstructions. To further enhance image quality, the pipeline leverages both supervised learning and adversarial losses, with the latter preserving fine structural details. Experimental results demonstrate that Direct3{\gamma} consistently outperforms conventional 200-ps time-of-flight (TOF) PET in terms of SSIM and PSNR. This pipeline provides a robust framework for 3{\gamma}-PET imaging, enabling more accurate localization of emission points and setting the stage for improved diagnostic capabilities in clinical and research settings., Comment: 10 pages, 11 figures, 1 table

In this paper we study the exponential twist, i.e. a path-integral exponential change of measure, of a Markovian reference probability measure $\P$. This type of transformation naturally appears in variational representation formulae originating from the theory of large deviations and can be interpreted in some cases, as the solution of a specific stochastic control problem. Under a very general Markovian assumption on $\P$, we fully characterize the exponential twist probability measure as the solution of a martingale problem and prove that it inherits the Markov property of the reference measure. The ''generator'' of the martingale problem shows a drift depending on a ''generalized gradient'' of some suitable ''value function'' $v$.

We have developed a minimal model of a swimmer without body deformation based on force and torque dipoles which allows accurate 3D Navier-Stokes calculations. Our model can reproduce swimmer propulsion for a large range of Reynolds numbers, and generate wake vortices in the inertial regime, reminiscent of the flow generated by the flapping tails of real fish. We performed a numerical exploration of the model from low to high Reynolds numbers and obtained universal laws using scaling arguments. We collected data from a wide variety of micro-organisms, thereby extending the experimental data presented in (M. Gazzola et al., Nature Physics 10, 758, 2014). Our theoretical scaling laws compare very well with experimental data across the different regimes, from Stokes to turbulent flows. We believe that this model, due to its relatively simple design, will be very useful for obtaining numerical simulations of collective effects within fish schools composed of hundreds of individuals.

We consider a Stackelberg game in which a principal (she) establishes a two-stage contract with a non-myopic agent (he) whose type is unknown. The contract takes the form of an incentive function mapping the agent's first-stage action to his second-stage incentive. While the first-stage action reveals the agent's type under truthful play, a non-myopic agent could benefit from portraying a false type in the first stage to obtain a larger incentive in the second stage. The challenge is thus for the principal to design the incentive function so as to induce truthful play. We show that this is only possible with a constant, non-reactive incentive functions when the type space is continuous, whereas it can be achieved with reactive functions for discrete types. Additionally, we show that introducing an adjustment mechanism that penalizes inconsistent behavior across both stages allows the principal to design more flexible incentive functions., Comment: To appear in the Proceedings of the 5th IFAC Workshop on Cyber-Physical Human Systems

We study coinductive invertibility of cells in weak $\omega$-categories. We use the inductive presentation of weak $\omega$-categories via an adjunction with the category of computads, and show that invertible cells are closed under all operations of $\omega$-categories. Moreover, we give a simple criterion for invertibility in computads, together with an algorithm computing the data witnessing the invertibility, including the inverse, and the cancellation data.

ESA's PLATO mission aims the detection and characterization of terrestrial planets around solar-type stars as well as the study of host star properties. The noise-to-signal ratio (NSR) is the main performance parameter of the PLATO instrument, which consists of 24 Normal Cameras and 2 Fast Cameras. In order to justify, verify and breakdown NSR-relevant requirements the software simulator PINE was developed. PINE models the signal pathway from a target star to the digital output of a camera based on physical models and considers the major noise contributors. In this paper, the simulator's coarse mode is introduced which allows fast performance analyses on instrument level. The added value of PINE is illustrated by exemplary applications., Comment: 17 pages, 8 figures, 3 tables

Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network. They can be learned in two ways: consistency distillation and consistency training. The former relies on the true velocity field of the corresponding differential equation, approximated by a pre-trained neural network. In contrast, the latter uses a single-sample Monte Carlo estimate of this velocity field. The related estimation error induces a discrepancy between consistency distillation and training that, we show, still holds in the continuous-time limit. To alleviate this issue, we propose a novel flow that transports noisy data towards their corresponding outputs derived from the currently trained model --~as a proxy of the true flow. Our empirical findings demonstrate that this approach mitigates the previously identified discrepancy. Furthermore, we present theoretical and empirical evidence indicating that our generator-induced flow surpasses dedicated optimal transport-based consistency models in effectively reducing the noise-data transport cost. Consequently, our method not only accelerates consistency training convergence but also enhances its overall performance. The code is available at: https://github.com/thibautissenhuth/consistency_GC.

The MPSDynamics.jl package provides an easy to use interface for performing open quantum systems simulations at zero and finite temperatures. The package has been developed with the aim of studying non-Markovian open system dynamics using the state-of-the-art numerically exact Thermalized-Time Evolving Density operator with Orthonormal Polynomials Algorithm (T-TEDOPA) based on environment chain mapping. The simulations rely on a tensor network representation of the quantum states as matrix product states (MPS) and tree tensor network (TTN) states. Written in the Julia programming language, MPSDynamics.jl is a versatile open-source package providing a choice of several variants of the Time-Dependent Variational Principle (TDVP) method for time evolution (including novel bond-adaptive one-site algorithms). The package also provides strong support for the measurement of single and multi-site observables, as well as the storing and logging of data, which makes it a useful tool for the study of many-body physics. It currently handles long-range interactions, time-dependent Hamiltonians, multiple environments, bosonic and fermionic environments, and joint system-environment observables., Comment: 11 pages, 3 figures

Cellulose ethers represent a class of water-soluble polymers widely utilized across diverse sectors, spanning from healthcare to the construction industry. This experimental study specifically delves into aqueous suspensions of carboxymethylcellulose (CMC), a polymer that undergoes gel formation in acidic environments due to attractive interactions between hydrophobic patches along its molecular chain. We use rheometry to determine the linear viscoelastic properties of both CMC suspensions and acid-induced gels at various temperatures. Then, applying the time-temperature superposition principle, we construct master curves for the viscoelastic spectra, effectively described by fractional models. The horizontal shift factors exhibit an Arrhenius-like temperature dependence, allowing us to extract activation energies compatible with hydrophobic interactions. Furthermore, we show that acid-induced CMC gels are physical gels that display a reversible yielding transition under external shear. In particular, we discuss the influence of pH on the non-linear viscoelastic response under large-amplitude oscillatory shear. Overall, our results offer a comprehensive description of the linear and non-linear rheological properties of a compelling case of physical hydrogel involving hydrophobic interactions., Comment: 23 pages, 9 figures

We prove optimal transport stability (in the sense of Andreasson and the second author) for reflexive Weyl polytopes: reflexive polytopes which are convex hulls of an orbit of a Weyl group. When the reflexive Weyl polytope is Delzant, it follows from work of Li, Andreasson, Hultgren, Jonsson, Mazzon, McCleerey, that the weak metric SYZ conjecture holds for the Dwork family in the corresponding toric Fano manifold. In particular, we show that the weak metric SYZ conjecture holds for centrally symmetric smooth Fano toric manifolds., Comment: 11 pages, comments welcome!

Bike-sharing systems play a crucial role in easing traffic congestion and promoting healthier lifestyles. However, ensuring their reliability and user acceptance requires effective strategies for rebalancing bikes. This study introduces a novel approach to address the real-time rebalancing problem with a fleet of vehicles. It employs a dual policy reinforcement learning algorithm that decouples inventory and routing decisions, enhancing realism and efficiency compared to previous methods where both decisions were made simultaneously. We first formulate the inventory and routing subproblems as a multi-agent Markov Decision Process within a continuous time framework. Subsequently, we propose a DQN-based dual policy framework to jointly estimate the value functions, minimizing the lost demand. To facilitate learning, a comprehensive simulator is applied to operate under a first-arrive-first-serve rule, which enables the computation of immediate rewards across diverse demand scenarios. We conduct extensive experiments on various datasets generated from historical real-world data, affected by both temporal and weather factors. Our proposed algorithm demonstrates significant performance improvements over previous baseline methods. It offers valuable practical insights for operators and further explores the incorporation of reinforcement learning into real-world dynamic programming problems, paving the way for more intelligent and robust urban mobility solutions.

Optimization layers in deep neural networks have enjoyed a growing popularity in structured learning, improving the state of the art on a variety of applications. Yet, these pipelines lack interpretability since they are made of two opaque layers: a highly non-linear prediction model, such as a deep neural network, and an optimization layer, which is typically a complex black-box solver. Our goal is to improve the transparency of such methods by providing counterfactual explanations. We build upon variational autoencoders a principled way of obtaining counterfactuals: working in the latent space leads to a natural notion of plausibility of explanations. We finally introduce a variant of the classic loss for VAE training that improves their performance in our specific structured context. These provide the foundations of CF-OPT, a first-order optimization algorithm that can find counterfactual explanations for a broad class of structured learning architectures. Our numerical results show that both close and plausible explanations can be obtained for problems from the recent literature.

We derive new constraints on the $E_G$ statistic as a test of gravity, combining the CMB lensing map estimated from Data Release 6 (DR6) of the Atacama Cosmology Telescope with SDSS BOSS CMASS and LOWZ galaxy data. We develop an analysis pipeline to measure the cross-correlation between CMB lensing maps and galaxy data, following a blinding policy and testing the approach through null and consistency checks. By testing the equivalence of the spatial and temporal gravitational potentials, the $E_G$ statistic can distinguish $\Lambda$CDM from alternative models of gravity. We find $E_G= 0.31^{+0.06}_{-0.05}$ for ACT and CMASS data at 68.28\% confidence level, and $E_G = 0.49^{+0.14}_{-0.11}$ for ACT and LOWZ. Systematic errors are estimated to be 3\% and 4\% respectively. Including CMB lensing information from Planck PR4 results in $E_G = 0.34^{+0.05}_{-0.05}$ with CMASS and $E_G= 0.43^{+0.11}_{-0.09}$ with LOWZ. These are consistent with predictions for the $\Lambda$CDM model that best fits the Planck CMB anisotropy and SDSS BOSS BAO, where $E_G^{\rm GR} (z_{\rm eff} = 0.555) = 0.401\pm 0.005$ for CMB lensing combined with CMASS and $E_G^{\rm GR} (z_{\rm eff} = 0.316) = 0.452\pm0.005$ combined with LOWZ. We also find $E_G$ to be scale independent, with PTE $>5\%$, as predicted by general relativity. The methods developed in this work are also applicable to improved future analyses with upcoming spectroscopic galaxy samples and CMB lensing measurements., Comment: 33 pages, 21 figures, prepared for submission to PRD

Flaws of a continuous limit order book mechanism raise the question of whether a continuous trading session and a periodic auction session would bring better efficiency. This paper wants to go further in designing a periodic auction when both a continuous market and a periodic auction market are available to traders. In a periodic auction, we discover that a strategic trader could take advantage of the accumulated information available along the auction duration by arriving at the latest moment before the auction closes, increasing the price impact on the market. Such price impact moves the clearing price away from the efficient price and may disturb the efficiency of a periodic auction market. We thus propose and quantify the effect of two remedies to mitigate these flaws: randomizing the auction's closing time and optimally designing a transaction fees policy for both the strategic traders and other market participants. Our results show that these policies encourage a strategic trader to send their orders earlier to enhance the efficiency of the auction market, illustrated by data extracted from Alphabet and Apple stocks., Comment: 34 pages, 10 figures