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We present an analytical model for density-split correlation functions, that probe galaxy clustering in different density environments. Specifically, we focus on the cross-correlation between density-split regions and the tracer density field. We show that these correlation functions can be expressed in terms of the two-point probability density function (PDF) of the density field, or equivalently, its bias function. We derive analytical predictions using three levels of approximation for the two-point PDF: a bivariate Gaussian distribution, a bivariate shifted log-normal distribution, and a prediction based on the Large Deviation Theory framework. Under spherical symmetry $\unicode{x2013}$ where spherical collapse dynamics apply, such as for count-in-cell densities with spherical top-hat smoothing $\unicode{x2013}$ LDT predicts the density two-point PDF in the large-separation regime relative to the smoothing radius. We validate our model against dark matter N-body simulations in real space, incorporating Poisson shot noise. Our results show that the LDT predictions outperform the log-normal approximation, and agrees with simulations on large scales within the cosmic variance of a typical DESI DR1 sample, despite relying on only one degree of freedom., Comment: 28 pages, 12 figures

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the expectation of the logarithm of an importance sampling estimate of the likelihood with respect to both the latent variable model parameters and the importance distribution parameters, the expectation being itself with respect to the importance samples. Despite its great empirical success in machine learning, a theoretical analysis of the limit properties of the resulting estimates is still lacking. We fill this gap by establishing consistency when both the Monte Carlo and the observed data sample sizes go to infinity simultaneously. We also establish asymptotic normality and efficiency under additional conditions relating the rate of growth between the Monte Carlo and the observed data samples sizes. We distinguish several regimes related to the smoothness of the importance ratio., Comment: 25 pages, 2 figures

Repeated waves of emerging variants during the SARS-CoV-2 pandemics have highlighted the urge of collecting longitudinal genomic data and developing statistical methods based on time series analyses for detecting new threatening lineages and estimating their fitness early in time. Most models study the evolution of the prevalence of particular lineages over time and require a prior classification of sequences into lineages. Such process is prone to induce delays and bias. More recently, few authors studied the evolution of the prevalence of mutations over time with alternative clustering approaches, avoiding specific lineage classification. Most of the aforementioned methods are however either non parametric or unsuited to pooled data characterizing, for instance, wastewater samples. In this context, we propose an alternative unsupervised method for clustering mutations according to their frequency trajectory over time and estimating group fitness from time series of pooled mutation prevalence data. Our model is a mixture of observed count data and latent group assignment and we use the expectation-maximization algorithm for model selection and parameter estimation. The application of our method to time series of SARS-CoV-2 sequencing data collected from wastewater treatment plants in France from October 2020 to April 2021 shows its ability to agnostically group mutations according to their probability of belonging to B.1.160, Alpha, Beta, B.1.177 variants with selection coefficient estimates per group in coherence with the viral dynamics in France reported by Nextstrain. Moreover, our method detected the Alpha variant as threatening as early as supervised methods (which track specific mutations over time) with the noticeable difference that, since unsupervised, it does not require any prior information on the set of mutations., Comment: 45 pages, 19 figures and tables

Speculative sampling is a popular technique for accelerating inference in Large Language Models by generating candidate tokens using a fast draft model and accepting or rejecting them based on the target model's distribution. While speculative sampling was previously limited to discrete sequences, we extend it to diffusion models, which generate samples via continuous, vector-valued Markov chains. In this context, the target model is a high-quality but computationally expensive diffusion model. We propose various drafting strategies, including a simple and effective approach that does not require training a draft model and is applicable out of the box to any diffusion model. Our experiments demonstrate significant generation speedup on various diffusion models, halving the number of function evaluations, while generating exact samples from the target model.

This paper is a continuation of previous work of the author. We use the categorical trace formalism to give a construction of the categorical Jordan decomposition for representations of finite groups of Lie type. As a second application, we study the endomorphism algebra of the Gelfand-Graev representation and recover a result of Li and Shotton-Li., Comment: Comments welcome !

Density Functional Theory (DFT) calculations not only allow to predict the vibrational and optical properties of solids but also to understand and disentangle the mechanisms playing a key role in the generation of coherent optical phonons. Recent experiments performed on a Bi$_2$Te$_3$ nanofilm have shown that a THz pulse launches at least a coherent $A_{1g}^1$ phonon as the transient transmittance measured using an isotropic detection scheme displays oscillations with a frequency matching the frequency of the $A_{1g}^1$ mode measured in Raman experiments. Such an observation can be explained by invoking either a sum frequency process or cubic/quartic phonon-phonon couplings as considered for Bi$_2$Se$_3$, a parent compound of Bi$_2$Te$_3$. By resorting to group theory and calculating energy surfaces from first-principles, the main phonon-phonon couplings can be identified. Furthermore, a minimal model can be built to compute the dynamics of the Raman active modes coupled to the infrared active mode driven by the experimental THz pulse. Our model firmly establishes that cubic phonon-phonon interactions are relevant as the agreement between the computed and experimental transmittance is noteworthy., Comment: 6 pages, 3 figures, submitted to Physical Review Letters

The pressure function is a fundamental object in various areas of mathematics. Its regularity is studied to derive insights into phase transitions in certain physical systems or to determine the Hausdorff dimension of self-affine sets. In this paper, we prove the analyticity of the pressure function for products of non-invertible matrices satisfying an irreducibility and a contractivity assumptions. Additionally, we establish a variational principle for the pressure function, thereby generalizing previous results., Comment: arXiv admin note: text overlap with arXiv:2402.03879 by other authors

Let X be a smooth cubic hypersurface. We prove that a general cubic surface is isomorphic to a hyperplane section of X .

Continuous gravitational waves (CWs) emission from neutron stars carries information about their internal structure and equation of state, and it can provide tests of General Relativity. We present a search for CWs from a set of 45 known pulsars in the first part of the fourth LIGO--Virgo--KAGRA observing run, known as O4a. We conducted a targeted search for each pulsar using three independent analysis methods considering the single-harmonic and the dual-harmonic emission models. We find no evidence of a CW signal in O4a data for both models and set upper limits on the signal amplitude and on the ellipticity, which quantifies the asymmetry in the neutron star mass distribution. For the single-harmonic emission model, 29 targets have the upper limit on the amplitude below the theoretical spin-down limit. The lowest upper limit on the amplitude is $6.4\!\times\!10^{-27}$ for the young energetic pulsar J0537-6910, while the lowest constraint on the ellipticity is $8.8\!\times\!10^{-9}$ for the bright nearby millisecond pulsar J0437-4715. Additionally, for a subset of 16 targets we performed a narrowband search that is more robust regarding the emission model, with no evidence of a signal. We also found no evidence of non-standard polarizations as predicted by the Brans-Dicke theory., Comment: main paper: 12 pages, 6 figures, 4 tables

The goal of this article is to study quantitatively the localisation/delocalisation properties of the discrete Gaussian chain with long-range interactions. Specifically, we consider the discrete Gaussian chain of length $N$, with Dirichlet boundary condition, range exponent $\alpha \in (1 , \infty)$ and inverse temperature $\beta \in (0,\infty)$, and show that: - For $\alpha \in (2 ,3)$ and $\beta \in (0 , \infty)$, the fluctuations of the chain are at least of order $N^{\frac{1}{2}(\alpha - 2)}$; - For $\alpha = 3$ and $\beta \in (0 , \infty)$, the fluctuations of the chain are of order $\sqrt{N / \ln N}$ (sharp upper and lower bounds up to multiplicative constants are derived). Combined with the results of Kjaer-Hilhorst, Fr\"{o}hlich-Zegarlinski and Garban, these estimates provide an (almost) complete picture for the localisation/delocalisation of the discrete Gaussian chain. The proofs are based on graph surgery techniques which have been recently developed by van Engelenburg-Lis and Aizenman-Harel-Peled-Shapiro to study the phase transitions of two dimensional integer-valued height functions (and of their dual spin systems). Additionally, by combining the previous strategy with a technique introduced by Sellke, we are able extend the method to study the $q$-SOS long-range chain with exponent $q \in (0 , 2)$ and show that, for any inverse temperature $\beta\in (0, \infty)$ and any range exponent $\alpha \in (1 , \infty)$: - The fluctuations of the chain are at least of order $N^{\frac{1}{q}(\alpha -2) \wedge \frac{1}{2}}$; - The fluctuations of the chain are at most of order $N^{\left( \frac{1}{q}\alpha - 1 \right) \wedge \frac 12}$., Comment: 44 pages, 25 Figures. Comments are welcome

In this paper, we present a method based on a modal decomposition to quantify the efficiency of photonic lanterns (PL) based free space optical (FSO) communication receivers. We fabricate a seven port PL and we evaluate numerically the free space to fiber coupling efficiency based on a reconstruction of the fields at the PL FSO multimode port. We validate the numerical approach with an experimental characterization of the PL. Then we compare the PL to a commercial multiplane light converter spatial demultiplexer. The PL shows better coupling efficiency for low order spatial modes with orders of magnitude of demultiplexer size reduction. Finally we evaluate the PL receiver with a simulation of received optical wavefront in a FSO communication

Achieving high conversion efficiencies in second-order nonlinear optical processes is a key challenge in integrated photonics for both classical and quantum applications. This paper presents the first demonstration of Transverse Orientation-Patterned gallium phosphide (TOP-GaP) waveguides showing high-efficiency second harmonic generation. In such devices, first order modal phase matching is unlocked and optimized through the inversion of the nonlinear susceptibility along the vertical direction. We discuss here the theory behind modal phase matching in TOP structures, describe the fabrication process, and present linear and nonlinear characterizations of the TOP-GaP waveguides.

This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024, building on the initial discussions during the inaugural workshop held at CERN in March 2023. Like the summary of the first workshop, this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions., Comment: Summary of the second Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at Imperial College London: https://indico.cern.ch/event/1369392/

The reasoning abilities of Large Language Models (LLMs) are attracting increasing attention. In this work, we focus on causal reasoning and address the task of establishing causal relationships based on correlation information, a highly challenging problem on which several LLMs have shown poor performance. We introduce a prompting strategy for this problem that breaks the original task into fixed subquestions, with each subquestion corresponding to one step of a formal causal discovery algorithm, the PC algorithm. The proposed prompting strategy, PC-SubQ, guides the LLM to follow these algorithmic steps, by sequentially prompting it with one subquestion at a time, augmenting the next subquestion's prompt with the answer to the previous one(s). We evaluate our approach on an existing causal benchmark, Corr2Cause: our experiments indicate a performance improvement across five LLMs when comparing PC-SubQ to baseline prompting strategies. Results are robust to causal query perturbations, when modifying the variable names or paraphrasing the expressions.

Let $\mathbf{G}$ be a connected reductive group over a finite field $\mathbb{F}_q$ of characteristic $p > 0$. In this paper, we study a category which we call Deligne--Lusztig category $\mathcal{O}$ and whose definition is similar to category $\mathcal{O}$. We use this to construct a collection of representations of $\mathbf{G}(\mathbb{F}_q)$ which we call the tilting representations. They form a generating collection of integral projective representations of $\mathbf{G}(\mathbb{F}_q)$. Finally we compute the character of these representations and relate their expression to previous calculations of Lusztig and we then use this to establish a conjecture of Dudas--Malle., Comment: Comments welcome !

The goal of this paper is to give a new construction of the free monodromic categories defined by Yun. We then use this formalism to give simpler constructions of the free monodromic Hecke categories and then compute the trace of Frobenius and of the identity on them. As a first application of the formalism, we produce new proofs of key theorems in Deligne--Lusztig theory., Comment: Comments welcome !

This work extends the adjoint-deep learning framework for runaway electron (RE) evolution developed in Ref. [C. McDevitt et al., A physics-constrained deep learning treatment of runaway electron dynamics, Submitted to Physics of Plasmas (2024)] to account for large-angle collisions. By incorporating large-angle collisions the framework allows the avalanche of REs to be captured, an essential component to RE dynamics. This extension is accomplished by using a Rosenbluth-Putvinski approximation to estimate the distribution of secondary electrons generated by large-angle collisions. By evolving both the primary and multiple generations of secondary electrons, the present formulation is able to capture both the detailed temporal evolution of a RE population beginning from an arbitrary initial momentum space distribution, along with providing approximations to the saturated growth and decay rates of the RE population. Predictions of the adjoint-deep learning framework are verified against a traditional RE solver, with good agreement present across a broad range of parameters.

An adjoint formulation leveraging a physics-informed neural network (PINN) is employed to advance the density moment of a runaway electron (RE) distribution forward in time. A distinguishing feature of this approach is that once the adjoint problem is solved, its solution can be used to project the RE density forward in time for an arbitrary initial momentum space distribution of REs. Furthermore, by employing a PINN, a parametric solution to the adjoint problem can be learned. Thus, once trained, this adjoint-deep learning framework is able to efficiently project the RE density forward in time across various plasma conditions while still including a fully kinetic description of RE dynamics. As an example application, the temporal evolution of the density of primary electrons is studied, with particular emphasis on evaluating the decay of a RE population when below threshold. Predictions from the adjoint-deep learning framework are found to be in good agreement with a traditional relativistic electron Fokker-Planck solver, for several distinct initial conditions, and across an array of physics parameters. Once trained the PINN thus provides a means of generating RE density time histories with exceptionally low online execution time.

Prime numbers are fascinating by the way they appear in the set of natural numbers. Despite several results enlighting us about their repartition, the set of prime numbers is often informally qualified as misterious. In the present paper, we introduce a formalism allowing to state a formal conjecture: the set of prime numbers is supernatural. Our conjecture has no analog in the existing literature. We explain that this conjecture is expected to be a hard challenge for any kind of intelligence. However it is really natural and even seems very close to be canonical., Comment: new version of https://hal.science/hal-02564341

A new method, based on comparing isotopic yield ratios measured at forward and sideward polar angles and on cross-bombarding heavy nuclei with different neutron-to-proton ratios, is used to quantify the stopping power in heavy-ion collisions. For central collisions of isotopically separated $^{124,129}$Xe+$^{112,124}$Sn at 100~MeV/nucleon bombarding energy, measured with the 4$\pi$ multidetector INDRA at GSI, a moderate transparency is deduced for hydrogen isotopes, whereas for heavier fragmentation products with atomic number $Z \ge 3$ a high transparency exceeding 50\% is observed. An anomalously large transparency is found for alpha particles, and possible explanations are presented., Comment: 15 pages, 5 figures

This study focuses on a radial alignment between Parker Solar Probe (PSP) and Solar Orbiter (SolO) on the 29$^{\text{th}}$ of April 2021 (during a solar minimum), when the two spacecraft were respectively located at $\sim 0.075$ and $\sim 0.9$~au from the Sun. A previous study of this alignment allowed the identification of the same density enhancement (with a time scale of $\sim$1.5~h), and substructures ($\sim$20-30~min timescale), passing first by PSP, and then SolO after a $\sim 138$~h propagation time in the inner heliosphere. We show here that this structure belongs to the large scale heliospheric magnetic sector boundary. In this region, the density is dominated by radial gradients, whereas the magnetic field reversal is consistent with longitudinal gradients in the Carrington reference frame. We estimate the density structure radial size to remain of the order L$_R \sim 10^6$~km, while its longitudinal and latitudinal sizes, are estimated to expand from L$_{\varphi, \theta} \sim 10^4$-$10^5$~km in the high solar corona, to L$_{\varphi, \theta} \sim 10^5$-$10^6$~km at PSP, and L$_{\varphi, \theta} \sim 10^6$-$10^7$~km at SolO. This implies a strong evolution of the structure's aspect ratio during the propagation, due to the plasma's nearly spherical expansion. The structure's shape is therefore inferred to evolve from elongated in the radial direction at $\sim$2-3 solar radii (high corona), to sizes of nearly the same order in all directions at PSP, and then becoming elongated in the directions transverse to the radial at SolO. Measurements are not concordant with local reconnection of open solar wind field lines, so we propose that the structure has been generated through interchange reconnection near the tip of a coronal streamer.

We transpose Jones' technology and the authors' C*-algebraic techniques to study representations of the Leavitt path algebra L (over an arbitrary row-finite graph) by using its quiver algebra A. We establish an equivalence of categories between certain full subcategories of Rep(A) and Rep(L) that preserves irreducibility and indecomposability. We define a dimension function on Rep(L), and for each finite dimension we provide a moduli space for the irreducible classes by transporting structures of King and Nakajima on quiver representations. Our techniques are both explicit and functorial., Comment: 28 pages, 4 diagrams

We investigate the nonparametric estimation problem of the density $\pi$, representing the stationary distribution of a two-dimensional system $\left(Z_t\right)_{t \in[0, T]}=\left(X_t, \lambda_t\right)_{t \in[0, T]}$. In this system, $X$ is a Hawkes-diffusion process, and $\lambda$ denotes the stochastic intensity of the Hawkes process driving the jumps of $X$. Based on the continuous observation of a path of $(X_t)$ over $[0, T]$, and initially assuming that $\lambda$ is known, we establish the convergence rate of a kernel estimator $\widehat\pi\left(x^*, y^*\right)$ of $\pi\left(x^*,y^*\right)$ as $T \rightarrow \infty$. Interestingly, this rate depends on the value of $y^*$ influenced by the baseline parameter of the Hawkes intensity process. From the rate of convergence of $\widehat\pi\left(x^*,y^*\right)$, we derive the rate of convergence for an estimator of the invariant density $\lambda$. Subsequently, we extend the study to the case where $\lambda$ is unknown, plugging an estimator of $\lambda$ in the kernel estimator and deducing new rates of convergence for the obtained estimator. The proofs establishing these convergence rates rely on probabilistic results that may hold independent interest. We introduce a Girsanov change of measure to transform the Hawkes process with intensity $\lambda$ into a Poisson process with constant intensity. To achieve this, we extend a bound for the exponential moments for the Hawkes process, originally established in the stationary case, to the non-stationary case. Lastly, we conduct a numerical study to illustrate the obtained rates of convergence of our estimators.

Denoising diffusion models (DDMs) offer a flexible framework for sampling from high dimensional data distributions. DDMs generate a path of probability distributions interpolating between a reference Gaussian distribution and a data distribution by incrementally injecting noise into the data. To numerically simulate the sampling process, a discretisation schedule from the reference back towards clean data must be chosen. An appropriate discretisation schedule is crucial to obtain high quality samples. However, beyond hand crafted heuristics, a general method for choosing this schedule remains elusive. This paper presents a novel algorithm for adaptively selecting an optimal discretisation schedule with respect to a cost that we derive. Our cost measures the work done by the simulation procedure to transport samples from one point in the diffusion path to the next. Our method does not require hyperparameter tuning and adapts to the dynamics and geometry of the diffusion path. Our algorithm only involves the evaluation of the estimated Stein score, making it scalable to existing pre-trained models at inference time and online during training. We find that our learned schedule recovers performant schedules previously only discovered through manual search and obtains competitive FID scores on image datasets., Comment: NeurIPS 2024 accepted paper

Density Functional Tight-Binding (DFTB), an approximative approach derived from Density Functional Theory (DFT), has the potential to pave the way for simulations of large periodic or non-periodic systems. We have specifically tailored DFTB parameters to enhance the accuracy of electronic band gap calculations in both 3D and 2D lead-iodide perovskites, at a significantly reduced computational cost relative to state-of-the-art ab initio calculations. Our electronic DFTB parameters allow computing not only the band gap but also effective masses of perovskite materials with reasonable accuracy compared to existing experimental data and state-of-the-art DFT calculations. The electronic band structures of vacancy-ordered and, lead- and iodide- deficient perovskites are also explored. Additionally, we demonstrate the efficiency of DFTB in computing electronic band alignments in perovskite heterostructures. The DFTB-based approach is anticipated to be beneficial for studying large-scale systems such as heterostructures and nanocrystals., Comment: 44 pages, 9 figures

In the early Universe, neutrinos decouple quickly from the primordial plasma and propagate without further interactions. The impact of free-streaming neutrinos is to create a temporal shift in the gravitational potential that impacts the acoustic waves known as baryon acoustic oscillations (BAOs), resulting in a non-linear spatial shift in the Fourier-space BAO signal. In this work, we make use of and extend upon an existing methodology to measure the phase shift amplitude $\beta_{\phi}$ and apply it to the DESI Data Release 1 (DR1) BAOs with an anisotropic BAO fitting pipeline. We validate the fitting methodology by testing the pipeline with two publicly available fitting codes applied to highly precise cubic box simulations and realistic simulations representative of the DESI DR1 data. We find further study towards the methods used in fitting the BAO signal will be necessary to ensure accurate constraints on $\beta_{\phi}$ in future DESI data releases. Using DESI DR1, we present individual measurements of the anisotropic BAO distortion parameters and the $\beta_{\phi}$ for the different tracers, and additionally a combined fit to $\beta_{\phi}$ resulting in $\beta_{\phi} = 2.7 \pm 1.7$. After including a prior on the distortion parameters from constraints using \textit{Planck} we find $\beta_{\phi} = 2.7^{+0.60}_{-0.67} $ suggesting $\beta_{\phi} > 0$ at 4.3$\sigma$ significance. This result may hint at a phase shift that is not purely sourced from the standard model expectation for $N_{\rm{eff}}$ or could be a upwards statistical fluctuation in the measured $\beta_{\phi}$; this result relaxes in models with additional freedom beyond $\Lambda$CDM.

We study best linear predictions in a context where the outcome of interest and some of the covariates are observed in two different datasets that cannot be matched. Traditional approaches obtain point identification by relying, often implicitly, on exclusion restrictions. We show that without such restrictions, coefficients of interest can still be partially identified and we derive a constructive characterization of the sharp identified set. We then build on this characterization to develop computationally simple and asymptotically normal estimators of the corresponding bounds. We show that these estimators exhibit good finite sample performances., Comment: 38 pages

Metals hosting strong electronic interactions, including high-temperature superconductors, behave in ways that do not conform to the normal Fermi liquid theory. To pinpoint the microscopic origin of this strange metal behavior, here we reexamine the transport and optical properties of the two-dimensional t-J model taking advantage of recent improvements made on the finite temperature Lanczos method (FTLM), enabling numerically exact calculations at unprecedentedly low temperatures and high spectral resolution. We find that strange metallicity is pervasive in the temperature-doping phase diagram wherever magnetic order is suppressed: it is driven by the presence of a fluctuating spin background, and it is therefore independent on hole concentration and unrelated to quantum criticality. Our results point to a two-step transport mechanism, with short- and long-time processes associated respectively with the charge and spin dynamics, the latter being responsible for both the strange metal character and the unconventional optical conductivities seen in experiments., Comment: 20 pages, 4 figures

Deformations of knots and links in ambient space can be studied combinatorially on their diagrams via local modifications called Reidemeister moves. While it is well-known that, in order to move between equivalent diagrams with Reidemeister moves, one sometimes needs to insert excess crossings, there are significant gaps between the best known lower and upper bounds on the required number of these added crossings. In this article, we study the problem of turning a diagram of a split link into a split diagram, and we show that there exist split links with diagrams requiring an arbitrarily large number of such additional crossings. More precisely, we provide a family of diagrams of split links, so that any sequence of Reidemeister moves transforming a diagram with $c$ crossings into a split diagram requires going through a diagram with $\Omega(\sqrt{c})$ extra crossings. Our proof relies on the framework of bubble tangles, as introduced by Lunel and de Mesmay, and a technique of Chambers and Liokumovitch to turn homotopies into isotopies in the context of Riemannian geometry.

The development of robotic grippers and hands for automation aims to emulate human dexterity without sacrificing the efficiency of industrial grippers. This study introduces Rotograb, a tendon-actuated robotic hand featuring a novel rotating thumb. The aim is to combine the dexterity of human hands with the efficiency of industrial grippers. The rotating thumb enlarges the workspace and allows in-hand manipulation. A novel joint design minimizes movement interference and simplifies kinematics, using a cutout for tendon routing. We integrate teleoperation, using a depth camera for real-time tracking and autonomous manipulation powered by reinforcement learning with proximal policy optimization. Experimental evaluations demonstrate that Rotograb's rotating thumb greatly improves both operational versatility and workspace. It can handle various grasping and manipulation tasks with objects from the YCB dataset, with particularly good results when rotating objects within its grasp. Rotograb represents a notable step towards bridging the capability gap between human hands and industrial grippers. The tendon-routing and thumb-rotating mechanisms allow for a new level of control and dexterity. Integrating teleoperation and autonomous learning underscores Rotograb's adaptability and sophistication, promising substantial advancements in both robotics research and practical applications.

High resolution rotational Terahertz (THz) spectroscopy has been widely applied to the studies of numerous polar gas phase molecules, in particular volatile organic compounds (VOCs). During the storage of foodstuffs packed under a protective atmosphere, microbial activity will lead to the generation of a complex mixture of trace gases that could be used as food spoilage indicators. Here we have demonstrated that the THz instrumentation presently available provides sufficient sensitivity and selectivity to monitor the generation of hydrogen sulfide (H2S) in the headspace of packed Atlantic salmon (Salmo salar) fillet portions. A comprehensive comparison was made by selective-ion flow-tube mass spectrometry (SIFT-MS) in order to validate the THz measurements and protocol. The detectivity of a range of alternative compounds for this application is also provided, based on the experimental detection limit observed and molecular spectroscopic properties. Molecules like ethanol, methyl mercaptan and ammonia are suitable indicators with the presently available sensitivity levels, while dimethyl sulfide, acetone and butanone may be considered with a sensitivity improvement of 2 orders of magnitude.

We characterize all totally elliptic surface group representations into $\mathrm{PSL}_2\mathbb{R}$ by showing that they are either representations into a compact subgroup or Deroin--Tholozan representations., Comment: 11 pages, 5 figures

In this work, we establish, for a strong Feller process, the large deviation principle for the occupation measure conditioned not to exit a given subregion. The rate function vanishes only at a unique measure, which is the so-called quasi-ergodic distribution of the process in this subregion. In addition, we show that the rate function is the Dirichlet form in the particular case when the process is reversible. We apply our results to several stochastic processes such as the solutions of elliptic stochastic differential equations driven by a rotationally invariant $\alpha$-stable process, the kinetic Langevin process, and the overdamped Langevin process driven by a Brownian motion.

We obtain Riesz transform bounds and characterise operator-adapted Hardy spaces to solve boundary value problems for singular Schr\"odinger equations $-\mathrm{div}(A\nabla u)+aVu=0$ in the upper half-space $\mathbb{R}^{1+n}_{+}$ with boundary dimension $n\geq 3$. The coefficients $(A,a,V)$ are assumed to be independent of the transversal direction to the boundary, and consist of a complex-elliptic pair $(A,a)$ that is bounded and measurable with a certain block structure, and a non-negative singular potential $V$ in the reverse H\"older class $\mathrm{RH}^{q}(\mathbb{R}^{n})$ for $q\geq \max\{\frac{n}{2},2\}$. We find extrapolation intervals for exponents $p$ around $2$ on which the Dirichlet problem is well-posed for boundary data in $L^{p}(\mathbb{R}^{n})$, and the associated Regularity problem is well-posed for boundary data in Sobolev spaces $\dot{\mathcal{V}}^{1,p}(\mathbb{R}^{n})$ that are adapted to the potential $V$, when $p>1$. The results permit boundary data in the Dziuba\`{n}ski--Zienkiewicz Hardy space $\mathrm{H}^{1}_{V}(\mathbb{R}^{n})$ and adapted Hardy--Sobolev spaces $\dot{\mathrm{H}}^{1,p}_{V}(\mathbb{R}^{n})$ when $p\leq 1$. We also obtain comparability of square functions and nontangential maximal functions for the solutions with their boundary data.

We study deformation spaces using multi-centered dilatations. Interpolating Fulton simple deformation space and Rost asymmetric double deformation space, we introduce (asymmetric) deformation spaces attached to chains of immersions of arbitrary lengths. One of the main results of this paper is the so-called panelization isomorphism, producing several isomorphisms between the deformation space of length $n$ and deformation spaces of smaller lengths. Combining these isomorphisms, we get a polyptych $\mathscr{P}(n)$ of deformation spaces. Having these panelization isomorphisms allows to compute the strata -- certain restrictions of special interests -- of deformation spaces.

Run-and-Tumble Particles (RTPs) are a key model of active matter. They are characterized by alternating phases of linear travel and random direction reshuffling. By this dynamic behavior, they break time reversibility and energy conservation at the microscopic level. It leads to complex out-of-equilibrium phenomena such as collective motion, pattern formation, and motility-induced phase separation (MIPS). In this work, we study two fundamental dynamical models of a pair of RTPs with jamming interactions and provide a rigorous link between their discrete- and continuous-space descriptions. We demonstrate that as the lattice spacing vanishes, the discrete models converge to a continuous RTP model on the torus, described by a Piecewise Deterministic Markov Process (PDMP). This establishes that the invariant measures of the discrete models converge to that of the continuous model, which reveals finite mass at jamming configurations and exponential decay away from them. This indicates effective attraction, which is consistent with MIPS. Furthermore, we quantitatively explore the convergence towards the invariant measure. Such convergence study is critical for understanding and characterizing how MIPS emerges over time. Because RTP systems are non-reversible, usual methods may fail or are limited to qualitative results. Instead, we adopt a coupling approach to obtain more accurate, non-asymptotic bounds on mixing times. The findings thus provide deeper theoretical insights into the mixing times of these RTP systems, revealing the presence of both persistent and diffusive regimes.

ICLabel is an important plug-in function in EEGLAB, the most widely used software for EEG data processing. A powerful approach to automated processing of EEG data involves decomposing the data by Independent Component Analysis (ICA) and then classifying the resulting independent components (ICs) using ICLabel. While EEGLAB pipelines support high-performance computing (HPC) platforms running the open-source Octave interpreter, the ICLabel plug-in is incompatible with Octave because of its specialized neural network architecture. To enhance cross-platform compatibility, we developed a Python version of ICLabel that uses standard EEGLAB data structures. We compared ICLabel MATLAB and Python implementations to data from 14 subjects. ICLabel returns the likelihood of classification in 7 classes of components for each ICA component. The returned IC classifications were virtually identical between Python and MATLAB, with differences in classification percentage below 0.001%.

In this work, we investigate the compactness and the long time behavior of killed Feynman-Kac semigroups of various processes arising from statistical physics with very general singular Schr{\"o}dinger potentials. The processes we consider cover a large class of processes used in statistical physics, with strong links with quantum mechanics and (local or not) Schr{\"o}dinger operators (including e.g. fractional Laplacians). For instance we consider solutions to elliptic differential equations, L{\'e}vy processes, the kinetic Langevin process with locally Lipschitz gradient fields, and systems of interacting L{\'e}vy particles. Our analysis relies on a Perron-Frobenius type theorem derived in a previous work [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.] for Feller kernels and on the tools introduced in [L. Wu, 2004, Probab. Theory Relat. Fields] to compute bounds on the essential spectral radius of a bounded nonnegative kernel.

We study forest-skein (FS) groups using dynamics. A simple Ore FS category produces three FS groups analogous to Richard Thompson's groups. Reconstruction theorems of McCleary and Rubin apply to these FS groups: each of them encodes a canonical rigid group action and thus carries powerful dynamical invariants. We then explicitly construct infinitely many isomorphism classes of finitely presented (of type $F_\infty$) infinite simple groups which act faithfully on the circle by (orientation-preserving) homeomorphisms, but admit no non-trivial finite piecewise linear actions nor finite piecewise projective actions. To the best of our knowledge these are the first examples witnessing these properties. We also show these groups fit into the finite germ extension framework of Belk, Hyde, and Matucci., Comment: 39 pages, 14 figures

The estimation of uncertainties in cosmological parameters is an important challenge in Large-Scale-Structure (LSS) analyses. For standard analyses such as Baryon Acoustic Oscillations (BAO) and Full Shape, two approaches are usually considered. First: analytical estimates of the covariance matrix use Gaussian approximations and (nonlinear) clustering measurements to estimate the matrix, which allows a relatively fast and computationally cheap way to generate matrices that adapt to an arbitrary clustering measurement. On the other hand, sample covariances are an empirical estimate of the matrix based on en ensemble of clustering measurements from fast and approximate simulations. While more computationally expensive due to the large amount of simulations and volume required, these allow us to take into account systematics that are impossible to model analytically. In this work we compare these two approaches in order to enable DESI's key analyses. We find that the configuration space analytical estimate performs satisfactorily in BAO analyses and its flexibility in terms of input clustering makes it the fiducial choice for DESI's 2024 BAO analysis. On the contrary, the analytical computation of the covariance matrix in Fourier space does not reproduce the expected measurements in terms of Full Shape analyses, which motivates the use of a corrected mock covariance for DESI's Full Shape analysis., Comment: 23 pages, 5 figures 7 tables, submitted to JCAP

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.

In the last few decades the development of ultrafast lasers has revolutionized our ability to gain insight into light-matter interactions. The appearance of few-cycle light sources available from the visible to the mid-infrared spectral range and the development of attosecond extreme ultraviolet and x-ray technologies provide for the first time the possibility to directly observe and control ultrafast electron dynamics in matter on their natural time scale. However, few-fs sources have hardly been available in the deep ultraviolet (DUV; 4-6 eV, 300-200 nm) and are unavailable in the vacuum ultraviolet (VUV; 6-12 eV, 200-100 nm) spectral range, corresponding to the photon energies required for valence excitation of atoms and molecules. Here, we generate VUV pulses with $\mu$J energy tunable between 160 and 190 nm via resonant dispersive wave emission during soliton self-compression in a capillary. We fully characterize the pulses in situ using frequency-resolved optical gating based on two-photon photoionization in noble gases. The measurements reveal that in most of the cases the pulses are shorter than 3 fs. These findings unlock the potential to investigate ultrafast electron dynamics with a time-resolution that has been hitherto inaccessible when using VUV pulses.

We analyze the many-body Hamiltonian describing a mobile impurity immersed in a Bose-Einstein condensate (BEC). Using exact unitary transformations and rigorous error estimates, we show the validity of the Bogoliubov-Fr\"ohlich Hamiltonian for the Bose polaron in the regime of moderately strong, repulsive interactions with a dilute BEC. Moreover, we calculate analytically the universal logarithmic correction to the ground state energy that arises from an impurity mediated phonon-phonon interaction., Comment: Updated bibliography

We prove that infinite mapping class group orbits are dense in the character variety of Deroin-Tholozan representations. In other words, the action is minimal except for finite orbits. Our arguments rely on the symplectic structure of the character variety, emphasizing this geometric perspective over its algebraic properties., Comment: 39 pages, 15 figures

An open question in \emph{Imprecise Probabilistic Machine Learning} is how to empirically derive a credal region (i.e., a closed and convex family of probabilities on the output space) from the available data, without any prior knowledge or assumption. In classification problems, credal regions are a tool that is able to provide provable guarantees under realistic assumptions by characterizing the uncertainty about the distribution of the labels. Building on previous work, we show that credal regions can be directly constructed using conformal methods. This allows us to provide a novel extension of classical conformal prediction to problems with ambiguous ground truth, that is, when the exact labels for given inputs are not exactly known. The resulting construction enjoys desirable practical and theoretical properties: (i) conformal coverage guarantees, (ii) smaller prediction sets (compared to classical conformal prediction regions) and (iii) disentanglement of uncertainty sources (epistemic, aleatoric). We empirically verify our findings on both synthetic and real datasets.

All-solid-state batteries hold great promise for electric vehicle applications due to their enhanced safety and higher energy density. However, further performance optimization requires a deeper understanding of their degradation mechanisms, particularly at the nanoscale. This study investigates the real-time degradation processes of an oxide-based all-solid-state micro-battery, using focused ion beam lamellae composed of LAGP as the solid electrolyte, LiFePO4 (LFP) composite as the positive electrode, and LiVPO4 (LVP) composite as the negative electrode. In situ electrochemical transmission electron microscopy (TEM) revealed critical degradation phenomena, including the formation of cracks along grain boundaries in the solid electrolyte due to lithium diffusion and mechanical stress. Additionally, the shrinkage of solid electrolyte particles and the formation of amorphous phases were observed. These findings highlight the importance of grain boundary dynamics and amorphization in the performance of solid electrolytes and provide insights into degradation mechanisms that can inform the design of more durable all-solid-state batteries., Comment: 26 pages, 6 figures

We investigate the shear flow of a sludge mimicking slurries produced by the nuclear industry and constituted of a dispersion of non-Brownian particles into an attractive colloidal dispersion at a total solid volume fraction of about 10%. Combining rheometry and ultrasound flow imaging, we show that, upon decreasing the shear rate, the flow transitions from a homogeneous shear profile in the bulk to a fully arrested plug-like state with total wall slip, through an oscillatory regime where strong fluctuations of the slip velocity propagate along the vorticity direction. When the shear stress is imposed close to the yield stress, the shear rate presents large, quasi-periodic peaks, associated with the propagation of local stick-and-slip events along the vorticity direction. Such complex dynamics, reminiscent of similar phenomena reported in much denser suspensions, highlight the importance of local flow characterization to fully understand sludge rheology., Comment: 22 pages, 7 figures