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This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a fixed point algorithm and a Riemannian optimization method based on the derived information geometry of Elliptical Wishart distributions. The existence and uniqueness of the MLE are characterized as well as the convergence of both estimation algorithms. Statistical properties of the MLE are also investigated such as consistency, asymptotic normality and an intrinsic version of Fisher efficiency. On the statistical learning side, novel classification and clustering methods are designed. For the $t$-Wishart distribution, the performance of the MLE and statistical learning algorithms are evaluated on both simulated and real EEG and hyperspectral data, showcasing the interest of our proposed methods.

Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex multiscale targets, there may not be one choice of step size that works well globally. In this work, we address this problem with a novel class of involutive MCMC methods -- AutoStep MCMC -- that selects an appropriate step size at each iteration adapted to the local geometry of the target distribution. We prove that AutoStep MCMC is $\pi$-invariant and has other desirable properties under mild assumptions on the target distribution $\pi$ and involutive proposal. Empirical results examine the effect of various step size selection design choices, and show that AutoStep MCMC is competitive with state-of-the-art methods in terms of effective sample size per unit cost on a range of challenging target distributions.

Generative retrieval for search and recommendation is a promising paradigm for retrieving items, offering an alternative to traditional methods that depend on external indexes and nearest-neighbor searches. Instead, generative models directly associate inputs with item IDs. Given the breakthroughs of Large Language Models (LLMs), these generative systems can play a crucial role in centralizing a variety of Information Retrieval (IR) tasks in a single model that performs tasks such as query understanding, retrieval, recommendation, explanation, re-ranking, and response generation. Despite the growing interest in such a unified generative approach for IR systems, the advantages of using a single, multi-task model over multiple specialized models are not well established in the literature. This paper investigates whether and when such a unified approach can outperform task-specific models in the IR tasks of search and recommendation, broadly co-existing in multiple industrial online platforms, such as Spotify, YouTube, and Netflix. Previous work shows that (1) the latent representations of items learned by generative recommenders are biased towards popularity, and (2) content-based and collaborative-filtering-based information can improve an item's representations. Motivated by this, our study is guided by two hypotheses: [H1] the joint training regularizes the estimation of each item's popularity, and [H2] the joint training regularizes the item's latent representations, where search captures content-based aspects of an item and recommendation captures collaborative-filtering aspects. Our extensive experiments with both simulated and real-world data support both [H1] and [H2] as key contributors to the effectiveness improvements observed in the unified search and recommendation generative models over the single-task approaches., Comment: Accepted for publication in the 18th ACM Conference on Recommender Systems (RecSys'24)

We introduce a technique for extracting microstructural geometry from NMR lineshape analysis in porous materials at angstrom-scale resolution with the use of weak magnetic field gradients. Diverging from the generally held view of FID signals undergoing simple exponential decay, we show that a detailed analysis of the line shape can unravel structural geometry on much smaller scales than previously thought. While the original q-space PFG NMR relies on strong magnetic field gradients in order to achieve high spatial resolution, our current approach reaches comparable or higher resolution using much weaker gradients. As a model system, we simulated gas diffusion for xenon confined within carbon nanotubes over a range of temperatures and nanotube diameters in order to unveil manifestations of confinement in the diffusion behavior. We report a multiscale scheme that couples the above MD simulations with the generalized Langevin equation to estimate the transport properties of interest for this problem, such as diffusivity coefficients and NMR lineshapes, using the Green-Kubo correlation function to correctly evaluate time-dependent diffusion. Our results highlight how NMR methodologies can be adapted as effective means towards structural investigation at very small scales when dealing with complicated geometries. This method is expected to find applications in materials science, catalysis, biomedicine and other areas., Comment: 8 pages, 5 figures

The Hamiltonian Monte Carlo (HMC) algorithm is often lauded for its ability to effectively sample from high-dimensional distributions. In this paper we challenge the presumed domination of HMC for the Bayesian analysis of GLMs. By utilizing the structure of the compute graph rather than the graphical model, we reduce the time per sweep of a full-scan Gibbs sampler from $O(d^2)$ to $O(d)$, where $d$ is the number of GLM parameters. Our simple changes to the implementation of the Gibbs sampler allow us to perform Bayesian inference on high-dimensional GLMs that are practically infeasible with traditional Gibbs sampler implementations. We empirically demonstrate a substantial increase in effective sample size per time when comparing our Gibbs algorithms to state-of-the-art HMC algorithms. While Gibbs is superior in terms of dimension scaling, neither Gibbs nor HMC dominate the other: we provide numerical and theoretical evidence that HMC retains an edge in certain circumstances thanks to its advantageous condition number scaling. Interestingly, for GLMs of fixed data size, we observe that increasing dimensionality can stabilize or even decrease condition number, shedding light on the empirical advantage of our efficient Gibbs sampler.

Multiphoton interference is crucial to many photonic quantum technologies. In particular, interference forms the basis of optical quantum information processing platforms and can lead to significant computational advantages. It is therefore interesting to study the interference arising from various states of light in large interferometric networks. Here, we implement a quantum walk in a highly stable, low-loss, multiport interferometer with up to 24 ultrafast time bins. This time-bin interferometer comprises a sequence of birefringent crystals which produce pulses separated by 4.3\,ps, all along a single optical axis. Ultrafast Kerr gating in an optical fiber is employed to time-demultiplex the output from the quantum walk. We measure one-, two-, and three-photon interference arising from various input state combinations, including a heralded single-photon state, a thermal state, and an attenuated coherent state at one or more input ports. Our results demonstrate that ultrafast time bins are a promising platform to observe large-scale multiphoton interference.

You may have seen the words "topological recursion" mentioned in papers on matrix models, Hurwitz theory, Gromov-Witten theory, topological string theory, knot theory, topological field theory, JT gravity, cohomological field theory, free probability theory, gauge theories, to name a few. The goal of these lecture notes is certainly not to explain all these applications of the topological recursion framework. Rather, the intention is to provide a down-to-earth (and hopefully accessible) introduction to topological recursion itself, so that when you see these words mentioned, you can understand what it is all about. These lecture notes accompanied a series of lectures at the Les Houches school "Quantum Geometry (Mathematical Methods for Gravity, Gauge Theories and Non-Perturbative Physics)" in Summer 2024., Comment: 54 pages. This is a first draft: comments, suggestions and corrections are welcome and encouraged!

The design of absorbing boundary conditions (ABC) in a numerical simulation is a challenging task. In the best cases, spurious reflections remain for some angles of incidence or at certain wave lengths. In the worst, ABC are not even possible for the set of equations and/or numerical schemes used in the simulation and reflections can not be avoided at all. Perflectly Matched Layer (PML) are layers of absorbing medium which can be added at the simulation edges in order to significantly damp both outgoing and reflected waves, thus effectively playing the role of an ABC. They are able to absorb waves and prevent reflections for all angles and frequencies at a modest computational cost. It increases the simulation accuracy and negates the need of oversizing the simulation usually imposed by ABC and leading to a waste of computational resources and power. PML for finite-difference time-domain (FDTD) schemes in Particle-In-cell (PIC) codes are presented for both Maxwell's equations and, for the first time, the envelope wave equation. Being of the second order, the latter requires significant evolutions with respect to the former. It applies in particular to simulations of lasers propagating in plasmas using the reduced Complex Envelope model. The implementation is done in the open source code Smilei for both Cartesian and azimuthal modes (AM) decomposition geometries.

Annealed Sequential Monte Carlo (SMC) samplers are special cases of SMC samplers where the sequence of distributions can be embedded in a smooth path of distributions. Using this underlying path of distributions and a performance model based on the variance of the normalisation constant estimator, we systematically study dense schedule and large particle limits. From our theory and adaptive methods emerges a notion of global barrier capturing the inherent complexity of normalisation constant approximation under our performance model. We then turn the resulting approximations into surrogate objective functions of algorithm performance, and use them for methodology development. We obtain novel adaptive methodologies, Sequential SMC (SSMC) and Sequential AIS (SAIS) samplers, which address practical difficulties inherent in previous adaptive SMC methods. First, our SSMC algorithms are predictable: they produce a sequence of increasingly precise estimates at deterministic and known times. Second, SAIS, a special case of SSMC, enables schedule adaptation at a memory cost constant in the number of particles and require much less communication. Finally, these characteristics make SAIS highly efficient on GPUs. We develop an open-source, high-performance GPU implementation based on our methodology and demonstrate up to a hundred-fold speed improvement compared to state-of-the-art adaptive AIS methods., Comment: 65 pages, 7 figures

In tissue engineering, we seek to address comprehensive tissue repair and regeneration needs. Aligned nanofibers have emerged as powerful and versatile tools, attributable to their structural and biochemical congruence with the natural extracellular matrix (ECM). This review delineates the contemporary applications of aligned nanofibers in tissue engineering, spotlighting their implementation across musculoskeletal, neural, and cardiovascular tissue domains. The influence of fiber alignment on critical cellular behaviors - cell adhesion, migration, orientation, and differentiation - is reviewed. We also discuss how nanofibers are improved by adding growth factors, peptides, and drugs to help tissues regenerate better. Comprehensive analyses of in vivo trials and clinical studies corroborate the efficacy and safety of these fibers in tissue engineering applications. The review culminates with exploring extant challenges, concurrently charting prospective avenues in aligned nanofiber-centric tissue engineering., Comment: 44 pages, 8 figures

Short-term changes in the resonance frequency of silicon nitride (SiN) nanomechanical resonators can be measured very precisely due to low thermomechanical fluctuations resulting from large mechanical quality factors. These properties enable high-performance detection of quasi-instantaneous stimuli, such as sudden exposure to radiation or adsorption of mass. However, practical use of such sensors will eventually raise questions regarding their less-studied longer-term stability, notably for calibration purposes. We characterize aging of an as-fabricated SiN membrane by continuously tracking changes of its resonance frequency over 135 days in a temperature-controlled high vacuum environment. The aging behavior is consistent with previously reported double-logarithmic and drift-reversal aging trends observed in quartz oscillators. The aging magnitude (300 ppm) is also comparable to typical temperature compensated quartz oscillators (TCXO), after normalization to account for the greater importance of interfaces in our thin (90 nm) resonator, compared to several microns thick TCXOs. Possible causes of aging due to surface adsorption are investigated. We review models on how water adsorption and desorption can cause significant frequency changes, predominantly due to chemisorption stress. Chemical species adsorbed on the resonator surface are also identified by X-ray photoelectron spectroscopy (XPS). These measurements show a significant increase in carbon every time the sample is placed under vacuum, while subsequent exposure to air causes an increase in oxidated carbon. Developing models for the contribution of carbon and oxygen to the membrane stress should therefore be an important future direction. Other contaminants, notably alkaline and halide ions, are detected in smaller quantities and briefly discussed.

There is overwhelming evidence that cognition, perception, and action rely on feedback control. However, if and how neural population dynamics are amenable to different control strategies is poorly understood, in large part because machine learning methods to directly assess controllability in neural population dynamics are lacking. To address this gap, we developed a novel dimensionality reduction method, Feedback Controllability Components Analysis (FCCA), that identifies subspaces of linear dynamical systems that are most feedback controllable based on a new measure of feedback controllability. We further show that PCA identifies subspaces of linear dynamical systems that maximize a measure of feedforward controllability. As such, FCCA and PCA are data-driven methods to identify subspaces of neural population data (approximated as linear dynamical systems) that are most feedback and feedforward controllable respectively, and are thus natural contrasts for hypothesis testing. We developed new theory that proves that non-normality of underlying dynamics determines the divergence between FCCA and PCA solutions, and confirmed this in numerical simulations. Applying FCCA to diverse neural population recordings, we find that feedback controllable dynamics are geometrically distinct from PCA subspaces and are better predictors of animal behavior. Our methods provide a novel approach towards analyzing neural population dynamics from a control theoretic perspective, and indicate that feedback controllable subspaces are important for behavior.

The SAFE tool is an open-source Radio Frequency (RF) propagation model designed for path loss predictions in foliage-dominant environments. It utilizes the ITU-R P.1812-6 model as its backbone, enhances predictions with the physics-based Radiative Energy Transfer (RET) model and makes use of high-resolution terrain and clutter elevation datasets, Comment: Conference

Large language models (LLMs) can exhibit bias in a variety of ways. Such biases can create or exacerbate unfair outcomes for certain groups within a protected attribute, including, but not limited to sex, race, sexual orientation, or age. This paper aims to provide a technical guide for practitioners to assess bias and fairness risks in LLM use cases. The main contribution of this work is a decision framework that allows practitioners to determine which metrics to use for a specific LLM use case. To achieve this, this study categorizes LLM bias and fairness risks, maps those risks to a taxonomy of LLM use cases, and then formally defines various metrics to assess each type of risk. As part of this work, several new bias and fairness metrics are introduced, including innovative counterfactual metrics as well as metrics based on stereotype classifiers. Instead of focusing solely on the model itself, the sensitivity of both prompt-risk and model-risk are taken into account by defining evaluations at the level of an LLM use case, characterized by a model and a population of prompts. Furthermore, because all of the evaluation metrics are calculated solely using the LLM output, the proposed framework is highly practical and easily actionable for practitioners., Comment: Comments: 21 pages, LaTeX; typos corrected, references added

Spin polarization in chiral molecules is a magnetic molecular response associated with electron transport and enantioselective bond polarization that occurs even in the absence of an external magnetic field. An unexpected finding by Santos and co-workers reported enantiospecific NMR responses in solid-state cross-polarization (CP) experiments, suggesting a possible additional contribution to the indirect nuclear spin-spin coupling in chiral molecules induced by bond polarization in the presence of spin-orbit coupling. Herein we provide a theoretical treatment for this phenomenon, presenting an effective spin-Hamiltonian for helical molecules like DNA and density functional theory (DFT) results on amino acids that confirm the dependence of J-couplings on the choice of enantiomer. The connection between nuclear spin dynamics and chirality could offer insights for molecular sensing and quantum information sciences. These results establish NMR as a potential tool for chiral discrimination without external agents., Comment: 102 pages, 16 figures, 40 tables

Autonomous vehicles require highly sophisticated decision-making to determine their motion. This paper describes how such functionality can be achieved with a practical rule engine learned from expert driving decisions. We propose an algorithm to create and maintain a rule-based behaviour planner, using a two-layer rule-based theory. The first layer determines a set of feasible parametrized behaviours, given the perceived state of the environment. From these, a resolution function chooses the most conservative high-level maneuver. The second layer then reconciles the parameters into a single behaviour. To demonstrate the practicality of our approach, we report results of its implementation in a level-3 autonomous vehicle and its field test in an urban environment., Comment: Use https://link.springer.com/chapter/10.1007/978-3-031-21541-4_17 for citations

Atmospheric turbulence is the main barrier to large-scale free-space quantum communication networks. Aberrations distort optical information carriers, thus limiting or preventing the possibility of establishing a secure link between two parties. For this reason, forecasting the turbulence strength within an optical channel is highly desirable, as it allows for knowing the optimal timing to establish a secure link in advance. Here, we train a Recurrent Neural Network, TAROCCO, to predict the turbulence strength within a free-space channel. The training is based on weather and turbulence data collected over 9 months for a 5.4 km intra-city free-space link across the City of Ottawa. The implications of accurate predictions from our network are demonstrated in a simulated high-dimensional Quantum Key Distribution protocol based on orbital angular momentum states of light across different turbulence regimes. TAROCCO will be crucial in validating a free-space channel to optimally route the key exchange for secure communications in real experimental scenarios.