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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.

Across many domains, large swaths of digital assets are being stored across distributed data repositories, e.g., the DANDI Archive [8]. The distribution and diversity of these repositories impede researchers from formally defining terminology within experiments, integrating information across datasets, and easily querying, reusing, and analyzing data that follow the FAIR principles [15]. As such, it has become increasingly important to have a standardized method to attach contextual metadata to datasets. Neuroscience is an exemplary use case of this issue due to the complex multimodal nature of experiments. Here, we present the HDMF External Resources Data (HERD) standard and related tools, enabling researchers to annotate new and existing datasets by mapping external references to the data without requiring modification of the original dataset. We integrated HERD closely with Neurodata Without Borders (NWB) [2], a widely used data standard for sharing and storing neurophysiology data. By integrating with NWB, our tools provide neuroscientists with the capability to more easily create and manage neurophysiology data in compliance with controlled sets of terms, enhancing rigor and accuracy of data and facilitating data reuse.

Non-reversible parallel tempering (NRPT) is an effective algorithm for sampling from target distributions with complex geometry, such as those arising from posterior distributions of weakly identifiable and high-dimensional Bayesian models. In this work we establish the uniform (geometric) ergodicity of NRPT under a model of efficient local exploration. The uniform ergodicity log rates are inversely proportional to an easily-estimable divergence, the global communication barrier (GCB), which was recently introduced in the literature. We obtain analogous ergodicity results for classical reversible parallel tempering, providing new evidence that NRPT dominates its reversible counterpart. Our results are based on an analysis of the hitting time of a continuous-time persistent random walk, which is also of independent interest. The rates that we obtain reflect real experiments well for distributions where global exploration is not possible without parallel tempering.

Strongly-driven nonlinear optical processes such as spontaneous parametric down-conversion and spontaneous four-wave mixing can produce multiphoton nonclassical beams of light which have applications in quantum information processing and sensing. In contrast to the low-gain regime, new physical effects arise in a high-gain regime due to the interactions between the nonclassical light and the strong pump driving the nonlinear process. Here, we describe and experimentally observe a gain-induced group delay between the multiphoton pulses generated in a high-gain type-II spontaneous parametric down-conversion source. Since the group delay introduces distinguishability between the generated photons, it will be important to compensate for it when designing quantum interference devices in which strong optical nonlinearities are required., Comment: 16 pages, 8 figures (including supplemental material)

In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr\'echet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means. Such means are leveraged in numerous machine-learning tasks. Relying on advanced statistical tools, we introduce a random matrix theory-based method that estimates Fr\'echet means, which is particularly beneficial when dealing with low sample support and a high number of matrices to average. Our experimental evaluation, involving both synthetic and real-world EEG and hyperspectral datasets, shows that we largely outperform state-of-the-art methods.

We propose a quantum information processing platform that utilizes the ultrafast time-bin encoding of photons. This approach offers a pathway to scalability by leveraging the inherent phase stability of collinear temporal interferometric networks at the femtosecond-to-picosecond timescale. The proposed architecture encodes information in ultrafast temporal bins processed using optically induced nonlinearities and birefringent materials while keeping photons in a single spatial mode. We demonstrate the potential for scalable photonic quantum information processing through two independent experiments that showcase the platform's programmability and scalability, respectively. The scheme's programmability is demonstrated in the first experiment, where we successfully program 362 different unitary transformations in up to 8 dimensions in a temporal circuit. In the second experiment, we show the scalability of ultrafast time-bin encoding by building a passive optical network, with increasing circuit depth, of up to 36 optical modes. In each experiment, fidelities exceed 97\%, while the interferometric phase remains passively stable for several days., Comment: 7 pages, 3 figures

This paper deals with matrix-variate distributions, from Wishart to Inverse Elliptical Wishart distributions over the set of symmetric definite positive matrices. Similar to the multivariate scenario, (Inverse) Elliptical Wishart distributions form a vast and general family of distributions, encompassing, for instance, Wishart or $t$-Wishart ones. The first objective of this study is to present a unified overview of Wishart, Inverse Wishart, Elliptical Wishart, and Inverse Elliptical Wishart distributions through their fundamental properties. This involves leveraging the stochastic representation of these distributions to establish key statistical properties of the Normalized Wishart distribution. Subsequently, this enables the computation of expectations, variances, and Kronecker moments for Elliptical Wishart and Inverse Elliptical Wishart distributions. As an illustrative application, the practical utility of these generalized Elliptical Wishart distributions is demonstrated using a real electroencephalographic dataset. This showcases their effectiveness in accurately modeling heterogeneous data.

Structural colors can be induced on metals not only to fabricate logos or decorative motives but also to embed anti-counterfeit features for product protection. In this study, stainless steel (EN 1.4301) plates are colorized by growing a thin oxide layer using direct laser writing (DLW) and hidden anti-counterfeit measures are included on their surfaces by direct laser interference patterning (DLIP) processing. The periodic microstructures resulting from the DLIP treatment have a spatial period of 1 um and act as relief diffraction gratings, featuring a characteristic diffraction pattern. These microstructures are not visible to the human eye but are easily detectable upon shining a coherent beam on the surface. Furthermore, the reflectance over the visible spectrum of the colorized surfaces with and without the DLIP microtexture is measured, giving low differences in the color perception following the so-called "CIE L*a*b*" color space. Finally, a demonstrator is fabricated, in which colorized fields with and without the security features are shown.

The Artificial Intelligence Ontology (AIO) is a systematization of artificial intelligence (AI) concepts, methodologies, and their interrelations. Developed via manual curation, with the additional assistance of large language models (LLMs), AIO aims to address the rapidly evolving landscape of AI by providing a comprehensive framework that encompasses both technical and ethical aspects of AI technologies. The primary audience for AIO includes AI researchers, developers, and educators seeking standardized terminology and concepts within the AI domain. The ontology is structured around six top-level branches: Networks, Layers, Functions, LLMs, Preprocessing, and Bias, each designed to support the modular composition of AI methods and facilitate a deeper understanding of deep learning architectures and ethical considerations in AI. AIO's development utilized the Ontology Development Kit (ODK) for its creation and maintenance, with its content being dynamically updated through AI-driven curation support. This approach not only ensures the ontology's relevance amidst the fast-paced advancements in AI but also significantly enhances its utility for researchers, developers, and educators by simplifying the integration of new AI concepts and methodologies. The ontology's utility is demonstrated through the annotation of AI methods data in a catalog of AI research publications and the integration into the BioPortal ontology resource, highlighting its potential for cross-disciplinary research. The AIO ontology is open source and is available on GitHub (https://github.com/berkeleybop/artificial-intelligence-ontology) and BioPortal (https://bioportal.bioontology.org/ontologies/AIO).

The quantum walk (QW) has proven to be a valuable testbed for fundamental inquiries in quantum technology applications such as quantum simulation and quantum search algorithms. Many benefits have been found by exploring implementations of QWs in various physical systems, including photonic platforms. Here, we propose a novel platform to perform quantum walks using an ultrafast time-bin encoding (UTBE) scheme. This platform supports the scalability of quantum walks to a large number of steps while retaining a significant degree of programmability. More importantly, ultrafast time bins are encoded at the picosecond time scale, far away from mechanical fluctuations. This enables the scalability of our platform to many modes while preserving excellent interferometric phase stability over extremely long periods of time without requiring active phase stabilization. Our 18-step QW is shown to preserve interferometric phase stability over a period of 50 hours, with an overall walk fidelity maintained above $95\%$, Comment: 13 pages, 8 figures

The human brain has immense learning capabilities at extreme energy efficiencies and scale that no artificial system has been able to match. For decades, reverse engineering the brain has been one of the top priorities of science and technology research. Despite numerous efforts, conventional electronics-based methods have failed to match the scalability, energy efficiency, and self-supervised learning capabilities of the human brain. On the other hand, very recent progress in the development of new generations of photonic and electronic memristive materials, device technologies, and 3D electronic-photonic integrated circuits (3D EPIC ) promise to realize new brain-derived neuromorphic systems with comparable connectivity, density, energy-efficiency, and scalability. When combined with bio-realistic learning algorithms and architectures, it may be possible to realize an 'artificial brain' prototype with general self-learning capabilities. This paper argues the possibility of reverse-engineering the brain through architecting a prototype of a brain-derived neuromorphic computing system consisting of artificial electronic, ionic, photonic materials, devices, and circuits with dynamicity resembling the bio-plausible molecular, neuro/synaptic, neuro-circuit, and multi-structural hierarchical macro-circuits of the brain based on well-tested computational models. We further argue the importance of bio-plausible local learning algorithms applicable to the neuromorphic computing system that capture the flexible and adaptive unsupervised and self-supervised learning mechanisms central to human intelligence. Most importantly, we emphasize that the unique capabilities in brain-derived neuromorphic computing prototype systems will enable us to understand links between specific neuronal and network-level properties with system-level functioning and behavior., Comment: 15 pages, 12 figures

In the ever-evolving digital audio landscape, Spotify, well-known for its music and talk content, has recently introduced audiobooks to its vast user base. While promising, this move presents significant challenges for personalized recommendations. Unlike music and podcasts, audiobooks, initially available for a fee, cannot be easily skimmed before purchase, posing higher stakes for the relevance of recommendations. Furthermore, introducing a new content type into an existing platform confronts extreme data sparsity, as most users are unfamiliar with this new content type. Lastly, recommending content to millions of users requires the model to react fast and be scalable. To address these challenges, we leverage podcast and music user preferences and introduce 2T-HGNN, a scalable recommendation system comprising Heterogeneous Graph Neural Networks (HGNNs) and a Two Tower (2T) model. This novel approach uncovers nuanced item relationships while ensuring low latency and complexity. We decouple users from the HGNN graph and propose an innovative multi-link neighbor sampler. These choices, together with the 2T component, significantly reduce the complexity of the HGNN model. Empirical evaluations involving millions of users show significant improvement in the quality of personalized recommendations, resulting in a +46% increase in new audiobooks start rate and a +23% boost in streaming rates. Intriguingly, our model's impact extends beyond audiobooks, benefiting established products like podcasts., Comment: To appear in The Web Conference 2024 proceedings

This paper is intended to appear as a chapter for the Handbook of Markov Chain Monte Carlo. The goal of this chapter is to unify various problems at the intersection of Markov chain Monte Carlo (MCMC) and machine learning$\unicode{x2014}$which includes black-box variational inference, adaptive MCMC, normalizing flow construction and transport-assisted MCMC, surrogate-likelihood MCMC, coreset construction for MCMC with big data, Markov chain gradient descent, Markovian score climbing, and more$\unicode{x2014}$within one common framework. By doing so, the theory and methods developed for each may be translated and generalized.

In recent years, neural networks have been used to solve phase retrieval problems in imaging with superior accuracy and speed than traditional techniques, especially in the presence of noise. However, in the context of interferometric imaging, phase noise has been largely unaddressed by existing neural network architectures. Such noise arises naturally in an interferometer due to mechanical instabilities or atmospheric turbulence, limiting measurement acquisition times and posing a challenge in scenarios with limited light intensity, such as remote sensing. Here, we introduce a 3D-2D Phase Retrieval U-Net (PRUNe) that takes noisy and randomly phase-shifted interferograms as inputs, and outputs a single 2D phase image. A 3D downsampling convolutional encoder captures correlations within and between frames to produce a 2D latent space, which is upsampled by a 2D decoder into a phase image. We test our model against a state-of-the-art singular value decomposition algorithm and find PRUNe reconstructions consistently show more accurate and smooth reconstructions, with a x2.5 - 4 lower mean squared error at multiple signal-to-noise ratios for interferograms with low (< 1 photon/pixel) and high (~100 photons/pixel) signal intensity. Our model presents a faster and more accurate approach to perform phase retrieval in extremely low light intensity interferometry in presence of phase noise, and will find application in other multi-frame noisy imaging techniques.

Selective control of individual spin qubits is needed for scalable quantum computing based on spin states. Achieving high-fidelity in both single and two-qubit gates, essential components of universal quantum computers, necessitates highly localized control fields. These fields must be capable of addressing specific spin qubits while minimizing gate errors and cross-talk in adjacent qubits. Overcoming the challenge of generating a localized radio-frequency magnetic field, in the absence of elementary magnetic monopoles, we introduce a technique that combines divergent and convergent nanoscale magnetic skyrmions. This approach produces a precise control field that manipulates spin qubits with high fidelity. We propose the use of 2D skyrmions, which are 2D analogues of 3D hedgehog structures. The latter are emergent magnetic monopoles, but difficult to fabricate. The 2D skyrmions, on the other hand, can be fabricated using standard semiconductor foundry processes. Our comparative analysis of the density matrix evolution and gate fidelities in scenarios involving proximal skyrmions and nanomagnets indicates potential gate fidelities surpassing 99.95% for {\pi}/2-gates and 99.90% for {\pi}-gates. Notably, the skyrmion configuration generates a significantly lower field on neighboring spin qubits, i.e. 15 times smaller field on a neighboring qubit compared to nanomagnets that produces the same field at the controlled qubit, making it a more suitable candidate for scalable quantum control architectures by reducing disturbances in adjacent qubits.

The development of robust signal unmixing algorithms is essential for leveraging multimodal datasets acquired through a wide array of scientific imaging technologies, including hyperspectral or time-resolved acquisitions. In experimental physics, enhancing the spatio-temporal resolution or expanding the number of detection channels often leads to diminished sampling rate and signal-to-noise ratio, significantly affecting the efficacy of signal unmixing algorithms. We propose applying band-pass filters to the latent space of a multi-dimensional convolutional neural network to disentangle overlapping signal components, enabling the isolation and quantification of their individual contributions. Using multi-dimensional convolution kernels to process all dimensions simultaneously enhances the network's ability to extract information from adjacent pixels, time- or spectral-bins. This approach enables more effective separation of components in cases where individual pixels do not provide clear, well-resolved information. We showcase the method's practical use in experimental physics through two test cases that highlight the versatility of our approach: fluorescence lifetime microscopy and mode decomposition in optical fibers. The latent unmixing method extracts valuable information from complex signals that cannot be resolved by standard methods. Application of latent unmixing to real FLIM experiments will increase the number of distinguishable fluorescent markers. It will also open new possibilities in optics and photonics for multichannel separations at increased sampling rate., Comment: 16 pages, 8 figures (main paper) + 18 pages, 9 figures (supplementary material)

We develop the information geometry of scaled Gaussian distributions for which the covariance matrix exhibits a Kronecker product structure. This model and its geometry are then used to propose an online change detection (CD) algorithm for multivariate image times series (MITS). The proposed approach relies mainly on the online estimation of the structured covariance matrix under the null hypothesis, which is performed through a recursive (natural) Riemannian gradient descent. This approach exhibits a practical interest compared to the corresponding offline version, as its computational cost remains constant for each new image added in the time series. Simulations show that the proposed recursive estimators reach the Intrinsic Cram\'er-Rao bound. The interest of the proposed online CD approach is demonstrated on both simulated and real data.

This paper presents a new performance bound for estimation problems where the parameter to estimate lies in a Riemannian manifold (a smooth manifold endowed with a Riemannian metric) and follows a given prior distribution. In this setup, the chosen Riemannian metric induces a geometry for the parameter manifold, as well as an intrinsic notion of the estimation error measure. Performance bound for such error measure were previously obtained in the non-Bayesian case (when the unknown parameter is assumed to deterministic), and referred to as \textit{intrinsic} Cram\'er-Rao bound. The presented result then appears either as: \textit{a}) an extension of the intrinsic Cram\'er-Rao bound to the Bayesian estimation framework; \textit{b}) a generalization of the Van-Trees inequality (Bayesian Cram\'er-Rao bound) that accounts for the aforementioned geometric structures. In a second part, we leverage this formalism to study the problem of covariance matrix estimation when the data follow a Gaussian distribution, and whose covariance matrix is drawn from an inverse Wishart distribution. Performance bounds for this problem are obtained for both the mean squared error (Euclidean metric) and the natural Riemannian distance for Hermitian positive definite matrices (affine invariant metric). Numerical simulation illustrate that assessing the error with the affine invariant metric is revealing of interesting properties of the maximum a posteriori and minimum mean square error estimator, which are not observed when using the Euclidean metric.