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Quantum computing has recently emerged as a transformative technology. Yet, its promised advantages rely on efficiently translating quantum operations into viable physical realizations. In this work, we use generative machine learning models, specifically denoising diffusion models (DMs), to facilitate this transformation. Leveraging text-conditioning, we steer the model to produce desired quantum operations within gate-based quantum circuits. Notably, DMs allow to sidestep during training the exponential overhead inherent in the classical simulation of quantum dynamics -- a consistent bottleneck in preceding ML techniques. We demonstrate the model's capabilities across two tasks: entanglement generation and unitary compilation. The model excels at generating new circuits and supports typical DM extensions such as masking and editing to, for instance, align the circuit generation to the constraints of the targeted quantum device. Given their flexibility and generalization abilities, we envision DMs as pivotal in quantum circuit synthesis, enhancing both practical applications but also insights into theoretical quantum computation.

Remotely sensed data are dominated by mixed Land Use and Land Cover (LULC) types. Spectral unmixing is a technique to extract information from mixed pixels into their constituent LULC types and corresponding abundance fractions. Traditionally, solving this task has relied on either classical methods that require prior knowledge of endmembers or machine learning methods that avoid explicit endmembers calculation, also known as blind spectral unmixing (BSU). Most BSU studies based on Deep Learning (DL) focus on one time-step hyperspectral or multispectral data. To our knowledge, here we provide the first study on BSU of LULC classes using MODIS multispectral time series, in presence of missing data, with end-to-end DL models. We further boost the performance of a Long-Short Term Memory (LSTM)-based model by incorporating geographic plus topographic (geo-topographic) and climatic ancillary information. Our experiments show that combining spectral-temporal input data together with geo-topographic and climatic information substantially improves the abundance estimation of LULC classes in mixed pixels. To carry out this study, we built a new labeled dataset of the region of Andalusia (Spain) with monthly multispectral time series of pixels for the year 2013 from MODIS at 460m resolution, for two hierarchical levels of LULC classes, named Andalusia MultiSpectral MultiTemporal Unmixing (Andalusia-MSMTU). This dataset provides, at the pixel level, a multispectral time series plus ancillary information annotated with the abundance of each LULC class inside each pixel. The dataset (//zenodo.org/record/7752348##.ZBmkkezMLdo) and code (//github.com/jrodriguezortega/MSMTU) are available to the public.

We determine the minimum possible column multiplicity of even, doubly-, and triply-even codes given their length. This refines a classification result for the possible lengths of $q^r$-divisible codes over $\mathbb{F}_q$. We also give a few computational results for field sizes $q>2$. Non-existence results of divisible codes with restricted column multiplicities for a given length have applications e.g. in Galois geometry and can be used for upper bounds on the maximum cardinality of subspace codes.

High-fidelity computational simulations and physical experiments of hypersonic flows are resource intensive. Training scientific machine learning (SciML) models on limited high-fidelity data offers one approach to rapidly predict behaviors for situations that have not been seen before. However, high-fidelity data is itself in limited quantity to validate all outputs of the SciML model in unexplored input space. As such, an uncertainty-aware SciML model is desired. The SciML model's output uncertainties could then be used to assess the reliability and confidence of the model's predictions. In this study, we extend a DeepONet using three different uncertainty quantification mechanisms: mean-variance estimation, evidential uncertainty, and ensembling. The uncertainty aware DeepONet models are trained and evaluated on the hypersonic flow around a blunt cone object with data generated via computational fluid dynamics over a wide range of Mach numbers and altitudes. We find that ensembling outperforms the other two uncertainty models in terms of minimizing error and calibrating uncertainty in both interpolative and extrapolative regimes.

In prediction settings where data are collected over time, it is often of interest to understand both the importance of variables for predicting the response at each time point and the importance summarized over the time series. Building on recent advances in estimation and inference for variable importance measures, we define summaries of variable importance trajectories. These measures can be estimated and the same approaches for inference can be applied regardless of the choice of the algorithm(s) used to estimate the prediction function. We propose a nonparametric efficient estimation and inference procedure as well as a null hypothesis testing procedure that are valid even when complex machine learning tools are used for prediction. Through simulations, we demonstrate that our proposed procedures have good operating characteristics, and we illustrate their use by investigating the longitudinal importance of risk factors for suicide attempt.

A comprehensive mathematical model of the multiphysics flow of blood and Cerebrospinal Fluid (CSF) in the brain can be expressed as the coupling of a poromechanics system and Stokes' equations: the first describes fluids filtration through the cerebral tissue and the tissue's elastic response, while the latter models the flow of the CSF in the brain ventricles. This model describes the functioning of the brain's waste clearance mechanism, which has been recently discovered to play an essential role in the progress of neurodegenerative diseases. To model the interactions between different scales in the porous medium, we propose a physically consistent coupling between Multi-compartment Poroelasticity (MPE) equations and Stokes' equations. In this work, we introduce a numerical scheme for the discretization of such coupled MPE-Stokes system, employing a high-order discontinuous Galerkin method on polytopal grids to efficiently account for the geometric complexity of the domain. We analyze the stability and convergence of the space semidiscretized formulation, we prove a-priori error estimates, and we present a temporal discretization based on a combination of Newmark's $\beta$-method for the elastic wave equation and the $\theta$-method for the other equations of the model. Numerical simulations carried out on test cases with manufactured solutions validate the theoretical error estimates. We also present numerical results on a two-dimensional slice of a patient-specific brain geometry reconstructed from diagnostic images, to test in practice the advantages of the proposed approach.

In this work, we present new proofs of convergence for Plug-and-Play (PnP) algorithms. PnP methods are efficient iterative algorithms for solving image inverse problems where regularization is performed by plugging a pre-trained denoiser in a proximal algorithm, such as Proximal Gradient Descent (PGD) or Douglas-Rachford Splitting (DRS). Recent research has explored convergence by incorporating a denoiser that writes exactly as a proximal operator. However, the corresponding PnP algorithm has then to be run with stepsize equal to $1$. The stepsize condition for nonconvex convergence of the proximal algorithm in use then translates to restrictive conditions on the regularization parameter of the inverse problem. This can severely degrade the restoration capacity of the algorithm. In this paper, we present two remedies for this limitation. First, we provide a novel convergence proof for PnP-DRS that does not impose any restrictions on the regularization parameter. Second, we examine a relaxed version of the PGD algorithm that converges across a broader range of regularization parameters. Our experimental study, conducted on deblurring and super-resolution experiments, demonstrate that both of these solutions enhance the accuracy of image restoration.

This paper presents a Bayesian optimization framework for the automatic tuning of shared controllers which are defined as a Model Predictive Control (MPC) problem. The proposed framework includes the design of performance metrics as well as the representation of user inputs for simulation-based optimization. The framework is applied to the optimization of a shared controller for an Image Guided Therapy robot. VR-based user experiments confirm the increase in performance of the automatically tuned MPC shared controller with respect to a hand-tuned baseline version as well as its generalization ability.

Data is a cornerstone for fine-tuning large language models, yet acquiring suitable data remains challenging. Challenges encompassed data scarcity, linguistic diversity, and domain-specific content. This paper presents lessons learned while crawling and refining data tailored for fine-tuning Vietnamese language models. Crafting such a dataset, while accounting for linguistic intricacies and striking a balance between inclusivity and accuracy, demands meticulous planning. Our paper presents a multidimensional strategy including leveraging existing datasets in the English language and developing customized data-crawling scripts with the assistance of generative AI tools. A fine-tuned LLM model for the Vietnamese language, which was produced using resultant datasets, demonstrated good performance while generating Vietnamese news articles from prompts. The study offers practical solutions and guidance for future fine-tuning models in languages like Vietnamese.

This paper presents the workspace optimization of one-translational two-rotational (1T2R) parallel manipulators using a dimensionally homogeneous constraint-embedded Jacobian. The mixed degrees of freedom of 1T2R parallel manipulators, which cause dimensional inconsistency, make it difficult to optimize their architectural parameters. To solve this problem, a point-based approach with a shifting property, selection matrix, and constraint-embedded inverse Jacobian is proposed. A simplified formulation is provided, eliminating the complex partial differentiation required in previous approaches. The dimensional homogeneity of the proposed method was analytically proven, and its validity was confirmed by comparing it with the conventional point-based method using a 3-PRS manipulator. Furthermore, the approach was applied to an asymmetric 2-RRS/RRRU manipulator with no parasitic motion. This mechanism has a T-shape combination of limbs with different kinematic parameters, making it challenging to derive a dimensionally homogeneous Jacobian using the conventional method. Finally, optimization was performed, and the results show that the proposed method is more efficient than the conventional approach. The efficiency and simplicity of the proposed method were verified using two distinct parallel manipulators.