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Multiple sclerosis (MS) is the leading cause of severe non-traumatic disability in young adults and its incidence is increasing worldwide. The variability of gait impairment in MS necessitates the development of a non-invasive, sensitive, and cost-effective tool for quantitative gait evaluation. The eGait movement sensor, designed to characterize human gait through unit quaternion time series (QTS) representing hip rotations, is a promising approach. However, the small sample sizes typical of clinical studies pose challenges for the stability of gait data analysis tools. To address these challenges, this article presents two key scientific contributions. First, a comprehensive framework is proposed for transforming QTS data into a form that preserves the essential geometric properties of gait while enabling the use of any tabular synthetic data generation method. Second, a synthetic data generation method is introduced, based on nearest neighbors weighting, which produces high-fidelity synthetic QTS data suitable for small datasets and private data environments. The effectiveness of the proposed method, is demonstrated through its application to MS gait data, showing very good fidelity and respect of the initial geometry of the data. Thanks to this work, we are able to produce synthetic data sets and work on the stability of clustering methods.

This research presents FDASynthesis, a novel algorithm designed to generate synthetic GPS trajectory data while preserving privacy. After pre-processing the input GPS data, human mobility traces are modeled as multidimensional curves using Functional Data Analysis (FDA). Then, the synthesis process identifies the K-nearest trajectories and averages their Square-Root Velocity Functions (SRVFs) to generate synthetic data. This results in synthetic trajectories that maintain the utility of the original data while ensuring privacy. Although applied for human mobility research, FDASynthesis is highly adaptable to different types of functional data, offering a scalable solution in various application domains., Comment: Updated version, correction of the notation

In this article, we derive fully guaranteed error bounds for the energy of convex nonlinear mean-field models. These results apply in particular to Kohn-Sham equations with convex density functionals, which includes the reduced Hartree-Fock (rHF) model, as well as the Kohn-Sham model with exact exchange-density functional (which is unfortunately not explicit and therefore not usable in practice). We then decompose the obtained bounds into two parts, one depending on the chosen discretization and one depending on the number of iterations performed in the self-consistent algorithm used to solve the nonlinear eigenvalue problem, paving the way for adaptive refinement strategies. The accuracy of the bounds is demonstrated on a series of test cases, including a Silicon crystal and an Hydrogen Fluoride molecule simulated with the rHF model and discretized with planewaves. We also show that, although not anymore guaranteed, the error bounds remain very accurate for a Silicon crystal simulated with the Kohn-Sham model using nonconvex exchangecorrelation functionals of practical interest.

We study eigenvalue problems and their approximation obtained by subspace projection, as in the reduced basis method. We provide bounds on the error between the exact eigenmodes and the approximated ones. Self-adjoint operators and degenerate cases are treated. We apply the bounds to the setting where the reduced space contains the vectors extracted from perturbation theory.

Electron-initiated chemistry with chemically relevant electron energies (10-200 eV) is at the heart of several high-energy processes and phenomena. To probe these dissociation and fragmentation reactions with femtosecond resolution requires the use of femtosecond lasers to induce ionization of the polyatomic molecules via electron rescattering. Here, we combine non-commensurate fields with intensity-difference spectra using methanol as a model system. Experimentally, we find orders of magnitude enhancement in several product ions of methanol when comparing coherent vs incoherent combinations of non-commensurate fields. This approach not only mitigates multi-photon ionization and multi-cycle effects during ionization but also enhances tunnel ionization and electron rescattering energy., Comment: 21 pages 8 figures

In this study, we analyze various Iterative Stockholder Analysis (ISA) methods for molecular density partitioning, focusing on the numerical performance of the recently proposed Linear approximation of Iterative Stockholder Analysis model (LISA) [J. Chem. Phys. 156, 164107 (2022)]. We first provide a systematic derivation of various iterative solvers to find the unique LISA solution. In a subsequent systematic numerical study, we evaluate their performance on 48 organic and inorganic, neutral and charged molecules and also compare LISA to two other well-known ISA variants: the Gaussian Iterative Stockholder Analysis (GISA) and Minimum Basis Iterative Stockholder analysis (MBIS). The study reveals that LISA-family methods can offer a numerically more efficient approach with better accuracy compared to the two comparative methods. Moreover, the well-known issue with the MBIS method, where atomic charges obtained for negatively charged molecules are anomalously negative, is not observed in LISA-family methods. Despite the fact that LISA occasionally exhibits elevated entropy as a consequence of the absence of more diffuse basis functions, this issue can be readily mitigated by incorporating additional or integrating supplementary basis functions within the LISA framework. This research provides the foundation for future studies on the efficiency and chemical accuracy of molecular density partitioning schemes.

Recent advances in generative AI have led to the development of techniques to generate visually realistic synthetic video. While a number of techniques have been developed to detect AI-generated synthetic images, in this paper we show that synthetic image detectors are unable to detect synthetic videos. We demonstrate that this is because synthetic video generators introduce substantially different traces than those left by image generators. Despite this, we show that synthetic video traces can be learned, and used to perform reliable synthetic video detection or generator source attribution even after H.264 re-compression. Furthermore, we demonstrate that while detecting videos from new generators through zero-shot transferability is challenging, accurate detection of videos from a new generator can be achieved through few-shot learning., Comment: To be published in CVPRW24

As generative AI progresses rapidly, new synthetic image generators continue to emerge at a swift pace. Traditional detection methods face two main challenges in adapting to these generators: the forensic traces of synthetic images from new techniques can vastly differ from those learned during training, and access to data for these new generators is often limited. To address these issues, we introduce the Ensemble of Expert Embedders (E3), a novel continual learning framework for updating synthetic image detectors. E3 enables the accurate detection of images from newly emerged generators using minimal training data. Our approach does this by first employing transfer learning to develop a suite of expert embedders, each specializing in the forensic traces of a specific generator. Then, all embeddings are jointly analyzed by an Expert Knowledge Fusion Network to produce accurate and reliable detection decisions. Our experiments demonstrate that E3 outperforms existing continual learning methods, including those developed specifically for synthetic image detection., Comment: 11 pages, 4 figures, To be published in CVPRWMF24

This paper deals with the numerical simulation of the Gross-Pitaevskii (GP) equation, for which a well-known feature is the appearance of quantized vortices with core size of the order of a small parameter $\varepsilon$. Without a magnetic field and with suitable initial conditions, these vortices interact, in the singular limit $\varepsilon\to0$, through an explicit Hamiltonian dynamics. Using this analytical framework, we develop and analyze a numerical strategy based on the reduced-order Hamiltonian system to efficiently simulate the infinite-dimensional GP equation for small, but finite, $\varepsilon$. This method allows us to avoid numerical stability issues in solving the GP equation, where small values of $\varepsilon$ typically require very fine meshes and time steps. We also provide a mathematical justification of our method in terms of rigorous error estimates of the error in the supercurrent, together with numerical illustrations.

In this paper we derive several (and in many cases sharp) estimates for the $\mathrm{L}^2$-trace norm of harmonic functions along circular arcs. More precisely, we obtain geometry-dependent estimates on the norm, spectral radius, and numerical range of the Dirchlet-to-Dirichlet (DtD) operator sending data on the boundary of the disk to the restriction of its harmonic extension along circular arcs inside the disk. The estimates we derive here have applications in the convergence analysis of the Schwarz domain decomposition method for overlapping disks in two dimensions. In particular, they allow us to establish a rigorous convergence proof for the discrete parallel Schwarz method applied to the Conductor-like Screening Model (COSMO) from theoretical chemistry in the two-disk case, and to derive error estimates with respect to the discretization parameter, the number of Schwarz iterations, and the geometry of the domain. Our analysis addresses challenges beyond classical domain decomposition theory, especially the weak enforcement of boundary conditions.

Microaggregation is a method to coarsen a dataset, by optimally clustering data points in groups of at least $k$ points, thereby providing a $k$-anonymity type disclosure guarantee for each point in the dataset. Previous algorithms for univariate microaggregation had a $O(k n)$ time complexity. By rephrasing microaggregation as an instance of the concave least weight subsequence problem, in this work we provide improved algorithms that provide an optimal univariate microaggregation on sorted data in $O(n)$ time and space. We further show that our algorithms work not only for sum of squares cost functions, as typically considered, but seamlessly extend to many other cost functions used for univariate microaggregation tasks. In experiments we show that the presented algorithms lead to real world performance improvements.

Accelerating iterative eigenvalue algorithms is often achieved by employing a spectral shifting strategy. Unfortunately, improved shifting typically leads to a smaller eigenvalue for the resulting shifted operator, which in turn results in a high condition number of the underlying solution matrix, posing a major challenge for iterative linear solvers. This paper introduces a two-level domain decomposition preconditioner that addresses this issue for the linear Schr\"odinger eigenvalue problem, even in the presence of a vanishing eigenvalue gap in non-uniform, expanding domains. Since the quasi-optimal shift, which is already available as the solution to a spectral cell problem, is required for the eigenvalue solver, it is logical to also use its associated eigenfunction as a generator to construct a coarse space. We analyze the resulting two-level additive Schwarz preconditioner and obtain a condition number bound that is independent of the domain's anisotropy, despite the need for only one basis function per subdomain for the coarse solver. Several numerical examples are presented to illustrate its flexibility and efficiency., Comment: 26 pages, 7 figures, 2 tables

Traditional adversarial attacks concentrate on manipulating clean examples in the pixel space by adding adversarial perturbations. By contrast, semantic adversarial attacks focus on changing semantic attributes of clean examples, such as color, context, and features, which are more feasible in the real world. In this paper, we propose a framework to quickly generate a semantic adversarial attack by leveraging recent diffusion models since semantic information is included in the latent space of well-trained diffusion models. Then there are two variants of this framework: 1) the Semantic Transformation (ST) approach fine-tunes the latent space of the generated image and/or the diffusion model itself; 2) the Latent Masking (LM) approach masks the latent space with another target image and local backpropagation-based interpretation methods. Additionally, the ST approach can be applied in either white-box or black-box settings. Extensive experiments are conducted on CelebA-HQ and AFHQ datasets, and our framework demonstrates great fidelity, generalizability, and transferability compared to other baselines. Our approaches achieve approximately 100% attack success rate in multiple settings with the best FID as 36.61. Code is available at https://github.com/steven202/semantic_adv_via_dm., Comment: To appear in BMVC 2023

In this paper, we develop a domain decomposition method for the nonlinear Poisson-Boltzmann equation based on a solvent-excluded surface widely used in computational chemistry. The model relies on a nonlinear equation defined in $\mathbb{R}^3$ with a space-dependent dielectric permittivity and an ion-exclusion function that accounts for steric effects. Potential theory arguments transform the nonlinear equation into two coupled equations defined in a bounded domain. Then, the Schwarz decomposition method is used to formulate local problems by decomposing the cavity into overlapping balls and only solving a set of coupled sub-equations in each ball. The main novelty of the proposed method is the introduction of a hybrid linear-nonlinear solver used to solve the equation. A series of numerical experiments are presented to test the method and show the importance of the nonlinear model.

AI-generated images have become increasingly realistic and have garnered significant public attention. While synthetic images are intriguing due to their realism, they also pose an important misinformation threat. To address this new threat, researchers have developed multiple algorithms to detect synthetic images and identify their source generators. However, most existing source attribution techniques are designed to operate in a closed-set scenario, i.e. they can only be used to discriminate between known image generators. By contrast, new image-generation techniques are rapidly emerging. To contend with this, there is a great need for open-set source attribution techniques that can identify when synthetic images have originated from new, unseen generators. To address this problem, we propose a new metric learning-based approach. Our technique works by learning transferrable embeddings capable of discriminating between generators, even when they are not seen during training. An image is first assigned to a candidate generator, then is accepted or rejected based on its distance in the embedding space from known generators' learned reference points. Importantly, we identify that initializing our source attribution embedding network by pretraining it on image camera identification can improve our embeddings' transferability. Through a series of experiments, we demonstrate our approach's ability to attribute the source of synthetic images in open-set scenarios.

This article proposes a so-called Quasi Time-Reversible (QTR G-Ext) scheme based on Grassmann extrapolation of density matrices for an accurate calculation of initial guesses in Born-Oppenheimer Molecular Dynamics simulations. The method shows excellent results on four large molecular systems, ranging from 21 to 94 atoms simulated with Kohn-Sham density functional theory surrounded with a classical environment with 6k to 16k atoms. Namely, it clearly reduces the number of self-consistent field iterations, while keeping a similar energy drift as in the extended Lagrangian Born-Oppenheimer method.

In this article, we extend the study of embedded corrector problems, that we have previously introduced in the context of the homogenization of scalar diffusive equations, to the context of homogenized elastic properties of materials. This extension is not trivial and requires mathematical arguments specific to the elasticity case. Starting from a linear elasticity model with highly-oscillatory coefficients, we introduce several effective approximations of the homogenized tensor. These approximations are based on the solution to an embedded corrector problem, where a finite-size domain made of the linear elastic heterogeneous material is embedded in a linear elastic homogeneous infinite medium, the constant elasticity tensor of which has to be appropriately determined. The approximations we provide are proven to converge to the homogenized elasticity tensor when the size of the embedded domain tends to infinity. Some particular attention is devoted to the case of isotropic materials.