Shared spaces aim to reduce the dominance of motor vehicles by promoting pedestrian and cyclist activity and minimizing segregation between road users. Despite the intended scope to improve the safety of vulnerable road users, only few works in the literature focused on before after safety evaluations, mainly analyzing changes in users trajectories and speeds, traffic volumes, and conflict counts, which, while useful, cannot univocally quantify road safety. Here, we propose a more advanced methodology, based on surrogate measures of safety and Extreme Value Theory, to assess road safety before and after the implementation of a shared space. The aim is to produce a crash risk estimation in different scenarios, obtaining a quantitative and comprehensive indicator, useful to practitioners for evaluating the safety of urban design solutions. A real world case study illustrates the proposed procedure. Video data were collected on two separate days, before and after a shared space implementation, and were semiautomatically processed to extract road users trajectories. Analysis of traffic volumes, trajectories, speeds and yield ratios allowed to understand the spatial behavior of road users in the two scenarios. Traffic conflicts, identified with an innovative surrogate measure of safety called time to avoided collision point, TTAC, were then used to estimate a Lomax distribution, and therefore to model the probabilistic relationship between conflicts and crashes, eventually retrieving a crash risk estimate. Results show that the analyzed shared space was able to significantly reduce the risk of crashes, and these findings are consistent with the observed changes in users speed and spatial behavior. The analyzed case study and its limitations were useful in highlighting the methodology main features and suggesting practical prescriptions for practitioners.
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The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions. Despite the broad use of Koopman operators over the past few years, there exist some misconceptions about the applicability of Koopman operators to dynamical systems with more than one fixed point. In this work, an explanation is provided for the mechanism of lifting for the Koopman operator of nonlinear systems with multiple attractors. Considering the example of the Duffing oscillator, we show that by exploiting the inherent symmetry between the basins of attraction, a linear reconstruction with three degrees of freedom in the Koopman observable space is sufficient to globally linearize the system.
We study various aspects of the first-order transduction quasi-order, which provides a way of measuring the relative complexity of classes of structures based on whether one can encode the other using a formula of first-order (FO) logic. In contrast with the conjectured simplicity of the transduction quasi-order for monadic second-order logic, the FO-transduction quasi-order is very complex; in particular, we prove that the quotient partial order is not a lattice, although it is a bounded distributive join-semilattice, as is the subposet of additive classes. Many standard properties from structural graph theory and model theory naturally appear in this quasi-order. For example, we characterize transductions of paths, cubic graphs, and cubic trees in terms of bandwidth, bounded degree, and treewidth. We establish that the classes of all graphs with pathwidth at most~$k$, for $k\geq 1$, form a strict hierarchy in the FO-transduction quasi-order and leave open whether same is true for treewidth. This leads to considering whether properties admit maximum or minimum classes in this quasi-order. We prove that many properties do not admit a maximum class, and that star forests are the minimum class that is not a transduction of a class with bounded degree, which can be seen as an instance of transduction duality. We close with a notion of dense analogues of sparse classes, and discuss several related conjectures. As a ubiquitous tool in our results, we prove a normal form for FO-transductions that manifests the locality of FO logic. This is among several other technical results about FO-transductions which we anticipate being broadly useful.
White matter bundle segmentation is a cornerstone of modern tractography to study the brain's structural connectivity in domains such as neurological disorders, neurosurgery, and aging. In this study, we present FIESTA (FIbEr Segmentation in Tractography using Autoencoders), a reliable and robust, fully automated, and easily semi-automatically calibrated pipeline based on deep autoencoders that can dissect and fully populate white matter bundles. This pipeline is built upon previous works that demonstrated how autoencoders can be used successfully for streamline filtering, bundle segmentation, and streamline generation in tractography. Our proposed method improves bundle segmentation coverage by recovering hard-to-track bundles with generative sampling through the latent space seeding of the subject bundle and the atlas bundle. A latent space of streamlines is learned using autoencoder-based modeling combined with contrastive learning. Using an atlas of bundles in standard space (MNI), our proposed method segments new tractograms using the autoencoder latent distance between each tractogram streamline and its closest neighbor bundle in the atlas of bundles. Intra-subject bundle reliability is improved by recovering hard-to-track streamlines, using the autoencoder to generate new streamlines that increase the spatial coverage of each bundle while remaining anatomically correct. Results show that our method is more reliable than state-of-the-art automated virtual dissection methods such as RecoBundles, RecoBundlesX, TractSeg, White Matter Analysis and XTRACT. Our framework allows for the transition from one anatomical bundle definition to another with marginal calibration efforts. Overall, these results show that our framework improves the practicality and usability of current state-of-the-art bundle segmentation framework.
We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, we use the Lagrange multiplier approach to derive a coupled forward-backward optimality system, which can then be solved using a time domain decomposition. Due to the forward-backward structure of the optimality system, three variants can be found for the Dirichlet-Neumann and Neumann-Dirichlet algorithms. We analyze their convergence behavior and determine the optimal relaxation parameter for each algorithm. Our analysis reveals that the most natural algorithms are actually only good smoothers, and there are better choices which lead to efficient solvers. We illustrate our analysis with numerical experiments.
Geometric quantiles are location parameters which extend classical univariate quantiles to normed spaces (possibly infinite-dimensional) and which include the geometric median as a special case. The infinite-dimensional setting is highly relevant in the modeling and analysis of functional data, as well as for kernel methods. We begin by providing new results on the existence and uniqueness of geometric quantiles. Estimation is then performed with an approximate M-estimator and we investigate its large-sample properties in infinite dimension. When the population quantile is not uniquely defined, we leverage the theory of variational convergence to obtain asymptotic statements on subsequences in the weak topology. When there is a unique population quantile, we show that the estimator is consistent in the norm topology for a wide range of Banach spaces including every separable uniformly convex space. In separable Hilbert spaces, we establish weak Bahadur-Kiefer representations of the estimator, from which $\sqrt n$-asymptotic normality follows.
In many scientific applications the aim is to infer a function which is smooth in some areas, but rough or even discontinuous in other areas of its domain. Such spatially inhomogeneous functions can be modelled in Besov spaces with suitable integrability parameters. In this work we study adaptive Bayesian inference over Besov spaces, in the white noise model from the point of view of rates of contraction, using $p$-exponential priors, which range between Laplace and Gaussian and possess regularity and scaling hyper-parameters. To achieve adaptation, we employ empirical and hierarchical Bayes approaches for tuning these hyper-parameters. Our results show that, while it is known that Gaussian priors can attain the minimax rate only in Besov spaces of spatially homogeneous functions, Laplace priors attain the minimax or nearly the minimax rate in both Besov spaces of spatially homogeneous functions and Besov spaces permitting spatial inhomogeneities.
MultiPA: a multi-task speech pronunciation assessment system for a closed and open response scenario
The design of automatic speech pronunciation assessment can be categorized into closed and open response scenarios, each with strengths and limitations. A system with the ability to function in both scenarios can cater to diverse learning needs and provide a more precise and holistic assessment of pronunciation skills. In this study, we propose a Multi-task Pronunciation Assessment model called MultiPA. MultiPA provides an alternative to Kaldi-based systems in that it has simpler format requirements and better compatibility with other neural network models. Compared with previous open response systems, MultiPA provides a wider range of evaluations, encompassing assessments at both the sentence and word-level. Our experimental results show that MultiPA achieves comparable performance when working in closed response scenarios and maintains more robust performance when directly used for open responses.
Autonomous vehicles (AVs) need to determine their position and orientation accurately with respect to global coordinate system or local features under different scene geometries, traffic conditions and environmental conditions. \cite{reid2019localization} provides a comprehensive framework for the localization requirements for AVs. However, the framework is too restrictive whereby - (a) only a very small deviation from the lane is tolerated (one every $10^{8}$ hours), (b) all roadway types are considered same without any attention to restriction provided by the environment onto the localization and (c) the temporal nature of the location and orientation is not considered in the requirements. In this research, we present a more practical view of the localization requirement aimed at keeping the AV safe during an operation. We present the following novel contributions - (a) we propose a deviation penalty as a cumulative distribution function of the Weibull distribution which starts from the adjacent lane boundary, (b) we customize the parameters of the deviation penalty according to the current roadway type, particular lane boundary that the ego vehicle is against and roadway curvature and (c) we update the deviation penalty based on the available gap in the adjacent lane. We postulate that this formulation can provide a more robust and achievable view of the localization requirements than previous research while focusing on safety.
We consider a linear implicit-explicit (IMEX) time discretization of the Cahn-Hilliard equation with a source term, endowed with Dirichlet boundary conditions. For every time step small enough, we build an exponential attractor of the discrete-in-time dynamical system associated to the discretization. We prove that, as the time step tends to 0, this attractor converges for the symmmetric Hausdorff distance to an exponential attractor of the continuous-in-time dynamical system associated with the PDE. We also prove that the fractal dimension of the exponential attractor (and consequently, of the global attractor) is bounded by a constant independent of the time step. The results also apply to the classical Cahn-Hilliard equation with Neumann boundary conditions.
Differential geometric approaches are ubiquitous in several fields of mathematics, physics and engineering, and their discretizations enable the development of network-based mathematical and computational frameworks, which are essential for large-scale data science. The Forman-Ricci curvature (FRC) - a statistical measure based on Riemannian geometry and designed for networks - is known for its high capacity for extracting geometric information from complex networks. However, extracting information from dense networks is still challenging due to the combinatorial explosion of high-order network structures. Motivated by this challenge we sought a set-theoretic representation theory for high-order network cells and FRC, as well as their associated concepts and properties, which together provide an alternative and efficient formulation for computing high-order FRC in complex networks. We provide a pseudo-code, a software implementation coined FastForman, as well as a benchmark comparison with alternative implementations. Crucially, our representation theory reveals previous computational bottlenecks and also accelerates the computation of FRC. As a consequence, our findings open new research possibilities in complex systems where higher-order geometric computations are required.
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