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This paper considers the numerical integration of semilinear evolution PDEs using the high order linearly implicit methods developped in a previous paper in the ODE setting. These methods use a collocation Runge--Kutta method as a basis, and additional variables that are updated explicitly and make the implicit part of the collocation Runge--Kutta method only linearly implicit. In this paper, we introduce several notions of stability for the underlying Runge--Kutta methods as well as for the explicit step on the additional variables necessary to fit the context of evolution PDE. We prove a main theorem about the high order of convergence of these linearly implicit methods in this PDE setting, using the stability hypotheses introduced before. We use nonlinear Schr\''odinger equations and heat equations as main examples but our results extend beyond these two classes of evolution PDEs. We illustrate our main result numerically in dimensions 1 and 2, and we compare the efficiency of the linearly implicit methods with other methods from the litterature. We also illustrate numerically the necessity of the stability conditions of our main result.

We characterize the Schr\"odinger bridge problems by a family of Mckean-Vlasov stochastic control problems with no terminal time distribution constraint. In doing so, we use the theory of Hilbert space embeddings of probability measures and then describe the constraint as penalty terms defined by the maximum mean discrepancy in the control problems. A sequence of the probability laws of the state processes resulting from $\epsilon$-optimal controls converges to a unique solution of the Schr\"odinger's problem under mild conditions on given initial and terminal time distributions and an underlying diffusion process. We propose a neural SDE based deep learning algorithm for the Mckean-Vlasov stochastic control problems. Several numerical experiments validate our methods.

The low cost and rapid provisioning capabilities have made the cloud a desirable platform to launch complex scientific applications. However, resource utilization optimization is a significant challenge for cloud service providers, since the earlier focus is provided on optimizing resources for the applications that run on the cloud, with a low emphasis being provided on optimizing resource utilization of the cloud computing internal processes. Code refactoring has been associated with improving the maintenance and understanding of software code. However, analyzing the impact of the refactoring source code of the cloud and studying its impact on cloud resource usage require further analysis. In this paper, we propose a framework called Unified Regression Modelling (URegM) which predicts the impact of code smell refactoring on cloud resource usage. We test our experiments in a real-life cloud environment using a complex scientific application as a workload. Results show that URegM is capable of accurately predicting resource consumption due to code smell refactoring. This will permit cloud service providers with advanced knowledge about the impact of refactoring code smells on resource consumption, thus allowing them to plan their resource provisioning and code refactoring more effectively.

Nonparametric maximum likelihood estimators (MLEs) in inverse problems often have non-normal limit distributions, like Chernoff's distribution. However, if one considers smooth functionals of the model, with corresponding functionals of the MLE, one gets normal limit distributions and faster rates of convergence. We demonstrate this for a model for the incubation time of a disease. The usual approach in the latter models is to use parametric distributions, like Weibull and gamma distributions, which leads to inconsistent estimators. Smoothed bootstrap methods are discussed for constructing confidence intervals. The classical bootstrap, based on the nonparametric MLE itself, has been proved to be inconsistent in this situation.

Existing datasets for autonomous driving (AD) often lack diversity and long-range capabilities, focusing instead on 360{\deg} perception and temporal reasoning. To address this gap, we introduce Zenseact Open Dataset (ZOD), a large-scale and diverse multimodal dataset collected over two years in various European countries, covering an area 9x that of existing datasets. ZOD boasts the highest range and resolution sensors among comparable datasets, coupled with detailed keyframe annotations for 2D and 3D objects (up to 245m), road instance/semantic segmentation, traffic sign recognition, and road classification. We believe that this unique combination will facilitate breakthroughs in long-range perception and multi-task learning. The dataset is composed of Frames, Sequences, and Drives, designed to encompass both data diversity and support for spatio-temporal learning, sensor fusion, localization, and mapping. Frames consist of 100k curated camera images with two seconds of other supporting sensor data, while the 1473 Sequences and 29 Drives include the entire sensor suite for 20 seconds and a few minutes, respectively. ZOD is the only large-scale AD dataset released under a permissive license, allowing for both research and commercial use. More information, and an extensive devkit, can be found at //zod.zenseact.com

Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the real line by the median, they provide a natural approach to defining median-like location estimators for more general types of data (in our case, fuzzy data). We analyze the relationships between depth-based medians, medians based on the support function, and some notions of a median for fuzzy data in the literature. We take advantage of specific depth functions for fuzzy data defined in our former papers: adaptations of Tukey depth, simplicial depth, $L^1$-depth and projection depth.

We observe a large variety of robots in terms of their bodies, sensors, and actuators. Given the commonalities in the skill sets, teaching each skill to each different robot independently is inefficient and not scalable when the large variety in the robotic landscape is considered. If we can learn the correspondences between the sensorimotor spaces of different robots, we can expect a skill that is learned in one robot can be more directly and easily transferred to the other robots. In this paper, we propose a method to learn correspondences between robots that have significant differences in their morphologies: a fixed-based manipulator robot with joint control and a differential drive mobile robot. For this, both robots are first given demonstrations that achieve the same tasks. A common latent representation is formed while learning the corresponding policies. After this initial learning stage, the observation of a new task execution by one robot becomes sufficient to generate a latent space representation pertaining to the other robot to achieve the same task. We verified our system in a set of experiments where the correspondence between two simulated robots is learned (1) when the robots need to follow the same paths to achieve the same task, (2) when the robots need to follow different trajectories to achieve the same task, and (3) when complexities of the required sensorimotor trajectories are different for the robots considered. We also provide a proof-of-the-concept realization of correspondence learning between a real manipulator robot and a simulated mobile robot.

Many attempts have been made at estimating discrete emotions (calmness, anxiety, boredom, surprise, anger) and continuous emotional measures commonly used in psychology, namely `valence' (The pleasantness of the emotion being displayed) and `arousal' (The intensity of the emotion being displayed). Existing methods to estimate arousal and valence rely on learning from data sets, where an expert annotator labels every image frame. Access to an expert annotator is not always possible, and the annotation can also be tedious. Hence it is more practical to obtain self-reported arousal and valence values directly from the human in a real-time Human-Robot collaborative setting. Hence this paper provides an emotion data set (HRI-AVC) obtained while conducting a human-robot interaction (HRI) task. The self-reported pair of labels in this data set is associated with a set of image frames. This paper also proposes a spatial and temporal attention-based network to estimate arousal and valence from this set of image frames. The results show that an attention-based network can estimate valence and arousal on the HRI-AVC data set even when Arousal and Valence values are unavailable per frame.

We formalize the simulation paradigm of cryptography in terms of category theory and show that protocols secure against abstract attacks form a symmetric monoidal category, thus giving an abstract model of composable security definitions in cryptography. Our model is able to incorporate computational security, set-up assumptions and various attack models such as colluding or independently acting subsets of adversaries in a modular, flexible fashion. We conclude by using string diagrams to rederive the security of the one-time pad, correctness of Diffie-Hellman key exchange and no-go results concerning the limits of bipartite and tripartite cryptography, ruling out e.g., composable commitments and broadcasting. On the way, we exhibit two categorical constructions of resource theories that might be of independent interest: one capturing resources shared among multiple parties and one capturing resource conversions that succeed asymptotically.

In recent years, object detection has experienced impressive progress. Despite these improvements, there is still a significant gap in the performance between the detection of small and large objects. We analyze the current state-of-the-art model, Mask-RCNN, on a challenging dataset, MS COCO. We show that the overlap between small ground-truth objects and the predicted anchors is much lower than the expected IoU threshold. We conjecture this is due to two factors; (1) only a few images are containing small objects, and (2) small objects do not appear enough even within each image containing them. We thus propose to oversample those images with small objects and augment each of those images by copy-pasting small objects many times. It allows us to trade off the quality of the detector on large objects with that on small objects. We evaluate different pasting augmentation strategies, and ultimately, we achieve 9.7\% relative improvement on the instance segmentation and 7.1\% on the object detection of small objects, compared to the current state of the art method on MS COCO.