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We first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient (N,N)-isogenies, for any odd N, both on the general Kummer surface and on the Fast model., Comment: 38 pages, 2 figures. To appear in Mathematics of Computation

The Listening in Spatialized Noise Sentences (LiSN-S) is a test to evaluate auditory spatial processing currently only available in the English language. It produces a three-dimensional auditory environment under headphones and uses a simple repetition response protocol to determine speech reception thresholds (SRTs) for sentences presented in competing speech under various conditions. In order to develop the LiSN-S test in Brazilian Portuguese, it was necessary to prepare a speech database recorded by professional voice actresses and to devise presentation software. These sentences were presented to 35 adults (aged between 19 and 40 years) and 24 children (aged between 8 and 10 years), all with normal hearing-verified through tone and speech audiometry and tympanometry-and good performance at school. We used a logistic curve describing word error rate versus presentation level, fitted for each sentence, to select a set of 120 sentences for the test. Furthermore, all selected sentences were adjusted in amplitude for equal intelligibility. The framework of LiSN-S in Brazilian Portuguese is ready for normative data analysis. After its conclusion, we believe it will contribute to diagnosing and rehabilitating Brazilian children with complaints related to hearing difficulties in noisy environments

As intelligent robots like autonomous vehicles become increasingly deployed in the presence of people, the extent to which these systems should leverage model-based game-theoretic planners versus data-driven policies for safe, interaction-aware motion planning remains an open question. Existing dynamic game formulations assume all agents are task-driven and behave optimally. However, in reality, humans tend to deviate from the decisions prescribed by these models, and their behavior is better approximated under a noisy-rational paradigm. In this work, we investigate a principled methodology to blend a data-driven reference policy with an optimization-based game-theoretic policy. We formulate KLGame, an algorithm for solving non-cooperative dynamic game with Kullback-Leibler (KL) regularization with respect to a general, stochastic, and possibly multi-modal reference policy. Our method incorporates, for each decision maker, a tunable parameter that permits modulation between task-driven and data-driven behaviors. We propose an efficient algorithm for computing multi-modal approximate feedback Nash equilibrium strategies of KLGame in real time. Through a series of simulated and real-world autonomous driving scenarios, we demonstrate that KLGame policies can more effectively incorporate guidance from the reference policy and account for noisily-rational human behaviors versus non-regularized baselines. Website with additional information, videos, and code: https://kl-games.github.io/., Comment: 20 pages, 12 figures

We give an alternative derivation of $(N,N)$-isogenies between fast Kummer surfaces which complements existing works based on the theory oftheta functions. We use this framework to produce explicit formulae for the case of $N = 3$, and show that the resulting algorithms are more efficient than all prior $(3, 3)$-isogeny algorithms.

Skin lesions are classified in benign or malignant. Among the malignant, melanoma is a very aggressive cancer and the major cause of deaths. So, early diagnosis of skin cancer is very desired. In the last few years, there is a growing interest in computer aided diagnostic (CAD) using most image and clinical data of the lesion. These sources of information present limitations due to their inability to provide information of the molecular structure of the lesion. NIR spectroscopy may provide an alternative source of information to automated CAD of skin lesions. The most commonly used techniques and classification algorithms used in spectroscopy are Principal Component Analysis (PCA), Partial Least Squares - Discriminant Analysis (PLS-DA), and Support Vector Machines (SVM). Nonetheless, there is a growing interest in applying the modern techniques of machine and deep learning (MDL) to spectroscopy. One of the main limitations to apply MDL to spectroscopy is the lack of public datasets. Since there is no public dataset of NIR spectral data to skin lesions, as far as we know, an effort has been made and a new dataset named NIR-SC-UFES, has been collected, annotated and analyzed generating the gold-standard for classification of NIR spectral data to skin cancer. Next, the machine learning algorithms XGBoost, CatBoost, LightGBM, 1D-convolutional neural network (1D-CNN) were investigated to classify cancer and non-cancer skin lesions. Experimental results indicate the best performance obtained by LightGBM with pre-processing using standard normal variate (SNV), feature extraction providing values of 0.839 for balanced accuracy, 0.851 for recall, 0.852 for precision, and 0.850 for F-score. The obtained results indicate the first steps in CAD of skin lesions aiming the automated triage of patients with skin lesions in vivo using NIR spectral data.

We determine a Simons' type formula for spacelike submanifolds within a broad class of semiRiemannian warped products. This formula extends the Simons' type formulas initially introduced by Nomizu and Smyth in 1969 for constant mean curvature hypersurfaces in space forms. Furthermore, it incorporates the 2013 extension by Fetcu and Rosenberg for submanifolds with parallel mean curvature vector field in product spaces. From a global standpoint, we establish that compact spacelike hypersurfaces with parallel mean curvature and non-negative sectional curvature are isoparametric hypersurfaces. This result constitutes a generalization of the Riemannian case within space forms, as demonstrated by Nomizu and Smyth. From a local standpoint, we extend analogous results previously established by Asperti, Lobos and Mercuri for pseudo-parallel immersions in Riemannian space forms. As consequences, we prove that any semi-parallel spacelike hypersurface with zero mean curvature in the de Sitter spacetime is totally geodesic. In contrast, there is no semi-parallel spacelike hypersurface with zero mean curvature in the Einstein-de Sitter spacetime.

We propose a threshold decision-making framework for controlling the physical dynamics of an agent switching between two spatial tasks. Our framework couples a nonlinear opinion dynamics model that represents the evolution of an agent's preference for a particular task with the physical dynamics of the agent. We prove the bifurcation that governs the behavior of the coupled dynamics. We show by means of the bifurcation behavior how the coupled dynamics are adaptive to the physical constraints of the agent. We also show how the bifurcation can be modulated to allow the agent to switch tasks based on thresholds adaptive to environmental conditions. We illustrate the benefits of the approach through a decentralized multi-robot task allocation application for trash collection.

The ability of executing multiple tasks simultaneously is an important feature of redundant robotic systems. As a matter of fact, complex behaviors can often be obtained as a result of the execution of several tasks. Moreover, in safety-critical applications, tasks designed to ensure the safety of the robot and its surroundings have to be executed along with other nominal tasks. In such cases, it is also important to prioritize the former over the latter. In this paper, we formalize the definition of extended set-based tasks, i.e., tasks which can be executed by rendering subsets of the task space asymptotically stable or forward invariant. We propose a mathematical representation of such tasks that allows for the execution of more complex and time-varying prioritized stacks of tasks using kinematic and dynamic robot models alike. We present and analyze an optimization-based framework which is computationally efficient, accounts for input bounds, and allows for the stable execution of time-varying prioritized stacks of extended set-based tasks. The proposed framework is validated using extensive simulations and experiments with robotic manipulators.

This paper proposes a distributed coverage control strategy for quadcopters equipped with downward-facing cameras that prevents the appearance of unmonitored areas in between the quadcopters' fields of view (FOVs). We derive a necessary and sufficient condition for eliminating any unsurveilled area that may arise in between the FOVs among a trio of quadcopters by utilizing a power diagram, i.e. a weighted Voronoi diagram defined by radii of FOVs. Because this condition can be described as logically combined constraints, we leverage nonsmooth control barrier functions (NCBFs) to prevent the appearance of unmonitored areas among a team's FOV. We then investigate the symmetric properties of the proposed NCBFs to develop a distributed algorithm. The proposed algorithm can support the switching of the NCBFs caused by changes of the quadcopters composing trios. The existence of the control input satisfying NCBF conditions is analyzed by employing the characteristics of the power diagram. The proposed framework is synthesized with a coverage control law that maximizes the monitoring quality while reducing overlaps of FOVs. The proposed method is demonstrated in simulation and experiment., Comment: 19 pages, 20 figures. This paper has been accepted for publication in the IEEE Transactions on Robotics. The DOI and the URL of the published version can be found in the header of the first page

We propose, analyze, and experimentally verify a new proactive approach for robot social navigation driven by the robot's "opinion" for which way and by how much to pass human movers crossing its path. The robot forms an opinion over time according to nonlinear dynamics that depend on the robot's observations of human movers and its level of attention to these social cues. For these dynamics, it is guaranteed that when the robot's attention is greater than a critical value, deadlock in decision making is broken, and the robot rapidly forms a strong opinion, passing each human mover even if the robot has no bias nor evidence for which way to pass. We enable proactive rapid and reliable social navigation by having the robot grow its attention across the critical value when a human mover approaches. With human-robot experiments we demonstrate the flexibility of our approach and validate our analytical results on deadlock-breaking. We also show that a single design parameter can tune the trade-off between efficiency and reliability in human-robot passing. The new approach has the additional advantage that it does not rely on a predictive model of human behavior., Comment: 8 pages, 7 figures