The paper contains a geometrization of the autonomous multi-time Lagrangian function of electrodynamics. We point out that this multi-time Lagrangian function comes from electrodynamics and the theory of bosonic strings.
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48 results for “autonomous Lagrangians”
New curvature-dimension condition for Lagrangians on manifolds.
problem Establishing a curvature-dimension condition for autonomous Lagrangians.
method Generalizing Klartag's needle decomposition technique to Lagrangian setting.
result Equivalence of curvature-dimension condition to displacement convexity of entropy.
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian. This problem in the general version remains unsolved. Here, we contribute to it w…
Geometry of Mechanicsmath-ph
Studies geometric mechanics for autonomous and nonautonomous systems.
problem Understanding the geometric basis of mechanics.
method Geometric descriptions, Lagrangian, Hamiltonian, unified formalisms, symmetries, variational principles.
result Characterization of dynamical systems' properties and characteristics.
Introduces a variational framework for indefinite Lagrangians with specific symmetries.
problem Handling indefinite Lagrangians with complex symmetries.
method Develops a variational setting for an indefinite Lagrangian with a specific Noether charge.
result Validates the existence of a variational setting for a broad class of Lagrangians.
We make use of a symmetry reduction technique called Routh reduction to show that the solutions of the Euler-Lagrange equations of a strongly convex autonomous Lagrangian which lie on a specific energy level can be thought of as geodesics of an associated Finsler function.
We present a unified approach to constrained implicit Lagrangian and Hamiltonian systems based on the introduced concept of Dirac algebroid. The latter is a certain almost Dirac structure associated with the Courant algebroid on the dual to a vector bundle . If this almost Dirac structure is integrable (Dir…
Study on bifurcations in Lagrangian systems and geodesics on manifolds.
problem Investigating bifurcations in Lagrangian systems and geodesics on Finsler and Riemannian manifolds.
method Employing Morse index and nullity techniques, and refining the Gauss lemma.
result Derivation of precise conditions for bifurcations in geodesic flows.
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for the system. The approach can be of help in finding constants of motion in the Jac…
Jet Methods in Time-Dependent Lagrangian Biomechanicsphysics.bio-ph
In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration…
Quantum propagation studied for Berezin-Toeplitz operators.
problem Asymptotic behavior of quantum propagators and spectral projectors.
method Geometric analysis of Hamiltonian flows and Maslov indices.
result Introduction of quantum states associated with Lagrangian submanifolds.
The integrability of multivector fields in a differentiable manifold is studied. Then, given a jet bundle , it is shown that integrable multivector fields in are equivalent to integrable connections in the bundle (that is, integrable jet fields in ). This result is applied to the part…
Proposes Constrained Q-learning for reinforcement learning with constraints.
problem Optimizing multiple objectives while adhering to constraints in reinforcement learning.
method Directly restricts the action space in Q-update to learn optimal Q-function for constrained MDP.
result Improves safety and optimality in high-level decision making for autonomous driving.
The paper proves a nonholonomic version of Maupertuis-Jacobi principle and shows that nonholonomic trajectories minimize length.
problem Nonholonomic dynamics and their length minimization.
method Contact bundle formulation and geometric equivalence between problems.
result Regular solutions of nonholonomic mechanical problems are reparametrizations of geodesics with minimized Riemannian length.
New geometric framework for non-conservative field theories with time-dependent terms.
problem Describing non-conservative field theories with explicit space-time dependence.
method Combining k-cosymplectic and k-contact formulations to develop Hamiltonian and Lagrangian formalisms.
result Illustrated with the nonlinear damped wave equation, demonstrating the new formalism's applicability.
We use a geometric construction to exhibit examples of autonomous Lagrangian systems admitting exactly two homoclinics emanating from a nondegenerate maximum of the potential energy and reaching a regular level of the potential having the same value of the maximum point. Similarly, we show examples of Hamiltonian syste…
The study improves deep learning models for safer autonomous vehicles.
problem Robustness of deep neural network models in autonomous driving.
method Analyzes and proposes solutions for deep learning model robustness.
result Enhanced deep learning models for safer autonomous vehicles.
This work improves safety validation of autonomous vehicles by finding interpretable failures.
problem Finding interpretable failures of autonomous systems in simulation.
method Signal temporal logic expressions optimized for high likelihood and human interpretability.
result Our methodology finds more interpretable failures with higher likelihood compared to baseline approaches.
On partially hyperbolic diffeomorphisms in dimension three via a notion of autonomous dynamicsmath.DS
Proves rigidity of 3D partially hyperbolic systems via autonomous dynamics.
problem Rigidity of partially hyperbolic diffeomorphisms in 3D.
method Introducing autonomous dynamical systems to prove rigidity.
result Rigidity of partially hyperbolic diffeomorphisms on 3-manifolds.
Generalizes energy-momentum method for non-autonomous Hamiltonian systems.
problem Stability analysis of non-autonomous Hamiltonian systems with symmetries.
method Develops a new approach to relative equilibrium points and stability conditions for non-autonomous systems.
result Conditions ensuring stability of relative equilibrium points in non-autonomous Hamiltonian systems.
This paper explores formal verification for autonomous systems, identifying limitations and proposing improvements.
problem Ensuring safety of autonomous systems like self-driving cars and drones.
method Formal verification techniques based on formal methods, analyzing three assumptions and their limitations.
result Preliminary work to improve the strength of evidence provided by formal verification.
We enhance autonomous materials research with problem-aware models.
problem Complex decision-making in autonomous materials.
method Bayesian framework, machine learning, physics-based models, operational considerations.
result Improved models reflect problem-specific structure.
The paper explores new risk models for autonomous driving.
problem Risk management and actuarial modeling for autonomous vehicles.
method Examines technical difficulties and proposes a novel risk model.
result The new model better reflects real-world driving safety.
Differential geometric mechanisms in Ostrohrads'kyj relativistic spherical top dynamicsphysics.class-ph
Some intrinsic tools from the formal theory of variational equations are being demonstrated at work in application to one concrete example of the third-order evolution equation of free relativistic top in three-dimensional space-time. The main goal is to introduce a combined approach consisting in the simultaneous util…
We prove that the autonomous norm on the group of Hamiltonian diffeomorphisms of the two-dimensional torus is unbounded. We provide explicit examples of Hamiltonian diffeomorphisms with arbitrarily large autonomous norm. For the proofs we construct quasimorphisms on and some of them are Calabi.
The study explores autonomous systems and their connections to contact geometry and Frobenius manifolds.
problem Understanding the connections between autonomous systems and geometric structures.
method Investigation of the Darboux-Halphen-Ramanujan system, contact geometry, and Frobenius manifolds.
result Highlighting the role of contact geometry in autonomous systems.
Adaptive framework generates challenging adversarial scenarios for autonomous vehicles.
problem Lack of efficient and adaptable evaluation methods for autonomous vehicles.
method Adaptive evaluation framework using ensemble models and nonparametric Bayesian clustering.
result Adversarial scenarios significantly degrade tested autonomous vehicles' performance.
Autonomous Vehicles(AV) are one of the brightest promises of the future which would help cut down fatalities and improve travel time while working in harmony. Autonomous vehicles will face with challenging situations and experiences not seen before. These experiences should be converted to knowledge and help the vehicl…
This paper presents a novel approach for automatic rule learning applicable to an autonomous driving system using real driving data.
Safe Reinforcement Learning for Autonomous Vehicles through Parallel Constrained Policy Optimizationcs.LG
Safe RL for autonomous vehicles using PCPO with trust regions and parallel learners.
problem Unexplainable behaviours and lack of safety guarantees in RL for real vehicles.
method PCPO framework with trust regions and parallel learners.
result Safe learning confirmed for autonomous vehicles with fast convergence.
ApolloRL offers a platform for RL research in autonomous driving.
problem Improving reinforcement learning for autonomous driving.
method Open platform with training, simulation, and evaluation components.
result Baseline agents perform well in the ApolloRL environment.
Autonomous vehicles rely on machine learning to solve challenging tasks in perception and motion planning. However, automotive software safety standards have not fully evolved to address the challenges of machine learning safety such as interpretability, verification, and performance limitations. In this paper, we revi…
A machine learning environment for detecting autonomous vehicle corner cases.
problem Testing autonomous driving software in the real world is difficult.
method Connecting CARLA simulation software to TensorFlow and custom AI client software.
result The system can identify situations where AI software fails to understand the scenario.
Scalable Autonomous Vehicle Safety Validation through Dynamic Programming and Scene Decompositioncs.RO
New approach uses dynamic programming to efficiently discover failures in autonomous vehicle simulations.
problem Efficiently discovering rare failure events in autonomous vehicle simulations.
method Approximate dynamic programming and scene decomposition to estimate failure distribution.
result Increased number of failures discovered compared to baseline approaches.
Real-time semantic segmentation for autonomous vehicles on FPGA reduces latency and power consumption.
problem Efficient real-time semantic segmentation for autonomous vehicles.
method Compressed ENet architecture, FPGA deployment, batch processing, filter reduction, quantization-aware training.
result Reduced latency to 3 ms per image with batch size of ten and 40% resource utilization.
Develops a method to simulate rare dangerous events in autonomous systems.
problem Rare dangerous events in safety-critical systems are hard to test in real-world settings.
method Combines exploration, exploitation, and optimization techniques for rare-event simulation.
result Provides rigorous guarantees for the performance of the method.
Gemini uses inexpensive measurements to correct biases in expensive property evaluations.
problem Accurate estimation of materials properties using expensive measurements is hindered in scientific discovery campaigns.
method Gemini is a data-driven model that corrects systematic biases between property evaluation methods using inexpensive measurements.
result Gemini reduces the number of expensive evaluations needed for Bayesian optimization in materials discovery.
Safe autonomous decisions made with machine learning predictions using Conformal Decision Theory.
problem Safe decisions from imperfect machine learning predictions.
method Conformal Decision Theory framework for producing safe decisions.
result Safe decisions with provable statistical guarantees of low risk.
This work improves autonomous racing by creating diverse opponents and adapting risk.
problem Balancing performance and safety in autonomous racing environments.
method Developed a self-play method using replica-exchange Markov chain Monte Carlo for diverse opponents and a distributionally robust bandit optimization for adaptive risk adjustment.
result Demonstrated real-time motion-planning methods achieving speeds comparable to Formula One racecars.
AI mirrors modern math's autonomous development, raising interpretive challenges.
problem AI's effectiveness in math mirrors historical autonomy of math.
method Analyzes historical evolution of modern mathematics and AI's role.
result AI's affinity with math's historical autonomy suggests interpretive limits.
To improve efficiency and reduce failures in autonomous vehicles, research has focused on developing robust and safe learning methods that take into account disturbances in the environment. Existing literature in robust reinforcement learning poses the learning problem as a two player game between the autonomous system…
DeepRacing uses neural networks to predict trajectories for autonomous racing in video games.
problem Training algorithms for high-speed autonomous racing in realistic environments.
method Developed a virtual testbed using F1 video games, trained neural networks to predict trajectories and control commands.
result Trajectory prediction outperforms end-to-end control methods in autonomous racing simulations.
Introduction to Latent Variable Energy-Based Models: A Path Towards Autonomous Machine Intelligencecs.LG
Future autonomous systems need reliable world models and complex action sequences.
problem Current automated systems lack reliable world models and complex action sequences.
method Introduce energy-based and latent variable models combined in a hierarchical joint embedding predictive architecture (H-JEPA).
result Combining energy-based and latent variable models in H-JEPA can lead to reliable world models and complex action sequences.
Highly Autonomous Driving (HAD) systems rely on deep neural networks for the visual perception of the driving environment. Such networks are trained on large manually annotated databases. In this work, a semi-parametric approach to one-shot learning is proposed, with the aim of bypassing the manual annotation step requ…
Constructing translating solitons from Lagrangian Grim Reapers.
problem Creating Lagrangian translating solitons from intersections of Grim Reapers.
method Desingularizing intersections with special Lagrangian Lawlor necks.
result Constructing Lagrangian translating solitons with multiple ends and loops.
Robots learn new tasks autonomously with minimal human intervention.
problem Lack of scalable data collection for robot learning.
method Multi-task imitation learning with autonomous data collection and one-shot generalization.
result Robots can continuously improve through autonomous data collection without reinforcement learning.
Nowadays autonomous technologies are a very heavily explored area and particularly computer vision as the main component of vehicle perception. The quality of the whole vision system based on neural networks relies on the dataset it was trained on. It is extremely difficult to find traffic sign datasets from most of th…
In this paper, we study the Lagrangian F-stability of closed Lagrangian self-shrinkers immersed in complex Euclidean space. We show that any closed Lagrangian self-shrinker with first Betti number greater than one is Lagrangian F-unstable. In particular, any two-dimensional embedded closed Lagrangian self-shrinker is L…