Related papers: Time-Dependent 2-D Vector Field Topology: An Appro…
Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze…
Gauge theories can be described by assigning a vector space V(x) to each space time point x. A common set of complex numbers, C, is usually assumed to be the set of scalars for all the V{x}. This is expanded here to assign a separate set of…
Topological edge states in systems of two (or more) dimensions offer scattering-free transport, exhibiting robustness to inhomogeneities and disorder. In a different domain, time-modulated systems, such as photonic time crystals (PTCs),…
We derive a theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active vector field, such as the linear momentum, the angular momentum or the vorticity, in general fluid flows. These special material…
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for…
Field theoretical models with first order Lagrangean can be formulated in a covariant Hamiltonian formalism. In this article, the geometrical construction of the Gerstenhaber structure that encodes the equations of motion is explained for…
A profound understanding of inter-agent relationships and motion behaviors is important to achieve high-quality planning when navigating in complex scenarios, especially at urban traffic intersections. We present a trajectory prediction…
Action principles of the BF type for diffeomorphism invariant topological field theories living in n-dimensional spacetime manifolds are presented. Their construction is inspired by Cuesta and Montesinos' recent paper where Cartan's first…
Anticipating the motion of other road users is crucial for automated driving systems (ADS), as it enables safe and informed downstream decision-making and motion planning. Unfortunately, contemporary learning-based approaches for motion…
Time is an important feature in many applications involving events that occur synchronously and/or asynchronously. To effectively consume time information, recent studies have focused on designing new architectures. In this paper, we take…
Viewpoint change invariance and action temporal consistency are critical aspects for the effective deployment of human action detection of untrimmed videos. Existing appearance-based video detection methods often struggle with limited…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a…
It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that…
Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with…
The purpose of the paper is to develop further a projection variational approach in relativistic hydrodynamics. The approach, previously proposed in [gr-qc/9908032], is based on the variation of the vector field and the projection tensor…
Time has entered the domain of topological phases in the field of non-Hermitian physics. Previous studies have relied on periodic modulation in time to make an intuitive connection to established spatial topological invariants, albeit with…
In this paper the asymptotic behavior of trajectories of discontinuous vector fields is studied. The vector fields are defined on a two-dimensional Riemannian manifold $M$ and the confinement of trajectories on some suitable compact set $K$…
We outline a program for incorporating holomorphic curves with Lagrangian boundary conditions into symplectic field theory, with an emphasis on ideas, geometric intuition, and a description of the resulting algebraic structures.