Related papers: Morse Theory for the Travel Time Brachistochrones …
One important global topological property of a spacetime manifold is orientability. It is widely believed that spatial orientability can only be tested by global journeys around the Universe to check for orientation-reversing closed paths.…
This paper endeavors to learn time-varying graphs by using structured temporal priors that assume underlying relations between arbitrary two graphs in the graph sequence. Different from many existing chain structure based methods in which…
We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.
Route-level travel time reliability requires characterizing the distribution of total travel time across correlated segments -- a problem where existing methods either assume independence (fast but miscalibrated) or model dependence via…
We develop an index theory for variational problems on noncompact quantum graphs. The main results are a spectral flow formula, relating the net change of eigenvalues to the Maslov index of boundary data, and a Morse index theorem, equating…
Multisymplectic variational integrators are structure preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton principles. The goal of this paper is to study the properties of the temporal and…
The problem of a rigorous theory of singularities in space-times with torsion is addressed. We define geodesics as curves whose tangent vector moves by parallel transport. This is different from what other authors have done, because their…
In this paper, we analyze the variation of the gravitational action on a bounded region of spacetime whose boundary contains segments with various characters, including null. We develop a systematic approach to decompose the derivative of…
In the present article, we derive the space-time action of the bosonic string in terms of geometrical quantities. First, we study the space-time geometry felt by probe bosonic string moving in antisymmetric and dilaton background fields. We…
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions…
The BRS transformations for gravity with torsion are discussed by using the Maurer-Cartan horizontality conditions. With the help of an operator $\d$ which allows to decompose the exterior space-time derivative as a BRS commutator we solve…
Morse complexes and Morse-Smale complexes are topological descriptors popular in topology-based visualization. Comparing these complexes plays an important role in their applications in feature correspondences, feature tracking, symmetry…
Travel time estimation is one of the core tasks for the development of intelligent transportation systems. Most previous works model the road segments or intersections separately by learning their spatio-temporal characteristics to estimate…
Inspired by the question of whether one can create a visually informative map in which distances reflect travel-times rather than physical proximity, we examine whether it is possible to construct a meaningful travel time function between…
We discuss a model of a conformal p-brane interacting with the world volume metric and connection. The purpose of the model is to suggest a mechanism by which gravity coupled to p-branes leads to the formation of structure rather than…
Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
Gravity whose nature is fundamental to the understanding of solar system, galaxies and the structure and evolution of the Universe, is theorized by the assumption of curved spacetime, according to Einstein`s general theory of relativity…
In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…
Space-time covariance modeling under the Lagrangian framework has been especially popular to study atmospheric phenomena in the presence of transport effects, such as prevailing winds or ocean currents, which are incompatible with the…