Related papers: Cinematica Topologica
Centre manifold techniques are used to derive rationally a description of the dynamics of thin films of fluid. The derived model is based on the free-surface $\eta(x,t)$ and the vertically averaged horizontal velocity $\avu(x,t)$. The…
A new method of estimating some statistical characteristics of TCP flows in the Internet is developed in this paper. For this purpose, a new set of random variables (referred to as observables) is defined. When dealing with sampled traffic,…
Generic motion understanding from video involves not only tracking objects, but also perceiving how their surfaces deform and move. This information is useful to make inferences about 3D shape, physical properties and object interactions.…
This paper presents an alternative approach for the computation of trajectory segments on slow manifolds of saddle type. This approach is based on iterative methods rather than collocation-type methods. Compared to collocation methods, that…
In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
A calculational approach in fluid turbulence is presented. Use is made of the attracting nature of the fluid-dynamic dynamical system. An approximate approach is offerred that effectively propagates the statistics in time. Loss of…
A new approach to estimating the velocity of the pole moving is considered. The method uses the model-calculated spatial distribution of the (vector) horizontal component \textbf{H} for a given year and its change relative to the closest…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
We investigate the topologies of random geometric complexes built over random points sampled on Riemannian manifolds in the so-called "thermodynamic" regime. We prove the existence of universal limit laws for the topologies; namely, the…
Multilevel strategies are an integral part of many image registration algorithms. These strategies are very well-known for avoiding undesirable local minima, providing an outstanding initial guess, and reducing overall computation time.…
Scene flow is a description of real world motion in 3D that contains more information than optical flow. Because of its complexity there exists no applicable variant for real-time scene flow estimation in an automotive or commercial vehicle…
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make…
Easily computable lower and upper bounds are found for the sum of Catalan numbers. The lower bound is proven to be tighter than the upper bound, which previously was declared to be only an asymptotic. The average of these bounds is proven…
Predicting a potential collision with leading vehicles is an essential functionality of any autonomous/assisted driving system. One bottleneck of existing vision-based solutions is that their updating rate is limited to the frame rate of…
We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.
Computing the epipolar geometry from feature points between cameras with very different viewpoints is often error prone, as an object's appearance can vary greatly between images. For such cases, it has been shown that using motion…
We define a norm on homology of punctured tori equipped with a complete hyperbolic metric of finite volume and use it to find asymptotics on the growth of the number of simple geodesics of bounded length.
Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…
We present and analyze a penalization method wich extends the the method of [1] to the case of a rigid body moving freely in an incompressible fluid. The fluid-solid system is viewed as a single variable density flow with an interface…