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Prior arts in the field of motion predictions for autonomous driving tend to focus on finding a trajectory that is close to the ground truth trajectory. Such problem formulations and approaches, however, frequently lead to loss of diversity…

Relativistic scalar fields are ubiquitous in modified theories of gravity. An important tool in understanding their impact on structure formation, especially in the context of N-body simulations, is the quasi-static approximation in which…

For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first…

We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…

Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…

In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…

In this paper we propose a new parameter-free method for trajectory classification which finds the best trajectory partition and dimension combination for robust trajectory classification. Preliminary experiments show that our approach is…

Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient…

We investigate the use of a logarithmic density variable in estimating the Lagrangian displacement field, motivated by the success of a logarithmic transformation in restoring information to the matter power spectrum. The logarithmic…

The paper shows the equivalence between the geometric frequency of an electric quantity, namely, voltage and current, and the Lagrange derivative of a stream-line of a fluid. The geometric frequency is a concept recently proposed by the…

We establish anomalous inertial range scaling of structure functions for a model of advection of a passive scalar by a random velocity field. The velocity statistics is taken gaussian with decorrelation in time and velocity differences…

The paper is concerned with the stability of the set of trajectories of a vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in AB to study…

We present a framework for the scale-invariance characterization of stochastic processes in reconstructed finite-dimensional phase spaces. This framework analyses the structural and dynamical properties of the phase space and is based on a…

Map matching of the GPS trajectory serves the purpose of recovering the original route on a road network from a sequence of noisy GPS observations. It is a fundamental technique to many Location Based Services. However, map matching of a…

In this work we consider a dissipative reaction-diffusion equation in a $d$-dimensional thin domain shrinking to a one dimensional segment and obtain good rates for the convergence of the attractors. To accomplish this, we use estimates on…

Radiography is often used to probe complex, evolving density fields in dynamic systems and in so doing gain insight into the underlying physics. This technique has been used in numerous fields including materials science, shock physics,…

Diffusion Map is a spectral dimensionality reduction technique which is able to uncover nonlinear submanifolds in high-dimensional data. And, it is increasingly applied across a wide range of scientific disciplines, such as biology,…

We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the…

We investigate the large intersection properties of the set of points that are approximated at a certain rate by a family of affine subspaces. We then apply our results to various sets arising in the metric theory of Diophantine…

In this paper we study a second-order mean-field stochastic differential systems describing the movement of a particle under the influence of a time-dependent force, a friction, a mean-field interaction and a space and time-dependent…