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The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
We introduce a novel semi-supervised video segmentation approach based on an efficient video representation, called as "super-trajectory". Each super-trajectory corresponds to a group of compact trajectories that exhibit consistent motion…
For aerial swarms, navigation in a prescribed formation is widely practiced in various scenarios. However, the associated planning strategies typically lack the capability of avoiding obstacles in cluttered environments. To address this…
The semiclassical approximation of coherent state path integrals is employed to study the dynamics of the Jaynes-Cummings model. Decomposing the Hilbert space into subspaces of given excitation quanta above the ground state, the…
In the present work, we introduce a Self-Consistent Density-Functional Embedding technique, which leaves the realm of standard energy-functional approaches in Density Functional Theory and targets directly the density-to-potential mapping…
This paper introduces the concept of a mean for trajectories and multi-object trajectories (defined as sets or multi-sets of trajectories) along with algorithms for computing them. Specifically, we use the Fr\'{e}chet mean, and metrics…
This note presents an online pseudospectral method for system identification using Chebyshev polynomial basis under aperiodic sampling. The system dynamics are approximated piecewise by introducing a sliding time window. The number of…
A new simple method for the first order phase transition kinetics is suggested. The metastable phase consumption can be imagined in frames of the modisperse approximation for the distribution of the droplets sizes. In all situations of the…
This paper is devoted to the robust approximation with a variational phase field approach of multiphase mean curvature flows with possibly highly contrasted mobilities. The case of harmonically additive mobilities has been addressed…
We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…
Traffic Matrix estimation has always caught attention from researchers for better network management and future planning. With the advent of high traffic loads due to Cloud Computing platforms and Software Defined Networking based tunable…
The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation,…
We combine the coherent modified Redfield theory (CMRT) with the equation of motion-phase matching approach (PMA) to calculate two-dimensional photon echo spectra for photoactive molecular complexes with an intermediate strength of the…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…
In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation…
A recent description of the motion of atoms in a classical monatomic system in liquid and supercooled liquid states divides the motion into two parts: oscillations within a given many-particle potential valley, and transit motion which…
We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not…