Related papers: Variational Analysis of Directional Minimal Time F…
Connectionist temporal classification (CTC) is commonly adopted for sequence modeling tasks like speech recognition, where it is necessary to preserve order between the input and target sequences. However, CTC is only applied to…
The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…
We introduce a new variational characterization of Gaussian diffusion processes as minimum uncertainty states. We then define a variational method constrained by kinematics of diffusions and Schr\"{o}dinger dynamics to seek states of local…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…
In this paper we study a new family of sinc--like functions, defined on an interval of finite width. These functions, which we call ``little sinc'', are orthogonal and share many of the properties of the sinc functions. We show that the…
A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed…
Interval approaches for the reachability analysis of initial value problems for sets of classical ordinary differential equations have been investigated and implemented by many researchers during the last decades. However, there exist…
Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
Constructing observables that describe the localization of relativistic particles is an important foundational problem in relativistic quantum field theory (QFT). The description of localization in terms of single-time observables leads to…
In this paper, we introduce a novel family of iterative algorithms which carry out $\alpha$-divergence minimisation in a Variational Inference context. They do so by ensuring a systematic decrease at each step in the $\alpha$-divergence…
Transportation companies and organizations routinely collect huge volumes of passenger transportation data. By aggregating these data (e.g., counting the number of passengers going from a place to another in every 30 minute interval), it…
Local time is the measure of how much time a random walk has visited a given position. In multiple scattering media, where waves are diffuse, local time measures the sensitivity of the waves to the local medium's properties. Local…
We study the time optimal control problem for differential inclusions with a general closed target. We first give the representation of the proximal horizontal subgradients of the minimum time function $\mathcal{T}$ and then, together with…
Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the…
The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrodinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact…
One of the main foci of robotics is nowadays centered in providing a great degree of autonomy to robots. A fundamental step in this direction is to give them the ability to plan in discrete and continuous spaces to find the required motions…
Analyzing flow of objects or data at different granularities of space and time can unveil interesting insights or trends. For example, transportation companies, by aggregating passenger travel data (e.g., counting passengers traveling from…