Related papers: The Collective Coordinate Fix
In large groups, every collaborative act requires balancing two pressures: the need to achieve behavioural synchrony and the need to keep free riding to a minimum. This paper introduces a model of collaboration that requires both…
We derive a stochastic path integral representation of counting statistics in semi-classical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to…
Since their introduction, anchoring methods in extragradient-type saddlepoint problems have inspired a flurry of research due to their ability to provide order-optimal rates of accelerated convergence in very general problem settings. Such…
The calculus of variation and the construction of path integrals is revisited within the framework of non-linear generalized functions. This allows us to make a rigorous analysis of the variation of an action that takes into account the…
Cooperative map matching (CMM) uses the Global Navigation Satellite System (GNSS) position information of a group of vehicles to improve the standalone localization accuracy. It has been shown, in our previous work, that the GNSS error can…
Coordinate descent (CD) algorithms have become the method of choice for solving a number of optimization problems in machine learning. They are particularly popular for training linear models, including linear support vector machine…
In this paper, we consider the coordination control of a group of autonomous mobile agents with multiple leaders. Different interconnection topologies are investigated. At first, a necessary and sufficient condition is proved in the case of…
When connected and autonomous vehicles (CAVs) are widely used in the future, we can foresee many essential applications, such as platoon formation and autonomous police patrolling, which need two CAVs, originally separated in a mixed…
Coordinated control of connected and automated vehicles (CAVs) emerges as a promising technology to improve traffic safety, efficiency, and sustainability. Meanwhile, mixed traffic, where CAVs coexist with conventional human-driven vehicles…
We consider fits to two or more datasets for which results from the sa me experiment share a common systematic uncertainty in addition to their individ ual statistical errors. This is important in extracting the maximum information from a…
Given a finite collection of $C^1$ vector fields on a $C^2$ manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields are real analytic. We give…
In this Thesis we study quantum corrections to the classical dynamics for mean values in field theory. To that end we make use of the formalism of the closed time path effective action to get real and causal equations of motion. We…
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
When a real saddle equilibrium in a three-dimensional vector field undergoes a homoclinic bifurcation, the associated two-dimensional invariant manifold of the equilibrium closes on itself in an orientable or non-orientable way. We are…
Path integral derivations are presented for two recently developed complex trajectory techniques for the propagation of wave packets, Complex WKB and BOMCA. Complex WKB is derived using a standard saddle point approximation of the path…
Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or…
In this paper we study the emergence of coherence in collective motion described by a system of interacting motiles endowed with an inner, adaptative, steering mechanism. By means of a nonlinear parametric coupling, the system elements are…
We develop a coordinate version of light-cone-ordered perturbation theory, for general time-ordered products of fields, by carrying out integrals over one light-cone coordinate for each interaction vertex. The resulting expressions depend…
The very early universe is understood in terms of quantum field theories on curved spacetime, where the classical background spacetime is typically an FLRW cosmology and the quantum fields which propagate on it include gravitational waves…