Related papers: Variational approximations to homoclinic snaking
Localized deformation patterns are a common motif in morphogenesis and are increasingly finding widespread applications in materials science, for instance as memory devices. Here we describe the emergence of spatially localized deformations…
Snake robots have the potential to maneuver through tightly packed and complex environments. One challenge in enabling them to do so is the complexity in determining how to coordinate their many degrees-of-freedom to create purposeful…
We investigate homological stability for the space of sections of Fano fibrations over curves in the context of weak approximation, and establish it for projective bundles, as well as for conic and quadric surface bundles over curves.
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
In this work, we propose a scalable Bayesian procedure for learning the local dependence structure in a high-dimensional model where the variables possess a natural ordering. The ordering of variables can be indexed by time, the vicinities…
The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local…
We consider the formation of temporal localized structures or Kerr comb generation in a microresonator with inhomogeneities. We show that the introduction of even a small inhomogeneity in the injected beam widens the stability region of…
We prove the existence of exponentially localised and time-periodic solutions in general nonlinear Hamiltonian lattice systems. Like normal modes, these localised solutions are characterised by collective oscillations at the lattice sites…
A number of mechanisms that lead to the confinement of patterns to a small part of a translationally symmetric pattern-forming system are reviewed: nonadiabatic locking of fronts, global coupling and conservation laws, dispersion, and…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
We consider large but finite systems of identical agents on the line with up to next nearest neighbor asymmetric coupling. Each agent is modelled by a linear second order differential equation, linearly coupled to up to four of its…
To calculate the intercept of the multigluon system in a symmetric spatial configuration a variational method is developed based on a complete system of one-gluon functions. The method is applied to two- and three- gluon cases to compare…
Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…
Variational inequalities are a formalism that includes games, minimization, saddle point, and equilibrium problems as special cases. Methods for variational inequalities are therefore universal approaches for many applied tasks, including…
This paper proposes a novel collocation-type numerical stochastic homogenization method for prototypical stochastic homogenization problems with random coefficient fields of small correlation lengths. The presented method is based on a…
Stochastic variational inference makes it possible to approximate posterior distributions induced by large datasets quickly using stochastic optimization. The algorithm relies on the use of fully factorized variational distributions.…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized…
Contact-rich problems, such as snake robot locomotion, offer unexplored yet rich opportunities for optimization-based trajectory and acyclic contact planning. So far, a substantial body of control research has focused on emulating snake…
This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet…