Related papers: Trickle-Down in Localization Schemes and Applicati…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

Proximal splitting algorithms for monotone inclusions (and convex optimization problems) in Hilbert spaces share the common feature to guarantee for the generated sequences in general weak convergence to a solution. In order to achieve…

Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…

We adapt the alternating linearization method for proximal decomposition to structured regularization problems, in particular, to the generalized lasso problems. The method is related to two well-known operator splitting methods, the…

We study the use of approximate Lagrange multipliers and discrete actions in solving convex optimisation problems. We observe that descent, which can be ensured using a wide range of approaches (gradient, subgradient, Newton, etc.), is…

We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…

Recent work by Woodworth et al. (2020) shows that the optimization dynamics of gradient descent for overparameterized problems can be viewed as low-dimensional dual dynamics induced by a mirror map, explaining the implicit regularization…

We present a novel approach for relocalization or place recognition, a fundamental problem to be solved in many robotics, automation, and AR applications. Rather than relying on often unstable appearance information, we consider a situation…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

We present a comprehensive analysis of Bredon's trick, a powerful local-to-global extension principle with broad applications across differential geometry and computational topology. Our main contributions include: (1) novel applications to…

Dynamics of spreading of small droplets on surfaces has been studied by the molecular dynamics method. Simulations have been performed for mixtures of solvent and dimer, and solvent and tetramer droplets. For solvent particles and dimers,…

The dynamical low-rank approximation (DLRA) is used to treat high-dimensional problems that arise in such diverse fields as kinetic transport and uncertainty quantification. Even though it is well known that certain spatial and temporal…

Tropical cyclone wind-intensity prediction is a challenging task considering drastic changes climate patterns over the last few decades. In order to develop robust prediction models, one needs to consider different characteristics of…

This paper deals with a bilevel approach of the location-allocation problem with dimensional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities and we prove the…

We propose a simplified version of the Multi-Scale Analysis of tight-binding Anderson models with strongly mixing random potentials which leads directly to uniform exponential bounds on decay of eigenfunctions in arbitrarily large finite…

The use of probe molecules to extract the local dynamical and structural properties of complex dynamical systems is an age-old technique both in simulations and experiments. A lot of important information which is not immediately accessible…

Dropout is a widely utilized regularization technique in the training of neural networks, nevertheless, its underlying mechanism and its impact on achieving good generalization abilities remain poorly understood. In this work, we derive the…

Deep unrolling, or unfolding, is an emerging learning-to-optimize method that unrolls a truncated iterative algorithm in the layers of a trainable neural network. However, the convergence guarantees and generalizability of the unrolled…

Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a…

Precision mapping of landslide inventory is crucial for hazard mitigation. Most landslides generally co-exist with other confusing geological features, and the presence of such areas can only be inferred unambiguously at a large scale. In…