Related papers: A uniform non-linear subdivision scheme reproducin…

This paper extends the matrix based approach to the setting of multiple subdivision schemes studied in [Sauer 2012]. Multiple subdivision schemes, in contrast to stationary and non-stationary schemes, allow for level dependent subdivision…

Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…

This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…

In view of the huge success of convolution neural networks (CNN) for image classification and object recognition, there have been attempts to generalize the method to general graph-structured data. One major direction is based on spectral…

In this paper we consider a problem of searching a space of predictive models for a given training data set. We propose an iterative procedure for deriving a sequence of improving models and a corresponding sequence of sets of non-linear…

We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasi-isometric information for a group. We show how these tilings detect…

Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…

In this work we describe a method to reconstruct the braid monodromy of the preimage of a curve by a Kummer cover. This method is interesting, since it combines two techniques, namely, the reconstruction of a highly non-generic braid…

In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in $\mathbb{R}^{2}$. The main idea is to smooth the parametrization of the curve by…

In this work, we present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We present unique challenges pertaining to the representation and reconstruction in…

We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some examples, crude schemes fail to capture the correct limiting…

Neural networks have been shown to be an effective tool for learning algorithms over graph-structured data. However, graph representation techniques---that convert graphs to real-valued vectors for use with neural networks---are still in…

This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…

We present a new approach to unsupervised shape correspondence learning between pairs of point clouds. We make the first attempt to adapt the classical locally linear embedding algorithm (LLE) -- originally designed for nonlinear…

We introduce a novel algorithm for nonlinear processing of data gathered by an active array of sensors which probes a medium with pulses and measures the resulting waves. The algorithm is motivated by the application of array imaging. We…

This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…

In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…

We propose a learning paradigm for numerical approximation of differential invariants of planar curves. Deep neural-networks' (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is…

In nonsmooth optimization, a negative subgradient is not necessarily a descent direction, making the design of convergent descent methods based on zeroth-order and first-order information a challenging task. The well-studied bundle methods…

We propose a new method for Unsupervised clustering in particle physics named UCluster, where information in the embedding space created by a neural network is used to categorise collision events into different clusters that share similar…