In this article we investigate a first order reparametrization-invariant Sobolev metric on the space of immersed curves. Motivated by applications in…

Langevin dynamics (LD) has been proven to be a powerful technique for optimizing a non-convex objective as an efficient algorithm to find local minim…

Following an approach developed by Gieseker, Kn\"orrer and Trubowitz for discretized Schr\"odinger operators, we study the spectral theory of Harper …

Our algorithm has been designed for some applications of lattice reduction. In this section we justify the importance of this algorithm by directly applying it to two classical applications of lattice reduction.

We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases wit…

Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two…

The arguments of Gluck [7], adapted to the setting of c-polyhedra, now apply to verify our main theorem. Here are the details.

We verify the infinitesimal inversive rigidity of almost all triangulated circle polyhedra in the Euclidean plane $\mathbb{E}^{2}$, as well as the in…

Motivated by applications in the field of shape analysis, we study reparametrization invariant, fractional order Sobolev-type metrics on the space of…

Understanding the underlying mechanisms that enable the empirical successes of deep neural networks is essential for further improving their performa…

Human beings are particularly good at reasoning and inference from just a few examples. When facing new tasks, humans will leverage knowledge and ski…

Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on i…

To improve the generalization of the representations for natural language processing tasks, words are commonly represented using vectors, where dista…

This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar cu…

In many fields such as bioinformatics, high energy physics, power distribution, etc., it is desirable to learn non-linear models where a small number…

We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. A…

We give a different geometric interpretation of the deletion–contraction relation proved in the previous section, which views the graph hypersurface of Γ as a Milnor fiber for hypersurfaces related to Γ∖e and Γ/e. An advantage of this point of view …

We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendiec…

The problem of estimating trend and seasonal variation in time-series data has been studied over several decades, although mostly using single time s…

We propose and study two second-order in time implicit-explicit (IMEX) methods for the coupled Stokes-Darcy system that governs flows in karst aquife…

A univariate Hawkes process is a simple point process that is self-exciting and has clustering effect. The intensity of this point process is given b…

Spherical regression explores relationships between variables on spherical domains. We develop a nonparametric model that uses a diffeomorphic map fr…

Tree ensembles are flexible predictive models that can capture relevant variables and to some extent their interactions in a compact and interpretabl…

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