Related papers: On sliced Cram\'er metrics
This study examines the roughness of mechanically cleaved edges in 2D crystals and glasses using molecular dynamics simulations with chemically accurate machine-learning force fields. Our results show that ultra-flat armchair and zigzag…
Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…
The optimization problem concerning the determination of the minimizer for the sum of convex functions holds significant importance in the realm of distributed and decentralized optimization. In scenarios where full knowledge of the…
In this paper,we obtain two results on closed Reimainnian manifold $M\times [0,T]$.When $T$ is small enough,to any prescribed scalar curvature, the existence and uniqueness of metrics are obtained on the volume element preserving…
In this review article we consider the crack growth resistance ofmicrometer and submicrometer sized samples from the fracture mechanics point of view. Standard fracture mechanics test procedures were developed for macroscale samples, and…
We estimate linear functionals in the classical deconvolution problem by kernel estimators. We obtain a uniform central limit theorem with $\sqrt{n}$-rate on the assumption that the smoothness of the functionals is larger than the…
In this paper, we propose a scalable approximate multiplier design, scaleTRIM, that approximates the multiplication operation using fitted linear functions, also referred to as linearization. We show that multiplication operations can be…
The basic disentanglement theorem established by the present authors states that estimates on a weighted geometric mean over (convex) families of functions can be disentangled into quantitatively linked estimates on each family separately.…
We have implemented a complex network description for metallic glasses, able to predict the elasto-plastic regime, the location of shear bands and the statistics that controls the plastic events that originate in the material due to a…
While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is known to be unstable in a certain precise sense. Until now, it has not…
X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…
Sliding friction is ubiquitous in nature as are harmonic oscillators. However, when treating harmonic oscillators the effect of sliding friction is often neglected. Here, we propose a simple analytical model to include both viscous and…
Cutting mechanics in soft solids have been a subject of study for several decades, an interest fuelled by the multitude of its applications, including material testing, manufacturing, and biomedical technology. Wire cutting is the simplest…
This paper studies sparse spikes deconvolution over the space of measures. We focus our attention to the recovery properties of the support of the measure, i.e. the location of the Dirac masses. For non-degenerate sums of Diracs, we show…
The decentralized gradient descent (DGD) algorithm, and its sibling, diffusion, are workhorses in decentralized machine learning, distributed inference and estimation, and multi-agent coordination. We propose a novel, principled framework…
In this paper, we deals with isoperimetric-type inequalities for closed convex curves in the Euclidean plane R^2. We derive a family of parametric inequalities involving the following geometric functionals associated to a given convex curve…
This paper uses the notion of algorithmic stability to derive novel generalization bounds for several families of transductive regression algorithms, both by using convexity and closed-form solutions. Our analysis helps compare the…
We study discrete dynamics governed by a difference inclusion whose increment is the sum of a selection from a set-valued map and a noise term. For any bounded realization, convergence follows once the inter-iterate diameter is controlled…
Deep neural networks are vulnerable to input deformations in the form of vector fields of pixel displacements and to other parameterized geometric deformations e.g. translations, rotations, etc. Current input deformation certification…
Large-scale graphs are widely used to represent object relationships in many real world applications. The occurrence of large-scale graphs presents significant computational challenges to process, analyze, and extract information. Graph…