arXiv research

Study on spectral asymptotics in elasticity on smooth manifolds.

Study on elasticity with mixed boundary conditions, proving spectral asymptotics.

Study of elastic models in non-Euclidean spaces via Γ-convergence.

Study on Transfer Elastic Net error bounds and grouping effect.

The spectral asymptotics for linear elasticity with mixed boundary conditions are shown to be old results.

A new method for semi-supervised learning of sparse features using elastic-net.

Characterizes null Lagrangians in Cosserat elasticity.

Variable selection plays an important role in the high-dimensional data analysis. However the high-dimensional data often induces the strongly correlated variables problem. In this paper, we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate. By a simulation study, we s…

Paper develops algorithms for sparse linear regression with generalized elastic net penalty.

We derive a dimensionally-reduced limit theory for an $n$-dimensional nonlinear elastic body that is slender along $k$ dimensions. The starting point is to view an elastic body as an $n$-dimensional Riemannian manifold together with a not necessarily isometric $W^{1,2}$-immersion in $n$-dimensional Euclidean space. The…

Corrects errors in previous work on spectral asymptotics in elasticity.

In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $Γ$-convergence of elastic energies for configurations of a converging sequence, $\mathcal{M}_n\to\mathcal{M}$, of body manifolds. This convergence result …

The paper generalizes the Cauchy-Schwarz-Bunyakovsky inequality and applies it to elasticity problems.

We propose a general strategy to derive null-homotopy operators for differential complexes based on the Bernstein-Gelfand-Gelfand (BGG) construction and properties of the de Rham complex. Focusing on the elasticity complex, we derive path integral operators $\mathscr{P}$ for elasticity satisfying $\mathscr{D}\mathscr{P…

A fast method estimates group-adaptive elastic net penalties using co-data.

Reformulates elasticity complex with new differential and Hodge star operators.

Enhanced ECCD speeds up elastic net model training.

This paper presents a phenomenon in neural networks that we refer to as \textit{local elasticity}. Roughly speaking, a classifier is said to be locally elastic if its prediction at a feature vector $\bx'$ is \textit{not} significantly perturbed, after the classifier is updated via stochastic gradient descent at a (labe…

ARGEN method improves variable selection and regularization in high-dimensional sparse models.

Corrects errors in previous work on linear elasticity calculations.

Elasticity images map biomechanical properties of soft tissues to aid in the detection and diagnosis of pathological states. In particular, quasi-static ultrasonic (US) elastography techniques use force-displacement measurements acquired during an US scan to parameterize the spatio-temporal stress-strain behavior. Curr…

Distributed machine learning training is one of the most common and important workloads running on data centers today, but it is rarely executed alone. Instead, to reduce costs, computing resources are consolidated and shared by different applications. In this scenario, elasticity and proper load balancing are vital to…

In this letter, we consider the problem of recovering an unknown sparse signal from noisy linear measurements, using an enhanced version of the popular Elastic-Net (EN) method. We modify the EN by adding a box-constraint, and we call it the Box-Elastic Net (Box-EN). We assume independent identically distributed (iid) r…

Renet improves Elastic Net by dynamically selecting between convex blending and refitting, enhancing prediction accuracy.

Revisits elastic string model to explain interest rate correlations.

The elastic energy functional of a thin elastic rod or sheet is generalized to the case of an M-dimensional manifold in N-dimensional space. We derive potentials for the stress field and curvatures and find the generalized von Karman equations for a manifold in elastic equilibrium. We perform a scaling analysis of an M…

Within the framework of statistical learning theory we analyze in detail the so-called elastic-net regularization scheme proposed by Zou and Hastie for the selection of groups of correlated variables. To investigate on the statistical properties of this scheme and in particular on its consistency properties, we set up …

The wave equation $u_{tt} = c^2 u_{xx}$ is generally regarded as a linear approximation to the equation describing the amplitude of a transversely vibrating elastic string in the plane. But, as is shown in \cite{BC96}, the assumption of transverse vibration in fact implies that the wave equation describes the vibration…

In this paper, we propose a one-pass algorithm on MapReduce for penalized linear regression \[f_λ(α, β) = \|Y - α\mathbf{1} - Xβ\|_2^2 + p_λ(β)\] where $α$ is the intercept which can be omitted depending on application; $β$ is the coefficients and $p_λ$ is the penalized function with penalizing parameter $λ$. $f_λ(α, β…

We minimize a linear combination of the Willmore and the length functional among networks in $\mathbb{R}^d$ belonging to a given class determined by the number of curves, the order of the junctions and the angles between curves at the junctions. Since this class lacks compactness, we characterize the set of limits of s…

We consider an infinite 3-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis which give…

The Poisson problem consists in finding an immersed surface $Σ\subset\mathbb{R}^m$ minimising Germain's elastic energy (known as Willmore energy in geometry) with prescribed boundary, boundary Gauss map and area which constitutes a non-linear model for the equilibrium state of thin, clamped elastic plates originating f…

Analyzes properties of stiffness tensors for elastic wave imaging.

This paper introduces an elasticity reconstruction method based on local displacement observations of elastic bodies. Sparse reconstruction theory is applied to formulate the underdetermined inverse problems of elasticity reconstruction including unobserved areas. An online local clustering scheme called a superelement…

The theme in this paper is the recombining binomial tree to price American put option when the underlying stock follows constant elasticity of variance(CEV) process. Recombining nodes of binomial tree are decided from finite difference scheme to emulate CEV process and the tree has a linear complexity. Also it is deriv…

We discuss some differential geometry pertaining to continuum mechanics and the route recently taken by D.N. Arnold, R.S. Falk, and R. Winther in deriving new improved finite element schemes in linear elasticity from constructions in projective geometry.

Elastic Cash adjusts money supply to stabilize interest rates.

LIT-LVM improves linear predictors by estimating interaction terms with latent vectors.

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target is linear this inequali…

Approximate 3D elastic curves with exact constraints

Paper introduces a new IV regression method for mixed-frequency data.

The paper studies rigidity and continuity in nonlinear elasticity on manifolds and hypersurfaces.

Study preserves planar and graphical properties of curves under elastic flow.

RENT selects stable features for robust model interpretation.

A new algorithm computes elastic shape distances between curves efficiently.

The paper studies the free elastic flow of closed curves and finds their asymptotic shape converges to a circle.

Motivated by the problem of finding an explicit description of a developable narrow Moebius strip of minimal bending energy, which was first formulated by M. Sadowsky in 1930, we will develop the theory of elastic strips. Recently E.L. Starostin and G.H.M. van der Heijden found a numerical description for an elastic Mo…

Study on migrating elastic flows of curves across half-planes.