arXiv research

Paper develops multivariate time series similarity and distance measures.

Reformulates elasticity complex with new differential and Hodge star operators.

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…

The edge of torn elastic sheets and growing leaves often form a hierarchical buckling pattern. Within non-Euclidean plate theory this complex morphology can be understood as low bending energy isometric immersions of hyperbolic Riemannian metrics. With this motivation we study the isometric immersion problem in strip a…

This paper develops a European option pricing formula for fractional market models. Although there exist option pricing results for a fractional Black-Scholes model, they are established without accounting for stochastic volatility. In this paper, a fractional version of the Constant Elasticity of Variance (CEV) model …

Distributing Neural Network training is of particular interest for several reasons including scaling using computing clusters, training at data sources such as IOT devices and edge servers, utilizing underutilized resources across heterogeneous environments, and so on. Most contemporary approaches primarily address sca…

The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology (i) emerges even in zero strain configurations, and (ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key…

Survival month for non-small lung cancer patients depend upon which stage of lung cancer is present. Our aim is to identify smoking specific gene expression biomarkers in the prognosis of lung cancer patients. In this paper, we introduce the network elastic net, a generalization of network lasso that allows for simulta…

We prove a relation between the scaling $h^β$ of the elastic energies of shrinking non-Euclidean bodies $S_h$ of thickness $h\to 0$, and the curvature along their mid-surface $S$. This extends and generalizes similar results for plates [BLS16, LRR] to any dimension and co-dimension. In particular, it proves that the na…

Novel defects in hyperbolic sheets explain complex wrinkling patterns in nature.

In this paper we study a class of Riemannian metrics on the space of unparametrized curves and develop a method to compute geodesics with given boundary conditions. It extends previous works on this topic in several important ways. The model and resulting matching algorithm integrate within one common setting both the …

This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error i…

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…

Elastic Cash adjusts money supply to stabilize interest rates.

Characterizes null Lagrangians in Cosserat elasticity.

Research on time-series similarity measures has emphasized the need for elastic methods which align the indices of pairs of time series and a plethora of non-parametric have been proposed for the task. On the other hand, deep learning approaches are dominant in closely related domains, such as learning image and text s…

Recent studies have highlighted the vulnerability of deep neural networks (DNNs) to adversarial examples - a visually indistinguishable adversarial image can easily be crafted to cause a well-trained model to misclassify. Existing methods for crafting adversarial examples are based on $L_2$ and $L_\infty$ distortion me…

Approximate 3D elastic curves with exact constraints

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

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

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.

Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.

Solves curve migration problem with elastic flows.

New insights into stability of special curves on spheres.

Due to the advantage of achieving a better performance under weak regularization, elastic net has attracted wide attention in statistics, machine learning, bioinformatics, and other fields. In particular, a variation of the elastic net, adaptive elastic net (AEN), integrates the adaptive grouping effect. In this paper,…

What is the longest rope on the unit sphere? Intuition tells us that the answer to this packing problem depends on the rope's thickness. For a countably infinite number of prescribed thickness values we construct and classify all solution curves. The simplest ones are similar to the seamlines of a tennis ball, others e…

Symmetric elastic knots are found for certain classes with dihedral symmetry.

We study a class of elastic energy functionals for maps between planar domains (among them the so-called squared distance functional) whose critical points (elastic maps) allow a far more complete theory than one would expect from general elasticity theory. For some of these functionals elastic maps even admit a "Weier…

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

New discrete curves defined in space forms with geometric properties.

Continual learning based on data stream mining deals with ubiquitous sources of Big Data arriving at high-velocity and in real-time. Adaptive Random Forest ({\em ARF}) is a popular ensemble method used for continual learning due to its simplicity in combining adaptive leveraging bagging with fast random Hoeffding trees…

Demand variance can result in a mismatch between planned supply and actual demand. Demand shaping strategies such as pricing can be used to shift elastic demand to reduce the imbalance. In this work, we propose to consider elastic demand in the forecasting phase. We present a method to reallocate the historical elastic…

New SSIM measure improves adversarial attacks' perceptual quality.

The elastic flow, which is the $L^2$-gradient flow of the elastic energy, has several applications in geometry and elasticity theory. We present stable discretizations for the elastic flow in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples in…

Unified survey of elastic flow for curves and networks.

Study on elastic curves with variable stiffness, derived from bending energy.

Study on closed $p$-elastic curves in hyperbolic and de Sitter planes.

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 …

Study on Transfer Elastic Net error bounds and grouping effect.

Study shows global invertibility in nonlinear elasticity with vanishing self-repulsion term.

Study on spectral asymptotics in elasticity on smooth manifolds.

Study on surfaces minimizing elastic energy with boundary constraints.

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

In this paper, the elastic Dirichlet-to-Neumann map $Ξ_g$ is studied for the stationary elasticity system in a compact Riemannian manifold $(Ω,g)$ with smooth boundary $\partial Ω$. By overcoming methodological difficulties, we explicitly get matrix-valued full symbol for the elastic Dirichlet-to-Neumann map $Ξ_g$. We …

Optimal thresholds ensure curves remain embedded in flows.