Study on evolving interfaces with complex curvature and density effects.
problem Understanding the dynamics of evolving heterogeneous elastic interfaces.
method Modeling an evolving curve with a density function, analyzing the associated gradient flow evolution.
result Analysis of the preservation and asymptotic behavior of geometric properties in the evolving system.
Common models for two-phase lipid bilayer membranes are based on an energy that consists of an elastic term for each lipid phase and a line energy at interfaces. Although such an energy controls only the length of interfaces, the membrane surface is usually assumed to be at least C1 across phase boundaries. We consi…
Study proves rigid spectral properties of planets with metric discontinuities.
problem Establishing spectral rigidity for spherically symmetric planets with discontinuities.
method Novel trace formula applied to two wave types in spherically symmetric manifolds with boundary and interior interfaces.
result Spectral rigidity of spherically symmetric planets with discontinuities is proven.
Variational approximations for curve flows on Riemannian manifolds.
problem Approximating solutions to curvature and elastic flow problems on Riemannian manifolds.
method Variational formulations, finite element approximations, piecewise linear elements, stability analysis.
result Derived schemes can compute rotationally symmetric self-shrinkers and geodesics.
Cyanure is an open-source C++ software package with a Python interface. The goal of Cyanure is to provide state-of-the-art solvers for learning linear models, based on stochastic variance-reduced stochastic optimization with acceleration mechanisms. Cyanure can handle a large variety of loss functions (logistic, square…
Analyzes properties of stiffness tensors for elastic wave imaging.
problem Characterizing stiffness tensor fields for elastic wave imaging.
method Finsler-geometric methods applied to anisotropic stiffness tensor fields.
result Conditions for Finsler-geometric methods to be applicable.
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.
problem Stabilizing interest rates in a decentralized system.
method Modifies supply to keep interest rate fixed by public market.
result Improves elasticity of US Dollar and new cryptocurrencies.
Characterizes null Lagrangians in Cosserat elasticity.
problem Understanding null Lagrangians in micropolar elasticity.
method Applying Olver and Sivaloganathan's theorem to characterize null Lagrangians.
result Complete characterization of null Lagrangians for three-dimensional bodies and shells.
Approximate 3D elastic curves with exact constraints
problem Designing and approximating 3D elastic curves
method Numerically stable method for recovering 11 parameters
result Fast and stable approximation of arbitrary curves
The paper studies rigidity and continuity in nonlinear elasticity on manifolds and hypersurfaces.
problem Rigidity and continuity properties of elastic bodies in non-Euclidean settings.
method Geometric rigidity estimates, asymptotic rigidity of elastic membranes, simplified geometric proof of continuous dependence.
result Established geometric rigidity estimate and proved asymptotic rigidity of elastic membranes.
Study preserves planar and graphical properties of curves under elastic flow.
problem Maintaining planar and graphical properties of non-compact curves under elastic flow.
method Extended recent work on adapted elastic energy to derive thresholds for planar and graphical embeddedness.
result Derived new Li--Yau type inequality for complete planar curves.
The paper studies the free elastic flow of closed curves and finds their asymptotic shape converges to a circle.
problem Challenges in studying the asymptotic behavior of the free elastic flow for closed curves.
method Analysis of the free elastic flow as an L2-gradient flow for Euler's elastic energy. result An appropriate rescaling of initial curves geometrically close to circles converges to a unique round 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.
problem Migrating elastic flows of curves from upper to lower half-planes.
method Analytical and numerical construction of migrating elastic flows.
result Construction of various migrating elastic flows.
Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.
problem Recover stiffness tensor and density from Dirichlet-to-Neumann map.
method Analyze invariance under coordinate transformations and gauge freedoms.
result Present gauge freedoms in the Dirichlet-to-Neumann map for Riemannian elastic wave equation.
Solves curve migration problem with elastic flows.
problem Curve migration problem with natural boundary conditions.
method Constructing migrating elastic flows.
result Extends previous work to purely local flow.
New insights into stability of special curves on spheres.
problem Stability of closed p-elastic curves on spheres. method Analytical proof and construction of curves.
result All closed spherical p-elastic curves for p∈(0,1) are unstable. 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,…
Symmetric elastic knots are found for certain classes with dihedral symmetry.
problem Finding elastic knots with specific symmetries.
method Minimizing bending energy under dihedral symmetry constraints.
result Existence of dihedral symmetric elastic knots, including a figure-eight union for the trefoil.
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.
problem Elasticity in non-Euclidean ambient spaces with incompatible local rest distances.
method Γ-convergence to derive a limit elastic model, relating minimum energy to curvature discrepancy.
result Linearized version of a conjecture in elasticity confirmed, linking energy to curvature.
Study shows diffused interface flows to single diffused balls over time.
problem Volume-preserving mean curvature flow in Euclidean space.
method Diffused interface version, exponential convergence proof.
result Exponential convergence to single diffused balls.
New discrete curves defined in space forms with geometric properties.
problem Defining discrete elastic and constrained elastic curves in space forms.
method Extending discrete Euclidean curvature to space forms and using Bäcklund transformations.
result Discrete elastic and constrained elastic curves are elements of a curve hierarchy.
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…
The elastic flow, which is the L2-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.
problem Understanding the evolution of curves and networks under elastic forces.
method Unified presentation and proof of global existence and convergence for closed curves.
result Global existence and smooth convergence to critical points for closed curves in R^2.
Study on elastic curves with variable stiffness, derived from bending energy.
problem Modeling elastic wires with varying thickness.
method Derive Euler-Lagrange equations for curves with variable bending stiffness.
result Characterizations of elastic curves with variable stiffness.
Study on closed p-elastic curves in hyperbolic and de Sitter planes.
problem Existence of closed p-elastic curves with nonconstant curvature. method Analysis of p-elastic curves in hyperbolic and de Sitter planes. result Existence of closed p-elastic curves in hyperbolic plane for p>1; in de Sitter plane for p<0. In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, Rk. We prove the Γ-convergence of elastic energies for configurations of a converging sequence, Mn→M, of body manifolds. This convergence result …
Study on Transfer Elastic Net error bounds and grouping effect.
problem Estimation error and grouping effect in Transfer Elastic Net.
method Derives non-asymptotic error bound and examines grouping effect scenarios.
result Effective error bounds and grouping effect observed in Transfer Elastic Net.
Study shows global invertibility in nonlinear elasticity with vanishing self-repulsion term.
problem Global invertibility in nonlinear elasticity with a vanishing nonlocal self-repulsion term.
method Proves global invertibility in the Γ-limit of elastic energy with a vanishing nonlocal self-repulsion term. result Global invertibility can be obtained in the Γ-limit of the elastic energy with a vanishing nonlocal self-repulsion term. Study on spectral asymptotics in elasticity on smooth manifolds.
problem Analyzing spectral asymptotics in linear elasticity on smooth manifolds.
method Established two-term spectral asymptotics for boundary value problems in linear elasticity.
result Corrected erroneous results in previous studies.
Study on surfaces minimizing elastic energy with boundary constraints.
problem Finding stable configurations of surfaces with elastic boundaries and surface energy.
method Investigation of critical surfaces with mean curvature and spontaneous curvature, coupled to boundary elastic energy.
result Characterization and minimization of surface energy for specific topological shapes.
Study on elasticity with mixed boundary conditions, proving spectral asymptotics.
problem Analyzing spectral asymptotics for linear elasticity with mixed boundary conditions.
method Established two-term spectral asymptotics for linear elasticity on smooth compact manifolds.
result Verification of general formulae through explicit examples in 2D and 3D.
In this paper, the elastic Dirichlet-to-Neumann map Ξg is studied for the stationary elasticity system in a compact Riemannian manifold (Ω,g) with smooth boundary ∂Ω. By overcoming methodological difficulties, we explicitly get matrix-valued full symbol for the elastic Dirichlet-to-Neumann map Ξg. We …
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…
Optimal thresholds ensure curves remain embedded in flows.
problem Preserving the embeddedness of elastic flows of curves.
method Variational characterization and minimization of bending energy.
result Optimal thresholds for preserving embeddedness are found.
Study of red blood cells using elastic surface theory.
problem Understanding the shape of red blood cells.
method Used Helfrich-Canham functional to model red blood cells as elastic surfaces.
result Cassinian ovals, except for the round sphere, do not solve the shape equation.
Straight lines are a basin of attraction for the elastic flow at least to level 1.9615π.
problem Understanding the basin of attraction for the free boundary free elastic flow.
method Steepest descent gradient flow for elastic energy, numerical evidence.
result Straight lines have a basin of attraction at least to level 1.9615π.
Model for material elasticity and plasticity using networks.
problem Understanding the elasticity and plasticity of materials.
method Developed a mathematical model based on networks, defining tension tensor for periodic graphs.
result The model explains elasticity and plasticity through local moves on graphs.
Study on hyperbolic elastic flow, proving convergence and quantifying singularities.
problem Understanding singularities and convergence of elastic flow in hyperbolic plane.
method Analyzes closed and open curves with clamped boundary conditions, proving convergence without small energy assumption.
result Each singularity carries an energy cost of at least 8, and blow-ups are explicitly classified.
New interface explains contextual bandits to non-experts.
problem Interpreting and managing contextual bandits for non-expert operators.
method Developed a metric 'value gain' for off-policy evaluation and designed an interface to explain bandit behavior.
result Empowered non-experts to manage complex machine learning systems through accessible presentation.
We investigate the elastic behavior of knotted loops of springy wire. To this end we minimize the classic bending energy Ebend=∫κ2 together with a small multiple of ropelength R=length/thickness in order to penalize selfintersection. Our main objective is to characterize elastic…
Study on dynamic curves with elastic energy and spontaneous curvature.
problem Modeling and analyzing dynamic planar curves with elastic energy.
method Gradient flow of inclination angle, nonlocal quasilinear system, local well-posedness, global existence, convergence.
result Local well-posedness, global existence, convergence of the flow for weak regularity initial data.
Efficiently solves Elastic Net in high dimensions with Newton method.
problem Feature selection in high-dimensional data with non-negligible collinearity.
method Semi-smooth Newton Augmented Lagrangian Method.
result Significantly reduces computational cost compared to competitors.
Statistical arbitrageurs have inelastic demand, contrary to classical models.
problem Understanding the demand elasticity of statistical arbitrageurs.
method Thirteen models from the literature and a quantitative equilibrium model.
result Aggregate demand remains inelastic even with statistical arbitrageurs.
The paper finds curves minimizing elastic energy pinned at endpoints.
problem Finding curves that minimize elastic energy with fixed endpoints.
method Applying the shooting method to identify and classify critical points.
result Critical points consist of wavelike elasticae, and minimizers have no loops or interior inflection points.