The paper studies elastic lines on surfaces in Galilean space.
problem Characterizing elastic lines on oriented surfaces in Galilean space.
method Developed Euler-Lagrange equations and used variational method.
result Investigated whether relaxed elastic curves lie on geodesics.
The paper studies surfaces with spherical curvature lines and their generation by constrained elastic curves.
problem Understanding surfaces with spherical curvature lines and their generation mechanisms.
method The approach involves Lie sphere transformations, Legendre curves, and polynomial conserved quantities of connections.
result Lie applicable surfaces with exactly one family of spherical curvature lines are generated by the lift of constrained elastic curves.
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.
Let α(s) be an arc on a connected oriented surface S in E3, parameterized by arc length s, with torsion τ and length l. The total square torsion F of α is defined by T=\int_{0}^{l}τ^{2}ds\ $. . The arc α is called a relaxed elastic line of second kind if it is an extremal for the variational problem of minimizing the v…
Let α be an arc on a connected oriented surface S in Minkowski 3-space, parameterized by arc length s, with torsion τ and length l. The total square torsion H of α is defined by . The arc is called a relaxed elastic line of second kind if it is an extremal for the variational prob…
Characterizes winding of braided vector fields in tubular domains.
problem Understanding the topology of braided vector fields in complex domains.
method Defines field line winding as a measure of entanglement, proving its uniqueness in classifying vector field topology.
result Field line winding uniquely classifies the topology of braided vector fields.
Neural networks struggle with certain geometric problems, but not all.
problem Neural networks' limitations in modeling certain geometric problems.
method Illustration through specific examples and analysis of integral functionals.
result There is no energy gap between Barron functions and Lipschitz functions for a large class of integral first-order functionals.
Bicycle paths form geodesics in 3D subspaces, related to Kirchhoff rods.
problem Optimizing bicycle paths between two points.
method Variational equations and geometric analysis of bicycle paths.
result Bicycle geodesics are contained in 3D subspaces and relate to Kirchhoff rods.
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical properties, e.g. the principal curvature directions dynamics on surfaces or the stress…
Study p-Willmore disks with boundary energies, finding equilibrium configurations.
problem Finding equilibrium configurations for p-Willmore disks with boundary energies.
method Model boundary as Kirchhoff elastic rod, interior term dependent on mean and Gaussian curvatures. Study among topological disks and p-Willmore examples.
result Equilibrium configurations for p-Willmore disks with boundary energies.
The past years have witnessed many dedicated open-source projects that built and maintain implementations of Support Vector Machines (SVM), parallelized for GPU, multi-core CPUs and distributed systems. Up to this point, no comparable effort has been made to parallelize the Elastic Net, despite its popularity in many h…
Researchers prove a generalized Piola identity for Riemannian manifolds.
problem Generalizing the Piola identity to Riemannian settings.
method Two approaches: Euclidean derivation and variational interpretation via Null-Lagrangians.
result Proof of generalized Piola identity for Riemannian manifolds.
Stable knots and links can exist in electromagnetic fields.
problem Stability of knots and links in electromagnetic fields.
method Proving the existence of electromagnetic fields preserving link topology.
result Every link can be realized as stable field lines in electromagnetic fields.
New method shortens and straightens curves, proving convergence and well-posedness.
problem Shortening and straightening of curves.
method Conceptual shift in curve shortening to tangent aligning, variational study of geometric flows.
result Proves convergence to a straight line and global well-posedness for various geometric flows.
Study on buckling of cylindrical shells using elastic energy scaling.
problem Buckling behavior of cylindrical shells under compression.
method Scaling analysis and solution of an obstacle problem for minimal elastic energy.
result Explicit bifurcation point between compression and buckling determined.
Revisits elastic string model to explain interest rate correlations.
problem Describing the forward interest rate curve using an elastic string model.
method Reinterprets Baaquie and Bouchaud's (2004) model to highlight market forces.
result Model accurately reproduces FRC correlation structure with minimal parameters.
Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an energetic point of view in recent years. Such pores permit targeted delivery of dru…
In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution …
Sparse elasticity reconstruction from local displacements reduces error.
problem Reconstructing elasticity from limited data.
method Sparse elasticity reconstruction theory, local clustering, alternating optimization.
result Higher spatial resolution elasticity distribution estimation.
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.
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.
Proposes using elastic demand to improve forecasting accuracy.
problem Mismatch between planned supply and actual demand due to demand variance.
method Reallocate historical elastic demand to reduce forecasting variance.
result Improves forecasting and supply planning effectiveness.
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
New algorithm selects genes for cancer classification using adaptive elastic net and conditional mutual information.
problem Selecting informative genes for microarray cancer classification.
method Adaptive Elastic Net with Conditional Mutual Information (AEN-CMI).
result AEN-CMI achieves the best classification performance with fewer genes.
Stable discretizations for elastic flow on Riemannian manifolds.
problem Discretizing elastic flow on curved spaces.
method Conformally flat Riemannian manifolds discretization.
result Robust and quadratic convergence of the method.
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. 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.
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.
Local elasticity in neural networks makes predictions resilient to dissimilar updates.
problem Understanding resilience of neural network predictions to updates from dissimilar data.
method Simulation and geometric interpretation using neural tangent kernel.
result Local elasticity persists in neural networks with nonlinear activation functions, not in linear ones.
We analyze the linear response of a market network to shocks based on the bipartite market model we introduced in an earlier paper, which we claimed to be able to identify the time-line of the 2009-2011 Eurozone crisis correctly. We show that this model has three distinct phases that can broadly be categorized as "stab…
Study elastic Dirichlet-to-Neumann map to uniquely determine metrics and spectral invariants.
problem Uniquely determine metrics of Riemannian manifolds from elastic Dirichlet-to-Neumann maps.
method Explicitly get matrix-valued full symbol for elastic Dirichlet-to-Neumann map, prove metric uniqueness, calculate spectral invariants.
result Elastic Dirichlet-to-Neumann map uniquely determines the metric of a real-analytic Riemannian manifold.
Enhanced Elastic-Net with box-constraint improves support recovery in noisy measurements.
problem Support recovery of sparse signals from noisy measurements.
method Box-Elastic Net (Box-EN) method with mean squared error and probability of support recovery analysis.
result The Box-Elastic Net outperforms the standard Elastic-Net in support recovery.
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.
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 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. Deep learning predicts synergistic drug combinations from multi-omics data.
problem Predicting effective drug combinations to overcome cancer drug resistance.
method AuDNNsynergy model integrating gene expression, copy number, genetic mutation data and drug properties.
result AuDNNsynergy model outperforms state-of-the-art approaches.
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.