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.
Cartesian neural network models learn soft tissue mechanical properties without shape assumptions.
problem Model-based methods limit elastography to imaging linear-elastic parameters.
method Data-driven neural network constitutive models (NNCMs) learn stress-strain relationships from force-displacement data.
result NNCMs can characterize mechanical properties and their spatial distribution without prior shape knowledge.
Dynamic SGD improves deep learning performance in elastic distributed training.
problem Dealing with varying numbers of machines in elastic distributed training environments.
method Smoothly adjust the learning rate over time to mitigate noisy momentum estimation.
result Dynamic SGD achieves stabilized performance across different numbers of GPUs.
AI-enhanced product embeddings boost demand analysis accuracy.
problem Traditional demand analysis struggles with nuanced product attributes.
method Combining text, images, and tabular data with transformer embeddings for causal inference.
result AI-enhanced embeddings improve sales rank and price predictions.
The generation of artificial data based on existing observations, known as data augmentation, is a technique used in machine learning to improve model accuracy, generalisation, and to control overfitting. Augmentor is a software package, available in both Python and Julia versions, that provides a high level API for th…
Enhances ML model explanations through Bayesian non-parametric approach.
problem Difficulty in understanding and interpreting ML model decisions.
method Augments a Bayesian non-parametric regression mixture model with elastic nets.
result Empirically outperforms state-of-the-art techniques in explaining individual decisions.
DET unifies geometric and functional alignment for high-dimensional scientific data.
problem Challenges in nonrigid registration for high-dimensional, irregular data.
method Domain Elastic Transform (DET) treats data as functions on irregular domains, using a Bayesian framework for elastic motion registration.
result DET achieves 92% topological preservation on MERFISH data and successfully registers whole-embryo Stereo-seq atlases.
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.
This work introduces methods to compute optimal Monge maps and learn elastic costs for efficient data mapping.
problem Efficiently mapping one probability distribution to another using elastic costs.
method Proposes numerical methods to compute optimal Monge maps and a learning loss for parameterized regularizers.
result Proves the optimality of computed Monge maps and learns the parameters of elastic costs.
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.
NeuralWarp aligns time-series indices using deep learning for improved similarity.
problem Need for elastic time-series similarity measures.
method Proposes NeuralWarp, a deep learning model for aligning time-series indices.
result NeuralWarp outperforms non-parametric and un-warped deep models.
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.
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 L2 and L∞ distortion me…
Elastic-InfoGAN learns object identity in class-imbalanced data.
problem Learning disentangled representations in class-imbalanced data.
method Invariance to identity-preserving transformations to learn object identity.
result Effectiveness in disentangling object identity in imbalanced datasets.
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.
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.
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.
New SSIM measure improves adversarial attacks' perceptual quality.
problem Lack of perceptual quality in traditional adversarial attacks.
method Replaced Lp norms with SSIM measure for better quality. result SSIM-constrained attacks achieve better quality and similar success rate.
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. 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. Elastic Gossip distributes neural network training using gossip-like protocols.
problem Distributing neural network training across heterogeneous environments.
method Pairwise-communication using Gossip-like protocols, building on Elastic Averaging SGD.
result Elastic Gossip performs better than Gossiping SGD in experiments, but hyper-parameter search may yield better configurations.
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 extends graph approach to elastic curves with fixed ends.
problem Existence of elastic curves with fixed ends under obstacles.
method Investigates nonexistence of graph solutions and extends curve class.
result Existence result obtained through penalization argument.
Chicle tackles elastic machine learning training by avoiding micro-tasks.
problem Elasticity and load balancing in distributed machine learning training.
method Chicle is a new elastic distributed training framework that exploits machine learning algorithms to implement elasticity and load balancing without micro-tasks.
result Chicle achieves performance competitive with state-of-the-art rigid frameworks while enabling elastic execution and dynamic load balancing.
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.
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.