Study on minimizing network energy in R^d, introducing degenerate elastic networks.
problem Minimizing network energy in R^d with constraints on curves and junctions.
method Characterizing limits of sequences of networks bounded in energy, providing explicit representation of the relaxed problem.
result Explicit representation of degenerate elastic networks, a new concept involving only given class properties.
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.
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.
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.
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…
Deformation estimation of elastic object assuming an internal organ is important for the computer navigation of surgery. The aim of this study is to estimate the deformation of an entire three-dimensional elastic object using displacement information of very few observation points. A learning approach with a neural net…
We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some properties of the minimal configurations.
Non-uniqueness found in option valuation for certain α values.
problem Non-uniqueness in the value of call options for specific α values.
method Mathematical theory of degenerate parabolic equations and boundary conditions.
result Non-uniqueness explained by initial data outside Täcklind class and absence of boundary condition at infinity.
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.
PIE-PINN estimates elastic properties from noisy, low-res displacement data.
problem Estimating heterogeneous elastic properties from low-resolution, noisy data.
method Probabilistic Physics-Informed Neural Network (PIE-PINN) framework combining B-spline and hierarchical scale model.
result Robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data.
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…
Study on local elasticity in neural network training, improving detection of class-specific changes.
problem Improving the detection of class-specific changes in neural network training.
method Comprehensive study of local elasticity, proposing a new definition to address limitations.
result New definition of local elasticity more sharply detects class-specific changes in neural network training.
A new ride-hailing subsidy system uses deep causal networks to estimate consumer elasticity.
problem Estimating consumer elasticity with subsidies in ride-hailing industry.
method Introduces a consumer subsidizing system using deep causal networks to address confounding effects.
result Effective in estimating the uplift effect of subsidies without confounding.
Study travel time tomography for transversely isotropic media using modified pseudodifferential calculus.
problem Travel time tomography problem for transversely isotropic media.
method Modified scattering pseudodifferential calculus to solve the tomography problem.
result Construction and use of modified pseudodifferential calculus to solve the tomography problem.
EWC helps prevent forgetting in neural networks by adjusting weights dynamically.
problem Preventing forgetting in neural networks during training.
method EWC adjusts weights dynamically to prevent forgetting.
result EWC effectively prevents catastrophic forgetting in neural networks.
The study examines how modernizing settlement infrastructure affects inside money elasticity and network efficiency.
problem Understanding the impact of modernizing settlement infrastructure on inside money elasticity and network efficiency.
method Constructed a panel dataset of 809 reform events across 24 advanced economies, decomposed into economic channels and phases, and used a T2S event-study and synthetic control method.
result Modernizing settlement infrastructure generates network-conditional balance sheet efficiencies, with an estimated +13.4 percent efficiency recovery from 2027-2032.
This study reduces Willmore flows of tori to simpler problems and finds new conformally constrained Willmore tori.
problem Analyzing singularities and existence of Willmore tori under specific constraints.
method Dimension reduction approach, strong relation with elastic flow, necessary condition for singularities, criterion for initial data.
result Existence of new conformally constrained Willmore tori and identification of inverted catenoid as a limit shape.
We introduce elastic geodesic grids for easy-to-fabricate, deployable structures.
problem Approximating freeform surfaces with deployable structures.
method Geodesic curves on target surfaces, kinematic mechanism, differential geometry.
result Elastic geodesic grids can approximate freeform surfaces easily and deployably.
Physics-informed GANs estimate elastic moduli from mechanical tests.
problem Estimating spatially-varying elastic moduli from measured deformations.
method Physics-informed Generative Adversarial Networks (PI-GANs) with PDE constraints.
result Generated stiffness samples match true distribution statistics.
This paper improves neural tangent kernels for better generalization and local elasticity.
problem Performance gap between neural tangent kernels and real-world neural networks.
method Introduces label-aware kernels using Hoeffding decomposition.
result Models trained with proposed kernels simulate NNs better in terms of generalization and local elasticity.
Study models deep learning training dynamics using locally elastic SDEs to reveal feature separability.
problem Understanding how deep learning models separate features from different classes during training.
method Modeling deep learning training using locally elastic SDEs with a drift term reflecting backpropagation impact.
result Local elasticity in SDEs leads to linear separability of features, resulting in vanishing training loss.
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…
IC-Network improves CNNs by integrating elastic collision units.
problem Designing more effective basic units in neural networks.
method Developed IC layer and IC block units combining the IC structure with convolution operations.
result Significant performance improvements in existing CNNs, reducing top-1 error from 22.85% to 21.49% on imagenet.
Classifies pinned p-elasticae and finds unique optimality exponents.
problem Classifying and understanding p-elasticae under pinned boundary conditions. method Classification and analysis of p-elasticae, proving uniqueness and existence. result Discovery of a unique exponent p≃1.5728 for full optimality. 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.
Recent applications of machine learning algorithms in the seismic domain have shown great potential in different areas such as seismic inversion and interpretation. However, such algorithms rarely enforce geophysical constraints - the lack of which might lead to undesirable results. To overcome this issue, we have deve…
Fiber nonlinear interference (NLI) modeling and monitoring are the key building blocks to support elastic optical networks (EONs). In the past, they were normally developed and investigated separately. Moreover, the accuracy of the previously proposed methods still needs to be improved for heterogenous dynamic optical …
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.
Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in Lorentz-Minkowski plane, focusing on spacelike and timelike curves. In this article, we study those curves in $\math…
Noise causes learning plateaus in neural networks.
problem Plateau phenomena in online learning due to vanishing gradients.
method Analysis of stochastic gradient descent in multi-layer perceptrons.
result Noise induces synchronisation leading to strong plateaus.
Blog post discusses various implementations of Fisher Information for EWC in continual learning.
problem Improving Elastic Weight Consolidation (EWC) results by optimizing Fisher Information computation.
method Empirically compares different implementations of Fisher Information for EWC.
result Many reported EWC results can be improved by changing Fisher Information computation methods.
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,…
Structure learning in random fields has attracted considerable attention due to its difficulty and importance in areas such as remote sensing, computational biology, natural language processing, protein networks, and social network analysis. We consider the problem of estimating the probabilistic graph structure associ…
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.
Paper analyzes shapes of brain arterial networks using statistical methods.
problem Quantifying and comparing shapes of brain arterial networks.
method Mathematical representation of BAN shapes as elastic shape graphs, development of Riemannian metrics and geometrical tools.
result Age has a clear, quantifiable effect on BAN shapes, with increased variance in shapes as age increases.