Improves functional linear regression with shape transfer learning.
problem Data scarcity in functional linear models.
method Shape-based transfer learning from auxiliary to target domains.
result Enhances robustness and generalizability of functional linear models.
New method groups similar functional covariates for better modeling.
problem Analyzing functional covariates with similar shapes.
method Coefficient shape alignment regularization approach.
result True grouping structure can be accurately identified under certain conditions.
We simplify complex regression coefficients using linearization and feature comparison.
problem Interpreting high-dimensional regression coefficients from nonlinear responses.
method Developed a linearization method to derive feature coefficients and compare them with regression coefficients.
result Shows how regression coefficients relate to linearized feature coefficients and how they change under regularization.
A novel regression algorithm uses shape analysis to predict curves without training data.
problem Predicting curves without training data for regression problems.
method Shape analysis of trained models to generate new shapes for prediction.
result Successfully predicts curves based on shape analysis of existing models.
Identifies smooth curves for financial models.
problem Consistent term structures with flexible diffusion.
method Analyzes manifolds of curves for Heath-Jarrow-Morton models.
result Term structures cannot be affine but must be linear-rational.
Local deformation factors for 3D shapes improve flexibility and interpretability.
problem Global support of shape deformation factors limits flexibility and interpretability.
method Graph-based structured matrix factorisation with sparsity and graph-based regularisation.
result Local support deformation factors outperform global ones in generalisation and shape reconstruction.
Study S-shaped utility maximization with VaR constraint and unobservable drift.
problem Maximizing utility with a Value at Risk (VaR) constraint and unknown drift.
method Bayesian filter, concavification principle, change of measure, semi-closed integral representation, algorithms (Lagrange, simulation, deep neural network).
result Critical wealth level determining solution feasibility and optimal solution existence.
The paper sharpens bounds on eigenvalue gaps on Riemannian manifolds.
problem Investigating the upper bounds of eigenvalue gaps on Riemannian manifolds.
method Constructing new trial functions to obtain sharp upper bounds.
result Affirmatively answers a conjecture about eigenvalue gaps.
Planes are the only calibrated submanifolds with flat normal bundles.
problem Characterizing submanifolds with specific geometric properties.
method Using constant-coefficient differential forms and parallel calibrations.
result Calibrated submanifolds with flat normal bundles are planes.
Classifies trees with strictly unimodal q-polynomials.
problem Classifying rooted trees with strictly unimodal q-polynomials.
method Classification based on plucking polynomials and criteria for trapezoidal shapes.
result Generalizes results on strict unimodality of q-binomial coefficients.
New method uses SPHARM coefficients to classify AD, MCI, and controls.
problem Discriminating between AD, MCI, and normal aging.
method Spherical harmonics (SPHARM) coefficients for hippocampal shape modeling, SVM classification, feature selection.
result High accuracy in classifying AD vs controls (94%) and MCI vs controls (83%).
Bayesian optimisation for expensive experiments with shape prior.
problem Expensive experiments with time-varying control variables.
method Developed a novel Bayesian optimisation framework using Bernstein polynomial basis and dynamic polynomial degree adjustment.
result Demonstrated effectiveness on polymer fibre design and learning rate optimisation.
Divide knots and links, defined by A'Campo in the singularity theory of complex curves, is a method to present knots or links by real plane curves. The present paper is a continuation of the author's previous result that every knot in the major subfamilies of Berge's lens space surgery (i.e., knots yielding a lens spac…
New friction model for geometric locomotion systems.
problem Modeling asymmetric friction in locomotion systems.
method Introducing asymmetric friction into geometric locomotion models using Finsler metrics.
result Generalized motility map for systems with asymmetric friction.
TLRS improves predictive power of mined formulaic alpha factors.
problem Sparse rewards in RL for mining formulaic alpha factors.
method Trajectory-level Reward Shaping (TLRS) with reward centering.
result TLRS boosts predictive power by 9.29% over existing methods.
High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current understanding of galaxy formation and evolution rests sensitively on relationships between…
A microeconomic model is developed, which accurately predicts the shape of personal income distribution (PID) in the United States and the evolution of the shape over time. The underlying concept is borrowed from geo-mechanics and thus can be considered as mechanics of income distribution. The model allows the resoluti…
CNN predicts airfoil lift coefficients across various conditions.
problem Developing a CNN for predicting airfoil lift coefficients under different conditions.
method Trained multiple CNN architectures on airfoil lift coefficients with varying flow conditions and object geometries.
result CNN model shows competitive prediction accuracy with minimal geometric constraints.
Compactness proven for isospectral Birkhoff billiard tables.
problem Proving compactness of isospectral Birkhoff billiard tables.
method Derived a hierarchical structure for integral invariants and used interpolating Hamiltonian.
result Compactness of equivalence classes of marked length isospectral Birkhoff billiard tables.
Optimizes material distribution on surfaces using topological derivatives.
problem Optimal distribution of two materials on smooth submanifolds in Rd. method Topological derivative approach for shape optimization constrained by PDEs.
result Numerical solution of topology optimization problem on surfaces.
The nullspace and regularization impact high-dimensional linear regression interpretability.
problem Interpreting high-dimensional linear regression coefficients in complex data.
method Optimization formulation to compare coefficients and physical knowledge.
result Regularization and z-scoring choices affect interpretability and true coefficient closeness.
Proves solution uniqueness for biomembrane shape prediction.
problem Proving solution uniqueness for the genus one Canham variational problem.
method Combining numeric analytic continuation and singularity analysis to prove non-negativity of a sequence.
result Proves positivity of the sequence, leading to solution uniqueness.
A new method combines EMD and diffusion maps for protein shape analysis.
problem Learning shape spaces of flexible macromolecules.
method Combines Earthmover's distance with diffusion maps for dimensionality reduction.
result EMD-based diffusion maps require fewer samples to recover intrinsic geometry.
Investigates surfaces with prescribed mean and skew curvatures in Lorentz-Minkowski space.
problem Finding surfaces with prescribed mean and skew curvatures in Lorentz-Minkowski space.
method Rewriting the equations for mean and skew curvatures as linear first order ODEs with coefficients in hypercomplex numbers or real numbers.
result Solutions for surfaces of revolution with prescribed mean and skew curvatures.
This paper proposes the k-generalized distribution as a model for describing the distribution and dispersion of income within a population. Formulas for the shape, moments and standard tools for inequality measurement - such as the Lorenz curve and the Gini coefficient - are given. A method for parameter estimation is …
We find the shape of the Donaldson invariants of a 4-manifold with b_1=0 and b^+>1, which may be not of simple type. The invariants appear as the q^0 coefficient of a expression given in terms of modular forms (as was predicted by Moore and Witten). We re-express the formula using complete elliptic integrals to prove a…
New MMM captures hierarchical marketing effects and sign restrictions.
problem Measuring effectiveness of marketing activities with hierarchical structure and sign constraints.
method Proposes a constrained maximum likelihood approach using Hamiltonian Monte Carlo algorithm.
result Demonstrates superior performance on real datasets compared to multi-stage methods.
T-Basis represents neural network tensors with fewer parameters.
problem Efficiently representing neural network tensors with fewer parameters.
method T-Basis uses Tensor Rings to represent tensors in a neural network, parameterizing them with a small number of coefficients.
result T-Basis achieves high compression rates with minimal performance loss.
Researchers confirm Mark Kac's question for specific 3D and 4D orbifold lens spaces.
problem Can one hear the shape of a drum?
method Investigated 3D and 4D lens spaces, used heat kernel coefficients.
result Confirmed isospectrality for specific lens spaces, showed coefficients not sufficient.
Method flattens complex surfaces with consistent density and shape.
problem Shape deformations and local geometric distortions in density-equalizing maps for multiply-connected surfaces.
method Formulates density diffusion as a quasiconformal flow, solving an energy minimization problem involving the Beltrami coefficient to ensure bijectivity and control distortion.
result Achieves optimal parameterization of multiply-connected surfaces with bijective and controlled geometric distortions.
The paper studies curvature measures and volume-preserving flows on convex bodies.
problem Characterizing and understanding convex bodies through anisotropic curvature measures.
method Developed anisotropic curvature measures, used Minkowski formulas and Heintze-Karcher inequalities, and analyzed volume-preserving flows.
result Characterized Wulff shapes via anisotropic curvature measures and proved convergence of volume-preserving flows.
Paper introduces rational Gaussian wavelets for efficient signal approximation.
problem Efficiently approximating complex signals with few coefficients.
method Continuous wavelet transform using rational Gaussian wavelets with adjustable parameters.
result Proposed rational Gaussian wavelets provide accurate signal approximations.
Proposes adaptive ridge regression for functional linear models with piecewise shapes.
problem Functional linear regression with unknown coefficient function.
method Adaptive piecewise function template with L2 penalization. result Improves predictive power and interpretability compared to standard methods.
Classifies negative-twisting structures on Seifert fibred spaces using Heegaard Floer homology.
problem Classifying negative-twisting tight contact structures on Seifert fibred spaces.
method Adapting Ozsváth-Szabó full path algorithm to star-shaped graphs and using Heegaard Floer homology.
result Complete classification of negative-twisting structures on Seifert fibred spaces.
Study shows how to make 3D shapes hyperbolic with specific curves.
problem Understanding hyperbolic structures on 3-manifolds.
method Analyzing Heegaard splittings and using specific curves to prove hyperbolicity.
result Computed the length of a curve in terms of projection coefficients.
It is proved that every knot in the major subfamilies of J. Berge's lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped (real) plane curve as a "divide knot" defined by N. A'Campo in the context of singularity theory of complex curves. For each knot given by Berge's parame…
The paper proves unique determination of Dehn fillings in hyperbolic 3-manifolds.
problem Unique determination of Dehn fillings in hyperbolic 3-manifolds with non-symmetric cusps.
method Analyzes core geodesics and their holonomies in Dehn fillings of hyperbolic 3-manifolds.
result Dehn fillings with sufficiently large coefficients are uniquely determined by the product of core geodesics' holonomies.
In this paper we develop a new theory of infinitesimal harmonic deformations for compact hyperbolic 3-manifolds with ``tubular boundary''. In particular, this applies to complements of tubes of radius at least $R_0 = \arctanh(1/\sqrt{3}) \approx 0.65848$ around the singular set of hyperbolic cone manifolds, removing th…
A new geometric perceptron model improves 3D shape classification.
problem Challenges in geometric tasks involving point clouds using machine learning.
method Introduces multilayer geometric perceptron (MLGP) with geometric neurons.
result MLGP outperforms vanilla MLP in 3D shape classification and noise resistance.
Quasi-conformal (QC) theory is an important topic in complex analysis, which studies geometric patterns of deformations between shapes. Recently, computational QC geometry has been developed and has made significant contributions to medical imaging, computer graphics and computer vision. Existing computational QC theor…
Language models fail to process hallucinated responses, and this study diagnoses the failure.
problem Language models fail to process hallucinated responses, leading to over-concentration or diffuse attention.
method The study uses forced scoring of benchmark-labeled responses to compute attention shapes and analyze the symmetric component of the degree-normalized attention operator.
result The study proves that every transpose-invariant spectral diagnostic of the attention operator is orientation-blind and bounds the sensitivity of any Lipschitz diagnostic by the asymmetry coefficient \(G\).
Enhanced deep learning model improves tumor segmentation in ultrasound images.
problem Challenges in integrating patient-specific medical priors into deep learning models.
method Integrates visual saliency into a U-Net architecture with attention blocks.
result Achieved a Dice similarity coefficient of 90.5 percent on a dataset of 510 images.
Study of hyperbolic 3-manifolds via fractional Dehn twists and cusp geometry.
problem Understanding the geometry of fibred hyperbolic 3-manifolds via combinatorial data.
method Relating Euclidean cusp geometry to fractional Dehn twist coefficients of monodromies.
result Uniform bounds on fractional Dehn twist coefficients for certain open book decompositions.
Paper develops a new method for curve matching using elastic metrics.
problem Matching unparametrized curves with elastic metrics.
method Develops a relaxed variational formulation for curve matching, integrating H2-metrics and quotienting out similarity groups. result Proposes a method that avoids optimizing over the reparametrization group and can handle boundary constraints.
By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the…
Recent advances suggest that encoding images through Symmetric Positive Definite (SPD) matrices and then interpreting such matrices as points on Riemannian manifolds can lead to increased classification performance. Taking into account manifold geometry is typically done via (1) embedding the manifolds in tangent space…
Flexible semiparametric model estimates volatility without strong assumptions.
problem Dynamic financial market volatility estimation with strong assumptions.
method Bayesian model averaging for flexible news impact function estimation.
result Semiparametric model learns news impact function from data.
Geomstats introduces shape module for analyzing shapes of objects.
problem Analyzing shapes of objects represented as landmarks, curves, and surfaces.
method Implementing shape spaces, group actions, fiber bundles, quotient spaces, and Riemannian metrics.
result Users can compare, average, and interpolate shapes inside shape spaces.