The paper defines a new algebra and provides a basis for it.
problem Understanding knot theory and 3-manifolds through algebraic structures.
method Defined the mixed Hecke algebra and provided a potential basis.
result The potential basis is a spanning set for the algebra.
Unified framework for imbalanced data resampling improves classification performance.
problem Data imbalance negatively impacts machine learning performance.
method Unified framework combining over- and undersampling with radial basis functions optimization.
result Potential Anchoring outperforms state-of-the-art resampling algorithms.
Study shows Calabi-Yau metrics converge to a specific form under certain conditions.
problem Degeneration of Calabi-Yau metrics and their limits.
method Optimal transport problem and minimisation of Kontorovich functional.
result Limit data of Calabi-Yau metrics can be encoded into a unique minimiser.
Option Encoder compresses reinforcement learning options into a policy basis.
problem Redundant options in reinforcement learning frameworks.
method Auto-encoder framework with constrained weights to discover a policy basis.
result Option Encoder reduces the number of options while maintaining performance.
Deep neural network predicts molecular wave functions in minimal basis.
problem Improving accuracy and efficiency in quantum chemistry calculations.
method Adapted SchNet for Orbitals (SchNOrb) model in quasi-atomic minimal basis.
result Model accurately predicts molecular orbital energies and wavefunctions for large molecules.
Paper proposes a method to recover point configurations from noisy distance data.
problem Recovering point configurations from noisy distance data.
method Robust Euclidean Distance Geometry via Dual Basis (RoDEoDB) algorithm.
result Exact recovery guarantees for point configuration and Gram matrix under mild conditions.
Two RBF methods solve complex financial derivatives pricing problems.
problem Pricing derivatives in models with multiple stochastic factors.
method Radial Basis Function Partition of Unity and Radial Basis Function generated Finite Differences methods.
result Both methods achieve high accuracy and are efficient for solving multi-dimensional PDEs.
We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers modes of wealth: random transfer, profit proportional to wealth and motivation of poor agents to …
Sharp results link DLN gradient flow to basis pursuit optimization and GHA phase transitions.
problem Understanding implicit regularization in Diagonal Linear Networks.
method Sharp convergence bounds and characterization of ℓ1 minimizers. result Gradient flow of DLNs with tiny initialization approximates minimizers of basis pursuit optimization problem.
Paper proposes TBSD for efficient anomaly detection in textured images.
problem Challenges in anomaly detection for textured images, especially in manufacturing systems.
method Texture basis integrated smooth decomposition (TBSD) approach.
result TBSD surpasses benchmarks with less misidentification and superior performance.
Gaussian process regression loses locality in high dimensions, affecting molecular energy surface fitting.
problem Loss of locality in high-dimensional Gaussian process regression.
method Analysis of Matern family kernels and multi-zeta basis functions.
result The property of locality disappears in high dimensions, impacting regression quality.
High-order financial derivative pricing method using Radial Basis Functions.
problem Pricing financial derivatives with high accuracy and efficiency.
method Radial Basis Function generated Finite Differences for non-uniform node layouts.
result Fourth-order convergence in space with non-uniform node layouts.
Researchers develop a new basis to simplify solving infinite systems for HOMFLYPT skein module of lens spaces.
problem Computing the HOMFLYPT skein module of lens spaces L(p,1) via braids. method Using a new basis Λ of the HOMFLYPT skein module of the solid torus, relating infinite systems of equations obtained by performing braid band moves on elements in Λ+ and Λ− via a map I. result Reduced complexity in solving the infinite system of equations for L(p,1) using braids. GLIS uses IDW and RBF for efficient global optimization.
problem Expensive objective function in optimization problems.
method Combines inverse distance weighting and radial basis functions for acquisition function.
result Competitive and computationally lighter than Bayesian optimization.
ELD compares graphs by their embedded Laplacian eigenvectors, resolving ambiguities.
problem Comparing graphs of different sizes and structures.
method ELD uses symmetrization and perturbation techniques to compare graph embeddings.
result ELD resolves ambiguities in graph comparisons, making it a natural pseudo-metric.
We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economists quantity theory (MV=PQ). To match the resulting quantity of money with the model assumption of a constant price, w…
This is the first in a series of papers in which we develop a twistor-based method of constructing hyperkaehler metrics from holomorphic functions and elliptic curves. As an application, we revisit the Atiyah-Hitchin manifold and derive in an explicit holomorphic coordinate basis closed-form formulas for, among other t…
Study of characteristic numbers in 24-dimensional String manifolds.
problem Characterizing and understanding characteristic numbers of 24-dimensional String manifolds.
method Using Pontryagin numbers, integral basis of String cobordism group, and divisibility results.
result Established 2- and 3-primary divisibilities of characteristic numbers.
Kernel balancing equalizes covariate distributions to unbiasedly estimate causal effects.
problem Non-uniform distribution of covariates between treated and control groups leads to biased causal effect estimates.
method Kernel balancing targets equal means of a kernel-based approximation of covariates for treated and control groups, producing unbiased ATT estimates.
result Kernel balancing produces weights that equalize the multivariate distribution of covariates for treated and control groups, leading to unbiased ATT estimation.
Optimized online learning with kernels for large-scale adversarial data.
problem Efficient online learning for large-scale, potentially adversarial datasets.
method Online variations of kernel Ridge regression using approximated basis functions.
result Optimal regret for a wide range of kernels with low per-round complexity.
Paper optimizes prices for better future profits using machine learning.
problem Optimizing prices to maximize future profit/revenue.
method Builds sales forecast formulas and constructs a binary quadratic programming optimization problem, then uses SDP relaxation for fast approximation.
result Simultaneously derives optimal prices for tens/hundreds of products with practical computational time, potentially improving gross profit by 8.2%.
Constellation learns group-level visual relationships for abstract reasoning.
problem Learning configurational properties of entire groups of objects.
method Introduces Constellation, a network that learns relational abstractions over static visual scenes.
result Offers a basis for abstract relational reasoning and sensory imagination.
Improves decision making by estimating bounds on potential outcomes.
problem Estimating individual treatment effects is complex and hard to estimate.
method Developed an algorithm to learn upper and lower bounds on potential outcomes that optimize an objective function defined by the decision maker.
result Our algorithm outperforms baselines, providing tighter, more reliable bounds.
New adaptive tests improve statistical dependence detection.
problem Testing statistical dependence between multivariate variables.
method Adaptive nonlinear monotonic transformations of distances.
result Empirical tests outperform existing methods.
In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model and the subsequent un-modeled dynamics as noise. The ability to more accurately ch…
Study automates feature selection and clustering for HFT stock price forecasting.
problem Manual feature selection and clustering for high-frequency trading (HFT) stock price forecasting.
method Dual competitive feature importance mechanism and clustering via shallow neural network topology.
result Enhanced forecasting ability of the RBFNN regressor through automated feature selection and clustering.
Paper proposes new methods for improving interatomic potentials.
problem Limitations of conventional SO(2) Linear architectures in MLIPs.
method Direct Cartesian construction, recursive Clebsch-Gordan construction, Edge Complex Product Basis, Radial Rotary Complex Attention.
result TECE-OAM-RRA-1.0 achieves SOTA performance on Matbench Discovery.
New method estimates and samples high-dimensional probability distributions avoiding optimization and approximation curse.
problem Estimating high-dimensional probability distributions from data samples.
method Hierarchic probability flow from coarse to fine scales, defined by conditional probabilities across scales.
result Sampling hierarchic models avoids critical slowing down at phase transitions and generates turbulence and dark matter images.
Short selling is key to exploiting arbitrage opportunities in financial markets.
problem Theoretical basis for differences in financial service regulations.
method Analyzing semimartingales to show arbitrage opportunities require short selling.
result Arbitrage opportunities can only be exploited through short selling.
Adapts POD basis for parametric ROMs using pGP.
problem Updating POD basis for accurate system behavior over parameter space.
method Formulates problem as supervised statistical learning, uses pGP to learn mapping between parameter space and Grassmann manifold.
result Proposes pGP for optimal estimation of POD basis parameters and quantifies uncertainty.
A new optimizer for deep learning improves accuracy and reduces training time.
problem Training deep neural networks for classification tasks.
method Hybrid Newton/Gradient Descent (NGD) method exploiting convexity of cross-entropy loss.
result Improves validation error and provides qualitative differences in hidden layer basis functions.
Justifies using posterior predictive for point predictions.
problem Justifying the use of posterior predictive for point predictions.
method Statistical decision theory.
result Justifies the use of posterior predictive for point predictions.
Unified proof for MU algorithm convergence in NMF with various divergences and regularizers.
problem Theoretical convergence guarantees for MU algorithm in NMF with diverse conditions.
method Unified proof strategy for MU algorithm convergence in NMF with various divergences and regularizers.
result Sequence of iterates converges to the set of stationary points of non-convex NMF optimization problem.
System identifies shifts in sketches for creative drawing.
problem Helping users create more creative sketches.
method Recognizes conceptual shifts between visual categories.
result Produces ambiguous sketches blending features from different categories.
The study explores rigid constraints on almost Ricci-Bourguignon solitons on contact metric three-manifolds.
problem Investigating constraints on almost Ricci-Bourguignon solitons on contact metric three-manifolds.
method Using a local orthonormal \(\varphi\)-basis, derived the full component form of the almost Ricci-Bourguignon soliton equation.
result For contact metric three-manifolds satisfying \(Qξ=σξ\), a collinear potential field must vanish on the non-Sasakian region whenever \(ξ(σ)=0\).
Paper shows strong convergence rates for fractional processes using Ornstein-Uhlenbeck representations.
problem Understanding and improving Monte Carlo schemes for fractional volatility models.
method Numerical discretizations of fractional processes using Ornstein-Uhlenbeck representations.
result Strong convergence rates of arbitrarily high polynomial order for fractional processes.
This paper improves Gaussian process predictions by integrating prior knowledge.
problem Gaussian processes lack predictive power when prior information is ignored.
method Derive mean and covariance functions from previous data using weighted sums of basis functions.
result Integrating prior knowledge significantly increases look-ahead time and accuracy.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, we considered the definition of orthonormal basis in Minkows…
The paper introduces new BSS contrasts based on PDF derivatives and potential theory.
problem Developing efficient BSS contrasts for blind source separation.
method Derives new independence measures and contrasts based on PDF derivatives and potential theory.
result Closed-form expressions for information field analysis using least squares.
Proposes adversarial normalization for multi-domain image segmentation.
problem Current image normalization is per-dataset, limiting multi-domain segmentation.
method Adversarial training to learn common normalizing functions across multiple datasets.
result Optimal normalizer improves segmentation accuracy and realism.
New basis confirms Thurston's conjecture and reveals knot configurations.
problem Understanding cluster algebras and their bases from surfaces.
method Topological construction of band basis and comparison with Kazhdan-Lusztig type basis.
result Common triangular basis matches band basis in quantum cluster algebras.
This work proposes a novel method for interpolating ROMs without solving FEM models.
problem Interpolating ROMs for unseen parameter values without solving FEM models.
method Non-intrusive Space-Time POD interpolation on compact Stiefel manifolds.
result Robust ROMs derived for unseen parameter values with strong correlations to high-fidelity simulations.
Bracelets and theta bases match in various cluster algebras.
problem Matching bracelet and theta bases in cluster algebras.
method Comparing skein and cluster algebras, defining quantum bracelets, and analyzing cluster scattering diagrams.
result Quantum bracelets coincide with theta functions in various cluster algebras.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, I considered the definition of orthonormal basis in Minkowsk…
We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factoria…
The paper identifies a 'small' set of functions containing Gaussian process samples.
problem Identifying a small set of functions containing Gaussian process samples.
method Using scaled RKHSs and Karhunen-Loève theorem, the paper defines the sample support set.
result The sample support set consists of functions with bounded squared basis coefficients.
Extends coisotropic embedding theorem to various geometric settings.
problem Regularization problem of singular Lagrangian systems.
method Generic methodology applied to cosymplectic, contact, and multisymplectic manifolds.
result Fundamental basis for applying results to regularization problem.
Bayesian method learns PDEs from noisy data.
problem Discovering PDEs from noisy data.
method Combining variational Bayes and sparse linear regression.
result Proposes a new method to discover PDEs accurately.