Study transitions between tableau and spider bases for Specht modules.
problem Transitioning between tableau and spider bases for Specht modules.
method Combinatorial path model to study transitioning matrix from tableau basis to spider basis.
result Positive entries in the transitioning matrix for upper-triangular portion.
A graph connects Specht and web bases; matrix is unipotent with vanishing entries.
problem Comparing two bases of irreducible representations of the symmetric group.
method Graph theory and combinatorial analysis to describe relations between bases and prove properties of the transition matrix.
result The transition matrix between Specht and web bases is unipotent with additional vanishing entries.
The study examines subgroups of braid groups related to symmetric groups.
problem Characterizing subgroups of braid groups that are extensions of symmetric groups.
method Analyzing normal subgroups of braid groups and their quotient structures.
result There are exactly 8 commensurability classes of such subgroups for n≥4. Ehrenborg and Jung recently related the order complex for the lattice of d-divisible partitions with the simplicial complex of pointed ordered set partitions via a homotopy equivalence. The latter has top homology naturally identified as a Specht module. Their work unifies that of Calderbank, Hanlon, Robinson, and Wach…
Diagrammatic approach to Springer fibers for types C and D.
problem Understanding Springer representations on fiber homology.
method Topological construction and diagrammatic description of Weyl and component group actions.
result Decomposition of Springer representations into irreducibles and presentations of cohomology rings.
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…
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.
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…
Study optimal dynamic basis trading strategies with stochastic basis model.
problem Optimal dynamic trading of futures and underlying asset under stochastic basis.
method Model basis evolution as stopped scaled Brownian bridge, solve utility maximization problem with HARA risk preferences.
result Derive exact conditions for optimal trading strategies and solve explicitly.
We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.
New framework models complex spatial data with basis functions and graphical vectors.
problem Modeling highly-multivariate spatial processes with varying resolutions.
method Extends graphical lasso to multivariate Gaussian processes with independent graphical vectors at different resolutions, using an orthogonal basis and fusion penalty.
result Linear complexity and parsimonious conditional independence structure in multilevel graphical model.
Machine learning model predicts DFT total energy to complete basis set limit.
problem Finding a model to extrapolate DFT calculations to complete basis set limit.
method Quantile-random-forest model trained on binary solids data.
result Random-forest model achieves <25% symmetric MAPE for both DFT codes.
The paper explains the fair basis in bond-CDS trading during financial crises.
problem Large basis trading losses during financial crises are not explained by reduced form models.
method Dynamic spread model with bond repo financing, economic capital approach.
result Unhedged and unhedgeable residual jump to default risk exists, affecting fair basis level.
Researchers found a special basis for cycles on a K3 surface.
problem Understanding the structure of two-cycles on K3 surfaces.
method Constructed a canonical basis of two-cycles using formal sums of smooth submanifolds.
result The intersection form of the basis takes a specific canonical form.
Optimizes basis for density-based atomic representations to enhance compactness and accuracy.
problem Improving the efficiency and accuracy of machine learning models for atomic properties.
method An unsupervised approach to determine the optimal basis set for atom density representations using splines.
result Optimal basis sets that encode structural information more compactly and accurately.
This study tackles basis risk in weather parametric insurance using Monte Carlo simulations.
problem Mismatch between actual loss and payout in weather parametric insurance leads to loss without payout or payout without loss.
method Empirical research using Monte Carlo simulations to test diversification and hedging strategies.
result Portfolio basis risk and volatility decrease with more contracts, and spatial relationships significantly impact basis risk.
We show that the twisted SL(2) skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers.
New basis for permutation equivariant layers reduces computation costs.
problem Efficiently computing permutation equivariant layers in neural networks.
method Generalized partition algebra basis with low-rank tensors.
result Low-rank tensors enable faster computation compared to orbit basis.
Investigates smoothness of specific algebra structures.
problem Smoothness of bi-quadratic algebras on three generators.
method Analyzes differential smoothness with PBW basis.
result Characterizes conditions for smoothness.
Harmonic basis vector fields on surfaces
problem Parameterizing surfaces with harmonic vector fields
method Introducing harmonic basis vector fields and deriving conditions for their existence
result Classifying parameterizations of surfaces with harmonic basis vector fields
Proves log-concavity of cluster algebra coefficients for type An.
problem Log-concavity of cluster algebra coefficients.
method Introduced atomic theta basis and proved log-concavity for type An. result Proved log-concavity of coefficients for cluster algebra variables of type An. Defines tensor eigenvalues and singular values without basis, simplifying analysis.
problem Defines tensor eigenvalues and singular values without basis.
method Intrinsic definition of tensor eigenvalues and singular values using concepts from pure mathematics.
result Shows the relationship between tensor analysis and pure mathematics.
The study explores various localized bases and their duals for scattered data approximation.
problem Scattered data approximation using radial basis functions.
method Examines different localized bases including Lagrange, Newton, and multiresolution versions, and their duals.
result Localized orthogonal bases, such as the Newton basis, offer symmetric preconditioners and are feasible for scattered data approximation.
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.
New method estimates density functionals using polynomial basis without full distribution knowledge.
problem Estimating quantities like information divergence functions requires complete distribution knowledge and integration.
method Introduces data-driven basis functions and develops methods for basis expansions of functionals of two distributions.
result Approximates functions of distributions as closely as desired using the new basis set.
This paper optimizes PCE for efficient surrogate modeling in engineering.
problem Efficiently selecting polynomial regressors for surrogate modeling in computationally expensive models.
method Three state-of-the-art basis-adaptive sparse PCE methods are compared and analyzed.
result Automatic selection of the best solver and basis-adaptive scheme improves surrogate model accuracy.
New algorithm improves asset pricing model for high-dimensional financial data.
problem Estimating high-dimensional financial data with many risk-factors.
method Groupwise Interpretable Basis Selection (GIBS) algorithm for adaptive multi-factor model.
result AMF model outperforms Fama-French 5-factor model in fitting and prediction.
Paper tackles spurious vanishing problem in approximate vanishing ideals.
problem Capturing nonlinear structure of perturbed data points leads to spurious vanishing problem.
method Proposes a general method integrating coefficient normalization and iterative basis construction.
result Proposed method overcomes spurious vanishing problem, resulting in shorter feature vectors.
In this paper we study a symmetry group of vector space. Basis manifold is a homogeneous space of a symmetry group. This concept leads us to the definition of active and passive transformations on basis manifold. Active transformation can be expressed as a transformation of vector space. Passive transformation gives ab…
Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most of existing work which deal with the problem by adding some sparsity penalties o…
A neural network predicts coarse-scale basis functions for efficient uncertainty quantification.
problem Efficiently estimating coarse-scale basis functions for multiscale methods.
method Data-driven approach using neural networks fitted to solution samples.
result Significant computational savings for uncertainty quantification tasks.
A new kernel improves statistical surrogates for stochastic manifolds with diverse data.
problem Handling statistical surrogates for stochastic manifolds with heterogeneous data.
method A transient anisotropic kernel is introduced to improve statistical surrogates for stochastic manifolds with heterogeneous data.
result The transient anisotropic kernel provides a better representation of statistical dependencies in the learned probability measure.
A new density model using Fourier basis achieves better approximations and compression.
problem Approximating multi-modal 1D densities.
method Constrained Fourier basis model for end-to-end training.
result Lower cross entropy compared to deep factorized models.
BASIS improves LLM reasoning by sharing batchwise rollout info, reducing MSE by 69%.
problem Improving large language model reasoning with limited rollouts and batch information.
method BASIS samples only one rollout per prompt but uses batch information to improve value function estimation.
result BASIS reduces MSE in value function estimation by 69% compared to REINFORCE++.
Alternative basis for Kauffman bracket skein module of solid torus found using braids.
problem Computing Kauffman bracket skein module of lens spaces.
method Using Temperley--Lieb algebra of type B and braids.
result Alternative basis BmST for ${
m KBSM}\left({
m ST}
ight)$. Derives representations invariant under crystallographic groups for functions.
problem Representing and learning functions invariant under crystallographic groups.
method Derives linear and nonlinear representations of functions invariant under crystallographic groups.
result Derives orthonormal crystallographically invariant basis functions and embedding maps.
We give an explicit graded cellular basis of the sl3-web algebra KS. In order to do this, we identify Kuperberg's basis for the sl3-web space WS with a version of Leclerc-Toffin's intermediate crystal basis and we identify Brundan, Kleshchev and Wang's degree of tableaux with the weigh…
Given a simple algebraic group G, a web is a directed trivalent graph with edges labelled by dominant minuscule weights. There is a natural surjection of webs onto the invariant space of tensor products of minuscule representations. Following the work of Westbury, we produce a set of webs for $\SL_n$ which form a bas…
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.
Optimizes basis functions for learning dynamical systems from data.
problem Learning suitable basis functions for dynamical systems from data.
method Gradient-based optimization framework for learning basis functions.
result Efficacy demonstrated on various benchmark problems.
A new method for efficient ordinal regression.
problem Efficiently modeling ordinal relationships in multi-label learning.
method Incremental Sparse Bayesian Ordinal Regression (ISBOR) approach.
result ISBOR achieves accurate predictions with fewer basis functions.
Study on smoothness of special algebra types.
problem Differential smoothness of bi-quadratic algebras with PBW basis.
method Investigation of algebra properties.
result Results on differential smoothness.
Introduces tunable basis functions for Gaussian processes.
problem Reduces computational complexity in Gaussian process approximations.
method Introduces tunable, local, and bounded basis functions for kernel approximation.
result Demonstrates superior performance compared to state-of-the-art methods, especially with poorly chosen kernel functions.
Study various image defenses against adversarial attacks using basis functions.
problem Defending against adversarial images in deep networks.
method Experiments with low-pass filtering, PCA, JPEG compression, wavelet approximation, and soft-thresholding.
result JPEG compression and soft-thresholding outperform other defenses in most settings, with specific cases showing different performance.
Improves deep neural network training and accuracy with adaptive basis approach.
problem Gap between theoretical and practical performance of deep neural networks.
method Adaptive basis viewpoint, novel initializations, hybrid optimizer.
result Dramatic increases in accuracy and convergence rate for various DNN applications.
The paper approximates supply curves using a one-step basis method.
problem Computing supply curves accurately and efficiently.
method Derives L2 approximation expression and proposes node selection procedure.
result Illustrates the approach with European electricity market bid curves.
Near-convex archetypal analysis improves interpretability and fitting error in NMF.
problem High data fitting error in traditional archetypal analysis.
method Introduces near-convex archetypal analysis (NCAA) that combines AA and NMF.
result NCAA achieves lower data fitting error than state-of-the-art methods.