New categorification method for infinite braids.
problem Categorifying highest-weight projectors for infinite braids.
method Limiting colored Khovanov-Rozansky homology of infinite braids.
result Partial isomorphism between HOMFLY-PT homology of braids and infinite torus knots.
The paper computes characteristic classes for Lie group representations.
problem Computing characteristic classes for Lie group representations.
method The paper outlines a procedure to compute characteristic classes of irreducible representations of Lie groups, expressing them as polynomial functions in the highest weight.
result The paper expresses characteristic classes of Lie group representations as polynomial functions in the highest weight.
We define invariants for colored oriented spatial graphs by generalizing CM invariants, which were defined via non-integral highest weight representations of Uq(sl2). We apply the same method to define Yokota's invariants, and we call these invariants Yokota type invariants. Then we propose a volume conjecture of t…
Paper refines Alesker-Bernig-Schuster theorem, proving Hodge-Riemann relations for Euclidean balls.
problem Understanding translation-invariant valuations and their geometric implications.
method Explicit construction of highest weight vectors and analysis of natural operations on these vectors.
result Proof of Hodge-Riemann relations for Euclidean balls, extending geometric inequalities.
This work is a continuation of the former paper in which principal bundles are given by compact spin toric manifolds and compact connected semisimple Lie groups. In this paper, ambient manifolds are assumed to be compact toric manifolds and Lie groups are compact connected. The main result is that locally smooth manifo…
For p>3 a prime, and g>2 an integer, we use Topological Quantum Field Theory (TQFT) to study a family of p-1 highest weight modules L_p(lambda) for the symplectic group Sp(2g,K) where K is an algebraically closed field of characteristic p. This permits explicit formulae for the dimension and the formal character of L_p…
Study shows bounds on Hausdorff dimension for limit sets of projective Anosov representations.
problem Understanding Hausdorff dimensions of limit sets for projective Anosov representations.
method Proved bounds on Hausdorff dimension using critical exponents associated to highest weight and simple root.
result Hausdorff dimension of symmetric limit set is bounded by critical exponents.
The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branch…
In this paper we discuss the highest weight kr-finite representations of the pair (gr,kr) consisting of gr, a real form of a complex basic Lie superalgebra of classical type g (g=A(n,n)), and the maximal compact subalgebra kr of gr,0, together …
New homology for infinite multi-colored braids, completing previous work.
problem Categorification of highest-weight projectors for infinite braids.
method Defining limiting Khovanov-Rozansky homology for semi-infinite braids.
result Categorifies highest-weight projectors for a large class of braids.
Using an algebraic Fourier transform of operators, we develop a method (F-method) to obtain explicit highest weight vectors in the branching laws by differential equations. This article gives a brief explanation of the F-method and its applications to a concrete construction of some natural equivariant operators that a…
The paper calculates Racah matrices for up to 3 strands of knots and links.
problem Systematic description of colored knot and link invariants.
method Highest weight method and use of Racah matrices.
result Explicit answers for Racah matrices and colored polynomials for 3-strand knots and links.
We study the analytic torsion of odd-dimensional hyperbolic orbifolds Γ\H2n+1, depending on a representation of Γ. Our main goal is to understand the asymptotic behavior of the analytic torsion with respect to sequences of representations associated to rays of highest weights.
In the present paper, we study the Sp-module structure of the cokernel of the Johnson homomorphism of the mapping class groups of surfaces. We detect the Sp-irreducible components with highest weight [1^k] (and [k]) in the cokernel. We also show that the multiplicities of them is equal to one.
BetaDataWeighter learns weights for unlabelled data to improve self-supervised learning accuracy.
problem Improving unsupervised representations with domain shift between unlabelled and target data.
method Learning Bayesian instance weights for unlabelled data to prioritize useful instances.
result BetaDataWeighter achieves highest average accuracy and prunes up to 78% of images without significant loss in accuracy.
Test-asset construction affects factor model performance.
problem How test assets are constructed impacts factor model performance.
method Forming characteristic-unsorted random portfolios and varying stock selection, initial weighting, holding, and rebalancing.
result Test-asset construction shifts factor model rankings materially.
Study on eigenvalues of Laplace operator on 1-forms for symmetric spaces.
problem Investigating the first eigenvalue of the Laplace operator on 1-forms in compact inner symmetric spaces.
method Analyzing the Casimir eigenvalue of the highest root for the isotropy representation.
result The first eigenvalue of the Laplace operator on 1-forms is the Casimir eigenvalue of the highest root.
Conformal Bayes under label shift: post-hoc calibration vs. in-training adaptation
problem Bayesian prediction sets under label shift
method Post-hoc calibration vs. In-training adaptation
result Both strategies achieve valid coverage equally in an unbiased training regime
A method improves deep network accuracy with low precision quantization.
problem Maintaining high accuracy in low precision deep networks.
method Learned Step Size Quantization, improving quantizer configuration and gradient estimation.
result Achieves highest accuracy on ImageNet with 2-4 bit precision models.
Study on default clustering in large networks using graph theory.
problem Understanding the impact of defaults in large interconnected systems.
method Law of large numbers applied to graph dynamics, singular value decomposition of adjacency matrix.
result Identification of components with highest contagion impact using eigenvalues.
We present a method of rank-optimal weighting which can be used to explore the best possible position of a subject in a ranking based on a composite indicator by means of a mathematical optimization problem. As an example, we explore the dataset of the OECD Better Life Index and compute for each country a weight vector…
Two approaches improve conformal Bayes for label shift, one post-hoc and one in-training.
problem Improving prediction sets for target domain under label shift.
method Two complementary approaches: post-hoc calibration and in-training adaptation.
result In-training adaptation achieves up to 43% width reduction at unchanged coverage.
Non-negative matrix factorization is a basic tool for decomposing data into the feature and weight matrices under non-negativity constraints, and in practice is often solved in the alternating minimization framework. However, it is unclear whether such algorithms can recover the ground-truth feature matrix when the wei…
Paper identifies key CpG methylation sites for breast cancer.
problem Early detection and treatment of breast cancer.
method Used machine learning on TCGA dataset to classify cancer vs. non-cancer samples.
result Reduced model with 25 key CpG sites achieves over 94% accuracy.
New technique trains DNNs with fewer weights, saving memory and energy.
problem Training deep neural networks requires many weights, increasing memory and energy costs.
method Constrain weight updates to those with highest gradients, regenerating others.
result Pruned networks maintain accuracy while significantly reducing weight count and memory usage.
Computes Lie algebra structure constants using a graphical calculus.
problem Computing Lie algebra structure constants efficiently.
method Graphical calculus for classical invariant theory.
result Generalizes known methods for sl2 to other Lie algebras. The paper studies weak singular Hermite-Einstein structures on homogeneous vector bundles.
problem Existence of weak singular Hermite-Einstein structures on homogeneous holomorphic vector bundles.
method Using Cartan's highest weight theory, the paper establishes an algebraic criterion for topological splitting and decouples the prescribed mean curvature equation.
result A sufficient algebraic condition for realizing an L2-function as the mean curvature of a singular Hermitian structure on an irreducible homogeneous bundle. Unified approach to aggregating models and preferences.
problem Consistent aggregation of models and preferences.
method Formal definition and weighted averaging of models and preferences.
result All rational aggregation rules are weighted averages of highest-ranked models/experts.
STRAPSim measures ETF portfolio similarity better than existing methods.
problem Measuring portfolio similarity for ETFs and portfolios.
method Semantic, two-level, residual-aware portfolio similarity computation.
result STRAPSim outperforms existing methods in predictive accuracy and ranking alignment.
We study the structure of abelian extensions of the group LqG of q-differentiable loops (in the Sobolev sense), generalizing from the case of central extension of the smooth loop group. This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules are…
In this paper we describe all the nilradicals of parabolic subalgebras of split real simple Lie algebras admitting symplectic structures. The main tools used to obtain this list are Kostant's description of the highest weight vectors (hwv) of the cohomology of these nilradicals and some necessary conditions obtained fo…
A novel method selects genes for high-dimensional gene expression data with class imbalance.
problem Class imbalance in gene expression datasets.
method Synthetic data balancing, greedy search, weighted robust score.
result The proposed method outperforms existing feature selection procedures.
Researchers find highest volumes for isospectral spherical orbifolds and space forms.
problem Finding the maximum volumes of isospectral spherical orbifolds and space forms.
method Analyzing isospectral properties and calculating volumes of spherical orbifolds and space forms.
result Highest volumes for specific dimensions and conditions of isospectral spherical orbifolds and space forms.
A feature-weighted mean shift algorithm improves clustering in high-dimensional data.
problem Clustering high-dimensional data with traditional mean shift algorithms.
method Feature-weighted mean shift algorithm.
result The algorithm outperforms conventional mean shift and preserves computational simplicity.
Study asymptotics of unitary matrix elements in quantum mechanics.
problem Asymptotic behavior of unitary matrix elements in quantum mechanics.
method Uses Berezin-Toeplitz quantization and symplectic geometry.
result Recover asymptotics of Wigner's d-matrix elements for spin representations.
WOTBoost improves minority class accuracy in imbalanced datasets.
problem Imbalanced datasets lead to low accuracy in minority class classification.
method Combines weighted oversampling and boosting techniques.
result WOTBoost achieves best G mean and highest AUC score on multiple datasets.
Diffusion models optimize objectives similar to ELBO with Gaussian noise augmentation.
problem Optimizing diffusion models for high perceptual quality.
method Showed diffusion objectives are weighted ELBOs over noise levels, with Gaussian noise augmentation.
result Diffusion objectives equate to ELBO with Gaussian noise augmentation under monotonic weighting.
SUNRISE improves off-policy RL algorithms by integrating ensemble methods.
problem Stability and exploration issues in off-policy RL algorithms.
method SUNRISE combines ensemble-based weighted Bellman backups and upper-confidence bounds for efficient exploration.
result SUNRISE improves the performance of off-policy RL algorithms across various domains.
We describe the inclusive Racah matrices for the first non-(anti)symmetric rectangular representation R=[2,2] for quantum groups U_q(sl_N). Most of them have sizes 2, 3, and 4 and are fully described by the eigenvalue hypothesis. Of two 6x6 matrices, one is also described in this way, but the other one corresponds to t…
Verma Howe duality connects tensor products of Verma modules to LKB representations.
problem Understanding the relationship between tensor products of Verma modules and LKB representations.
method Established a quantized version of Verma Howe duality and used it to prove the simplicity of LKB representations.
result LKB representations arise from the quantized Verma Howe duality and are shown to be simple modules.
Generative framework improves causal estimation from observational data.
problem Estimating individualized treatment effects from non-randomized data.
method Importance-Weighted Diffusion Distillation (IWDD) combining diffusion models and IPW.
result IWDD achieves state-of-the-art prediction performance and significantly improves causal estimation.
PPO optimizes LLM-generated alpha weights for better trading performance.
problem Adapting LLM-generated alphas for varying market conditions.
method Proximal Policy Optimization (PPO) for dynamic alpha weight adjustment.
result PPO-optimized strategy achieves higher Sharpe ratios and smaller drawdowns.
New method compresses neural networks using random code, improving efficiency.
problem Large memory footprint of deep neural networks.
method Training a variational distribution over weights, encoding using Kullback-Leibler divergence.
result Achieves state-of-the-art compression rates and test performance.
Study geometric criteria for cone structures on flag varieties.
problem Geometric criteria for isotrivial cone structures on flag varieties.
method Complete classification of flag varieties satisfying a projective-geometric criterion.
result Characterization of flag varieties with an injective Gaussian map.
A hybrid model reduces graph complexity for improved classification accuracy.
problem High computational complexity and large number of parameters in higher-order graph convolutional networks.
method Weight sharing mechanism and novel fusion pooling layer to reduce parameters and complexity.
result The proposed model achieves highest classification accuracy with fewer trainable parameters.
Conformal Prediction Regions match Imprecise Highest Density Regions under consonance.
problem Matching conformal prediction regions with highest density regions.
method Using consonance and the Imprecise Probability theory of clouds.
result Imprecise Highest Density Regions are equivalent to Conformal Prediction Regions under consonance.
We introduce a new general framework for constructing the best trading strategy for a given historical indicator. We construct the unique trading strategy with the highest expected return. This optimal strategy may be implemented directly, or its expected return may be used as a benchmark to evaluate how far away from …
G-FuNK learns solutions for nonlinear PDEs on multiple domains and parameters.
problem Predicting time-dependent dynamics of complex systems governed by nonlinear PDEs with varying parameters and domains.
method Graph Fourier Neural Kernels combining domain-adapted and transferable components for non-diffusive and diffusive terms.
result G-FuNK achieves low relative errors on unseen domains and fiber fields, significantly accelerating predictions.