Paper shows affine constraint is unnecessary for high-dimensional data.
problem The necessity of an affine constraint in affine subspace clustering.
method Theoretical and empirical analysis of conditions for correctness of affine subspace clustering methods.
result Affine constraint has negligible effect on clustering performance for high-dimensional data.
Random features enhance control of complex systems.
problem Flexible nonlinear models for control-affine systems.
method Random features approximations for control-affine structure.
result Methods formalized and shown to relate to ADP and AD kernels.
New metrics for SPD matrices explore affine invariance and symmetry principles.
problem Choosing appropriate metrics for SPD matrices based on invariance principles.
method Investigates power-affine and deformed-affine metrics within a continuum of SPD metrics.
result Introduces new families of metrics based on affine invariance and symmetry.
Empirical study finds variance swap rate is affine in spot variance for S&P500 data.
problem Investigating the relationship between variance swap rate and spot variance.
method Empirical analysis using S&P500 data from 2006-2018, testing different models.
result Affine relationship between variance swap rate and spot variance is supported.
A new affinity measure for spectral clustering using conformal prediction improves clustering performance.
problem Improving the performance of spectral clustering by enhancing the affinity matrix.
method Employing the concept of non-conformity from Conformal Prediction to define a novel affinity measure.
result The proposed affinity measure leads to better clustering results compared to state-of-the-art methods.
We construct a sequence of commuting central affine curve flows on Rn\0 invariant under the action of SL(n,R) and prove the following results: (a) The central affine curvatures of a solution of the j-th central affine curve flow is a solution of the j-th flow of Gelfand-Dickey (GDn) hierarchy on the s…
3S-SC framework improves SC accuracy by optimizing affinity matrices.
problem Inaccurate clustering results due to flawed affinity matrices.
method 3S-SC framework with GBTO to optimize affinity matrices.
result Improves connectivity and accuracy in SC methods.
A new method for clustering high-dimensional data into subspaces efficiently and accurately.
problem Inaccurate clustering due to poor intra-subspace similarity in existing methods.
method Iterative Maximum Correlation (IMC) for affinity matrix learning and Piecewise Correlation Estimation (PCE) for densification.
result SDSC framework improves clustering accuracy and efficiency for large-scale data.
Constructs positive energy representations from Toda equations Stokes data.
problem Creating positive energy representations of affine algebras.
method Using Stokes data of tt*-Toda equations to construct representations.
result Illustrates construction with examples in conformal field theory.
PCA adapted for curved spaces improves data analysis.
problem PCA's limitations in curved spaces.
method Space Form PCA (SFPCA) for Riemannian manifolds.
result SFPCA provides faster and more accurate subspaces estimation.
New method detects symmetries beyond affine transformations.
problem Current methods limit symmetry detection to affine transformations.
method Framework for discovering continuous symmetry beyond affine transformations.
result Method is competitive for large sample sizes and superior for small sample sizes.
The paper constructs new structures for manifolds using connections and combinations.
problem Understanding smooth manifolds with precise infinitesimal affine structures.
method Constructing new infinitesimal structures for higher-order neighbourhoods of the diagonal.
result Any symmetric affine connection on a manifold extends to a second-order infinitesimally affine structure.
DeepDTA predicts drug-target binding affinities using deep learning.
problem Predicting the continuum of binding strength values between drugs and targets.
method Uses deep learning, specifically CNNs, to model 1D representations of drug and target sequences.
result Deep learning model outperforms state-of-the-art methods in predicting DT binding affinities.
The paper constructs submanifolds with corners in Delzant polytopes from affine subspaces.
problem Understanding submanifolds with corners in Delzant polytopes.
method Constructing submanifolds with corners in Delzant polytopes from affine subspaces.
result Conditions for submanifolds with corners are equivalent to those for torus-equivariantly embedded toric manifolds.
We test for departures from normal and independent and identically distributed (NIID) returns, when returns under the alternative hypothesis are self-affine. Self-affine returns are either fractionally integrated and long-range dependent, or drawn randomly from an L-stable distribution with infinite higher-order moment…
New measures quantify how data augmentation improves model performance.
problem Understanding the effectiveness of data augmentation in deep learning.
method Introduced Affinity and Diversity measures to quantify augmentation performance.
result Augmentation performance is best achieved by optimizing both Affinity and Diversity.
BN refines local partition geometry in piecewise-affine networks during training.
problem Understanding the effect of BN on the function realized during training in piecewise-affine networks.
method Analyzing the geometry of switching hyperplanes and affine-region partition conditioned on a mini-batch.
result BN increases expected local partition refinement in ReLU and piecewise-affine networks.
Topology of space line arrangements depends on line count and multiple points.
problem Understanding the topology of space line arrangements.
method Determined by the number of lines and data on multiple points.
result Topology of complements is determined by line count and multiple points.
New dissimilarity measures enhance affinity propagation for complex network clustering.
problem Improving community detection in complex networks using affinity propagation.
method Leverage network latent geometry to design dissimilarity matrices.
result Affinity propagation outperforms state-of-the-art methods in community detection.
Special Lagrangian submanifolds emerge from K3 surface collapse.
problem Understanding special Lagrangian submanifolds in K3 surface collapse.
method Lifting affine lines to degenerating sequences of special Lagrangian submanifolds.
result Constructing special Lagrangian two-spheres connecting Taub-NUT bubbles.
This abstract reviews recent methods for predicting protein-ligand binding affinity.
problem Predicting protein-ligand binding affinity for various applications in life sciences.
method Traditional and deep learning models for binding affinity prediction.
result Improved predictive performance of AI-driven models.
A new ranking algorithm learns data affinity and ranking scores simultaneously.
problem Retrieving similar objects in large databases is challenging.
method Proposes a ranking algorithm that learns data affinity and ranking scores simultaneously, using adaptive neighbors and smoothness constraints.
result The proposed algorithm outperforms existing methods in synthetic and real datasets.
The study examines lower and upper bounds of Wasserstein distances for affine transformations of random vectors.
problem Understanding Wasserstein distances for affine transformations of random vectors.
method Lower and upper bounds for affine transformations of random vectors in Rn are derived using Bures metric and compositions of affine maps. result Concrete lower bounds and upper bounds for affine transformations are derived and applied to various distributions.
Paper tackles robust federated learning for affine distribution shifts.
problem Statistical heterogeneity and distribution shifts degrade model performance in federated learning.
method Develops a robust federated learning algorithm (FLRA) for affine distribution shifts.
result FLRA achieves significant performance gains against affine distribution shifts.
New algorithm reveals piecewise affine structure of neural networks.
problem Lack of strong guarantees on deep neural networks' behavior in safety-critical applications.
method Developed a novel algorithm to compute the piecewise affine form of neural networks.
result Computed piecewise affine representations of neural networks with rectified linear unit activations.
DeepAffinity predicts compound-protein affinity from sequences, outperforming existing methods.
problem Lack of methods to predict compound-protein affinity from sequences alone.
method Unified RNN/GCNN-CNN model that unifies recurrent and convolutional neural networks.
result Model outperforms conventional options in predicting affinities with high accuracy.
Improves MCMC performance with adaptive affine transformations.
problem Improving the performance of Markov Chain Monte Carlo samplers.
method Adaptive learning of bijective affine transformations during sampling.
result Adaptive affine transformations improve the quality of samples at low computational cost.
MASC balances dataset representation using affinity clustering and distribution discrepancies.
problem Representation bias in datasets due to group imbalance.
method MASC uses affinity clustering and pairwise distribution discrepancies to balance non-protected and protected groups.
result MASC effectively debiases target datasets, comparable to existing methods.
Pole ladder improves parallel transport in affine spaces, showing exact results in symmetric spaces.
problem Improving numerical stability and accuracy in parallel transport algorithms.
method Developed a third-order parallel transport scheme using pole ladder in affine connection spaces, showing exact results in symmetric spaces.
result Pole ladder is a third-order scheme in general affine connection spaces and is exact in locally symmetric spaces.
Study geodesic and affine Killing completeness in homogeneous affine surfaces.
problem Geodesic and affine Killing completeness in homogeneous affine surfaces.
method Examined using the solution space of the quasi-Einstein equation.
result Characterized geodesic and affine Killing completeness in homogeneous affine surfaces.
Almost Zoll affine surface found on cylinder.
problem Finding surfaces with special geodesic properties.
method Exhibited an affine structure on a cylinder.
result Affine structure on cylinder is almost Zoll.
We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the affine structure of an affine manifold. We found various conditions which make the…
This article investigates parameter estimation of affine term structure models by means of the generalized method of moments. Exact moments of the affine latent process as well as of the yields are obtained by using results derived for p-polynomial processes. Then the generalized method of moments, combined with Quasi-…
Study finds solutions for degenerate affine curve shortening flow.
problem Analyzing degenerate affine curve shortening flow.
method Solved equations for affine self-similar solutions.
result New special solutions discovered for affine curve shortening flow.
Spectrahedral regression fits convex functions via a non-convex optimization problem.
problem Fitting convex functions to data sets.
method Fitting a spectrahedral function (maximum eigenvalue of an affine matrix expression) to the data via an alternating minimization algorithm.
result The alternating minimization algorithm converges geometrically to a small ball around the optimal parameter.
Study affine curvature lines on surfaces in 3D space.
problem Understanding the behavior of affine curvature lines on surfaces.
method Analyzing binary differential equations and topological models.
result Obtained topological models and generic behavior of affine curvature lines.
In this article, we propose the notion of the general p-affine capacity and prove some basic properties for the general p-affine capacity, such as affine invariance and monotonicity. The newly proposed general p-affine capacity is compared with several classical geometric quantities, e.g., the volume, the p-var…
An affine manifold is a manifold with torsion-free flat affine connection. A geometric topologist's definition of an affine manifold is a manifold with an atlas of charts to the affine space with affine transition functions; a radiant affine manifold is an affine manifold with holonomy consisting of affine transformati…
In this paper, we show that a compact affine manifold endowed with an Affine Anosov transformation is finitely covered by a complete affine nilmanifold.
Proofs for decomposing branched affine surfaces into triangles and cylinders.
problem Decomposing branched affine surfaces into simpler geometric shapes.
method Proof of Veech's theorem and introduction of invariant α.
result Any pair of decompositions can be connected by flips.
This thesis is devoted to the study of affine processes and their applications in financial mathematics. In the first part we consider the theory of time-inhomogeneous affine processes on general state spaces. We present a concise setup for time-inhomogeneous Markov processes. For stochastically continuous affine proce…
Study on completeness in affine and statistical geometry.
problem Completeness of affine connections on statistical manifolds and affine hypersurfaces.
method Collect basic facts, prove new theorems, provide examples.
result New theorems on completeness of affine connections.
Two families of general affine surface areas are introduced. Basic properties and affine isoperimetric inequalities for these new affine surface areas as well as for Lφ affine surface areas are established.
We study affine Jacobi structures on an affine bundle π:A→M, i.e. Jacobi brackets that close on affine functions. We prove that there is a one-to-one correspondence between affine Jacobi structures on A and Lie algebroid structures on the vector bundle A+=⋃p∈MAff(Ap,R) of affine functionals. Som…
A (flat) affine 3-manifold is a 3-manifold with an atlas of charts to an affine space R3 with transition maps in the affine transformation group Aff(R3). We will show that a connected closed affine 3-manifold is either an affine Hopf 3-manifold or decomposes canonically to conca…
The paper studies elliptical surfaces in 3D affine space, classifying them based on curvature.
problem Classifying regular elliptical surfaces in affine space A3 based on curvature. method Defined a moving frame of minimal order for regular elliptical surfaces and derived differential invariants.
result Classified regular elliptical surfaces of constant curvatures up to affine congruence.
New algorithm estimates task affinities without repeated training, improving model performance and efficiency.
problem Efficiently estimating task affinities among multiple tasks for model training.
method Grad-TAG algorithm: trains a base model for all tasks and uses gradient-based linearization to estimate task affinities.
result Estimates task affinities with high accuracy and low computational cost.
The paper explores flat affine and symplectic structures on Lie groups.
problem Exploring flat affine and symplectic structures on Lie groups.
method Left invariant affine structures, immersion of Lie groups, Koszul's method, Lagrangian bi-foliation.
result Flat left invariant affine symplectic connections and their associated affine symplectomorphisms.