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.
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.
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 method constructs translationally equivariant hyperbolic affine spheres.
problem Constructing translationally equivariant hyperbolic affine spheres.
method Noncompact Iwasawa factorization via DPW method and Weierstrass elliptic functions.
result Every translationally equivariant hyperbolic affine sphere is equiaffinely equivalent to one with a circle, hyperbola, or parabola slice curve.
Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.
problem Optimizing smooth unconstrained problems with geometrically adapted directions.
method Yau's Affine Normal Descent (YAND) uses the equi-affine normal of level-set hypersurfaces as search directions.
result YAND converges globally under standard smoothness assumptions and locally quadratically near nondegenerate minimizers.
Characterizes flat affine symplectic Lie groups and their properties.
problem Characterizing flat affine symplectic Lie groups.
method Using symplectic étale affine representations and central translations.
result Obtains nontrivial examples of flat affine symplectic Lie groups in every even dimension.
Calculates affine transformations for specific homogeneous spaces.
problem Computing groups of affine transformations on homogeneous spaces.
method Analyzes conditions for affine connections and uses them to establish group isomorphisms.
result Groups of affine transformations are locally isomorphic under specified conditions.
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.
New methods classify convex lattice polygons for affine dimers.
problem Not all convex lattice polygons are characteristic polygons of affine dimers.
method General constructions and algorithm for finding affine dimers with prescribed polygons.
result All lattice triangles, generalised parallelograms, and polygons of genus at most two admit an affine dimer.
New method constructs proper affine actions of groups in higher dimensions.
problem Finding proper affine actions of discrete groups in higher-dimensional spaces.
method Higher strip deformations and Margulis invariant for properness.
result Affine actions of convex cocompact groups and virtually free groups are constructed properly.
Geometric methods solve the Hessian one equation.
problem Solving the Hessian one equation.
method Geometric methods for improper affine spheres.
result Advances in solving the Hessian one equation.
The affine Grassmannian is a noncompact smooth manifold that parameterizes all affine subspaces of a fixed dimension. It is a natural generalization of Euclidean space, points being zero-dimensional affine subspaces. We will realize the affine Grassmannian as a matrix manifold and extend Riemannian optimization algorit…
PANDA predicts protein binding affinity changes from sequences, outperforming existing methods.
problem Accurately predicting changes in protein binding affinity due to mutations.
method Sequence-based machine learning approach using protein sequence information.
result PANDA achieves higher Pearson correlation coefficients than existing methods.
The paper develops methods to generate invariant quantities in Metric-Affine Geometry.
problem Developing methods to generate invariant quantities in Metric-Affine Geometry.
method The paper introduces a theorem to generate invariant quantities under transformations of the affine connection, proving invariance conditions.
result Theorem establishing conditions for invariance of functionals under transformations of the affine connection.
We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the definition of an affine process, namely as stochastically continuous time-homogeneous Markov process with exponential affine Fourier-…
Affine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this article is to present both theoretical foundations as well as empirical aspects of the affine model class. Starting from the original one-fac…
This work extends variance reduction for path-dependent derivatives to affine stochastic volatility models.
problem Pricing path-dependent derivatives in affine stochastic volatility models.
method Prove large deviations principle, apply Esscher transform, use Varadhan's lemma.
result Numerical efficiency demonstrated on Heston model with and without jumps.
We investigate the geometric properties of hyperbolic affine flat, affine minimal surfaces in the equiaffine space A3. We use Cartan's method of moving frames to compute a complete set of local invariants for such surfaces. Using these invariants, we give a complete local classification of such surfaces and…
New method for multiway clustering of 3rd order tensors.
problem Clustering of 3rd order tensors.
method MCAM method based on affinity matrix and clustering.
result Competitive results on synthetic and real datasets.
The paper matches features in images using centro-affine invariants and heat flow.
problem Feature matching in images with invariant algorithms.
method Developed an invariant algorithm using centro-affine invariants and heat flow.
result The algorithm compares favorably with existing feature matching methods.
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.
This paper is a review of the twistor theory of irreducible G-structures and affine connections. Long ago, Berger presented a very restricted list of possible irreducibly acting holonomies of torsion-free affine connections. His list was complete in the part of metric connections, while the situation with holonomies of…
In this paper we classify convex compact ancient solutions to the affine curve shortening flow: namely, any convex compact ancient solution to the affine curve shortening flow must be a shrinking ellipse. The method combines a rescaling argument inspired by \cite{Wang}, affine invariance of the equation and monotonicit…
The paper generalizes fractals to higher dimensions using affine transformations.
problem Generalizing fractals to higher dimensions.
method Using affine transformations and characterizations of affinely-equivalent Sierpinski carpet.
result Menger sponge and Sierpinski simplex in 4-dimensional space can be drawn out clearly.
The goal of this paper is to provide a method, based on the theory of extensions of left-symmetric algebras, for classifying left-invariant affine structures on a given solvable Lie group of low dimension. To better illustrate our method, we shall apply it to classify complete left-invariant affine structures on the os…
New framework for probabilistic linear solvers reduces manual effort.
problem Manual implementation of probabilistic iterative methods is laborious.
method Affine Tracing: Automatically constructs PIMs from standard implementations.
result Any realistic affine PIM is calibrated, motivating their adoption.
Developed moment estimators for affine stochastic volatility models.
problem Estimating parameters of affine stochastic volatility models.
method Introduced recursive equations for moments and proposed moment estimators.
result Established a central limit theorem and derived asymptotic covariance matrix.
Researchers discover all affinely homogeneous models for surfaces in 4D space.
problem Identifying all affinely homogeneous models for surfaces in 4D space.
method Improved power series method of equivalence, capturing invariants at the origin, creating branches, and infinitesimalizing calculations.
result Find several inequivalent terminal branches yielding each to some nonempty moduli space of homogeneous models.
Max-affine regression method converges linearly using GD and SGD.
problem Regression of max-affine models in signal processing and statistics.
method Gradient descent and mini-batch stochastic gradient descent analysis.
result GD and SGD converge linearly to a neighborhood of the ground truth under sub-Gaussian assumptions.
This paper studies closed 3-manifolds which are the attractors of a system of finitely many affine contractions that tile R3. Such attractors are called self-affine tiles. Effective characterization and recognition theorems for these 3-manifolds as well as theoretical generalizations of these results to hig…
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-…
Corrected proof of geodesics in homogeneous Finsler spaces using affine method.
problem Proving the existence of homogeneous geodesics in homogeneous Finsler spaces.
method Used affine method to correct the proof of the algebraic method.
result Correctly proved that any homogeneous Finsler space admits a homogeneous geodesic through any point.
The paper explores genericity of triples of antipodal chambers in affine buildings.
problem Investigating genericity of triples of antipodal ideal chambers in locally finite affine buildings.
method Defined ideal-genericity and affine-genericity at the ideal boundary and within the affine building, respectively. Established a barycenter map and showed its continuity.
result Affine-genericity implies ideal-genericity, but the latter is more suitable for constructing a barycenter map.
Researchers study invariants of specific mappings in affine spaces.
problem Investigating invariants of second type almost geodesic mappings in non-symmetric affine spaces.
method Used computational methods to derive invariants, including generalized Thomas and Weyl projective tensors.
result Generalized invariants of second type almost geodesic mappings were successfully derived.
Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of Cartan's lemma and then, state a necessary and sufficient condition for classificatio…
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.
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…
We develop the foundations of the deformation theory of compact complete affine space forms and affine crystallographic groups. Using methods from the theory of linear algebraic groups we show that these deformation spaces inherit an algebraic structure from the space of crystallographic homomorphisms. We also study th…
Develops efficient methods for approximating densities of financial models with jumps.
problem Approximating densities of affine jump diffusions with state-independent jump intensities.
method Recursive approach for deriving closed-form solutions to moments, constructing density approximations via moment matching.
result Superior computational efficiency and precision in option pricing and simulation compared to existing techniques.
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.
This paper introduces a new transfer learning method for regression.
problem Boosting predictive power in scenarios with scarce data.
method Affine model transfer, following expected-square loss minimization.
result The affine model transfer method encompasses various existing methods and clarifies its theoretical properties.
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.
By considering the projectivized spectrum of the Jacobi operator, we introduce the concept of projective Osserman manifold in both the affine and in the pseudo-Riemannian settings. If M is an affine projective Osserman manifold, then the modified Riemannian extension metric on the cotangent bundle is both spacelike and…
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.
Solves Minkowski problem for affine invariant convex domains.
problem Finding convex sets with given area measures in affine spaces.
method Variational method using Steiner formula and covolume functional.
result Solves the affine invariant Minkowski problem.
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.
Perfect pairing for tropical cycles on integral affine manifolds.
problem Computing period integrals and versality of Calabi-Yau degenerations.
method Introducing a cap product pairing and using simplicial methods for constructible sheaves.
result The pairing is perfect in degree one for symplectic singularities.