We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar diagram produces a coherently diagonal complex.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,341 papers · 148 categories
Trend · papers per month
48 results for “diagonal complexes”
Diagonal complexes and symmetric complexes study surfaces with involution and punctures.
problem Understanding surfaces with involution and punctures through diagonal complexes.
method Construction and study of diagonal and symmetric diagonal complexes, their barycentric subdivisions, and homotopy equivalence.
result Symmetric diagonal complex is homotopy equivalent to a punctured symmetric surface.
The main goal of this paper is a calculation of the integral (co)homology of the group of symmetric automorphisms of a free product. We proceed by giving a geometric interpretation of symmetric automorphisms via a moduli space of certain diagrams, which we name cactus products. To describe this moduli space a theory of…
Classify projective subvarieties in Bogomolov-Guan manifolds using quasi-diagonals.
problem Classify projective subvarieties in non-Kahler holomorphically symplectic manifolds.
method Use quasi-diagonals to classify projective subvarieties.
result Prove that any projective subvariety belongs to a fiber of the Lagrangian fibration.
Constructs coordinates to diagonalize Toda flow on matrices with simple spectrum.
problem Diagonalizing the Toda flow on matrices with simple spectrum.
method Lie theoretic methods applied to complex semisimple Lie algebras and their real forms.
result Decouples the Toda vector field into simpler components.
Authors conjecture categorically diagonalizable complex for full twists.
problem Categorically diagonalizing the complex of Soergel bimodules for full twists.
method Utilizes categorical diagonalization theory.
result Proves conjecture in type A, categorifies Young idempotents.
Defines tensor products for A-infinity structures using diagonals.
problem No specific problem stated; focuses on new definitions.
method Uses diagonals of associahedra and multiplihedra to define tensor products.
result Defines tensor products for various A-infinity structures.
New MCMC method learns sparse preconditioner for high-dimensional problems.
problem High-dimensional sampling with complex correlation structures.
method Adaptive MCMC with sparse preconditioner using online PCA.
result Significant reduction in computational complexity and improved performance.
The topological complexity and the homotopy cofiber of the diagonal map for non-orientable surfacesmath.GT
We show that the Lusternik-Schnirelmann category of the homotopy cofiber of the diagonal map for non-orientable surfaces equals three. Also, we prove that the topological complexity of non-orientable surfaces of genus is four.
The author connects Poincaré embeddings to Reidemeister traces and diagonal maps.
problem Existence of Poincaré embeddings for specific spaces.
method Relates total obstruction to Reidemeister trace and uses Poincaré duality.
result Diagonal maps admit Poincaré embeddings under certain conditions.
Diagonal complexesmath.GT
Diagonal complexes generalize associahedra to surfaces, providing models for ribbon graphs and tautological bundles.
problem Generalizing associahedra to surfaces with marked points.
method Defining cell complexes and their barycentric subdivisions on surfaces, proving homotopy equivalences and contraction properties.
result Homotopy equivalence of diagonal complexes to ribbon graph spaces and tautological bundles.
New Spencer complexes for Lie groupoids developed.
problem Developing Spencer complexes for Lie groupoids.
method Extending Malgrange's diagonal calculus to .
result Construction of non-linear and linear Spencer complexes.
Study smooth embeddings of line configurations in complex projective plane.
problem Realizing line configurations as smooth 2-spheres.
method Lattice-theoretic arguments based on Donaldson's diagonalization theorem.
result Established a stronger obstruction in the smooth category.
We study when a smooth variety , embedded diagonally in its Cartesian square, is the zero scheme of a section of a vector bundle of rank on . We call this the diagonal property (D). It was known that it holds for all flag manifolds . We consider mainly the cases of proper smooth va…
Study of Lorentz hypersurfaces with specific curvature properties.
problem Characterizing Lorentz hypersurfaces with complex eigenvalues and constant mean curvature.
method Analyzing hypersurfaces in satisfying with non-diagonal shape operator.
result Hypersurfaces with at most five distinct principal curvatures have constant mean curvature.
Localized sketching improves matrix multiplication and ridge regression complexity.
problem Efficiently approximate matrix multiplication and ridge regression with limited data availability.
method Localized sketching matrices for block diagonal structure, reducing sample complexity.
result Localized sketching achieves sample complexity matching global sketching methods.
This paper optimizes diagonal preconditioning to improve matrix condition numbers.
problem Optimizing diagonal preconditioning to reduce matrix condition numbers.
method Reformulated as a quasi-convex problem, solved with bisection and Newton updates.
result Optimal diagonal preconditioners can significantly improve iterative methods.
The paper explores spinors and polyforms using quaternions and octonions.
problem Understanding spinors and polyforms in Clifford algebras.
method Generalizes Pauli matrices to quaternions and octonions, and relates these to spinor models.
result Explicitly describes Weyl spinors of Spin(4,4) related to quaternions and octonions.
Study on diagonal and separating coordinates for symmetric spaces of rank 1.
problem Existence and nonexistence of diagonal and separating coordinates for symmetric spaces of rank 1.
method Generalization of results by Gauduchon and Moroianu, 2020, and analysis of constant sectional curvature and orthogonal separation of variables.
result Diagonal coordinates exist if and only if the symmetric space has constant sectional curvature.
We describe a "concentration on the diagonal" condition on the Khovanov complex of tangles, show that this condition is satisfied by the Khovanov complex of the single crossing tangles, and prove that it is preserved by alternating planar algebra compositions. Hence, this condition is satisfied by the Khovanov complex …
We continue the study the Dolbeault dga of the formal neighborhood of an arbitary closed embedding of complex manifolds previously defined by the author in \cite{DolbeaultDGA}. The special case of the diagonal embedding has been studied in \cite{Diagonal}. We describe the Dolbeault dga explicitly in terms of the formal…
New probabilistic invariants bound classical topological complexity and category.
problem Bounding classical topological complexity and category.
method Developed probabilistic variants of one-category and diagonal topological complexity.
result Identified new invariants with distributional category and complexity on Eilenberg-Mac Lane spaces.
CompAdaGrad improves AdaGrad's performance without its computational cost.
problem Improving AdaGrad's performance without its high computational cost.
method CompAdaGrad combines full-matrix and diagonal regularization in a low-dimensional subspace.
result CompAdaGrad achieves better results than diagonal AdaGrad with linear computational complexity.
Paper develops methods for solving complex stochastic equations using Malliavin calculus.
problem Existence, uniqueness, and regularity of solutions to BSVIEs.
method Malliavin calculus for tackling diagonal processes and nonlinear dependence.
result Developed well-posedness results for BSVIEs, including probabilistic interpretation of PDEs and portfolio optimization.
Gradient methods work well on overparameterized diagonal linear networks.
problem Understanding why gradient-based methods work well in overparameterized models.
method Study of Deep Diagonal Linear Networks with gradient flow analysis.
result Gradient flow on layer parameters induces a mirror-flow dynamic in the effective parameter space, leading to explicit convergence guarantees.
New model handles complex non-linear relationships with hidden graph structures.
problem Modeling non-linear relationships with hidden graph-structured interactions.
method Block-diagonal localized mixture of polynomial experts (BLoMPE) regression model with penalized maximum likelihood selection criterion.
result Strong theoretical guarantee for finite-sample oracle inequality.
New phase harmonic covariance models capture non-Gaussian properties of stationary processes.
problem Capturing non-Gaussian properties of stationary processes using Fourier phase.
method Introduce phase harmonic covariance moments and maximum entropy models conditioned by these moments.
result Maximum entropy models from phase harmonic covariances improve image synthesis of turbulent flows.
Researchers find non-diagonal Einstein metrics in various signatures.
problem Finding non-diagonal four-dimensional cohomogeneity-one Einstein metrics in different signatures.
method Explicitly seeking and constructing new examples of non-diagonal Einstein metrics, particularly in neutral signature.
result Construct new examples of neutral signature non-diagonal Bianchi type VIII Einstein metrics with self-dual Weyl tensor.
This paper solves matrix blind joint block diagonalization with noise.
problem Identifying the diagonalizer and block diagonal structure of matrices under noise.
method Bi-block diagonalization method.
result The method can identify the exact solution under certain conditions.
Diagonalizes metrics of 3D Lorentzian manifolds.
problem Diagonalizing metrics of 3D Lorentzian manifolds.
method Applying the technique of moving frames.
result Every smooth Lorentzian 3-manifold admits an atlas with a diagonal metric.
Study Ricci vector fields on 2D space with diagonal metrics.
problem Understanding Ricci vector fields on 2D space with specific metrics.
method Examined Ricci vector fields on with a diagonal metric.
result Characterized Ricci vector fields on with a diagonal metric.
Develops a novel stochastic algorithm for diagonal estimation of large matrices.
problem Efficient diagonal estimation for large or implicit matrices.
method Adaptive parameter selection in a stochastic algorithm.
result Lower bound on random query vectors needed for estimation.
We consider moment matching techniques for estimation in Latent Dirichlet Allocation (LDA). By drawing explicit links between LDA and discrete versions of independent component analysis (ICA), we first derive a new set of cumulant-based tensors, with an improved sample complexity. Moreover, we reuse standard ICA techni…
Two Fisher information matrix estimators are analyzed for neural networks, focusing on their variances and trade-offs.
problem Estimating the Fisher information matrix in neural networks due to its high computational cost.
method Examined two popular diagonal Fisher information matrix estimators and their variances in neural networks for regression and classification.
result The variances of the estimators depend on the non-linearity with respect to different parameter groups and should not be neglected.
Study on invariant Einstein metrics on specific flag manifolds.
problem Existence of invariant Einstein metrics on real flag manifolds.
method Analysis of isotropy representations and Riemannian metrics.
result Existence of non-diagonal Einstein metrics on real flag manifolds.
Octagon map accelerates diagonal changes algorithm.
problem Improving the efficiency of diagonal changes algorithm.
method Octagon Farey map as an acceleration.
result Octagon map accelerates diagonal changes algorithm.
New diagonal knots found with non-torus structure.
problem Identifying knots with diagonal grid diagrams.
method Analysis of knots represented by diagonal grid diagrams.
result All diagonal knots are positive, and a new non-torus example is found.
Study finds symmetries in a special 3D space with a diagonal metric.
problem Identifying symmetries in a specific 3D space.
method Determining Killing vector fields on a diagonal metric in .
result Killing vector fields on the space with a diagonal metric have been identified.
Apollo improves nonconvex stochastic optimization efficiency.
problem Nonconvex stochastic optimization challenges.
method Adaptive parameter-wise diagonal quasi-Newton method approximating Hessian.
result Significant improvements in convergence speed and generalization over SGD and Adam.
Paper proves conditions for rational homology complex projective planes with singularities.
problem Proving conditions for rational homology complex projective planes with singularities.
method Leveraging results from smooth 4-manifolds, including Donaldson diagonalization theorem and Heegaard Floer correction terms.
result Eliminates the possibility of a rational homology complex projective plane with four singularities and identifies families of singularities obstructed by smooth conditions.
Structured State-Space Duality connects SSMs to masked attention.
problem Connecting SSMs and attention mechanisms for efficient modeling.
method Formalizing and generalizing SSD from scalar-identity to diagonal state matrices.
result Diagonal SSMs match training complexity lower bounds and support richer dynamics.
New method improves Pham's algorithm for joint diagonalization.
problem Optimizing joint diagonalization of matrices for statistical learning.
method Quasi-Newton method for Pham's diagonalization criterion.
result Proposed method outperforms Pham's algorithm in experiments.
Complex tensor factorization improves knowledge graph completion.
problem Automatically understanding and predicting missing relationships in large knowledge graphs.
method Use of complex-valued embeddings and unitary diagonalization.
result Complex embeddings lead to scalable and expressive models that outperform existing methods.
Equal diagonal energies proven on Liouville surfaces.
problem Diagonal energies on Liouville surfaces.
method Analyzing parameter curves and rectangles on Liouville surfaces.
result Diagonal energies are equal in n-dimensional Liouville manifolds.
Efficient subspace clustering using Kronecker product reduces computational complexity.
problem Efficiency and scalability issues in traditional subspace clustering methods for large datasets.
method Proposes a subspace clustering model based on the Kronecker product to reduce computational complexity.
result Significantly improved efficiency compared to state-of-the-art methods on public datasets.
Diagonal linear networks converge to lasso regularization path during training.
problem Understanding the regularization behavior of diagonal linear networks.
method Analyzing the training trajectory of diagonal linear networks and comparing it to the lasso regularization path.
result The training trajectory of diagonal linear networks is closely related to the lasso regularization path.
Diagonal RNNs improve music modeling performance and speed.
problem Improving symbolic music modeling efficiency and accuracy.
method Introduced diagonal recurrent matrices in RNNs for music modeling.
result Diagonal RNNs achieve better test likelihood and faster convergence.
We show that a basis of a semisimple Lie algebra of compact type, for which any diagonal left-invariant metric has a diagonal Ricci tensor, is characterized by the Lie algebraic condition of being "nice". Namely, the bracket of any two basis elements is a multiple of another basis element. This extends the work of Laur…