The study uses machine learning to model semantic drift in digital content.
problem Detecting and measuring semantic drift in evolving digital content.
method Employing machine learning algorithms on a dataset of Tate Galleries metadata.
result Semantic drift can be modeled using a metaphor of social mechanics.
DGD Gallery stores and shares digital research data online.
problem Storing and sharing of digital research data.
method Online web service for storage, sharing, and publication.
result Publicly available digital research data.
Study on knots formed by Coxeter galleries, finding bounds and symmetric trefoils.
problem Understanding knots created by Coxeter galleries.
method Examined knots in affine Coxeter complex of type \widewedge{B3}, constructing galleries and proving properties.
result Found bounds on stick number and smallest length of symmetric trefoils.
Machine learning accurately distinguishes Sato-Tate groups for hyperelliptic curves.
problem Arithmetic of hyperelliptic curves and Sato-Tate conjecture.
method Bayesian classifier and machine learning techniques applied to L-functions of hyperelliptic curves.
result Machine learning can distinguish Sato-Tate groups with high accuracy and speed.
For a Liouville domain W W W satisfying c 1 ( W ) = 0 c_1(W)=0 c 1 ( W ) = 0 , we propose in this note two versions of symplectic Tate homology H → T ← ( W ) \underrightarrow{H}\underleftarrow{T}(W) H T ( W ) and H ← T → ( W ) \underleftarrow{H}\underrightarrow{T}(W) H T ( W ) which are related by a canonical map $κ\colon \underrightarrow{H}\underleftarrow{T}(W) \to \underleftarrow{H}\under…
New spectral sequence connects to topological Hochschild homology.
problem Connecting spectral sequences to topological Hochschild homology.
method Developed a spectral sequence and applied Tate diagonal techniques.
result Spectral sequence converges to localized topological Hochschild homology.
Machine learning predicts Shafarevich-Tate group orders of elliptic curves.
problem Predicting the order of the Shafarevich-Tate group of elliptic curves.
method Train feed-forward neural network and regression models on elliptic curve invariants.
result Models achieve high accuracy ( > 0.9 > 0.9 > 0.9 ) and predict orders not seen during training. The Koszul-Tate resolution is described in the context of the geometry of jet spaces and differential equations. The application due to Barnich, Brandt, and Henneaux of this resolution to computing the horizontal cohomology is analyzed. Relations with the Vinogradov spectral sequence are discussed.
The paper connects Chern-Simons invariants to mixed Tate motives in hyperbolic 3-manifolds.
problem Understanding the relationship between Chern-Simons invariants and mixed Tate motives in hyperbolic 3-manifolds.
method Constructing a mixed Tate motive over the invariant trace field whose image equals the Chern-Simons invariant and complex volume.
result The mixed Hodge realization of the motive is a quotient of the path torsor of the augmented character variety.
Constructs a new graded variety from algebraic data.
problem Creating a Z \mathbb Z Z -graded extension of differential varieties. method Algorithm using homotopy retract data of Koszul-Tate resolution.
result Significantly reduced number of homological computations.
From an operad C with an action of a group G, we construct new operads using the homotopy fixed point and orbit spectra. These new operads are shown to be equivalent when the generalized G-Tate cohomology of C is trivial. Applying this theory to the little disk operad C_2 (which is an S^1 operad) we obtain variations o…
Study shows spectral action coefficients are periods in specific spacetimes.
problem Understanding spectral action coefficients in Robertson-Walker spacetimes.
method Analyzes asymptotic expansion coefficients as periods of mixed Tate motives.
result Coefficients are periods involving relative motives of complements of unions of hyperplanes and quadric hypersurfaces.
Study heat kernel coefficients in Bianchi IX gravity models.
problem Analyzing gravitational wave properties in Bianchi IX models.
method Algebraic geometry and motives applied to heat kernel coefficients.
result Coefficients are algebro-geometric periods of motives.
Normal forms for Q-structures on graded manifolds explained.
problem Understanding structures of Q-manifolds on graded manifolds.
method Local and global normal forms results for Q-structures.
result Structures are concentrated along the zero-locus of curvatures.
The paper shows that certain geometric structures remain unchanged under specific twists.
problem The rational Beauville-Bogomolov-Fujiki lattices of related fibrations are similar.
method Analytic and étale topologies, Hodge structures, and degenerate twistor deformations.
result Isomorphisms of graded vector spaces and Hodge-similar lattices.
The paper defines slant submanifolds in Norden manifolds.
problem None explicitly stated; focuses on definition and properties.
method Definition and study of properties of slant submanifolds.
result Properties and examples of slant submanifolds in Norden manifolds.
If G 1 G_1 G 1 and G 2 G_2 G 2 are finite groups with periodic Tate cohomology, then G 1 × G 2 G_1\times G_2 G 1 × G 2 acts freely and smoothly on some product S n × S n S^n \times S^n S n × S n .
Cyclification of orbifolds explained in cohesive higher topos theory.
problem Understanding cyclification of orbifolds in geometric and algebraic contexts.
method Cohesive higher topos theory and transgression of cohomological charges.
result Cyclification of orbifolds is a fundamental base-change construction.
Paper studies Iwasawa invariants for 3-manifolds, proving a formula similar to Kida's.
problem Analogizing Iwasawa invariants to 3-dimensional topology.
method Using p p p -adic representations of a finite group and parallel to Iwasawa's second proof. result Proves an analogue of Kida's formula for λ λ λ -invariants in p p p -extensions of Z p \mathbb{Z}_p Z p -fields for 3-manifolds. Open geometry puzzles keep the author engaged.
problem Open problems in geometry that challenge the author.
method Collection of open problems based on puzzle-charm.
result No spare hands in solving the problems.
New method designs joint initial noises for diffusion models to improve diversity and alignment.
problem Independent initial noises limit diversity in generated images.
method Coupling of initial noises, maintaining Gaussian distribution while allowing dependence.
result Repulsive Gaussian coupling improves diversity without increasing sampling cost.
Constructs a topological cover of real line's multiplicative group.
problem Topological cover of real line's multiplicative group.
method Homological algebra, 2D Lorentz geometry, high-school trigonometry.
result Interesting topological cover constructed.
Given a generic Lagrangian system, its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. This construction is generalized to arbitrary differential operators on a smooth fiber bundle. Namely, if a certain necessary and sufficient condi…
Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford-Tate domains, arise as open G R G_{\mathbb{R}} G R --orbits in flag varieties G / P G/P G / P . We investigate Hodge--theoretic aspects of the geometry and representation theory associated with these flag varieties. In particular, w…
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties: not on…
A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. However, non-tri…
The paper generalizes convex and star-shaped concepts to symplectic spaces and studies variational problems.
problem Generalizing convex and star-shaped concepts to symplectic vector spaces.
method Study of variational problems for symplectically convex and star-shaped curves.
result Extremal points of the variational problem are rigid multiply traversed conics for a range of parameters.
Constructs spectral sequences for Morava E-theory of configuration spaces.
problem Computing Morava E-theory of configuration spaces and related spaces.
method Uses spectral sequences and Chevalley-Eilenberg-like complexes for Hecke Lie algebras.
result Identifies E2-page of spectral sequence and computes Morava E-theory groups.
The paper studies deformations of Lagrangian fibrations on symplectic manifolds.
problem Understanding deformations of Lagrangian fibrations on holomorphic symplectic manifolds.
method Analyzes degenerate twistor deformations and meromorphic sections.
result Compact hyperkahler manifolds with primitive fibers admit meromorphic sections.
Refines intersection product in equivariant homology, generalizing string products.
problem Unified string products on manifolds and classifying spaces.
method Equivariant intersection product, string product, secondary product.
result Defines secondary versions of string products, reducing to cup product in Tate cohomology.
New instanton homology theories for 3-manifolds and bundles.
problem Defining instanton homology for a class of 3-manifolds and bundles.
method Functorial construction for 4-manifold cobordisms, algebraic construction of homology theories for dg-modules.
result Isomorphic to Floer's instanton homology for admissible bundles, calculates I ∞ I^\infty I ∞ in all cases it is defined. System learns user preferences to synthesize materials quickly.
problem Slow material synthesis for novice and expert users.
method Gaussian Process Regression for user preferences, neural network for real-time image predictions.
result Real-time material synthesis enables novice users to generate hundreds of models.
Study the moduli space of polynomials with resultant 1, linking topology, geometry, and arithmetic.
problem Understanding the moduli space of polynomials with resultant 1.
method Relate the topology, geometry, and arithmetic of the moduli space, compute étale cohomology, eigenvalues of Frobenius, and cardinality of points.
result Showed the étale cohomology of the moduli space is pure and of Tate type under certain conditions.
A new method for cross-view classification using divide-and-conquer.
problem Cross-view classification with nonlinear manifolds and outliers.
method Divide-and-Conquer strategy applied to three subproblems: view discrepancy, intrinsic structure, and discriminability.
result Significant improvement in classification accuracy and robustness compared to state-of-the-art methods.
Data science reveals patterns in elliptic curve ranks and coefficients.
problem Understanding rational points on elliptic curves via BSD conjecture.
method Data science, machine learning, topological data analysis.
result Patterns and distributions in rank versus Weierstrass coefficients.
FORBES learns flexible belief states for POMDPs using normalizing flows.
problem Accurately modeling belief states in POMDPs for high-dimensional, continuous spaces.
method Integrates normalizing flows into variational inference for continuous belief state learning.
result FORBES learns flexible belief states that enable multi-modal predictions and high-quality reconstructions.
Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image s…
Unified theory of orbifolds and cohomology.
problem Formulating a general theory of orbifolds unifying differential and equivariant cohomology.
method Abstract axiomatization in higher topos theory and concrete models for various orbifolds.
result Fully faithful embedding of orbifolds into a cohesive infinity-topos with proper equivariant cohomology.
Advances data-driven coarse-graining for complex systems.
problem Extracting governing equations from high-dimensional, time-scale disparity problems.
method Probabilistic state-space model with Stochastic Variational Inference for sparse Bayesian learning.
result Quantifies predictive uncertainty and reconstructs fine-scale system evolution.
A new system combines vision and language for person re-identification.
problem Real-world surveillance lacks visual data for person re-identification.
method Two-stream CNN framework with shared logits, CCA for modalities, multi-modal testing protocol.
result 22% improvement in re-identification performance with multi-modal queries.
NFT art market shows strong preferential ties among sellers and buyers.
problem Reducing preferential ties in NFT art market.
method Analyzing NFT art sales data from multiple galleries.
result NFT art market is highly concentrated with preferential ties.
WARPd method solves inverse problems with approximate sharpness conditions.
problem Reconstruction of signals from undersampled and noisy measurements.
method First-order method based on primal-dual iterations with restart-reweight scheme.
result WARPd achieves stable linear convergence under generic approximate sharpness condition.
This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting the conformal representation upon the disc of a {\it compact bordered Riemann surface}. The theory in question has some well-known…
Study explores how dataset breadth and depth affect Siamese Neural Network performance.
problem Impact of dataset breadth and depth on Siamese Neural Network performance.
method Experiments with three keystroke datasets varying breadth and depth factors.
result Increasing dataset breadth improves model performance, while depth's impact varies by dataset type.
Paper proposes a deep learning method for person re-identification using set to set distance.
problem Matching images of the same person across different camera views with large appearance variations.
method Uses deep learning to model set to set (S2S) distance, focusing on intra-class compactness and inter-class separation.
result The method effectively finds matched targets in video galleries, outperforming state-of-the-art approaches.