Generalizes graded bundles with more flexible transformation laws.
problem No specific problem stated; focuses on generalization of graded bundles.
method Introduces filtered bundles with more general polynomial transformation laws.
result Linearisation of filtered bundles is well-defined.
We show that a diffeological bundle gives rise to an exact sequence of internal tangent spaces. We then introduce two new classes of diffeological spaces, which we call weakly filtered and filtered diffeological spaces, whose tangent spaces are easier to understand. These are the diffeological spaces whose categories o…
Proves correspondence between harmonic and Higgs bundles.
problem Connecting harmonic and Higgs bundles for study.
method Kobayashi-Hitchin correspondence for polystable bundles.
result Establishes correspondence between good wild harmonic bundles and polystable good filtered λ-flat bundles. This research explores canonical Cartan connections for filtered G-structures.
problem Determining canonical Cartan connections for filtered G-structures.
method Generalization of parabolic geometries, Lie algebra valued forms, and explicit characterization.
result Existence of canonical Cartan connections for filtered G-structures, with specific features.
We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show th…
We study the geometry and topology of (filtered) algebra-bundles ΨZ over a smooth manifold X with typical fibre ΨZ(Z;V), the algebra of classical pseudodifferential operators of integral order on the compact manifold Z acting on smooth sections of a vector bundle V. First a theorem…
Geometry arising from two diffusion operators (smooth semi-elliptic, second order differential operators) on different spaces but intertwined by a smooth map is described. Particular cases arise from Riemannian submersions when the operators are Laplace-Beltrami operators, from equivariant operators on the total space …
Study Higgs bundles on CP1 with specific singularities, linking fixed points to W-algebra representations.
problem Analyzing Higgs bundles with irregular singularities and their fixed points.
method Introduced a C×-action on MK,N and classified its fixed points. result Found a 1-1 correspondence between fixed points and certain W-algebra representations.
A new approach to symbol calculus on filtered manifolds using C∗-algebras.
problem Symbol calculus on filtered manifolds with local isomorphism to stratified Lie groups.
method Establishing a surjective ∗-homomorphism between a C∗-algebra bundle and the algebra of bounded continuous sections. result Existence of a surjective ∗-homomorphism sym_M: Π_M → C_b(E_hom) with specific kernel properties. Let K be a null-homologous knot in a three-manifold Y. We give a description of the Heegaard Floer homology of integer surgeries on Y along K in terms of the filtered homotopy type of the knot invariant for K. As an illustration, we calculate the Heegaard Floer homology groups of non-trivial circle bundles ov…
Study of BGG sequences on foliated manifolds with transverse parabolic geometry.
problem Analysis of BGG sequences on foliated manifolds with transverse parabolic structures.
method Filtered calculus and transversal index theory for filtered manifolds.
result Derived curved BGG sequences for foliated manifolds with transverse parabolic geometry.
The paper establishes a correspondence between Higgs torsors and connections on curves.
problem Establishing a correspondence between Higgs torsors and connections on curves.
method Introduced a stability condition on filtered Stokes local systems and used it to prove a one-to-one correspondence.
result One-to-one correspondence between stable meromorphic parahoric Higgs torsors and stable meromorphic parahoric connections.
Motivated by the geometric theory of differential equations and the variational approach to the equivalence problem for geometric structures on manifolds, we consider the problem of equivalence for distributions with fixed submanifolds of flags on each fiber. We call them flag structures. The construction of the canoni…
We generalize Fulton and MacPherson's configuration space construction to weighted filtered manifolds.
problem Infinitesimal collision data in filtered manifolds with higher-order compatibility.
method Generalizing Fulton and MacPherson's blow-up approach to weighted arrangements of submanifolds.
result Smoothness of the weighted blow-up under reasonable assumptions.
Currents on Lie groups form a Hopf algebra structure.
problem Understanding algebraic structure of currents on Lie groups.
method Defined Hopf algebra structure on currents using convolution and wedge product.
result Explicit formulas for Hopf algebra operations on currents are derived.
We construct a new invariant of transverse links in the standard contact structure on R^3. This invariant is a doubly filtered version of the knot contact homology differential graded algebra (DGA) of the link. Here the knot contact homology of a link in R^3 is the Legendrian contact homology DGA of its conormal lift i…
Reduces path integrals for interacting systems using dependent coordinates.
problem Reducing path integrals for systems with symmetry.
method Reduction procedure based on Wiener-type path integral, optimal nonlinear filtering, and projection of mean curvature vector field.
result Shows non-invariance of the measure in the path integral under reduction and generates the Jacobian.
We show that if K: P \to R is an autonomous Hamiltonian on a symplectic manifold (P,Ω) which attains 0 as a Morse-Bott nondegenerate minimum along a symplectic submanifold M, and if c_1(TP)|_M vanishes in real cohomology, then the Hamiltonian flow of K has contractible periodic orbits with bounded period on all suffici…
Defines a bundle map for currents on manifolds using higher covariant derivatives.
problem Defining a bundle map for currents on manifolds.
method Using higher covariant derivatives on a manifold equipped with a torsion-free connection.
result The bundle of generalized Weyl algebras and its properties.
In principle, Floer theory can be extended to define homotopy invariants of families of equivalent objects (e.g. Hamiltonian isotopic symplectomorphisms, 3-manifolds, Legendrian knots, etc.) parametrized by a smooth manifold B. The invariant of a family consists of a filtered chain homotopy type, which gives rise to a …
Defines transverse symbols for foliated manifolds and proves their K-homology class.
problem Transverse index theory for foliated manifolds.
method Using filtrations of tangent bundles, defining transverse symbols, and constructing equivariant KK-classes.
result Transversally Rockland operators yield a K-homology class and there is a Poincare duality result.
Paper proves spectral filters can be transferred between graphs.
problem Proving spectral filters can be transferred between graphs.
method Introducing the Cayley smoothness space and proving filters in this space are linearly stable.
result Graph spectral filters are transferable if they are in the Cayley smoothness space.
This work prunes CNN filters based on their functionality, not just size.
problem Redundant filters in CNNs waste computation resources.
method Functionality-oriented filter pruning method.
result Pruning based on functionality optimizes computation and interprets filter importance.
A new SOHP filter improves trend estimation in economic time series.
problem Improving trend estimation in nonlinear economic time series.
method Recursive application of one-sided HP filter on updated cyclical components, combined with an incremental HP filtering algorithm.
result Better performance of SOHP filter compared to other HP-type filters on real economic data.
Deep density methods improve filtering in high-dimensional systems.
problem Nonlinear filtering in high-dimensional systems.
method Two deep density methods based on Feynman-Kac formulas and neural networks.
result Logarithmic deep backward stochastic differential equation filter outperforms classical methods in high dimensions.
The paper explores modifications to filter banks for speech recognition.
problem Improving speech recognition accuracy using modified filter banks.
method The authors investigate replacing triangular filters with Gabor or Gammatone filters, and rearranging filter bank computations to integrate features over smaller time scales.
result No significant improvements in phone error rate were observed with the modifications.
Pruning filters in CNNs improves interpretability, showing shape-selective filters are crucial for object recognition.
problem Interpreting the complex decision-making process of CNNs is challenging due to their large number of parameters.
method We developed a greedy structural compression scheme that prunes filters based on the classification accuracy reduction (CAR) index.
result Pruned filters in CNNs, especially those in the first and second layers, are more likely to be shape-selective, indicating their importance in object recognition.
Gradient filters track moving parameters under noisy data and misspecification.
problem Tracking multidimensional time-varying parameters under noisy observations and model misspecification.
method Gradient-based filters update parameters using the gradient of a postulated objective function, evaluated at either the predicted or updated parameters.
result Novel sufficient conditions for exponential stability of the filtered parameter path, and finite-sample and asymptotic mean squared error bounds.
We simplify Bayesian filtering by framing it as optimization, making it practical for high-dimensional systems.
problem Bayesian filtering struggles in high-dimensional state spaces like neural networks.
method We frame Bayesian filtering as optimization, using gradient descent for nonlinear cases.
result Our method results in effective, robust, and scalable filters for high-dimensional systems.
A new model optimizes Bloom filters using machine learning.
problem Improving the efficiency of Bloom filters for data sets.
method Modeling learned Bloom filters with machine learning, optimizing with sandwiching method.
result Optimized learned Bloom filters provide improved performance.
Develops an inverse particle filter for cognitive systems.
problem Tracking cognitive adversaries in counter-adversarial applications.
method Global filtering approach using Monte Carlo methods and differentiable I-PF.
result Demonstrates convergence to optimal inverse filter and improved estimation performance.
A novel method reduces dimensionality for filtering SRNs with observed variables.
problem Challenges in estimating hidden state variables in SRNs with limited observations.
method Filtered Markovian Projection (Filtered MP) for dimensionality reduction in filtering.
result Filtered MP guarantees consistency and superior computational efficiency in high dimensions.
Kernel learning FBSDE filter improves nonlinear filtering efficiency.
problem Nonlinear filtering problem in high-dimensional systems.
method Iterative and adaptive meshfree approach using forward backward SDE and KDE.
result Rigorous convergence analysis provided, supporting empirical results.
Paper develops a particle filter for rapid model parameter adaptation and change detection.
problem Rapidly adapting to changes in model parameters and distinguishing between regime shifts and stochastic volatility.
method Incorporates genetic algorithm elements into a particle filter for accelerated adaptation and change detection.
result The filter adapts to regime shifts extremely rapidly and provides a clear heuristic for distinguishing between regime shifts and stochastic volatility.
New method filters large networks from financial data to reveal key subnetworks.
problem Filtering large dimensional networks to isolate key constituents.
method Exploits spectral properties of high-dimensional data networks, tuning for sparsity and consistency.
result Shows method can interpolate between zero and maximal filtering, preserving spectral properties.
Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential esti…
Constructs tangent groupoid for filtered manifolds without coordinates.
problem No specific problem stated; intrinsic construction of tangent groupoid.
method Intrinsic construction of tangent groupoid.
result Intrinsic construction of tangent groupoid for filtered manifolds.
This work analyzes the stability of graph filters under large perturbations.
problem Stability of graph filters under large edge rewires.
method Proves a bound on stability using frequency response and community structure.
result Graph filter stability depends on perturbation to community structure.
Improved Kalman filter for non-linear, non-Gaussian data.
problem Estimating hidden variables with non-linear, non-Gaussian observations.
method Reproduces and extends Burkhart et al.'s discriminative Kalman filter.
result Enhanced filter performance for complex observation models.
Paper proves convergence of Kalman filter on Stiefel manifolds with measurement errors.
problem Filtering constant particle with measurement errors on Stiefel manifolds.
method Extended Kalman filter applied to Stiefel manifold-valued observations.
result Convergence of the extended Kalman filter proved for constant system process.
Advances deep network embedding through multi-filtering GCN.
problem Existing attribute embedding methods fail to capture different aspects of node features.
method Multi-filtering Graph Convolution Neural Network (GCN) framework.
result Significant improvement in link prediction and node classification tasks with limited training data.
Net2Vec maps filters to vectors to reveal complex concept encoding.
problem Understanding how deep neural networks encode semantic concepts.
method Net2Vec framework that maps semantic concepts to vectorial embeddings based on filter responses.
result Multiple filters are often required to code for a concept, and filters help encode multiple concepts.
This work preserves linear invariants in ensemble filters for non-Gaussian data assimilation.
problem Maintaining critical invariants like mass, stoichiometric balance, and charge in non-Gaussian data assimilation.
method Introducing a novel class of nonlinear ensemble filters using measure transport theory.
result Recovery of a constrained Kalman filter for Gaussian settings and combination with regularization techniques.
Convolutional Bayesian filtering generalizes state estimation by incorporating inequality conditions.
problem Standard Bayesian filtering assumes exact conditional probabilities, limiting its applicability.
method Introducing inequality conditions transforms conditional probabilities into convolutional forms, expanding the filtering framework.
result Convolutional Bayesian filtering encompasses standard Bayesian filtering and allows for more nuanced model consideration.
Paper learns to rotate filters for group convolutions.
problem Difficult to rotate 3x3 filters on pixel grids.
method Learn filter basis and rotation-invariant coefficients; switch basis for rotation.
result Produces feature maps insensitive to input rotations.
EnSF improves accuracy in tracking high-dimensional nonlinear systems.
problem Low accuracy in high-dimensional, nonlinear filtering problems.
method Score-based diffusion model, mini-batch Monte Carlo estimator.
result EnSF outperforms state-of-the-art methods in tracking high-dimensional systems.
Non-linear filter aggregation improves image denoising.
problem Efficiently denoise images with complex noise patterns.
method Non-linear aggregation of preliminary filters using a new proximity metric.
result The aggregated filters outperform individual filters in denoising.
Improved Kalman filter for Stiefel manifold measurements.
problem Improving accuracy in measurements on Stiefel manifolds.
method Generalization of extended Kalman filter for Stiefel manifold-valued measurements.
result Significant improvement over raw measurements.