Instantons on ALE spaces described for classical groups.
problem Instantons on ALE spaces for classical groups.
method ADHM type description extension of unitary groups.
result Description of instantons on ALE spaces for classical groups.
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48 results for “ADHM method”
Paper localizes ADHM construction for ASD instantons over smooth domains.
problem Characterizing ASD instantons over smooth bounded domains.
method Develops a local analogue of ADHM construction using Hilbert spaces and bounded Hermitian operators.
result Describes degeneration of construction when instantons develop curvature singularity.
Instantons on various spaces can be constructed via a generalization of the Fourier transform called the ADHM-Nahm transform. An explicit use of this construction, however, involves rather tedious calculations. Here we derive a simple formula for instantons on a space with one periodic direction. It simplifies the ADHM…
We examine the anomalies arising in instanton calculus as detailed by Damiano Anslemi in 1994. Whereas Anselmi uses BRST theory, we use the ADHM construction to arrive at the same conclusions from a differential-geometric way. We observe that Anselmi's TQFT is similar to Donaldson Theory applied to charge 1 instantons …
Study finds unique instanton for small α values in SU(2) Hopf fibration.
problem Identifying Yang-Mills connections in the context of α-energy.
method Approximations with Yang-Mills α-energy, focusing on SU(2) Hopf fibration.
result SO(4) invariant ADHM instanton is the unique α-critical point for small α values.
We consider the action on instanton moduli spaces of the non-local symmetries of the self-dual Yang-Mills equations on discovered by Chau and coauthors. Beginning with the ADHM construction, we show that a sub-algebra of the symmetry algebra generates the tangent space to the instanton moduli space at ea…
Monads link instantons and bow solutions in complex geometry.
problem Linking instantons and bow solutions via monads.
method Generalized ADHM-Nahm transform and monads.
result Established one-to-one correspondence between instantons and bow solutions.
On the compactness problem for a family of generalized Seiberg-Witten equations in dimension threemath.DG
Abstract: Proves compactness theorem for generalized Seiberg-Witten equations in 3D.
problem Compactness of solutions to generalized Seiberg-Witten equations in 3D.
method Abstract compactness theorem for a family of generalized Seiberg-Witten equations in dimension three.
result Recovers and extends known compactness theorems for stable flat connections and Seiberg-Witten equations.
Study of calorons with rotation map symmetry.
problem Understanding the symmetry groups of calorons.
method Utilizing a modified ADHM construction for calorons, derived from Charbonneau and Hurtubise's work.
result Construction of new calorons through fixed points of symmetry groups.
We make some comments on noncommutative -instantons on . We elaborate on the equations for the ASD-connection for free modules. Further we make some remarks on the computation of the topological index of ADHM instantons.
Explains a 1978 construction for Yang-Mills instantons.
problem None explicitly stated; focuses on explaining a construction.
method Atiyah-Drinfeld-Hitchin-Manin construction
result Explains the ADHM construction of Yang-Mills instantons.
We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.
The paper studies chambered invariants of real Cauchy-Riemann operators on Riemann surfaces.
problem Counting pseudo-holomorphic curves in symplectic Calabi-Yau 3-folds.
method Constructs three chambered invariants: , , , defined by counting solutions to ADHM vortex equations and pseudo-holomorphic sections of bundles.
result Conjectures a relationship between and and symplectic invariants.
New instantons found on Euclidean Schwarzschild manifold, challenging existing theories.
problem Challenging the understanding of instantons on the Euclidean Schwarzschild manifold.
method Exploring a correspondence between planar Abelian vortices and spherically symmetric instantons.
result Complete description of a connected component of the moduli space of unit energy SU(2) instantons.
A new method counts associative submanifolds and Seiberg-Witten monopoles.
problem Counting associative submanifolds and Seiberg-Witten monopoles in G2-manifolds.
method Floer homology groups generated by associative submanifolds and solutions of Seiberg-Witten equations.
result Construction of Floer homology groups associated with G2-manifolds.
We show that the integral of the first Pontrjagin class is given by an integer and it is identified with instanton number of the U(n) gauge theory on noncommutative . Here the dimension of the vector space that appear in the ADHM construction is called Instanton number. The calculation is done in operato…
Detects anomalies in multiple processes using hidden Markov models.
problem Detecting an anomalous process among many with hidden states.
method Sequential search strategy using ADHM algorithm.
result ADHM algorithm effectively leverages temporal correlations.
We present ADHM-Nahm data for instantons on the Taub-NUT space and encode these data in terms of Bow Diagrams. We study the moduli spaces of the instantons and present these spaces as finite hyperkahler quotients. As an example, we find an explicit expression for the metric on the moduli space of one SU(2) instanton. W…
Co-Higgs bundles on P^1math.AG
Co-Higgs bundles are Higgs bundles in the sense of Simpson, but with Higgs fields that take values in the tangent bundle instead of the cotangent bundle. Given a vector bundle on P^1, we find necessary and sufficient conditions on its Grothendieck splitting for it to admit a stable Higgs field. We characterize the rank…
The paper introduces new knot invariants using singular instanton gauge theory.
problem Developing new knot invariants using singular instanton gauge theory.
method Using singular instanton gauge theory, the paper constructs invariants and Morse chain complexes.
result The constructions lead to a triad of groups and several concordance invariants.
Nakajima quiver bundlesmath.AG
Introduces Nakajima bundles on algebraic curves, generalizing quiver representations and bundles.
problem Generalizing quiver representations and bundles on algebraic curves.
method Assigns complex vector bundles and sections/connections to nodes and edges of a quiver, using gauge-theoretic characterizations.
result Proves Hitchin-Kobayashi correspondence between stable quiver bundles and Nakajima bundle representations.
A trisymplectic structure on a complex 2n-manifold is a triple of holomorphic symplectic forms such that any linear combination of these forms has constant rank 2n, n or 0, and degenerate forms in belong to a non-degenerate quadric hypersurface. We show that a trisymplectic manifold is equipped with a holomorphic 3…
We consider SU(2)-equivariant dimensional reduction of Yang-Mills theory on manifolds of the form , where is a smooth manifold and is a three-dimensional Sasaki-Einstein orbifold. We obtain new quiver gauge theories on whose quiver bundles are based on the affine ADE Dynkin diagram associ…
This article provides an explicit construction for a family of singular instantons on S^4 S^2 with arbitrary real holonomy parameter α. This family includes the original α= 1/4, c_2 = 3/2 solution discovered by P. Forgacs, Z. Horvath, and L. Palla, and our approach is modeled on that of their 1981 paper. Our primary to…
New method for moduli spaces of twisted quiver representations and Higgs bundles.
problem Computing moduli spaces of twisted quiver representations and Higgs bundles.
method Extending twisted A-type quiver representations to any genus using Hitchin stability and deformation theory.
result Explicit geometric identifications of moduli spaces of twisted representations of argyle quivers on .
Improved iterative methods for risk parity portfolio weights.
problem Solving for portfolio weights in risk parity allocation.
method Enhanced CCD and Newton methods, including a rescaling step and improved initial guess.
result Improved CCD method is the best, three times faster with 40% fewer iterations.
We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than o…
A new method combines Laplace and Variational Bayes for scalable inference.
problem Complex models and large datasets make exact inference infeasible.
method Low-Rank Variational Bayes Correction (VBC) using Laplace method and Variational Bayes correction in a lower dimension.
result The method ensures scalability in both model complexity and data size.
Unified framework for model explanation methods based on feature removal.
problem Unclear relationships and preferences among various model explanation methods.
method Characterizes removal-based explanations along three dimensions.
result Unified 26 existing methods, including widely used approaches.
This work reviews and evaluates methods for predicting prediction intervals in regression problems.
problem Calibration of prediction intervals in regression problems.
method Four classes of methods: Bayesian, ensemble, direct interval estimation, and conformal prediction.
result Conformal prediction can be used as a general calibration procedure.
Derives kernel PCA with Nyström method for scalability.
problem Scalability of kernel PCA.
method Nyström method for kernel PCA.
result Provides scalable alternative to full kernel PCA.
In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …
Develops a fast method for pricing American options under variance gamma model.
problem Inefficient methods for pricing American options under variance gamma model.
method Inspired by quadratic approximation method, uses machine learning on pre-calculated quantities to reduce error.
result Proposed method is efficient and accurate for practical use.
Pricing Derivatives under Multiple Stochastic Factors by Localized Radial Basis Function Methodsq-fin.CP
Two RBF methods solve complex financial derivatives pricing problems.
problem Pricing derivatives in models with multiple stochastic factors.
method Radial Basis Function Partition of Unity and Radial Basis Function generated Finite Differences methods.
result Both methods achieve high accuracy and are efficient for solving multi-dimensional PDEs.
New method combines spectral and sparse methods for Gaussian processes.
problem Efficiently fitting Gaussian processes to large datasets.
method Orthogonally decoupled variational Fourier features.
result Competitive performance on synthetic and real-world data.
Simple stochastic Newton and cubic Newton methods with fast convergence.
problem Minimizing large numbers of smooth and strongly convex functions.
method Stochastic Newton and cubic Newton methods with simple local linear-quadratic rates.
result Local linear-quadratic convergence results with fast adaptation to problem's curvature.
Improved spectral methods of moments for robust latent variable model learning.
problem Limited robustness of spectral methods of moments to model misspecification.
method Hierarchical approach using approximate joint diagonalization instead of tensor decomposition.
result Our method outperforms previous tensor decomposition methods in speed and model quality.
VAN method optimizes learning tasks with unified methods.
problem Optimizing learning tasks in active and reinforcement learning.
method Variational Adaptive-Newton method that unifies optimization, inference, and evolution strategies.
result VAN performs well on various learning tasks.
A Large-Scale Comparative Analysis of Imputation Methods for Single-Cell RNA Sequencing Dataq-bio.GN
A comprehensive benchmark of 15 scRNA-seq imputation methods across various datasets and analyses.
problem Imputation of single-cell RNA sequencing data to recover latent transcriptional signals.
method Evaluation of 15 imputation methods across 30 datasets and 6 downstream analyses.
result Traditional methods generally outperform DL-based methods in scRNA-seq data analysis.
New methods using natural gradient for structured optimization.
problem Structured optimization problems.
method Structured second-order methods via natural gradient descent.
result Efficiency demonstrated on non-convex and deep learning problems.
Improved A2C method with lower variance.
problem Reducing variance in deep policy gradient methods.
method Using control variate theory, derived a new A2C formulation with lower variance.
result New A2C method has lower variance and improved performance.
Unified Convergence Analysis of Stochastic Momentum Methods for Convex and Non-convex Optimizationmath.OC
Recently, {\it stochastic momentum} methods have been widely adopted in training deep neural networks. However, their convergence analysis is still underexplored at the moment, in particular for non-convex optimization. This paper fills the gap between practice and theory by developing a basic convergence analysis of t…
A new method speeds up deep neural network training.
problem Nonconvex optimization in deep neural networks.
method Scaled conjugate gradient method for nonconvex optimization.
result The method converges faster and achieves lower scores in practical applications.
We propose a new stochastic dual coordinate ascent technique that can be applied to a wide range of regularized learning problems. Our method is based on Alternating Direction Multiplier Method (ADMM) to deal with complex regularization functions such as structured regularizations. Although the original ADMM is a batch…
NCG methods improve shape optimization efficiency.
problem Shape optimization problems
method Nonlinear conjugate gradient methods
result NCG methods are efficient for shape optimization
Uncertainty Aware Trader-Company Method: Interpretable Stock Price Prediction Capturing Uncertaintyq-fin.CP
Proposes UTC method for stock price prediction with uncertainty quantification.
problem Lack of uncertainty estimates in stock prediction methods.
method Combines TC method with probabilistic modeling for point and uncertainty predictions.
result UTC method achieves higher returns and lower risks than baselines.
Various approaches to gene selection for cancer classification based on microarray data can be found in the literature and they may be grouped into two categories: univariate methods and multivariate methods. Univariate methods look at each gene in the data in isolation from others. They measure the contribution of a p…
Survey of spectral, probabilistic, and deep metric learning methods.
problem Developing effective distance metrics for various machine learning tasks.
method Divided into spectral, probabilistic, and deep approaches, covering various techniques and their applications.
result Comprehensive overview of metric learning methods, including new developments and applications.