We develop a method for finding the zero modes of the Dirac operator in the presence of BPS monopoles. We use it to find the zero modes in the case of Abelian BPS monopoles in .
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48 results for “zero modes”
Revisits zero modes of Dirac operator on Eguchi-Hanson space.
problem Determining zero modes of the Dirac operator on Eguchi-Hanson space.
method Uses spin- spinors and formalism of differential forms to simplify calculations.
result Reproduces known normalisable zero modes of the twisted Eguchi-Hanson Dirac operator.
The paper analyzes zero modes on product manifolds and provides estimates for their norms.
problem Analyzing zero modes on product Riemannian manifolds.
method Using the zero mode equation and non-increasing condition on |\varphi|, the paper derives estimates for the norms of the vector field A.
result The derived estimates are sharp in even dimensions and provide insights into the behavior of zero modes.
The paper proves inequalities for zero mode equations on spin manifolds.
problem Sharp inequalities for zero mode equations on spin manifolds.
method Simple proof and classification of equality cases.
result Equality holds if and only if the solution is a Killing spinor and the manifold is Sasaki-Einstein.
We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature configurations, for which the spin connection has zero torsion and the associated R…
Introduces a massive variant of Ray-Singer Torsion to avoid zero modes in topological field theories.
problem Avoiding zero modes in the evaluation of path integrals for topological field theories.
method Introduces a massive variant of the Ray-Singer Torsion, involving determinants of the twisted Laplacian with mass but without zero modes.
result Explicitly evaluates the massive Ray-Singer Torsion on product manifolds and mapping tori.
Paper proves a spinor inequality for magnetic fields on spin manifolds.
problem Proving a spinor inequality for magnetic fields on spin manifolds.
method Analyzing the zero mode equation and using the Yamabe constant.
result The inequality holds for non-trivial solutions.
Let be an asymptotically conic manifold, in the sense that compactifies to a manifold with boundary in such a way that becomes a scattering metric on . A special case of particular interest is that of asymptotically Euclidean manifolds, where and the induced me…
Study Dirac operators on finite warped cylinders with gauge fields.
problem Characterize spectral flow on finite warped cylinders with gauge fields.
method Identify endpoint operators, derive determinant characterization, introduce regularized APS conditions.
result Regularized APS conditions admit a spectral-flow framework, matching zero-mode sets.
Vortex solutions on flat surfaces map to harmonic spinors on Nappi-Witten space.
problem Constructing Abelian magnetic zero-modes on flat spacetime.
method Establishing a correspondence between vortex equations and harmonic spinors on the Nappi-Witten space.
result Explicit solutions of a twisted Dirac equation induce harmonic spinors on Minkowski space.
New method uses random projections to estimate densities and modes efficiently.
problem Estimating densities and modes from sparse representations.
method Expand-and-sparsify representations followed by linear function and mode recovery algorithms.
result Optimal rates for density and mode estimation achieved.
This paper studies the space of harmonic forms and harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find a 2-parameter family of zero mod…
New principle for supersymmetric localization on Lie groups.
problem Computing supertrace of non-supersymmetric observables.
method Invariant supersymmetric deformations and fermionic zero modes.
result Path integral localizes to periodic orbits.
GAN+VER improves GANs by regularizing entropy to reduce mode collapse.
problem Mode collapse in GANs where the generator fails to capture all modes.
method Maximizing a variational lower bound on the entropy of generated samples.
result Significant improvement in evaluation metrics for real and generated samples.
We give estimates for the eigenvalues of multi-form modified Dirac operators which are constructed from a standard Dirac operator with the addition of a Clifford algebra element associated to a multi-degree form. In particular such estimates are presented for modified Dirac operators with a -degree form $0\leq k\leq…
We quantify forgetting in post-training models, distinguishing mass and drift.
problem Understanding and preventing forgetting in post-training generative models.
method Developed theoretical results under a two-mode mixture abstraction, formalizing mass and drift forgetting.
result Forgetting can be precisely quantified based on divergence direction, geometric overlap, and training regime.
Human computer interaction facilitates intelligent communication between humans and computers, in which gesture recognition plays a prominent role. This paper proposes a machine learning system to identify dynamic gestures using tri-axial acceleration data acquired from two public datasets. These datasets, uWave and So…
LMC loss barrier decreases to zero with large network width.
problem Understanding the LMC phenomenon in neural networks.
method Fine-grained analysis of LMC for two-layer ReLU networks.
result LMC loss barrier decreases to zero at a rate of O(m^-1/2) for large network width.
This study evaluates zero-shot LLMs in finance, finding ChatGPT performs well but fine-tuned models are better.
problem Evaluating zero-shot LLMs in financial tasks.
method Comparison of ChatGPT and fine-tuned models on annotated data.
result Fine-tuned models generally outperform zero-shot LLMs.
Study shows zero-shot super-resolution in neural operators is impossible in many cases.
problem Understanding the theoretical limits of zero-shot super-resolution in neural operators.
method Systematic theoretical study including information-theoretic and generalization bounds analysis.
result Zero-shot super-resolution is information-theoretically impossible in many settings.
We present a scalable Bayesian model for low-rank factorization of massive tensors with binary observations. The proposed model has the following key properties: (1) in contrast to the models based on the logistic or probit likelihood, using a zero-truncated Poisson likelihood for binary data allows our model to scale …
VINNAS uses variational inference to avoid mode collapse in neural architecture search.
problem Mode collapse in gradient-based NAS methods, leading to suboptimal architectures.
method Differentiable variational inference with variational dropout and automatic relevance determination.
result State-of-the-art accuracy with up to twice fewer non-zero parameters.
Mean shift clustering finds the modes of the data probability density by identifying the zero points of the density gradient. Since it does not require to fix the number of clusters in advance, the mean shift has been a popular clustering algorithm in various application fields. A typical implementation of the mean shi…
Using the submanifold quantum mechanical scheme, the restricted Dirac operator in a submanifold is defined. Then it is shown that the zero mode of the Dirac operator expresses the local properties of the submanifold, such as the Frenet-Serret and generalized Weierstrass relations. In other words this article gives a re…
Unified framework connects different neural network models.
problem Understanding the geometry of neural network loss landscapes.
method Unified framework capturing four symmetry classes.
result First discovery of low- and zero-barrier linear interpolation paths.
We analyze the resolvent of Schrödinger operators with short range potential on asymptotically conic manifolds (this setting includes asymptotically Euclidean manifolds) near . We make the assumption that the dimension is greater or equal to 3 and that has no null …
How periodic surfaces bendmath.DG
Periodic surfaces have a limited number of bending modes, equal to their membrane modes.
problem Understanding the limitations of bending modes in periodic surfaces.
method Analyzing deformation modes of periodic, piecewise smooth, simply connected surfaces.
result Effective membrane modes and bending modes are orthogonal, limiting the total number of modes to 3.
New method uses KL-divergence to create non-informative priors for multivariate Gaussian.
problem Handling hyperparameters for non-informative limits in multivariate Gaussian conjugate priors.
method Using scaled KL-divergence between multivariate Gaussians to construct Wishart and normal-Wishart conjugate priors.
result Forming non-informative priors without violating Wishart shape parameter restrictions.
LLMs learn to recommend models and hyperparameters from dataset metadata.
problem Model and hyperparameter selection in machine learning is challenging and resource-intensive.
method Converted datasets into metadata and prompted LLMs to recommend models and hyperparameters.
result LLMs can recommend competitive models and hyperparameters without search.
Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.
problem Disambiguating local and global modes in spatiotemporal data.
method Sparse-mode DMD with sparsity-promoting regularization.
result Explicitly constructs discrete and continuous spectra.
Dissertation tackles zero-shot anomaly detection, focusing on consistent anomalies and proposing CoDeGraph framework.
problem Consistent anomalies bias distance-based zero-shot anomaly detection methods.
method Formalized consistent anomalies, identified similarity scaling and neighbor-burnout phenomena, introduced CoDeGraph framework.
result CoDeGraph effectively suppresses consistent anomalies in zero-shot anomaly detection.
Motivated by advantages of current-mode design, this brief contribution explores the implementation of weight matrices in neuromemristive systems via current-mode memristor crossbar circuits. After deriving theoretical results for the range and distribution of weights in the current-mode design, it is shown that any we…
We introduce a novel approach for training adversarial models by replacing the discriminator score with a bi-modal Gaussian distribution over the real/fake indicator variables. In order to do this, we train the Gaussian classifier to match the target bi-modal distribution implicitly through meta-adversarial training. W…
We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose ex…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mod…
In a previous paper [\AS], we used superspace techniques to prove that perturbation theory (around a classical solution with no zero modes) for Chern--Simons quantum field theory on a general -manifold is finite. We conjectured (and proved for the case of -loops) that, after adding counterterms of the expecte…
Characterizes neutral deformation modes of minimal surfaces.
problem Understanding the energy content of deformation modes of minimal surfaces.
method Analyzes the energy content of stretching, drilling, and bending modes of minimal surfaces.
result All isometries of a minimal surface are globally neutral and give rise to soft elasticity.
Annealing in variational inference mitigates mode collapse: A theoretical study on Gaussian mixturesstat.ML
Mathematical analysis shows annealing prevents mode collapse in Gaussian mixtures.
problem Mode collapse in variational inference for multimodal distributions.
method Analyzed annealing strategies for Gaussian mixtures, derived formulas, and tested on neural networks.
result Appropriately chosen annealing schemes can robustly prevent mode collapse.
Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.
problem Manual tuning of sparsity parameters in traditional DMD.
method Time-delay embedding and Orthogonal Matching Pursuit.
result Autonomously determines optimally sparse subset of modes.
Geodesics connect model modes in neural network loss landscapes.
problem Connecting modes in neural network loss landscapes.
method Reframed mode connectivity in Information Geometry, hypothesized geodesics as mode-connecting paths, proposed algorithm to approximate geodesics.
result Geodesics achieve mode connectivity in neural networks.
A new, efficient -modes algorithm improves clustering of categorical data.
problem Clustering categorical data using existing methods like -means is inefficient.
method Developed a novel -modes algorithm called OTQT, which improves on existing methods.
result OTQT finds more accurate clusters per iteration and is faster overall.
Multimodal clustering is an unsupervised technique for mining interesting patterns in -adic binary relations or -mode networks. Among different types of such generalized patterns one can find biclusters and formal concepts (maximal bicliques) for 2-mode case, triclusters and triconcepts for 3-mode case, closed $n…
Mean Shift Rejection: Training Deep Neural Networks Without Minibatch Statistics or Normalizationcs.LG
Deep convolutional neural networks are known to be unstable during training at high learning rate unless normalization techniques are employed. Normalizing weights or activations allows the use of higher learning rates, resulting in faster convergence and higher test accuracy. Batch normalization requires minibatch sta…
Reflection Symmetry, APS Boundary Conditions, and Equivariant Spectral Flow on a Warped Cylindermath-ph
Study reflection symmetry and APS boundary conditions on a warped cylinder.
problem Analyzing reflection symmetry and APS boundary conditions for twisted Dirac operators on a finite warped cylinder.
method Examined reflection symmetry and APS boundary conditions for twisted Dirac operators on a finite warped cylinder, considering both fixed and varying holonomy.
result Reflection symmetry lifts to a unitary symmetry under specific conditions, and the spectral flow admits an RO(O(2))-valued decomposition for fixed holonomy.
EDLP samples flat modes in discrete spaces using entropy.
problem Sampling flat modes in discrete spaces is challenging.
method EDLP uses a continuous auxiliary variable and local entropy to guide sampling.
result EDLP consistently outperforms traditional methods in various tasks.
Proposes a Gaussian process for Koopman mode decomposition.
problem Estimating Koopman mode decomposition quantities and latent variables.
method Unsupervised Gaussian process for simultaneous estimation.
result Efficient parameter estimation through low-rank approximations.
Deep learning helps remove secondary -mode polarization to detect primordial gravitational waves.
problem Removing secondary -mode polarization from CMB data to detect primordial gravitational waves.
method Applied deep learning (ResUNet-CMB) to estimate and remove multiple sources of secondary -mode polarization.
result Deep learning can produce nearly optimal, unbiased estimates of the amplitude of primordial gravitational waves.
A new method for continual learning in GANs learns new modes with limited data.
problem Learning new target modes with limited samples while preserving previously learned ones.
method Mode-affinity score for generative modeling, generator replay, and weighted label generation.
result Gains over state-of-the-art methods, even with fewer training samples.