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.
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.
Study examines deformations of Kerr-(A)dS near horizon geometry.
problem Analyzing deformations of Kerr-(A)dS near horizon geometry.
method Two-part proof: elimination of Fourier modes and analyticity argument.
result No odd Fourier modes found for linear perturbations.
New solutions found for bending of flat surfaces and origami structures.
problem Understanding the energy-efficient bending modes of origami tessellations and corrugated shells.
method Direct construction of closed-form solutions for surfaces of translation.
result Three inextensional modes identified for surfaces of translation, including stretching, bending, and twisting.
Study explores kinematics of surfaces under metric restrictions.
problem Understanding the kinematics of surfaces under metric constraints.
method Analyzed three energy contents: stretching, drilling, and bending.
result Metric restrictions can hinder the elastic response of a shell.
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.
Study finds how periodic surfaces can bend without stretching.
problem Understanding isometric deformations of periodic surfaces.
method Characterization of isometric deformations using a constraint derived from Gauss theorem.
result Relates surface stretching to bending and twisting.
User interfaces provide an interactive window between physical and virtual environments. A new concept in the field of human-computer interaction is a soft user interface; a compliant surface that facilitates touch interaction through deformation. Despite the potential of these interfaces, they currently lack a signal …
We study massless deformations of generalized calibrated cycles, which describe, in the language of generalized complex geometry, supersymmetric D-branes in N=1 supersymmetric compactifications with fluxes. We find that the deformations are classified by the first cohomology group of a Lie algebroid canonically associa…
New geometric theory explains nonuniform origami responses.
problem Understanding nonuniform responses in origami sheets.
method Purely geometric continuum theory capturing nonuniform, nonlinear response.
result Three modes govern nonuniform response, varying smoothly across the sheet.
We compute the noncommutative de Rham cohomology for the finite-dimensional q-deformed coordinate ring Cq[SL2] at odd roots of unity and with its standard 4-dimensional differential structure. We find that H1 and H3 have three additional modes beyond the generic q-case where they are 1-dimensional, while $H…
Spectral flow connects manifold geometry to rigidity criteria.
problem Tackling rigidity of simply-connected closed manifolds.
method Spectral deformation flow and invariant-based approach.
result Spherical profile is the unique manifold-compatible asymptotic realization.
Frustration causes buckling-like behavior in tubular foldable mechanisms.
problem Kinematic coupling and geometric confinement in tubular foldable mechanisms.
method Analytical and numerical solutions of exact kinematics.
result Frustration propagates axially as if by buckling in tubular states.
A new method for non-rigid point set registration reduces computational complexity.
problem Efficiently registering non-rigid point sets with large numbers of points.
method Structured Analytic Coherent Point Drift (Analytic-CPD) reformulates CPD for structured analytic mappings.
result Analytic-CPD reduces computational complexity by controlling the deformation model's dimensionality.
A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that equipping Lie algebroids E with a fiber metric having sufficiently …
In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several desirable mathematical …
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.
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…
Compactification of M- / string theory on manifolds with G2 structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a non-trivial g…
We prove a trace formula for three-dimensional spherically symmetric Riemannian manifolds with boundary which satisfy the Herglotz condition: The wave trace is singular precisely at the length spectrum of periodic broken rays. In particular, the Neumann spectrum of the Laplace--Beltrami operator uniquely determines the…
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…
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 k-modes algorithm improves clustering of categorical data.
problem Clustering categorical data using existing methods like k-means is inefficient. method Developed a novel k-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 n-adic binary relations or n-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…
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 B-mode polarization to detect primordial gravitational waves.
problem Removing secondary B-mode polarization from CMB data to detect primordial gravitational waves. method Applied deep learning (ResUNet-CMB) to estimate and remove multiple sources of secondary B-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.
Empirical study shows GANs overfit and drop modes when training is deterministic.
problem Understanding overfitting and mode drop in GAN training.
method Empirical analysis of GAN training with and without stochasticity.
result GANs overfit and drop modes when training is deterministic.
The paper finds shape modes for vortices in a specific sigma model.
problem Existence of internal modes in CP1 vortices. method Developed a geometric formalism based on the Bogomol'nyi decomposition of the energy functional.
result Proved the existence of at least one shape mode for a general CP1 vortex solution. Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Reg…
This paper is inspired from the nice result of Andrew Hassell on the eigenfunctions in the stadium billiard. From a classical paper of V. Arnol'd, we know that quasi-modes are not always close to exact modes. We show that, for almost all Riemannian metrics on closed surfaces with an elliptic generic closed geodesic C, …
Mode clustering is a nonparametric method for clustering that defines clusters using the basins of attraction of a density estimator's modes. We provide several enhancements to mode clustering: (i) a soft variant of cluster assignment, (ii) a measure of connectivity between clusters, (iii) a technique for choosing the …
New tool detects 'fleeting modes' causing excess risk in financial markets.
problem Detecting portfolios with statistically significant excess risk in financial markets.
method Random Matrix Theory to identify 'fleeting modes' independent of underlying correlation structure.
result Fleeting modes exist in both futures and equity markets, and momentum is a source of excess risk.
Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical an…
Unified model predicts multi-mode failure with multi-sensor data.
problem Independent failure mode and RUL prediction ignores inherent relationship.
method Hierarchical Bayesian framework with Cox model, Gaussian process, and multinomial distributions.
result Robust uncertainty quantification and accurate prediction of multi-mode failure.
Hybrid model for multimodal distributions using diffusion and classification.
problem Sampling from multimodal distributions with correct proportions.
method Divide-and-conquer strategy: identify modes, train classifiers, diffusion models, bridge sampling.
result Framework effectively handles multimodal distributions in high dimensions.
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 R3.
Density mode clustering is a nonparametric clustering method. The clusters are the basins of attraction of the modes of a density estimator. We study the risk of mode-based clustering. We show that the clustering risk over the cluster cores --- the regions where the density is high --- is very small even in high dimens…
A new method learns from multi-modal sequences with external memory.
problem Learning new modes in a dynamic environment without prior knowledge.
method Maintains a neural episodic memory with a Dirichlet Process prior to store mode descriptors and transfers knowledge through retrieval.
result Performs continual learning favorably compared to mainstream approaches.
The paper evaluates samplers on multi-modal targets, focusing on mode separation and recovery.
problem Handling multi-modality in sampling.
method Synthetic experimental setting focusing on mode relative importance recovery.
result Illustrates the challenges and potential of samplers in multi-modality.
Improves generative model coverage of underrepresented modes.
problem Generative models miss underrepresented modes in data.
method Leverage score sampling for complete mode coverage.
result Significantly improves mode coverage compared to standard methods.
The paper improves GP regression for sparse sensor data in structural mode shape reconstruction.
problem Reconstructing full-field structural mode shapes from sparse sensor data.
method Physics-Constrained Single-Output Gaussian Process (CONS-SOGP) framework.
result The proposed method provides more accurate and reliable mode shapes.
New model generates data without mode collapse or mixture.
problem Mode collapse and mode mixture in generative models.
method Inspired by AE-OT, improved sample generation algorithm.
result Free from mode collapse and mixture issues.
Study guarantees convergence of mean shift mode estimation.
problem Ensuring reliable mode estimation in KDE using mean shift.
method Utilizes Łojasiewicz inequality to prove convergence rate.
result Extends convergence guarantees to biweight kernel.
Simple mode exploration methods do not improve performance in neural networks.
problem Improving predictive probabilities in neural networks.
method Exploring local regions around diverse solutions using simple methods.
result Simple mode exploration methods do not improve performance.