New Khovanov homology for links with multiple punctures.
problem Defining a new Khovanov homology for links with multiple punctures.
method Defined a variant of Khovanov homology for links in thickened disks with multiple punctures, related to previous work by spectral sequences.
result Spectral sequences recover annular Khovanov homology to Khovanov homology.
The paper calculates spectral torsion for rescaled Dirac operators on manifolds.
problem Computing spectral torsion for rescaled Dirac operators.
method Using trilinear Clifford multiplication and functional of differential one-forms.
result Computed spectral torsion for four types of rescaled Dirac operators.
Proposes RNSE for clustering with adaptive similarity matrix learning.
problem Sub-optimal results due to mismatch between stages in Spectral Clustering.
method End-to-end single-stage learning with adaptive similarity matrix and non-negative constraints.
result Superior clustering performance on synthetic and real-world datasets.
We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In e…
HSSE framework embeds single-cell RNA-seq data at multiple scales.
problem Capturing heterogeneous local structure in single-cell RNA-seq data.
method Hierarchical sheaf spectral embedding (HSSE) framework.
result HSSE achieves competitive or improved performance in single-cell RNA-seq data representation learning.
New method detects and analyzes correlation in multiple network data.
problem Detecting and analyzing correlation in multiple network data.
method Generalized omnibus embedding methodology.
result Induced correlation can significantly extend the reach of spectral inference procedures.
We construct certain spectral triples in the sense of A. ~Connes and H. Moscovici (``The local index formula in noncommutative geometry'' {\it Geom. Funct. Anal.}, 5(2):174--243, 1995) that is transversally elliptic but not necessarily elliptic. We prove that these spectral triples satisfie the conditions which ensure …
New method extrapolates spectral densities from smaller models to larger ones.
problem Limited practical computations for large machine learning models.
method Algebraic spectral curve theory for free decompression.
result Framework enables extrapolation of spectral densities with multiple or multi-modal bulks.
Constructs non-isometric iso-length-spectral surfaces.
problem Creating non-isometric surfaces with identical geodesic lengths.
method Combining Sunada's construction with amalgams of hyperbolic surfaces.
result Found non-isometric surfaces with the same geodesic lengths.
The paper studies obstructions to homotopy invariance of loop coproducts.
problem Characterizing obstructions to homotopy invariance of loop coproducts.
method Using a construction of Geoghegan and Nicas, the paper defines the Reidemeister trace and realizes the Goresky-Hingston coproduct as a map of spectra.
result The failure of a map to entwine spectral coproducts can be characterized by Chas-Sullivan multiplication with the Reidemeister trace.
We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely related to Variational Monte Carlo methods from computational physics. As such, the…
Proposes CRG_IMSC for better clustering of multi-view data.
problem Lack of effective connectivity in clustering results.
method Directly obtains clustering result with nonnegative constraint; constructs connectivity matrix based on spectral clustering result; uses multiplicative update algorithm.
result Improves clustering performance on benchmark datasets.
We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta between 0.5 and 2. Furthermore, we analyze the relation between the power-law autoco…
A new method detects hidden driving forces in systems with multiple observables.
problem Hidden driving forces in systems with multiple observables cannot be detected by scalar statistics.
method Cross-spectral witness for hidden nonequilibrium.
result Two simultaneously observed channels retain an off-diagonal cross-spectral sector inaccessible to scalar reductions.
Proposes a spectral method to assess and combine multiple data visualizations.
problem Evaluating and combining the strengths of different data visualization algorithms.
method Spectral method for assessing and combining multiple visualizations.
result Proposes a visualization eigenscore to quantify relative performance and a consensus visualization.
Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely depend on the number of transactions. We introduce the multiplicative stochastic mod…
We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a Hidden Markov Model (HMM); we model the relationship between multiple cell types by…
Enhancing spectral embedding for low-dimensional embeddings in rare disease cohorts
problem Representing clinical concepts and patients in electronic health records
method Spectral-based unsupervised learning with flexible knowledge transfer
result Outperforms competing approaches in challenging scenarios
Sharp spectral theorem splits certain non-compact manifolds.
problem Proving spectral splitting for non-compact manifolds with specific curvature conditions.
method Sharp spectral analysis and geometric splitting theorem.
result Non-compact manifolds split as RimesN under given curvature constraints. The (stochastic) gradient descent and the multiplicative update method are probably the most popular algorithms in machine learning. We introduce and study a new regularization which provides a unification of the additive and multiplicative updates. This regularization is derived from an hyperbolic analogue of the entr…
Optimizes data power control in cell-free networks for better spectral efficiency.
problem Maximizing overall spectral efficiency in cell-free networks with multi-objective optimisation.
method Applied scalable multi-objective Bayesian optimisation to solve convergence-time limitations.
result Improved radio resource management in cell-free networks.
Quantum reservoir computing needs coherence influx for effective information processing.
problem Understanding and optimizing quantum reservoir computing.
method Theoretical and numerical analysis of quantum systems, focusing on coherence influx and spectral radius of Pauli transfer matrix.
result Coherence influx is essential for realizing nonstationary echo state property in quantum reservoir computing.
Paper proposes a forecasting model combining autoregressive models with spectral attention.
problem Time series forecasting across various domains.
method Combines deep autoregressive models with Spectral Attention (SA) module.
result SAAM consistently demonstrates improved forecasting accuracy compared to state-of-the-art approaches.
Researchers prove Seifert-Weber dodecahedral space is an L-space.
problem Proving the Seifert-Weber dodecahedral space is an L-space.
method Relating Floer homology and spectral geometry of hyperbolic three-manifolds, exploiting symmetry and arithmetic structure.
result Small eigenvalues on coexact 1-forms must have large multiplicity in Seifert-Weber dodecahedral space.
Proposes a spectral method for jointly smooth functions on multiple manifolds.
problem Registering measurements from different sensors and rejecting noise.
method Two steps: kernel subspace span and spectral method.
result Guaranteed orthogonal functions that are as jointly smooth as possible.
SG-NTF completes HDI tensors with spectral mapping and spatio-temporal gating.
problem High-dimensional and incomplete tensor completion.
method Spectra-Guided Neural Tucker Factorization (SG-NTF) with Spatio-Temporal Co-Gating (STCG).
result Maintains competitive completion accuracy with parameter efficiency.
In this paper, we provide a novel construction of the linear-sized spectral sparsifiers of Batson, Spielman and Srivastava [BSS14]. While previous constructions required Ω(n4) running time [BSS14, Zou12], our sparsification routine can be implemented in almost-quadratic running time O(n2+ε). The funda…
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the Kaczmarz algorithm was shown to converge exponentially and independent of number of …
We present a novel spectral learning algorithm for simultaneous localization and mapping (SLAM) from range data with known correspondences. This algorithm is an instance of a general spectral system identification framework, from which it inherits several desirable properties, including statistical consistency and no l…
New kernel models multi-output Gaussian processes accurately.
problem Challenges in modelling cross-covariances for multiple-output Gaussian processes.
method Replaced Gaussian components with block components of finite bandwidth in spectral mixture kernel.
result First multi-output generalization of spectral mixture kernel that can approximate any stationary multi-output kernel to arbitrary precision.
We study the triple $(G,π,\prs)$ where G is a connected and simply connected Lie group, π and $\prs$ are, respectively, a multiplicative Poisson tensor and a left invariant Riemannian metric on G such that the necessary conditions, introduced by Hawkins, to the existence of a non commutative deformation (in the d…
Multi-output Gaussian processes (MOGPs) are an extension of Gaussian Processes (GPs) for predicting multiple output variables (also called channels, tasks) simultaneously. In this paper we use the convolution theorem to design a new kernel for MOGPs, by modeling cross channel dependencies through cross convolution of t…
L2SC improves spectral clustering performance by selectively transferring knowledge across tasks.
problem L2SC tackles the challenge of incorporating new spectral clustering tasks without relearning all previous tasks.
method L2SC uses an orthogonal basis library and feature embedding library to selectively transfer knowledge from previously learned tasks to new tasks.
result L2SC outperforms state-of-the-art spectral clustering algorithms on real-world benchmark datasets.
Spectral portfolio theory links neural networks to wealth dynamics via SGD weight matrices.
problem Understanding wealth dynamics from neural network training.
method Direct identification of weight matrices as portfolio allocation matrices, linking SGD forces to portfolio dynamics.
result Spectral properties of SGD weight matrices transition between additive and multiplicative regimes, influencing wealth dynamics.
In remote sensing, it is often challenging to acquire or collect a large dataset that is accurately labeled. This difficulty is usually due to several issues, including but not limited to the study site's spatial area and accessibility, errors in the global positioning system (GPS), and mixed pixels caused by an image'…
For generic torus-invariant metrics, eigenspaces are 2D and nodal sets are connected hypersurfaces.
problem Understanding spectral multiplicity and nodal sets for generic torus-invariant metrics.
method Analyzing real Δg-eigenspaces and nodal sets for generic T-invariant metrics. result For generic T-invariant metrics, real Δg-eigenspaces are irreducible and have dimension at most 2, and nodal sets are connected hypersurfaces with specific properties. New algorithm clusters hyperspectral images at multiple scales.
problem Clustering hyperspectral images at various scales.
method M-SRDL algorithm using spectral-spatial diffusion distances.
result More accurate clustering labels achieved with spatial regularization.
Paper proposes a new method for sparse spectral clustering on Stiefel manifold.
problem Sparse spectral clustering on Stiefel manifold with nonsmooth and nonconvex objective.
method Proposes a manifold proximal linear method (ManPL) to solve the original SSC formulation.
result Demonstrates the advantage of ManPL over existing methods on single-cell RNA sequencing data.
Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is a Brownian fluctuation of the average interevent time between subsequent pulses of the pulse sequence. In this paper we generalize the model of interevent time to reproduce a variety of self-affine time series exhibiting power spec…
The article discusses extensions of Harish-Chandra's admissibility theorem.
problem Restrictions of irreducible representations to non-compact subgroups.
method Representation-theoretic developments for new spectral analysis.
result Powerful methods for spectral analysis of standard locally symmetric spaces.
This paper analyzes AJIVE for estimating shared subspace across multiple datasets, revealing its strengths and limitations.
problem Estimating shared subspace across multiple datasets with varying degrees of misalignment.
method Angle-based Joint and Individual Variation Explained (AJIVE) method, a two-stage spectral approach.
result AJIVE's performance in high signal-to-noise ratio (SNR) regimes and its non-diminishing error in low-SNR settings.
Improved guarantees and multiple-descent curve for data approximations.
problem Improving the effectiveness of small low-rank approximations of large datasets.
method Spectral properties of the data matrix to obtain improved approximation guarantees.
result Revealed a multiple-descent curve in approximation factor as a function of k.
We present a new description of the spectrum of the (spin-) Dirac operator D on lens spaces. Viewing a spin lens space L as a locally symmetric space Γ\Spin(2m)/Spin(2m−1) and exploiting the representation theory of the Spin groups, we obtain explicit formu…
A novel nonstationary permanental process relaxes kernel constraints and captures complex data patterns.
problem Limitations of existing permanental processes in terms of kernel types and stationarity.
method Sparse spectral representation of nonstationary kernels and hierarchical stacking of spectral feature mappings.
result Enhanced model expressiveness and reduced computational complexity.
For the multiple differential algebra of iterated differential forms (see math.DG/0605113 and math.DG/0609287) on a diffiety (O,C) an analogue of C-spectral sequence is constructed. The first term of it is naturally interpreted as the algebra of secondary iterated differential forms on (O,C). This allows to develop sec…
Study shows convex contact spheres resemble contact ellipsoids.
problem Characterizing the structure of convex contact spheres.
method Stratification by Reeb orbit periods and analysis of spectral invariants.
result Any stratum of a convex contact sphere is an integral homology sphere, and spectral invariants coincide with action values.
The study proves optimal spectral gaps for hyperbolic surfaces.
problem Proving optimal spectral gaps for hyperbolic surfaces.
method Proving the absence of eigenvalues in a specific range for random covers of hyperbolic surfaces.
result The first non-zero eigenvalue of the Laplacian on a sequence of closed hyperbolic surfaces tends to 1/4.
Spectral methods improve signal recovery in mixed GLMs with precise asymptotics.
problem Estimating multiple signals from unlabeled observations in mixed GLMs.
method Developed exact asymptotics for spectral methods in a proportional regime.
result Optimized spectral method combined with a linear estimator minimizes estimation error.