arXiv research

The paper extends the Manhattan curve concept to complex dynamics and studies its relation to multiplier spectra.

In this paper, we study the dynamics of degenerating sequences of rational maps on Riemann sphere $\hat{\mathbb{C}}$ using $\mathbb{R}$-trees. Given a sequence of degenerating rational maps, we give two constructions for limiting dynamics on $\mathbb{R}$-trees: one geometric and one algebraic. The geometric constructio…

Investigates point spectra of vector fields and their properties.

Khovanov spectra are shown to be functorial under certain conditions.

We give a simple sufficient condition for Quinn's "bordism-type spectra" to be weakly equivalent to strictly associative ring spectra. We also show that Poincare bordism and symmetric L-theory are naturally weakly equivalent to monoidal functors. Part of the proof of these statements involves showing that Quinn's funct…

Method calculates spectra of Rarita-Schwinger operator on symmetric spaces.

Proves spectra equivalence for Riemannian manifolds.

We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.

Study calculates spectra of minimal hypersurfaces in hyperbolic space.

Paper resolves decades-old problem about $L$-spectra.

New metrics compare rational spectra using optimal transport.

In this paper, we numerically investigate the length spectra and the low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero eigenvalues have been successfully computed using the periodic orbit sum method, which are compar…

Tomova, along with results of Bachman and Schleimer, showed that any high distance knot has a stair-step bridge spectrum. In this paper, we compute the bridge spectra and distance of generalized Montesinos knots. In particular, we produce the first example of a class of knots which attain the stair-step bridge spectra …

New ICA method for sources with mixed spectra.

Jones-Wenzl projectors lifted to Khovanov spectra, proving knot conjectures.

We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in terms of modules over a stack of parametrized spectra and in terms of diagrams o…

Functor decomposes Khovanov spectra for non-alternating diagrams.

Novel construction of Bauer--Furuta invariant using sheaves of spectra.

Study on sine-cones' spectra and stability under Ricci-de Turck flow.

We prove explicit upper and lower bounds for the $L^1$-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds $P^m$ in ambient Riemannian spaces $N^{n}$. We assume that $P$ and $N$ both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as view…

The paper describes correlations of spectra for higher rank Anosov representations.

Formulas for spectra of higher spin operators on sphere subbundles.

Approximate multipliers boost CNN training speed, power, and area at slight accuracy cost.

Study bottom of spectra on orbifolds via coverings.

Integrally splits L-spectra of integers into simpler components.

We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are available at regular primes, but we seek more conceptual answers in terms of lo…

New unoriented versions of Schur and Bogomolov multipliers for finite groups.

Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.

In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the multiply twisted products with a semi-symmetric metric connection and show that t…

Manifold methods improve amino acid classification in LIBS spectra.

The statistical properties of the multipliers of the absolute returns are investigated using one-minute high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size $s$ when $s$ is larger than some crossover scale, providing direct evidence of the existence of sca…

This paper describes a novel energy-based probabilistic distribution that represents complex-valued data and explains how to apply it to direct feature extraction from complex-valued spectra. The proposed model, the complex-valued restricted Boltzmann machine (CRBM), is designed to deal with complex-valued visible unit…

We take prior-to-crash market prices (NASDAQ, Dow Jones Industrial Average) as a signal, a function of time, we project these discrete values onto a vertical axis, thus obtaining a Cantordust. We study said cantordust with the tools of multifractal analysis, obtaining spectra by definition and by lagrangian coordinates…

We prove an analogue of Farb-Masur's theorem that the length-spectra metric on moduli space is "almost isometric" to a simple model $\mathcal {V}(S)$ which is induced by the cone metric over the complex of curves. As an application, we know that the Teichmüller metric and the length-spectra metric are "almost isometric…

Length spectra for Riemannian metrics are well studied, while sub-Riemannian length spectra have been largely unexplored. Here we give the length spectrum for a canonical sub-Riemannian structure attached to any compact Lie group by restricting its Killing form to the sum of the root spaces. Surprisingly, the shortest …

Derives formula for present value of future consumer goods multiplier.

In this article we use the "escape from subvarieties lemma" introduced by Eskin--Mozes--Oh to prove finite step rigidity results for the Jordan-Lyapunov projection spectra of Hitchin representations and the Margulis-Smilga invariant spectra of some special Margulis-Smilga spacetimes. In the process, we also prove a sim…

Article establishes criteria for multiplier Hermitian-Einstein metrics on KSM-manifolds.

We introduce a new quasi-isometry invariant, called the divergence spectrum, to study finitely generated groups. We compare the concept of divergence spectrum with the other classical notions of divergence and we examine the divergence spectra of relatively hyperbolic groups. We show the existence of an infinite collec…

Bayesian framework integrates spectral deconvolution with expert reasoning for robust peak estimation.

For mass spectra acquired from cancer patients by MALDI or SELDI techniques, automated discrimination between cancer types or stages has often been implemented by machine learnings. These techniques typically generate "black-box" classifiers, which are difficult to interpret biologically. We develop new and efficient s…

Spaces with similar long paths have similar shapes.

Cycle-StarNet bridges theory and data by adapting synthetic spectra to observational data.

Researchers describe a new method to compute Seiberg-Witten-Floer spectra for a specific class of manifolds.

This paper proposes a new loss using short-time Fourier transform (STFT) spectra for the aim of training a high-performance neural speech waveform model that predicts raw continuous speech waveform samples directly. Not only amplitude spectra but also phase spectra obtained from generated speech waveforms are used to c…

Spectral measurements reveal hidden representation geometry in language model training.

The paper extends Laplacian spectra approximations to vector bundles.

Method maps imperfect simulations to observed stellar spectra using unsupervised domain adaptation.