arXiv research

A machine learning framework predicts self-induced stochastic resonance in neurons.

Analyzes how transient conditions affect first-passage times in random walks.

We compare correlations and coherent structures in nuclei and financial markets. In the nuclear physics part we review giant resonances which can be interpreted as a coherent structure embedded in chaos. With similar methods we investigate the financial empirical correlation matrix of the DAX and Dow Jones. We will sho…

Holomorphic vector bundles on Hopf manifolds admit flat connections.

New resonance theory for Anosov flows connects spectral properties to mixing measures.

We study the distribution of resonances for geometrically finite hyperbolic surfaces of infinite area by countting resonances numerically. The resonances are computed as zeros of the Selberg zeta function, using an algorithm for computation of the zeta function for Schottky groups. Our particular focus is on three aspe…

Inverse problem solved for rotationally symmetric manifolds using eigenvalues and resonances.

Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of interest. In human functional brain networks, the network structure is often inferred from functional m…

Resonator Networks solve high-dimensional vector factorization better than optimization methods.

Study reveals a link between Ruelle-Pollicott resonances and cohomology eigenvalues for Anosov diffeomorphisms.

For compact and for convex co-compact oriented hyperbolic surfaces, we prove an explicit correspondence between classical Ruelle resonant states and quantum resonant states, except at negative integers where the correspondence involves holomorphic sections of line bundles.

Proves new fixed point formulae for complex manifolds with boundary.

The study finds resonance points in polarised curves with polynomial conserved quantities.

Study of spectral properties of Lorentzian quasi-Fuchsian manifolds.

The resonant band is a useful notion for the computation of the nontrivial monodromy eigenspaces of the Milnor fiber of a real line arrangement. In this article, we develop the resonant band description for the cohomology of the Aomoto complex. As an application, we prove that real 4-nets do not exist.

We show that the resolvent of the Laplacian on SL(3,$\mathbb{R}$)/SO(3) can be lifted to a meromorphic function on a Riemann surface which is a branched covering of $\mathbb{C}$. The poles of this function are called the resonances of the Laplacian. We determine all resonances and show that the corresponding residue op…

We find a resonance free region polynomially close to the critical line on Conformally compact manifolds with polyhomogeneous metric.

Uniform spectral gap for convex cocompact hyperbolic surfaces and expanders.

We investigate the resonance varieties, lower central series ranks, and Chen ranks of the pure virtual braid groups and their upper-triangular subgroups. As an application, we give a complete answer to the 1-formality question for this class of groups. In the process, we explore various connections between the Alexande…

For a conformally compact manifold that is hyperbolic near infinity and of dimension $n+1$, we complete the proof of the optimal $O(r^{n+1})$ upper bound on the resonance counting function, correcting a mistake in the existing literature. In the case of a compactly supported perturbation of a hyperbolic manifold, we es…

SGDm with fixed step-size diverges under covariate shift, similar to a parametric oscillator.

Procedure maps quantum systems to curved spacetimes with resonant frequencies.

We propose a novel method to embed a functional magnetic resonance imaging (fMRI) dataset in a low-dimensional space. The embedding optimally preserves the local functional coupling between fMRI time series and provides a low-dimensional coordinate system for detecting activated voxels. To compute the embedding, we bui…

Study resonant forms for dissipative Anosov flows on 3-manifolds.

The isoresidual fibration maps Riemann sphere strata to resonance arrangements.

Study geometric structures on LVM threefolds, focusing on resonant structures.

Study of resonances and residue operators for hyperbolic spaces.

We study the spectral theory of asymptotically hyperbolic manifolds with ends of warped product type. Our main result is an upper bound on the resonance counting function with a geometric constant expressed in terms of the respective Weyl constants for the core of the manifold and the base manifold defining the ends.

We prove the meromorphic extension to C for the resolvent of the Laplacian on a class of geometrically finite hyperbolic manifolds with infinite volume and we give a polynomial bound on the number of resonances. This class notably contains the geometrically finite quotients with rational non-maximal rank cusps previous…

Designs chiral photonic structures using machine learning for efficient optical properties.

On manifolds with an even Riemannian conformally compact Einstein metric, the resolvent of the Lichnerowicz Laplacian, acting on trace-free, divergence-free, symmetric 2-tensors is shown to have a meromorphic continuation to the complex plane, defining quantum resonances of this Laplacian. For higher rank symmetric ten…

Resonant machine learning uses electrical network dynamics to optimize learning efficiently.

Defines coherent manifolds and their quantum applications.

As a consequence of a result of Cardoso and Vodev, we show that the resolvent of the Laplacian on asymptotically hyperbolic manifolds is analytic in an exponential neighbourhood of the critical line. The case of non-trapping metrics with constant curvature near infinity is also considered: there exists a strip with at …

On an asymptotically hyperbolic manifold (X,g), we show that the resolvent resonances coincide, with multiplicities, with the poles of the renormalized scattering operator, except for the special points n/2-k (with k>0 integer) where an additional term appears: this is the dimension of the kernel of the k-conformal Lap…

CoRe method improves time series forecasting coherency without strict constraints.

In this paper we present a theoretical framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures, and we establish a duality between them. We derive a representation theorem for dynamic coherent risk measures in terms of …

We consider actions of Z^k, k \ge 2, by Anosov diffeomorphisms which are uniformly quasiconformal on each coarse Lyapunov distribution. These actions generalize Cartan actions for which coarse Lyapunov distributions are one-dimensional. We show that, under certain non-resonance assumptions on the Lyapunov exponents, a …

Deep learning removes aliasing in MRI scans with fast computation.

In this paper, we establish first the resonance identity for non-contractible homologically visible prime closed geodesics on Finsler $n$-dimensional real projective space $(\mathbb{R}P^n,F)$ when there exist only finitely many distinct non-contractible closed geodesics on $(\mathbb{R}P^n,F)$, where the integer $n\geq2…

Suppose that $(X, g)$ is a conformally compact $(n+1)$-dimensional manifold that is hyperbolic at infinity in the sense that outside of a compact set $K \subset X$ the sectional curvatures of $g$ are identically equal to minus one. We prove that the counting function for the resolvent resonances has maximal order of gr…

Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.

Paper proves existence of at least two non-contractible geodesics on Finsler space forms.

Unified model improves coherence tasks, especially local contexts.

On geometrically finite hyperbolic manifolds $Γ\backslash H^{d}$, including those with non-maximal rank cusps, we give upper bounds on the number $N(R)$ of resonances of the Laplacian in disks of size $R$ as $R\to \infty$. In particular, if the parabolic subgroups of $Γ$ satisfy a certain Diophantine condition, the bou…

SBI provides more accurate pole positions than chi-squared minimization in model misspecification.

We construct a determinant of the Laplacian for infinite-area surfaces which are hyperbolic near infinity and without cusps. In the case of a convex co-compact hyperbolic metric, the determinant can be related to the Selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalue…

The transition amplitudes between coherent states on a coherent state manifold are expressed in terms of the embedding of the coherent state manifold into a projective Hilbert space. Consequences for the dimension of projective Hilbert space and a simple geometric interpretation of Calabi's diastasis follows.