Resonator Networks solve high-dimensional vector factorization better than optimization methods.
problem High-dimensional vector factorization problem in Vector Symbolic Architectures.
method Recurrent neural network (Resonator Networks) that combines nonlinear dynamics and superposition search.
result Resonator Networks outperform optimization methods in solving high-dimensional vector factorization.
Resonant machine learning uses electrical network dynamics to optimize learning efficiently.
problem Traditional energy-based learning models are dissipative and inefficient.
method Proposes a new learning framework with two energy components (active and reactive) to ensure active-power dissipation during learning.
result Support vectors in resonant SVMs correspond to self-sustained oscillations in an LC network.
A machine learning framework predicts self-induced stochastic resonance in neurons.
problem Predicting coherent oscillations in slow-fast excitable systems driven by noise.
method Physics-informed machine learning with a Noise-Augmented State Predictor architecture and Kramers' escape theory constraints.
result Trained PINN accurately predicts spike-train coherence on noise intensity, excitability, and timescale separation.
SGDm with fixed step-size diverges under covariate shift, similar to a parametric oscillator.
problem SGDm with fixed step-size diverges under covariate shift.
method Approximated learning system as a time-varying system of ODEs and characterized divergence/convergence modes.
result SGDm with fixed step-size can diverge under covariate shift, similar to resonance in oscillators.
Holomorphic vector bundles on Hopf manifolds admit flat connections.
problem Understanding flat connections on holomorphic vector bundles over Hopf manifolds.
method Defining resonant and non-resonant Mall bundles, proving the existence of flat connections on non-resonant bundles, and applying the Poincare-Dulac theorem.
result Non-resonant Hopf manifolds are linearizable, generalizing Kodaira's result.
New resonance theory for Anosov flows connects spectral properties to mixing measures.
problem Defining and analyzing Ruelle-Taylor resonances for Anosov actions.
method Combining microlocal methods and J. Taylor's cohomological theory, defining Ruelle-Taylor resonances and proving Fredholm theory.
result Ruelle-Taylor resonances form a discrete subset of Cκ with λ=0 being a leading resonance. 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…
Study reveals a link between Ruelle-Pollicott resonances and cohomology eigenvalues for Anosov diffeomorphisms.
problem Understanding the speed of mixing in Anosov diffeomorphisms.
method Investigates Ruelle-Pollicott resonances on manifolds of any dimension, connecting them to cohomology eigenvalues of a quasi-compact transfer operator.
result Established a cohomological bound for the speed of mixing of 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.
We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M=(0,∞)×Y whose rotation radius is constant outside some compact interval. The Laplacian on M is unitarily equivalent to a direct sum of one-dimensional Schrödinger operators with compactly supported potenti…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized to perform this task. The algorithm has been applied to several examples of direc…
The study finds resonance points in polarised curves with polynomial conserved quantities.
problem Finding resonance points in polarised curves with polynomial conserved quantities.
method Using the non-orthogonality assumption on the conserved quantity, the study deduces the existence of resonance points.
result Every finite type polarised curve in the conformal 2-sphere with a polynomial conserved quantity admits a resonance point.
SrvfNet aligns multiple functional data to templates without supervision.
problem Aligning large collections of functional data to templates without labeled data.
method Generative deep learning framework using SRVF and fully-connected layers.
result Framework achieves alignment and optimal template prediction without supervision.
Bayesian neural network predicts planetary instability.
problem Predicting planetary instability in compact systems.
method Novel Bayesian neural network trained on raw orbital elements.
result Model predicts planetary instability times with high accuracy and robust generalization.
Study of spectral properties of Lorentzian quasi-Fuchsian manifolds.
problem Understanding the spectral properties of Lorentzian quasi-Fuchsian manifolds.
method Analyzing the geodesic flow, Ruelle resonances, and pseudo-Riemannian Laplacian.
result Meromorphic extension of the resolvent of the pseudo-Riemannian Laplacian with poles of finite rank.
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.
SBI provides more accurate pole positions than chi-squared minimization in model misspecification.
problem Accurate pole position estimation in pi-pi scattering models.
method Simulation Based Inference (SBI) method compared to chi-squared minimization.
result SBI leads to more robust predictions of pole positions in models of pi-pi scattering.
This survey samples from the ever-growing family of adaptive resonance theory (ART) neural network models used to perform the three primary machine learning modalities, namely, unsupervised, supervised and reinforcement learning. It comprises a representative list from classic to modern ART models, thereby painting a g…
We show that the resolvent of the Laplacian on SL(3,R)/SO(3) can be lifted to a meromorphic function on a Riemann surface which is a branched covering of 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.
problem Spectral gap for convex cocompact hyperbolic surfaces and their covers.
method Using thermodynamic formalism for twisted Selberg zeta functions.
result Uniform resonance-free regions for convex cocompact hyperbolic surfaces and expanders.
We describe a strategy for constructing a neural network jet substructure tagger which powerfully discriminates boosted decay signals while remaining largely uncorrelated with the jet mass. This reduces the impact of systematic uncertainties in background modeling while enhancing signal purity, resulting in improved di…
Deep learning detects Crohn's disease in MRI images.
problem Detecting Crohn's disease in MRI images.
method Residual Networks for feature extraction and soft attention mechanisms for interpretability.
result Deep learning algorithms perform comparably to clinical standards with faster inference.
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…
Current popular methods for Magnetic Resonance Fingerprint (MRF) recovery are bottlenecked by the heavy storage and computation requirements of a dictionary-matching (DM) step due to the growing size and complexity of the fingerprint dictionaries in multi-parametric quantitative MRI applications. In this paper we study…
SFCNeXt estimates brain age from small MRI datasets.
problem Efficiently estimating brain age from limited MRI data.
method Simple fully convolutional network (SFCNeXt) with SPEC and HRL.
result SFCNeXt outperforms complex models in small sample size scenarios.
Neural network improves aneurysm classification accuracy in MRI images.
problem Classifying aneurysm status in MRI images with varying radiologist expertise.
method Constructed neural network trained on radiologists' annotations, compared to a control model.
result Proposed model had a higher area under the curve (0.845 vs. 0.793).
ANNs extrapolate without training data, leading to uncertain predictions.
problem Uncertainty in ANN predictions for unseen data.
method Quantitative approach based on long-standing methods.
result Quantitative uncertainty assessment for ANN predictions.
For a conformally compact manifold that is hyperbolic near infinity and of dimension n+1, we complete the proof of the optimal O(rn+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…
Proposes a deep neural network approach for image response regression.
problem Associations between medical images and covariates.
method Spatially varying coefficient models with deep neural networks.
result Explicitly accounts for spatial smoothness and subject heterogeneity.
Study resonant forms for dissipative Anosov flows on 3-manifolds.
problem Determine resonant forms and their cohomology classes for dissipative Anosov flows.
method General theory including horocyclic invariance and local geometry analysis.
result Explicit computation of resonant forms and helicity for quasi-Fuchsian flows.
The isoresidual fibration maps Riemann sphere strata to resonance arrangements.
problem Mapping Riemann sphere strata to resonance arrangements.
method Defining isoresidual fibration and studying its properties using tree structures.
result The isoresidual fibration is an unramified cover of degree a!/(a+2-p)! above the complement of a hyperplane arrangement.
Study geometric structures on LVM threefolds, focusing on resonant structures.
problem Understanding deformations of geometric structures on LVM threefolds.
method Using the Ehresmann-Thurston principle and Kuranishi family construction.
result Construction of a family containing all LVM threefolds and complete at every point.
Study of resonances and residue operators for hyperbolic spaces.
problem Understanding resonances and residue operators for pseudo-Riemannian hyperbolic spaces.
method Analyzing the resolvent of the Laplace-Beltrami operator on pseudo-Riemannian hyperbolic spaces.
result Explicit determination of resonances and identification of residue representations.
Proposes a method to improve skull stripping accuracy in MRI images.
problem Skull stripping accuracy in MRI images is improved.
method Context-encoding method to empower 2D networks with 3D semantic information.
result Achieves superior accuracy (dice score 99.6% on NFBS, 99.09% on LPBA40, 99.17% on OASIS) compared to state-of-the-art methods.
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…
Traditionally, nonlinear inversion, direct inversion, or wave estimation methods have been used for reconstructing images from MRE displacement data. In this work, we propose a convolutional neural network architecture that can map MRE displacement data directly into elastograms, circumventing the costly and computatio…
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…
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…
Automated labeling of intracranial arteries improves accuracy and efficiency.
problem Challenges in accurately labeling intracranial arteries due to variations and limited datasets.
method Graph Neural Network (GNN) combined with hierarchical refinement for improved accuracy.
result Achieved 97.5% node labeling accuracy on a testing set of 105 scans.
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 …
Decreasing magnetic resonance (MR) image acquisition times can potentially reduce procedural cost and make MR examinations more accessible. Compressed sensing (CS)-based image reconstruction methods, for example, decrease MR acquisition time by reconstructing high-quality images from data that were originally sampled a…
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⊂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…
In this paper, we establish first the resonance identity for non-contractible homologically visible prime closed geodesics on Finsler n-dimensional real projective space (RPn,F) when there exist only finitely many distinct non-contractible closed geodesics on (RPn,F), where the integer $n\geq2…
On geometrically finite hyperbolic manifolds Γ\Hd, 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→∞. In particular, if the parabolic subgroups of Γ satisfy a certain Diophantine condition, the bou…
Deep learning improves brain tumor detection with few data.
problem Scarce training data and data corruption in medical diagnosis.
method Data distillation and augmentation to improve deep neural network training.
result Reaches human expert-level accuracy with just a few thousand training examples.