Data & Analytics

Large fluctuation theory for open quantum systems — analyzing atypical measurement outcomes in driven dissipative steady states. Shows large-deviation functions develop lines and surfaces with discontinuous derivatives, unlike equilibrium analytic Wigner functions. Provides framework for rare event statistics in non-equilibrium quantum systems. Activation: large fluctuations, open quantum systems, large-deviation, non-equilibrium, driven dissipative, Wigner function, rare events, steady state...

LARGE: Locally Adaptive Regularization for estimating Gaussian Graphical Models — improving brain network connectivity estimation via node-specific penalty tuning. Activation: Gaussian graphical model, GGM, graphical Lasso, GLASSO, brain connectivity, functional connectivity, precision matrix, adaptive regularization, network neuroscience.

Kuramoto-von Mises时间序列模型用于耦合振荡器的概率建模。无需假设热力学平衡，通过Langevin动力学构造实现非平衡 regime的准确建模，在高采样率下具有闭式代数解。

Kuramoto模型脑网络相位动力学分析方法论。使用振荡器同步框架研究脑网络相位耦合，分析催产素等神经调节物质对脑网络动态的影响。适用于脑网络同步性分析、神经调节研究、网络神经科学。触发词：Kuramoto模型、脑网络、相位耦合、同步性、神经调节、催产素、oxytocin、phase coupling、synchronization、brain network dynamics。

Theoretical framework demonstrating that mean-field chaos in random recurrent networks is predictable from continuous past history

Spectral interpretation of the Riemann xi-function via Krein space quantization in de Sitter QFT. Uses invariant two-point functions, Legendre functions, Lorentzian harmonic analysis, and Mehler-Fock transform to construct a retarded propagator with xi-function spectral weight. Activation: Krein space quantization, Riemann xi-function spectral, de Sitter QFT, Legendre function, Mehler-Fock transform, Hilbert-Polya, critical line zeros

Koopman-von Neumann (KvN) molecular dynamics methodology for computing Green-Kubo transport coefficients as quantum algorithm readout problems. Formulates classical NVE and NVT dynamics as unitary evolutions on Hilbert spaces, enabling quantum speedup for molecular property estimation with O(log(1/ε)) qubit scaling.

Conserved Kinematic Representations for Zero-Shot Decoding in Handwriting BCIs. Methodology aligning neural activity to imagined kinematics for zero-shot capable ML decoding of unseen characters in BCI systems. Use when: researching brain-computer interfaces, motor cortex representations, zero-shot decoding, handwriting BCIs, kinematic primitives, logographic language neuroprosthetics, compositional motor control. Keywords: zero-shot BCI, kinematic representation, handwriting decoding, motor ...

Geometric analysis of attractor boundaries and storage capacity limits in kernel Hopfield networks trained with Kernel Logistic Regression (KLR). Covers attractor basin geometry, Ridge of Optimization, morphing analysis, SNR vs Cover's theorem, and dynamical stability. Activation: kernel Hopfield, KLR associative memory, attractor basin geometry, Ridge of Optimization, morphing analysis Hopfield, storage capacity Hopfield, SNR analysis Hopfield, Cover's theorem associative memory, crosstalk n...

Kernel Hopfield networks: geometric analysis of attractor boundaries and storage capacity limits. KLR-trained associative memories with P/N ~16 for random sequences and ~20 for structured data. Trigger words: kernel Hopfield, associative memory, KLR, attractor basin, storage capacity, kernel logistic regression.

Just EEG Transformer (JET) — generative EEG framework using conditional flow matching to model neural signals as continuous trajectories, preserving spectral structure, temporal stationarity, and signal statistics. ICML 2026. Reduces TS-FID by >40% on large-scale benchmarks. arXiv:2605.21280

Jeffreys Flow framework for robust Boltzmann generators and rare event sampling. Addresses mode collapse in multi-modal distributions using Jeffreys divergence + Parallel Tempering distillation. Use when: sampling rough energy landscapes, Boltzmann generators, rare events, quantum thermal states, path integral Monte Carlo, avoiding KL divergence mode collapse.

First-passage-time analysis of inter-spike interval (ISI) statistics for excitatory-inhibitory (EI) integrate-and-fire neurons with depolarizing and hyperpolarizing adaptive thresholds. Use when studying stochastic neuronal firing, ISI variability, adaptive threshold mechanisms, or EI balance effects on spike-time statistics.

Tensor-based framework for higher-order Markov chains with memory on hypergraphs. Use when modeling complex systems with group interactions, memory effects, non-pairwise connections, or analyzing higher-order networks. Keywords: hypergraph, Markov chains, memory, tensor, higher-order networks, complex systems, random walks.

Hyperbolic Graph Convolutional Network (Brain-HGCN) for brain functional network analysis using Lorentz model and signed aggregation for excitatory/inhibitory connections. Activation triggers: hyperbolic GNN, brain network, fMRI analysis, geometric deep learning, Lorentz model.

HyFuHAD: Hybrid Quantum-Fuzzy Hyperspectral Anomaly Detection methodology. Combines Einstein fuzzy computing for classical inference with lightweight quantum defuzzifier for final detection. Uses multi-criteria decision framework with morphological, geometrical, and statistical membership functions. Use when: hyperspectral image anomaly detection, quantum neural network for remote sensing, fuzzy computing for image processing, Einstein fuzzy operations, or hybrid quantum-classical image analy...

Hybrid quantum-classical neural network methodology for medical image classification, particularly thermographic breast cancer detection. Integrates quantum neural network layers with classical CNN backbones to enhance pattern recognition in complex medical imaging data. Use when: (1) hybrid quantum-classical architectures for medical diagnosis, (2) quantum-enhanced image classification in healthcare, (3) thermographic/thermal image analysis with quantum methods, (4) quanvolutional networks f...

Design and evaluate hybrid quantum-classical machine learning pipelines for medical image classification and diagnosis. Covers HQNN, HQCNN, CV-QNN architectures, federated learning with tensor-network frontends, and quantum-enhanced feature extraction for healthcare applications. Use when: (1) building quantum-enhanced medical diagnosis systems, (2) designing hybrid quantum-classical ML pipelines for healthcare, (3) evaluating QML for medical imaging, (4) federated medical learning with quant...

Hybrid biophysical neuron modeling methodology combining conductance-based models with neural ODEs. Captures unknown ion channel kinetics while preserving mechanistic interpretability. Enables single-compartment reduction of multi-compartment models.

Hybrid Quantum-Classical Neural Network (HQNN) methodology for medical image classification, specifically blood cell classification. Combines pre-trained classical backbone (ResNet-50) with variational quantum circuit for enhanced feature representation. Use when: (1) medical image classification with limited data, (2) hybrid quantum-classical ML pipeline design, (3) comparing quantum vs classical feature transformations, (4) NISQ-era quantum advantage in medical imaging. Activation: HQNN, hy...

Statistical-mechanical theory of dreaming in multidirectional associative memories using DLAM architecture. Use when: (1) implementing energy-based models with dreaming capabilities; (2) designing multi-layer Hebbian architectures; (3) analyzing pattern disentanglement in neural networks; (4) studying statistical mechanics of neural memory; (5) developing heteroassociative memory systems. Trigger words: Hopfield dreaming, DLAM, associative memory, energy-based models, pattern disentanglement.

Homology-based Morphometry (HBM) methodology for analyzing brain atrophy using persistent homology. Two complementary pipelines for quantifying multiscale geometric features of structural T1-weighted MRI scans: Pipeline 1 for regional thinning via Euclidean distance transform, Pipeline 2 for structural similarity via α-filtrations. Use for Alzheimer's disease detection, longitudinal brain change tracking, and topological biomarker extraction. Keywords: brain atrophy, persistent homology, TDA,...

Homology-based morphometry methods for analyzing brain atrophy using topological data analysis. Activation triggers: homology morphometry, brain atrophy, topological neuroimaging, persistent homology brain, TDA neuroimaging

Extracting interpretable higher-order topological features across multiple scales for Alzheimer's Disease classification using persistent homology. Captures connected components, cycles, and cavities from fMRI brain networks. Activation: higher-order topology, Alzheimer classification, persistent homology, brain network topology, topological features.