Study identifies key brain regions and model architectures for ASD diagnosis.
problem Subjective and time-consuming ASD diagnosis by clinicians.
method Comparative analysis of model architectures and atlas granularities.
result High-performing models use 2-4 hidden layers and 16-64 neurons per layer, and cerebellum is predictive of ASD.
Expanded Legendrian knot atlas for 10-arc index knots.
problem Lack of Legendrian knot data for knots with high arc index.
method Created an atlas of Legendrian knots up to arc index 10.
result Legendrian knots of arc index 10 have been cataloged.
Atlas models are systems of Ito processes with parameters that depend on rank. We show that the parameters of a simple Atlas model can be identified by measuring the variance of the top-ranked process for different sampling intervals.
This research uses Siamese networks to identify partial mouse brain images from the Allen atlas.
problem Identifying precise mouse brain microscopy images from the Allen atlas.
method Siamese Networks with contrastive learning to find corresponding atlas plates for partial images.
result Siamese CNNs achieved 25% TOP-1 and 100% TOP-5 accuracy in identifying brain slices from the Allen atlas.
Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets with a stable capital distribution, in which the growth rates and variances depend on rank. The simplest such model assigns the same, constant variance to all stocks; zero rate of growth to all stocks but the smallest; and positiv…
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
problem Simulation of complex 3D geometries with thin features or non-trivial topology.
method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.
result The learned atlas enables different solvers without re-meshing or re-parametrization.
Generative models learn manifold structure; new approach uses atlas and geodesic interpolation.
problem Challenges in representing manifolds with topology different from Euclidean space.
method Atlas Generative Models (AGMs) with hybrid latent spaces and geodesic interpolation.
result Geodesic interpolation can be extended to AGMs, improving manifold representation.
ATLAS adapts HMC step size and trajectory length for complex geometries.
problem Sampling complex geometries with constant step size HMC/NUTS.
method Adapts step size and trajectory length using local Hessian and no U-turn condition.
result ATLAS accurately samples complex geometries, outperforming NUTS.
We present an atlas of Legendrian knots in standard contact three-space. This gives a conjectural Legendrian classification for all knots with arc index at most 9, including alternating knots through 7 crossings and nonalternating knots through 9 crossings. Our method involves a computer search of grid diagrams and app…
GBOC detects anomalies in time series data using granular-ball vectors.
problem Challenges in modeling normal behavior in dynamic, nonlinear time series data.
method Granular-ball Vector Data Description (GVDD) and Granular-ball One-Class Network (GBOC).
result GBOC improves anomaly detection in time series data.
Higher granularity in MoE models boosts expressivity exponentially.
problem Expressivity of Mixture-of-Experts models with varying granularity.
method Comparing models with different numbers of active experts (granularity).
result Exponential separation in network expressivity based on granularity.
ATLAS separates invariant and transferable latent factors across diverse environments.
problem Transfer learning and robust prediction in heterogeneous environments.
method ATLAS leverages invariance principle to disentangle latent factors and uses auxiliary labels for robust prediction.
result Near-oracle performance and robust transferable prediction in new environments.
Busemann G-spaces with Finsler metrics
problem Admitting a differentiable DC atlas with a continuous Finsler metric
method Comparison geometry
result Generalizes previous work on G-spaces with Riemannian curvature bounds
We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to the theory of reflected Brownian motions in polyhedral domains. In the context of …
ATLAS uses LLMs to adaptively trade by optimizing prompts and coordinating agents.
problem Adapting LLMs for real-time financial decision-making in noisy markets.
method ATLAS integrates structured market data, uses Adaptive-OPRO for prompt optimization, and employs multi-agent coordination.
result Adaptive-OPRO consistently outperforms fixed prompts in financial trading.
New HDP-HMM model accurately segments Internet path delays.
problem Automating the statistical analysis of large-scale network delay measurements.
method Infinite Hidden Markov Model (HDP-HMM) for trace segmentation.
result The HDP-HMM model performs as well as human cognition in pattern recognition.
GACAN combines multi-granularity time series for traffic forecasting.
problem High dynamics and complex spatial-temporal dependency of road networks in traffic forecasting.
method Graph Attention-Convolution-Attention Networks (GACAN) with Att-Conv-Att (ACA) block.
result GACAN outperforms state-of-the-art baselines in traffic forecasting.
Chaos in cerebellar cells enhances complexity of neural patterns.
problem Understanding how cerebellar granular layer represents complex information.
method Constructed a model of cerebellar granular layer with gap junctions, evaluated using reservoir computing.
result Chaotic dynamics in the cerebellar granular layer produce complex and diverse output patterns.
New method detects anomalies in computing centers' logs.
problem Anomaly detection in continuously changing log data for predictive maintenance.
method Evolving granular classifiers using Fuzzy-set-Based evolving Modeling and evolving Granular Neural Network.
result Classification model prioritizes maintenance based on anomaly severity.
Paper finds essential regularity in singular connections.
problem Determining if singularities in connections are removable or essential.
method Introduces RT-equations and a procedure to lift connections to essential regularity.
result A computable procedure to lift connections to essential regularity.
Patients initially diagnosed with early mild cognitive impairment (eMCI) are known to be a clinically heterogeneous group with very subtle patterns of brain atrophy. To examine the boarders between normal controls (NC) and eMCI, Magnetic Resonance Imaging (MRI) was extensively used as a non-invasive imaging modality to…
New method improves Gaussian process regression on complex, sparse point clouds.
problem Traditional Gaussian processes struggle with restricted domains and point clouds.
method Atlas Gaussian Processes (RC-AGPs) combining heat kernel and RBF kernels.
result RC-AGPs outperform existing methods in regression accuracy.
We introduce an atlas adapted to the Toda flow on the manifold of full flags of any non-compact real semisimple Lie algebra, and on its Hessenberg-type submanifolds. In our local coordinates the Toda flow becomes linear. We use these new coordinates to show that the Toda flow on the manifold of full flags is Morse-Smal…
In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold Gr(Rk) of linear subspaces of dimension r<k in Rk which avoids the use of equivalence classes. The set $\mathbb{…
Machine learning uncovers hidden correlations in granular material behavior.
problem Predicting mechanical behavior of granular materials from particle size distributions.
method Used Discrete Element Method to generate packings, trained artificial Neural Network.
result Artificial Neural Network revealed hidden correlations between particle size distributions and mechanical behavior.
We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity g) as a proxy for liquidity. This leads to a Price Impact Surface which depends on both volume ω and g. The dependence …
INGB improves oversampling for noisy imbalanced datasets.
problem Imbalanced, noisy, and complex datasets in classification problems.
method INGB uses granular balls to simulate spatial distribution and informed entropy for optimization, followed by nonlinear oversampling.
result INGB outperforms traditional linear sampling frameworks and algorithms on complex datasets.
An Atlas model is a rank-based system of continuous semimartingales for which the steady-state values of the processes follow a power law, or Pareto distribution. For a power law, the log-log plot of these steady-state values versus rank is a straight line. Zipf's law is a power law for which the slope of this line is …
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data set…
Revisits granular models explaining firm growth rates and sizes.
problem Understanding the relationship between firm size and growth rate statistics.
method Developed new theoretical insights linking firm size and growth rate statistics within granular models.
result Growth volatility distribution is size-independent but fat-tailed, challenging granular models.
We introduce a hierarchical architecture for video understanding that exploits the structure of real world actions by capturing targets at different levels of granularity. We design the model such that it first learns simpler coarse-grained tasks, and then moves on to learn more fine-grained targets. The model is train…
Graph Neural Networks model 3D granular flow simulations.
problem Accurate modeling of complex 3D granular flow processes.
method Graph Neural Networks approach to simulate 3D granular flow using LIGGGHTS.
result Machine learning trajectories match physical granular flow processes.
New method predicts bankruptcy by imputing missing data with granular semantics.
problem Missing data, high dimensional data, and class imbalance in bankruptcy prediction.
method Granular computing for missing data imputation with feature semantics and AI-driven pipeline.
result Efficient solution for big datasets with high imputation rates.
We study a mean-field version of rank-based models of equity markets such as the Atlas model introduced by Fernholz in the framework of Stochastic Portfolio Theory. We obtain an asymptotic description of the market when the number of companies grows to infinity. Then, we discuss the long-term capital distribution. We r…
Motivated by the practical demands for simplification of data towards being consistent with human thinking and problem solving as well as tolerance of uncertainty, information granules are becoming important entities in data processing at different levels of data abstraction. This paper proposes a method to construct c…
Tree++ graph kernel captures similarities at multiple granularities.
problem Lack of scale-adaptivity in existing graph kernels.
method Tree++ uses truncated BFS trees and super paths to represent graphs at different granularities.
result Tree++ achieves best classification accuracy on real-world graphs.
Network analysis reveals distinct financial relationships among Euro Area banks.
problem Understanding complex interbank relationships in the Euro Area.
method Multi-layer network approach using granular financial data.
result A more complete picture of the Euro Area interbank market topology.
Study uses trajectory embedding to measure place function similarity at fine spatial granularity.
problem Measuring place function similarity at fine spatial granularity.
method Trajectory embedding to reduce dimensions and measure similarity of place functions.
result Embedding similarity can be a metric proxy for place functions at fine spatial granularity.
Here, we present the World Trade Atlas 1870-2013, a collection of annual world trade maps in which distance combines economic size and the different dimensions that affect international trade beyond mere geography. Trade distances, which are based on a gravity model predicting the existence of significant trade channel…
SM-netFusion estimates brain network atlas by considering multiple topological measures.
problem Limited BNA estimation methods that overlook topological measures and lack discriminative power.
method Supervised multi-topology network cross-diffusion framework using degree, closeness, and eigenvector centrality measures.
result SM-netFusion produces more centered and representative templates, and improves classification accuracy.
The clustering ensemble technique aims to combine multiple clusterings into a probably better and more robust clustering and has been receiving an increasing attention in recent years. There are mainly two aspects of limitations in the existing clustering ensemble approaches. Firstly, many approaches lack the ability t…
Paper tackles cross-granularity few-shot learning with meta-embedder.
problem Few-shot learning with coarse labels and fine-grained testing.
method Meta-embedder that optimizes visual and semantic discrimination across coarse and fine classes.
result Meta-embedder achieves effective cross-granularity few-shot classification.
Develops MgCSL for discovering causal structures in high-dimensional data.
problem Discovering causal relationships from high-dimensional data with complex interplay of variables.
method MgCSL uses sparse auto-encoders for coarse-graining and multi-layer perceptrons for detailed analysis, introducing simplified acyclicity constraints.
result MgCSL outperforms existing methods and finds explainable causal connections in fMRI datasets.
We prove that the underlying set of an orbifold equipped with the ring of smooth real-valued functions completely determines the orbifold atlas. Consequently, we obtain an essentially injective functor from orbifolds to differential spaces.
New method learns fusion rules from few images using granular ball priors.
problem Challenges in supervised learning for image fusion with limited data.
method Introduces incomplete priors and Granular Ball Pixel Computation (GBPC) algorithm.
result Lightweight neural network learns effective fusion rules from few images.
Neural HMM with AGA captures multi-scale dynamics in financial markets.
problem Capturing multi-scale temporal dynamics in financial markets.
method Parallel multi-resolution encoders, adaptive gating, and multi-head attention.
result Outperforms fixed-resolution baselines in predicting price movements and liquidity shocks.
We generalize geometric prequantization of symplectic manifolds to differentiable stacks. Our approach is atlas-independent and provides a bijection between isomorphism classes of principal circle bundles (with or without connections) and second cohomology groups of certain chain complexes.
Robust RL with learned optimal adversary improves agent performance under adversarial state observations.
problem Ensuring reinforcement learning agents' robustness against adversarial perturbations of state observations.
method Proposed a framework of alternating training with learned adversaries (ATLA) to find optimal adversarial policies and enhance agent robustness.
result ATLA achieves state-of-the-art performance under strong adversaries in continuous control environments.