arXiv research

Study identifies key brain regions and model architectures for ASD diagnosis.

Expanded Legendrian knot atlas for 10-arc index knots.

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.

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.

Generative models learn manifold structure; new approach uses atlas and geodesic interpolation.

ATLAS adapts HMC step size and trajectory length for complex geometries.

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.

Higher granularity in MoE models boosts expressivity exponentially.

ATLAS separates invariant and transferable latent factors across diverse environments.

Busemann G-spaces with Finsler metrics

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.

GACAN combines multi-granularity time series for traffic forecasting.

Chaos in cerebellar cells enhances complexity of neural patterns.

New method detects anomalies in computing centers' logs.

Paper finds essential regularity in singular connections.

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.

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 $\mathbb{G}_r(\mathbb{R}^k)$ of linear subspaces of dimension $r<k$ in $\mathbb{R}^k$ which avoids the use of equivalence classes. The set $\mathbb{…

Machine learning uncovers hidden correlations in granular material 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.

Round-Trip Times are one of the most commonly collected performance metrics in computer networks. Measurement platforms such as RIPE Atlas provide researchers and network operators with an unprecedented amount of historical Internet delay measurements. It would be very useful to automate the processing of these measure…

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.

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.

New method predicts bankruptcy by imputing missing data with granular semantics.

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.

Network analysis reveals distinct financial relationships among Euro Area banks.

Study uses trajectory embedding to measure place function similarity 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.

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.

Develops MgCSL for discovering causal structures in high-dimensional data.

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.

Neural HMM with AGA captures multi-scale dynamics in financial markets.

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.