arXiv research

Predict and classify brain image evolution trajectories from a single MRI timepoint.

Expanded Legendrian knot atlas for 10-arc index knots.

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

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.

With the growing prevalence of smart grid technology, short-term load forecasting (STLF) becomes particularly important in power system operations. There is a large collection of methods developed for STLF, but selecting a suitable method under varying conditions is still challenging. This paper develops a novel reinfo…

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.

SM-netFusion estimates brain network atlas by considering multiple topological measures.

Bayesian Cox model identifies biomarkers from multi-omics data.

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…

Eigenrank selects images for deep learning training and predicts segmentation failures.

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.

New HDP-HMM model accurately segments Internet path delays.

New method clusters disease subtypes from model explanations.

Paper finds essential regularity in singular connections.

Study compares single vs ensemble feature selection for cancer diagnosis.

New method improves Gaussian process regression on complex, sparse point clouds.

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{…

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 …

New coordinates show Toda flow is Morse-Smale.

VICatMix clusters categorical biomedical data efficiently and selects relevant variables.

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…

GRIP2 improves deep learning feature selection robustness in correlated and noisy data.

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…

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.

Deep learning model approximates stochastic responses.

The increased availability of the multi-view data (data on the same samples from multiple sources) has led to strong interest in models based on low-rank matrix factorizations. These models represent each data view via shared and individual components, and have been successfully applied for exploratory dimension reduct…

Gene expression data represents a unique challenge in predictive model building, because of the small number of samples $(n)$ compared to the huge amount of features $(p)$. This "$n<<p$" property has hampered application of deep learning techniques for disease outcome classification. Sparse learning by incorporating ex…

Atlas dataset categorizes clothing products with high accuracy.

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.

New method defines Gysin maps for stratified spaces, preserving signatures.

An (flat) affine $3$-manifold is a $3$-manifold with an atlas of charts to an affine space ${\mathbf R}^3$ with transition maps in the affine transformation group $Aff({\mathbf R}^3)$. Equivalently an affine $3$-manifold is a $3$-manifold with a flat torsion-free affine connection. We show that a closed affine $3$-mani…

We present two related methods for deriving connectivity-based brain atlases from individual connectomes. The proposed methods exploit a previously proposed dense connectivity representation, termed continuous connectivity, by first performing graph-based hierarchical clustering of individual brains, and subsequently a…

The paper conjectures Khovanov homology can distinguish torus and twist knots.

Good atlases are defined for effective orbifolds, and a spark complex is constructed on each good atlas. It is proved that this process is 2-functorial with compatible systems playing as morphisms between good atlases, and that the spark character 2-functor factors through this 2-functor.

In this paper, we investigate a new form of automated curriculum learning based on adaptive selection of accuracy requirements, called accuracy-based curriculum learning. Using a reinforcement learning agent based on the Deep Deterministic Policy Gradient algorithm and addressing the Reacher environment, we first show …

A new framework enhances generative modeling by learning local flows over complex manifolds.

In this paper, we explore the theme of orbifold stratified spaces and establish a general criterion for them to be smooth orbifolds. This criterion utilizes the notion of linear stratification on the gluing bundles for the orbifold stratified spaces. We introduce a concept of good gluing structure to ensure a smooth st…

Paper proposes a method to select base classes for few-shot learning.

Feature selection, which searches for the most representative features in observed data, is critical for health data analysis. Unlike feature extraction, such as PCA and autoencoder based methods, feature selection preserves interpretability, meaning that the selected features provide direct information about certain h…

The problem of learning a manifold structure on a dataset is framed in terms of a generative model, to which we use ideas behind autoencoders (namely adversarial/Wasserstein autoencoders) to fit deep neural networks. From a machine learning perspective, the resulting structure, an atlas of a manifold, may be viewed as …