This paper tackles quantum machine learning by embedding nonlinear functions in topographic representations.
problem Challenges of nonlinear processes in quantum machine learning.
method Topographic representation of information for quantum machine learning.
result Nonlinear functions can be embedded in unitary processes.
NTFA models participant and stimulus variations in fMRI data.
problem Lack of statistical tools to examine participant differences in neuroimaging studies.
method NTFA, a probabilistic factor analysis model inferring embeddings for participants and stimuli.
result NTFA improves predictive generalization and downstream tasks.
Visualizes DNNs using topographic maps for better understanding.
problem Difficulty in understanding how DNNs solve tasks.
method Adapting neuroscience methods to visualize DNN activations.
result Improved transparency and interpretability of DNN-based systems.
Visualizes deep neural networks for speech recognition using learned topographic filter maps.
problem Unintuitive internal structure of deep neural networks complicates activation visualization.
method Trains a convolutional speech recognition model with filters arranged in a 2D grid, highlighting similar filters.
result Topographic filter maps visualize artificial neuron activations more intuitively.
This paper proposes an organized generalization of Newman and Girvan's modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to faithful and readable graph representations based on clustering induced graphs. Topog…
The paper develops models to understand sensory coding and cortical topography.
problem Understanding how visual cortical areas' receptive fields and topographic maps relate to environmental statistical structure.
method Energy-based models applied to probability density estimation, constrained by biological constraints.
result The models qualitatively reproduce receptive field and map properties found in vivo.
We prove recognition theorems for codimension one manifold factors of dimension n≥4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that X×R i…
DBS uses swarm intelligence to cluster data without needing a global objective function.
problem Clustering high-dimensional data with unknown natural clusters.
method Databionic swarm (DBS) system that self-organizes and adapts to data structures.
result DBS outperforms traditional clustering methods in scenarios with no prior knowledge.
This paper considers the problem of low-dimensional visualisation of very high dimensional information sources for the purpose of situation awareness in the maritime environment. In response to the requirement for human decision support aids to reduce information overload (and specifically, data amenable to inter-point…
In some applications and in order to address real world situations better, data may be more complex than simple vectors. In some examples, they can be known through their pairwise dissimilarities only. Several variants of the Self Organizing Map algorithm were introduced to generalize the original algorithm to this fra…
Machine learning recreates the periodic table from element properties.
problem Recreating the periodic table using machine learning.
method Unsupervised machine learning with GTM for feature embedding.
result PTG autonomously generates various periodic table layouts.
Enhances ocean floor mapping with adaptive uncertainty estimates.
problem Inaccurate bathymetric data for precise ocean modeling.
method Block-based conformal prediction with VQ-VAE architecture.
result Significant improvements in reconstruction quality and uncertainty estimation reliability.
New method learns complex brain signal patterns from EEG/MEG data.
problem Complex waveforms in brain signals not captured by linear filters.
method Multivariate convolutional sparse coding (CSC) algorithm.
result Reveals non-sinusoidal mu-shaped patterns in brain signals.
New non-isotopic Seifert surfaces found in 4-ball.
problem Finding non-isotopic Seifert surfaces for knots and links.
method Using double branched covers and Seifert forms, with an algorithm based on quadratic forms.
result Families of knots and links with non-isotopic Seifert surfaces in D4. Computed linking number of modular knots and Lorenz links.
problem Computing the linking number of modular knots in a specific space.
method Using correspondence between modular links and Lorenz links, and intersection number involving Conway topographs.
result Computed linking number of modular knots and compared to a previous formula.
Mixtures of Gaussians, factor analyzers (probabilistic PCA) and hidden Markov models are staples of static and dynamic data modeling and image and video modeling in particular. We show how topographic transformations in the input, such as translation and shearing in images, can be accounted for in these models by inclu…
Study assesses drought and late-frost risks in Bavaria using vine copulas.
problem Assessing risks of late-frost and drought in Bavaria due to climate change.
method Used vine copula models for non-Gaussian and asymmetric dependencies, with univariate and bivariate regression analyses.
result Identified 'at-risk' regions for forest adaptation.
The scale of functional magnetic resonance image data is rapidly increasing as large multi-subject datasets are becoming widely available and high-resolution scanners are adopted. The inherent low-dimensionality of the information in this data has led neuroscientists to consider factor analysis methods to extract and a…
Deep learning improves cancer report classification accuracy.
problem Automatically assigning ICD-O3 codes to cancer reports.
method State-of-the-art deep learning techniques, including hierarchical and flat models, with attention mechanisms.
result Best model achieves 90.3% accuracy on topography site assignment and 84.8% on morphology type assignment.
New method aligns brain surfaces based on functional signatures.
problem Inter-individual variability in neuroimaging data.
method Fused Unbalanced Gromov-Wasserstein (FUGW) based on Optimal Transport.
result FUGW significantly increases between-subject correlation of activity.
Spatially-aware model improves earthquake hazard assessment accuracy.
problem Misrepresentation of seismic effects across diverse landscapes.
method Causal Bayesian network with Gaussian Processes and normalizing flows.
result Achieves up to 35.2% AUC improvement over existing methods.
We consider a class of learning problems regularized by a structured sparsity-inducing norm defined as the sum of l_2- or l_infinity-norms over groups of variables. Whereas much effort has been put in developing fast optimization techniques when the groups are disjoint or embedded in a hierarchy, we address here the ca…
Novel method transfers orometric measures to metric data sets, identifying key items.
problem Identifying key items in metric data sets like knowledge graphs.
method Transfers orometric measures to bounded metric spaces, using 'isolation' and 'prominence' functions.
result Identifies structurally relevant items in geographic data sets of Germany and France.
Novel path planning improves UAV detection of extreme anomalies.
problem Improper criteria for UAV anomaly detection.
method Mathematical criteria guiding UAV towards strong anomalies.
result Proposed approach outperforms traditional methods in various applications.
Develops approximately equivariant neural processes for better data modeling.
problem Real-world data often breaks exact equivariance; how to model this?
method General approach to creating approximately equivariant architectures, applicable to any model and symmetry group.
result Approximately equivariant neural processes outperform non-equivariant and strictly equivariant models in regression tasks.
Deep learning classifies seven types of maps for better access.
problem Efficiently accessing the right map type from digital maps.
method Used deep convolutional neural networks to classify seven types of maps.
result Deep learning can accurately classify different types of maps.
PeakWeather provides Swiss weather station data for machine learning.
problem Accurate weather forecasting for various activities and decision-making.
method High-quality dataset of surface weather observations from 8 years of Swiss stations.
result Dataset supports a wide range of spatiotemporal tasks.
We introduce the problem of reconstructing a sequence of multidimensional real vectors where some of the data are missing. This problem contains regression and mapping inversion as particular cases where the pattern of missing data is independent of the sequence index. The problem is hard because it involves possibly m…
Develops deep models to handle nonstationary spatial extremal dependence.
problem Challenges in modeling nonstationary extremal dependence in spatial data.
method Deep compositional spatial models to capture nonstationarity in extremal dependence.
result Efficient estimation of warped space for nonstationary spatial data.
Deep learning detects snow avalanches in SAR images with high accuracy.
problem Accurate detection of snow avalanches in remote areas using satellite imagery.
method Fully Convolutional Neural Network trained on manually labeled Sentinel-1 radar images.
result Deep learning model achieves F1 score above 66% compared to 38% for state-of-the-art methods.
Paper uses Gaussian processes and neural nets to model sub-km wind accurately.
problem Accurately modeling sub-kilometer surface wind for optimal decision-making.
method Integrates Gaussian processes and neural networks to model wind gusts at sub-kilometer resolution.
result Modeling covariance structure improves prediction quality and calibration.
New framework uses time series features for predicting streamflow in ungauged areas.
problem Predicting streamflow in areas without gauging stations.
method Developed regression-based streamflow regionalization using a wide range of time series features from large datasets.
result Certain time series features, like entropy and autocorrelation, are better predictors of streamflow than traditional catchment attributes.
Deep learning classifies keratoconus patients with high accuracy.
problem Accurately identifying keratoconus patients for early intervention.
method Unsupervised and semi-supervised machine learning models using corneal topography and clinical data.
result Unsupervised method with 29 variables shows better classification accuracy.
Study proposes CNN for reconstructing high-res urban DEMs.
problem Lack of high-res urban DEM datasets for flood modeling.
method Multi-scale CNN model trained on urban DEMs of varying resolutions.
result CNN-based method produces superior high-res urban DEMs.
Study examines equity in post-Snow Uri recovery, finds disparities.
problem Disproportionate impacts on vulnerable populations during recovery.
method County and census tract level data analysis, satellite imagery, statistical procedures.
result Negative associations between non-Hispanic whites and outages, positive associations with certain demographic variables.
New representation theory for closed geodesic subflows.
problem Classifying representations with good geometric properties.
method Restricting to invariant closed geodesic subflows.
result Equivalent characterizations and properties of new representations.
Proves EGF representations in specific geometric contexts.
problem Understanding representations of groups with hyperbolic properties.
method Analyzes projectively convex cocompact manifolds and convex projective manifolds with generalized cusps.
result Holonomy representations of specific geometric manifolds are EGF representations.
The paper establishes isomorphisms and constructs colored versions of Lawrence representations.
problem Understanding isomorphisms and colored versions of Lawrence representations.
method Explicit isomorphisms and construction of colored versions.
result Matrices for colored versions of BKL and Lawrence representations provided.
Study k-positive surface group representations and their degenerations.
problem Understanding the behavior of surface group representations under degenerations.
method Introduced k-positive representations and studied their degenerations using a limit theorem for positively ratioed representations.
result Degenerations of k-positive representations can lead to limits that are at least (k-3)-positive and irreducible limits are (k-1)-positive.
Develops theory of Anosov representations for Fuchsian groups, showing stability and analytical properties.
problem Understanding geometrically finite Fuchsian groups and their representations.
method Theory of Anosov representations, type-preserving deformations, limit maps, relative Anosov and dominated representations.
result Cusped Hitchin representations are Borel Anosov, stable under deformations, and limit maps vary analytically.
This article reviews statistical methods for learning data representations.
problem Learning meaningful representations of data.
method Statistical perspective on unsupervised and supervised representation learning.
result Recent advances in representation learning from a statistical viewpoint.
New representations defined for groups and graphs, with applications to stable representations.
problem Defining and constructing new types of representations for groups and graphs.
method Introducing (R,Λ)-directed Anosov representations and using Fock-Goncharov positivity to construct them. result Constructs large families of primitive stable representations from F2 to PGL(V), including non-discrete and non-faithful examples. New representation connects two link invariants.
problem Link invariants of different types.
method Augmentation representation of link group.
result Connects two types of link invariants.
Collar lemma proven for certain surface group representations.
problem Proving a collar lemma for specific surface group representations.
method Using partial hyperconvexity properties and Anosov representations.
result 'Positivity properties' hold for partially hyperconvex representations.
Study subgroup actions on mapping class groups using Heisenberg representations.
problem Untwisting representations of mapping class groups on Heisenberg subgroups.
method Restrict and analyze twisted representations of mapping class groups to Heisenberg subgroups.
result Untwisting representations on Torelli group for any Heisenberg representation.
Characterizes groups for specific types of representations into SL(d,R).
problem Understanding groups admitting certain types of representations into SL(d,R).
method Characterization and bounds on cohomological dimension.
result Bounds on cohomological dimension and characterizations of representations.
Researchers describe unitary representations of mixed braid groups.
problem Understanding unitary representations of mixed braid groups.
method Explicitly describe unitary representations on cohomology of Abelian branched covers.
result Image of the representation is generated by complex reflections and related to the multivariate Burau representation.
This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness -- in a sense specified in the paper -- of the risk measure's Kusuoka r…