New method creates personalized brain atlases from large datasets.
problem Limited generalizability and spatial specificity of traditional probabilistic atlases.
method Data-driven clustering of regions using point distribution models.
result Personalized probabilistic atlases adapt quickly to new subjects.
Spark complexes defined on good effective orbifold atlases.
problem Constructing a structured representation for effective orbifolds.
method Defining good atlases and constructing spark complexes categorically.
result Spark character 2-functor factors through the constructed 2-functor.
We give a definition of atlases for ineffective orbifolds, and prove that this definition leads to the same notion of orbifold as that defined via topological groupoids.
Fine-grained atlases improve fMRI analysis of brain activity.
problem Large fMRI datasets require scalable brain network summaries.
method Trained on millions of fMRI volumes, DiFuMo dictionaries of 64-1024 networks.
result Fine-grained atlases enhance classic fMRI analysis pipelines.
Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the "virtual structure" of its orbit space, the equivalence between atlases being here the smooth Morita equivalence. This "structure" kee…
New method uses entropy to generate multiple plausible causal maps.
problem Learning causal relationships from noisy data can lead to artifacts in DAGs.
method Entropy-based inference to generate an ensemble of plausible causal graphs.
result Multiple causal maps consistent with underlying data variability.
Analyzes how suborbifolds relate to groupoid embeddings.
problem Understanding the relationship between suborbifolds and groupoid embeddings.
method Examines the correspondence between suborbifolds and groupoid embeddings via atlases and effective orbifold groupoids.
result Identifies classes of suborbifolds that naturally lead to groupoid embeddings.
New method combines prior knowledge and brain atlases for fMRI analysis.
problem Matrix factorization formulation of task-related fMRI problem.
method Incorporates prior knowledge from experimental design and brain atlases, uses novel sparsity promoting constraint.
result Efficiently copes with uncertainties and selection of sparsity parameters.
DET unifies geometric and functional alignment for high-dimensional scientific data.
problem Challenges in nonrigid registration for high-dimensional, irregular data.
method Domain Elastic Transform (DET) treats data as functions on irregular domains, using a Bayesian framework for elastic motion registration.
result DET achieves 92% topological preservation on MERFISH data and successfully registers whole-embryo Stereo-seq atlases.
We study the number of Darboux charts needed to cover a closed connected symplectic manifold (M,ω), and effectively estimate this number from below and from above in terms of the Lusternik--Schnirelmann category of M and the Gromov width of (M,ω).
We construct an infinite sequence of projectively flat manifolds by using castling transformations of prehomogeneous vector spaces. We also give a classification of manifolds equipped with a flat projective structure obtained by a finite number of castling transformations, and describe these flat projective structures …
The Jacobian conjecture is simplified using polynomial mappings.
problem Simplifying the Jacobian conjecture over the real field.
method Using polynomial mappings to restrict transitions on manifolds.
result An equivalent statement of the Jacobian conjecture.
New brain atlas method improves classification accuracy.
problem Creating accurate brain atlases from connectomes.
method Connectivity-based hierarchical clustering and consensus aggregation.
result Consensus parcellation outperforms existing atlases in classification tasks.
Wider networks learn more interpretable features and improve performance during fine-tuning.
problem Transferability of learned features between tasks and the effect of network width on feature learning.
method Activation atlases to visualize and analyze features learned by wide and narrow networks.
result The hidden state of a wide network contains more information about the inputs than a narrow network, leading to improved performance during fine-tuning.
Toric quasifolds extend toric geometry to non-rational polytopes.
problem Extending toric geometry to non-rational polytopes.
method Introduced toric quasifolds to solve symplectic extension problem.
result Illustrated toric quasifolds and their atlases.
We describe a bicategory (RedOrb) of reduced orbifolds in the framework of classical differential geometry (i.e. without any explicit reference to notions of Lie groupoids or differentiable stacks, but only using orbifold atlases, local lifts and changes of charts). In order to construct such a …
New bridge between diffeology and noncommutative geometry.
problem Connecting diffeology and noncommutative geometry.
method Embedding quasifolds into diffeology and associating C*-algebras.
result Morita classes of C*-algebras associated with diffeomorphic quasifolds.
Accumulation of standardized data collections is opening up novel opportunities for holistic characterization of genome function. The limited scalability of current preprocessing techniques has, however, formed a bottleneck for full utilization of contemporary microarray collections. While short oligonucleotide arrays …
In this paper we compute the minimal number of Darboux chart needed to cover a Hermitian symmetric space of compact type in terms of the degree of their embeddings in CPN. The proof is based on the recent work of Y. B. Rudyak and F. Schlenk [18] and on the symplectic geometry tool developed by the first au…
We study the minimal number C(M,ξ) of contact charts that one needs to cover a closed connected contact manifold (M,ξ). Our basic result is C(M,ξ) \le \dim M + 1. We compute C(M,ξ) for all closed connected contact 3-manifolds: C (M,ξ) = 2 if M = S^3 and ξis tight, 3 if M = S^3 and ξis overtwisted or if M = #_k (S^2 \ti…
We analyze the possibility of defining infinite-dimensional manifolds as ringed spaces. More precisely, we consider three definitions of manifolds modeled on locally convex spaces: in terms of charts and atlases, in terms of ringed spaces, and in terms of functored spaces, as introduced by Douady in his thesis. It is s…
The first, second and fourth Painlevé equations are studied by means of dynamical systems theory and three dimensional weighted projective spaces $\C P^3(p,q,r,s)$ with suitable weights (p,q,r,s) determined by the Newton diagrams of the equations or the versal deformations of vector fields. Singular normal forms of t…
The paper develops a theory of Ehresmann structures in positive characteristic.
problem Developing a theory for Ehresmann structures in positive characteristic.
method Comparing Frobenius-Ehresmann structures with Cartan geometries and studying their equivalence.
result Formulating and proving the Ehresmann-Weil-Thurston principle for Frobenius-Ehresmann structures.
Novel framework for medical image segmentation using deep learning.
problem Class imbalance and domain adaptation in medical image segmentation.
method Biophysics-based domain adaptation and automatic segmentation of white, gray, and cerebrospinal fluid.
result Improved segmentation performance, especially with the biophysics-based domain adaptation.
Ensemble learning improves rs-fMRI predictions using 3D CNNs.
problem Improving specificity and sensitivity of rs-fMRI measurements through better parcellation schemes.
method Ensemble learning with 3D CNNs to combine predictions from different parcellations.
result Ensemble learning with 3D CNNs outperforms traditional methods in rs-fMRI classification and regression tasks.
Probabilistic deep learning uses neural networks and models to handle uncertainty.
problem Handling uncertainty in deep learning models.
method Two approaches: probabilistic neural networks and deep probabilistic models.
result TensorFlow Probability library supports both approaches.
The study classifies rational 1-forms on the Riemann sphere with simple poles.
problem Classifying rational 1-forms on the Riemann sphere with specified pole conditions.
method Recognized three equivalent atlases, proved submanifold properties, and used PSL(2,C) action.
result Quotients of isochronous 1-forms admit stratified orbit types.
Stochastic programs simplify complex models with noise and nondeterminism.
problem Handling models with nuisance parameters, noise, and nondeterminism.
method Developed a reference implementation for stochastic probabilistic programs and inference.
result Efficient inference in models with noise and nondeterminism is possible.
Probabilistic models with deep neural networks now handle large data sets.
problem Historical constraints on probabilistic modeling.
method Variational inference, stochastic gradient descent, distributed computation.
result Probabilistic models can now handle large data sets and complex relationships.
Transformers interpret as probabilistic mixtures, offering new insights.
problem Understanding Transformers from a probabilistic perspective.
method Modeling Transformers as mixtures of Gaussian models.
result Transformers can be seen as maximum posterior probability estimators.
Deployable probabilistic programming for Go and other languages.
problem Adding probabilistic programming to mainstream languages.
method Design guidelines and Infergo implementation for Go.
result Infergo demonstrates performance and applicability in various use cases.
Improves probabilistic programming by analyzing program structure.
problem Inefficiency and limitations of single inference algorithms in probabilistic programming.
method Three novel techniques: static and dynamic analyses to adapt programs for more efficient inference.
result Improves probabilistic programming by making inference more efficient.
Probabilistic ML improves healthcare data analysis.
problem Insufficient understanding and incomplete data in healthcare.
method Examination of probabilistic machine learning models for healthcare challenges.
result Probabilistic models enhance healthcare data analysis and model building.
Graph Neural Network identifies ASD biomarkers from fMRI data.
problem Finding biomarkers for Autism Spectrum Disorder (ASD).
method Graph Neural Network (GNN) for analyzing task-fMRI brain networks, 2-stage pipeline to interpret feature importance.
result GNN achieves high accuracy in identifying ASD biomarkers and reveals their association with social behaviors.
Birch automates probabilistic modeling using a Turing-complete language.
problem Automating the matching of probabilistic models with inference methods.
method Formally describes models as programs, revealing structure and form dynamically.
result Probabilistic programming languages can tailor inference methods based on model structure and form.
Probabilistic pseudo knots model uncertain knot diagrams.
problem Modeling knots with unresolved crossings.
method Assign probabilities to undetermined crossings; define probabilistic equivalence and extend classical knot invariants.
result Capture uncertainty in physical, biological, and computational contexts.
Synthesizes static analysis for probabilistic programs.
problem Optimize learning process, verify models, improve programming interface.
method Organize and analyze static analysis techniques for probabilistic programming.
result Future directions for improvement in statistical machine learning.
Pyro enables scalable AI models using probabilistic programming.
problem Developing complex probabilistic models for large datasets.
method Stochastic variational inference, PyTorch, Poutine.
result Pyro supports scalable AI models with high-dimensional data.
Paper introduces a new probabilistic model for class-specific discriminant analysis.
problem Lack of multi-modal structure consideration in existing class-specific methods.
method Formulates a probabilistic model that incorporates multi-modal negative class structure.
result Proposed model can be directly used for class-specific probabilistic classification.
Probabilistic programming allows specification of probabilistic models in a declarative manner. Recently, several new software systems and languages for probabilistic programming have been developed on the basis of newly developed and improved methods for approximate inference in probabilistic models. In this contribut…
This paper introduces the probabilistic module interface, which allows encapsulation of complex probabilistic models with latent variables alongside custom stochastic approximate inference machinery, and provides a platform-agnostic abstraction barrier separating the model internals from the host probabilistic inferenc…
Probabilistic solvers improve stability for stiff systems.
problem Performance penalties for small steps in stiff systems.
method Probabilistic exponential integrators that include fast linear dynamics in the prior.
result Proven L-stability and probabilistic error accounting.
We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly practical for distributions which are not analytically tractable, including highly struc…
Forward inference techniques such as sequential Monte Carlo and particle Markov chain Monte Carlo for probabilistic programming can be implemented in any programming language by creative use of standardized operating system functionality including processes, forking, mutexes, and shared memory. Exploiting this we have …
SPPL simplifies probabilistic programming for exact inference.
problem Efficient exact inference in probabilistic models.
method SPPL translates probabilistic programs into sum-product expressions, leveraging new techniques for scalability.
result SPPL achieves up to 3500x speedups in exact inference.
The paper extends calibration to sets of probabilistic classifiers, finding many ensembles are poorly calibrated.
problem Evaluating the validity of epistemic uncertainty in sets of probabilistic classifiers.
method Proposed a novel nonparametric calibration test for sets of probabilistic classifiers.
result Ensembles of deep neural networks are often not well calibrated.
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
problem Analyzing nonlinear dynamical systems with probabilistic understanding.
method Combines deep learning and probabilistic modeling, using KL annealing and normalizing flows.
result Captures latent dynamics in sequential datasets with improved convergence and flexibility.
MultiVerse uses importance sampling for efficient causal reasoning in probabilistic programming.
problem Efficient causal reasoning in probabilistic models, especially counterfactual inference.
method Native implementation of importance sampling in probabilistic programming, optimizing inference through query structure.
result Significant optimisation of inference process through careful design choices and query structure consideration.