This work extends locally conformal analysis to multi-Hamiltonian settings, providing new geometric structures and Hamiltonian dynamics.
problem Globalization problem in multi-Hamiltonian formalisms due to incompatibilities on chart overlaps.
method Investigation of locally conformally Nambu--Poisson and locally conformally generalized Poisson manifolds, constructing Hamiltonian-type evolution equations.
result Unified framework for classical, Nambu--Poisson, and generalized Poisson manifolds within a locally conformal context.
COLoKe adapts Koopman embeddings online, reducing overfitting and improving long-term predictions.
problem Online adaptation of Koopman embeddings to avoid overfitting and maintain long-term predictive accuracy.
method Combines deep feature learning with multistep prediction consistency in a lifted space, using a conformal-style mechanism for selective updates.
result Empirically effective in reducing overfitting and maintaining long-term predictive accuracy.
The aim of the paper is to understand the local forms of conformal vector fields in the neighborhood of a singularity. We begin a general study in this direction, for any pseudo-Riemannian type, and give a complete answer in the Riemannian case. This is done using geometric methods, and studying local dynamics of seque…
Survey explores interactions between four conformal dynamics branches.
problem Understanding complex dynamics through different mathematical concepts.
method Examples and general results with technical tools.
result Dynamical relations between Schwarz reflection parameter spaces and anti-rational maps/ reflection groups.
Valid prediction sets for dynamic graphs using conformal prediction.
problem Uncertainty quantification in dynamic graph neural networks.
method Dynamic graph unfolding for input to GNNs, combined with conformal prediction.
result Valid prediction sets with minimal assumptions, even in challenging scenarios.
We present a novel machine learning approach to understanding conformation dynamics of biomolecules. The approach combines kernel-based techniques that are popular in the machine learning community with transfer operator theory for analyzing dynamical systems in order to identify conformation dynamics based on molecula…
Study risk-controlling prediction sets for single trajectory data from dynamical systems.
problem Performance guarantees for risk-controlling prediction sets in single trajectory data from unknown stochastic dynamical systems.
method Used blocking and decoupling techniques to analyze performance guarantees under different data generating processes.
result Performance guarantees similar to iid setting when data is stationary and contractive, with graceful degradation otherwise.
The configuration space of the reduced Hamiltonian formulation of quantum gravity has been shown, for non-Ricci flat metrics, to be a higher-dimensional analogue of the Teichmüller space of conformal structures on a Riemann surface. In this article we show that the configuration space of conformal connection-dynamics i…
Study on symmetries and equilibria in Poisson manifolds, with applications to rigid body dynamics.
problem Characterizing conformal relative equilibria on Poisson manifolds.
method Introducing conformally Poisson actions and momentum maps, establishing algebraic criteria.
result Classification of nontrivial conformal relative equilibria in Lie algebras, with applications to rigid body dynamics.
Researchers tackle the globalization problem of locally cosymplectic Hamiltonian dynamics.
problem Globalization problem of locally cosymplectic Hamiltonian dynamics.
method Investigate the geometry of locally conformally cosymplectic manifolds and provide a geometric Hamilton-Jacobi theory.
result Provide a geometric Hamilton-Jacobi theory on locally conformally cosymplectic manifolds.
In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds with variable negative curvature. Applying results from dynamics on these spaces,…
A new method for predicting uncertainties in stream networks.
problem Uncertainty quantification in spatiotemporal graphs with directional flow constraints.
method Spatio-Temporal Adaptive Conformal Inference (STACI) integrating network topology and temporal dynamics.
result STACI effectively balances prediction efficiency and coverage, outperforming existing methods.
ConfEviSurrogate improves surrogate model accuracy and uncertainty quantification.
problem Uncertainty in surrogate models hinders reliable analysis.
method Introduces ConfEviSurrogate, a novel model that learns evidential distributions, separates uncertainty sources, and provides reliable prediction intervals.
result Demonstrates accurate predictions and robust uncertainty estimates in various simulations.
ResCP uses reservoir computing to create efficient, scalable time series prediction intervals.
problem Building distribution-free prediction intervals for time series data with small sample sizes and changing distributions.
method Reservoir Conformal Prediction (ResCP) leverages reservoir computing to dynamically reweight conformity scores based on similarity among reservoir states.
result ResCP achieves asymptotic conditional coverage and is effective across diverse forecasting tasks.
The conformal module of conjugacy classes of braids implicitly appeared in a paper of Lin and Gorin in connection with their interest in the 13. Hilbert Problem. This invariant is the supremum of conformal modules (in the sense of Ahlfors) of certain annuli related to the conjugacy class. This note states that the conf…
By a conformal string in Euclidean space is meant a closed critical curve with non-constant conformal curvatures of the conformal arclength functional. We prove that (1) the set of conformal classes of conformal strings is in 1-1 correspondence with the rational points of the complex domain $\{q\in \mathbb{C} \,:\, 1/2…
Investigates multifractal scaling in critical dynamics of random surfaces.
problem Analyzing multifractal scaling in critical dynamics of random surfaces.
method Examined multifractal scaling in various conformal field theories on random surfaces.
result Higher moments of time variations of the order parameter exhibit multifractal scaling.
Recent developments in specialized computer hardware have greatly accelerated atomic level Molecular Dynamics (MD) simulations. A single GPU-attached cluster is capable of producing microsecond-length trajectories in reasonable amounts of time. Multiple protein states and a large number of microstates associated with f…
New method optimizes prediction set volume in conformal prediction.
problem Achieving volume optimality in conformal prediction without sacrificing coverage guarantees.
method Dynamic programming algorithm for finding near-optimal volume unions of k-intervals.
result Efficient algorithm finds unions of k-intervals with near-optimal volume for any distribution.
A new method improves quantile regression for high-dimensional data.
problem Handling heteroscedastic, multimodal, or skewed data in quantile regression.
method Dynamic prototypes-based probability density estimation with conformalized high-density quantile regression.
result Enhanced prediction regions with valid coverage guarantees and scalability to higher dimensions.
Geometrically transforms nonconservative dynamics to linearize Kepler and Manev systems.
problem Regularizing and linearizing nonconservative central force dynamics.
method Projective transformation and conformal scaling in configuration and phase spaces.
result Full linearization of Kepler and Manev dynamics in any finite dimension.
The Weinstein conjecture is extended to a new class of manifolds.
problem Existence of Reeb 2-curves in locally conformally symplectic manifolds.
method Extended Gromov-Witten theory and elliptic curve counts.
result Partial verification of the conjecture in higher dimensions.
The paper analyzes null infinity's geometry without restrictions.
problem Understanding null infinity's geometry without constraints.
method Coordinate-free approach, treating conformal factor as dynamical.
result Isometric spacetimes with identical free data at null infinity.
Characterizes potential function of almost conformal Ricci solitons on Sasakian manifolds.
problem Characterizing potential functions of almost conformal Ricci solitons on Sasakian manifolds.
method Characterization through the potential function f and non-dynamical scalar field p. result Established a sufficient condition for an almost conformal Ricci soliton to be an almost conformal gradient Ricci soliton.
Generative models accelerate molecular dynamics by four orders of magnitude.
problem Femtosecond time steps limit access to slow molecular processes.
method Deep generative modeling framework that accelerates sampling.
result Quantitative characterization of equilibrium ensembles and dynamical relaxation processes.
Proposes a recursive MPC scheme with probabilistic safety guarantees for uncertain dynamic systems.
problem Probabilistic safety guarantees for MPC in dynamic environments with unknown stochastic agents.
method Uses conformal prediction to derive high-confidence prediction regions and gradually relax safety constraints online.
result Ensures recursive feasibility of MPC schemes by relaxing safety constraints over time.
ConfFlow uses transformer networks to generate molecular conformations efficiently.
problem Efficient generation of valid conformations for large molecules.
method Flow-based model using transformer networks that directly samples in coordinate space.
result ConfFlow improves accuracy by up to 40% for large molecule conformations.
New methods improve uncertainty quantification in dynamic biological systems.
problem Uncertainty in dynamic biological models due to nonlinearity and parameter sensitivity.
method Conformal inference methods for non-asymptotic guarantees.
result Enhanced robustness and scalability for diverse biological data structures.
We provide obstructions to the existence of conformally Anosov Reeb flows on a 3-manifold that partially generalize similar obstructions to Anosov Reeb flows. In particular, we show S3 does not admit conformally Anosov Reeb flows. We also give a Riemannian geometric condition on a metric compatible with a c…
Surveying 33 mapping questions posed by Heinonen and Semmes.
problem Mapping questions posed by Heinonen and Semmes.
method Survey and review of existing research.
result Current status of 33 mapping questions.
We prove dynamical stability and instability theorems for compact Einstein metrics under the Ricci flow. We give a nearly complete charactarization of dynamical stability and instability in terms of the conformal Yamabe invariant and the Laplace spectrum. In particular, we prove dynamical stability of some classes of E…
New framework for conformal equivariant cycles in KK-theory.
problem Tackles conformal equivariance in unbounded KK-theory.
method Extends unbounded Kasparov theory with novel perturbation theory.
result Defines new unbounded representatives of Kasparov classes.
A machine learning model captures non-Newtonian fluid dynamics from molecular details.
problem Creating accurate non-Newtonian fluid models from molecular data.
method Developed a machine learning framework that maps micro-scale polymer configurations to macro-scale fluid dynamics, preserving molecular fidelity.
result The deep non-Newtonian model (DeePN2) accurately predicts fluid behavior without empirical closures. MPS selects models for nonstationary time series in real-time.
problem Model selection under nonstationary time series.
method Combines conformal inference with model confidence sets.
result Reliably identifies optimal models under nonstationarity.
We here present a model of the dynamics of extremism based on opinion dynamics in order to understand the circumstances which favour its emergence and development in large fractions of the general public. Our model is based on the bounded confidence hypothesis and on the evolution of initially anti-conformist agents to…
TorsionNet uses reinforcement learning to efficiently generate conformers of flexible molecules.
problem Efficiently generating diverse and representative conformer sets for flexible molecules.
method Sequential conformer search technique based on reinforcement learning under the rigid rotor approximation, trained via curriculum learning.
result TorsionNet outperforms chemoinformatics methods by 4x on large branched alkanes and several orders of magnitude on biopolymer lignin.
GAIF enhances online multiple testing with feedback, improving statistical power.
problem Sequential online multiple testing with delayed feedback.
method GAIF framework using dynamic threshold adjustment and feedback-driven model selection.
result Improves statistical power through feedback-driven model selection.
The paper develops a theory of conformal density at infinity for groups with contracting elements.
problem Understanding conformal dynamics at infinity for groups with contracting elements.
method Introducing a class of convergence boundary and establishing the basic theory of conformal density on it.
result Unified theory of conformal density on various boundaries for different types of groups.
TRACE improves conformal prediction for multi-dimensional outputs.
problem Challenges in constructing valid and informative conformal prediction regions for multi-dimensional outputs.
method TRACE uses transport alignment in diffusion and flow matching models to define nonconformity scores.
result TRACE yields valid and adaptive conformal prediction regions for multimodal and non-convex distributions.
Given a simple Lie group G of rank 1, we consider compact pseudo-Riemannian manifolds (M,g) of signature (p,q) on which G can act conformally. Precisely, we determine the smallest possible value for the index min(p,q) of the metric. When the index is optimal and G non-exceptional, we prove that the metric must be confo…
ECI improves time series prediction uncertainty quantification by smoothing miscoverage error.
problem Challenges in uncertainty quantification for time series prediction due to temporal dependence and distribution shift.
method Error-quantified Conformal Inference (ECI) by smoothing quantile loss function and introducing adaptive feedback scale.
result ECI achieves valid miscoverage control and tighter prediction sets than existing methods.
The paper uses conformal prediction for forecasting conflict sequences in Markov processes.
problem Forecasting future conflict states for national policy decisions.
method Conformal prediction on Markov processes for temporally-dependent data.
result Conformal prediction provides valid uncertainty quantification and robustness to model misspecification.
We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead a choice of ways to reverse the conformal compactification of a Euclidean vector…
BCI provides calibrated prediction intervals for time series forecasts.
problem Calibration of prediction intervals for time series forecasts.
method BCI wraps around any time series forecasting models and optimizes interval lengths using dynamic programming.
result BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence.
CASCADE improves uncertainty communication in Parkinson's disease medication management.
problem Uncertainty in clinical decision-making for Parkinson's disease patients.
method CASCADE uses a novel conformal prediction framework to adaptively scale prediction intervals based on classification uncertainty.
result CASCADE produces more efficient and robust prediction intervals for Parkinson's disease patients.
We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their generating smooth contact Hamiltonians and conformal factors to the group of top…
SAFER improves personalized treatment recommendations for dynamic clinical contexts.
problem Personalized treatment optimization in evolving clinical contexts with safety concerns.
method Integrates structured EHR and clinical notes, uses conformal prediction for safe recommendations.
result SAFER outperforms state-of-the-art baselines in recommendation metrics and mortality rates.
The paper introduces a new method to create stable ergodic actions on higher-dimensional manifolds.
problem Stable ergodicity of group actions on smooth manifolds restricted to one-dimensional cases.
method Geometric method using quasi-conformal blender for constructing stable local dynamics.
result Every closed manifold admits stably ergodic finitely generated group actions by diffeomorphisms of class C1+α.