New neural processes use stacked Markov operators to improve flexibility.
problem Improving flexibility in neural processes.
method Stacking neural parameterized Markov transition operators in function space.
result MNPs outperform baseline models on various tasks.
Algorithm learns graph operator from sparse space-time samples.
problem Learning time-varying graph signals from partial observations.
method Non-convex IRLS algorithm for low-rank matrix completion.
result No more than O(rn log(nT)) space-time samples needed for accurate recovery.
Study optimal holomorphic extensions on complex manifolds with transitivity property.
problem Optimal holomorphic extensions on complex manifolds with transitivity property.
method Use Toeplitz operators and transitivity property for optimal holomorphic extensions.
result Transitivity property of optimal holomorphic extensions with small defect.
Cut-DeepONet handles discontinuities and sharp transitions in neural operators.
problem Neural operators struggle with discontinuities and sharp transitions in PDEs.
method Two-stage training framework that explicitly models discontinuities via a lifting strategy and input-dependent discontinuity prediction.
result Cut-DeepONet outperforms state-of-the-art methods on benchmark PDEs with low-resolution datasets.
ISOKANN learns collective variables and effective dynamics for metastable transitions.
problem Understanding metastable transitions in complex molecular systems.
method Integrates Koopman operators with neural networks to extract CVs and effective dynamics.
result Reconstructs coarse-grained kinetics and reproduces transition times across barriers.
Generative Stochastic Networks (GSNs) have been recently introduced as an alternative to traditional probabilistic modeling: instead of parametrizing the data distribution directly, one parametrizes a transition operator for a Markov chain whose stationary distribution is an estimator of the data generating distributio…
We propose a novel method to directly learn a stochastic transition operator whose repeated application provides generated samples. Traditional undirected graphical models approach this problem indirectly by learning a Markov chain model whose stationary distribution obeys detailed balance with respect to a parameteriz…
Study of correlated Wigner matrices with BBP transitions.
problem Understanding spectral transitions in correlated Wigner matrices.
method Analyzes a Wigner-type matrix with row/column correlations, decomposes into bulk and outliers, and uses integral operators to model transitions.
result Correlated Wigner matrices exhibit multiple BBP transitions at critical points.
Study shows continuity of non-Kähler Calabi-Yau conifold transitions.
problem Understanding the geometry of Calabi-Yau conifold transitions.
method Use of balanced and Hermitian-Yang-Mills metrics to analyze conifold transitions.
result The conifold transition is continuous in the Gromov-Hausdorff topology.
In this paper we explore the functional correlation approach to operational risk. We consider networks with heterogeneous a-priori conditional and unconditional failure probability. In the limit of sparse connectivity, self-consistent expressions for the dynamical evolution of order parameters are obtained. Under equil…
Study identifies transitions between traffic modes on Cologne motorways.
problem Understanding transitions between different traffic modes.
method Constructed state transition network, identified dominant states using PageRank algorithm.
result Identified seasonal dependence in traffic modes.
A method to reduce bias in model-based policy evaluation by shifting operators.
problem Bias in value function computation from noisy estimated models.
method Operator shifting method to reduce the residual norm error.
result The shifting factor is always positive and upper bounded by $1+O\left(1/n
ight)$.
The paper studies convergence of kernel autocovariance operators for stationary processes.
problem Estimating autocovariance operators of stationary processes on Polish spaces.
method Investigates convergence of empirical estimates of autocovariance operators under various conditions.
result Provides consistency results for kernel PCA and spectral analysis methods.
Quantum theory reinterprets financial pricing by focusing on observable price transitions.
problem Traditional financial models rely on latent variables; this paper proposes a new observable approach.
method Shift operators, spectral calculus, and Lindblad semigroups are used to define observable frequency operators and convolution generators.
result The framework leads to a nonlocal pricing equation that converges to classical Black-Scholes-Merton under small mesh limits.
In this paper we study the local description of spaces of forms on transitive Lie algebroids. We use this local description to introduce global structures like metrics, ∗-Hodge operation and integration along the algebraic part of the transitive Lie algebroid (its kernel). We construct a Čech-de Rham bicomplex wit…
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase transition as splitting an underlying manifold into two sub-manifolds with distinct…
Fold maps associated to geodesic random walks on curved spaces.
problem Understanding the behavior of geodesic random walks on curved surfaces.
method Analyzing mappings from the unit tangent sphere to a manifold with non-positive curvature.
result For odd powers of the unit tangent sphere, these mappings are fold maps.
Let M be a most singular orbit of the isotropy representation of a simple symmetric space. Let (νi,Φi) be an irreducible factor of the normal holonomy representation (νpM,Φ(p)). We prove that there exists a basis of a section Σi⊂νi of Φi such that the corresponding shape operators have rational…
HOFLON automates process start-ups and grade-changes using offline RL and online optimization.
problem Manual operation of start-ups and grade-changes by experts is declining, leaving plant owners without the necessary tacit know-how.
method HOFLON combines offline RL to learn a latent manifold and long-horizon Q-critic, and online optimization to maximize Q-critic while penalizing deviations and excessive variable changes.
result HOFLON outperforms standard offline RL in industrial case studies, delivering better cumulative rewards than historical data.
Theory of T-duality for transitive Courant algebroids developed.
problem Developing T-duality for transitive Courant algebroids.
method Introducing a map between sections of canonical spinor bundles and proving isomorphisms of invariant spinors and sections.
result Isomorphisms between spaces of invariant sections and spinors under T-duality.
Neural networks parameterize time-varying Markov dynamics in financial time series.
problem Estimating Markov transition matrices in high-resolution, high-noise financial data.
method Introduces a neural network framework to generate explicit, time-varying Markov transition matrices, constraining neural outputs to formal stochastic operators.
result Learned operators capture regime shifts, with high-volatility regimes homogenizing transition dynamics.
Researchers approximate conditional expectation operators using kernel methods.
problem Statistical approximation of conditional expectation operators under minimal assumptions.
method Modifying the domain of the operator, approximating it by Hilbert-Schmidt operators in a reproducing kernel Hilbert space.
result The nonparametric estimate of the operator converges to a specific limiting object.
A new algorithm for deep Q-learning with robustness to state transition uncertainty.
problem Model uncertainty in state transitions for non-tabular, continuous state spaces.
method Distributionally robust approach using worst-case transition ball and dualized Bellman operator with Sinkhorn distance.
result Optimal policy found through solving non-linear Bellman equation with neural network parameterization.
In industrial systems, certain process variables that need to be monitored for detecting faults are often difficult or impossible to measure. Soft sensor techniques are widely used to estimate such difficult-to-measure process variables from easy-to-measure ones. Soft sensor modeling requires training datasets includin…
Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a description in terms of a configuration of branes or alternatively anti-branes in the …
A new method for ILO with transition model disparity using an intermediary policy.
problem Learning tasks from expert observations with different transition dynamics.
method Training an intermediary policy to match the state transitions of the expert dataset.
result Our method outperforms existing ILO approaches with transition model mismatch.
In this work, we investigate a novel training procedure to learn a generative model as the transition operator of a Markov chain, such that, when applied repeatedly on an unstructured random noise sample, it will denoise it into a sample that matches the target distribution from the training set. The novel training pro…
In this paper we introduce and study some mathematical structures on top of transitive Lie algebroids in order to formulate gauge theories in terms of generalized connections and their curvature: metrics, Hodge star operator and integration along the algebraic part of the transitive Lie algebroid (its kernel). Explicit…
The paper studies dynamical systems with evolving geometric structure using numerical methods.
problem Qualitative behavior of ODEs with varying geometric structure.
method Fourth-order Runge-Kutta scheme for numerical analysis.
result Qualitative transitions in system dynamics as rotation parameter varies.
Study generalizes Picard iteration for nonlinear PDEs, deriving bounds on error.
problem Generalize Picard iteration for nonlinear parabolic PDEs.
method Formulate Picard iteration as abstract state-transition model, derive generalization error bounds.
result Picard depth reduction reduces Picard truncation error without increasing estimation error.
A new model uses Toeplitz matrices to analyze time-series data transitions.
problem Analyzing transitions in time-series data from nonautonomous systems.
method Deep Koopman-layered models with learnable Toeplitz matrices, leveraging Toeplitz matrices' universal property.
result The model demonstrates universality and generalization, outperforming existing methods.
New STH distance finds patterns in event timeseries without resampling.
problem Lack of efficient analysis methods for event and state timeseries.
method Define STE-ts, propose STH, leveraging both time and state duration.
result Improved precision and computation time compared to resampled metrics.
RRPI improves offline RL by optimizing policies against worst-case dynamics.
problem Offline RL's performance degrades under distribution shift and transition uncertainty.
method Formulates offline RL as robust policy optimization, treating transition kernel as decision variable.
result RRPI achieves strong average performance on D4RL benchmarks, outperforming recent baselines.
In most sampling algorithms, including Hamiltonian Monte Carlo, transition rates between states correspond to the probability of making a transition in a single time step, and are constrained to be less than or equal to 1. We derive a Hamiltonian Monte Carlo algorithm using a continuous time Markov jump process, and ar…
Classifies invariant differential operators on a specific geometric space.
problem Identifying invariant differential operators on curved geometries.
method Classification of strongly invariant operators between vector bundles induced by semi-holonomic Verma modules.
result Classification of invariant differential operators on Gr(3,3). Persistent entropy detects phase transitions in complex systems.
problem Detecting phase transitions in complex systems.
method Established a general theorem for persistent entropy to reliably detect phase transitions, introduced operational framework for finite-time computations.
result Persistent entropy exhibits an asymptotically non-vanishing gap across phases, robust numerical signatures across experiments.
We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure…
Paper introduces TtT, market-implied transition time, from greenium term structure.
problem Estimating market-implied transition time to a low-carbon economy.
method Develops inference theory for TtT, introduces two stochastic models.
result Combines two-layer analysis for consistent estimation of diffusion parameters.
Chemical plants are complex and dynamical systems consisting of many components for manipulation and sensing, whose state transitions depend on various factors such as time, disturbance, and operation procedures. For the purpose of supporting human operators of chemical plants, we are developing an AI system that can s…
A novel multi-resolution Gaussian process model for efficient time traversal.
problem Inference for long sequences with fast and slow transitions is difficult.
method A novel Gaussian process state-space architecture composed of multiple components, each trained on a different resolution.
result The combined model allows efficient inference for arbitrarily long sequences with complex dynamics.
These letters, written in 1998-2000, contain various basic results about Courant algebroids (CAs), such as classification of exact and transitive CAs, reduction of CAs, description in terms of symplectic dg manifolds, a canonical generating Dirac operator, and a relation with Poisson-Lie T-duality.
New efficient method for inverse Z-transform reduces complexity significantly.
problem Efficient numerical realization of inverse Z-transform for large n.
method Derives sufficient conditions for new scheme, applies to option pricing.
result Significant reduction in complexity for large n, especially for European options.
A framework combining HSMM and survival analysis for lifecycle-oriented mobility analysis.
problem Understanding individual metro usage dynamics over multi-year horizons.
method A state-based lifecycle modeling framework integrating HSMM and discrete-time survival analysis.
result Identification of interpretable mobility states, transition dynamics, and state-dependent exit and re-entry processes.
We explain a persistent cost-of-carry spread in EUA market and suggest ECB policy change.
problem Persistent cost-of-carry spread in EUA market.
method Cointegration analysis of EUA spread with credit spread and risk-free rate.
result Cointegration found between EUA spread, credit spread, and risk-free rate.
We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann sphere due to the automatic coopeartion of many kinds of maps in the system, ev…
Introduces Floer functions and Floerfolds for intrinsic properties.
problem Complex transformation of Hessian under chart transition.
method Introduces Floer functions and Floerfolds to address intrinsic properties.
result Floer functions and Floerfolds provide intrinsic conditions for Hessian.
Reinforcement learning agents have been mostly developed and evaluated under the assumption that they will operate in a fully autonomous manner -- they will take all actions. In this work, our goal is to develop algorithms that, by learning to switch control between agents, allow existing reinforcement learning agents …
Graph diffusion processes approximate manifold heat semigroups using graph transition matrices.
problem Approximating manifold heat semigroups from graph data under low regularity conditions.
method Iterating graph transition matrix P to approximate Qt=etΔ, bounding error in ∞-norm. result Convergence rates O(N−2/(d+6)) for manifold heat semigroup approximation, valid for in-sample and out-of-sample.