Results 11 to 20 of about 15,156 (142)
Split invariance principles for stationary processes
, 2011 The results of Koml\'{o}s, Major and Tusn\'{a}dy give optimal Wiener approximation of partial sums of i.i.d. random variables and provide an extremely powerful tool in probability and statistical inference. Recently Wu [Ann. Probab. 35 (2007) 2294--2320]
Berkes, István +2 more
core +1 more source
Weak Convergence to Stable L\'evy Processes for Nonuniformly Hyperbolic Dynamical Systems [PDF]
, 2013 We consider weak invariance principles (functional limit theorems) in the domain of a stable law. A general result is obtained on lifting such limit laws from an induced dynamical system to the original system.
Melbourne, Ian, Zweimüller, Roland
core
Invariance principles for linear processes with application to isotonic regression
, 2011 In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range dependence and the
Dedecker, Jérôme +2 more
core +3 more sources
Linearizing and Forecasting: A Reservoir Computing Route to Digital Twins of the Brain
Advanced Science, EarlyView.A new approach uses simple neural networks to create digital twins of brain activity, capturing how different patterns unfold over time. The method generates and recovers key dynamics even from noisy data. When applied to fMRI, it predicts brain signals and reveals distinctive activity patterns across regions and individuals, opening possibilities for ...
Gabriele Di Antonio +3 more
wiley +1 more source
A Perspective on Interactive Theorem Provers in Physics
Advanced Science, EarlyView.Into an interactive theorem provers (ITPs), one can write mathematical definitions, theorems and proofs, and the correctness of those results is automatically checked. This perspective goes over the best usage of ITPs within physics and motivates the open‐source community run project PhysLean, the aim of which is to be a library for digitalized physics
Joseph Tooby‐Smith
wiley +1 more source
Effective Choice and Boundedness Principles in Computable Analysis
, 2009 In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other?
Brattka +13 more
core +2 more sources
Advanced Science, EarlyView.This work provides a practical guide for neuroengineers to design advanced neural interfaces, embracing and tailoring the concept of functional disorder. By bridging 2D and 3D in vitro models, this work highlights how non‐periodic, spatially heterogeneous, multiscale nanotopography can enable more physiologically relevant platforms for studying neural ...
F. Maita +4 more
wiley +1 more source
On the functional central limit theorem via martingale approximation
, 2011 In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors.
Gordin, Mikhail, Peligrad, Magda
core +1 more source
A Unifying Approach to Self‐Organizing Systems Interacting via Conservation Laws
Advanced Intelligent Discovery, EarlyView.The article develops a unified way to model and analyze self‐organizing systems whose interactions are constrained by conservation laws. It represents physical/biological/engineered networks as graphs and builds projection operators (from incidence/cycle structure) that enforce those constraints and decompose network variables into constrained versus ...
F. Barrows +7 more
wiley +1 more source
, 2008 Invariance principles are obtained for a Markov process on a half-line with continuous paths on the interior. The domains of attraction of the two different types of self-similar processes are investigated.
Yano, Kouji
core +3 more sources