On the question of construction of an attraction set under constraints of asymptotic nature

2015 ◽  
Vol 291 (S1) ◽  
pp. 40-55
Author(s):  
A. G. Chentsov ◽  
A. P. Baklanov
Keyword(s):  
Attraction Set ◽  
Asymptotic Nature

scholarly journals An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions

Stats ◽  
2020 ◽  
Vol 4 (1) ◽  
pp. 1-17
Author(s):  
Samuele Tosatto ◽  
Riad Akrour ◽  
Jan Peters
Keyword(s):  
Upper Bound ◽  
Prediction Error ◽  
Kernel Estimator ◽  
Asymptotic Bias ◽  
Surgical Robots ◽  
Related Literature ◽  
Asymptotic Nature ◽  
Potential Applications ◽  
Self Driving Cars ◽  
Automated Decision Making

The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in several related literature. However, given its asymptotic nature, it gives no access to a hard bound. The increasing popularity of predictive tools for automated decision-making surges the need for hard (non-probabilistic) guarantees. To alleviate this issue, we propose an upper bound of the bias which holds for finite bandwidths using Lipschitz assumptions and mitigating some of the prerequisites of Rosenblatt’s analysis. Our bound has potential applications in fields like surgical robots or self-driving cars, where some hard guarantees on the prediction-error are needed.

scholarly journals Dissipativity and Error Feedback Controller Design of Time-Delay Genetic Regulatory Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yonggang Ma ◽  
Junmei Liu ◽  
Jiao Ai
Keyword(s):  
Time Delay ◽  
Regulatory Networks ◽  
Controller Design ◽  
Estimation Error ◽  
Rapid Development ◽  
Genetic Regulation ◽  
Genetic Regulatory Networks ◽  
Error Feedback ◽  
Attraction Set ◽  
Parameter Dependent

Genetic regulatory networks (GRNs) play an important role in the development and evolution of the biological system. With the rapid development of DNA technology, further research on GRNs becomes possible. In this paper, we discuss a class of time-delay genetic regulatory networks with external inputs. Firstly, under some reasonable assumptions, using matrix measures, matrix norm inequalities, and Halanay inequalities, we give the global dissipative properties of the solution of the time-delay genetic regulation networks and estimate the parameter-dependent global attraction set. Secondly, an error feedback control system is designed for the time-delay genetic control networks. Furthermore, we prove that the estimation error of the model is asymptotically stable. Finally, two examples are used to illustrate the validity of the theoretical results.

scholarly journals On the relation between pole and running heavy quark masses beyond the four-loop approximation

2018 ◽  
Vol 191 ◽  
pp. 04005 ◽  
Author(s):  
A. L. Kataev ◽  
V. S. Molokoedov
Keyword(s):  
Heavy Quark ◽  
Perturbative Qcd ◽  
Mass Relation ◽  
Coupling Constant ◽  
Quark Masses ◽  
Asymptotic Nature ◽  
Asymptotic Expressions ◽  
Loop Approximation ◽  
Euclidean Region ◽  
Direct Calculations

The effective charges motivated method is applied to the relation between pole and M̅S̅-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors nl, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to π2 effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the t-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the b-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.

scholarly journals The Maximum Displacement for Linear Probing Hashing

2013 ◽  
Vol 22 (3) ◽  
pp. 455-476
Author(s):  
NICLAS PETERSSON
Keyword(s):  
Probabilistic Model ◽  
Hash Table ◽  
Critical Value ◽  
Hash Tables ◽  
Maximum Displacement ◽  
Asymptotic Nature ◽  
Process Convergence

In this paper we study the maximum displacement for linear probing hashing. We use the standard probabilistic model together with the insertion policy known as First-Come-(First-Served). The results are of asymptotic nature and focus on dense hash tables. That is, the number of occupied cellsnand the size of the hash tablemtend to infinity with ration/m→ 1. We present distributions and moments for the size of the maximum displacement, as well as for the number of items with displacement larger than some critical value. This is done via process convergence of the (appropriately normalized) length of the largest block of consecutive occupied cells, when the total number of occupied cellsnvaries.

scholarly journals On inertial-range scaling laws

1996 ◽  
Vol 306 ◽  
pp. 167-181 ◽  
Author(s):  
John C. Bowman
Keyword(s):  
Steady State ◽  
High Resolution ◽  
Scaling Laws ◽  
State Energy ◽  
Three Dimensional ◽  
Inertial Range ◽  
Energy Spectra ◽  
Two Dimensional ◽  
Unified Framework ◽  
Asymptotic Nature

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's k−5/3 scaling is derived for the energy inertial range. A related modification is found to Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at the injection wavenumber. The significance of these corrections is illustrated with steady-state energy spectra from recent high-resolution closure computations. Implications for conventional numerical simulations are discussed. These results underscore the asymptotic nature of inertial-range scaling laws.

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