A simple alternative to the Barbalat lemma

1997 ◽  
Vol 42 (5) ◽  
pp. 698 ◽  
Author(s):  
G. Tao
Keyword(s):  
Simple Alternative ◽  
Barbalat Lemma

Stabilization for a class of delayed switched inertial neural networks via non-reduced order method

2021 ◽  
pp. 014233122098594
Author(s):  
Xuan Chen ◽  
Dongyun Lin
Keyword(s):  
Neural Networks ◽  
Comparative Research ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Global Stabilization ◽  
Order Method ◽  
Reduced Order ◽  
Global Asymptotic Stabilization ◽  
Inertial Neural Networks ◽  
Barbalat Lemma

This paper tackles the issue of global stabilization for a class of delayed switched inertial neural networks (SINN). Distinct from the frequently employed reduced-order technique, this paper studies SINN directly through non-reduced order method. By constructing a novel Lyapunov functional and using Barbalat Lemma, sufficient conditions for the global asymptotic stabilization issue and global exponential stabilization issue of the considered SINN are established. Numerical simulations further confirm the feasibility of the main results. The comparative research shows that global stabilization results of this paper complement and improve some existing work.

scholarly journals Personalized medicine for reconstruction of critical-size bone defects – a translational approach with customizable vascularized bone tissue

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Annika Kengelbach-Weigand ◽  
Carolina Thielen ◽  
Tobias Bäuerle ◽  
Rebekka Götzl ◽  
Thomas Gerber ◽  
...  
Keyword(s):  
Personalized Medicine ◽  
Large Scale ◽  
Critical Size ◽  
Therapeutic Option ◽  
Living Organism ◽  
Bone Defects ◽  
Sheep Model ◽  
Simple Alternative ◽  
Translational Approach ◽  
Near Future

AbstractTissue engineering principles allow the generation of functional tissues for biomedical applications. Reconstruction of large-scale bone defects with tissue-engineered bone has still not entered the clinical routine. In the present study, a bone substitute in combination with mesenchymal stem cells (MSC) and endothelial progenitor cells (EPC) with or without growth factors BMP-2 and VEGF-A was prevascularized by an arteriovenous (AV) loop and transplanted into a critical-size tibia defect in the sheep model. With 3D imaging and immunohistochemistry, we could show that this approach is a feasible and simple alternative to the current clinical therapeutic option. This study serves as proof of concept for using large-scale transplantable, vascularized, and customizable bone, generated in a living organism for the reconstruction of load-bearing bone defects, individually tailored to the patient’s needs. With this approach in personalized medicine for the reconstruction of critical-size bone defects, regeneration of parts of the human body will become possible in the near future.

scholarly journals Asymptotic relative submajorization of multiple-state boxes

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Gergely Bunth ◽  
Péter Vrana
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Standard Form ◽  
Point Of View ◽  
State Discrimination ◽  
Simple Alternative ◽  
Multiple State ◽  
Error Probabilities

AbstractPairs of states, or “boxes” are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde in Phys Rev Res 1(3):033170, 2019. 10.1103/PhysRevResearch.1.033170), where free operations are arbitrary quantum channels that are applied to both states. From this point of view, hypothesis testing is seen as a process by which a standard form of distinguishability is distilled. Motivated by the more general problem of quantum state discrimination, we consider boxes of a fixed finite number of states and study an extension of the relative submajorization preorder to such objects. In this relation, a tuple of positive operators is greater than another if there is a completely positive trace nonincreasing map under which the image of the first tuple satisfies certain semidefinite constraints relative to the other one. This preorder characterizes error probabilities in the case of testing a composite null hypothesis against a simple alternative hypothesis, as well as certain error probabilities in state discrimination. We present a sufficient condition for the existence of catalytic transformations between boxes, and a characterization of an associated asymptotic preorder, both expressed in terms of sandwiched Rényi divergences. This characterization of the asymptotic preorder directly shows that the strong converse exponent for a composite null hypothesis is equal to the maximum of the corresponding exponents for the pairwise simple hypothesis testing tasks.

scholarly journals Calendar Spread Exchange Options Pricing with Gaussian Random Fields

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 77
Author(s):  
Donatien Hainaut
Keyword(s):  
Covariance Structure ◽  
Gaussian Random Fields ◽  
Options Pricing ◽  
Option Prices ◽  
Numerical Illustration ◽  
Simple Alternative ◽  
Asset Values ◽  
Brownian Model ◽  
Exchange Options ◽  
Empirical Covariance

Most of the models leading to an analytical expression for option prices are based on the assumption that underlying asset returns evolve according to a Brownian motion with drift. For some asset classes like commodities, a Brownian model does not fit empirical covariance and autocorrelation structures. This failure to replicate the covariance introduces a bias in the valuation of calendar spread exchange options. As the payoff of these options depends on two asset values at different times, particular care must be taken for the modeling of covariance and autocorrelation. This article proposes a simple alternative model for asset prices with sub-exponential, exponential and hyper-exponential autocovariance structures. In the proposed approach, price processes are seen as conditional Gaussian fields indexed by the time. In general, this process is not a semi-martingale, and therefore, we cannot rely on stochastic differential calculus to evaluate options. However, option prices are still calculable by the technique of the change of numeraire. A numerical illustration confirms the important influence of the covariance structure in the valuation of calendar spread exchange options for Brent against WTI crude oil and for gold against silver.

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