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Jun Wang - One of the best experts on this subject based on the ideXlab platform.
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Robustness analysis of global exponential stability of non-linear systems with time delays and neutral terms
IET Control Theory & Applications, 2013Co-Authors: Yi Shen, Jun WangAbstract:The global stability of non-linear dynamical systems has been investigated extensively in recent decades. It is well known that time delay and neutral term could derail the stability of non-linear systems. This study presents new results on the robustness of the global exponential stability of non-linear systems with respect to time delay and neutral term. Given globally exponentially stable non-linear systems, the problems to be addressed herein are how much time delay and neutral term Contraction Coefficient are allowed so that the non-linear systems can remain to be globally exponentially stable, in the presence of time delay and neutral term. Upper bounds of allowable time delay and neutral term Contraction Coefficient will be derived for non-linear systems to sustain their global exponential stability. A numerical example is provided to illustrate the results.
Lizhong Zheng - One of the best experts on this subject based on the ideXlab platform.
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Comparison of Contraction Coefficients for f-Divergences
Problems of Information Transmission, 2020Co-Authors: Anuran Makur, Lizhong ZhengAbstract:Contraction Coefficients are distribution dependent constants that are used to sharpen standard data processing inequalities for f -divergences (or relative f -entropies) and produce so-called “strong” data processing inequalities. For any bivariate joint distribution, i.e., any probability vector and stochastic matrix pair, it is known that Contraction Coefficients for f -divergences are upper bounded by unity and lower bounded by the Contraction Coefficient for χ ^2-divergence. In this paper, we elucidate that the upper bound is achieved when the joint distribution is decomposable, and the lower bound can be achieved by driving the input f -divergences of the Contraction Coefficients to zero. Then, we establish a linear upper bound on the Contraction Coefficients of joint distributions for a certain class of f -divergences using the Contraction Coefficient for χ ^2-divergence, and refine this upper bound for the salient special case of Kullback-Leibler (KL) divergence. Furthermore, we present an alternative proof of the fact that the Contraction Coefficients for KL and χ ^2-divergences are equal for bivariate Gaussian distributions (where the former Coefficient may impose a bounded second moment constraint). Finally, we generalize the well-known result that Contraction Coefficients of stochastic matrices (after extremizing over all possible probability vectors) for all nonlinear operator convex f -divergences are equal. In particular, we prove that the so-called “less noisy” preorder over stochastic matrices can be equivalently characterized by any nonlinear operator convex f -divergence. As an application of this characterization, we also derive a generalization of Samorodnitsky’s strong data processing inequality.
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Bounds between Contraction Coefficients
arXiv: Information Theory, 2015Co-Authors: Anuran Makur, Lizhong ZhengAbstract:In this paper, we delineate how the Contraction Coefficient of the strong data processing inequality for KL divergence can be used to learn likelihood models. We then present an alternative formulation to learn likelihood models that forces the input KL divergence of the data processing inequality to vanish, and achieves a Contraction Coefficient equivalent to the squared maximal correlation. This formulation turns out to admit a linear algebraic solution. To analyze the performance loss in using this simple but suboptimal procedure, we bound these Contraction Coefficients in the discrete and finite regime, and prove their equivalence in the Gaussian regime.
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Linear Bounds between Contraction Coefficients for $f$-Divergences
arXiv: Information Theory, 2015Co-Authors: Anuran Makur, Lizhong ZhengAbstract:Data processing inequalities for $f$-divergences can be sharpened using constants called "Contraction Coefficients" to produce strong data processing inequalities. For any discrete source-channel pair, the Contraction Coefficients for $f$-divergences are lower bounded by the Contraction Coefficient for $\chi^2$-divergence. In this paper, we elucidate that this lower bound can be achieved by driving the input $f$-divergences of the Contraction Coefficients to zero. Then, we establish a linear upper bound on the Contraction Coefficients for a certain class of $f$-divergences using the Contraction Coefficient for $\chi^2$-divergence, and refine this upper bound for the salient special case of Kullback-Leibler (KL) divergence. Furthermore, we present an alternative proof of the fact that the Contraction Coefficients for KL and $\chi^2$-divergences are equal for a Gaussian source with an additive Gaussian noise channel (where the former Coefficient can be power constrained). Finally, we generalize the well-known result that Contraction Coefficients of channels (after extremizing over all possible sources) for all $f$-divergences with non-linear operator convex $f$ are equal. In particular, we prove that the so called "less noisy" preorder over channels can be equivalently characterized by any non-linear operator convex $f$-divergence.
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Allerton - Bounds between Contraction Coefficients
2015 53rd Annual Allerton Conference on Communication Control and Computing (Allerton), 2015Co-Authors: Anuran Makur, Lizhong ZhengAbstract:In this paper, we delineate how the Contraction Coefficient of the strong data processing inequality for KL divergence can be used to learn likelihood models. We then present an alternative formulation that forces the input KL divergence to vanish, and achieves a Contraction Coefficient equivalent to the squared maximal correlation using a linear algebraic solution. To analyze the performance loss in using this simple but suboptimal procedure, we bound these Coefficients in the discrete and finite regime, and prove their equivalence in the Gaussian regime.
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Bounds between Contraction Coefficients
2015 53rd Annual Allerton Conference on Communication Control and Computing (Allerton), 2015Co-Authors: Anuran Makur, Lizhong ZhengAbstract:In this paper, we delineate how the Contraction Coefficient of the strong data processing inequality for KL divergence can be used to learn likelihood models. We then present an alternative formulation that forces the input KL divergence to vanish, and achieves a Contraction Coefficient equivalent to the squared maximal correlation using a linear algebraic solution. To analyze the performance loss in using this simple but suboptimal procedure, we bound these Coefficients in the discrete and finite regime, and prove their equivalence in the Gaussian regime.
H Mekias - One of the best experts on this subject based on the ideXlab platform.
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the effect of surface tension on the Contraction Coefficient of a jet
Journal of Physics A, 2003Co-Authors: A Gasmi, H MekiasAbstract:Two-dimensional free surface potential flow issued from an opening of a container is considered. The flow is assumed to be inviscid and incompressible. The mathematical problem, which is characterized by the nonlinear boundary condition on the free surface of an unknown equation, is solved via a series truncation. We computed solutions for all Weber numbers. Our problem is an extension of the work done by Ackerberg and Liu (1987 Phys. Fluids 30 289–96), the results confirm and extend their results.
M V Swain - One of the best experts on this subject based on the ideXlab platform.
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residual stresses in y tzp crowns due to changes in the thermal Contraction Coefficient of veneers
Dental Materials, 2013Co-Authors: J B C Meira, Bruno Rodrigues Reis, Carina B Tanaka, Rafael Yague Ballester, Paulo Francisco Cesar, Antheunis Versluis, M V SwainAbstract:Abstract Objective To test the hypothesis that the difference in the Coefficient of thermal Contraction of the veneering porcelain above (αliquid) and below (αsolid) its Tg plays an important role in stress development during a fast cooling protocol of Y-TZP crowns. Methods Three-dimensional finite element models of veneered Y-TZP crowns were developed. Heat transfer analyses were conducted with two cooling protocols: slow (group A) and fast (groups B–F). Calculated temperatures as a function of time were used to determine the thermal stresses. Porcelain αsolid was kept constant while its αliquid was varied, creating different Δα/αsolid conditions: 0, 1, 1.5, 2 and 3 (groups B–F, respectively). Maximum (σ1) and minimum (σ3) residual principal stress distributions in the porcelain layer were compared. Results For the slowly cooled crown, positive σ1 were observed in the porcelain, orientated perpendicular to the core–veneer interface (“radial” orientation). Simultaneously, negative σ3 were observed within the porcelain, mostly in a hoop orientation (“hoop–arch”). For rapidly cooled crowns, stress patterns varied depending on Δα/αsolid ratios. For groups B and C, the patterns were similar to those found in group A for σ1 (“radial”) and σ3 (“hoop–arch”). For groups D–F, stress distribution changed significantly, with σ1 forming a “hoop-arch” pattern while σ3 developed a “radial” pattern. Significance Hoop tensile stresses generated in the veneering layer during fast cooling protocols due to porcelain high Δα/αsolid ratio will facilitate flaw propagation from the surface toward the core, which negatively affects the potential clinical longevity of a crown.
Yi Shen - One of the best experts on this subject based on the ideXlab platform.
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Robustness analysis of global exponential stability of non-linear systems with time delays and neutral terms
IET Control Theory & Applications, 2013Co-Authors: Yi Shen, Jun WangAbstract:The global stability of non-linear dynamical systems has been investigated extensively in recent decades. It is well known that time delay and neutral term could derail the stability of non-linear systems. This study presents new results on the robustness of the global exponential stability of non-linear systems with respect to time delay and neutral term. Given globally exponentially stable non-linear systems, the problems to be addressed herein are how much time delay and neutral term Contraction Coefficient are allowed so that the non-linear systems can remain to be globally exponentially stable, in the presence of time delay and neutral term. Upper bounds of allowable time delay and neutral term Contraction Coefficient will be derived for non-linear systems to sustain their global exponential stability. A numerical example is provided to illustrate the results.