Application of the linear matching method to creep-fatigue failure analysis of cruciform weldment manufactured of the austenitic steel AISI type 316N(L)

This paper demonstrates the recent extension of the Linear Matching Method (LMM) to include cyclic creep assessment [1] in application to a creep-fatigue analysis of a cruciform weldment made of the stainless steel AISI type 316N(L). The obtained results are compared with the results of experimental studies implemented by Bretherton et al. [2] with the overall objective to identify fatigue strength reduction factors (FSRF) of austenitic weldments for further design application. These studies included a series of strain-controlled tests at 550°C with different combinations of reversed bending moment and dwell time Δt. Five levels of reversed bending moment histories corresponding to defined values of total strain range Δεtot in remote parent material (1%, 0.6%, 0.4%, 0.3%, 0.25%) were used in combination with three variants of creep-fatigue conditions: pure fatigue, 1 hour and 5 hours of dwell period Δt of hold in tension. An overview of previous works devoted to analysis and simulation of these experiments [2] and highlight of the LMM development progress could be found in [3]

Stein meets Malliavin in normal approximation

Stein's method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation the functional equation is a first order differential equation. Malliavin calculus is an infinite-dimensional differential calculus whose operators act on functionals of general Gaussian processes. Nourdin and Peccati (2009) established a fundamental connection between Stein's method for normal approximation and Malliavin calculus through integration by parts. This connection is exploited to obtain error bounds in total variation in central limit theorems for functionals of general Gaussian processes. Of particular interest is the fourth moment theorem which provides error bounds of the order $\sqrt{\mathbb{E}(F_n^4)-3}$ in the central limit theorem for elements $\{F_n\}_{n\ge 1}$ of Wiener chaos of any fixed order such that $\mathbb{E}(F_n^2) = 1$. This paper is an exposition of the work of Nourdin and Peccati with a brief introduction to Stein's method and Malliavin calculus. It is based on a lecture delivered at the Annual Meeting of the Vietnam Institute for Advanced Study in Mathematics in July 2014.Comment: arXiv admin note: text overlap with arXiv:1404.478

Factorizations of Matrices Over Projective-free Rings

An element of a ring $R$ is called strongly $J^{\#}$-clean provided that it can be written as the sum of an idempotent and an element in $J^{\#}(R)$ that commute. We characterize, in this article, the strongly $J^{\#}$-cleanness of matrices over projective-free rings. These extend many known results on strongly clean matrices over commutative local rings

Compression of Deep Neural Networks on the Fly

Thanks to their state-of-the-art performance, deep neural networks are increasingly used for object recognition. To achieve these results, they use millions of parameters to be trained. However, when targeting embedded applications the size of these models becomes problematic. As a consequence, their usage on smartphones or other resource limited devices is prohibited. In this paper we introduce a novel compression method for deep neural networks that is performed during the learning phase. It consists in adding an extra regularization term to the cost function of fully-connected layers. We combine this method with Product Quantization (PQ) of the trained weights for higher savings in storage consumption. We evaluate our method on two data sets (MNIST and CIFAR10), on which we achieve significantly larger compression rates than state-of-the-art methods

Poisson process approximation: From Palm theory to Stein's method

This exposition explains the basic ideas of Stein's method for Poisson random variable approximation and Poisson process approximation from the point of view of the immigration-death process and Palm theory. The latter approach also enables us to define local dependence of point processes [Chen and Xia (2004)] and use it to study Poisson process approximation for locally dependent point processes and for dependent superposition of point processes.Comment: Published at http://dx.doi.org/10.1214/074921706000001076 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Stein's method, Malliavin calculus, Dirichlet forms and the fourth moment theorem

The fourth moment theorem provides error bounds of the order $\sqrt{{\mathbb E}(F^4) - 3}$ in the central limit theorem for elements $F$ of Wiener chaos of any order such that ${\mathbb E}(F^2) = 1$. It was proved by Nourdin and Peccati (2009) using Stein's method and the Malliavin calculus. It was also proved by Azmoodeh, Campese and Poly (2014) using Stein's method and Dirichlet forms. This paper is an exposition on the connections between Stein's method and the Malliavin calculus and between Stein's method and Dirichlet forms, and on how these connections are exploited in proving the fourth moment theorem