Algebraic expressions for averaging linear and nonlinear stiffness tensors from general anisotropy to different effective symmetries (11 Laue classes elastically representing all 32 crystal classes, and two non-crystalline symmetries: isotropic and cylindrical) have been derived by automatic symbolic computations of the arithmetic mean over the set of rotational transforms determining a given symmetry. This approach generalizes the Voigt average to nonlinear constants and desired approximate symmetries other than isotropic, which can be useful for a description of textured polycrystals and rocks preserving some symmetry aspects. Low-symmetry averages have been used to derive averages of higher symmetry to speed up computations. Relationships between the elastic constants of each symmetry have been deduced from their corresponding averages by resolving the rank-deficient system of linear equations. Isotropy has also been considered in terms of generalized Lamé constants. The results are published in the form of appendices in the supporting information for this article and have been deposited in the Mendeley database.

A multi-objective genetic algorithm (MOGA) is a powerful global optimization tool, but its results are considerably affected by the crossover parameter ηc. Finding an appropriate ηc demands too much computing time because MOGA needs be run several times in order to find a good ηc. In this paper, a self-adaptive crossover parameter is introduced in a strategy to adopt a new ηc for every generation while running MOGA. This new scheme has also been adopted for a multi-generation Gaussian process optimization (MGGPO) when producing trial solutions. Compared with the existing MGGPO and MOGA, the MGGPO and MOGA with the new strategy show better performance in nonlinear optimization for the design of low-emittance storage rings.

Location: Engineering Library- TA1522.N66 2016

Location: Engineering Library- TK9211.7.Z46 2015

Anh Tuan Nguyen, Tómas Caraballo and Nguyen Huy Tuan
Proc. Amer. Math. Soc. 152 (), 5175-5189.
Abstract, references and article information

SEquence Evaluation through k-mer Representation (SEEKR) is a method of sequence comparison that uses sequence substrings called k-mers to quantify the nonlinear similarity between nucleic acid species. We describe the development of new functions within SEEKR that enable end-users to estimate P-values that ascribe statistical significance to SEEKR-derived similarities, as well as visualize different aspects of k-mer similarity. We apply the new functions to identify chromatin-enriched lncRNAs that contain XIST-like sequence features, and we demonstrate the utility of applying SEEKR on lncRNA fragments to identify potential RNA-protein interaction domains. We also highlight ways in which SEEKR can be applied to augment studies of lncRNA conservation, and we outline the best practice of visualizing RNA-seq read density to evaluate support for lncRNA annotations before their in-depth study in cell types of interest.

This paper highlights the many enhancements to SAS/ETS software and demonstrates how these features can help your organization increase revenue and enhance productivity.

National Bureau of Economic Research

IEEE / Institute of Electrical and Electronics Engineers Incorporated

Boston : Birkhäuser, 2006

This paper highlights the many enhancements to SAS/ETS software and demonstrates how these features can help your organization increase revenue and enhance productivity.

The structural and nonlinear optical properties of a new anilinium hybrid crystal of chemical formula (C6H7NCl+·NO3−)3 have been investigated. The crystal structure was determined from single-crystal X-ray diffraction measurements performed at a temperature of 100 K which show that the compound crystallizes in a noncentrosymmetric space group (Pna21). The structural analysis was coupled with Hirshfeld surface analysis to evaluate the contribution of the different intermolecular interactions to the formation of supramolecular assemblies in the solid state that exhibit nonlinear optical features. This analysis reveals that the studied compound is characterized by a three-dimensional network of hydrogen bonds and the main contributions are provided by the O...H, C...H, H...H and Cl...H interactions, which alone represent ∼85% of the total contributions to the Hirshfeld surfaces. It is noteworthy that the halogen...H contributions are quite comparable with those of the H...H contacts. The nonlinear optical properties were investigated by nonlinear diffuse femtosecond-pulse reflectometry and the obtained results were compared with those of the reference material LiNbO3. The hybrid crystals exhibit notable second (SHG) and third (THG) harmonic generation which confirms its polarity is generated by the different intermolecular interactions. These measurements also highlight that the THG signal of the new anilinium compound normalized to its SHG counterpart is more pronounced than for LiNbO3.

One proves the existence and uniqueness of a generalized (mild) solution for the nonlinear Fokker--Planck equation (FPE) egin{align*} &u_t-Delta (eta(u))+{mathrm{ div}}(D(x)b(u)u)=0, quad tgeq0, xinmathbb{R}^d, d e2, \ &u(0,cdot)=u_0,mbox{in }mathbb{R}^d, end{align*} where $u_0in L^1(mathbb{R}^d)$, $etain C^2(mathbb{R})$ is a nondecreasing function, $bin C^1$, bounded, $bgeq 0$, $Din(L^2cap L^infty)(mathbb{R}^d;mathbb{R}^d)$ with ${ m div}, Din L^infty(mathbb{R}^d)$, and ${ m div},Dgeq0$, $eta$ strictly increasing, if $b$ is not constant. Moreover, $t o u(t,u_0)$ is a semigroup of contractions in $L^1(mathbb{R}^d)$, which leaves invariant the set of probability density functions in $mathbb{R}^d$. If ${ m div},Dgeq0$, $eta'(r)geq a|r|^{alpha-1}$, and $|eta(r)|leq C r^alpha$, $alphageq1,$ $alpha>frac{d-2}d$, $dgeq3$, then $|u(t)|_{L^infty}le Ct^{-frac d{d+(alpha-1)d}} |u_0|^{frac2{2+(m-1)d}},$ $t>0$, and the existence extends to initial data $u_0$ in the space $mathcal{M}_b$ of bounded measures in $mathbb{R}^d$. The solution map $mumapsto S(t)mu$, $tgeq0$, is a Lipschitz contractions on $mathcal{M}_b$ and weakly continuous in $tin[0,infty)$. As a consequence for arbitrary initial laws, we obtain weak solutions to a class of McKean-Vlasov SDEs with coefficients which have singular dependence on the time marginal laws.

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator plus an indefinite potential. In the reaction we have the competing effects of a singular term and of concave and convex nonlinearities. In this paper the concave term is parametric. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter $lambda$ varies. This work continues our research published in arXiv:2004.12583, where $xi equiv 0 $ and in the reaction the parametric term is the singular one.

In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with prescribed generalized symmetric asymptotic behavior at infinity. Moreover, we give some new results for the Hessian equations, Hessian quotient equations and the special Lagrangian equations, which have been studied previously.

This paper is devoted to the study of the singularity phenomenon of timelike extremal hypersurfaces in Minkowski spacetime $mathbb{R}^{1+3}$. We find that there are two explicit lightlike self-similar solutions to a graph representation of timelike extremal hypersurfaces in Minkowski spacetime $mathbb{R}^{1+3}$, the geometry of them are two spheres. The linear mode unstable of those lightlike self-similar solutions for the radially symmetric membranes equation is given. After that, we show those self-similar solutions of the radially symmetric membranes equation are nonlinearly stable inside a strictly proper subset of the backward lightcone. This means that the dynamical behavior of those two spheres is as attractors. Meanwhile, we overcome the double roots case (the theorem of Poincar'{e} can't be used) in solving the difference equation by construction of a Newton's polygon when we carry out the analysis of spectrum for the linear operator.

We study a class of fourth order nonlinear parabolic equations which include the thin-film equation and the quantum drift-diffusion model as special cases. We investigate these equations by first developing functional inequalities of the type $ int_Omega u^{2gamma-alpha-eta}Delta u^alphaDelta u^eta dx geq cint_Omega|Delta u^gamma |^2dx $, which seem to be of interest on their own right.

Several nonlinear model reduction techniques are compared for the three cases of the non-parallel version of the Kuramoto-Sivashinsky equation, the transient regime of flow past a cylinder at $Re=100$ and fully developed flow past a cylinder at the same Reynolds number. The linear terms of the governing equations are reduced by Galerkin projection onto a POD basis of the flow state, while the reduced nonlinear convection terms are obtained either by a Galerkin projection onto the same state basis, by a Galerkin projection onto a POD basis representing the nonlinearities or by applying the Discrete Empirical Interpolation Method (DEIM) to a POD basis of the nonlinearities. The quality of the reduced order models is assessed as to their stability, accuracy and robustness, and appropriate quantitative measures are introduced and compared. In particular, the properties of the reduced linear terms are compared to those of the full-scale terms, and the structure of the nonlinear quadratic terms is analyzed as to the conservation of kinetic energy. It is shown that all three reduction techniques provide excellent and similar results for the cases of the Kuramoto-Sivashinsky equation and the limit-cycle cylinder flow. For the case of the transient regime of flow past a cylinder, only the pure Galerkin techniques are successful, while the DEIM technique produces reduced-order models that diverge in finite time.

A. G. Sergeev and Kh. A. Khachatryan
Trans. Moscow Math. Soc. 80 (2020), 95-111.
Abstract, references and article information

S. A. Kashchenko
Trans. Moscow Math. Soc. 80 (2020), 53-71.
Abstract, references and article information

Côme Huré, Huyên Pham and Xavier Warin
Math. Comp. 89 (2020), 1547-1579.
Abstract, references and article information

Kamen G. Ivanov and Pencho Petrushev
Trans. Amer. Math. Soc. 373 (2020), 3117-3176.
Abstract, references and article information

A. Seesanea and I. E. Verbitsky
St. Petersburg Math. J. 31 (2020), 557-572.
Abstract, references and article information

S.-S. Byun, D. K. Palagachev and L. G. Softova
St. Petersburg Math. J. 31 (2020), 401-419.
Abstract, references and article information

Mohamed Jleli, Bessem Samet and Philippe Souplet
Proc. Amer. Math. Soc. 148 (2020), 2579-2593.
Abstract, references and article information

Michiya Mori
Proc. Amer. Math. Soc. 148 (2020), 2477-2485.
Abstract, references and article information

Hongbin Zhang, Lang Wu.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2140--2157.

Abstract:
For a time-to-event outcome with censored time-varying covariates, a joint Cox model with a linear mixed effects model is the standard modeling approach. In some applications such as AIDS studies, mechanistic nonlinear models are available for some covariate process such as viral load during anti-HIV treatments, derived from the underlying data-generation mechanisms and disease progression. Such a mechanistic nonlinear covariate model may provide better-predicted values when the covariates are left censored or mismeasured. When the focus is on the impact of the time-varying covariate process on the survival outcome, an accelerated failure time (AFT) model provides an excellent alternative to the Cox proportional hazard model since an AFT model is formulated to allow the influence of the outcome by the entire covariate process. In this article, we consider a nonlinear mixed effects model for the censored covariates in an AFT model, implemented using a Monte Carlo EM algorithm, under the framework of a joint model for simultaneous inference. We apply the joint model to an HIV/AIDS data to gain insights for assessing the association between viral load and immunological restoration during antiretroviral therapy. Simulation is conducted to compare model performance when the covariate model and the survival model are misspecified.

Bank of Italy Working Papers by Luca Metelli, Filippo Natoli and Luca Rossi

Actuation remains a significant challenge in soft robotics. Actuation by light has important advantages: Objects can be actuated from a distance, distinct frequencies can be used to actuate and control distinct modes with minimal interference, and significant power can be transmitted over long distances through corrosion-free, lightweight fiber optic cables....

The economics profession seems to increasingly endorse the existence of a strongly negative nonlinear effect of public debt on economic growth. Reinhart and Rogoff (2010) were the first to point out that a public debt to GDP ratio higher than 90% of GDP is associated with considerably lower economic performance in advanced and emerging economies alike.

Cham, Switzerland : Birkhäuser, [2019]

Cham, Switzerland : Springer, [2019]