Bi-level iterative regularization for inverse problems in nonlinear PDEs

We investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution PDEs. We propose a bi-level Landweber scheme, where the upper-level parameter reconstruction embeds a lower-level state approximation. This can be seen as combining the classical reduced setting and the newer all-at-once setting, allowing us to, respectively, utilize well-posedness of the parameter-to-state map, and to bypass having to solve nonlinear PDEs exactly. Using this, we derive stopping rules for lower- and upper-level iterations and convergence of the bi-level method. We discuss application to parameter identification for the Landau-Lifshitz-Gilbert equation in magnetic particle imaging

Discretization of parameter identification in PDEs using Neural Networks

We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determined alongside other unknown physical parameters and the unknown state. Hence, it is not possible to construct input-output data pairs to perform a supervised training process. Proposing an all-at-once approach, we bypass the need for training data and recover all the unknowns simultaneously. In the general case, the approximation via a neural network can be realized as a discretization scheme, and the training with noisy data can be viewed as an ill-posed inverse problem. Therefore, we study discretization of regularization in terms of Tikhonov and projected Landweber methods for discretization of inverse problems, and prove convergence when the discretization error (network approximation error) and the noise level tend to zero

THE RELATIONSHIP BETWEEN BILINGUALISM AND EMOTION PERCEIVED BY VIETNAMESE COLLEGE STUDENTS

Studies of the correlation between language and emotion have demonstrated the existence of a causal relationship between switching languages and feeling different in bi-/ multilinguals. Adopting the mixed-method approach, the current research aims to extend this line of enquiry to Vietnam – a monolingual country – by investigating 160 Vietnamese-English speaking students at International University (IU) (VNU-HCMC). They were required to complete a questionnaire based on the Bilingualism and Emotion Questionnaire (Dewaele & Pavlenko, 2001–2003). It includes closed questions concerning shifts on five scales of feelings and an open explanatory question on the difference perceived. The scales, chosen with reference to the research of Dewaele and Nakano (2012), consist of feeling logical, serious, emotional, fake, and different. Statistical analyses revealed a regular shift on most scales, with most participants feeling more logical, more serious, more fake, more different, and less emotional when using the L2. Simple linear regression revealed that the variation in certain feelings scales was mostly predicted by self-perceived proficiency in the L

Chemical composition and antibacterial activities of essential oils from fruits of Melicope pteleifolia (Champ. Ex Benth.) T.G. Hartley grown in Lam Dong Province, Vietnam

In the present study, chemical composition and antibacterial properties of essential oil obtained from the aerial parts of the Melicope pteleifolia (Champ. ex Benth.) T.G Hartley in Dalat were evaluated. Essential oil was isolated through hydro-distillation. Twenty-nine constituents comprising 100% of the essential oil were characterized by gas chromatography/mass spectrometry (GC-MS) techniques. The major compounds in the essential oil were (+)-Sabinene (34.73%), Cis-α-bergamotene (13.15%), Z-α-trans-bergamotol (5.28%), β-mycrene (4.98%), and 1,3,6-octatriene, 3,7-dimethyl-(4.71%). Antibacterial activities of Melicope pteleifolia essential oil were investigated against Gram-positive and-negative bacteria. Results showed significant activities against Streptococcus pyogenes and Escherichia coli using an agar well diffusion method. The application of this essential oil in preventing and eliminating bacteria could be useful in fields as medicine and cosmetics.