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In this paper, we introduce and analyze a numerical scheme for solving the Cauchy-Dirichlet problem associated with fractional nonlinear diffusion equations. These equations generalize the porous medium equation and the fast diffusion equation by incorporating a fractional diffusion term. We provide a rigorous analysis showing that the discretization preserves main properties of the continuous equations, including algebraic decay in the fractional porous medium case and the extinction phenomenon in the fractional fast diffusion case. The study is supported by extensive numerical simulations. In addition, we propose a novel method for accurately computing the extinction time for the fractional fast diffusion equation and illustrate numerically the convergence of rescaled solutions towards asymptotic profiles near the extinction time.

The present paper is concerned with the Cauchy-Dirichlet problem for fractional (and non-fractional) nonlinear diffusion equations posed in bounded domains. Main results consist of well-posedness in an energy class with no sign restriction and convergence of such (possibly sign-changing) energy solutions to asymptotic profiles after a proper rescaling. They will be proved in a variational scheme only, without any use of semigroup theories nor classical quasilinear parabolic theories. Proofs are self-contained and performed in a totally unified fashion for both fractional and non-fractional cases as well as for both porous medium and fast diffusion cases.

This article presents an evaluation of biliary tract segmentation methods used for 3D reconstruction, which may be very usefull in various critical interventions, such as endoscopic retrograde cholangiopancreatography (ERCP), using the 3D Slicer software. This article provides an assessment of biliary tract segmentation techniques employed for 3D reconstruction, which can prove highly valuable in diverse critical procedures like endoscopic retrograde cholangiopancreatography (ERCP) through the utilization of 3D Slicer software. Three different methods, namely thresholding, flood filling, and region growing, were assessed in terms of their advantages and disadvantages. The study involved 10 patient cases and employed quantitative indices and qualitative evaluation to assess the segmentations obtained by the different segmentation methods against ground truth. The results indicate that the thresholding method is almost manual and time-consuming, while the flood filling method is semi-automatic and also time-consuming. Although both methods improve segmentation quality, they are not reproducible. Therefore, an automatic method based on region growing was developed to reduce segmentation time, albeit at the expense of quality. These findings highlight the pros and cons of different conventional segmentation methods and underscore the need to explore alternative approaches, such as deep learning, to optimize biliary tract segmentation in the context of ERCP.

Photometry is a convenient operational method for monitoring such dynamically evolving phenomena as wind waves. Nowadays machine learning allows one to avoid explicit derivation of the solution to the problem, describing all the instructions for transforming the input data into the final result. Instead, an algorithm is used to independently find solutions through the integrated use of statistical data, from which patterns are derived, on the basis of which forecasts are made. An example of a problem for which a regular solution has traditionally been applied is the prediction of wave height from the input brightness of a water surface. The task is complicated by the multitude of possible physical models and the need to apply calibration coefficients. In this paper, we solve the problem of how, basing on the obtained brightness values and the corresponding heights, to train the neural network to further predict the heights from the incoming brightness values with the greatest accuracy., Comment: 10 pages, 8 figures, submitted to conference proceedings CCIE 2023, to be published in Lecture Notes in Electrical Engineering

Carica papaya (CP) leaf is long known for its traditional pharmacological effects against dengue virus and malaria. Therefore, CP could also be a potential solution for the treatment of other infectious diseases, such as coronavirus. In this study, we evaluate the potential effect of the ethanolic CP leaf extract in inhibiting the enzymatic activity of three protein targets in SARS-CoV-2 life cycle, which include the 3-chymotrypsin-like protease (3CLpro), papain-like protease (PLpro) and the human transmembrane protein serine 2 (TMPRSS2). Results demonstrate that CP leaf extract inhibits 3CLpro and PLpro significantly with IC50 of 0.02 microgram/mL and 0.06 microgram/mL, respectively, but it is inactive towards TMPRSS2. Phenol, 2-methyl-5-(1,2,2-trimethylcyclopentyl)-(S)- (17a) and beta-mannofuranoside, farnesyl- (21a) were identified in the extract using GC-MS. These two compounds demonstrated a stronger binding affinity towards the main proteases than TMPRSS2 during the docking simulation, which agrees with the in-vitro study. Further pharmacophore mapping suggests that 17a has a fit score higher than 21a to the SARS-CoV-2 3CLpro pharmacophore model concluding that CP leaf extract has the potential to be developed as a herbal SARS-CoV-2 antiviral agent., Comment: 28 pages, 7 figures, 2 tables

Recent advances in vision-and-language modeling have seen the development of Transformer architectures that achieve remarkable performance on multimodal reasoning tasks. Yet, the exact capabilities of these black-box models are still poorly understood. While much of previous work has focused on studying their ability to learn meaning at the word-level, their ability to track syntactic dependencies between words has received less attention. We take a first step in closing this gap by creating a new multimodal task targeted at evaluating understanding of predicate-noun dependencies in a controlled setup. We evaluate a range of state-of-the-art models and find that their performance on the task varies considerably, with some models performing relatively well and others at chance level. In an effort to explain this variability, our analyses indicate that the quality (and not only sheer quantity) of pretraining data is essential. Additionally, the best performing models leverage fine-grained multimodal pretraining objectives in addition to the standard image-text matching objectives. This study highlights that targeted and controlled evaluations are a crucial step for a precise and rigorous test of the multimodal knowledge of vision-and-language models., Comment: To appear at EMNLP 2022

New data was obtained for a frequency band that had not been so well-studied for sea surface probing applications before. During the described 2-weeks sea experiment 1-3 kHz tonal pulses were emitted from a platform, located on the northern Black Sea shelf, and Doppler spectrum of reverberation was studied. We believe that this band is worth further studying due the sound propagation range is large enough to meet practical needs in coastal zone while the angle-distance resolution is quite moderate. However it is quite difficult to interpret the obtained data since backscattering spectrum shape is influenced by a series of effects and has a complicated link to wind waves and currents parameters. Backscattering of acoustical signals was received for distances around 2 nautical miles. Significant wave height, dominant wave frequency were estimated as the result of such signals processing with the use of machine learning tools. A decision-tree-based mathematical regression model was trained to solve the inverse problem. Wind waves prediction is in a good agreement with direct measurements, made on the platform, and machine learning results allow physical interpretation., Comment: 18 pages, 11 figures, accepted to the Journal of Marine Science and Engineering; supplementary data is available at: https://doi.org/10.5281/zenodo.6530915

Securing a secret master key is a non-trivial task, we even argue it is impossible to fully secure it, hence we must make it as difficult as possible for any powerful adversary to steal or use the key. We introduce the reader to interesting cryptography which is starting to get more attention in terms of addressing the above problem, and we briefly overview some commercial and open-source products that can be used. Finally, we propose a set of solutions on how to secure master keys, more as guidelines rather than exact technical specifications, with aim to inspire and raise awareness of how to increase the security as much as possible.

This paper presents Masked ELMo, a new RNN-based model for language model pre-training, evolved from the ELMo language model. Contrary to ELMo which only uses independent left-to-right and right-to-left contexts, Masked ELMo learns fully bidirectional word representations. To achieve this, we use the same Masked language model objective as BERT. Additionally, thanks to optimizations on the LSTM neuron, the integration of mask accumulation and bidirectional truncated backpropagation through time, we have increased the training speed of the model substantially. All these improvements make it possible to pre-train a better language model than ELMo while maintaining a low computational cost. We evaluate Masked ELMo by comparing it to ELMo within the same protocol on the GLUE benchmark, where our model outperforms significantly ELMo and is competitive with transformer approaches.