A Novel Design of Morlet Wavelet to Solve the Dynamics of Nervous Stomach Nonlinear Model

The present study introduces a novel design of Morlet wavelet neural network (MWNN) models to solve a class of a nonlinear nervous stomach system represented with governing ODEs systems via three categories, tension, food and medicine, i.e., TFM model. The comprehensive detail of each category is designated together with the sleep factor, food rate, tension rate, medicine factor and death rate are also provided. The computational structure of MWNNs along with the global search ability of genetic algorithm (GA) and local search competence of active-set algorithms (ASAs), i.e., MWNN-GA-ASAs is applied to solve the TFM model. The optimization of an error function, for nonlinear TFM model and its related boundary conditions, is performed using the hybrid heuristics of GA-ASAs. The performance of the obtained outcomes through MWNN-GA-ASAs for solving the nonlinear TFM model is compared with the results of state of the article numerical computing paradigm via Adams methods to validate the precision of the MWNN-GA-ASAs. Moreover, statistical assessments studies for 50 independent trials with 10 neuron-based networks further authenticate the efficacy, reliability and consistent convergence of the proposed MWNN-GA-ASAs.

Magnetohydrodynamic Flow Past a Nonlinear Stretching or Shrinking Cylinder in Nanofluid with Viscous Dissipation and Heat Generation Effect

The Tiwari-Das model is used to investigate magnetohydrodynamic stagnation point flow and heat transfer past a nonlinear stretching or shrinking cylinder in nanofluid with viscous dissipation and heat generation using. The partial differential equations, also known as governing equations, were reduced to nonlinear ordinary differential equations using similarity transformation. MATLAB with the bvp4c solver is used for numerical computing. The controlling parameter, such as nanoparticle volume fraction, magnetic, curvature, nonlinear, radiation, and heat generation parameters, as well as Eckert and Grashof numbers, influence the skin friction coefficient, heat transfer rate, velocity, and temperature profiles. The results are presented as graphs to show the influence of the variables studied. In some circumstances of stretching and shrinking cases, dual solutions can be obtained.

A learning based approach for designing extended unit cell metagratings

The possibility of arbitrary spatial control of incident wavefronts with the subwavelength resolution has driven research into dielectric optical metasurfaces in the last decade. The unit-cell based metasurface design approach that relies on a library of single element responses is known to result in reduced efficiency attributed to the inadequate accounting of the coupling effects between meta-atoms. Metasurfaces with extended unit-cells containing multiple resonators can improve design outcomes but their design requires extensive numerical computing and optimizations. We report a deep learning based design methodology for the inverse design of extended unit-cell metagratings. In contrast to previous reports, our approach learns the metagrating spectral response across its reflected and transmitted orders. Through systematic exploration, we discover network architectures and training dataset sampling strategies that allow such learning without requiring extensive ground-truth generation. The one-time investment of model creation can then be used to significantly accelerate numerical optimization of multiple functionalities as demonstrated by considering the inverse design of various spectral and polarization dependent splitters and filters. The proposed methodology is not limited to these proof-of-concept demonstrations and can be broadly applied to meta-atom-based nanophotonic system design and in realising the next generation of metasurface functionalities with improved performance.

Stochastic Numerical Investigations for a Food Web System of Prey-Predation, Competition and Commensalism

Employing Levenberg-Marquardt backpropagation(LMB) neural network, the system of three species nonlinear equations are illuminated by designing an integrated numerical computing-based plot. The proposed dynamical system comprises of two competing species which are growing logistically in nature and, the third species is predating with Holling type II functional response mode on second species and also acts host for the first prey species. Besides, the prey species protect themselves to refuge high predation. The designed LMB neural network has been used to exhibits the solutions of the dynamical frame work. In each case of the species, a reference dataset of the planned LMB neural network is initiated in comparison of Adam numerical program. The approximate results of the food web system are displayed within the training, confirmation and testing strategies to redesign the neural network to minimize the mean square error (MSE) function employing the designed LMB. The investigations depend on the corresponding achievements and the examinations based on MSE out comes, correlation, regression and error histograms signify the proficiency, rightness as well as the potency of the suggested LMB neural network conspire.

Path-based knowledge reasoning with textual semantic information for medical knowledge graph completion

Background Knowledge graphs (KGs), especially medical knowledge graphs, are often significantly incomplete, so it necessitating a demand for medical knowledge graph completion (MedKGC). MedKGC can find new facts based on the existed knowledge in the KGs. The path-based knowledge reasoning algorithm is one of the most important approaches to this task. This type of method has received great attention in recent years because of its high performance and interpretability. In fact, traditional methods such as path ranking algorithm take the paths between an entity pair as atomic features. However, the medical KGs are very sparse, which makes it difficult to model effective semantic representation for extremely sparse path features. The sparsity in the medical KGs is mainly reflected in the long-tailed distribution of entities and paths. Previous methods merely consider the context structure in the paths of knowledge graph and ignore the textual semantics of the symbols in the path. Therefore, their performance cannot be further improved due to the two aspects of entity sparseness and path sparseness. Methods To address the above issues, this paper proposes two novel path-based reasoning methods to solve the sparsity issues of entity and path respectively, which adopts the textual semantic information of entities and paths for MedKGC. By using the pre-trained model BERT, combining the textual semantic representations of the entities and the relationships, we model the task of symbolic reasoning in the medical KG as a numerical computing issue in textual semantic representation. Results Experiments results on the publicly authoritative Chinese symptom knowledge graph demonstrated that the proposed method is significantly better than the state-of-the-art path-based knowledge graph reasoning methods, and the average performance is improved by 5.83% for all relations. Conclusions In this paper, we propose two new knowledge graph reasoning algorithms, which adopt textual semantic information of entities and paths and can effectively alleviate the sparsity problem of entities and paths in the MedKGC. As far as we know, it is the first method to use pre-trained language models and text path representations for medical knowledge reasoning. Our method can complete the impaired symptom knowledge graph in an interpretable way, and it outperforms the state-of-the-art path-based reasoning methods.

Intelligent Numerical Computing Methods for Determining the Concentration of Citric Acid by Accurate Measurement and Calculation

According to the Bronsted-Lowry theory, an acid is a proton donor, and a base is a proton acceptor. An acid-base reaction involves the proton transfer between chemicals, where a base containing hydroxide ion (OH-) accepts a proton (H+) from an acidic solution to form water (Khan,2016). In the above equation, HCl as an acid donates one H+ ion, and NaOH as a base accepts the proton to form one water molecule (H2O). So, a proton from the acid is transferred to the anion of the base. Then, the metal cation (Na+) and the conjugate base anion (Cl-) form the salt NaCl.

High-performance symbolic-numerics via multiple dispatch

As mathematical computing becomes more democratized in high-level languages, high-performance symbolic-numeric systems are necessary for domain scientists and engineers to get the best performance out of their machine without deep knowledge of code optimization. Naturally, users need different term types either to have different algebraic properties for them, or to use efficient data structures. To this end, we developed Symbolics.jl, an extendable symbolic system which uses dynamic multiple dispatch to change behavior depending on the domain needs. In this work we detail an underlying abstract term interface which allows for speed without sacrificing generality. We show that by formalizing a generic API on actions independent of implementation, we can retroactively add optimized data structures to our system without changing the pre-existing term rewriters. We showcase how this can be used to optimize term construction and give a 113x acceleration on general symbolic transformations. Further, we show that such a generic API allows for complementary term-rewriting implementations. Exploiting this feature, we demonstrate the ability to swap between classical term-rewriting simplifiers and e-graph-based term-rewriting simplifiers. We illustrate how this symbolic system improves numerical computing tasks by showcasing an e-graph ruleset which minimizes the number of CPU cycles during expression evaluation, and demonstrate how it simplifies a real-world reaction-network simulation to halve the runtime. Additionally, we show a reaction-diffusion partial differential equation solver which is able to be automatically converted into symbolic expressions via multiple dispatch tracing, which is subsequently accelerated and parallelized to give a 157x simulation speedup. Together, this presents Symbolics.jl as a next-generation symbolic-numeric computing environment geared towards modeling and simulation.