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Graph labeling allows for the representation of additional attributes or properties associated with the vertices, edges, or both of graphs. This can provide a more comprehensive and detailed representation of the system being modeled, allowing for a richer analysis and interpretation of the graph. Graph labeling in ladder graphs has a wide range of applications in engineering, computer science, physics, biology, and other fields. It can be applied to various problem domains, such as image processing, wireless sensor networks, VLSI design, bioinformatics, social network analysis, transportation networks, and many others. The versatility of ladder graphs and the ability to apply graph labeling to them make them a powerful tool for modeling and analyzing diverse systems. If a function Υ is an injective vertex assignment in { 1 , 2 , ... q + 1 } and the inductive edge assignment function Υ * in { 1 , 2 , ... q } is expressed as a graph with q edges, defined as Υ * (u v) = 2 [ Υ (u) 2 + Υ (u) Υ (v) + Υ (v) 2 ] 3 [ Υ (u) + Υ (v) ] , then the function is referred to as F-centroidal mean labeling. This is known as the F-centroidal mean criterion. Here, we have determined the F-centroidal mean criteria of the graph ladder, slanting ladder, triangular ladder, T L n ∘ S m , S L n ∘ S m for m ≤ 2 , double-sided step ladder, D n * , and diamond ladder. [ABSTRACT FROM AUTHOR]

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discrete fractional calculus, the discrete Laplace transform, and the theory of fractional-order discrete Mittag–Leffler functions. In order to guarantee the global asymptotic stability, adequate criteria are determined using Lyapunov's direct technique, the Lyapunov approach, and some novel analysis techniques of fractional calculation. Thus, some sufficient conditions are obtained to guarantee the global stability. The validity of the theoretical results are finally shown using numerical examples. [ABSTRACT FROM AUTHOR]

Deep learning and Neural Network algorithms are a branch of Machine learning that can automatically identify patterns in the data, and then use the uncovered patterns to predict future data, or to perform other alternative kinds of decision making under unreliability. Neural Networks is a method of computing, which is based on a collection of large number of neural units, which acts as a biological brain and solve problems with large clusters of biological neurons connected by axons. Deep Learning algorithms are used to model high level abstractions in data. Digit Recognition is a combination of Deep Learning and Neural Network algorithms, which uses TensorFlow tool as an interface to develop a model. This paper describes the recognition of handwritten scanned digits by a system and displays the output as digital numbers by using Machine Learning methods with the help of TensorFlow tool. [ABSTRACT FROM AUTHOR]

The present work aimed to study the impact of different carbon and nitrogen sources on the effective production of L-asparaginase by isolated Bacillus circulans using Plackett-Burman design (PBD). Among carbon sources; lactose, galactose, starch, sucrose, maltose, arabinose and among nitrogen sources; proline, tryptone, sodium glutamate, corn steep liquor, beef extract, ammonium chloride, yeast extract at selected concentration produced a maximum of 105 and 164 U mL-1 L-asparaginase enzyme, respectively. Initial analysis of L-asparaginase data with different carbon and nitrogen sources as per PBD did not reveal standardized effects as well as 'p' and 't' values. Regression coefficient and t-values were calculated by subjecting the experimental data to statistical analysis after pooling the least two nutrient components into error. Among selected 26 components, xylose, galactose, yeast extract and proline denoted least significance, while glucose, mannose, ammonium chloride and ammonium sulphate showed maximum significance on enzyme production. Saturated PBD can be effectively utilized for analysis of the data by pooling the least significant factors based on the effects on metabolite/product/enzyme production. Ammonium chloride and glucose were observed to be the most significant carbon and nitrogen sources, respectively in L-asparaginase production in this bacterial strain. The presented approach is highly useful in bioprocess optimization procedure where all selected parameters show little degree of freedom and subsequent significant factors. [ABSTRACT FROM AUTHOR]

This article examines the drive-response synchronization of a class of fractional order uncertain BAM (Bidirectional Associative Memory) competitive neural networks. By using the differential inclusions theory, and constructing a proper Lyapunov-Krasovskii functional, novel sufficient conditions are obtained to achieve global asymptotic stability of fractional order uncertain BAM competitive neural networks. This novel approach is based on the linear matrix inequality (LMI) technique and the derived conditions are easy to verify via the LMI toolbox. Moreover, numerical examples are presented to show the feasibility and effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]