This work proves the local vertex anti-magic coloring of even regular circulant bipartite graphs C ( m ; L ) . Let G be either K r , r or K r , r - F , F is a 1-factor. Also, we discover the local vertex anti-magic coloring for union of bipartite graphs; join graphs G ∨ H , where H ∈ { O r , K r , C r , K r , s } ; and the upper bound of corona product G ⊙ O r . It was a problem Lau and Shiu (2023) [1] that: For any G 1 and G 2 , determine χ ℓ v a ( G 1 × G 2 ) . We give partial answer to this problem by proving the followings:1. χ ℓ v a ( C 2 m × C 2 n ) ;2. χ ℓ v a ( C 2 m + 1 × C 2 n + 2 ) ; and3. χ ℓ v a ( P 3 × H ) , where H ∈ { K r , K m , m } .

UNASSIGNED: Food insecurity and vulnerability in Ethiopia are historical problems due to natural- and human-made disasters, which affect a wide range of areas at a higher magnitude with adverse effects on the overall health of households. In Ethiopia, the problem is wider with higher magnitude. Moreover, this geographical distribution of this challenge remains unexplored regarding the effects of cultures and shocks, despite previous case studies suggesting the effects of shocks and other factors. Hence, this study aims to assess the geographic distribution of corrected-food insecurity levels (FCSL) across zones and explore the comprehensive effects of diverse factors on each level of a household\'s food insecurity.
UNASSIGNED: This study analyzes three-term household-based panel data for years 2012, 2014, and 2016 with a total sample size of 11505 covering the all regional states of the country. An extended additive model, with empirical Bayes estimation by modeling both structured spatial effects using Markov random field or tensor product and unstructured effects using Gaussian, was adopted to assess the spatial distribution of FCSL across zones and to further explore the comprehensive effect of geographic, environmental, and socioeconomic factors on the locally adjusted measure.
UNASSIGNED: Despite a chronological decline, a substantial portion of Ethiopian households remains food insecure (25%) and vulnerable (27.08%). The Markov random field (MRF) model is the best fit based on GVC, revealing that 90.04% of the total variation is explained by the spatial effects. Most of the northern and south-western areas and south-east and north-west areas are hot spot zones of food insecurity and vulnerability in the country. Moreover, factors such as education, urbanization, having a job, fertilizer usage in cropping, sanitation, and farming livestock and crops have a significant influence on reducing a household\'s probability of being at higher food insecurity levels (insecurity and vulnerability), whereas shocks occurrence and small land size ownership have worsened it.
UNASSIGNED: Chronically food insecure zones showed a strong cluster in the northern and south-western areas of the country, even though higher levels of household food insecurity in Ethiopia have shown a declining trend over the years. Therefore, in these areas, interventions addressing spatial structure factors, particularly urbanization, education, early marriage control, and job creation, along with controlling conflict and drought effect by food aid and selected coping strategies, and performing integrated farming by conserving land and the environment of zones can help to reduce a household\'s probability of being at higher food insecurity levels.

We have developed a novel 3D asynchronous correlation method (3D-ACM) designed for the classification and identification of Chinese handmade paper samples using Raman spectra and machine learning. The 3D-ACM approach involves two rounds of tensor product and Hilbert transform operations. In the tensor product process, the outer product of the spectral data from different samples within the same category is computed, establishing inner connections among all samples within that category. The Hilbert transform introduces a 90-degree phase shift, resulting in a true three-dimensional spectral data structure. This expansion significantly increases the number of equivalent frequency points and samples within each category. This enhancement substantially boosts spectral resolution and reveals more hidden information within the spectral data. To maximize the potential of 3D-ACM, we employed six machine learning models: principal component analysis (PCA) with linear regression (LR), support vector machine (SVM) with LR, k-Nearest Neighbors (KNN), random forest (RF), and convolutional neural network (CNN). When applied to the 3D-ACM data preprocessing method, R-squared values of PLS-LR, KNN, RF and CNN supervised models, approached or equaled 1. This indicates exceptional performance comparable to unsupervised models like PCA. 3D-ACM stands as a versatile mathematical technique not confined to spectral data. It also eliminates the necessity for additional experimental setups or external control conditions, distinct from traditional two-dimensional correlation spectroscopy. Moreover, it preserves the original experimental data, setting it apart from conventional data preprocessing methods. This positions 3D-ACM as a promising tool for future material classification and identification in conjunction with machine learning.

In this article, we find an α-valuation for disjoint union of some bipartite graphs and the tensor product of paths and even cycles.

Explaining the foundation of cognitive abilities in the processing of information by neural systems has been in the beginnings of biophysics since McCulloch and Pitts pioneered work within the biophysics school of Chicago in the 1940s and the interdisciplinary cybernetists meetings in the 1950s, inseparable from the birth of computing and artificial intelligence. Since then, neural network models have traveled a long path, both in the biophysical and the computational disciplines. The biological, neurocomputational aspect reached its representational maturity with the Distributed Associative Memory models developed in the early 70 s. In this framework, the inclusion of signal-signal multiplication within neural network models was presented as a necessity to provide matrix associative memories with adaptive, context-sensitive associations, while greatly enhancing their computational capabilities. In this review, we show that several of the most successful neural network models use a form of multiplication of signals. We present several classical models that included such kind of multiplication and the computational reasons for the inclusion. We then turn to the different proposals about the possible biophysical implementation that underlies these computational capacities. We pinpoint the important ideas put forth by different theoretical models using a tensor product representation and show that these models endow memories with the context-dependent adaptive capabilities necessary to allow for evolutionary adaptation to changing and unpredictable environments. Finally, we show how the powerful abilities of contemporary computationally deep-learning models, inspired in neural networks, also depend on multiplications, and discuss some perspectives in view of the wide panorama unfolded. The computational relevance of multiplications calls for the development of new avenues of research that uncover the mechanisms our nervous system uses to achieve multiplication.

The paper introduces two new methods, namely the cross correlation method (CCM) and two-dimensional correlation method (TDCM), for preprocessing Raman spectroscopy data for analyzing Chinese handmade paper samples. CCM expands the spectral dimension from 1×N to 1×2N-1 by taking cross-correlation between two spectral data of the same category. TDCM includes two-dimensional synchronous correlation method (TDSCM) and two-dimensional asynchronous correlation method (TDACM), which expand the spectral dimension from 1×N to N×N by taking tensor products between two spectral data and between one spectral data and the Hilbert transformation of the other spectral data of the same category, respectively. The experimental data were preprocessed using baseline removal, CCM, TDSCM, and TDACM methods. Four machine learning models were employed to evaluate the effects of these methods: principal component analysis (PCA) combined with linear regression (LR), support vector machine (SVM) combined with LR, k-Nearest Neighbors (KNN), and random forest (RF). The results show that the R-squared values for the PCA model were nearly 1 for all types of data, indicating high accuracy. However, for SVM-LR, KNN, and RF models, the R-squared values were sorted in the order of raw data, baseline removal data, CCM, TDSCM, and TDACM preprocessed data. The R-squared values of KNN and RF machine learning models for TDACM preprocessed data were approaching 1, indicating that the accuracy of machine learning was significantly improved by nearly 100%. This has led to a remarkable improvement in the accuracy of supervised models such as KNN and RF, bringing them closer to the level of unsupervised models such as PCA.

Gaussian processes (GPs) are common components in Bayesian non-parametric models having a rich methodological literature and strong theoretical grounding. The use of exact GPs in Bayesian models is limited to problems containing several thousand observations due to their prohibitive computational demands. We develop a posterior sampling algorithm using H -matrix approximations that scales at O ( n log 2 n ) . We show that this approximation\'s Kullback-Leibler divergence to the true posterior can be made arbitrarily small. Though multidimensional GPs could be used with our algorithm, d-dimensional surfaces are modeled as tensor products of univariate GPs to minimize the cost of matrix construction and maximize computational efficiency. We illustrate the performance of this fast increased fidelity approximate GP, FIFA-GP, using both simulated and non-synthetic data sets.

The article is devoted to the author\'s results of the algebraic analysis of molecular genetic systems, including a set of structured DNA alphabets and long nucleotide sequences in single-stranded DNA of eukaryotic and prokaryotic genomes. A connection of the system of DNA n-plets alphabets with principles of algebraic holography is shown, which concerns a popular theme of holography principles in genetically inherited physiology. In addition, a relation between DNA n-plets alphabets and the Poincaré disk model of Lobachevski hyperbolic geometry is revealed. This relation can explain known facts of the relationship of physiological phenomena with hyperbolic geometry. Considering long DNA sequences as a bunch of many parallel texts written in different n-plets alphabets led to the discovery of some universal rules of the stochastic organization of genomic DNAs. These rules are discussed concerning the general problem of the biological dualism \"probability-vs-determinism\". In general, the presented results give pieces of evidence in favor of the efficiency of a model approach to living organisms as quantum-informational algebraic-harmonic essences.

Large agricultural field trials may display irregular spatial trends that cannot be fully captured by a purely randomization-based analysis. For this reason, paralleling the development of analysis-of-variance procedures for randomized field trials, there is a long history of spatial modeling for field trials, starting with the early work of Papadakis on nearest neighbor analysis, which can be cast in terms of first or second differences among neighboring plot values. This kind of spatial modeling is amenable to a natural extension using splines, as has been demonstrated in recent publications in the field. Here, we consider the P-spline framework, focusing on model options that are easy to implement in linear mixed model packages. Two examples serve to illustrate and evaluate the methods. A key conclusion is that first differences are rather competitive with second differences. A further key observation is that second differences require special attention regarding the representation of the null space of the smooth terms for spatial interaction, and that an unstructured variance-covariance structure is required to ensure invariance to translation and rotation of eigenvectors associated with that null space. We develop a strategy that permits fitting this model with ease, but the approach is more demanding than that needed for fitting models using first differences. Hence, even though in other areas, second differences are very commonly used in the application of P-splines, our conclusion is that with field trials, first differences have advantages for routine use.

The article is devoted to the possibilities of considering the evolution of biological systems in connection with the unique emergent properties of antenna arrays, that is, systems of mutually matched antennas widely used in technology. Materials are presented in favor of the proposition that the evolution of biosystems can be formally considered as the evolution of systems of bio-antenna arrays and their energy-information wave activity, which participates in biological computation and contributes to the unification of body parts into a coherent whole. The use of digital antenna arrays in technology is based on their tensor-matrix theory. The author discovers a structural analogy of this theory with the tensor-matrix features of genetic coding systems, as well as algebraic modeling of the universal rules for the stochastic DNA organization of the genomes of higher and lower organisms. This analogy is just one of the facts presented in the article in favor of the usefulness of borrowing knowledge from modern antenna technology to consider the evolution of biosystems. The described new approach may exist along with other known approaches in evolutionary biology.