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The adjoint of a matrix in the Lie algebra associated with a matrix algebra is a fundamental operator, which can be generalized to a more general operator $ \varphi _{AB}: X\rightarrow AX-XB $ φ AB : X → AX − XB by two matrices A and B. The kernel of the operator is very well-known and it can be found in Gantmacher's book. The formulas for the dimensions of the kernels of arbitrary powers of the operator $ \varphi _{AB} $ φ AB were given in terms of the Segre characteristics of these two matrices by the second and third authors in this paper and their collaborators. This paper provides an alternative approach to this problem via the Weyr characteristic in a more essential method. We obtain formulas for the dimensions of the kernels of arbitrary powers of the operator in terms of the Weyr characteristics. Furthermore, the basis for kernel of each power of the operator is described explicitly. As a consequence, for arbitrary square matrices A and B over an algebraically closed field, the dimension of the kernel of each power of the operator $ \varphi _{A-\lambda I,B} $ φ A − λI , B for eigenvalues λ of $ \varphi _{AB} $ φ AB can be viewed as a similarity invariant of the operator $ \varphi _{AB} $ φ AB , so we characterize the operator within similarity, which should be of interest to a number of people (including physicists). [ABSTRACT FROM AUTHOR]

The understanding of the characteristics and metabolite changes in waxy and normal maize kernels after cooking is rather limited. This study was designed to meticulously analyze the differences in characteristics and metabolites of these kernels before and after steaming. To cut environmental impacts, samples were obtained by pollinating one ear with mixed pollen. Non-targeted metabolomics was used to analyze metabolites comprehensively. The results demonstrated that a total of 4043 annotated metabolites were identified. Principal component analysis (PCA) indicated distinct variances between kernels before and after steaming and between the two maize types. Steaming led to an increase in differential metabolites (DEMs) for both maize varieties, noticeably in waxy maize. In waxy maize, the down-regulated DEMs were associated with lipid metabolism, while the up-regulated ones were related to amino acid, phenylpropanoid, and flavone metabolism. Compared to steamed normal maize kernels, waxy maize had more DEMs in purine and steroid pathways, fewer in fatty acid, α-linolenic acid, and phenylpropanoid ones, with marked differences in secondary metabolites like those in amino acid metabolism. This study offers a vital foundation and direction for future research on metabolic pathways regarding maize quality improvement and flavor regulation. [ABSTRACT FROM AUTHOR]

Simple Summary: This study examined the juvenile dispersal behaviour of seven Hen Harriers tracked with GPS/GSM transmitters. We analyse movement patterns, differences between sexes, and changes between the first and second years of dispersal. The results highlight that dispersal in the first year is more extensive and variable, whereas in the second year, the movements become more efficient, reflecting a progressive adaptation to the environment. The Hen Harrier (Circus cyaneus) is a medium-sized raptor with a broad distribution across the Palearctic. In Spain, Hen Harrier behaviour is diverse due to being at the southern limit of its distribution, and the margins of distributions tend to show greater variability in the strategies and behaviours of animals. This study focused on juvenile dispersal, using GPS/GSM data from seven individuals to define movement patterns, compare variables between sexes, and analyse differences between the first and second years of dispersal. To analyse the movements during each annual period, six variables were considered, namely the mean distance from nest location, maximum distance from nest location, mean daily distance travelled, total distance travelled, 95% weekly kernel, and 95% total kernel. In their first year after leaving the nest, the Hen Harriers began dispersal movements on 21 August ± 34.41 days, with highly variable distances and durations among individuals. They travelled an average total of 6774.66 ± 5360.46 km over the two first years, with some significant differences between sexes and periods in terms of movement patterns, particularly in the daily and total distances travelled. Overall, the maximum distance from nest location and the total distance travelled were greater in the first year of dispersal than in the second year, indicating, as expected, an improved understanding of their environment and more efficient movements. The juvenile dispersal behaviour of the Hen Harrier is highly variable and represents the most vulnerable season for survival as the birds navigate new and unexplored territories. [ABSTRACT FROM AUTHOR]

On completely regular semirings, we give alternative characterizations for the kernel of a congruence and idempotent pure congruences. Then we give alternative characterizations for the trace of a congruence and idempotent separating congruences. In addition, we conclude that a congruence is uniquely determined by its kernel and trace. [ABSTRACT FROM AUTHOR]

Internet of Things (IoT) refers to a network of interconnected objects, computer systems, and physical or mechanical devices that are capable of sending and receiving data over a network without the intervention of a human. A growing number of undesirable security issues are occurring as a result of the rapid advancements in IoT infrastructures. IoT devices are therefore becoming more vulnerable to security threats and network attacks. IoT services and innovative ecosystem devices can be severely damaged as a result of these attacks and issues. So we propose a multi-kernel-based intensive learning machine model to improve security and overcome the above challenges. To enhance the performance of the insider threat detection model, significant feature sets are generated using correlation coefficient, random forest mean (RFM) reduction accuracy, and gain ratio. To obtain an optimal feature set, the features are combined using an appropriate mechanism (AND function). Afterward, the combined feature set is fed into a machine-learning model based on multi-kernel optimization (MKELM). MKELM is optimized using the Adaptive Crocodile Optimization Algorithm (ACOA) to increase its performance in this detection model. Java is used for the implementation of this proposed approach. In order to analyze performance, NSL-KDD 99 dataset and UNSW-NB15 dataset have been used. The performance of the proposed scheme is evaluated in terms of detection rate, precision, accuracy, recall, F-measure, and detection rate. [ABSTRACT FROM AUTHOR]

This letter proposes a new scheme that improves throughput and reduces queuing delay while running multiple inferences in embedded graphics processing unit (GPU)-based systems. We observe that an embedded system runs inference with a fixed number of deep learning models and that inference requests often use the same model. Unlike prior work that proposed kernel fusion or scheduling techniques, this letter proposes a new software technique that merges and fuses kernels by monitoring the requests in a queue. The proposed technique first monitors a fixed number of requests and groups the requests running the same model. Then, it creates the kernels that iteratively process the grouped requests. We call such a technique kernel merging. After that, the proposed technique performs kernel fusion with merged kernels. Eventually, our idea minimizes the number of concurrent kernels, thus mitigating stalls caused by frequent context switching in a GPU. In our evaluation, the proposed kernel merge and fusion achieve $2.7\times $ better throughput, 47% shorter average kernel execution time, and 63% shorter tail latency than prior work. [ABSTRACT FROM AUTHOR]

Let L(H) denote the algebra of all bounded linear operators on a complex infinite dimensional Hilbert space H into itself. Given A,B,C,D ∈ L(H), the elementary operator Δ(A,C),(B,D) ∈ L(L(H)) is defined by Δ(A,C),(B,D)(X) = AXB - CXD. In the present paper, we give necessary and sufficient conditions that (i) the range of the elementary operator Δ(A,C),(B,D) is dense in the weak and the ultraweak operator topologies, (ii) the norm closure of the range of Δ(A,C),(B,D) contains the ideal of compact operators. We initiate the study on the class of operators such that the norm closure of the range of Δ(A,C),(B,D) is closed under taking adjoints. We establish some basic properties concerning these operators. [ABSTRACT FROM AUTHOR]

In this article, we propose three non parametric kernel estimators for the mean residual life function when the data are selected proportionally to their length. We evaluate the mean squared error of the three estimators and investigate the consistency for all three of them. [ABSTRACT FROM AUTHOR]

This study uses the triple-phase lag model to investigate how higher-order fractional order and memory-dependent derivatives affect reflection at the free surface of an orthotropic piezo-thermoelastic medium. The performance of both kinds of derivatives is studied using the normal mode analysis technique. Four different types of coupled reflected plane waves are identified and explore the impact of various parameters, fractional order parameter, kernel function, the higher-order time differential fractional, and memory-dependent heat conduction parameters on energy distribution with respect to the angle of incidence. The results are presented graphically, providing numerical data for reflected waves, amplitude, and energy ratios. [ABSTRACT FROM AUTHOR]

Abstract Obesity, a major risk factor for various metabolic diseases, often results in dysfunctional white adipose tissue and altered adipogenesis leading to ectopic fat accumulation, inflammation, and insulin resistance. On the other hand, cashew (Anacardium occidentale L.) nut worldwide consumption and production is increasing steadily, which augments the mass of byproducts to be discarded. Indeed, cashew apples and cashew shells have shown potent effects to lower adiposity weight in human and animal models. However, the direct effect on adipocyte differentiation still remains unexplored. Therefore, this study aimed to investigate the biological effect of cashew nut or kernel (CK), dried cashew apple (DA), and cashew shell (SH) ethanolic extracts on 3T3-L1 adipocyte differentiation and lipid accumulation. SH showed strong inhibition on adipocyte differentiation by downregulating transcription factors, PPARγ, C/EBPα, and SREBP-1. DA also inhibited the transcription factors accompanied by reduced lipid accumulation, while proteins for de novo lipogenesis were unchanged. Finally, CK did not alter any markers in adipocyte differentiation, however, interestingly adiponectin level was significantly increased. Concisely, our findings showed that CK ameliorates adiponectin production without interfering adipogenesis, while DA lowers lipid accumulation and SH suppresses adipogenesis.

Interest in incorporating historical data in the clinical trial has increased with the rising cost of conducting clinical trials. The intervention arm for the current trial often requires prospective data to assess a novel treatment, and thus borrowing historical control data commensurate in distribution to current control data is motivated in order to increase the allocation ratio to the current intervention arm. Existing historical control borrowing adaptive designs adjust allocation ratios based on the commensurability assessed through study-level summary statistics of the response agnostic of the distributions of the trial subject characteristics in the current and historical trials. This can lead to distributional imbalance of the current trial subject characteristics across the treatment arms as well as between current control data and borrowed historical control data. Such covariate imbalance may threaten the internal validity of the current trial by introducing confounding factors that affect study endpoints. In this article, we propose a Bayesian design which borrows and updates the treatment allocation ratios both covariate-adaptively and commensurate to covariate dependently assessed similarity between the current and historical control data. We employ covariate-dependent discrepancy parameters which are allowed to grow with the sample size and propose a regularized local regression procedure for the estimation of the parameters. The proposed design also permits the current and the historical controls to be similar to varying degree, depending on the subject level characteristics. We evaluate the proposed design extensively under the settings derived from two placebo-controlled randomized trials on vertebral fracture risk in post-menopausal women.

Recently Yang–Roh–Jun introduced the notion of OBCI-algebras as a generalization of BCI-algebras. Here we introduce homomorphisms and kernels of OBCI-algebras and investigate related properties. More exactly, we first define the homomorphism and kernel of OBCI-algebras. We then investigate properties related to (ordered) subalgebras, (ordered) filters and direct products of OBCI-algebras. [ABSTRACT FROM AUTHOR]

Cocoa (Theobroma cacao L.), indigenous to the tropical forests of the Americas, is renowned not only as the primary raw material for chocolate and its derivatives (cocoa liquor and butter) but also as a rich source of phytonutrients with beneficial health effects. Current research has elucidated that within the post-harvest process, fermentation stands as the critical stage for the formation of the principal biochemical quality markers in cocoa, known as polyphenols. These compounds contribute to the bitterness and astringency that constitute the complex flavor profile of chocolate; however, their excessive presence can be organoleptically undesirable. A high phenolic content (>10%) is associated with insufficient fermentation and certain varieties of ordinary cocoa, thereby serving as a discriminatory parameter between fine-flavor cocoa (Nacional) and bulk cocoa (CCN-51). Beyond their technological significance, these components have garnered substantial scientific interest, as polyphenol consumption is associated with potential protective effects against the development of non-communicable chronic diseases (including diabetes, cancer, and atherosclerosis), attributable to their potent antioxidant properties. In this context, the objective of this study was to evaluate the impact of fermentation time on the antioxidant capacity (AC) and total polyphenol content (TPC) in the principal Ecuadorian cocoa varieties (i.e., CCN-51 clone and Nacional). Pilot-scale fermentation experiments demonstrated significant variations in antioxidant capacity (CCN-51 clone: 785.61 to 1852.78 and Nacional: 564.32 to 1428.60 µmol TE/g) and total polyphenol content (CCN-51 clone: 52.92 to 162.82; Nacional: 40.55 to 157.50 mg gallic acid/g). Both parameters decreased markedly throughout the process, with the CCN-51 clone exhibiting greater retention.

旨在寻找油茶果最佳采后处理方式，为其后续研究奠定基础，采用液相色谱-质谱联用法（LC-MS/MS）对油茶果采后不同处理〔不处理（F8）、堆沤处理（FC）、去壳摊晒（NS）、带壳摊晒（WS）〕10、30 d种仁代谢物进行测定，并用相关软件对代谢产物进行分析。结果表明：鉴定出1 107种特征代谢物，其中正离子模式和负离子模式下鉴定的代谢物数量分别为763种和344种，代谢物主要为脂类和类脂分子（277种），苯丙烷类和聚酮类（193种），有机酸及其衍生物（172种），类苯（97种），有机杂环化合物（94种），有机氧化合物（84种），核苷、核苷酸和类似物（33种）；通过比较差异代谢物不饱和脂肪酸发现，去壳摊晒处理30 d（NS2） vs 10 d（NS1）比较组中检测到亚油酸、顺式-9-十六碳烯酸、8（9）-环氧-5Z，11Z，14Z-二十碳三烯酸、亚麻酸、蓖麻油酸、9,10-环氧十八碳烯酸共6种不饱和脂肪酸，且都表达上调；对差异代谢物进行富集分析发现，主要参与的代谢途径有苯丙氨酸代谢、类黄酮生物合成、甘油磷脂代谢、甘油酯代谢、玉米素生物合成、植物次生代谢产物的生物合成、谷胱甘肽代谢、氨基酸的生物合成、次生代谢产物的生物合成。综上，油茶果采后最佳处理方式为去壳摊晒30 d。In order to find the optimal postharvest treatment of Camellia oleifera fruit, and lay the foundation for subsequent research, liquid chromatography-tandem mass spectrometry (LC-MS/MS) was used to determine the metabolites of the kernels of different postharvest treatments of Camellia oleifera fruit 〔without treatment （F8）, composting treatment（FC） , sun dried without shell （NS）, and sun dried with shell（WS）〕 for 10 d and 30 d, and relevant software was used to analyze the metabolites. The results showed that a total of 1 107 characteristic metabolites were identified, with 763 and 344 metabolites identified in the positive and negative ion modes, respectively. The main metabolites were lipids and lipid-like molecules( 277 kinds), phenylpropanoids and polykettides (193 kinds), organic acids and derivatives(172 kinds), benzenoids (97 kinds), organoheterocyclic compounds (94 kinds), organic oxygen compounds (84 kinds), nucleosides, nucleotides and analogues(33 kinds). By comparison of the unsaturated fatty acid of differential metabolites, six unsaturated fatty acids, namely linoleic acid, cis-9-hexadecenoic acid, 8 (9) - epoxy-5Z, 11Z, 14Z-eicosatrienoic acid, linolenic acid, ricinolic acid, 9,10-epoxy-octadecenoic acid, were detected in 30 d (NS2) and 10 d (NS1) of the sun dried without shell treatment, and their expressions were up-regulated. The enrichment analysis of differential metabolites results showed that the main metabolic pathways included phenylalanine metabolism, flavonoid biosynthesis, glycerol phospholipid metabolism, glycerol ester metabolism, zeatin biosynthesis, plant secondary metabolites biosynthesis, glutathione metabolism, amino acid biosynthesis, and secondary metabolites biosynthesis. Overall, the best postharvest treatment of Camellia oleifera fruit is sun dried without shell treatment for 30 d.

This paper explores the concept of multipliers in Hilbert algebras, unveiling various intriguing properties. We delve into the intricate relationships between fixed sets, kernels, and near filters of multipliers, shedding light on their interconnected roles within Hilbert algebras. This investigation aims to provide a deeper understanding of algebraic structures and their dynamic interactions. [ABSTRACT FROM AUTHOR]

The lack of effective theoretical guidance for the migration of device driver modules and application system libraries caused by kernel upgrades brings many inconveniences to the development and deployment of operating systems. In response to the above situation, this paper proposes a quantitative analysis method for kernel compatibility based on kernel module difference detection and dependency analysis. Combining with the open-source Linux kernel, it constructs a kernel module dependency graph, statistics graph features that affect kernel compatibility such as indegree, out-degree, dependency depth, and centrality of kernel modules, analyzes the changes in system calls and exported functions, which are two types of functions strongly related to compatibility, and their impact on kernel compatibility. It also provides a basic method to measure the compatibility rate and influence domain of kernel modules, and experimental verification is conducted in the Linux kernel 5.x series and typical versions of Kylin. [ABSTRACT FROM AUTHOR]

Mobile Ad-Hoc Network (MANETs) is referred to as the mobile wireless nodes that make up ad hoc networks. The network topology may fluctuate on a regular basis due to node mobility. Each node serves as a router, passing traffic throughout the network, and they construct the network's infrastructure on their own. MANET routing protocols need to be able to store routing information and adjust to changes in the network topology in order to forward packets to their destinations. While mobile networks are the main application for MANET routing techniques, networks with stationary nodes and no network infrastructure can also benefit from using them. In this paper, we proposed a Self Adaptive Tasmanian Devil Optimization (SATDO) based Routing and Data Aggregation in MANET. The first step in the process is clustering, where the best cluster heads are chosen according to a number of limitations, such as energy, distance, delay, and enhanced risk factor assessment on security conditions. In this study, the SATDO algorithm is proposed for this optimal selection. Subsequent to the clustering process, routing will optimally take place via the same SATDO algorithm introduced in this work. Finally, an improved kernel least mean square-based data aggregation method is carried out to avoid data redundancy. The efficiency of the suggested routing model is contrasted with the conventional algorithms via different performance measures. [ABSTRACT FROM AUTHOR]

Context. Many invasive animals are typically active across large areas, making monitoring and control programs expensive. To be efficacious, monitoring devices and control tools need to be strategically located to maximise the probability of encounter. This requires an understanding of how the target species uses the landscape, through identifying key habitat or landscape features that are preferred and used disproportionately more frequently by the species. Spatial analysis of animal movements can help identify high use areas. Aims. The variability introduced by different range calculation methods can lead to uncertainty in subsequent habitat analyses. We aimed to determine which method is superior for accurate delineation of core areas for feral cats. Methods. We analysed spatial data from 35 collared feral cats across four Australian study sites between 2016 and 2019, and compared the core areas generated using seven commonly used home range estimation methods. Key results. We found that the a-hull method provided a higher precision of polygon placement, resulting in lower Type I and II errors and higher conformity to landscape features than other methods. The a-hull used a single default parameter and required no subjective input, making it a more objective, superior method. Conclusions. We recommend that the a-hull method be used to define core activity areas for feral cats, enabling more robust habitat analysis, and identification of key habitat and landscape features to strategically target for monitoring and control programs. Implications. This strategic approach could significantly improve cost efficiencies, particularly where existing management is widely dispersed, and core activity areas are clumped. [ABSTRACT FROM AUTHOR]

A subset K of vertices of digraph D = (V(D), A(D)) is a kernel if the following two conditions are fulfilled: (i) no two vertices of are connected by an arc in any direction and (ii) every vertex not in has an ingoing arc from some vertex in K. A quasi-kernel of D is a subset Q of vertices satisfying condition (i) and furthermore every vertex can be reached in at most two steps from Q. A vertex is source-free if it has at least one ingoing arc. In 1976, P.L. Erdös and L.A. Székely conjectured that every source-free digraph D has a quasi-kernel of size at most |V(D)| /2Recently, this conjecture has been shown to be true by Allan van Hulst for digraphs having kernels. In this note, we provide a short and simple proof of van Hulst's result. We additionally characterize all source-free digraphs D having kernels with smallest quasi-kernels of size |V (D)| /2. [ABSTRACT FROM AUTHOR]

Quantitative analysis of diffusion‐weighted magnetic resonance imaging (DW‐MRI) has been explored for many clinical applications since its development. In particular, the intravoxel incoherent motion (IVIM) model for DW‐MRI has been commonly utilized in various organs. However, because of the presence of excessive noise, the IVIM parameter maps obtained from pixel‐wise fitting are often unreliable. In this study, we propose a kernelized total difference‐based curve‐fitting method to estimate the IVIM parameters. Simulated DW‐MRI data at five signal‐to‐noise ratios (i.e., 10, 20, 30, 50, and 100) and real abdominal DW‐MRI data acquired on a 1.5‐T MRI scanner with nine b‐values (i.e., 0, 10, 25, 50, 100, 200, 300, 400, and 500 s/mm2) and six diffusion‐encoding gradient directions were used to evaluate the performance of the proposed method. The results were compared with those obtained by three existing methods: trust‐region reflective (TRR) algorithm, Bayesian probability (BP), and deep neural network (DNN). Our simulation results showed that the proposed method outperformed the other three comparing methods in terms of root‐mean‐square error. Moreover, the proposed method could preserve small details in the estimated IVIM parameter maps. The experimental results showed that, compared with the TRR method, the proposed method as well as the BP (and DNN) method could reduce the overestimation of the pseudodiffusion coefficient and improve the quality of IVIM parameter maps. For all studied abdominal organs except the pancreas, both the proposed method and the BP method could provide IVIM parameter estimates close to the reference values; the former had higher precision. The kernelized total difference‐based curve‐fitting method has the potential to improve the reliability of IVIM parametric imaging. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish the existence of multiple positive solutions for a coupled system of second-order undamped Sturm-Liouville boundary value problems. The technique is based on the Six functionals fixed point theorem. [ABSTRACT FROM AUTHOR]

The current study envisioned to assess the physical traits of sorghum grain for selected sorghum genotypes. Seed for the genotypes was sourced from the Lupane State University Gene Bank and grown during the 2022/23 agricultural season at Lupane State University Farm experimental plots. At maturity, laboratory tests on kernel/grain hardness, 100 kernel weight, bulk density, kernel diameter, colour and determination of presence of tannins through qualitative tests were done for all the 24 sorghum genotypes. Results from analysis of variance demonstrated highly significant differences (P<0.001) on kernel weight, kernel diameter, kernel hardness and grain hardness showing a great diversity of physical traits among all the 22 genotypes and 2 commercial varieties of sorghum. Mean 100 kernel weight was 2.59g, kernel diameter was 3.49mm, bulk density was 1.23g/cm3 and kernel hardness was 28.9%. Visual assessment was done on grain colour and seed was classified under red, cream, white and brown sorghums, and mixed colours. A chi-square test found a significant relationship between grain colour and presence of tannins. Genotypes NPGRC3124, IS9405 showed moderate levels of tannins while IS13996, IS29925, NPGRC1699, NPGRC1156 and NPGRC1478 had high levels. A highly significant strong positive correlation was shown for sorghum genotype between kernel diameter and kernel weight (r=0.81 at p=0.05). Highly significant positive correlation was also observed between bulk density and kernel weight (r=0.4173 at p=0.001). Kernel hardness has a strong positive correlation with bulk density (r=0.6242). Quantification of tannins is recommended to prevent negative effects on human and livestock health. [ABSTRACT FROM AUTHOR]

Wheat is used for making many food products due to its diverse quality profile among different wheat classes. Since laboratory analysis of these end-use quality traits is costly and time-consuming, genetic dissection of the traits is preferential. This study used a genome-wide association study (GWAS) of ten end-use quality traits, including kernel protein, flour protein, flour yield, softness equivalence, solvent's retention capacity, cookie diameter, and top-grain, in soft red winter wheat (SRWW) adapted to US southeast. The GWAS included 266 SRWW genotypes that were evaluated in two locations over two years (2020–2022). A total of 27,466 single nucleotide markers were used, and a total of 80 significant marker-trait associations were identified. There were 13 major-effect quantitative trait loci (QTLs) explaining >10% phenotypic variance, out of which, 12 were considered to be novel. Five of the major-effect QTLs were found to be stably expressed across multiple datasets, and four showed associations with multiple traits. Candidate genes were identified for eight of the major-effect QTLs, including genes associated with starch biosynthesis and nutritional homeostasis in plants. These findings increase genetic comprehension of these end-use quality traits and could potentially be used for improving the quality of SRWW. [ABSTRACT FROM AUTHOR]

The aim of the present work is a comparative study of different persistence kernels applied to various classification problems. After some necessary preliminaries on homology and persistence diagrams, we introduce five different kernels that are then used to compare their performances of classification on various datasets. We also provide the Python codes for the reproducibility of results and, thanks to the symmetry of kernels, we can reduce the computational costs of the Gram matrices. [ABSTRACT FROM AUTHOR]

Gaussian processes are popular in spatial statistics, data mining and machine learning because of their versatility in quantifying spatial variability and in propagating uncertainty. Although there has been a prolific research activity about Gaussian processes over Euclidean domains, only recently this research has extended to non-Euclidean manifolds. This paper digs into vector-valued Gaussian processes defined over the product of a hypersphere and a Euclidean space of arbitrary dimension, which are of interest in various disciplines of the natural sciences and engineering. Under mild regularity conditions, we establish a surprising one-to-one correspondence between matrix-valued kernels associated with vector Gaussian processes over the product space, and what we term partial ultraspherical and Fourier transforms that are taken over either the sphere or the Euclidean subspace. The properties of our approach are illustrated in terms of new parametric classes of matrix-valued kernels for product spaces of a hypersphere crossed with a Euclidean space. We also provide two algorithms that allow for fast simulation of approximately Gaussian (in the sense of the central limit theorem) processes in such product spaces. [ABSTRACT FROM AUTHOR]

The variability of food resources considerably affects the habitat preferences of animals. In mast years, the availability of highly nutritive food increases significantly. We tested whether changes in the distribution of the areas of wisents, Bison bonasus L. concentration, in the Bieszczady Mountains, Poland, were connected with the availability of beechnuts. In the two beech masting years of 2013 and 2022, we considered the months with the highest availability of beechnuts, namely September and October. The beechnut crop varied significantly between as little as 2.4 g dry matter/m2, recorded within the Baligród herd's home range in 2013, and up to 238.8 g dry matter/m2 within the Tworylne herd's range, also in 2013. The analysis of the spatial distribution of beech stands within various parts of the wisents' home range showed that within the 95% kernel area, their share was mostly high, varying between 25.7% and 42.8%. Meanwhile, within the 50% kernel area, it was generally much lower, except for the year 2022 in the case of the Baligród herd. The densities of wisents varied significantly between the kernel areas of 95% and 50%, ranging between 0.04 and 0.08 animals/ha and 0.17 and 0.48 animals/ha, respectively. However, there was no statistical difference between the figures for all plots tested within the home range of the wisent population and plots dominated by beech. Based on the data obtained in this study, habitat selection patterns of wisents in the Bieszczady Mountains cannot be explained by the availability of beech stands and the phenomenon of mast years. [ABSTRACT FROM AUTHOR]

Digitalization and automation in the agricultural sector enable the enhancement of production processes, leading to increased yields. Specifically, the medications administration or complementary treatments in animals often prove to be a demanding task for human operators. This letter introduces an embedded system prototype that facilitates monitoring the level of capsules coverage in troughs through image processing. The suggested system enables an innovative antiparasitic treatment using biological control agents. The prototype utilizes a Raspberry Pi 3B as the platform to execute the developed image processing algorithm. The obtained results successfully demonstrate the algorithm’s accurate functionality estimating capsules coverage within the troughs. [ABSTRACT FROM AUTHOR]

This paper considers the problem of kernel regression and classification with possibly unobservable response variables in the data, where the mechanism that causes the absence of information can depend on both predictors and the response variables. Our proposed approach involves two steps: First we construct a family of models (possibly infinite dimensional) indexed by the unknown parameter of the missing probability mechanism. In the second step, a search is carried out to find the empirically optimal member of an appropriate cover (or subclass) of the underlying family in the sense of minimizing the mean squared prediction error. The main focus of the paper is to look into some of the theoretical properties of these estimators. The issue of identifiability is also addressed. Our methods use a data-splitting approach which is quite easy to implement. We also derive exponential bounds on the performance of the resulting estimators in terms of their deviations from the true regression curve in general L p norms, where we allow the size of the cover or subclass to diverge as the sample size n increases. These bounds immediately yield various strong convergence results for the proposed estimators. As an application of our findings, we consider the problem of statistical classification based on the proposed regression estimators and also look into their rates of convergence under different settings. Although this work is mainly stated for kernel-type estimators, it can also be extended to other popular local-averaging methods such as nearest-neighbor and histogram estimators. [ABSTRACT FROM AUTHOR]

Bandwidth selection is key for kernel quantile estimators (KQEs), which estimate quantiles by averaging all of the order statistics with appropriate kernel-weighting functions. This paper provides a new data-driven bandwidth selection method for KQEs, named the exact bootstrap-based bandwidth selection (EBS) rule. By relying on the exact analytic expressions for the bootstrap mean and variance of KQEs, the error due to bootstrap resampling is eliminated, and thus the optimal bandwidth can be obtained by minimizing the mean squared error (MSE) estimate. The effectiveness of this EBS rule is confirmed by numerical experiments. First, the bandwidth selection performance of the EBS method is compared to that of a benchmark approach. Simulation studies show that the EBS method performs well, especially in selecting bandwidths for extreme quantiles and when applied to small sample sizes with skewed distributions and relatively large variances. Second, KQEs with a bandwidth determined by our EBS rule is compared with five other state-of-the-art quantile estimators over six typical distributions. The results further validate the efficiency of the EBS method. Third, the results of simulations of controlling actual type-I error rates that occur when two independent groups are compared through quantiles further demonstrate the precision of our EBS-based KQEs. [ABSTRACT FROM AUTHOR]

The semiconductor industry is the core industry of the information age. As a key link in the semiconductor industry, wafer fabrication plays a key role in its development. In the testing stage of the wafer, each die of the wafer is detected and marked, and a wafer map with a certain spatial pattern can be formed. The analysis and classification of these spatial patterns can identify the cause of wafer defects, thereby improving production yield. However, as wafer size increases, line widths become smaller, etc., the probability of a mixed defect mode wafer pattern increases. Moreover, the mixed defect mode wafer map is more difficult to identify and classify than the single defect mode wafer map. Therefore, this paper proposes an improved deep convolutional neural network (DCNN) structure model for the recognition and classification of mixed defect pattern wafer maps. From the perspective of increasing the width of the DCNN, the improved network structure can avoid problems such as over-fitting and limited extraction of features due to the continuous deepening of the DCNN. The network is called Multi-Path DCNN (MP-DCNN) structure. The experimental results show that the proposed Multi-Path DCNN structure has better performance and higher classification accuracy than existing methods. [ABSTRACT FROM AUTHOR]

The class of nonlinear integral equations on the positive half-line with a monotone operator of Hammerstein type is studied. With various partial representations of the corresponding kernel and nonlinearity, this class of equations has applications in the dynamic theory of -adic strings, in the kinetic theory of gases, in the theory of radiation transfer and in the mathematical theory of the geographical spread of epidemic diseases. A constructive theorem for the existence of a nontrivial bounded solution is proved. The asymptotic behavior of the constructed solution at infinity is studied. We also prove a theorem for the uniqueness of a solution in the class of nonnegative nontrivial and bounded functions. At the end of the work, specific particular examples of the kernel and nonlinearity of this class of equations are given, which are of independent interest. [ABSTRACT FROM AUTHOR]

In this paper we consider the semiclassical version of pseudo-differential operators on the lattice space ħ Z n . The current work is an extension of the previous work (Botchway et al. in J Funct Anal 278(11):108473, 33, 2020) and agrees with it in the limit of the parameter ħ → 1 . The various representations of the operators will be studied as well as the composition, transpose, adjoint and the link between ellipticity and parametrix of operators. We also give the conditions for the ℓ p , weighted ℓ 2 boundedness and ℓ p compactness of operators. We investigate the relation between the classical and semi-classical quantization in the spirit of Ruzhansky and Turunen (Pseudo-differential operators and symmetries. Pseudo-differential operators, vol 2. Theory and Applications, Birkhäuser, Basel, 2010; J Fourier Anal Appl 16(6):943–982, 2010) RTspsJFAA and employ its applications to Schatten–von Neumann classes on ℓ 2 (ħ Z n) . We establish Gårding and sharp Gårding inequalities, with an application to the well-posedness of parabolic equations on the lattice ħ Z n . Finally we verify that in the limiting case where ħ → 0 the semi-classical calculus of pseudo-differential operators recovers the classical Euclidean calculus, but with a twist. [ABSTRACT FROM AUTHOR]

With an explosive increase of data produced annually, researchers have been attempting to develop solutions for systems that can effectively handle large amounts of data. Single-operating-system (OS) non-uniform memory access (NUMA) abstraction technology is an important technology that ensures the compatibility of single-node programming interfaces across multiple nodes owing to its higher cost efficiency compared with scale-up systems. However, existing technologies have not been successful in optimizing user performance. In this paper, we introduce a single-OS NUMA abstraction technology that ensures full compatibility with the existing OS while improving the performance at both hypervisor and guest levels. Benchmark results show that the proposed technique can improve performance by up to 4.74X on average in terms of execution time compared with the existing state-of-the-art opensource technology.

Image reconstruction of low-count positron emission tomography (PET) data is challenging. Kernel methods address the challenge by incorporating image prior information in the forward model of iterative PET image reconstruction. The kernelized expectation-maximization (KEM) algorithm has been developed and demonstrated to be effective and easy to implement. A common approach for a further improvement of the kernel method would be adding an explicit regularization, which however leads to a complex optimization problem. In this paper, we propose an implicit regularization for the kernel method by using a deep coefficient prior, which represents the kernel coefficient image in the PET forward model using a convolutional neural-network. To solve the maximum-likelihood neural network-based reconstruction problem, we apply the principle of optimization transfer to derive a neural KEM algorithm. Each iteration of the algorithm consists of two separate steps: a KEM step for image update from the projection data and a deep-learning step in the image domain for updating the kernel coefficient image using the neural network. This optimization algorithm is guaranteed to monotonically increase the data likelihood. The results from computer simulations and real patient data have demonstrated that the neural KEM can outperform existing KEM and deep image prior methods.

Nowadays, a large number of aromatic and medicinal plants possess highly significant bioproperties, with numerous applications in medicine, pharmacy, cosmetology, and agriculture. This work aimed to conduct a phytochemical screening and assay of phytomarkers with biopharmaceutical potential and to assess the antioxidant and antibacterial activity of Persea americana Mill. kernel extracts in vitro. P. americana plant samples were collected in May 2017 in Kinshasa. Three standard strains were selected namely Escherichia coli ATCC 25922, Staphylococcus aureus ATCC 25923, and Pseudomonas aeroginosa ATCC 9027 for microbiological assays. The phytomarker assay was used to detect total polyphenols, and the antibacterial activity was determined using the solid diffusion method on the Mueller Hinton medium to establish the minimal inhibitory concentration. Antioxidant activity was evaluated by the DPPH, ABTS, and Phosphomolybdate techniques. The findings showed that P. americana kernels contain secondary metabolites such as flavonoids, polyphenols, alkaloids, tannins, and triterpenoids, which may confer interesting biological activities. Quantitative phytomarker analysis of P. americana extracts showed a concentration of 69.70±3.07 mg/QE of total polyphenols and 27.53±1.15 mg/QE of flavonoids. All the extracts tested had low antibacterial activity against the three strains tested. However, the methanolic extract showed better antioxidant activity. In view of the IC50 values of our various fractions, it is clear that P. americana kernels possess interesting antioxidant properties. [ABSTRACT FROM AUTHOR]

Cocoa (Theobroma cacao L.), indigenous to the tropical forests of the Americas, is renowned not only as the primary raw material for chocolate and its derivatives (cocoa liquor and butter) but also as a rich source of phytonutrients with beneficial health effects. Current research has elucidated that within the post-harvest process, fermentation stands as the critical stage for the formation of the principal biochemical quality markers in cocoa, known as polyphenols. These compounds contribute to the bitterness and astringency that constitute the complex flavor profile of chocolate; however, their excessive presence can be organoleptically undesirable. A high phenolic content (>10%) is associated with insufficient fermentation and certain varieties of ordinary cocoa, thereby serving as a discriminatory parameter between fine-flavor cocoa (Nacional) and bulk cocoa (CCN-51). Beyond their technological significance, these components have garnered substantial scientific interest, as polyphenol consumption is associated with potential protective effects against the development of non-communicable chronic diseases (including diabetes, cancer, and atherosclerosis), attributable to their potent antioxidant properties. In this context, the objective of this study was to evaluate the impact of fermentation time on the antioxidant capacity (AC) and total polyphenol content (TPC) in the principal Ecuadorian cocoa varieties (i.e., CCN-51 clone and Nacional). Pilot-scale fermentation experiments demonstrated significant variations in antioxidant capacity (CCN-51 clone: 785.61 to 1852.78 and Nacional: 564.32 to 1428.60 µmol TE/g) and total polyphenol content (CCN-51 clone: 52.92 to 162.82; Nacional: 40.55 to 157.50 mg gallic acid/g). Both parameters decreased markedly throughout the process, with the CCN-51 clone exhibiting greater retention. [ABSTRACT FROM AUTHOR]

In the framework of Clifford analysis, we study higher order Dirac operators constructed with k-vectors. We find a necessary and sufficient condition to determine whether a function cancels them. [ABSTRACT FROM AUTHOR]

Yield in many crops is affected by abscission during the early stages of fruitlet development. The reasons for fruitlet abscission are often unclear but they may include genetic factors because, in some crops, self-pollinated fruitlets are more likely to abscise than cross-pollinated fruitlets. Pollen parentage can also affect final fruit size and fruit quality. Here, we aimed to understand the effects of pollen parentage on fruitlet retention and nut quality in orchards of macadamia (Macadamia integrifolia Maiden & Betche). We identified the pollen parent of macadamia 'cultivar '816' embryos by analysing single nucleotide polymorphisms (SNPs) in their DNA using customised MassARRAY and Single Allele Base Extension Reaction (SABER) methods. This allowed us to determine the proportions of self-fertilised and cross-fertilised progeny during premature fruit drop at 6 weeks and 10 weeks after peak anthesis, as well as at nut maturity. We determined how pollen parentage affected nut-in-shell (NIS) mass, kernel mass, kernel recovery, and oil concentration. Macadamia trees retained cross-fertilised fruitlets rather than self-fertilised fruitlets. The percentage of progeny that were cross-fertilised increased from 6% at 6 weeks after peak anthesis to 97% at nut maturity, with each tree producing on average 22 self-fertilised nuts and 881 cross-fertilised nuts. Three of the four cross-pollen parents provided fruit with significantly higher NIS mass, kernel mass, or kernel recovery than the few remaining self-fertilised fruit. Fruit that were cross-fertilised by '842', 'A4', or 'A203' had 16–29% higher NIS mass and 24–44% higher kernel mass than self-fertilised fruit. Nuts that were cross-fertilised by 'A4' or 'A203' also had 5% or 6% higher kernel recovery, worth approximately $US460–540 more per ton for growers than self-fertilised nuts. The highly selective abscission of self-fertilised fruitlets and the lower nut quality of self-fertilised fruit highlight the critical importance of cross-pollination for macadamia productivity. [ABSTRACT FROM AUTHOR]

Kernel weight is a critical agronomic trait in maize production. Many genes are related to kernel weight but only a few of them have been applied to maize breeding and cultivation. Here, we identify a novel function of maize mitogen-activated protein kinase 6 (ZmMPK6) in the regulation of maize kernel weight. Kernel weight was reduced in zmmpk6 mutants and increased in ZmMPK6 -overexpressing lines. In addition, starch granules, starch content, protein content, and grain-filling characteristics were also affected by the ZmMPK6 expression level. ZmMPK6 is mainly localized in the nucleus and cytoplasm, widely distributed across various tissues, and is expressed during kernel development, which is consistent with its role in kernel weight. Thus, these results provide new insights into the role of ZmMPK6, a mitogen-activated protein kinase, in maize kernel weight, and could be applied to further molecular breeding for kernel quality and yield in maize. [ABSTRACT FROM AUTHOR]