Functional Analysis Techniques Research Articles

Reliability Analysis and Numerical Simulation of the Five-Robot System with Early Warning Function

The rapid advancement of robotic technologies has demonstrated the significant potential of Multi-Robot Systems (MRS) for application across various fields, particularly in automation, manufacturing, and rescue operations. However, enhancing the reliability of Multi-Robot Systems, particularly in critical applications, has emerged as a primary focus of research. A mathematical model of a five-robot system, equipped with early warning capabilities, is developed using Markov process theory and the supplementary variable method in this paper. A model of an abstract Cauchy problem system is developed, employing semigroup theory to investigate the well-posedness of solutions for this five-robot system. The stability of the system is verified using analytical methods, confinal correlation theory, and modern functional analysis techniques. Several key reliability indicators are presented using the eigenvector method. Numerical simulations and comparative methods effectively demonstrate the efficacy of the proposed eigenvector method. Firstly, the innovation of this paper lies in the combination of qualitative and quantitative analyses to improve and enrich the theory and methods of repairable systems. Secondly, mathematical analysis methods and the mathematical software are employed to provide both analytical and numerical solutions for the system.

Middle-throughput LC-MS-based platelet proteomics with minute sample amounts using semi-automated positive pressure FASP in 384-well format (PF384).

Comprehensive characterization of platelets requires various functional assays and analysis techniques, including omics-disciplines, each requiring an individual aliquot of a given sample. Consequently, the sample material per assay is often highly limited rendering downscaling a prerequisite for effective sample exploitation. Here we present a transfer of our recently introduced 96-well-based proteomics workflow (PF96) into the 384-well format (PF384) allowing for a significant increase in sensitivity when processing minute platelet protein amounts. In addition, the 4-fold higher throughput (1500 samples per lab worker per week) allows to easily meet the throughput capacities of modern LC-MS instruments. We determined optimal sample loads followed by highlighting the strengths in comparison to our previous sample preparation approach by processing only 3 µg of purified platelet protein from 22 healthy donors. Major advantages are: (I) improved identification and analyte recovery, especially of low copy number proteins, with signal intensity gains of +130 % and +107 % (peptide and protein level, respectively) (II) substantial intensity gains for key-players in platelet activation including the membrane receptors PAR4, P2X1, GPVI, GPV, GPIX and the downstream mediators AKT, PKA, Rap1, Lyn (III) improved reproducibility with a reduction of technical variance from 22 / 25 % down to 16 / 19 % for detection of lower / higher abundant disease markers and (IV) a 4-fold increase in sample preparation throughput. Taken together, these advantages render PF384 a promising future in clinical proteomics and might pave the way of platelet proteomics with minute sample amounts into molecular diagnostics.

The construction conditions of a Hilbert-type local fractional integral operator and the norm of the operator

<p>The parameterized local fractional singular integral operator $ \mathit{ T}^{(\tau)} $ is defined on the space $ L_p^{\tau\mu}(\mathbb{R}_+^\tau) $ as $ \mathit{T}^{(\tau)}: L_p^{\tau \mu}(\mathbb{R}_+^\tau)\rightarrow L_p^{\tau\nu(1-p)}(\mathbb{R}_+^\tau) $, $ \mathit{T} ^{(\tau)}(f_\tau)(y) = \, _0\mathscr{Y}_{+\infty}^{(\tau)}\Big[\frac{ |x-y|^{\tau\alpha}}{(x+y)^{\tau\beta}}f_\tau(x)\Big], y\in\mathbb{R}_+ $. By employing the weight function method and analysis techniques on the fractal real line number set $ \mathbb{R}_+^\tau $, a general Hilbert-type local fractional integral inequality has been established, thereby demonstrating the boundedness of the defined integral operator. Through optimization of parameters, it was determined that the necessary and sufficient condition for the constant factor in this general Hilbert-type local fractional inequality to be the best possible is that the power parameters $ \sigma $ and $ \sigma_1 $ satisfy $ \sigma+\sigma_1 = \beta-\alpha $. Consequently, the formula for calculating the operator norm has been derived.</p>

Molecular dynamic studies of gold nanoparticles in a dental material TEGDMA.

In the context of biomaterials, triethylene glycol dimethacrylate (TEGDMA) is a widely used monomer in dental resins due to its favorable mechanical properties and ease of polymerization. However, improving its structural stability and enhancing its performance in biological applications remain crucial goals. This study examines the impact of incorporating gold (Au) nanoparticles into the TEGDMA matrix, focusing on their potential to improve mechanical, thermal, and optical properties for biomedical applications. Gold is known for its bio-compatibility, antimicrobial properties, and ability to improve material conductivity, making it an attractive addition for dental and tissue engineering composites. By introducing Au nanoparticles at varying concentrations (0%, 3%, 4%, and 5%), this research aims to optimize TEGDMA's performance in medical grade materials, particularly in dental composites where enhanced strength and durability are vital. Molecular dynamics (MD) simulations were employed to investigate the structural, thermal, and mechanical properties of TEGDMA with varying concentrations of Au nanoparticles. LAMMPS software was used to compute cohesive energy, surface tension, viscosity, and mechanical moduli. Quantum chemical calculations were conducted using Gaussian and RDKit to optimize the molecular structure and obtain electronic properties, including UV-Vis and IR spectra. Phonon spectra and lattice energy were analyzed to evaluate the vibrational properties and thermal stability of the Au-doped TEGDMA matrix. The results were benchmarked against experimental data, offering a comprehensive computational analysis of the impact of Au nanoparticles on the material's performance. Functional data analysis techniques were applied to correlate nanoparticle concentration with the computed properties.

Optimal control analysis in a reaction-diffusion SIRC model with cross-immune class

In this paper, we propose a reaction-diffusion SIRC model with cross-immunization. The model includes the implementation of vaccination measures for susceptible, and treatment and quarantine measures for infected in order to control the spread of the disease. The optimal control strategies for the spread of disease are mainly investigated. Our research focuses on four main aspects. Firstly, we prove the existence and uniqueness of the global positive strong solution to the control system by employing the theories of semigroups of operators. Secondly, we demonstrate the existence of optimal control through the utilization of functional analysis techniques. Thirdly, we establish the first-order necessary optimality conditions that the optimal control must satisfy, employing the methods of convex perturbation. Lastly, we provide numerical examples and simulations to verify the feasibility of optimal control.

Short and medium range order in the rapidly solidified metallic liquid Ta: Atomic packing, connection modes, and pressure effect

In this study, molecular dynamics (MD) simulations were utilized to explore the Short and Medium-Range Order (MRO) in the rapidly solidified metallic liquid tantalum (Ta). Radial distribution function (RDF) and Voronoi tessellation analysis (VTA) techniques were employed to thoroughly explore the effect of pressure on the connectivity and structural properties at the Short-Range Order (SRO) and MRO levels. Our findings indicate that, at a quenching rate of 1013 K s-1, glassy states are achieved at or below 20 GPa, while crystalline phases emerge at 25 GPa. VTA analysis indicates a significant alteration in the local structure of glassy Ta with increasing pressure. Specifically, the fraction of icosahedral-like clusters decreases while the fraction of crystal-like clusters rises notably.Furthermore, we highlight that icosahedral-like clusters strongly tend to form 3-atom connection mode, while crystal-like clusters prefer 2-atom and 4-atom connection modes. Notably, icosahedral-like clusters are identified as the primary contributors to the emergence of the left sub-peak in the second peak of the RDF. In contrast, all cluster types contribute to the appearance of the right sub-peak.

Identification and validation of autophagy-related genes and exploration of their relationship with disease severity in chronic rhinosinusitis with nasal polyps.

Chronic rhinosinusitis with nasal polyps (CRSwNP) pathogenesis might be impacted by autophagy. Nevertheless, autophagy-related gene utilization as a disease indicator about the course of CRSwNP has yet to be elucidated. This investigation aimed at discovering pivotal molecules related to autophagy to identify potential treatment targets for CRSwNP. The dataset GSE136825 was obtained via the Gene Expression Omnibus (GEO) database, and afterward, differentially expressed genes (DEGs) analysis linked to autophagy was employed via the R software. A comprehensive examination of autophagy-related DEGs was conducted using functional analytic techniques. The utilization of the protein-protein interaction (PPI) network facilitated hub gene identification. Quantitative real-time polymerase chain reaction (qRT-PCR), western blot, and immunohistochemistry staining techniques were performed to validate the expression levels of the central genes in clinical samples. Correlation analysis was performed to examine the correlation between hub genes and disease severity parameters. A comprehensive set of 86 autophagy-related DEGs were discovered. The functional enrichment analysis of autophagy-related DEGs revealed the identification of enrichment terms involved with the autophagy process. The results obtained from the PPI analysis suggest that there was interaction among the autophagy-related genes. The qRT-PCR, immunohistochemistry staining, and western blot techniques yielded results, demonstrated that CXCR4, HMOX1, and SPP1 expression levels in CRSwNP agreed with the bioinformatics analysis of the dataset. Furthermore, a favorable association between CXCR4, HMOX1, and SPP1 expression levels with illness severity indicators was found. Bioinformatics analysis yielded 86 autophagy-related DEGs in CRSwNP. CXCR4, HMOX1, and SPP1 regulation of autophagy has been confirmed in CRSwNP progression and pathogenesis.

Application of data element mapping and analysis for system definition to enable model‐based systems engineering

AbstractIn the connected age of the model‐based enterprise and model‐based systems engineering (MBSE), new systems engineering tools are needed to move from a functional, document‐centric, hierarchical view of data and information to the individual units of data or data element level view. Data element mapping and analysis (DEMA) is a technology‐agnostic analytical methodology that combines traditional functional analysis techniques, systems engineering elicitation practices, and novel data mapping techniques to provide a holistic view of a system's data and information flows at the individual units of data (data element level). In this research, DEMA was utilized to enable an enhanced system definition for the development of a verification and validation process as applied to a modeling and simulation environment. DEMA uncovered and visually mapped the hidden flow of approximately 1600 data vessel occurrences as inputs or outputs to 79 functional activities in 23 disparate storage locations. The results reveal that DEMA is a practical tool for both improving existing systems and defining new systems. The data element level view captured by DEMA can be used to define the interconnections between the system elements that are input to systems modeling language (SysML) models. Therefore, DEMA is a necessary and novel tool that can be used to enable system digitalization.

Multimodal functional deep learning for multiomics data.

With rapidly evolving high-throughput technologies and consistently decreasing costs, collecting multimodal omics data in large-scale studies has become feasible. Although studying multiomics provides a new comprehensive approach in understanding the complex biological mechanisms of human diseases, the high dimensionality of omics data and the complexity of the interactions among various omics levels in contributing to disease phenotypes present tremendous analytical challenges. There is a great need of novel analytical methods to address these challenges and to facilitate multiomics analyses. In this paper, we propose a multimodal functional deep learning (MFDL) method for the analysis of high-dimensional multiomics data. The MFDL method models the complex relationships between multiomics variants and disease phenotypes through the hierarchical structure of deep neural networks and handles high-dimensional omics data using the functional data analysis technique. Furthermore, MFDL leverages the structure of the multimodal model to capture interactions between different types of omics data. Through simulation studies and real-data applications, we demonstrate the advantages of MFDL in terms of prediction accuracy and its robustness to the high dimensionality and noise within the data.

Detecting Alzheimer’s Patients using Features in Differential Waveforms of Pupil Light Reflex for Chromatic Stimuli

A procedure to detect irregular signal responses to pupil light reflex (PLR) was developed to detect Alzheimer’s Disease (AD) using a functional data analysis (FDA) technique and classification with an Elastic Net. In considering the differences in features of PLRs between AD and normal control (NC) participants, signals of summations and differentials between experimental conditions were analysed. The coefficient vectors for B-spline basis functions were introduced, and the number of basis was controlled for an optimised model. Model trained data was created using a data extension technique in order to enhance the number of participant observations. In the results, the required number of basis functions for differential signals is larger than the number for the their summation signals, and the features of differential signals contribute to classification performance.

Existence, Uniqueness, and Stability of a Nonlinear Tripled Fractional Order Differential System

This manuscript investigates the existence, uniqueness, and different forms of Ulam stability for a system of three coupled differential equations involving the Riemann–Liouville (RL) fractional operator. The Leray–Schauder alternative is employed to confirm the existence of solutions, while the Banach contraction principle is used to establish their uniqueness. Stability conditions are derived utilizing classical nonlinear functional analysis techniques. Theoretical findings are illustrated with an example. The proposed system generalizes third-order ordinary differential equations (ODEs) with different boundary conditions (BCs).

A Novel Construction of the g-Riesz Decomposition in Hilbert Spaces

The concept of the g-frame, a generalized frame in Hilbert spaces, has garnered attention in recent research. While numerous properties of g-frames have been explored, certain aspects remain unexamined, including a novel construction approach for the g-Riesz decomposition in Hilbert spaces. While prior works such as [12] presented the equivalence conditions for g-Riesz decomposition and Khosravi [10] proposed a new construction method for g-frames, neither addressed a new construction method for g-Riesz decomposition. This paper aims to fill this gap by investigating a novel construction method for the specialized g-frame-g-Riesz decomposition. Leveraging operator theory from generalized functional analysis and function space techniques in complex Hilbert spaces, we establish necessary and sufficient conditions for constructing g-Riesz decompositions, an area insufficiently explored by Khosravi and [12]. Furthermore, we introduce two annotations and provide proofs demonstrating that g-Riesz bases are equivalent to Riesz bases, aligning with the findings of W.C. Sun in [6]. This underscores the significance of our research. The newly proposed g-Riesz decomposition not only contributes to mathematical inquiry but also holds promise for various applications, particularly in signal and image processing.

Establishing a fluorescence-based technique for ABC transporters functional analysis in metabolism of insecticides in a Lepidopteron

The insecticide resistance development poses challenges to the pest control effectiveness. As phase III detoxification enzyme, ATP-binding cassette (ABC) transporters play a crucial role in conferring resistance by facilitating the elimination of insecticides. However, the precise involvement of ABCs in insecticides metabolism remains unclear. In this study, a competitive assay utilizing microinjection of the ABC substrate Texas Red (TR) was established in Lepidoptera for the first time to investigate the contribution of ABCs to the detoxification process of Cydia pomonella towards lambda-cyhalothrin (LCT) and abamectin (ABM). Results revealed that the elimination of TR was hindered by ABC inhibitor verapamil, LCT, or a combination of both, implying a shared subsets of ABCs involved in the transportation of TR and LCT. Moreover, the application of ABM alone led to marked inhibition of TR elimination, with verapamil not further exacerbating this inhibitory effect, indicating that ABM exhibited a highly competitive ABC substrate characteristic and has a strong interaction with them. Furthermore, silencing key resistance associated ABC genes through RNAi resulted in increased mortality of larvae under LCT or ABM exposure, affecting TR elimination and ATP hydrolysis. These findings imply that ABC genes are critical for the active transport function of ABCs energized by ATP, ultimately reducing larvae tolerance to insecticides. In conclusion, our findings not only validated the feasibility of a competitive bioassay using fluorescent ABC substrate in lepidopteran larvae but also highlighted that ABCs in enhancing the efflux capacity of C. pomonella larvae, facilitating the binding and transportation of insecticides and their metabolites.

Quantum Boltzmann machines: Clifford algebras and asymptotic analysis

We analyze mathematical aspects related to general quantum Boltzmann machine models through representations of algebras and functional analytic techniques. In this context, based on algebraic formulation we show the existence of a symmetry group for a class of Hamiltonians based on generators of Clifford algebras and discuss its implications for the learning scheme. Also, we have developed a rigorous mathematical analysis that allows us to investigate issues related to the asymptotic behavior of quantum Boltzmann machines. Particularly, we obtain a lower bound of fidelity in terms of the upper limit of quantum relative entropy.

Estimation of rice yield using multivariate analysis techniques based on meteorological parameters

This study aims to develop predictive models for rice yield by applying multivariate techniques. It utilizes stepwise multiple regression, discriminant function analysis and logistic regression techniques to forecast crop yield in specific districts of Haryana. The time series data on rice crop have been divided into two and three classes based on crop yield. The yearly time series data of rice yield from 1980–81 to 2020–21 have been taken from various issues of Statistical s of Haryana. The study also utilized fortnightly meteorological data sourced from the Agrometeorology Department of CCS HAU, India. For comparing various predictive models' performance, evaluation of measures like Root Mean Square Error, Predicted Error Sum of Squares, Mean Absolute Deviation and Mean Absolute Percentage Error have been used. Results of the study indicated that discriminant function analysis emerged as the most effective to predict the rice yield accurately as compared to logistic regression. Importantly, the research highlighted that the optimum time for forecasting the rice yield is 1 month prior to the crops harvesting, offering valuable insight for agricultural planning and decision-making. This approach demonstrates the fusion of weather data and advanced statistical techniques, showcasing the potential for more precise and informed agricultural practices.

APPLICATION OF VALUE ENGINEERING IN ARCHITECTURAL WORK ON THE LAHAIROI LATERI CHURCH, AMBON CITY

Effective construction cost control such as saving construction costs will increase the chances of project success and user satisfaction. The biggest component in construction costs is material. High material costs necessitate a review of building functions. Construction savings are made by reviewing the largest cost components in architectural work. Review of material components is carried out using the value engineering method. Value engineering is a method for getting an alternative picture so that the costs incurred are more efficient than the initial planning costs. The application of value engineering to construction projects has a major impact on planning by generating reviews to obtain cost effectiveness. Research was conducted at the Lahairoi Lateri Church Building project located in Ambon City. The aim of this research is to find alternative material substitutes for architectural work and obtain total cost savings by using the concept of value engineering. The use of the value engineering concept is carried out by information phase, analyzing the function of using index function analysis techniques, identifying alternative materials, and evaluating the results of the alternative materials. Research using the value engineering concept on the Lahairoi Lateri Church Building Construction project, Ambon City achieved cost savings of 861,116,841.05 IDR. This amount saves 5.32% of the initial architectural work costs of 16,170,539,500 IDR. These results show that value engineering can eliminate unnecessary costs in church-type building without changing the building function.

Compact convergence, deformation of the $L^{2}$-$\overline{\partial}$-complex and canonical $K$-homology classes

Let (X,\gamma) be a compact, irreducible Hermitian complex space of complex dimension m and with \dim(\mathrm{sing}(X))=0 . Let (F,\tau)\rightarrow X be a Hermitian holomorphic vector bundle over X , and let us denote by \overline{\eth}_{F,m,\mathrm{abs}} the rolled-up operator of the maximal L^{2} - \overline{\partial} -complex of F -valued (m,\bullet) -forms. Let \pi:M\rightarrow X be a resolution of singularities, g a metric on M , E:=\pi^{*}F and \rho:=\pi^{*}\tau . In this paper, under quite general assumptions on \tau , we prove the following equality of analytic K -homology classes [\overline{\eth}_{F,m,\mathrm{abs}}]=\pi_{*}[\overline{\eth}_{E,m}] , with \overline{\eth}_{E,m} the rolled-up operator of the L^{2} - \overline{\partial} -complex of E -valued (m,\bullet) -forms on M . Our proof is based on functional analytic techniques developed in Kuwae and Shioya (2003) and provides an explicit homotopy between the even unbounded Fredholm modules induced by \overline{\eth}_{F,m,\mathrm{abs}} and \overline{\eth}_{E,m} .

Synchronization of delayed stochastic reaction–diffusion Hopfield neural networks via sliding mode control

Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.

Equilibrium analysis in game theory using nonlinear functional analysis techniques

Game theory provides a mathematical framework for analyzing the tactical choices of rational decision makers. The idea of equilibrium, which states that no player has a motivation to change their existing approach given the strategies of other players, is one of the core ideas of game theory. This study examines a type of undirected graph-based distributed quadratic game. The problem of communication topology constraints is presented and nonlinear dynamics with uncertain time-dependent perturbations are present in the participant's dynamics. Based on a high-gain observer approach, a distributed Nash equilibrium (NE) finding technique is given, and the Lyapunov stability theory is used to study the convergence. It represents that every player approximates the positions of their rival players and that there are differences between the NE and the placements of the minor limitation that finally restricts the players. In addition, chattering problems are eliminated since the offered theory's formulation employs the hyperbolic tangent function to control the perturbation rather than the signum function. In an imitation of the oligopoly match, five enterprises manufacture identical materials in a duopoly market framework; this is done to confirm the effectiveness of the recommended strategy. Our results provide novel perspectives and methods for understanding complicated strategic situations, helping to close the gap between mathematical theory and real-world applications.

Exploring the dynamic microbial tapestry of South Asian rivers: insights from the Ganges and Yamuna ecosystems

AbstractThis review meticulously examines the dynamics of river microbiomes, with an emphasis on the Ganges and Yamuna rivers of South Asia. These rivers are vital for both ecological and cultural landscapes and offer to understand the interaction between ecological and anthropogenic factors and their impact on microbial communities and activities. Ecological and hydrological factors such as seasonal changes, water flow and physico‐chemical properties of rivers influence microbial diversity and abundance. The effect of heavy metals from industrial and agricultural sources on the river microbiome and how these pollutants modify microbial community structures and ecosystem health are not understood well yet. This underscores the need for sustainable water treatment and remediations for practical engineering solutions. The study reveals how these interactions, whether symbiotic or competitive, affect the composition and functionality of riverine microbial communities. An innovative aspect of our research is the potential of river microbiomes as indicators of urban sewage contamination. We demonstrate how microbial patterns can signal pollution levels, proving valuable for environmental monitoring, management and mitigation. A special attention to the role of microbes in river ecosystems' biogeochemical cycles has been paid to how these microbes contribute to nutrient recycling, organic matter decomposition and overall ecosystem productivity, underlining their crucial role in maintaining the aesthetic value of the river. Additionally, study evaluates the latest methodologies for analysing microbiome metagenomic data, including functional annotation and microbial community analysis techniques. Findings highlight the key importance of understanding river microbiomes for hydrology, ecology and microbiology researchers.