Space Variables Research Articles

A Singular Tempered Sub-Diffusion Fractional Model Involving a Non-Symmetrically Quasi-Homogeneous Operator

In this paper, we focus on the existence of positive solutions for a singular tempered sub-diffusion fractional model involving a quasi-homogeneous nonlinear operator. By using the spectrum theory and computing the fixed point index, some new sufficient conditions for the existence of positive solutions are derived. It is worth pointing out that the nonlinearity of the equation contains a tempered fractional sub-diffusion term, and is allowed to possess strong singularities in time and space variables. In particular, the quasi-homogeneous operator is a nonlinear and non-symmetrical operator.

Chemoinformatic regression methods and their applicability domain.

The growing interest in chemoinformatic model uncertainty calls for a summary of the most widely used regression techniques and how to estimate their reliability. Regression models learn a mapping from the space of explanatory variables to the space of continuous output values. Among other limitations, the predictive performance of the model is restricted by the training data used for model fitting. Identification of unusual objects by outlier detection methods can improve model performance. Additionally, proper model evaluation necessitates defining the limitations of the model, often called the applicability domain. Comparable to certain classifiers, some regression techniques come with built-in methods or augmentations to quantify their (un)certainty, while others rely on generic procedures. The theoretical background of their working principles and how to deduce specific and general definitions for their domain of applicability shall be explained.

Revealing the Effect of Stereocontrol on Intermolecular Interactions between Abiotic, Sequence-Defined Polyurethanes and a Ligand.

The development of precision polymer synthesis has facilitated access to a diverse library of abiotic structures wherein chiral monomers are positioned at specific locations within macromolecular chains. These structures are anticipated to exhibit folding characteristics similar to those of biotic macromolecules and possess comparable functionalities. However, the extensive sequence space and numerous variables make selecting a sequence with the desired function challenging. Therefore, revealing sequence-function dependencies and developing practical tools are necessary to analyze their conformations and molecular interactions. In this study, we investigate the effect of stereochemistry, which dictates the spatial location of backbone and pendant groups, on the interaction between sequence-defined oligourethanes and bisphenol A ligands. Various methods are explored to analyze the receptor-like properties of model oligomers and the ligand. The accuracy of molecular dynamics simulations and experimental techniques is assessed to uncover the impact of discrete changes in stereochemical arrangements on the structures of the resulting complexes and their binding strengths. Detailed computational investigations providing atomistic details show that the formed complexes demonstrate significant structural diversity depending on the sequence of stereocenters, thus affecting the oligomer-ligand binding strength. Among the tested techniques, the fluorescence spectroscopy data, fitted to the Stern-Volmer equation, are consistently aligned with the calculations, thus validating the developed simulation methodology. The developed methodology opens a way to engineer the structure of sequence-defined oligomers with receptor-like functionality to explore their practical applications, e.g., as sensory materials.

A retrospective view on non-linear methods in chemometrics, and future directions

This perspective article reviews how the chemometrics community approached non-linear methods in the early years. In addition to the basic chemometric methods, some methods that fall under the term “machine learning” are also mentioned. Thereafter, types of non-linearity are briefly presented, followed by discussions on important aspects of modeling related to non-linear data. Lastly, a simulated data set with non-linear properties is analyzed for quantitative prediction and batch monitoring. The conclusion is that the latent variable methods to a large extent handle non-linearities by adding more linear combinations of the original variables. Nevertheless, with strong non-linearities between the X and Y space, non-linear methods such as Support Vector Machines might improve prediction performance at the cost of interpretability into both the sample and variable space. Applying multiple local models can improve performance compared to a single global model, of both linear and non-linear nature. When non-linear methods are applied, the need for conservative model validation is even more important. Another approach is pre-processing of the data which can make the data more linear before the actual modeling and prediction phase.

On Weighted Cauchy-Type Problem of Riemann-Liouville Fractional Differential Equations in Lebesgue Spaces with Variable Exponent

This paper aims to investigate the existence, uniqueness, and stability properties for a class of fractional weighted Cauchy-type problem in the variable exponent Lebesgue space $L^{p(.)}$. The obtained results are set up by employing generalized intervals and piece-wise constant functions so that the $L^{p(.)}$ is transformed into the classical Lebesgue spaces. Moreover, the usual Banach Contraction Principle is utilized, and the Ulam-Hyers (UH) stability is studied. At the final stage, we provide an example to support the accuracy of the obtained results.

Splines finite element solver for one-dimensional time-dependent Maxwell's equations via Fourier Transform Discretization

In this article, we solve the time-dependent Maxwell coupled equations in their one-dimensional version relatively to space-variable. We effectuate a variable reduction via Fourier transform to make the time variable as a frequency parameter easy and quickly to manage. A Galerkin variational method based on higher-order spline interpolations is used to approximate the solution relatively to the spacial variable. So, the state of existence of the solution, its uniqueness, and its regularity are studied and proved, and the study is also provided by an error estimate and the order of convergence of the proposed method. Also, we use the critical Nyquist frequency to calculate numerically the solution of the Inverse Fourier Transform(IFT); and for all numerical computations, we consider several quadrature methods. Finally, we give some experiments to illustrate the success of such an approach.

Multiple Solutions for a Class of Biharmonic Nonlocal Elliptic Systems

We prove the existence of three distinct solutions for a biharmonic nonlocal elliptic system with singular terms under the Navier boundary conditions, by using variational methods and the theory of the variable exponent Sobolev space.

Unified Roadmap for ZIF-8 Nucleation and Growth: Machine Learning Analysis of Synthetic Variables and Their Impact on Particle Size and Morphology.

Metal-organic frameworks (MOFs) have settled in the scientific community over the last decades as versatile materials with several applications. Among those, zeolitic imidazolate framework 8 (ZIF-8) is a well-known MOF that has been applied in various and diverse fields, from drug-delivery platforms to microelectronics. However, the complex role played by the reaction parameters in controlling the size and morphology of ZIF-8 particles is still not fully understood. Even further, many individual reports propose different nucleation and growth mechanisms for ZIF-8, thus creating a fragmented view for the behavior of the system. To provide a unified view, we have generated a comprehensive data set of synthetic conditions and their final outputs and applied machine learning techniques to analyze the data. Our approach has enabled us to identify the nucleation and growth mechanisms operating for ZIF-8 in a given sub-space of synthetic variables space (chemical space) and to reveal their impact on important features such as final particle size and morphology. By doing so, we draw connections and establish a hierarchy for the role of each synthetic variable and provide with rule of thumb for attaining control on the final particle size. Our results provide a unified roadmap for the nucleation and growth mechanisms of ZIF-8 in agreement with mainstream reported trends, which can guide the rational design of ZIF-8 particles which ultimately determine their suitability for any given targeted application. Altogether, our work represents a step forward in seeking control of the properties of MOFs through a deeper understanding of the rationale behind the synthesis procedures employed for their synthesis.

Assessing downscaling methods to simulate hydrologically relevant weather scenarios from a global atmospheric reanalysis: case study of the upper Rhône River (1902–2009)

Abstract. We assess the ability of two modelling chains to reproduce, over the last century (1902–2009) and from large-scale atmospheric information only, the temporal variations in river discharges, low-flow sequences and flood events observed at different locations of the upper Rhône River catchment, an alpine river straddling France and Switzerland (10 900 km2). The two modelling chains are made up of a downscaling model, either statistical (Sequential Constructive Atmospheric Analogues for Multivariate weather Predictions – SCAMP) or dynamical (Modèle Atmosphérique Régional – MAR), and the Glacier and SnowMelt SOil CONTribution (GSM-SOCONT) model. Both downscaling models, forced by atmospheric information from the global atmospheric reanalysis ERA-20C, provide time series of daily scenarios of precipitation and temperature used as inputs to the hydrological model. With hydrological regimes ranging from highly glaciated ones in its upper part to mixed ones dominated by snow and rain downstream, the upper Rhône River catchment is ideal for evaluating the different downscaling models in contrasting and demanding hydro-meteorological configurations where the interplay between weather variables in both space and time is determinant. Whatever the river sub-basin considered, the simulated discharges are in good agreement with the reference ones, provided that the weather scenarios are bias-corrected. The observed multi-scale variations in discharges (daily, seasonal, and interannual) are reproduced well. The low-frequency hydrological situations, such as annual monthly discharge minima (used as low-flow proxy indicators) and annual daily discharge maxima (used as flood proxy indicators), are reproduced reasonably well. The observed increase in flood activity over the last century is also reproduced rather well. The observed low-flow activity is conversely overestimated, and its variations from one sub-period to another are only partially reproduced. Bias correction is crucial for both precipitation and temperature and for both downscaling models. For the dynamical one, a bias correction is also essential for getting realistic daily temperature lapse rates. Uncorrected scenarios lead to irrelevant hydrological simulations, especially for the sub-basins at high elevation, due mainly to irrelevant snowpack dynamic simulations. The simulations also highlight the difficulty in simulating precipitation dependency on elevation over mountainous areas.

Existence of Solutions for p(x)-Laplacian Elliptic BVPs on a Variable Sobolev Space Via Fixed Point Theorems

In this paper, we prove some existence theorems for elliptic boundary value problems within the p(x)-Laplacian on a variable Sobolev space. For this purpose, the main problem is transformed into a fixed point problem and then fixed point arguments such as Schaefer’s and Schauder’s theorems are used. Our approach involves fewer stringent assumptions on the nonlinearity function than the prior findings. An interesting example is presented to examine the validity of the theoretical findings.

On Numerical Simulations of Variable-Order Fractional Cable Equation Arising in Neuronal Dynamics

In recent years, various complex systems and real-world phenomena have been shown to include memory and hereditary properties that change with respect to time, space, or other variables. Consequently, fractional partial differential equations containing variable-order fractional operators have been extensively resorted for modeling such phenomena accurately. In this paper, we consider the two-dimensional fractional cable equation with the Caputo variable-order fractional derivative in the time direction, which is preferable for describing neuronal dynamics in biological systems. A point-wise scheme, namely, the Crank–Nicolson finite difference method, along with a group-wise scheme referred to as the explicit decoupled group method are proposed to solve the problem under consideration. The stability and convergence analyses of the numerical schemes are provided with complete details. To demonstrate the validity of the proposed methods, numerical simulations with results represented in tabular and graphical forms are given. A quantitative analysis based on the CPU timing, iteration counting, and maximum absolute error indicates that the explicit decoupled group method is more efficient than the Crank–Nicolson finite difference scheme for solving the variable-order fractional equation.

Law-invariant return and star-shaped risk measures

This paper presents novel characterization results for classes of law-invariant star-shaped functionals. We begin by establishing characterizations for positively homogeneous and star-shaped functionals that exhibit second- or convex-order stochastic dominance consistency. Building on these characterizations, we proceed to derive Kusuoka-type representations for these functionals, shedding light on their mathematical structure and intimate connections to Value-at-Risk and Expected Shortfall. Furthermore, we offer representations of general law-invariant star-shaped functionals as robustifications of Value-at-Risk. Notably, our results are versatile, accommodating settings that may, or may not, involve monotonicity and/or cash-additivity. All of these characterizations are developed within a general locally convex topological space of random variables, ensuring the broad applicability of our results in various financial, insurance and probabilistic contexts.

Real-time prediction of fuel consumption and emissions based on deep autoencoding support vector regression for cylinder pressure-based feedback control of marine diesel engines

Predictive models serving as virtual sensors for online optimization and feedback control of diesel engines is gaining increasing attention. However, existing prediction models fall short in simultaneously achieving high prediction accuracy and fast computational speed. In this paper, a novel machine learning algorithm called deep autoencoding support vector regression (DASVR) was proposed, which combines the powerful non-linear feature extraction capability of artificial neural network (ANN) with the good adaptability of support vector regression (SVR) to low-dimensional input spaces. ANN-based autoencoder is firstly employed to extract features from the original high-dimensional input space, forming a low-dimensional latent variable space. SVR is then employed to perform non-linear mapping between latent variables and target output variables. Experiments were conducted on a 16-cylinder marine diesel engine under different load, rail pressure, and injection timing conditions. Prediction models for fuel consumption, NOx, PM, HC, and PM emissions were established based on experimental data and DASVR algorithm. The maximum error of DASVR-based models for the five desired output variables is less than 3.8 % under different operating conditions. DAVSR-based predictive models outperform conventional ANN-based and SVR-based models in terms of both prediction accuracy and real-time capability, and can theoretically meet the real-time requirement below 3000 r/min.

Hyperspectral and Fluorescence Imaging Approaches for Nondestructive Detection of Rice Chlorophyll.

Estimating and monitoring chlorophyll content is a critical step in crop spectral image analysis. The quick, non-destructive assessment of chlorophyll content in rice leaves can optimize nitrogen fertilization, benefit the environment and economy, and improve rice production management and quality. In this research, spectral analysis of rice leaves is performed using hyperspectral and fluorescence spectroscopy for the detection of chlorophyll content in rice leaves. This study generated ninety experimental spectral datasets by collecting rice leaf samples from a farm in Sichuan Province, China. By implementing a feature extraction algorithm, this study compresses redundant spectral bands and subsequently constructs machine learning models to reveal latent correlations among the extracted features. The prediction capabilities of six feature extraction methods and four machine learning algorithms in two types of spectral data are examined, and an accurate method of predicting chlorophyll concentration in rice leaves was devised. The IVSO-IVISSA (Iteratively Variable Subset Optimization-Interval Variable Iterative Space Shrinkage Approach) quadratic feature combination approach, based on fluorescence spectrum data, has the best prediction performance among the CNN+LSTM (Convolutional Neural Network Long Short-Term Memory) algorithms, with corresponding RMSE-Train (Root Mean Squared Error), RMSE-Test, and RPD (Ratio of standard deviation of the validation set to standard error of prediction) indexes of 0.26, 0.29, and 2.64, respectively. We demonstrated in this study that hyperspectral and fluorescence spectroscopy, when analyzed with feature extraction and machine learning methods, provide a new avenue for rapid and non-destructive crop health monitoring, which is critical to the advancement of smart and precision agriculture.

Laser induced spark ignition of a gaseous methane–oxygen model rocket combustor

The spatio-temporal evolution of laser induced spark ignition of non-premixed gaseous methane and oxygen is investigated. The reactants are injected into an optically accessible combustion chamber from an oxidizer centered shear-coaxial injector. High-speed schlieren imaging and measurements of laser energy deposited are used to characterize ignition behavior at various spark locations throughout the chamber. A spatial map of ignition probability is generated from tests at multiple axial and radial locations from the point of propellant injection. The rate of pressure rise from successful tests reveals two modes of ignition dependent on the location of the laser-induced breakdown, direct and indirect, based on laser-induced breakdown occurring within reactant jet or in the recirculation region, respectively. Physical processes occurring over multiple timescales throughout the direct ignition method are first discussed. Ignition outcomes associated with the indirect method are determined by the hydrodynamic ejection protruding from the laser spark, the behavior of which is explored in detail using flow statistics extracted from images taken at a single spark location. The spatial–temporal progression of this jet is found to be dependent on deposited laser energy, leading to a relationship between the amount of energy added to the flow and ignition outcome. General bounds for spark location, deposited laser energy, and ejection behavior are identified to predict ignition outcomes. Cases that are an exception from these bounds are investigated in detail to understand the cause of unique behavior. These cases lie within regions of the variable space that are susceptible to stochastic elements of the flow.Novelty and Significance Statement: This work investigates laser induced spark ignition of O2 and CH4 issuing from a shear-coaxial injector in a model rocket combustor. Probability of ignition as a function of deposited energy and spatial location is studied with high-speed schlieren imaging and pressure measurements. Two distinct ignition modes that have previously not been identified, direct and indirect, are dependent on the laser deposition location with respect to the reactant jet. For indirect cases, where laser deposition is at a distance from the reactants, the hydrodynamic jet ejection generated from the breakdown of the plasma plays a critical role on ignition probability. The behavior of the ejection jet is characterized to provide a phenomenological description of the ignition process. The results of this research show the important interaction between chemical, fluid dynamic, and thermodynamic processes and their impact on laser ignition.

Noise as an Extrinsic Variable in the Animal Research Facility.

Animal research facilities are noisy environments. The high air change rates required in animal housing spaces tend to create higher noise levels from the heating and cooling systems. Housing rooms are typically constructed of hard wall material that is easily cleaned but simultaneously highly reverberant, meaning that the sound cannot be controlled/attenuated so the sounds that are generated bounce around the room uncontrolled. (Soft, sound-absorbing surfaces generally cannot be used in animal facilities because they collect microbes; various wall surface features and sound control panel options are available, although rarely used.) In addition, many of our husbandry tasks such as cage changing, animal health checks, cleaning, and transporting animals produce high levels of noise. Finally, much of the equipment we have increasingly employed in animal housing spaces, such as ventilated caging motors, biosafety, or procedure cabinets, can generate high levels of background noise, including ultrasound. These and many additional factors conspire to create an acoustic environment that is neither naturalistic nor conducive to a stress-free environment. The acoustic variability both within and between institutions can serve as an enormous confounder for research studies and a threat to our ability to reproduce studies over time and between research laboratories. By gaining a better appreciation for the acoustic variables, paired with transparency in reporting the levels, we might be able to gain a better understanding of their impacts and thereby gain some level of control over such acoustic variables in the animal housing space. The result of this could improve both animal welfare and study reproducibility, helping to address our 3Rs goals of Replacement, Reduction, and Refinement in the animal biomedical research enterprise.

A time-fuel hybrid optimal guidance for micro/nano satellite’s glideslope approach

Aimed at the trajectory planning problem of micro/nano satellites’ approaching missions under multiple constraints, this paper proposes a V-bar glideslope maneuver optimization method considering both time and fuel consumption. A dual-objective trajectory optimization model is established based on the CW motion equation, considering the constraints of trajectory and impulse. The optimal solution set of the glideslope point position and maneuvering time is obtained by employing the NSGA2 algorithm. In order to reduce computational complexity, a method for simplifying trajectory optimization is proposed. By solving a constrained dual-impulse optimization problem, the feasible range of distance and transfer time between adjacent glideslope points are obtained, which transforms the constraint equations of the glideslope maneuver optimization into the search space of optimization variables. The problem is simplified to an unconstrained optimization problem. Finally, a simulation is conducted with the approaching mission of a typical micro/nano satellite. The results demonstrate that the proposed method can provide an optimal solution set considering both fuel and time consumption, offering a flexible maneuver planning strategy for on-orbit application.

Variable Hybrid Action Space Deep Q-Networks for Optimal Power Allocation and User Association in Heterogeneous Networks

Variable Hybrid Action Space Deep Q-Networks for Optimal Power Allocation and User Association in Heterogeneous Networks

Complex symmetry in the Fock space of several variables

In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex symmetric with respect to a concrete conjugation. Using this characterization, we study complex symmetric semigroups and their generators. We realize such generators as first-order differential operators.

Effect of spatial setting angle on vibration of elastically restrained rotating beams

For a fully articulated rotor system, there may exist a spatial setting angle and elastically restrained root for each individual blade in rotation procedure due to flapping, drag and pitch hinges. Most of previous studies on rotating blades or beams focused on pitch angle and clamped root. In this paper, a three-dimensional dynamic model is proposed for elastically restrained rotating beams with spatial setting angle. The elastic deformation of the beam is expressed by three scalar variables in three-dimensional space including stretch deformation instead of the conventional axial deformation. The longitudinal shrinkage is considered to capture centrifugal forces. The penalty method is adopted to deal with the elastic constraints, which greatly simplifies the construction of admissible functions. A unified formulation is derived by a variational principle combined with Chebyshev orthogonal polynomials. One of the advantages of the present method is that any linearly independent and complete basis functions can be used as admissible function regardless of boundary conditions, and another advantage is that the present method is capable of handling arbitrary boundary conditions by only adjusting the values of penalty factor. The convergence and accuracy of the present method are validated by comparison, and the effects of boundary conditions, angular velocity and spatial setting angle on vibration characteristics are discussed in detail. The results show that natural frequencies increase as the spring stiffness rises in a certain range and the spatial setting angle plays a more significant role on dynamic characteristics for rotating beams.