Linear Part Research Articles

Predicting air quality index using attention hybrid deep learning and quantum-inspired particle swarm optimization

Air pollution poses a significant threat to the health of the environment and human well-being. The air quality index (AQI) is an important measure of air pollution that describes the degree of air pollution and its impact on health. Therefore, accurate and reliable prediction of the AQI is critical but challenging due to the non-linearity and stochastic nature of air particles. This research aims to propose an AQI prediction hybrid deep learning model based on the Attention Convolutional Neural Networks (ACNN), Autoregressive Integrated Moving Average (ARIMA), Quantum Particle Swarm Optimization (QPSO)-enhanced-Long Short-Term Memory (LSTM) and XGBoost modelling techniques. Daily air quality data were collected from the official Seoul Air registry for the period 2021 to 2022. The data were first preprocessed through the ARIMA model to capture and fit the linear part of the data and followed by a hybrid deep learning architecture developed in the pretraining–finetuning framework for the non-linear part of the data. This hybrid model first used convolution to extract the deep features of the original air quality data, and then used the QPSO to optimize the hyperparameter for LSTM network for mining the long-terms time series features, and the XGBoost model was adopted to fine-tune the final AQI prediction model. The robustness and reliability of the resulting model were assessed and compared with other widely used models and across meteorological stations. Our proposed model achieves up to 31.13% reduction in MSE, 19.03% reduction in MAE and 2% improvement in R-squared compared to the best appropriate conventional model, indicating a much stronger magnitude of relationships between predicted and actual values. The overall results show that the attentive hybrid deep Quantum inspired Particle Swarm Optimization model is more feasible and efficient in predicting air quality index at both city-wide and station-specific levels.

A novel semi-analytical model for laterally loaded piles

A new model for laterally loaded piles is proposed, consisting of a linear part and a non-linear iterative part. The linear part is based on the Green's function method, which strictly satisfies the displacement and stress continuity conditions at the pile-soil interface and leads to a rigorous solution. The non-linear iterative part assumes that the shear modulus of the soil around the pile decreases with the average strain of the soil layer. Only two soil parameters need to be calibrated, including the initial shear modulus of the soil and the reference shear strain at half the initial modulus. Compared to the finite element model, the advantage of this model is that it converges quickly while maintaining accuracy, which greatly improves computational efficiency. The advantage of this model over the p-y curve model is that it does not have the difficulty of selecting p-y spring parameters, especially for monopiles. The accuracy of this model is verified by comparison with three-dimensional finite element models and nine existing studies, including numerical models, field tests and centrifuge tests. These cases cover various piles with diameters of D∼0.273–10 m and aspect ratios of L/D∼3–40, installed in sand or clay by driving, jacking or vibration.

Temperature Evolution of Composition, Thermal, Electrical and Magnetic Properties of Ti3C2Tx-MXene

MXenes are a family of two-dimensional nanomaterials. Titanium carbide MXene (Ti3C2Tx-MXene), reported in 2011, is the first inorganic compound reported among the MXene family. In the present work, we report on the study of the composition and various physical properties of Ti3C2Tx-MXene nanomaterial, as well as their temperature evolution, to consider MXenes for space applications. X-ray diffraction, thermal analysis and mass spectroscopy measurements confirmed the structure and terminating groups of the MXene surface, revealing a predominant single OH layer character. The temperature dependence of the specific heat shows a Debye-like character in the measured range of 2 K–300 K with a linear part below 10 K, characteristic of conduction electrons of metallic materials. The electron density of states (DOS) calculations for Ti3C2OH-MXene reveal a significant DOS value at the Fermi level, with a large slope, confirming its metallic character, which is consistent with the experimental findings. The temperature dependence of electrical resistivity of the MXene samples was tested for a wide temperature range (3 K–350 K) and shows a decrease on lowering temperature with an upturn at low temperatures, where negative magnetoresistance is observed. The magnetoresistance versus field is approximately linear and increases its magnitude with decreasing temperature. The magnetization curves are straight lines with temperature-independent positive slopes, indicating Pauli paramagnetism due to conduction electrons.

The Role of the Unbinding Cycle on the Coordination Abilities of the Bi-Cyclopeptides toward Cu(II) Ions

Bicyclic peptides have attracted the interest of pharmaceutical companies because of their remarkable properties, putting them on a new path in medicine. Their conformational rigidity improves proteolytic stability and leads to rapid penetration into tissues via any possible route of administration. Moreover, elimination of renal metabolism is of great importance, for example, for people with a history of liver diseases. In addition, each ring can function independently, making bicyclic peptides extremely versatile molecules for further optimization. In this paper, we compared the potentiometric and spectroscopic properties studied by UV–vis, MCD, and EPR of four synthetic analogues of the bi-cyclic peptide c(PKKHP-c(CFWKTC)-PKKH) (BCL). In particular, we correlated the structural and spectral properties of complexes with coordinating abilities toward Cu(II) ions of MCL1 (Ac-PKKHPc(CFWKTC)PKKH-NH2) that contains the unbinding cycle and N- and C-terminal linear parts with two histidine residues, one per part; two monocyclic ligands containing one histidine residue, both in the N-terminal position, i.e., MCL2 (Ac-PKKHPc(CFWKTC)PKKS-NH2) and in the C-terminal position, i.e., MCL3 (Ac-PKKSPc(CFWKTC)PKKH-NH2), respectively; and the linear structure LNL (Ac-PKKHPSFWKTSPKKH-NH2). Potentiometric results have shown that the bicyclic structure promotes the involvement of the side chain imidazole donors in Cu(II) binding. On the other hand, the results obtained for the mono-cyclic analogues lead to the conclusion that the coordination of the histidine moiety as an anchoring group is promoted by its location in the peptide sequence further from the nonbinding cycle, strongly influencing the involvement of the amide donors in Cu(II) coordination.

Dominant subspaces of high-fidelity polynomial structured parametric dynamical systems and model reduction

In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial functions, and the linear part corresponds to a linear structured model, such as second-order, time-delay, or fractional-order systems. Our approach relies on the Volterra series representation of these dynamical systems. Using this representation, we identify the kernels and, thus, the generalized multivariate transfer functions associated with these systems. Consequently, we present results allowing the construction of reduced-order models whose generalized transfer functions interpolate these of the original system at pre-defined frequency points. For efficient calculations, we also need the concept of a symmetric Kronecker product representation of a tensor and derive particular properties of them. Moreover, we propose an algorithm that extracts dominant subspaces from the prescribed interpolation conditions. This allows the construction of reduced-order models that preserve the structure. We also extend these results to parametric systems and a special case (delay in input/output). We demonstrate the efficiency of the proposed method by means of various numerical benchmarks.

Generalization of Balian–Brezin decomposition for exponentials with linear fermionic part

Fermionic Gaussian states have garnered considerable attention due to their intriguing properties, most notably Wick’s theorem. Expanding upon the work of Balian and Brezin, who generalized properties of fermionic Gaussian operators and states, we further extend their findings to incorporate Gaussian operators with a linear component. Leveraging a technique introduced by Colpa, we streamline the analysis and present a comprehensive extension of the Balian–Brezin decomposition to encompass exponentials involving linear terms. Furthermore, we introduce Gaussian states featuring a linear part and derive corresponding overlap formulas. Additionally, we generalize Wick’s theorem to encompass scenarios involving linear terms, facilitating the expression of generic expectation values in relation to one and two-point correlation functions. We also provide a brief commentary on the applicability of the BB decomposition in addressing the BCH (Zassenhaus) formulas within the so(N) Lie algebra.

A New Sub-Class Linear Discriminant for Miniature Spectrometer Based Food Analysis

The well-known and extensively studied Linear Discriminant Analysis (LDA) can have its performance lowered in scenarios where data is not homoscedastic or not Gaussian. That is, the classical assumptions when LDA models are built are not applicable, and consequently LDA projections would not be able to extract the needed features to explain the intrinsic structure of data and for classes to be separated. As with many real word data sets, data obtained using miniature spectrometers can suffer from such drawbacks which would limit the deployment of such technology needed for food analysis. The solution presented in the paper is to divide classes into subclasses and to use means of sub classes, classes, and data in the suggested between classes scatter metric. Further, samples belonging to the same subclass are used to build a measure of within subclass scatterness. Such a solution solves the shortcoming of the classical LDA. The obtained results when using the proposed solution on food data and on general machine learning datasets show that the work in this paper compares well to and is very competitive with similar sub-class LDA algorithms in the literature. An extension to a Hilbert space is also presented; and the kernel version of the presented solution can be fused with its linear counter parts to yield improved classification rates.

High order well-balanced asymptotic preserving IMEX RKDG schemes for the two-dimensional nonlinear shallow water equations

In this paper, a high order well-balanced asymptotic preserving scheme is presented for the two-dimensional nonlinear shallow water equations over variable bottom topography in all Froude number regimes. To obtain the well-balanced property, the system is first reformulated as a new form by introducing an auxiliary parameter. The flux is then split into a linear stiff part to be treated implicitly and a nonlinear non-stiff part to be treated explicitly, and the source term is treated explicitly. An implicit-explicit Runge-Kutta discontinuous Galerkin scheme is designed for solving the equations. The proposed scheme can be proved to be well-balanced, asymptotic preserving and asymptotically accurate. Finally, several numerical tests are carried out to validate the performance of our proposed scheme.

Simultaneous robust model predictive control and state estimation for nonlinear systems with state‐ and input‐dependent uncertainties

AbstractThe convergence and stability of uncertain nonlinear systems is a challenging problem in the nonlinear control area. Besides, in many practical cases, all states are not measurable and are affected by measurement noise. Based on this motivation, the first objective of this paper is to design a novel output feedback robust model predictive control approach for nonlinear systems with state‐ and input‐dependent uncertainties and measurement noise. This approach combines state estimation and robust model predictive control (MPC) into one min–max optimization and by solving the optimization, these two tasks are performed simultaneously. The studied nonlinear system comprises a linear part, a nonlinear part, and a function that denotes the state‐ and input‐dependent uncertainties. Therefore, the other objective is to reduce the computational complexity; thus, the system's nonlinear term and the aforementioned uncertainties are converted into additional disturbances. Subsequently, the optimization problem becomes a quadratic form, which leads to global convergence with the appropriate selection of objective function weights. Besides, this paper explores the convergence of the closed‐loop system states and the sufficient synthesis conditions to guarantee input‐to‐state stability. The implementation on a numerical example and a CSTR process demonstrate the applicability and reliability of the proposed approach.

New Study on the Controllability of Non-Instantaneous Impulsive Hilfer Fractional Neutral Stochastic Evolution Equations with Non-Dense Domain

The purpose of this work is to investigate the controllability of non-instantaneous impulsive (NII) Hilfer fractional (HF) neutral stochastic evolution equations with a non-dense domain. We construct a new set of adequate assumptions for the existence of mild solutions using fractional calculus, semigroup theory, stochastic analysis, and the fixed point theorem. Then, the discussion is driven by some suitable assumptions, including the Hille–Yosida condition without the compactness of the semigroup of the linear part. Finally, we provide examples to illustrate our main result.

Cohomology operations for moment-angle complexes and resolutions of Stanley–Reisner rings

A fundamental result in toric topology identifies the cohomology ring of the moment-angle complex Z K \mathcal {Z}_K associated to a simplicial complex K K with the Koszul homology of the Stanley–Reisner ring of K K . By studying cohomology operations induced by the standard torus action on the moment-angle complex, we extend this to a topological interpretation of the minimal free resolution of the Stanley–Reisner ring. The exterior algebra module structure in cohomology induced by the torus action recovers the linear part of the minimal free resolution, and we show that higher cohomology operations induced by the action (in the sense of Goresky–Kottwitz–MacPherson [Invent. Math. 131 (1998), pp. 25–83]) can be assembled into an explicit differential on the resolution. Describing these operations in terms of Hochster’s formula, we recover and extend a result due to Katthän [Mathematics 7 (2019), no. 7, p. 605]. We then apply all of this to study the equivariant formality of torus actions on moment-angle complexes. For these spaces, we obtain complete algebraic and combinatorial characterisations of which subtori of the naturally acting torus act equivariantly formally.

Effect of Salt Content on Solubilization of Hydrophobic Polymer by Wormlike Micelles of Ionic Surfactant

The effect of concentration of inorganic salt KCl on solubilization of hydrophobic polymer poly(4-vinylpyridine) (P4VP) in aqueous solutions of ionic surfactant potassium oleate was experimentally investigated. As was shown by rheology, in the range of concentrations from 1 to 5 wt.% of salt the polymer-free solutions of surfactant mainly contain linear wormlike micelles (WLMs). The formation of branched WLMs was observed in the solutions containing 5-9 wt.% of KCl. In the presence of higher salt content the phase separation occurred, indicating the formation of a highly branched saturated network of WLMs. Enhanced screening of the charged groups of potassium oleate by oppositely charged ions of KCl caused elongation and branching of micelles that reflected in zero-shear viscosity of the solutions passing through the maximum. In the phase diagram, the saturation concentration with P4VP of both linear and branched WLMs decreased with increasing salt content. In the case of linear WLMs, this could be explained by the constant number of embedded polymer chains per 1 WLM, while simultaneously decreasing number of WLMs in the system. As for the branched WLMs, it was caused by shortening of the linear parts of micelles due to the formation of branching points. For this reason, almost no P4VP was dissolved in the solution containing the highly branched saturated network.

Low-regularity exponential-type integrators for the Zakharov system with rough data in all dimensions

We propose and analyze a type of low-regularity exponential-type integrators (LREIs) for the Zakharov system (ZS) with rough solutions. Our LREIs include a first-order integrator and a second-order one, and they achieve optimal convergence under weaker regularity assumptions on the exact solution compared to the existing numerical methods in literature. Specifically, the first-order integrator exhibits linear convergence in H m + 2 ( T d ) × H m + 1 ( T d ) × H m ( T d ) H^{m+2}(\mathbb {T}^d)\times H^{m+1}(\mathbb {T}^d)\times H^m(\mathbb {T}^d) for solutions in H m + 3 ( T d ) × H m + 2 ( T d ) × H m + 1 ( T d ) H^{m+3}(\mathbb {T}^d)\times H^{m+2}(\mathbb {T}^d)\times H^{m+1}(\mathbb {T}^d) if m > d / 2 m>d/2 , meaning that only the boundedness of one additional derivative of the solution is required to achieve the first-order convergence. While for the second-order integrator, we show that it achieves second-order accuracy by requiring the boundedness of two additional spatial derivatives of the solution. The order of additional derivatives required is reduced by half compared to the classical trigonometric integrators. The main techniques to design the integrators include a reformulation by introducing new variables to exclude the loss of spatial regularity in the original ZS, accurate integration for the dominant term in the linear part of the equations and appropriate approximations (or averaging approximations) to the exponential phase functions involving the nonlinear interactions. Numerical comparisons with classical integrators confirm that our newly proposed LREIs are superior in accuracy and robustness for handling rough data.

Tensile Yield Strain of Human Cortical Bone from the Femoral Diaphysis Is Constant among Healthy Adults and across the Anatomical Quadrants.

The literature suggests that the yield strain of cortical bone is invariant to its stiffness (elastic modulus) and strength (yield stress). However, data about intra-individual variations, e.g., the influence of different collagen/mineral organisations observed in bone aspects withstanding different habitual loads, are lacking. The hypothesis that the yield strain of human cortical bone tissue, retrieved from femoral diaphyseal quadrants subjected to different habitual loads, is invariant was tested. Four flat dumbbell-shaped specimens were machined from each quadrant of the proximal femoral diaphysis of five adult donors for a total of 80 specimens. Two extensometers attached to the narrow specimen region were used to measure deformation during monotonic tensile testing. The elastic modulus (linear part of the stress-strain curve) and yield strain/stress at a 0.2% offset were obtained. Elastic modulus and yield stress values were, respectively, in the range of 12.2-20.5 GPa and 75.9-136.6 MPa and exhibited a positive linear correlation. All yield strain values were in the narrow range of 0.77-0.87%, regardless of the stiffness and strength of the tissue and the anatomical quadrant. In summary, the results corroborate the hypothesis that tensile yield strain in cortical bone is invariant, irrespective also of the anatomical quadrant. The mean yield strain value found in this study is similar to what was reported by inter-species and evolution studies but slightly higher than previous reports in humans, possibly because of the younger age of our subjects. Further investigations are needed to elucidate a possible dependence of yield strain on age.

On fixed-time interlayer synchronization of two-layer multiweighted complex dynamic networks: An economic and practical non-chattering adaptive control approach

This paper investigates the adaptive fixed-time (FxT) interlayer synchronization issue of two-layer complex dynamic networks (CDNs), where both multiple weights and interlayer links are considered. Above all, a new FxT stability lemma is given, which offers a more flexible condition and some more precise estimates of stabilized convergence time compared with the existing results. Subsequently, an economic and practical non-chattering continuous adaptive controller is designed, which is superior to the currently available ones by excluding the signum function and linear part and removing the parity restriction on the exponents in control law. Furthermore, by means of the Lyapunov method and the newly-established FxT stability theory, some novel FxT interlayer synchronization criteria are derived for the addressed two-layer multiweighted CDNs with the designed non-chattering continuous adaptive controller, and the synchronized settling time (SST) is also reckoned. It is found that the interlayer links weights can contribute to the interlayer synchronization, and the SST becomes smaller with the increase of interlayer link weight. Finally, the proposed results are validated by numerical examples.

Random walks on tori and normal numbers in self-similar sets

abstract: We study random walks on a $d$-dimensional torus by affine expanding maps whose linear parts commute. Assuming an irrationality condition on their translation parts, we prove that the Haar measure is the unique stationary measure. We deduce that if $K\subset\mathbb{R}^d$ is an attractor of a finite iterated function system of $n\geq 2$ maps of the form $x\mapsto D^{-1}x+t_i$ ($i=1,\dotsc,n$), where $D$ is an expanding $d\times d$ integer matrix, and is the same for all the maps, under an irrationality condition on the translation parts $t_i$, almost every point in $K$ (w.r.t. any Bernoulli measure) has an equidistributed orbit under the map $x\mapsto Dx$ (multiplication mod $\mathbb{Z}^d$). In the one-dimensional case, this conclusion amounts to normality to base $D$. Thus for example, almost every point in an irrational dilation of the middle-thirds Cantor set is normal to base $3$.

Water quality prediction using ARIMA-SSA-LSTM combination model

Abstract The water quality index model is a popular tool for evaluating drinking water quality. To overcome low precision and significant errors in the traditional single prediction model, a novel autoregressive integrated moving average (ARIMA)-sparrow search algorithm (SSA)-long short-term memory (LSTM) combination model is proposed to accurately predict residual chlorine, turbidity, and pH in drinking water. First, the ARIMA model is used to extract the linear part of water quality data and output the nonlinear residual. Then, the LSTM model is used to predict the residual, and the SSA is used to find the optimal hyperparameters of the LSTM model, which plays an essential role in reducing the error of the model. To prove the superiority of the model developed, the ARIMA-SSA-LSTM model is compared with SSA-LSTM, whale optimization algorithm-LSTM, PSO-LSTM, ARIMA-LSTM, ARIMA, and LSTM. The results show that the coefficient of determination (R2) of the combination model for residual chlorine, turbidity, and pH are 0.950, 0.990, and 0.998, respectively, which are greater than all comparison models. Therefore, the model is more suitable for the prediction and analysis of water quality data.

An adaptive low-rank splitting approach for the extended Fisher–Kolmogorov equation

The extended Fisher–Kolmogorov (EFK) equation has been used to describe some phenomena in physical, material and biological systems. In this paper, we propose a full-rank splitting scheme and a rank-adaptive splitting approach for this equation. We first use a finite difference method to approximate the space derivatives. Then, the resulting semi-discrete system is split into two stiff linear parts and a nonstiff nonlinear part. This leads to our full-rank splitting scheme. The convergence of the proposed scheme is proved rigorously. Based on the frame of the full-rank splitting scheme, we design a rank-adaptive splitting approach for obtaining a low-rank solution of the EFK equation. Numerical examples show that our methods are robust and accurate. They can also preserve the energy dissipation.

Statistical inference for the extended non linear models

In this article, an orthogonality-projection-based estimation method is first employed to study an extended non linear model, which can separately estimate the linear and non linear parts without losing some efficiency and increasing computation burden. To overcome the non robustness of classical least squares methods, we further propose a robust and efficient estimation procedure based on the exponential squares loss function, which is robust against outliers or heavy-tailed errors while asymptotically efficient as the non linear least squares estimation under the normal error case. Under some regularity conditions, the asymptotic properties of the proposed estimators are established. In addition, simulation studies are conducted to examine the finite sample performance of the proposed estimation methods.

Data driven modeling of heavy-duty joint system for DEMO manipulators: An initial study from MPD joint simulation

This study investigates the subspace modeling method in developing surrogate model of a heavy-duty joint system in a muti-purpose deployer. The joint system is constructed in the Matlab SIMULINK Simscape environment, which includes the multibody dynamics with friction models, meshing loss models and viscous models. The input and output data generated in simulation are used to develop the subspace model. The result shows the subspace modeling method can accurately identify the system order and linear part of dynamics in this joint system. The nonlinearity contributed by the gear friction, meshing and viscosity can't be neglected in the surrogate model. Further model augmentation technics are needed to improve the capability of subspace modeling method applying in nonlinear system.