Linear Part Research Articles

Differences in non-linearities determine retinal cell types.

Classifying neurons in different types is still an open challenge. In the retina, recent works have taken advantage of the ability to record a large number of cells to classify ganglion cells into different types based on functional information. While the first attempts in this direction used the receptive field properties of each cell to classify them, more recent approaches have proposed to cluster ganglion cells directly based on their response to standard stimuli. These two approaches have not been compared directly. Here we recorded the responses of a large number of ganglion cells and compared two methods for classifying them into types, one based on the receptive field properties, and the other one using their responses to standard stimuli. We show that the stimulus-based approach allows separating more types than the receptive field-based method, leading to a better classification. This better granularity is due to the fact that the stimulus-based method takes into account not only the linear part of ganglion cell function, but also non-linearities. A careful characterization of non-linear processing is thus key to allow functional classification of sensory neurons.

Translation of Monoclonal Antibodies Pharmacokinetics from Animal to Human Using Physiologically Based Modeling in Open Systems Pharmacology (OSP) Suite: A Retrospective Analysis of Bevacizumab.

Interspecies translation of monoclonal antibodies (mAbs) pharmacokinetics (PK) in presence of target-mediated drug disposition (TMDD) is particularly challenging. Incorporation of TMDD in physiologically based PK (PBPK) modeling is recent and needs to be consolidated and generalized to provide better prediction of TMDD regarding inter-species translation during preclinical and clinical development steps of mAbs. The objective of this study was to develop a generic PBPK translational approach for mAbs using the open-source software (PK-Sim® and Mobi®). The translation of bevacizumab based on data in non-human primates (NHP), healthy volunteers (HV), and cancer patients was used as a case example for model demonstration purpose. A PBPK model for bevacizumab concentration-time data was developed using data from literature and the Open Systems Pharmacology (OSP) Suite version 10. PK-sim® was used to build the linear part of bevacizumab PK (mainly FcRn-mediated), whereas MoBi® was used to develop the target-mediated part. The model was first developed for NHP and used for a priori PK prediction in HV. Then, the refined model obtained in HV was used for a priori prediction in cancer patients. A priori predictions were within 2-fold prediction error (predicted/observed) for both area under the concentration-time curve (AUC) and maximum concentration (Cmax) and all the predicted concentrations were within 2-fold average fold error (AFE) and average absolute fold error (AAFE). Sensitivity analysis showed that FcRn-mediated distribution and elimination processes must be accounted for at all mAb concentration levels, whereas the lower the mAb concentration, the more significant the target-mediated elimination. This project is the first step to generalize the full PBPK translational approach in Model-Informed Drug Development (MIDD) of mAbs using OSP Suite.

Estimation and variable selection of quantile partially linear additive models for correlated data

Longitudinal data arise frequently in many economic studies and epidemiological research. In this paper, we investigate the partially linear additive model for longitudinal data in the framework of quantile regression. To incorporate the within-subject correlation, we develop an estimation procedure using quadratic inference function (QIF) and polynomial spline approximation for unknown nonparametric functions. The theoretical properties of the resulting estimators are established, where the nonparametric functions achieve the optimal convergence rate and the parametric components are asymptotically normal even when the number of parameters in the linear part is diverging. We also propose a variable selection procedure based on penalization. Since the objective function is discontinuous, a practical estimation procedure is proposed using induced smoothing and we prove that the smoothed estimator is asymptotically equivalent to the original estimator. The proposed methods are evaluated via simulation studies and a real data application.

Invariant curves of quasi-periodic reversible mappings and its application

We consider the existence of invariant curves of real analytic reversible mappings which are quasi-periodic in the angle variables. By the normal form theorem, we prove that under some assumptions, the original mapping is changed into its linear part via an analytic convergent transformation, so that invariants curves are obtained. In the iterative process, by solving the modified homological equations, we ensure that the transformed mapping is still reversible. As an application, we investigate the invariant curves of a class of nonlinear resonant oscillators, with the Birkhoff constants of the corresponding Poincaré mapping all zeros or not.

RETRACTED ARTICLE: Graph Neural Network on Psychological Prediction of College Students Special Education.

With the closer life rhythm of college students and closer contact with social life, these aspects may increase the pressure of college students' life. Some students have not experienced professional psychological counseling, which will cause extreme psychological stress. When faced with a variety of everyday life demands such as study, love and friendship, job, and future career design, college students should have an optimistic, positive, and courageous mentality. Most of the problems of mental health are the result of college students' excessive stress, trivial family life events and other social factors. In this paper, a spatiotemporal graph neural network college student psychological prediction model for information augmentation transmission is proposed and an information augmentation transmission mechanism is designed to capture the complex dependencies of data. The adaptive graph learning structure can dynamically learn the dependencies between nodes and the enhanced information transmission mechanism can increase the area of information transmission to capture richer spatial information and select the effective information through the attention mechanism, and eliminate the invalid information; and design a data linear and nonlinear fusion mechanism, the mechanism includes linear and nonlinear parts, the two parts capture the linear and nonlinear characteristics of the data, and then Fusion.

IDENTIFICATION OF SEPARATION CURVES OF STRONGLY CONTRASTING ENVIRONMENTS USING COMPLEX ANALYSIS METHODS

When modeling mass transfer processes (for example, filtration) in porous media, there may be cases of the existence of highly permeable layers, which are separated from the corresponding studied parts by some curves that must be found (identified) in the process of solving the problem. When constructing a mathematical model of the corresponding physical process, we will consider a highly permeable medium as "ideally (theoretically infinitely) permeable." In this case, the desired curve can be considered an equipotential line. This work considers the stationary process of fluid movement in a homogeneous horizontal layer of infinitely large dimensions - a soil massif, which is limited by infinite sections of curves, in particular by the desired curve of theoretical water resistance and the horizontal axis, on which the local speed of movement is known. On the basis of the methods of conformal reflections and total images, an approach to the identification of the curve of the separation of media is proposed. The constructed algorithm is modified for solving nonlinear inverse boundary value problems on quasi-conformal mappings of curvilinear polygonal regions bounded by uncertain streamlines and equipotential lines. The feature of the method proposed is that the summary representation formulae allow to explicitly write the solution to the localized linear (main) part of the obtained system of equations. The unknown coefficients are determined here by solving a non-linear system generated solely by the boundary conditions and numerical analogues of the Cauchy–Riemann equations.

Integrable Cases of the Polynomial Liénard-type Equation with Resonance in the Linear Part

Integrable Cases of the Polynomial Liénard-type Equation with Resonance in the Linear Part

High performance of solid electrolyte endowed by SiO2 cross-linking agent towards lithium metal battery

A dual network solid polymer electrolyte is prepared, the cross-linked part is constructed using ring-opening polymerization reaction, in which SiO2 particles connect with polyethylene glycol diglycidyl ether (PEGDE) and polyetheramine (PEA) as cross-linking point. The introduction of SiO2 is conducive to reduce the crystallization of polymer matrix, improve the strength and promote the fast migration of Li ions. The abundant C-O segments in PEGDE and PEA are advantageous to the hopping behavior of Li ions and improve the ionic conductivity of electrolyte. Poly (vinylidenefluoride-hexaflouropropylene) (PVDF-HFP) is selected as linear part due to its robust mechanical behavior and outstanding electrochemical property. The obtained SiO2 functionalized PEGDE and PEA-PVDF-HFP solid polymer electrolyte (referred to as SGPP-ASPE) demonstrates excellent ionic conductivity of 2.4 × 10−4 S cm−1, high lithium-ion transference number of 0.54 and minor interfacial polarization of 0.09 V after 1000 h using Li//Li symmetrical cell. After assembling Li/LiFePO4 cell, a favorable cycling stability with the capacity retention of 93.8% after 100 cycles at 0.2 C is delivered. The reasonable design of advanced polymer electrolytes with dual network opens up a new path for the development of solid high-performance LMBs.

Absolute stability of a class of nonlinear systems with nonpositive linear parts

Absolute stability of a class of nonlinear systems with nonpositive linear parts

AUTOMATED PIPELINE INSPECTION USING UNMANNED AERIAL VEHICLES

Monitoring the condition of pipelines and site facilities of the oil and gas trunk transportation system, as well as other facilities of the oil and gas complex, allows you to collect the necessary information quickly, getting into hard-to-reach places where land transport or a person cannot get to, and reduce the response time to emergency situations and eliminate their consequences.
 The paper considers the existing designs of unmanned aerial vehicles used in systems for remote monitoring of technological facilities, analyzes their advantages and disadvantages while inspecting the linear part of the trunk pipeline. Two variants for automated platforms placing along the route for taking off and recharging unmanned aerial vehicles are proposed. The first variant allows more thorough inspection while flying around, the second one allows using fewer platforms and longer inspection area.

Air-quality prediction based on the ARIMA-CNN-LSTM combination model optimized by dung beetle optimizer

Air pollution is a serious problem that affects economic development and people’s health, so an efficient and accurate air quality prediction model would help to manage the air pollution problem. In this paper, we build a combined model to accurately predict the AQI based on real AQI data from four cities. First, we use an ARIMA model to fit the linear part of the data and a CNN-LSTM model to fit the non-linear part of the data to avoid the problem of blinding in the CNN-LSTM hyperparameter setting. Then, to avoid the blinding dilemma in the CNN-LSTM hyperparameter setting, we use the Dung Beetle Optimizer algorithm to find the hyperparameters of the CNN-LSTM model, determine the optimal hyperparameters, and check the accuracy of the model. Finally, we compare the proposed model with nine other widely used models. The experimental results show that the model proposed in this paper outperforms the comparison models in terms of root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2). The RMSE values for the four cities were 7.594, 14.94, 7.841 and 5.496; the MAE values were 5.285, 10.839, 5.12 and 3.77; and the R2 values were 0.989, 0.962, 0.953 and 0.953 respectively.

Uniformly valid inference for partially linear high-dimensional single-index models

Uniformly valid inference is obtained for the linear part of a partially linear single-index model with a high-dimensional variable in the single-index part of the model. The linear model part consists of a fixed and limited number of variables, while the control variables in the single-index might consist of a large number of variables that is allowed to grow with the sample size and potentially exceeds the sample size. The unknown function in the nonlinear model part is estimated via B-splines in combination with a ℓ1-regularization to take the high dimensionality into account. We establish uniformly valid inferential properties for the parameters in the linear model part under imperfect selection of the control variables. The numerical results showcase the method’s behavior in practice.

The hunt for the Kármán ‘constant’ revisited

The log law of the wall, joining the inner, near-wall mean velocity profile (MVP) in wall-bounded turbulent flows to the outer region, has been a permanent fixture of turbulence research for over hundred years, but there is still no general agreement on the value of the prefactor, the inverse of the Kármán ‘constant’ $\kappa$ , or on its universality. The choice diagnostic tool to locate logarithmic parts of the MVP is to look for regions where the indicator function $\varXi$ (equal to the wall-normal coordinate $y^+$ times the mean velocity derivative $\mathrm {d} U^+/\mathrm {d} y^+$ ) is constant. In pressure-driven flows, however, such as channel and pipe flows, $\varXi$ is significantly affected by a term proportional to the wall-normal coordinate, of order $O({Re}_{\tau }^{-1})$ in the inner expansion, but moving up across the overlap to the leading $O(1)$ in the outer expansion. Here we show that, due to this linear overlap term, ${Re}_{\tau }$ values well beyond $10^5$ are required to produce one decade of near constant $\varXi$ in channels and pipes. The problem is resolved by considering the common part of the inner asymptotic expansion carried to $O({Re}_{\tau }^{-1})$ , and the leading order of the outer expansion. This common part contains a superposition of the log law and a linear term $S_0 \,y^+{Re}_{\tau }^{-1}$ , and corresponds to the linear part of $\varXi$ , which, in channel and pipe, is concealed up to $y^+ \approx 500\unicode{x2013}1000$ by terms of the inner expansion. A new and robust method is devised to simultaneously determine $\kappa$ and $S_0$ in pressure-driven flows at currently accessible ${Re}_{\tau }$ values, yielding $\kappa$ values which are consistent with the $\kappa$ values deduced from the Reynolds number dependence of centreline velocities. A comparison with the zero-pressure-gradient turbulent boundary layer, further clarifies the issues and improves our understanding.

Center conditions to find certain degenerate centers with characteristic directions

We consider the two-dimensional autonomous systems of differential equations where the origin is a monodromic degenerate singular point, i.e., with null linear part. In this work we give two heuristic procedures to obtain some center conditions (perhaps not necessary) for certain degenerate centers at the origin although they have characteristic directions.

Exponential control design on fixed-time synchronization of fully quaternion-valued memristive delayed neural networks without decomposition

This article mainly explores fixed-time (FXT) synchronization of fully quaternion-valued memristive neural networks (QVMNNs) with generalized delays. Firstly, based on the set-valued mapping theory and the nonsmooth approach, the discontinuity of quaternion-valued memristive connection weights is successfully solved. Next, by introducing the signum function, absolute-like norm and quadratic norm in the quaternion field, a direct non-decomposing method is put forward. Under this framework, several exponential-type controllers are designed, which have only one exponential term and no longer contain the traditional linear part and the power-law terms. Compared with designing four real-value controllers, the control schemes proposed in this article are simpler in form. Besides, several criteria of FXT synchronization and the upper bound of the setting time are deduced based on Lyapunov method and Taylor expansion. Lastly, the achieved synchronization results are confirmed via numerical examples.

Parameterized shadowing for nonautonomous dynamics

For nonautonomous and nonlinear differential and difference equations depending on a parameter, we formulate sufficient conditions under which they exhibit Ck, k∈N shadowing with respect to a parameter. Our results are applicable to situations when the linear part is not hyperbolic. In the case when the linear part is hyperbolic, we obtain results dealing with parameterized Hyers-Ulam stability.

Existence results on nonautonomous partial functional differential equations with state-dependent infinite delay

The aim of this work is to establish the existence of mild solutions for some nondensely nonau-tonomous partial functional differential equations with state-dependent infinite delay in Banachspace. We assume that, the linear part is not necessarily densely defined and generates an evolution family under the hyperbolique conditions. We use the classic Shauder Fixed Point Theorem, the Nonlinear Alternative Leray-Schauder Fixed Point Theorem and the theory of evolution family, we show the existence of mild solutions. Secondly, we obtain the existence of mild solution in a maximal interval using Banach’s Fixed Point Theorem which may blow up at the finite time, weshow that this solution depends continuously on the initial data under the global Lipschitz condition on the second argument of F and we get the existence of global mild solution. We proposesome model arising in dynamic population for the application of our results.

Local Solvability, Blow-Up, and Hölder Regularity of Solutions to Some Cauchy Problems for Nonlinear Plasma Wave Equations: III. Cauchy Problems

Three Cauchy problems for Sobolev-type equations with a common linear part from the theory of ion acoustic and drift waves in a plasma are considered. The problems are reduced to equivalent integral equations. We prove the existence of unextendable solutions for two problems and the existence of a local-in-time solution for the third problem. For one of the problems, by applying a modified method of Kh.A. Levin, sufficient conditions for finite time blow-up of solutions are obtained and an upper bound for the solution blow-up time is found. For another problem, S.I. Pohozaev’s nonlinear capacity method is used to obtain a finite time blow-up result and two results concerning the nonexistence of even local solutions, and an upper bound for the solution blow-up time is obtained as well.

Mathematical Models for the Integrity Control of the Linear Parts of Gas Mains

Mathematical Models for the Integrity Control of the Linear Parts of Gas Mains

A radio-jet-driven outflow in the Seyfert 2 galaxy NGC 2110?

We present a spatially resolved study of the ionized gas in the central 2 kpc of the Seyfert 2 galaxy NGC 2110 and investigate the role of its moderate-luminosity radio jet (kinetic radio power of Pjet = 2.3 × 1043 erg s−1). We used new optical integral-field observations taken with the MEGARA spectrograph at the Gran Telescopio Canarias, which cover the 4300 − 5200 Å and 6100 − 7300 Å ranges with a spectral resolution of R ≃ 5000 − 5900. We fitted the emission lines with a maximum of two Gaussian components, except at the position of the active galactic nucleus (AGN), where we used three. Aided by existing stellar kinematics, we used the observed velocity and velocity dispersion (σ) of the emission lines to classify the different kinematic components. The disk component is characterized by lines with σ ≃ 60 − 200 km s−1. The outflow component has typical values of σ ≃ 700 km s−1 and is confined to the central 2.5″ ≃ 400 pc, which is coincident with the linear part of the radio jet detected in NGC 2110. At the AGN position, the [O III]λ5007 line shows high velocity components that reach at least 1000 km s−1. This and the high velocity dispersions indicate the presence of outflowing gas outside the galaxy plane. Spatially resolved diagnostic diagrams reveal mostly low ionization (nuclear) emitting region-like excitation in the outflow and some regions in the disk, which could be due to the presence of shocks. However, there is also Seyfert-like excitation beyond the bending of the radio jet, which probably traces the edge of the ionization cone that intercepts with the disk of the galaxy. NGC 2110 follows the observational trends between the outflow properties and the jet radio power found for a few nearby Seyfert galaxies. All these pieces of information suggest that part of the observed ionized outflow in NGC 2110 might be driven by the radio jet. However, the radio jet was bent at radial distances of ∼200 pc (in projection) from the AGN, and beyond there, most of the gas in the galaxy disk is rotating.