Theoretical Results Research Articles

Global regulation for uncertain feedforward nonlinear systems based on event-triggered impulsive control: a time-varying gain scaling approach

This paper addresses the problem of global regulation for uncertain feedforward nonlinear systems using event-triggered impulsive control. By constructing a state transformation with a time-varying scaling gain, both the state-feedback and output-feedback event-triggered impulsive control strategies are established. It is proven that the proposed impulsive controllers ensure the global regulation of the concerned systems while avoiding the Zeno behaviour. Furthermore, the derived results of this work are generalised to a broader class of uncertain feedforward nonlinear systems incorporating time-varying nonlinearities, as well as to a class of uncertain strict-feedback nonlinear systems. It is noteworthy that this paper is the first attempt to design an impulsive regulating controller for feedforward nonlinear systems. Finally, a simulation example is presented to verify the effectiveness of our theoretical results.

Analysis of the transmission dynamics and effects of containment strategies on the eradication of malaria

A debilitating disease such as malaria has been a global health challenge for a long time. Mathematical models have provided insights on how best to control, prevent, or eradicate the disease. Most of the models used parameters to represent control strategies. The current research aims at using control strategies as disease compartments for both vector control and human-protection. By this, the long-time evolution of containment measures can be assessed. Consequently, a model of nine disease compartments is constructed using first-order ordinary differential equations. A qualitative analysis of the malaria-free equilibrium was carried out. The results indicate that the malaria-free equilibrium state is locally and globally asymptotically stable when R0HV<1, which implies that the disease-free state will always be attained from any initial conditions. A bifurcation analysis also shows that the malaria-endemic and malaria-free equilibria cannot overlap. Numerical simulations show that vector control is more effective in the containment of malaria than human-protection, which confirms the findings of Ross 53 years ago. Numerical results also show that solutions attain a disease-free steady state with time, which agrees with the theoretical results. The implication of the findings is that more attention should be paid to vector control if malaria is to be eradicated.

Regulating the microenvironments and the d-band center of hierarchical NiMoS/TS-1 catalyst by ZrO2 to enhance the hydrodesulfurization performance of dibenzothiophene

The microenvironments including the surface hydroxyls, the oxygen vacancies, and the d-band center of hierarchical TS-1 zeolite pickled by hydrochloric acid were regulated by ZrO2, the effect of ZrO2 on the physicochemical properties and the catalytic performances of the corresponding NiMoS supported catalysts were studied. The experimental and theoretical calculation results show that the d-band center, the surface hydroxyl groups, and the oxygen vacancies were regulated after incorporation of ZrO2. Resulting in the modulated acidity of the support and the metal support interaction of the catalysts, further promoting the formation of type-II NiMoS active phases. The catalytic performance evaluations show that catalyst NiMo/1-ZAT exhibits the superior HDS performance, kinetic study further demonstrated that the enhanced catalytic activity was mainly contributed by the improved direct desulfurization activity generated from the moderate support acidity, suitable MSI, highest sulfidation degrees, most type-II NiMoS active phase and highest activity of individual active sites.

The asymptotic behavior of Riemann solutions for the Aw-Rascle-Zhang traffic flow model with the polytropic and logarithmic combined pressure term

The exact Riemann solutions for a specially designated Aw-Rascle-Zhang traffic flow model are explicitly obtained by using the combination of 1-rarefaction or 1-shock wave with 2-contact discontinuity. The vacuum and delta shock formation is carefully identified and analyzed in the Riemann solutions when both the two perturbed parameters in the combined pressure term drop to zero simultaneously, where the intrinsic cavitation and concentration phenomena are concretely surveyed and explored. Additionally, our theoretical analysis results are also validated through several representative numerical simulations.

Strategic ignorance and procedural fairness preferences

This paper shows that procedural fairness concerns might be a possible explanation for strategic ignorance, that is, that some people avoid information on how their behavior might hurt others. Decision makers with procedural fairness preferences suffer disutility from inequality in ex-ante expected payoffs. Such preferences lead to strategic ignorance if decision makers are in some sense focused on extremes: they generally dislike inequality in expected payoffs, but care little about changes in intermediate inequality. Importantly, this property does not imply a particular curvature of the loss function measuring the suffering from inequality. The theoretical possibility result suggests that more empirical research on strategic ignorance might be warranted.

Mathematical modeling of unemployment dynamics with skills development and cyclical effects

In the present work, a new mathematical model is introduced to investigate the effects of skills development on the governance of cyclical unemployment. A system of non-linear differential equations is formed and analyzed. In the modeling approach, we categorize the considered workforce into three distinct classes: the fundamentally unemployed Us, employed individuals E and cyclically unemployed people Uc. We also make the assumption that some government programs can qualify individuals who have been out of work for a period to reintegrate and prevent them from becoming long-term unemployed. The qualitative analysis of differential equations is used to analyze the proposed model. It has been demonstrated that the suggested model has only one equilibrium that is globally asymptotically stable under particular conditions. The impact of key parameters is analyzed by examining their sensitivity. In order to verify the important theoretical results, numerical illustrations of the model have been performed. The obtained results demonstrate that the development of skills among the cyclically unemployed is effective in reducing unemployment.

Optimizing control efficiency in discrete-time multi-agent systems via event-triggered containment techniques combining disturbance handling and input delay management

The goal of this paper is to mitigate disturbances and input delays while optimizing controller actuation updates for discrete-time multi-agent systems through the use of an event-triggered confinement control system, especially in resource-constrained scenarios. This approach when combined with event-triggered control techniques, then every follower in the system adjusts its condition at specified times based on an event-triggered condition that is suggested. The containment control system issue in the presence of disturbances and input delays was tackled by using both decentralized and centralized event-triggered control systems. Using matrix theory and the Lyapunov technique, convergence analysis is conducted to show that the proposed strategy stays free of zeno phenomena. Numerical boosts are used to further illustrate the impact of theoretical results.

Bulky Alkyl Substituents Enhance the Photocatalytic Activity of Pyridine-Based Donor-Acceptor Molecules in the Direct Reductive Cleavage of the C-Br Bond of Aliphatic Bromides.

We report new pyridine-based donor-acceptor (D-A) molecules that enable the direct reductive transformation of a variety of secondary and tertiary aliphatic bromides. A series of experimental and theoretical results suggested that the D-A molecules promote direct C-Br bond cleavage triggered by the excitation of the complex between the catalyst and the aliphatic bromide and that the alkyl groups significantly contribute to the stabilization of the complex, which improves the efficiency of its excitation.

A novel resistorless memristor emulator circuit and its implementation of chaotic Jerk system

This work presents a novel resistorless memristor emulator circuit designed in both grounded and floating configurations. The grounded memristor consists of a Current-Controlled Current Conveyor Transconductance Amplifier (CC-CCTA) and a capacitor. On the other hand, a floating memristor includes a CC-CCTA and a capacitor, along with an additional Operational Transconductance Amplifier (OTA). These proposed emulators are electronically controllable owing to the internal structures of active elements. Theoretical analysis and simulation results have been obtained for the proposed designs. Simulation results have been conducted utilizing the LTspice program and TSMC 180 nm technology has been used for internal structures. In these results, the effects of the changing capacitor values, different frequencies, electronic tunability, reactions to temperature change, and pulse response have been investigated. Subsequently, a chaotic Jerk circuit has been implemented incorporating the proposed memristor emulator. The chaotic behavior of the floating memristor has been investigated using the LTspice simulation software.

Petal-Shaped Graphene Porous Films with Enhanced Absorption-Dominated Electromagnetic Shielding Performance and Mechanical Properties.

The absorption-dominated graphene porous materials, considered ideal for mitigating electromagnetic pollution, encounter challenges related to intricate structural design. Herein, petal-like graphene porous films with dendritic-like and honeycomb-like pores are prepared by controlling the phase inversion process. The theoretical simulation and experimental results show that PVP K30 modified on the graphene surface via van der Waals interactions promotes graphene to be uniformly enriched on the pore walls. Benefiting from the regulation of graphene distribution and the construction of honeycomb pore structure, when 15 wt % graphene is added, the porous film exhibits absorption-dominated electromagnetic shielding performance, compared with the absence of PVP K30 modification. The total electromagnetic shielding effectiveness is 24.1 dB, an increase of 170%; the electromagnetic reflection coefficient reduces to 2.82 dB; The thermal conductivity reaches 1.1 W/(m K), representing a 104% increase. In addition, the porous film exhibits improved mechanical properties, the tensile strength increases to 6.9 MPa, and the elongation at break increases by 131%. The method adopted in this paper to control the enrichment of graphene in the pore walls during the preparation of honeycomb porous films by the phase inversion method can avoid the agglomeration of graphene and improve the overall performance of the porous graphene porous films.

A restarted large-scale spectral clustering with self-guiding and block diagonal representation

Spectral clustering, a prominent unsupervised machine learning method, involves a critical task of constructing a similarity matrix. In existing approaches, this matrix is either computed once for all or updated alternatively. However, the former struggles to capture comprehensive relationships among data points, and the latter is often impractical for large-scale problems. This study introduces a new clustering framework with self-guidance and a block diagonal representation, retaining valuable information from previous cycles. To our knowledge, this is the first application of such a framework to spectral clustering, with a key distinction being the reclassification of samples in each cycle. To reduce computational overhead, we employ a block diagonal representation with Nyström approximation for constructing the similarity matrix. Theoretical results justify the rationality of approximate computations in spectral clustering. Comprehensive experiments on benchmark datasets demonstrate the superiority of our proposed algorithms over state-of-the-art methods for large-scale clustering. Notably, our framework has the potential to enhance clustering algorithms, performing well even with a randomly chosen initial guess.

Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources

In this paper, we establish the uniqueness of identifying a smooth grating profile with a mixed boundary condition (MBC) or transmission boundary conditions (TBCs) from phaseless data. The existing uniqueness result requires the measured data to be in a bounded domain. To break this restriction, we design an incident system consisting of the superposition of point sources to reduce the measurement data from a bounded domain to a line above the grating profile. We derive reciprocity relations for point sources, diffracted fields, and total fields, respectively. Based on Rayleigh’s expansion and reciprocity relation of the total field, a grating profile with a MBC or TBCs can be uniquely determined from the phaseless total field data. An iterative algorithm is proposed to recover the Fourier modes of grating profiles at a fixed wavenumber. To implement this algorithm, we derive the Fréchet derivative of the total field operator and its adjoint operator. Some numerical examples are presented to verify the correctness of theoretical results and to show the effectiveness of our numerical algorithm.

Spacing distribution for quantum Rabi models * *Dedicated to Mr. Hiromichi Shinohara, who was instrumental in establishing NTT-IFM, on his 70th birthday.

The asymmetric quantum Rabi model (AQRM) is a fundamental model in quantum optics describing the interaction of light and matter. Besides its immediate physical interest, the AQRM possesses an intriguing mathematical structure which is far from being completely understood. In this paper, we focus on the distribution of the level spacing, the difference between consecutive eigenvalues of the AQRM in the limit of high energies, i.e. large quantum numbers. In the symmetric case, that is the quantum Rabi model (QRM), the spacing distribution for each parity (given by the Z2 -symmetry) is fully clarified by an asymptotic expression derived by de Monvel and Zielinski, though some questions remain for the full spectrum spacing. However, in the general AQRM case, there is no parity decomposition for the eigenvalues. In connection with numerically exact studies and recent theoretical results, we describe the spacing distribution for the AQRM which is characterized by a new type of periodicity and symmetric behavior of the distribution with respect to the bias parameter, reflecting the hidden symmetry of the AQRM. In addition, we observe in the AQRM the excited state quantum phase transition for large values of the bias parameter, analogous to the QRM with large qubit energy, and an internal symmetry of the level spacing distribution for fixed bias. This novel symmetry is independent from the symmetry for half-integer bias and not explained by current theoretical knowledge.

On the complexity of a quadratic regularization algorithm for minimizing nonsmooth and nonconvex functions

In this paper, we consider the problem of minimizing the function f ( x ) = g 1 ( x ) + g 2 ( x ) − h ( x ) over R n , where g 1 is a proper and lower semicontinuous function, g 2 is continuously differentiable with a Hölder continuous gradient and h is a convex function that may be nondifferentiable. This problem has important practical applications but is challenging to solve due to the presence of nonconvexities and nonsmoothness. To address this issue, we propose an algorithm based on a proximal gradient method that uses a quadratic approximation of the function g 2 and a nonconvex regularization term. We show that the number of iterations required to reach our stopping criterion is O ( max { ϵ − β + 1 β , η 2 β ϵ − 2 ( β + 1 ) β } ) . Our approach offers a promising strategy for solving this challenging optimization problem and has potential applications in various fields. Numerical examples are provided to illustrate the theoretical results.

LMI-based boundary control of flexible manipulator with external disturbance

In this paper, we address the LMI-based boundary control issue of a flexible manipulator subject to external disturbance. First, the dynamics of the system is characterised by several partial differential equations (PDEs). Second, in order to realise the disturbance rejection, we propose two disturbance observers. Based on these observers, two boundary control protocols are designed via the linear matrix inequality (LMI) method for suppressing elastic vibration and regulating the angle of the joint. A significant feature of LMI is that the control gains can be efficiently solved. Finally, some simulation examples illustrate the effectiveness of the proposed theoretical results.

Beyond the echo chamber: modelling open-mindedness in citizens’ assemblies

A Citizens’ assembly (CA) is a democratic innovation tool where a randomly selected group of citizens deliberate a topic over multiple rounds to generate, and then vote upon, policy recommendations. Despite growing popularity, little work exists on understanding how CA inputs, such as the expert selection process and the mixing method used for discussion groups, affect results. In this work, we model CA deliberation and opinion change as a multi-agent systems problem. We introduce and formalise a set of criteria for evaluating successful CAs using insight from previous CA trials and theoretical results. Although real-world trials meet these criteria, we show that finding a model that does so is non-trivial; through simulations and theoretical arguments, we show that established opinion change models fail at least one of these criteria. We therefore propose an augmented opinion change model with a latent ‘open-mindedness’ variable, which sufficiently captures people’s propensity to change opinion. We show that data from the CA of Scotland indicates a latent variable both exists and resembles the concept of open-mindedness in the literature. We calibrate parameters against real CA data, demonstrating our model’s ecological validity, before running simulations across a range of realistic global parameters, with each simulation satisfying our criteria. Specifically, simulations meet criteria regardless of expert selection, expert ordering, participant extremism, and sub-optimal participant grouping, which has ramifications for optimised algorithmic approaches in the computational CA space.

On the Origin of the Photoplethysmography Signal: Modeling of Volumetric and Aggregation Effects

This study aimed to examine the mechanisms of the photoplethysmography (PPG) signal formation using Monte Carlo simulations of light transport in biological tissues and experimental observations. Based on a three-layer skin model in backscattering geometry, we sequentially simulated volumetric blood changes and the aggregation/disaggregation of erythrocytes in the dermal layer and estimated their contribution to the registered PPG signal. The calculations were conducted for two wavelengths: 525 nm and 810 nm. For green light, absorption predominates over scattering in the formation of a PPG signal, whereas, for near-infrared light, scattering prevails over absorption. This theoretical result was verified using the Modified Beer–Lambert law and clinical in vivo PPG data of seven healthy subjects. Changes in the size of the scatterers during erythrocyte aggregation and disaggregation can significantly contribute to the PPG signal at near-infrared light. Thus, for the green waveband, the classical volumetric model can be considered dominant in the PPG signal formation. In contrast, for the near-infrared range, both volumetric and aggregation effects must be considered as being approximately equal.

Robust Matrix Completion with Heavy-tailed Noise

This paper studies noisy low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries. Though the matrix completion problem has attracted much attention in the past decade, there is still lack of theoretical understanding when the observations are contaminated by heavy-tailed noises. Prior theory falls short of explaining the empirical results and is unable to capture the optimal dependence of the estimation error on the noise level. In this paper, we adopt an adaptive Huber loss to accommodate heavy-tailed noise, which is robust against large and possibly asymmetric errors when the parameter in the Huber loss function is carefully designed to balance the Huberization biases and robustness to outliers. Then, we propose an efficient nonconvex algorithm via a balanced low-rank Burer-Monteiro matrix factorization and gradient descent with robust spectral initialization. We prove that under merely a bounded second-moment condition on the error distributions, rather than the sub-Gaussian assumption, the Euclidean errors of the iterates generated by the proposed algorithm decrease geometrically fast until achieving a minimax-optimal statistical estimation error, which has the same order as that in the sub-Gaussian case. The key technique behind this significant advancement is a powerful leave-one-out analysis framework. The theoretical results are corroborated by our numerical studies.

Spectral splitting phenomenon caused by strong coupling of surface plasmon polariton mode and epsilon-near-zero mode

The strong coupling effect plays an important role in optimizing the optical properties of nano-photonics and improves the efficiency of manipulating light. However, coupling systems for nano-photonic devices usually have problems with complex structure, large size and low coupling strength. To address these issues, we design a nanograting structure to realize the strong coupling between the surface plasmon polariton mode and the epsilon-near-zero mode. The reflection spectra of the designed nanostructure show obvious Rabi splitting phenomenon. The Rabi splitting phenomenon is further verified by the theoretical result. In addition, the factors influencing the coupling effect strength in the nanostructure are analyzed. The proposed nanostructure can be used in nano-photonic devices such as sensors.

Three Dimensions of Cultivating New Generations: Value Implication, Scientific Connotation, and Cultivation Path

The new generation of the times is the latest requirement for young people in the new era, and it is the latest training goal for young people put forward by the Party and the country in the face of the second centennial goal. At the 19th National Congress, it was put forward by the country that the concept of “new generation of the times” for the first time, indicating the training direction and theoretical guidance for the new generation of the times. The new age requires young people to have firm ideals and beliefs, excellent skills, and a great spirit of responsibility. The proposition of cultivating a new generation of the times is a deep exploration and summary of Marx’s theory of “all-round human development,” Lenin’s youth view and the education view of excellent traditional Chinese culture, and the proposition needs to strengthen the leadership of the Party, give play to the leading role of socialist core values, and the youth themselves should actively act to realize the transformation of theoretical and practical results.