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This paper proposes a new geometric fault detection and isolation (FDI) strategy for uncertain neutral time-delay systems (UNTDS). Firstly, the concept of unobservability subspace is extended to the considered system. Subsequently, utilizing the geometric properties of factor space and canonical projection, the fault is divided into different unobservability subspaces. Therefore, an algorithm for constructing the subspace is developed for fault isolation. Finally, a set of observers is designed for the subsystems, and generates a set of structured residuals which is sensitive only to a specific fault. Additionally, the H∞ technique is utilized to suppress the disturbances and error signals due to time-varying delays on the residual. The simulation examples verify the effectiveness of the proposed approach.

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In the context of this investigation, we introduce an innovative mathematical model designed to elucidate the intricate dynamics underlying the transmission of Anthroponotic Cutaneous Leishmania. This model offers a comprehensive exploration of the qualitative characteristics associated with the transmission process. Employing the next-generation method, we deduce the threshold value $ R_0 $ for this model. We rigorously explore both local and global stability conditions in the disease-free scenario, contingent upon $ R_0 $ being less than unity. Furthermore, we elucidate the global stability at the disease-free equilibrium point by leveraging the Castillo-Chavez method. In contrast, at the endemic equilibrium point, we establish conditions for local and global stability, when $ R_0 $ exceeds unity. To achieve global stability at the endemic equilibrium, we employ a geometric approach, a Lyapunov theory extension, incorporating a secondary additive compound matrix. Additionally, we conduct sensitivity analysis to assess the impact of various parameters on the threshold number. Employing center manifold theory, we delve into bifurcation analysis. Estimation of parameter values is carried out using least squares curve fitting techniques. Finally, we present a comprehensive discussion with graphical representation of key parameters in the concluding section of the paper.

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In this paper, we propose the application of a new geometric procedure in order to calculate a set of transmission zeros of a propagation environment. Since the transmission zeros play a crucial role in modern communication systems, there is a need to apply the efficient solutions characterized by a maximum speed operation. It turns out that the classical method based on the Smith-McMillan factorization is time-consuming, so its contribution to the detection of transmission zeros could be unsatisfactory. Therefore, in order to fill the gap, we present a new algorithm strictly dedicated to the multivariable telecommunications systems described by the transfer-function approach. Consequently, a set of new achievements resulted, particularly in terms of computational efforts. Indeed, the proposed procedure allows us to overcome obstacles derived from technological limitations. The representative simulation examples confirm the great potential of this new method. Finally, it has been pointed out that the newly introduced geometric-originated approach has significantly reduced the computational burden. Indeed, for the randomly selected matrix of the 5×5 dimension describing the sensor-related propagation environment, two representative scenarios were performed in order to manifest the crucial properties. In the first scenario, the sets of multiple transmission zeros were analyzed, ultimately leading to intriguing results. The Smith-McMillan solution took three times longer to discover the mentioned sets. On the other hand, the second instance brought us the same result. Naturally, the discussed difference has increased as a function of the number of matrix elements. For the square matrices involving 100 components, we have observed the respective differences, both over QI=100 and QII=60. It should be emphasized that the finding derived from the Smith-McMillan factorization corresponds to the geometric-related approach in the context of some mechanisms. This is particularly visible when appointing the greatest common divisors.

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This paper presents a geometric approach for real-time forward kinematics of the general Stewart platform, which consists of two rigid bodies connected by six general serial manipulators. By describing the rigid-body motion as exponential of twist, and taking advantage of the product of exponentials formula, a step-by-step derivation of the proposed algorithm is presented. As the algorithm naturally solves all passive joint displacements, the correctness is then verified by comparing the forward-kinematic solutions from all chains. The convergence ability and robustness of the proposed algorithm are demonstrated with large amounts of numerical simulations. In all test cases, the proposed algorithm terminates within four iterations, converging with near-quadratic speed. Finally, the proposed algorithm is also implemented on a mainstream embedded motion controller. Compared with the incremental method, the proposed algorithm is more robust, with an average execution time of 0.48 ms, meeting the requirements of most applications, such as kinematic calibration, motion simulation, and real-time control.

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This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20-43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of Cai and Li (AMM 33:2919-2926, 2009) are effectively solved. The corresponding optimal control system with vaccination, awareness campaigns and treatment is further established and four different control strategies are compared by numerical simulations to contain hepatitis B. It is concluded that joint implementation of these measures can minimize the numbers of exposed and infectious individuals in the shortest time, so it is the most efficient strategy to curb the hepatitis B epidemic. Moreover, vaccination for newborns plays the core role and maintains the high level of population immunity.

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Super-substantivalism (of the type we'll consider) roughly comprises two core tenets: (1) the physical properties which we attribute to matter (e.g. charge or mass) can be attributed to spacetime directly, with no need for matter as an extraneous carrier "on top of" spacetime; (2) spacetime is more fundamental than (ontologically prior to) matter. In the present paper, we revisit a recent argument in favour of super-substantivalism, based on General Relativity. A critique is offered that highlights the difference between (various accounts of) fundamentality and (various forms of) ontological dependence. This affords a metaphysically more perspicuous view of what super-substantivalism's tenets actually assert, and how it may be defended. We tentatively propose a re-formulation of the original argument that not only seems to apply to all classical physics, but also chimes with a standard interpretation of spacetime theories in the philosophy of physics.

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Identification of microorganisms by MALDI-TOF mass spectrometry is a very efficient method with high throughput, speed, and accuracy. However, it is significantly limited by the absence of a universal database of reference mass spectra. This problem can be solved by creating an Internet platform for open databases of protein spectra of microorganisms. Choosing the optimal mathematical apparatus is the pivotal issue for this task. In our previous study we proposed the geometric approach for processing mass spectrometry data, which represented a mass spectrum as a vector in a multidimensional Euclidean space. This algorithm was implemented in a Jacob4 stand-alone package. We demonstrated its efficiency in delimiting two closely related species of the Bacillus pumilus group. In this study, the geometric approach was realized as R scripts which allowed us to design a Web-based application. We also studied the possibility of using full spectra analysis (FSA) without calculating mass peaks (PPA), which is the logical development of the method. We used 74 microbial strains from the collections of ICiG SB RAS, UNIQEM, IEGM, KMM, and VGM as the models. We demonstrated that the algorithms based on peak-picking and analysis of complete data have accuracy no less than that of Biotyper 3.1 software. We proposed a method for calculating cut-off thresholds based on averaged intraspecific distances. The resulting database, raw data, and the set of R scripts are available online at https://icg-test.mydisk.nsc.ru/s/qj6cfZg57g6qwzN.

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In this paper, SEIRS epidemiological model with disease caused death and varying total population size is discussed. Based on the geometric approach developed by Li and Muldowney, a new criterion to determine the global asymptotic stability for nonlinear system is proposed. By applying this new criterion, global asymptotic stability of the endemic equilibrium when it is unique is proved. The above global result shows that the basic reproduction number is a sharp threshold for SEIRS model which removes restrictions of rate of loss of immunity and rate of disease caused death in Li and Muldowney's result.

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In this paper, a susceptible-vaccinated-exposed-infectious-recovered (SVEIR) epidemic model for an infectious disease that spreads in the host population through horizontal transmission is investigated, assuming that the horizontal transmission is governed by an unspecified function f ( S , I ) . The role that temporary immunity (vaccinated-induced) and treatment of infected people play in the spread of disease, is incorporated in the model. The basic reproduction number R 0 is found, under certain conditions on the incidence rate and treatment function. It is shown that the model exhibits two equilibria, namely, the disease-free equilibrium and the endemic equilibrium. By constructing a suitable Lyapunov function, it is observed that the global asymptotic stability of the disease-free equilibrium depends on R 0 as well as on the treatment rate. If R 0 > 1 , then the endemic equilibrium is globally asymptotically stable with the help of the Li and Muldowney geometric approach applied to four dimensional systems. Numerical simulations are also presented to illustrate our main results.

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Singular Perturbations represent an advantageous theory to deal with systems characterized by a two-time scale separation, such as the longitudinal dynamics of aircraft which are called phugoid and short period. In this work, the combination of the NonLinear Geometric Approach and the Singular Perturbations leads to an innovative Fault Detection and Isolation system dedicated to the isolation of faults affecting the air data system of a general aviation aircraft. The isolation capabilities, obtained by means of the approach proposed in this work, allow for the solution of a fault isolation problem otherwise not solvable by means of standard geometric techniques. Extensive Monte-Carlo simulations, exploiting a high fidelity aircraft simulator, show the effectiveness of the proposed Fault Detection and Isolation system.

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In this paper, we consider a deterministic malaria transmission model with standard incidence rate and treatment. Human population is divided into susceptible, infectious and recovered subclasses, and mosquito population is split into susceptible and infectious classes. It is assumed that, among individuals with malaria who are treated or recovered spontaneously, a proportion moves to the recovered class with temporary immunity and the other proportion returns to the susceptible class. Firstly, it is shown that two endemic equilibria may exist when the basic reproduction number R0<1 and a unique endemic equilibrium exists if R0>1. The presence of a backward bifurcation implies that it is possible for malaria to persist even if R0<1. Secondly, using geometric method, some sufficient conditions for global stability of the unique endemic equilibrium are obtained when R0>1. To deal with this problem, the estimate of the Lozinskii˘ measure of a 6 × 6 matrix is discussed. Finally, numerical simulations are provided to support our theoretical results. The model is also used to simulate the human malaria data reported by the Chinese Ministry of Health from 2002 to 2013. It is estimated that the basic reproduction number R0≈0.0161 for the malaria transmission in China and it is found that the plan of eliminating malaria in China is practical under the current control strategies.

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In this work, we propose novel epidemic models (named, susceptible-infected-recovered-susceptible-bacteria) for cholera dynamics by incorporating a general formulation of bacteria growth and spatial variation. In the first part, a generalized ordinary differential equation (ODE) model is presented and it is found that bacterial growth contributes to the increase in the basic reproduction number, [Formula: see text]. With the derived basic reproduction number, we analyse the local and global dynamics of the model. Particularly, we give a rigorous proof on the endemic global stability by employing the geometric approach. In the second part, we extend the ODE model to a partial differential equation (PDE) model with the inclusion of diffusion to capture the movement of human hosts and bacteria in a heterogeneous environment. The disease threshold of this PDE model is studied again by using the basic reproduction number. The results on the threshold dynamics of the ODE and PDE models are compared, and verified through numerical simulation. Additionally, our analysis shows that incorporating diffusive spatial spread does not produce a Turing instability when [Formula: see text] associated with the ODE model is less than the unity.

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