Singular Reduction Research Articles

Singular Perturbation-Based Large-Signal Order Reduction of Microgrids for Stability and Accuracy Synthesis With Control

Singular Perturbation-Based Large-Signal Order Reduction of Microgrids for Stability and Accuracy Synthesis With Control

Influence of the value of singular reductions on stress-strain state in deformation area during drawing of steel wire in monolithic dies

Influence of the value of singular reductions on stress-strain state in deformation area during drawing of steel wire in monolithic dies

Heart rate variability as a marker and predictor of inflammation, nosocomial infection, and sepsis - A systematic review.

The autonomic nervous system interacts with the immune system via the inflammatory response. Heart rate variability (HRV), a marker of autonomic activity, is associated with inflammation, and nosocomial infections/sepsis, and has clinical implications for the monitoring of at-risk patients. Due to the vagal tone's influence on anti-inflammatory immune response, this association may predominately be reflected by vagally-mediated HRV indices. However, HRV's predictive significance on inflammation/infection remains unclear. 843 studies examining the associations/prognostic value of HRV indices on inflammation, and nosocomial infection/sepsis were screened in this systematic review. According to inclusion and exclusion criteria, 68 associative studies and 14 prediction studies were included. HRV and pro-inflammatory state were consistently associated in healthy subjects and patient groups. Pro-inflammatory state was related to reduced total power HRV including vagally- and non-vagally-mediated HRV indices. Similar, compared to controls, HRV reductions were observed during nosocomial infections/sepsis. Only limited evidence supports the predictive value of HRV in the development of nosocomial infections/sepsis. Reduced very low frequency power HRV showed the highest predictive value in adults, even with different clinical conditions. In neonates, an increased heart rate characteristic score, combining reduced total power HRV, decreased complexity, and vagally-dominated asymmetry, predicted sepsis. Pro-inflammatory state is related to an overall reduction in HRV rather than a singular reduction in vagally-mediated HRV indices, reflecting the complex autonomic-regulatory changes occurring during inflammation. The potential benefit of using continuous HRV monitoring for detecting nosocomial infection-related states, and the implications for clinical outcome, need further clarification.

Stratified reduction of singularities of generalized analytic functions

Generalized analytic functions are naturally defined in manifolds with boundary and are built from sums of convergent real power series with non-negative real exponents. In this paper we deal with the problem of reduction of singularities of these functions. Namely, we prove that a germ of generalized analytic function can be transformed by a finite sequence of blowing-ups into a function which is locally of monomial type with respect to the coordinates defining the boundary of the manifold where it is defined.

Reduced fibrous capsule elastic fibers from biologic ECM-enveloped CIEDs in minipigs, supported with a novel compression mechanics model.

Fibrous capsules (Fb) in response to cardiovascular implantable electronic devices (CIEDs), including a pacemaker (P) system, can produce patient discomfort and difficulties in revision surgery due partially to their increased compressive strength, previously linked to elevated tissue fibers. A preliminary study to quantify structural proteins, determine if biologic extracellular matrix-enveloped CIEDs (PECM) caused differential Fb properties, and to implement a realistic mechanical model. Retrieved Fb (-P and -PECM) from minipigs were subjected to biomechanical (shear oscillation and uniaxial compression) and histological (collagen I and elastin) analyses. Fb-PECM showed significant decreases compared to Fb-P in: low strain-loss modulus (390 vs. 541Pa) across angular frequencies, high strain-compressive elastic modulus (1043 vs. 2042kPa), and elastic fiber content (1.92 vs. 3.15μg/mg tissue). Decreases in elastin were particularly noted closer to the implant's surface (Fb-PECM = 71% vs. Fb-P = 143% relative to dermal elastin at mid-tangential sections) and verified with a solid mechanics hyperelasticity with direction-dependent fiber viscoelasticity compression simulation (r2 ≥98.9%). The biologic envelope composed of decellularized porcine small intestine submucosa ECM for CIEDs promoted fibrous tissues with less elastic fibers. Novel compression modeling analyses directly correlated this singular reduction to more desirable subcutaneous tissue mechanics.

Natural Parameter Conditions for Singular Perturbations of Chemical and Biochemical Reaction Networks

We consider reaction networks that admit a singular perturbation reduction in a certain parameter range. The focus of this paper is on deriving "small parameters" (briefly for small perturbation parameters), to gauge the accuracy of the reduction, in a manner that is consistent, amenable to computation and permits an interpretation in chemical or biochemical terms. Our work is based on local timescale estimates via ratios of the real parts of eigenvalues of the Jacobian near critical manifolds. This approach modifies the one introduced by Segel and Slemrod and is familiar from computational singular perturbation theory. While parameters derived by this method cannot provide universal quantitative estimates for the accuracy of a reduction, they represent a critical first step toward this end. Working directly with eigenvalues is generally unfeasible, and at best cumbersome. Therefore we focus on the coefficients of the characteristic polynomial to derive parameters, and relate them to timescales. Thus, we obtain distinguished parameters for systems of arbitrary dimension, with particular emphasis on reduction to dimension one. As a first application, we discuss the Michaelis-Menten reaction mechanism system in various settings, with new and perhaps surprising results. We proceed to investigate more complex enzyme catalyzed reaction mechanisms (uncompetitive, competitive inhibition and cooperativity) of dimension three, with reductions to dimension one and two. The distinguished parameters we derive for these three-dimensional systems are new. In fact, no rigorous derivation of small parameters seems to exist in the literature so far. Numerical simulations are included to illustrate the efficacy of the parameters obtained, but also to show that certain limitations must be observed.

Research on HVDC Supplementary Two-Stage Transient Control and Smooth Switching

HVDC additional transient control is an essential means to elevate the transient stability of AC/DC interconnected systems and the inevitable requirement of intelligent transmission. Two-stage transient additional control and a smooth switching strategy are proposed. By establishing an extended state observer for unbalanced power in the system disturbance, the real-time and accurate estimation of unstable power is realized, and an adaptive emergency power support controller is constructed. The mathematical model of the system is identified by using Total Least Squares-Estimation on Signal Parameters via Rotational Technique (TLS-ESPRIT). Based on the singular value reduction theory, the HVDC additional Active Disturbance Rejection Damping Controller (ADRDC) that can inhibit the low-frequency oscillation of the system is designed. Finally, two switching strategies are designed based on the change in the state of the network fault switch and the change in the power angle oscillation curve. The three-in-feed HVDC system is built in PSCAD, and the simulation analysis is carried out. The simulation results confirm the validity of the proposed method.

Multiple vehicles tracking and detection using weight high order singular value decomposition dimensionality reduction and double classifiers

Controlling and managing city traffic is one of them. In order to use image processing to prevent accidents on the road, vehicle tracking and detection are essential. By following moving objects, surveillance video monitoring and human activity recording are carried out. By taking this into account, a useful technique for image processing that detects automobiles from the image is suggested. For numerous vehicle tracking and detection systems, the ECNN-SVM (Enhanced Convolution Neural Network with Support Vector Machine) has just been introduced. However, the larger dimensional data space and inaccurate edge recognition make this system’s performance difficult. The WHOSVD (Weight High Order Singular Value Decomposition) approach, which reduces the dimension and breaks up the positive and negative training picture samples, is established to improve training speed and visual vehicle recognition. To effectively identify the edges at corners, improved canny edge detection is used for edge detection. Mean Kernel Fuzzy C Means (MKFCM) clustering algorithm-based three-dimensional bounding box estimation is used to identify the vehicle items. By merging the feature value of samples with their class labels, the Speed Factor Based Cuckoo Search Algorithm (SFCSA) is introduced for feature selection. The WHOSVD algorithm was used as the input for the enhanced convolutional neural network (ECNN), which is introduced for low-dimensional space and is used for vehicle detection and tracking. Occlusion problems are resolved and target features are further identified using a machine learning classifier. For common algorithms like CNN+SVM, Support Vector Machine (SVM), and the proposed technique, experimentation is done in regards to the metrics of accuracy, f-measure, precision, and recall for performance evaluation.

Stratification of three-dimensional real flows I: Fitting domains

Let ξ be an analytic vector field in R3 with an isolated singularity at the origin and having only hyperbolic singular points after a reduction of singularities π:M→R3. The union of the images by π of the local invariant manifolds at those hyperbolic points, denoted by Λ, is composed of trajectories of ξ accumulating to 0∈R3. Assuming that there are no cycles nor polycycles on the divisor of π, together with a Morse-Smale type property and a non-resonance condition on the eigenvalues at these points, in this paper we prove the existence of a fundamental system {Vn} of neighborhoods well adapted for the description of the local dynamics of ξ: the frontier Fr(Vn) is everywhere tangent to ξ except around Fr(Vn)∩Λ, where transversality is mandatory.

Application of Extended Matrix Pencil Method in Multiport Frequency-Dependent Network Equivalent and the Transient Analysis of Multiconductor Transmission Line System

In this paper, an extended matrix pencil method (EMPM) is proposed to achieve the equivalent analysis of a multiport system. First, the Hankel matrix constructed by the sampling data from multiple ports is integrated into an extended matrix. Then, operations, including singular value decomposition, order reduction, and solution of matrix pencil, are carried out for the extended matrix to calculate the common poles. Further, the residue matrix of the multiport system is solved by the least square method. Furthermore, for the multiconductor transmission line (MTL) system containing the frequency-dependent network (FDN) loads, a combination of the EMPM and piecewise linear recursive convolution (PLRC) is proposed to complete its transient analysis. The corresponding voltage expressions at the connection point of the MTL and FDN are analytically derived. Finally, the effectiveness of the EMPM in analyzing the FDN equivalent and that of the proposed combination of the EMPM and PLRC in analyzing the transient response of the MTL system containing the FDN are verified by numerical examples.

Algebraic Symplectic Reduction and Quantization of Singular Spaces

The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of singular Poisson spaces the deformation quantization is explicitly constructed. In is shown that for the flat phase space with the classical moment map and the orthogonal group action the deformation quantization converges for the entire arguments of exponential type.

Critical Parameters for Singular Perturbation Reductions of Chemical Reaction Networks

We are concerned with polynomial ordinary differential systems that arise from modelling chemical reaction networks. For such systems, which may be of high dimension and may depend on many parameters, it is frequently of interest to obtain a reduction of dimension in certain parameter ranges. Singular perturbation theory, as initiated by Tikhonov and Fenichel, provides a path towards such reductions. In the present paper, we discuss parameter values that lead to singular perturbation reductions (so-called Tikhonov–Fenichel parameter values, or TFPVs). An algorithmic approach is known, but it is feasible for small dimensions only. Here, we characterize conditions for classes of reaction networks for which TFPVs arise by turning off reactions (by setting rate parameters to zero) or by removing certain species (which relates to the classical quasi-steady state approach to model reduction). In particular, we obtain definitive results for the class of complex-balanced reaction networks (of deficiency zero) and first-order reaction networks.

Quasi-Steady-State and Singular Perturbation Reduction for Reaction Networks with Noninteracting Species

Quasi-steady state (QSS) reduction is a commonly used method to lower the dimension of a differential equation model of a chemical reaction network. From a mathematical perspective, QSS reduction is generally interpreted as a special type of singular perturbation reduction, but in many instances the correspondence is not worked out rigorously, and the QSS reduction may yield incorrect results. The present paper contains a thorough discussion of QSS reduction and its relation to singular perturbation reduction for the special, but important, case when the right hand side of the differential equation is linear in the variables to be eliminated. For this class we give necessary and sufficient conditions for a singular perturbation reduction (in the sense of Tikhonov and Fenichel) to exist, and to agree with QSS reduction. We then apply the general results to chemical reaction networks with non-interacting species, generalizing earlier results and methods for steady states to quasi-steady state scenarios. We provide easy-to-check graphical conditions to select parameter values yielding to singular perturbation reductions and additionally, we identify a choice of parameters for which the corresponding singular perturbation reduction agrees with the QSS reduction. Finally we consider a number of examples.

A 5-DOF redundantly actuated parallel mechanism for large tilting five-face machining

This paper introduces the design, analysis, and control of a novel 5 degrees of freedom (DOFs) redundantly actuated parallel mechanism with a large tilting capacity. Firstly, a novel parallel mechanism consisting of four prismatic-universal-spherical (PUS) peripheral limbs and one special central prismatic-prismatic-prismatic-universal (PPPU) limb (4PUS-PPPU) is proposed. Secondary, analytical solution for the inverse kinematics of the proposed 4PUS-PPPU parallel mechanism is solved, singularity reduction by using a redundantly actuated central limb is analyzed, the workspace is also analyzed to show the perfect tilting capability of the proposed mechanism. Thirdly, computed-torque synchronization control is constructed to obtain the desired torque for each actuator when tracking a given trajectory. Fourthly, the adaptive hybrid position/force control strategy which is suitable for the redundantly actuated parallel mechanism is proposed to effectively adjust the internal force of the mechanism. Finally, a physical prototype is fabricated, the titling capacity and the effectiveness of the adaptive hybrid position/force control strategy are verified, polishing machining is employed as an example to demonstrate the performance of the proposed 4PUS-PPPU parallel mechanism.

Graded matrix factorizations of size two and reduction

We associate a complete intersection singularity to a graded matrix factorization of size two of a polynomial in three variables. We show that we get an inverse to the reduction of singularities considered by C. T. C. Wall. We study this for the full strongly exceptional collections in the triangulated category of graded matrix factorizations constructed by H. Kajiura, K. Saito, and the second author.

Separatrices for Real Analytic Vector Fields in the Plane

Let $X$ be a germ of real analytic vector field at $({\mathbb R}^{2},0)$ with an algebracally isolated singularity. We say that $X$ is a topological generalized curve if there are no topological saddle-nodes in its reduction of singularities. In this case, we prove that if either the order $\nu_{0}(X)$ or the Milnor number $\mu_{0}(X)$ is even, then $X$ has a formal separatrix, that is, a formal invariant curve at $0 \in {\mathbb R}^{2}$. This result is optimal, in the sense that these hypotheses do not assure the existence of a convergent separatrix.

Stratification of singular hyperkähler quotients

Abstract Hyperkähler quotients by non-free actions are typically singular, but are nevertheless partitioned into smooth hyperkähler manifolds. We show that these partitions are topological stratifications, in a strong sense. We also endow the quotients with global Poisson structures which recover the hyperkähler structures on the strata. Finally, we give a local model which shows that these quotients are locally isomorphic to linear complex-symplectic reductions in the GIT sense. These results can be thought of as the hyperkähler analogues of Sjamaar–Lerman’s theorems for singular symplectic reduction. They are based on a local normal form for the underlying complex-Hamiltonian manifold, which may be of independent interest.

Phase singularity reduction in speckle interferometry by tailoring the spatial coherence of light.

Reducing the number of phase singularities in speckle interferometry by physical means increases the quality of the phase deconvolution and enhances the separability of fringe systems, especially for highly dynamic fringe systems. The reduction is achieved by tailoring the spatial coherence of the light source at the entrance of the interferometer. The reduction mechanism is non-intuitive and rests on a change of size and of position of the speckle patterns as a result of the spatially shaped coherence. After demonstrating the amount of reduction that may be achieved, the reduction mechanism is explained theoretically and via simulations, and it is vindicated in an experiment using a Michelson-Mach-Zehnder interferometer hybrid.

Analytical approximations for the speed of pacemaker-generated waves.

In oscillatory media, waves can be generated by pacemaker regions which oscillate faster than their surroundings. In many chemical and biological systems, such waves can synchronize the whole medium and as such they are a means of transmitting information at a fixed speed over large distances. In this paper, we apply analytical tools to investigate the factors that determine the speed of these waves. More precisely, we apply singular perturbation and phase reduction methods to two types of negative-feedback oscillators, one built on underlying bistability and one including a time delay in the negative feedback. In both systems, we investigate the influence of time-scale separation on the resulting wave speed, as well as the effect of size and frequency of the pacemaker region. We compare our analytical estimates to numerical simulations which we described previously [J. Rombouts and L. Gelens, Phys. Rev. Research 2, 043038 (2020)2643-156410.1103/PhysRevResearch.2.043038].

Pairs of foliations and Mattei-Moussu's Theorem

We prove a reduction of singularities for pairs of foliations by blowing-up, and then investigate the analytic classification of the reduced models. Those reduced pairs of regular foliations are well understood. The case of a regular and a singular foliation is dealt with Mattei-Moussu's Theorem for which we provide a new proof, avoiding Gronwall's inequality. We end-up announcing results recently obtained by the first author in the case of a pair of reduced foliations sharing the same separatrices.