Function Perturbation Research Articles

Perturbational Analysis of Magnetic Force Theorem for Magnetic Exchange Interactions in Molecules and Solids.

There have been increasing efforts to compute magnetic exchange coupling constants for transition metal complexes and magnetic insulators using the magnetic force theorem and Green's function-based linear response methods. These were originally conceived for magnetic metals, yet it has not been clear how these methods fare conceptually with the conventional models based on electron-correlation interactions among so-called magnetic orbitals. We present a spinor-based theoretical analysis pertinent to the magnetic force theorem and linear response theory using Brillouin-Wigner perturbation method and Green's function perturbation method, and we shed light on the conceptual nature of the Lichtenstein formula in its applications for calculations of the total energy and magnetic exchange coupling constants for both molecules and solids. Derivation of the magnetic force theorem in this perturbational analysis identifies the first-order energy correction terms, which are considered as the ferromagnetic component for the magnetic exchange interactions of transition metal compounds but are not included in the Lichtenstein formula. Detailed perturbational analysis of the energy components involved in the magnetic force theorem identifies the energy components that are missing in the Lichtenstein formula but are critical in the Anderson's model for transition metal complexes and magnetic insulators where magnetic orbitals can overlap.

Antimony exposure affects oocyte quality and early embryo development via excessive mitochondrial oxidation and dysfunction

Antimony (Sb) is a metalloid, widely presents in the environment and associates with human health. In this study, we aimed to decipher whether Sb exposure is harmful to female reproduction and explore the underlying mechanisms. The ICR mice were exposed to 0, 5, 10, and 20 mg/kg acetate potassium Sb tartrate trihydrate by intraperitoneal injection for 10 days, then mouse oocytes were collected for further analysis. We first found a significant decrease in the proportion of MII-stage oocytes obtained from supernumerary ovulation in the fallopian tubes and early embryo development under Sb treatment. Then a series of tests showed Sb affects oocyte maturation by damaging the cytoskeleton of microtubule and actin. Moreover, the abnormal distribution of cortical granules and their component Ovastacin in oocytes, combined with reduced expression levels of Juno, affected sperm-oocyte binding and led to fertilization failure. Based on the sequencing results and experimental validation, it was demonstrated that Sb exposure impairs mitochondrial distribution and membrane potential, elevated levels of mitochondrial superoxide, finally caused energy supply deficits. Mitochondrial damage in oocytes after Sb exposure results in the excessive oxidative stress and early apoptosis. Taken together, these data suggest that Sb exposure decreases oocyte quality and female fertilization ability by impairing mitochondrial function and redox perturbation.

Green/WeakCoupling: Implementation of fully self-consistent finite-temperature many-body perturbation theory for molecules and solids

The accurate ab-initio simulation of molecules and periodic solids with diagrammatic perturbation theory is an important task in quantum chemistry, condensed matter physics, and materials science. In this article, we present the WeakCoupling module of the open-source software package Green, which implements fully self-consistent diagrammatic weak coupling simulations, capable of dealing with real materials in the finite-temperature formalism. The code is licensed under the permissive MIT license. We provide self-consistent GW (scGW) and self-consistent second-order Green's function perturbation theory (GF2) solvers, analysis tools, and post-processing methods. This paper summarises the theoretical methods implemented and provides background, tutorials and practical instructions for running simulations. Program summaryProgram Title:Green/WeakCouplingCPC Library link to program files:https://doi.org/10.17632/2ysyhzww6t.1Developer's repository link:https://github.com/Green-Phys/green-mbptProgramming language:C++17, CUDA, PythonLicensing provisions: MIT LicenseExternal routines/libraries:MPI >= 3.0, BLAS, Eigen >= 3.4.0, cmake >= 3.18, cuBLAS.Nature of problem: The simulation of periodic solids and molecules using diagrammatic perturbation theorySolution method: We present an open-source implementation of the fully self-consistent finite-temperature many-body perturbation theory formalism at the GW and second-order perturbation theory level.

Impulsive fractional integro-delay differential equation-controllability through delayed Mittag-Leffler function perturbation

Impulsive fractional integro-delay differential equation-controllability through delayed Mittag-Leffler function perturbation

One-Bit Function Perturbation Impact on Robust Set Stability of Boolean Networks with Disturbances

This paper investigates the one-bit function perturbation (OBFP) impact on the robust set stability of Boolean networks with disturbances (DBNs). Firstly, the dynamics of these networks are converted into the algebraic forms utilizing the semi-tensor product (STP) method. Secondly, OBFP’s impact on the robust set stability of DBNs is divided into two situations. Then, by constructing a state set and defining an index vector, several necessary and sufficient conditions to guarantee that a DBN under OBFP can stay robust set stable unchanged are provided. Finally, a biological example is proposed to demonstrate the effectiveness of the obtained theoretical results.

A modified generalized harmonic function perturbation method and its application in analyzing generalized Duffing–Harmonic–Rayleigh–Liénard oscillator

A modified generalized harmonic function perturbation method is proposed in this paper. Compared with the classical version of this method, the modified version can execute its procedures pure symbolically without the need to assign any system parameters even for some complicated nonlinear oscillators. This means that the relations between amplitude of limit cycles and system parameters can be derived analytically from the proposed method. Meanwhile, the analytical expression of characteristic quantity of limit cycles can be also obtained. Via these analytical expressions, the evolutional process of limit cycles can be studied quantitatively in amplitude domain. It demonstrates the entire live period of each limit cycle from its generation to bifurcation to destination. To show the feasibility of the proposed method, a complicated oscillator named generalized Duffing–Harmonic–Rayleigh–Liénard oscillator is investigated in this paper. First, the two analytical expressions mentioned above are derived and the global evolution of its limit cycles are analyzed quantitatively. Second, the critical value of homoclinic and heteroclinic bifurcation parameters are also predicted via this two analytical expressions. Moreover, the analytical approximate solutions of both limit cycles and homo-heteroclinic orbits are calculated. To prove the accuracy, all the above results obtained via the proposed methods are confirmed by the Runge–Kutta method, which show a good accordance. Therefore, the proposed method can be considered as an effective modification for a classical perturbation method. It provides another feasible and reliable analytical quantitative method for analyzing global dynamics of strongly nonlinear oscillators.

A modified perturbation method for global dynamic analysis of generalized mixed Rayleigh–Liénard oscillator with cubic and quintic nonlinearities

Deriving analytical relationship between the system parameters and amplitude of the limit cycle is a meaningful and challenging task. Currently, numerous existing analytical approximate methods struggle to achieve this goal when expressions of restoring force or nonlinear damping is complicated. To overcome this shortcoming, this study proposes a modified generalized harmonic function perturbation method. Using the proposed method, a generalized mixed RayleighLiénard oscillator with cubic and quintic nonlinearities was investigated. The analytical relationships between the system parameters and amplitude of the limit cycle, as well as the expression of its characteristic quantity, were derived. By employing these analytical relationships, the existence, stability, number, position, and amplitude of each limit cycle are quantitatively analysed. The homoclinic and heteroclinic bifurcations were also predicted using the above analytical relationships. Additionally, analytical approximate solutions for this oscillator were calculated using the proposed method. All results obtained in this study were subsequently confirmed numerically to demonstrate their feasibility and validity. Consequently, the proposed method can be considered an effective supplement to perturbation-based methods. This also implies that the work presented in this paper has a certain theoretical significance and application value in the research area of quantitative analysis methods for strongly nonlinear oscillators.

Total-activity conservation of probabilistic Boolean networks and its applications

Conservation law is a basic property of biological networks, which exhibits the total-activity conservation in Boolean networks (BNs). This article analyzes the total-activity conservation of probabilistic Boolean networks (PBNs) based on the algebraic state space representation approach. The concept of total-activity conservation is proposed for PBNs, and a vector-based criterion is presented to verify the total-activity conservation of PBNs. Moreover, the impact of deterministic function perturbation on the total-activity conservation of PBNs is analyzed. Finally, as an application of total-activity conservation for PBNs, the robust total-activity conservation of BNs subject to stochastic function perturbation is explored.

Can GW handle multireference systems?

Due to the infinite summation of bubble diagrams, the GW approximation of Green's function perturbation theory has proven particularly effective in the weak correlation regime, where this family of Feynman diagrams is important. However, the performance of GW in multireference molecular systems, characterized by strong electron correlation, remains relatively unexplored. In the present study, we investigate the ability of GW to handle closed-shell multireference systems in their singlet ground state by examining four paradigmatic scenarios. First, we analyze a prototypical example of a chemical reaction involving strong correlation: the potential energy curve of BeH2 during the insertion of a beryllium atom into a hydrogen molecule. Second, we compute the electron detachment and attachment energies of a set of molecules that exhibit a variable degree of multireference character at their respective equilibrium geometries: LiF, BeO, BN, C2, B2, and O3. Third, we consider a H6 cluster with a triangular arrangement, which features a notable degree of spin frustration. Finally, the dissociation curve of the HF molecule is studied as an example of single bond breaking. These investigations highlight a nuanced perspective on the performance of GW for strong correlation depending on the level of self-consistency, the choice of initial guess, and the presence of spin-symmetry breaking at the Hartree-Fock level.

Set Controllability of Boolean Control Networks Under Stochastic Function Perturbation

Set Controllability of Boolean Control Networks Under Stochastic Function Perturbation

Robust Set Stability for Switched Boolean Networks Under One-Bit Function Perturbation

Robust Set Stability for Switched Boolean Networks Under One-Bit Function Perturbation

Online impedance measurement of operational batteries utilizing Sinc function signal injection via DC-DC power converter

This paper presents a novel method for the online impedance measurement of operational batteries that utilizes Sinc function signal injection via a DC-DC power converter. The Sinc function perturbation signal, with its multiple frequency components, enables simultaneous impedance measurement of the battery at various frequencies, thus ensuring high measurement efficiency. Additionally, the generation and injection processes for this perturbation signal are simple and straightforward. Its power spectrum, characterized by a uniform distribution and relatively high power content, enables precise measurements across the entire frequency range of interest. The paper extensively discusses the measurement principle and properties using the perturbation signal, followed by an analysis of the circuit topology to derive the transfer functions, and a simulation to examine the battery’s responses under the perturbation signal. Finally, a case study using a 2.8 Ah 883860-size lithium polymer battery demonstrates the feasibility and accuracy of the proposed method.

2-Deoxy-glucose ameliorates the peritoneal mesothelial and endothelial barrier function perturbation occurring due to Peritoneal Dialysis fluids exposure

Peritoneal dialysis (PD) and prolonged exposure to PD fluids (PDF) induce peritoneal membrane (PM) fibrosis and hypervascularity, leading to functional PM degeneration. 2-deoxy-glucose (2-DG) has shown potential as PM antifibrotic by inhibiting hyper-glycolysis induced mesothelial-to-mesenchymal transition (MMT). We investigated whether administration of 2-DG with several PDF affects the permeability of mesothelial and endothelial barrier of the PM.The antifibrotic effect of 2-DG was confirmed by the gel contraction assay with embedded mesothelial (MeT-5A) or endothelial (EA.hy926) cells cultured in Dianeal® 2.5 % (CPDF), BicaVera® 2.3 % (BPDF), Balance® 2.3 % (LPDF) with/without 2-DG addition (0.2 mM), and qPCR for αSMA, CDH2 genes. Moreover, 2-DG effect was tested on the permeability of monolayers of mesothelial and endothelial cells by monitoring the transmembrane resistance (RTM), FITC-dextran (10, 70 kDa) diffusion and mRNA expression levels of CLDN-1 to -5, ZO1, SGLT1, and SGLT2 genes. Contractility of MeT-5A cells in CPDF/2-DG was decreased, accompanied by αSMA (0.17 ± 0.03) and CDH2 (2.92 ± 0.29) gene expression fold changes. Changes in αSMA, CDH2 were found in EA.hy926 cells, though αSMA also decreased under LPDF/2-DG incubation (0.42 ± 0.02). Overall, 2-DG mitigated the PDF-induced alterations in mesothelial and endothelial barrier function as shown by RTM, dextran transport and expression levels of the CLDN-1 to -5, ZO1, and SGLT2. Thus, supplementation of PDF with 2-DG not only reduces MMT but also improves functional permeability characteristics of the PM mesothelial and endothelial barrier.

Study on the vertical well seepage model in composite carbonate reservoirs

Introduction: Carbonate reservoirs are widely distributed throughout the world. Due to the good physical properties of the reservoirs, they are easily contaminated by mud during drilling opening, so they are often put into production after acidification. After acidification, the near-well reservoir’s physical property is improved, while the far-well reservoir’s physical property remains unchanged. Such reservoirs are commonly called composite reservoirs. Composite carbonate reservoir seepage law is more complicated.Methods: In this paper, the point source function of a triple-medium composite reservoir is established using the source function theory, Laplace transform, perturbation transform, and linear superposition principle of partial differential equation.Results: Second, the vertical well seepage model of a composite reservoir is obtained through the new point source function.Discussion: Finally, the correctness of the model is verified, and the sensitivity analysis of the key parameters affecting the seepage law is carried out. The applicability of the model established in this paper is demonstrated by two wells in the field. This paper provides a theoretical basis for vertical well test analysis of composite reservoirs.

Circulating myomiRNAs as biomarkers in patients with Cushing’s syndrome

PurposeImpairment of skeletal muscle mass and strength affects 40–70% of patients with active Cushing’s syndrome (CS). Glucocorticoid excess sustains muscle atrophy and weakness, while muscle-specific microRNAs (myomiRs) level changes were associated with muscle organization and function perturbation. The aim of the current study is to explore changes in circulating myomiRs in CS patients compared to healthy controls and their involvement in IGFI/PI3K/Akt/mTOR pathway regulation in skeletal muscle.MethodsC2C12, mouse myocytes, were exposed to hydrocortisone (HC), and atrophy-related gene expression was investigated by RT-qPCR, WB and IF to assess HC-mediated atrophic signalling. miRNAs were evaluated in HC-treated C2C12 by PCR Arrays. MyomiRs significantly overexpressed in C2C12 were investigated in 37 CS patients and 24 healthy controls serum by RT-qPCR. The anti-anabolic role of circulating miRNAs significantly upregulated in CS patients was explored in C2C12 by investigating the IGFI/PI3K/Akt/mTOR pathway regulation.ResultsHC induced higher expression of atrophy-related genes, miR-133a-3p, miR-122-5p and miR-200b-3p in C2C12 compared to untreated cells. Conversely, the anabolic IGFI/PI3K/Akt/mTOR signalling was reduced and this effect was mediated by miR-133a-3p. In CS patients miR-133a-3p and miR-200b-3p revealed higher circulating levels (p < 0.0001, respectively) compared to controls. ROC curves for miR-133a-3p (AUC 0.823, p < 0.0001) and miR-200b-3p (AUC 0.850, p < 0.0001) demonstrated that both myomiRs represent potential biomarkers to discriminate between CS and healthy subjects. Pearson’s correlation analysis revealed that circulating levels of miR-133a-3p are directly correlated with 24 h urinary-free cortisol level (r = 0.468, p = 0.004) in CS patients.ConclusionsHC induces atrophic signals by miR-133a-3p overexpression in mouse myocytes and humans. Circulating miR-133a-3p is promising biomarkers of hypercortisolism.

Total-Activity Conservation Analysis and Design of Boolean Networks.

The law of conservation of mass, represented in Boolean networks (BNs) as total-activity conservation, is one of the typical properties of biological networks. This article analyzes the total-activity conservation of BNs based on the algebraic state-space representation (ASSR) approach. First, the total-activity-conservative matrix is defined and a matrix-based criterion is proposed to verify the total-activity conservation of BNs. Meanwhile, when function perturbation is considered, robust total-activity conservation is investigated. Second, by means of the pseudo-Boolean function generated by total-activity conservation, a constructive design procedure of the Boolean dynamics is given to achieve the total-activity conservation. Third, the total-activity conservation of switched Boolean networks (SBNs) under arbitrary switching signal is studied, which together with network aggregation achieves the total-activity conservation of large-scale BNs.

Robust minimal strong reconstructibility problem of Boolean control networks

In this paper, the problem of robust minimal strong reconstructibility (RMSR) of Boolean control networks (BCNs) with multi-bit perturbations is studied by using graph theory. The problem takes the premise that BCNs are strongly reconstructible before function perturbation. We analyze the effect of the multi-bit perturbation on the strong reconstructibility of BCNs and present two valid criteria for the robust strong reconstructibility of BCNs. Then, to avoid the effect of function perturbation on the strong reconstructibility of BCNs, the problem of adding a minimal sensor set is considered, thereby making the BCNs robust minimal strong reconstructible after function perturbation. Finally, the results are applied to a biological example.

Theory and phenomenology of stressed wave-dark-matter soliton

Soliton in the hostile turbulent wave dark matter ($\mathrm{\ensuremath{\Psi}}\mathrm{DM}$) halo of a galaxy agitates with various kinds of excitation, and the soliton even breathes heavily under great stress. A theory of collective excitation for a $\mathrm{\ensuremath{\Psi}}\mathrm{DM}$ soliton is presented. The collective excitation has different degrees of coupling to negative energy modes, where lower-order excitation generally necessitates more negative energy coupling. A constrained variational principle is developed to assess the frequencies and mode structures of small-amplitude perturbations. The predicted frequencies are in good agreement with those found in simulations. Soliton breathing at amplitudes on the verge of breakup is also a highlight of this work. Even in this extreme nonlinear regime, the wave function perturbation amplitudes are moderate. The simulation data show a stable oscillation with frequency weakly dependent on the oscillation amplitude and hint at a self-consistent quasilinear model for the wave function that accounts for modifications in the ground-state wave function and the equilibrium density. The mock solution, constructed from the simulation data, can shed light on the dynamics of the large-amplitude breathing soliton and support the quasilinear model, as evidenced by its ability to predict well the nonlinear eigenfrequency shifts and large-amplitude breathing frequency observed in simulations.

Robust optimal control of logical control networks with function perturbation

Optimal control is an important branch in modern control theory. In this article, the robustness of optimal control sequence is investigated for logical control networks (LCNs) subject to function perturbation. Firstly, the impact of function perturbation on the Bolza-type optimal control problem of LCNs is analyzed, and several sufficient conditions are presented for the robustness of optimal control sequence. Secondly, combining the characteristics of state transition matrix and stage cost function, a kind of optimal matrix is constructed, which brings a new way for the solvability of Bolza-type optimal control problem. Thirdly, the optimal matrix is used to measure the deviation of cost function with respect to function perturbation, and several necessary and sufficient conditions are proposed to guarantee the robustness of optimal control sequence. Finally, the robustness of optimal control sequence in the Bolza-type optimal control problem is applied to other types of finite-horizon and infinite-horizon optimal control problems of LCNs.

Introducing the Random Phase Approximation Theory

Random Phase Approximation (RPA) is the theory most commonly used to describe the excitations of many-body systems. In this article, the secular equations of the theory are obtained by using three different approaches: the equation of motion method, the Green function perturbation theory and the time-dependent Hartree–Fock theory. Each approach emphasizes specific aspects of the theory overlooked by the other methods. Extensions of the RPA secular equations to treat the continuum part of the excitation spectrum and also the pairing between the particles composing the system are presented. Theoretical approaches which overcome the intrinsic approximations of RPA are outlined.