General Relation Research Articles

Statistical Properties of SIS Processes with Heterogeneous Nodal Recovery Rates in Networks

The modeling and analysis of epidemic processes in networks have attracted much attention over the past few decades. A major underlying assumption is that the recovery process and infection process are homogeneous, allowing the associated theoretical studies to be conducted in a convenient manner. However, the recovery and infection processes usually exhibit heterogeneous rates in the real world, which makes it difficult to characterize the general relations between the dynamics and the underlying network structure. In this work, we focus on the susceptible–infected–susceptible (SIS) epidemic process with heterogeneous recovery rates in a finite-size complete graph. Specifically, we study the metastable-state statistical properties of SIS epidemic dynamics with two different nodal recovery rates in complete graphs. We propose approximate solutions to the metastable-state expectation and the variance in the number of infected nodes within the framework of the mean-field approximation method. We also derive several upper and lower bounds of the steady-state probability that a node is in the infected state. We verify the proposed approximate solutions of the mean and variance via simulations. This work provides insights into the fluctuations in the statistical properties of epidemic processes with complex dynamical behaviors in networks.

Impact of COVID-19 on the Effectiveness of Financial Management of Insurance Companies in Mainland China

The COVID-19 pandemic starting in 2019 has brought significant disruption and turbulence to the global economy, specifically the financial sector. At the same time, the increased awareness of risk in businesses, governments, and individuals should alleviate this disruption to the insurance industry. However, the general trend of the Chinese insurance industry varies among companies, specifically into three types: companies with healthy financial conditions and positive subsidiary expansion, unhealthy financial conditions and negative subsidiary expansion, and unhealthy financial conditions and positive subsidiary expansion. By studying five listed prominent insurance companies in China using qualitative methods, researchers found a general relation between the financial metrics of an insurance company and the subsidiary expansion number, but this relationship isn’t inclusive. The cause of this variation is the difference in choosing a risky or prudent financial strategy and the adaptation to digital transformation.

Effects of zonal fields on energetic-particle excitations of reversed shear Alfvén eigenmode: Simulation and theory

Abstract Employing both nonlinear gyrokinetic simulation and analytical theory, we have investigated the effects of zonal (electromagnetic) fields on the energetic particle's drive of reversed shear Alfv'en eigenmodes in tokamak plasmas. Contrary to the conventional expectation, simulations with zonal fields turned on and off in the energetic particle dynamics while keeping the full nonlinear dynamics
of the thermal plasma indicate that zonal fields further enhance the instability drive and lead, thus, to a higher saturation level. These puzzling simulation results can be understood analytically in terms of the general fishbone-like dispersion relation with the correspondingly different energetic-particle phase-space structures induced by the zonal fields. Analytical expressions for the zonal fields beat driven by the reversed shear Alfv'en eigenmodes are also derived, and shown to be in good agreement with the simulation results.

The Performance of Employees of The Secretariat of The General and Public Relations Section In The Office of The Regional People's Representative Council (DPRD) Gorontalo City

This study aims to determine the performance of employees of the secretariat of the general and public relations section at the Gorontalo City Regional People's Representative Council (DPRD) office. This type of research is descriptive research using a qualitative approach. Data collection techniques were conducted through interviews with a number of informants, observation and documentation. The research focus consists of discipline, ability and work environment The results showed that: 1) Employee discipline in the general and public relations section is not optimal because there are still some employees who are not disciplined about working time. due to lack of awareness of the responsibilities given even though each employee is bound by a Work Agreement (PK) which requires employees to be orderly in carrying out their duties to prepare secretarial administration and sterilize meeting or session rooms. 2) The ability of employees in the general and public relations sections is in accordance with their respective duties and functions but has not been maximized when carrying it out. Because there are still some employees who do not understand the tasks distributed, one of which is secretarial administration. 3) The work environment in the general and public relations section is not conducive because there is noise during working hours in the form of booming voices and music everywhere, making work disturbed.

Scattering on the worldvolume: Amplitude relations in Brower-Goddard string models

We investigate the Brower-Goddard extension of the Veneziano and Virasoro-Shapiro four-point amplitudes obtained by generalizing the Koba-Nielsen integrals to d-dimensional conformally invariant integrals. The amplitudes derived from this framework exhibit polynomial residues and can be shown to adhere to polynomial bounds at high energies. In odd dimensions, the amplitudes decompose into sums of three partial amplitudes, enabling the formulation of general amplitude relations that subsume the Kawai-Lewellen-Tye (KLT) formula as a particular case. The amplitudes contain multiple tachyons in their spectra. Still, we demonstrate that their residues comply with the positivity conditions mandated by unitarity for spacetime dimensions at or below critical values Dcrit(d), where Dcrit(6)=26 and Dcrit(∞)=10. In closing, we contemplate physical applications for membranes and potential extensions of the formalism. Published by the American Physical Society 2024

Steiner 3-Wiener Index of Zigzag Polyhex Nanotubes.

Let G be a connected graph and S be a k element subset of the vertex set V(G) of G. Steiner distance is a natural generalization of the usual graph distance. The Steiner-k distance dG(S) between the vertices of S is the minimum size among all connected subgraphs whose vertex set contains S. The generalized indices based on Steiner distances have several applications in the real world. It is a well-known fact that "Steiner Problem" is NP-complete and hence any parameter based on Steiner distance is also an NP problem. The objective of this work is to determine the Steiner 3-Wiener index for an important chemical structure called the zigzag polyhex nanotube. In this paper, we present an algorithm for computing the Steiner 3-Wiener index (SW3) for zigzag polyhex nanotubes. The developed algorithm addresses the complexities associated with exponential increments in the number of vertices as the nanotube's circumference or length expands. The obtained SW3 values for zigzag polyhex nanotubes can be used for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR) analyses. We have presented an algorithm and listed the numerical values of SW3 for various parameters of circumference and length of a zigzag polyhex nanotube to facilitate their utilization in QSAR/ QSPR analyses. We have obtained the time complexity for the algorithm, which shows that the SW3 values are computationally intensive. To explain this complex nature, we have used multiple linear regression to fit log SW3 values corresponding to log p and log q, the radius and length of a nanotube. The algorithm addresses the complexities associated with the exponential increase in vertices as the nanotube's circumference or length expands. Furthermore, we provide SW3 values for various parameter combinations up to circumference or length 17, and a general relation to determine the value of SW3, facilitating its utilization in real-world applications. These values serve as crucial descriptors for understanding the structural nuances of zigzag polyhex nanotubes, that find applications in material science, drug design, drug discovery, etc.

A universal formulation of uncertainty relation for errors

We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement of statistical nature. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable. Our relation violates the traditional naïve bound ħ/2 for the position-momentum measurement while respecting Heisenberg's original philosophy of the uncertainty principle. Our relation entails, among others, the Arthurs–Kelly–Goodman and Ozawa relations as corollaries to its special cases, and also seamlessly reduces itself to the standard Kennard–Robertson (Schrödinger) relation when the measurement is non-informative.

Exact results of the one-dimensional repulsive Hubbard model

We present analytical results of the fundamental properties of the one-dimensional (1D) Hubbard model with a repulsive interaction. The new model results with arbitrary external fields include: (I) using the exact solutions of the Bethe ansatz equations of the Hubbard model, we first rigorously calculate the gapless spin and charge excitations, exhibiting exotic features of fractionalized spinons and holons. We then investigate the gapped excitations in terms of the spin string and thek-Λstring bound states at arbitrary driving fields, showing subtle differences in spin magnons and chargeη-pair excitations. (II) For a high-density and high spin magnetization region, i.e. near the quadruple critical point, we further analytically obtain the thermodynamic properties, dimensionless ratios and scaling functions near quantum phase transitions. (III) Importantly, we give the general scaling functions at quantum criticality for arbitrary filling and interaction strength. These can directly apply to other integrable models. (IV) Based on the fractional excitations and the scaling laws, the spin-incoherent Luttinger liquid (SILL) with only the charge propagation mode is elucidated by the asymptotic of the two-point correlation functions with the help of conformal field theory. We also, for the first time, obtain the analytical results of the thermodynamics for the SILL. (V) Finally, to capture deeper insights into the Mott insulator and interaction-driven criticality, we further study the double occupancy and propose its associated contact and contact susceptibilities, through which an adiabatic cooling scheme based upon quantum criticality is proposed. In this scenario, we build up general relations among arbitrary external- and internal-potential-driven quantum phase transitions, providing a comprehensive understanding of quantum criticality. Our methods offer rich perspectives of quantum integrability and offer promising guidance for future experiments with interacting electrons and ultracold atoms, both with and without a lattice.

B-311 Relation of Free Immunoglobulin Ligh Chain Concentration to Overflow Proteinuria

Abstract Background Free immunoglobulin light chains are small proteins that undergo substantial glomerular filtration. When high serum concentrations of free light chains occur in multiple myeloma, the high filtered load of light chains exceeds the uptake capacity of proximal tubules, and overflow proteinuria ensues. Massive excretion of light chains can lead to cast formation and renal injury. The present study sought to determine the relation of serum light chain concentration to overflow proteinuria. Methods Results for patients with plasma cell disorders were reviewed as approved by an institutional review board. A Binding Site Optilite analyzer measured serum free light chain concentrations. Urine and serum protein electrophoresis were performed on Helena agarose gels. A total of 170 paired serum and 24-hour urine specimens were evaluated for 36 patients with increased kappa light chains and 26 patients with increased lambda light chains. Results Overflow proteinuria with either immunoglobulin light chain presented with light chain as the major urinary protein and limited increases of urinary albumin. Light chain excretion exceeded albumin excretion when light chain excretion surpassed 100 mg/d. Similar results were obtained for cases with increased kappa and lambda free light chains. There was a general relation of increased serum kappa and lambda light chains and urinary excretion of the corresponding light chain. Limited urinary excretion of light chains (<120 mg/d) was seen when the serum light chain concentration was < 250 mg/L, representing an approximate threshold for substantial overflow proteinuria. Overflow proteinuria exceeding 2,000 g/d was seen only when serum free light chain concentrations exceeded 800 mg/L. However, a few patients with high serum light chain values (>1,000/L) had low urinary light chain excretion that was discordant from the relation of serum light chain concentration to light chain excretion. Serum light chain values >4,000 mg/L (N = 10) were all associated with overflow proteinuria of > 1,500 mg/d and, in 7 cases, >10,000 mg/d. In a few cases, there was evidence that serum light chain assays overestimated light chain concentrations. In one case, the serum free light chain value was twice the total protein and about 12-fold higher than the serum M-spike, suggestive of substantial overestimation. Conclusions Defining the relation between serum free light chain concentrations and the magnitude of overflow proteinuria helps identify patients at low and high risk of massive overflow proteinuria that can cause renal injury. Limited overflow proteinuria (<120 mg/d) occurred when serum light chain concentration was < 250 mg/L, and substantial overflow proteinuria occurred when serum light chains exceeded 4,000 mg/L Serum free light chain concentrations above 250 mg/L were incompletely predictive of urinary free light chain excretion; a few discordant cases with high measured serum light chain concentrations (>1,000 mg/L) and low excretion of light chains were observed. Further investigation is indicated for cases with possible overestimation of free light chains or discordance between serum light chain values and urinary light chain excretion. Unexpected results in some cases could relate to polymerization of free light chains as previously reported.

On ELSV-type formulae and relations between Ω-integrals via deformations of spectral curves

The general relation between Chekhov–Eynard–Orantin topological recursion and the intersection theory on the moduli space of curves, the deformation techniques in topological recursion, and the polynomiality properties with respect to deformation parameters can be combined to derive vanishing relations involving intersection indices of tautological classes. We apply this strategy to three different families of spectral curves and show they give vanishing relations for integrals involving Ω-classes. The first class of vanishing relations are genus-independent and generalises the vanishings found by Johnson–Pandharipande–Tseng [34] and by the authors jointly with Do and Moskovsky [7]. The two other classes of vanishing relations are of a different nature and depend on the genus.

Differential Diagnosis of Tuberculosis and Sarcoidosis by Immunological Features Using Machine Learning.

Despite the achievements of modern medicine, tuberculosis remains one of the leading causes of mortality globally. The difficulties in differential diagnosis have particular relevance in the case of suspicion of tuberculosis with other granulomatous diseases. The most similar clinical and radiologic changes are sarcoidosis. The aim of this study is to apply mathematical modeling to determine diagnostically significant immunological parameters and an algorithm for the differential diagnosis of tuberculosis and sarcoidosis. Materials and methods: The serum samples of patients with sarcoidosis (SD) (n = 29), patients with pulmonary tuberculosis (TB) (n = 32) and the control group (n = 31) (healthy subjects) collected from 2017 to 2022 (the average age 43.4 ± 5.3 years) were examined. Circulating 'polarized' T-helper cell subsets were analyzed by multicolor flow cytometry. A symbolic regression method was used to find general mathematical relations between cell concentrations and diagnosis. The parameters of the selected model were finally fitted through multi-objective optimization applied to two conflicting indices: sensitivity to sarcoidosis and sensitivity to tuberculosis. Results: The difference in Bm2 and CD5-CD27- concentrations was found to be more significant for the differential diagnosis of sarcoidosis and tuberculosis than any individual concentrations: the combined feature Bm2 - [CD5-CD27-] differentiates sarcoidosis and tuberculosis with p < 0.00001 and AUC = 0.823. An algorithm for differential diagnosis was developed. It is based on the linear model with two variables: the first variable is the difference Bm2 - [CD5-CD27-] mentioned above, and the second is the naïve-Tregs concentration. The algorithm uses the model twice and returns "dubious" in 26.7% of cases for patients with sarcoidosis and in 16.1% of cases for patients with tuberculosis. For the remaining patients with one of these two diagnoses, its sensitivity to sarcoidosis is 90.5%, and its sensitivity to tuberculosis is 88.5%. Conclusions: A simple algorithm was developed that can distinguish, by certain immunological features, the cases in which sarcoidosis is likely to be present instead of tuberculosis. Such cases may be further investigated to rule out tuberculosis conclusively. The mathematical model underlying the algorithm is based on the analysis of "naive" T-regulatory cells and "naive" B-cells. This may be a promising approach for differential diagnosis between pulmonary sarcoidosis and pulmonary tuberculosis. The findings may be useful in the absence of clear differential diagnostic criteria between pulmonary tuberculosis and sarcoidosis.

Hydride induced embrittlement and fracture of non-hardening metals under hydrogen chemical equilibrium

The stress field in the hydride precipitation zone is examined, under conditions of hydrogen chemical equilibrium and constant temperature, in the case of non-hardening metals, by applying slip-line theory. It is proven that the hydride precipitation zone, in any geometry, is a constant stress area. In this area, the principal stresses are equal to the respective principal stresses, before hydride precipitation, minus the difference of hydrostatic stress before and after hydride precipitation. The general relations are applied to the case of a stationary sharp mode-I plane-strain crack and the deviations from Prandtl-field are derived, in the [-π/4, +π/4] sector ahead of the tip, where hydrides precipitate. In this case, the hydride precipitation sector is characterized by a constant hydride volume fraction. In addition, hydride precipitation is associated with the development of elastic sectors along the crack faces and the reduction of the centered fan sectors; the relation between hydride precipitation zone stress trace and the extent of the centered fan sector is presented. The mode-I plane-strain blunted crack is also considered and the deviations from the logarithmic spiral slip-lines is discussed together with the reduction of hydride volume fraction as the blunted crack-tip is approached. A general fracture criterion, based on the strength of hydride platelets, is derived, which indicates that fracture occurs, when a critical hydride precipitation zone stress trace dominates. The criterion is applied, under the condition of a dominant K-field annulus, surrounding the plastic zone, and the estimated threshold stress intensity factor of delayed hydride cracking correlates favorably with experimental measurements.

A modified linear drag induced deceleration using a transformation of Newton’s second equation of motion

The drag force exerted on a body moving in a fluid is empirically known to follow a linear drag law at low Reynolds numbers and a quadratic drag law at very high Reynolds numbers. The major challenge with the empirical description of the drag lies in the uncertainty of the description of the drag coefficient as a function of velocity. If the function is precisely known, it may be possible to find a general formula for the drag, which would, in principle, be applicable for all Reynolds numbers. The general law can consequently be tested using the linear and quadratic drag laws within their validity regimes to confirm its reliability and validity. The current absence of such a general law implies that the prediction of the dynamics of a body moving under drag forces in the intermediate regime of the Reynolds number can only be approximate and inaccurate since it is not guided by any valid law. In this study, we derive a general relation for the drag force, which may be applicable in all the Reynolds number regimes. We achieve this through a simple transformation of Newton’s second equation for uniformly decelerated motion. It turns out that our general relation is a modification of the linear drag law. The effect of the introduced correction term in the dynamics of a projectile is evidently promising, as can be seen in the more realistic results generated.

Mathematical derivation of a unified equations for adjoint lattice Boltzmann method in airfoil and wing aerodynamic shape optimization

Unified equations of the adjoint lattice Boltzmann method (ALBM) are derived for five applicable objective functions in 2D/3D aerodynamic shape optimization problems. The derived equations include the adjoint equation, boundary condition, terminal condition and gradient of the cost function. In this research, firstly, these relations are extracted for each objective in details and then the general form of ALBM equations are presented for all defined practical aerodynamic objective function. Five applicable cost functions which are the most important objectives in optimization of aerodynamic geometries include desired pressure and viscous shear stress (VSS) inverse design, drag and moment at fixed lift and finally lift to drag ratio at fixed angle of attack. The new extracted relations are based on the circular and spherical function scheme, and are valid for viscous/inviscid, compressible/incompressible and 2D/3D flows in all continuous flow regimes. Proof of new extracted general relations have been performed by authors.

Origins of complexity in the rheology of Soft Earth suspensions

When wet soil becomes fully saturated by intense rainfall, or is shaken by an earthquake, it may fluidize catastrophically. Sand-rich slurries are treated as granular suspensions, where the failure is related to an unjamming transition, and friction is controlled by particle concentration and pore pressure. Mud flows are modeled as gels, where yielding and shear-thinning behaviors arise from inter-particle attraction and clustering. Here we show that the full range of complex flow behaviors previously reported for natural debris flows can be reproduced with three ingredients: water, silica sand, and kaolin clay. Going from sand-rich to clay-rich suspensions, we observe continuous transition from brittle (Coulomb-like) to ductile (plastic) yielding. We propose a general constitutive relation for soil suspensions, with a particle rearrangement time that is controlled by yield stress and jamming distance. Our experimental results are supported by models for amorphous solids, suggesting that the paradigm of non-equilibrium phase transitions can help us understand and predict the complex behaviors of Soft Earth suspensions.

General Relations between Stress Fluctuations and Viscoelasticity in Amorphous Polymer and Glass-Forming Systems.

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard-Jones particles.

Non-Gaussianity consistency relations and their consequences for the peaks

Strong deviations from scale invariance and the appearance of high peaks in the primordial power spectrum have been extensively studied for generating primordial black holes (PBHs) or gravitational waves (GWs). It is also well-known that the effect of non-linearities can be significant in both phenomena. In this paper, we advocate the existence of a general single-field consistency relation that relates the amplitude of non-Gaussianity in the squeezed limit f NL to the power spectrum and remains valid when almost all other consistency relations are violated. In particular, it is suitable for studying scenarios where scale invariance is strongly violated.We discuss the general and model-independent consequences of the consistency relation on the behavior of f NL at different scales.Specifically, we study the size, sign and slope of f NL at the scales where the power spectrum peaks and argue that generally the peaks of f NL and the power spectrum occur at different scales.As an implication of our results, we argue that non-linearities can shift or extend the range of scales responsible for the production of PBHs or GWs, relative to the window as determined by the largest peak of the power spectrum, and may also open up new windows for both phenomena.

Nonlinear hydroelastic vibration of foamed concrete beams via peridynamic differential operator

Evaluating the hydroelastic responses of underwater cementitious structural elements is critical for ensuring the sustainability and durability of energy-saving marine infrastructures. Existing work on the hydroelastic analysis of porous structures has been mostly developed using the general elastic constitutive relation; however, it fails to capture the influence of saturation. To fill this knowledge gap, we for the first time propose a novel fluid-porous structure interactive model that incorporates the combined effects of hydrodynamic pressure and saturation-induced pore pressure. One more pioneering effort is to solve this nonlinear hydroelastic problem by introducing peridynamic differential operator (PDDO). It is worth noting that the introduction of PDDO removes the inherent drawback employing the local-theory based techniques, namely being prone to singularities arising from the presence of discontinuity. The accuracy and reliability of the proposed numerical framework are validated by comparing the results with the degraded model in the reported literature. Moreover, our results highlight that the angular frequencies are underestimated when ignoring the effect of saturation in foamed concrete beams. The presented method provides a profound understanding of the underwater structural dynamic monitoring that benefits the design of marine infrastructures.

Non-piecewise hereditary Nakayama algebras

Happel and Seidel gave a classification of piecewise hereditary Nakayama algebras, where the relations are given by some power of the radical.Here we explore what happens for general relations. We develop techniques for showing that a given algebra is not piecewise hereditary, illustrating them on numerous mid-sized examples. Then we observe cases where the property of being non-piecewise hereditary can be extended to other (larger) Nakayama algebras. While a complete classification remains elusive, we are able to identify two types of patterns of relations preventing piecewise heredity, indicating that for large quivers many Nakayama algebras are non-piecewise hereditary.

Zhang-Rice singlets dominate critical temperature evolution of cuprate superconductivity

We show that formation of Zhang-Rice singlets (ZRS) naturally explains the empirical superconducting dome by random distribution of holes in copper-oxygen plane of cuprates. A general relation Tc/Tcmax=25(c-0.04), where c is the concentration of the ZRS and Tcmax is the maximum of critical temperature Tc, is obtained and reproduces the doping-dependent critical temperature evolution in the whole superconducting dome. The relation has been applied to estimate the effects of impurities substituting copper in the copper-oxygen plane. Our relation successfully predicts the suppression of superconductivity due to the substitution of Cu by the impurities. We demonstrate that Tc decreases linearly with the increase of the impurity concentration and the scattering range plays a key role in the suppression of the superconductivity. These results agree well with the experimental observations of the substitutions by Zinc and Nickel. Our relation is universal for all families of cuprates and explains the formation of the superconducting dome in the phase diagram.