Approximate Analysis Research Articles

Evolutionary games on networks: Phase transition, quasi-equilibrium, and mathematical principles

The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such “stable” cooperation ratios obtained via approximate methods might not be actually stable, but correspond to quasi-equilibriums instead. We find that various classic game models, like the evolutionary snowdrift game, evolutionary prisoner’s dilemma, and spatial public goods game on square lattices and scale-free networks, exhibit the phase transition in convergence time to the equilibrium state. Moreover, mathematical principles are provided to explain the phase transition of convergence time and quasi-equilibrium of cooperation ratio. The findings explain why and when cooperation and defection have a long-term coexistence.

Застосування згладжуючих кубічних сплайнів у моделюванні процесів повзучості лінійно-вʼязкопружних матеріалів за умов складного напруженого стану

The processes of creep of thin-walled tubular elements made of linear viscoelastic materials under complex stress conditions are considered. The discrete values of basic experimental data on uniaxial tension and pure torsion are considered. These discrete values are used for identification of hereditary kernels normally used in creep modeling processes under complex stress conditions. As an example material, plexiglass ST1 is used for calculations. The area of linearity of the model is substantiated by the value of the quantile of statistics and the hypothesis of the existence of a unified creep function in a certain, predetermined confidence interval. The creep function is invariant with respect to stresses and is built with making use of the yield curves. Constitutive equations of the model contain a set of functions and coefficients determined from basic experiments. For further calculations, the experimental data are approximated by a power function followed by the smoothing with cubic splines. Approximation analysis is carried out by evaluation of the least squared deviation of experimental data from the calculated data. The approximating function is analyzed with making use of minimum of the quadratic deviation.

Approximation and error analysis of forward–backward SDEs driven by general Lévy processes using shot noise series representations

We consider the simulation of a system of decoupled forward–backward stochastic differential equations (FBSDEs) driven by a pure jump Lévy process L and an independent Brownian motion B. We allow the Lévy process L to have an infinite jump activity. Therefore, it is necessary for the simulation to employ a finite approximation of its Lévy measure. We use the generalized shot noise series representation method by [26] to approximate the driving Lévy process L. We compute the Lp error, p ≥ 2, between the true and the approximated FBSDEs which arises from the finite truncation of the shot noise series (given sufficient conditions for existence and uniqueness of the FBSDE). We also derive the Lp error between the true solution and the discretization of the approximated FBSDE using an appropriate backward Euler scheme.

A Novel Operation Optimization Method Based on Mechanism Analytics for the Quality of Molten Steel in the BOF Steelmaking Process

This paper investigates a dynamic analytics and operation optimization method for the basic oxygen furnace (BOF) steelmaking process, which is a multi-stage process. First, based on reaction kinetics, fluid dynamics and conservation of mass, that a novel discrete-time nonlinear system with process disturbance, time delay and the constrained operation input is established characterizes the dynamics of the quality (the carbon content and the temperature) of molten steel in the BOF steelmaking process. It is difficult and complicated to realize analytics and operation optimization for the BOF steelmaking process by using the established nonlinear system directly, so a surrogate-model-based discrete-time switched system with time delay and actuator saturation is given to describe the multi-stage BOF steelmaking process. Then, sufficient conditions are derived under which the stability is guaranteed and the tracking performance is achieved. The parameters of analytics-based operation optimization algorithm can be obtained by solving linear matrix inequality problems (LMIPs). Finally, the effectiveness of the proposed method is verified by a BOF steelmaking numerical experiment example. Note to Practitioners—This paper deals with the problem of dynamic analytics and operation optimization arising from the BOF steelmaking process. Based on the real-time estimation of the carbon content and the temperature of molten steel, the plan for the operation of oxygen lance and the addition of auxiliary materials is given to produce the qualified molten steel. This paper establishes a system model based on the mechanism, and the model parameters are derived from papers verified by a large amount of data to ensure the correctness of the model. In addition, actuator saturation is applied to describe the phenomenon of restricted operation variables. Through a surrogate model approximation and theoretical analysis, the parameters of dynamic analytics and operation optimization algorithm can be obtained by solving LMIPs, which is a convex optimization problem that is easy to solve. The numerical experiment results show that the proposed method can give operators some desired references.

Differentiated approach to the diagnostics of economic security and resilience of Russian regions (case of the Volga federal district)

Relevance. Given the volatile global economy, unfriendly policy towards Russia and other external challenges, it is necessary to improve tools for predicting threats and risks to regional economic security and resilience. To this end, individual projections and indicators, as well as complex models should be examined. Research objective. The study aims to develop a new differentiated approach to diagnostics of indicators (projections) of economic security and resilience at the regional level, which can help visualize and evaluate threats to economic meso-systems. Data and Methods. Comparative and indicative approaches, ranking, piecewise linear approximation (scaling) and correlation analysis were used in the study. Results. As a result, the study presents the author's system of indicators of economic security and risks to the regional economy based on a differentiated approach. 36 indicators were grouped into 4 projections – general economic, social, technological and financial – and divided into sub-projections. In order to provide adequate and comparable estimates in the regional and temporal context, various methodological principles were used: application of relative indicators; assessment of cost indicators of regional development using the number of fixed market baskets (FMB) of the region (ratio of the regional cost indicator and the cost of a fixed market basket). Such approach allowed us to evaluate regional economic security in dynamics. The diagnostics of resilience of regional economic systems was performed in the context of individual projections by comparing crisis and relatively stable periods. Conclusions. The methodology was tested using data from regions of the Volga Federal District. The study revealed specific projections, sub-projections and indicators affected by threats, as well as demonstrated the ability of regions of the Volga Federal District to face the crisis and, in particular, resist sanctions.

Analysis of approximations of the gas compressibility factor derived from genetic algorithms

Hydraulic calculations are the primary tool for rational technical decisions related to the design and operation of pipeline systems. The compressibility factor is introduced into the gas equation of state to account for its real properties and depends on the pressure, temperature, and gas component composition. At present, the search for an accurate and computationally efficient approximation for the compressibility factor remains an urgent problem. This paper presents a methodology for constructing an approximation based on symbolic regression, and the proposed dependencies analysis provided. The average relative error of the presented models is 0.03%.

Error analysis of approximation of derivatives by means of the Sinc approximation for double-exponentially decaying functions

Error analysis of approximation of derivatives by means of the Sinc approximation for double-exponentially decaying functions

Approximation Analysis of Convolutional Neural Networks

Approximation Analysis of Convolutional Neural Networks

Research on AC Electronic Load with Energy Recovery Based on Finite Control Set Model Predictive Control

Nowadays, AC electronic loads with energy recovery are widely used in the testing of uninterruptible power supplies and power supply equipment. To tackle the problems of control difficulty, strategy complexity, and poor dynamic performance of AC electronic load with energy recovery of the conventional control strategy, a control strategy of AC electronic load with energy recovery based on Finite Control Set Model Predictive Control (FCS-MPC) is developed. To further reduce the computation burden of the FCS-MPC, a simplified FCS-MPC with transforming the predicted variables and using sector to select expected state is proposed. Through simplified model and equivalent approximation analysis, the transfer function of the system is obtained, and the stability and robustness of the system are analyzed. The performance of the simplified FCS-MPC is compared with space vector control (SVPWM) and conventional FCS-MPC. The results show that the FCS-MPC method performs better dynamic response and this advantage is more obvious when simulating high power loads. The simplified FCS-MPC shows similar control performance to conventional FCS-MPC at less computation burden. The control performance of the system also shows better simulation results.

Theoretical and Numerical Estimate of Signal-to-Noise Ratio in the Analysis of Josephson Junctions Lifetime for Photon Detection

The performances of a Josephson junction employed to reveal a train of pulses (a rough model for single photon detection) are analyzed with a theoretical estimate that exploits an index employed in statistical decision theory, the Kumar–Carroll index. The approximate analysis compares the numerically simulated performances of the device through the receiver operating characteristics, that offer an overview of the rate of false detection, as well as the probability to miss a signal (in this case, a pulse train). It is thus demonstrated the usefulness and the limits of the succinct Kumar–Carroll parameter. On the first side, it is proven that an increase of the parameter corresponds to an improvement of the detection. However, on the side of the limitations, the expected performances are not quite accurate, for the actual performances are systematically worse than the theoretical estimates. The results may be relevant to characterize Josephson junctions as detectors of weak signals, as those stemming from axions.

Composite wing vibration coupling control

The paper discusses the possibility to control coupled bending-twisting vibrations of composite wing by means of the monoclinic structures in the reinforcement of the plating. Decomposing the potential straining energy and kinetic energy of natural vibration modes into interacting and non-interacting parts, it became possible to introduce the two coefficients that integrally consider the effect of geometry and reinforcement structure upon the dynamic response parameters of the wing. The first of these coefficients describes the elastic coupling of the natural vibration modes, the second coefficient describes the inertial one. The paper describes the numerical studies showing how the orientation of considerably anisotropic CRP layers in the plating affects natural frequencies, loss factors, coefficients of elastic and inertial coupling for several lower tones of natural bending-twisting vibrations of the wing. Besides, for each vibration mode, partial values of the above mentioned dynamic response parameters were determined by means of the relationships for orthotropic structures where instead of “free” shearing modulus in the reinforcement plant, “pure” shearing modulus is used. Joint analysis of the obtained results has shown that each pair of bendingtwisting vibration modes has its orientation angle ranges of the reinforcing layers where the inertial coupling caused by asymmetry of the cross-section profile with respect to the main axes of inertia decreases, down to the complete extinction, due to the generation of the elastic coupling in the plating material. These ranges are characterized by the two main features: 1) the difference in the natural frequencies of the investigated pair of bendingtwisting vibration modes is the minimum and 2) natural frequencies of bending-twisting vibrations belong to a stretch restricted by corresponding partial natural frequencies of the investigated pair of vibration modes. This result is of practical importance because it enables approximate analysis of real composite wings with complex geometry in the existing commercial software packages.

축류펌프의 입구 안내깃 모사에 따른 성능 및 내부 유동장에 관한 수치해석적 연구

In this study, an absolute flow angle was numerically assigned to the inlet of an axial pump in order to predict its performance and internal flow field prior to the design process of an inlet guide vane. The finite volume method, which is an approximate analysis method based on the three-dimensional Reynolds-averaged Navier-Stokes (RANS) equation, was applied for discretization of governing equations. The shear stress transport (SST) model was used as the turbulence model and the hexahedral grid system was selected as the appropriate number of nodes through the grid dependency test. The change in the performance curve and internal flow field was found with respect to the difference in the absolute flow angle at the impeller inlet. When installing a variable inlet guide vane of an axial flow pump, an efficient operation plan by adjusting the angle of an inlet guide vane might be established with the results of this study.

Single-nucleus RNA and ATAC sequencing uncovers the molecular and cellular characteristics in the musk gland of Chinese forest musk deer (Moschus berezovskii).

The Chinese forest musk deer (FMD; Moschus berezovskii) is an endangered artiodactyl mammal. Musk secreted by the musk gland of male has extremely high economic and medicinal value. However, the molecular and cellular characteristics of the musk gland have not been studied. Here, we investigated the diversity and transcriptional composition of musk gland cell types and the effect of cell type-specific chromatin accessibility on gene expression using single-nucleus RNA sequencing (snRNA-seq) and single-nucleus ATAC sequencing (snATAC-seq) association analysis. Based on uniform manifold approximation and projection (UMAP) analysis, we identified 13 cell types from the musk gland, which included two different acinar cells (cluster 0 and cluster 10). Kyoto Encyclopedia of Genes and Genomes (KEGG) enrichment analysis indicated that many pathways related to musk secretion were enriched in acinar cells. Our analysis also revealed acinar cell core transcription factors and core target genes, and further constructed acinar cell-specific regulatory networks. In cluster 0, 11 core target genes (Nedd4l, Adcy9, Akr1c1, Vapb, Me1, Acsl1, Acss3, Srd5a1, Scnn1a, Acadm, and Nceh1) possibly related to musk secretion were regulated by 24 core transcription factors (SP3, NFIC, NR6A1, EHF, RUNX1, TFAP2A, RREB1, GRHL2, NFIB, ELF1, MAX, KLF5, REL, HES1, POU2F3, TFDP1, NR2C1, ATF7, MEIS1, NR4A2, NFIA, PBX1, ZNF652, and NFKB1). In cluster 10, four core target genes (Akr1c1, Pcca, Atp1b1, and Sgk1) possibly related to musk secretion were regulated by 10 core transcription factors (BARX2, EHF, PBX1, RUNX1, NFIB, FOXP1, KLF3, KLF6, ETV6, and NR3C2). Moreover, the credibility of snRNA-seq and snATAC-seq data was verified by fluorescence in situ hybridization and immunohistochemistry. Finally, cell communication analysis demonstrated that the two types of acinar cells mainly have communications in musk secretion-related processes. In conclusion, we provided important insights and invaluable resources for the molecular and cellular characteristics of the musk gland, which will lay a foundation for the study of musk secretion mechanism in the future.

A Symbolic Approach to Detecting Hardware Trojans Triggered by Don’t Care Transitions

Due to the globalization of Integrated Circuit supply chain, hardware Trojans and the attacks that can trigger them have become an important security issue. One type of hardware Trojans leverages the “don’t care transitions” in Finite-state Machines (FSMs) of hardware designs. In this article, we present a symbolic approach to detecting don’t care transitions and the hidden Trojans. Our detection approach works at both register-transfer level (RTL) and gate level, does not require a golden design, and works in three stages. In the first stage, it explores the reachable states. In the second stage, it performs an approximate analysis to find the don’t care transitions and any discrepancies in the register values or output lines due to don’t care transitions. The second stage can be used for both predicting don’t care triggered Trojans and for guiding don’t care aware reachability analysis. In the third stage, it performs a state-space exploration from reachable states that have incoming don’t care transitions to explore the Trojan payload and to find behavioral discrepancies with respect to what has been observed in the first stage. We also present a pruning technique based on the reachability of FSM states. We present a methodology that leverages both RTL and gate-level for soundness and efficiency. Specifically, we show that don’t care transitions and Trojans that leverage them must be detected at the gate-level, i.e., after synthesis has been performed, for soundness. However, under specific conditions, Trojan payload exploration can be performed more efficiently at RTL. Additionally, the modular design of our approach also provides a fast Trojan prediction method even at the gate level when the reachable states of the FSM is known a priori . Evaluation of our approach on a set of benchmarks from OpenCores and TrustHub and using gate-level representation generated by two synthesis tools, YOSYS and Synopsis Design Compiler (SDC), shows that our approach is both efficient (up to 10× speedup w.r.t. no pruning) and precise (0% false positives both at RTL and gate-level netlist) in detecting don’t care transitions and the Trojans that leverage them. Additionally, the total analysis time can achieve up to 1.62× (using YOSYS) and 1.92× (using SDC) speedup when synthesis preserves the FSM structure, the foundry is trusted, and the Trojan detection is performed at RTL.

Analytic structure of the Landau gauge quark propagator from Padé analysis

The analytic structure of the two flavorful QCD lattice Landau gauge quark propagator is investigated with Pad\'e approximants applied to its vector and scalar form factors. No poles at complex momentum are observed for the propagator. Moreover, there is clear evidence of a pole at real on-axis negative Euclidean momentum, i.e., for a Minkowski type of momentum. This pole occurs at Euclidean momenta $p\ensuremath{\sim}\ensuremath{-}300\text{ }\text{ }\mathrm{MeV}$ and it reproduces typical quark mass values used in phenomenological effective quark models. The Pad\'e approximant analysis also gives hints on the presence of a branch cut. Our results also show a clear correlation between the position of this pole, understood as an effective quark mass, and the pion mass that is compatible with partial conservation of the axial current. Slightly differences between the poles for the two quark form factors are observed which can be viewed either as a limitation of the method or as a suggestion that the quark propagator has no spectral representation.

String stability in traffic flows

String stability or instability is a fundamental issue in traffic flow about whether the speed oscillations of the leading vehicle are damped or amplified as such oscillations pass through the platoon. If they are amplified, then traffic jams will occur. In this paper, we propose a suitable notion of string stability for continuum models of traffic flows, and study what kinds of driving behaviors lead to string stability or instability. We find that the well-known Lighthill-Whitham-Richards model and Aw-Rascle-Zhang model are string stable for wide classes of perturbations. As a consequence, the driving behaviors described by these models suppress speed oscillations and hence do not cause traffic jams. Once the hysteresis behavior is added to the Lighthill-Whitham-Richards model, an example is given to show that string instability can occur for large perturbations, leading to phantom jams. Under small perturbations, however, examples as well as approximate solution analysis suggest that the hysteretic traffic flow is string stable. The approximation solution analysis is developed to replace linear stability analysis, as hysteretic flow model cannot be linearized.

Approximate entropy analysis across electroencephalographic rhythmic frequency bands during physiological aging of human brain.

Aging is the inevitable biological process that results in a progressive structural and functional decline associated with alterations in the resting/task-related brain activity, morphology, plasticity, and functionality. In the present study, we analyzed the effects of physiological aging on the human brain through entropy measures of electroencephalographic (EEG) signals. One hundred sixty-one participants were recruited and divided according to their age into young (n = 72) and elderly (n = 89) groups. Approximate entropy (ApEn) values were calculated in each participant for each EEG recording channel and both for the total EEG spectrum and for each of the main EEG frequency rhythms: delta (2-4Hz), theta (4-8Hz), alpha 1 (8-11Hz), alpha 2 (11-13Hz), beta 1 (13-20Hz), beta 2 (20-30Hz), and gamma (30-45Hz), to identify eventual statistical differences between young and elderly. To demonstrate that the ApEn represents the age-related brain changes, the computed ApEn values were used as features in an age-related classification of subjects (young vs elderly), through linear, quadratic, and cubic support vector machine (SVM). Topographic maps of the statistical results showed statistically significant difference between the ApEn values of the two groups found in the total spectrum and in delta, theta, beta 2, and gamma. The classifiers (linear, quadratic, and cubic SVMs) revealed high levels of accuracy (respectively 93.20 ± 0.37, 93.16 ± 0.30, 90.62 ± 0.62) and area under the curve (respectively 0.95, 0.94, 0.93). ApEn seems to be a powerful, very sensitive-specific measure for the study of cognitive decline and global cortical alteration/degeneration in the elderly EEG activity.

Analysis of using Newton’s ring to test lens surface radius of curvature

When using Newton’s ring to test lens surface radius of curvature, the air gap in between the master plate and the lens can have either a positive or a negative meniscus shape. The optics for the negative meniscus shape air gap has been widely analyzed and the results are assumed to be valid for the positive meniscus shape air gap. Accurate and approximate analysis are performed in this paper for the positive meniscus shape air gap. Analysis results of this paper show that for the same parameters involved, the Newton’s ring number for the positive meniscus shape air gap is larger than the Newton’s ring number for the negative meniscus shape air gap. The difference between these two Newton’s ring numbers increases as the value of h / r increases, where h is the lens half diameter and r is the master plate surface radius of curvature. For h / r = 0.87, the ratio of these two numbers can be as large as 2.

DETERMINATION, ANALYSIS AND SYNTHESIS OF THE ROOTS OF VALID ALGEBRAIC EQUATIONS USING LOGARITHMIC AMPLITUDE-PHASE FREQUENCY CHARACTERISTICS

The article considers the method of approximate determination, analysis and synthesis of the roots of real algebraic equations of high order. The solution of such problems is relevant in the case of designing information-measuring and control systems, studying the dynamics of movement of various mechanisms (industrial robots, quadrocopters, etc.), determining the trajectories of aircraft, etc. The analytical solution of such problems is limited to equations of the third (sometimes fourth) degree, in other cases it is necessary to use either special sequential algorithms or packages of applied computer programs such as "Wolfram.Matematica", which allow only to find the roots of the equations, but not to synthesize them. The proposed method is based on the application for the decomposition of the studied polyomial (corresponding to the equation) into the simplest multipliers corresponding to aperiodic and/or oscillatory links, asymptotic logarithmic amplitude and phase-frequency characteristics. The form and values of the roots of the equation are proposed to be judged by the slopes at the fracture points of the logarithmic amplitude and phase-frequency characteristics of the polyparticle under study. The construction of logarithmic amplitude and phase-frequency characteristics is carried out by discarding the "small" terms of the polygamy at separate frequency intervals. A feature of the method is the possibility of its use both in conjunction with the computer and without it. Manual use of the method assumes that the user has a calculator and a ruler. The method allows to determine not only the roots of real algebraic equations (both real and complex), but also to establish a visual relationship between the coefficients for the terms of the equations with the type and values of the roots and purposefully change the necessary coefficients to change the parameters and type of roots. The possibilities of the method are not limited to solving real algebraic equations with positive coefficients and integer powers, it shows quite satisfactory results for equations with mixed coefficients and fractional powers. The method is quite simple, clear, has a small error in the case of far spaced roots, but in the case of closely spaced roots, its error increases, although it remains quite acceptable. The article presents the substantiation of the method, shows numerous examples of its capabilities, compares the results obtained with the results obtained with the help of the package of applied computer programs "Wolfram.Matematica".

Convergence rate analysis of Galerkin approximation of inverse potential problem

In this work we analyze the inverse problem of recovering a space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very mild conditions on the problem data. Then we provide an error analysis of a standard reconstruction scheme based on the standard output least-squares formulation with Tikhonov regularization (by an H 1-seminorm penalty), which is then discretized by the Galerkin finite element method with continuous piecewise linear finite elements in space (and also backward Euler method in time for parabolic problems). We present a detailed error analysis of the discrete scheme, and provide convergence rates in a weighted for discrete approximations with respect to the exact potential. The error bounds explicitly depend on the noise level, regularization parameter and discretization parameter(s). Under suitable conditions, we also derive error estimates in the standard and interior L 2 norms. The analysis employs sharp a priori error estimates and nonstandard test functions. Several numerical experiments are given to complement the theoretical analysis.