Influence Matrix Research Articles

К ВОПРОСУ О ПОСТРОЕНИИ КОГНИТИВНЫХ КАРТ КОМПЕТЕНЦИЙ РАЗВИТИЯ ЧЕЛОВЕЧЕСКОГО КАПИТАЛА

An algorithm for the development of a matrix of implicit mutual influence of the competences of human capital development in high-tech and knowledge-intensive sectors of the economy is proposed and the degree of their interaction is determined. The Ishikawa diagram is constructed, which allows to visually determine the most significant casual connections between the estimated predictors. A cognitive map of human capital development competencies in high-tech and knowledge-intensive sectors of the economy is proposed, which is a formalized relationship between variables and allows one to assess the predictors that most strongly influence each other.

Applications of degenerate kernels to potential flow across circular, elliptical cylinders and a thin airfoil

In this paper, we employ the boundary integral equation (BIE) to analytically derive the solution of potential flow across a circular cylinder, an elliptical cylinder and a thin airfoil. It is found that the symmetric or antisymmetric potential flow problem can be solved by using the UT or the LM equation alone. Both analytical and numerical approaches were considered. The key tool is using the degenerate kernel instead of the closed-form fundamental solution. A closed-form fundamental solution is expressed in terms of degenerate kernel by using polar and elliptical coordinates for a circular cylinder and an elliptical cylinder, respectively. The role of the dual BEM is also examined by showing the singular vectors of influence matrix. Besides, either the singular or the hypersingular BIE are respectively employed alone to solve the problem of symmetric and anti-symmetric flow field. Analytical derivation as well as the BEM is demonstrated. The orientation of the ellipse, as well as the angle of attack for the thin airfoil, is considered. The result shows that the degenerate kernel can be an alternative tool for solving some BVPs, although the complex variable is always employed. Once the degenerate kernel for the closed-form fundamental solution is available, the BIE is nothing more than the linear algebra and an analytical study is possible. The extension to 3-D object is promising once the degenerate kernel is available.

Scaling of temporal entanglement in proximity to integrability

Describing dynamics of quantum many-body systems is a formidable challenge due to rapid generation of quantum entanglement between remote degrees of freedom. A promising approach to tackle this challenge, which has been proposed recently, is to characterize the quantum dynamics of a many-body system and its properties as a bath via the Feynman-Vernon influence matrix (IM), which is an operator in the space of time trajectories of local degrees of freedom. Physical understanding of the general scaling of the IM's temporal entanglement and its relation to basic dynamical properties is highly incomplete to present day. In this Article, we analytically compute the exact IM for a family of integrable Floquet models - the transverse-field kicked Ising chain - finding a Bardeen-Cooper-Schrieffer-like "wavefunction" on the Schwinger-Keldysh contour with algebraically decaying correlations. We demonstrate that the IM exhibits area-law temporal entanglement scaling for all parameter values. Furthermore, the entanglement pattern of the IM reveals the system's phase diagram, exhibiting jumps across transitions between distinct Floquet phases. Near criticality, a non-trivial scaling behavior of temporal entanglement is found. The area-law temporal entanglement allows us to efficiently describe the effects of sizeable integrability-breaking perturbations for long evolution times by using matrix product state methods. This work shows that tensor network methods are efficient in describing the effect of non-interacting baths on open quantum systems, and provides a new approach to studying quantum many-body systems with weakly broken integrability.

A new type of wind-resistance cable net for narrow suspension bridges and wind-resistance cable element for its calculation

In this paper, a new-style cable net structure consisting of a wind-resistance main cable, wind-resistance secondary cable and pulleys is proposed to improve the wind-resistance stability of narrow suspension bridges. In the improved structure, the wind-resistance secondary cable which slides on pulleys to achieve uniform distribution of cable force. However, the calculation for this structure is very difficult due to the sliding cable, which means the unstressed length of the cable between the pulleys is not fixed. To this end, a multi-node wind cable element considering the cable sliding on nodes is proposed for the wind-resistance secondary cable. Additionally, an analytical model of the wind cable element is established according to the structural features. The unstressed state method, virtual work principle and influence matrix method are all used to deduce and verify the tangent stiffness matrix of the element. As a result, the exact nodal forces can be calculated according to the static equilibrium conditions and the proposed element implemented for the nonlinear finite element analysis of the suspension bridge. Numerical and bridge examples are used to demonstrate that the new element can successfully simulate the sliding of the cable on the pulleys, and be applied to the nonlinear finite element calculation like any normal element. By means of this method, a wind-resistance secondary cable with any cable section connected by pulleys to the wind-resistance main cable and stiffening girder, can be accurately simulated with only one wind cable element. Hence, the calculation problem of the wind-resistance cable is resolved and overall calculation accuracy and efficiency are improved.

Study on Secondary Cable Adjustment for Cable-stayed Bridges Without back Cables

The structure of cable-stayed bridge without back cable is a new breakthrough.In this paper, the cable adjustment process of linzhou yingbin bridge is studied. the whole bridge model is established using the finite element software MIDAS CIVIL.This paper compares the measured cable force with the designed cable force and gets range of cable force difference, The influence matrix method is used for the second cable adjustment to ensure that the stress and structural deformation in the process of cable adjustment are within the range of the design requirements.The cable force variation of the whole bridge is detected by dynamic measuring instrument to ensure the construction safety in the process of cable adjustment.

Influence Matrix Approach to Many-Body Floquet Dynamics

In this work, we introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional. Focusing on a family of interacting, Floquet spin chains, we consider a Keldysh path-integral description of the dynamics. The central object in our approach is the influence matrix (IM), which describes the effect of the system on the dynamics of a local subsystem. For translationally invariant models, we formulate a self-consistency equation for the influence matrix. For certain special values of the model parameters, we obtain an exact solution which represents a perfect dephaser (PD). Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself: at each period, it measures every spin. For the models considered here, we establish that PD points include dual-unitary circuits investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the IM temporal entanglement is low. A combination of analytical insights and MPS computations allows us to characterize the structure of the influence matrix in terms of an effective "statistical-mechanics" description. We finally illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes. The influence matrix approach formulated here provides an intuitive view of the quantum many-body dynamics problem, opening a path to constructing models of thermalizing dynamics that are solvable or can be efficiently treated by MPS-based methods, and to further characterizing quantum ergodicity or lack thereof.

A wavelet immersed boundary method for two-variable coupled fluid-structure interactions

In this paper, a wavelet immersed boundary (IB) method is proposed to solve fluid-structure interaction (FSI) problems with two-variable coupling, in which it is an interaction between fluid force and boundary deformation. This wavelet IB method is developed by introducing a wavelet finite element method to calculate the FSI force affected by the two-variable coupling. Furthermore, a boundary influence matrix and a series of B-spline wavelet delta functions are constructed to restrain the non-physical force oscillations. Finally, several FSI problems are simulated, which include flows past a fixed circular cylinder and a crosswise oscillating circular cylinder, as well as an in-line oscillating circular cylinder in a rest fluid. The numerical examples show that the new method is a simple and efficient method for two-variable coupled FSI problems.

Multi-attribute group decision making with opinion dynamics based on social trust network

Social trust network (STN) has facilitated information exchange between experts during interactions. Some feedback mechanisms have been used to provide advices for opinion change to improve their consensus levels. However, they do not consider the experts’ willingness and their self-confidence values. To analyze the influence of the relationship between experts on the decision-making results, this paper proposes a multi-attribute group decision making (MAGDM) with opinion dynamics based on STN. Three stages are included in the proposed approach: trust propagation, consensus reaching process and alternative selection. In the trust propagation stage, the social weight influence matrix and the weights of experts are obtained based on the complete social trust matrix which is constructed by trust aggregation and the given self-confidence values of experts. In the consensus reaching process, the consensus measure is used to determine the consensus between the experts or not, and the feedback mechanism based on opinion dynamics is used to adjust the opinions which do not reach consensus. The appropriate alternative is selected based on the assessable value of the alternative in the selection process. Finally, a numerical experiment about supplier selection is introduced to illustrate the efficiency of the proposed approach and comparison analyses show that the proposed approach can improve efficiency compared with the MAGDM in the social network.

Mathematical Development of a Novel Discrete Hip Deformation Algorithm for the In Silico Elasto-Hydrodynamic Lubrication Modelling of Total Hip Replacements

In this paper, the procedure to achieve an accurate deformation model of a total hip replacement (THR) was proposed with the aim to obtain a numerical tool to be simply merged into THR elasto-hydrodynamic computational synovial lubrication algorithms. The approach was based on the Finite Element Method (FEM) and was developed in a Matlab code, allowing the definition of the influence matrix and of a boundary conditions vector. It works with linear tetrahedra and performs the displacement calculation for both the acetabular cup and the femoral head, taking into account the anatomical hip relative motion, by coupling them with a cubic interpolation matrix. Two simulations were conducted in order to validate the algorithm and the results were compared with the ones obtained by the commercial software Ansys. The comparison provides a satisfactory agreement in terms of surface deformation, Von Mises stress and strain energy, proving the reliability of the model and the possibility to use the model in the in silico prostheses tribological simulations, avoiding the complexity and the high computational resource requirement coming from the coupling between complex lubrication algorithms and FEM commercial software, and with the possibility to directly act on many key parameter characteristics of the investigated problem.

Active Optical Control with Machine Learning: A Proof of Concept for the Vera C. Rubin Observatory

Abstract The Active Optics System of the Vera C. Rubin Observatory (Rubin) uses information provided by four wave front sensors to determine deviations between the reconstructed wave front and the ideal wave front. The observed deviations are used to adjust the control parameters of the optical system to maintain image quality across the 3.°5 field of view. The baseline approach from the project is to obtain amplitudes of the Zernike polynomials describing the distorted wave front from out-of-focus images collected by the wave front sensors. These Zernike amplitudes are related via an “influence matrix” to the control parameters necessary to correct the wave front. In this paper, we use deep-learning methods to extract the control parameters directly from the images captured by the wave front sensors. Our neural net model uses anti-aliasing pooling to boost performance, and a domain-specific loss function to aid learning and generalization. The accuracy of the control parameters derived from our model exceeds Rubin requirements even in the presence of full-moon background levels and mis-centering of reference stars. Although the training process is time consuming, model evaluation requires only a few milliseconds. This low latency should allow for the correction of the optical configuration during the readout and slew interval between successive exposures.

Методы моделирования и идентификация параметров неоднородных анормальных неврологических движений многокомпонентных нейробиосистемах с когнитивными обратными связями

Разработаны основы математического моделирования и идентификации параметров неоднородных анормальных неврологических движений (АНР) в многокомпонентных нейробиосистемах с обратными когнитивными связями. На основе развитых авторами методов интегральных превращений и спектрального анализа для неоднородных сред предложен новый подход к построению гибридных моделей распространения волнового сигнала, описывающего нежелательные дрожания конечности руки пациента (Т-объекта) в результате самопроизвольного сокращения скелетных мышц. за счет когнитивных воздействий отдельной группы нейронных узлов коры головного мозга (КГМ). Разработана гибридная модель нейробиосистемы, описывающая состояние и поведение Т-объектов, а именно посегментное описание 3D-элементов траекторий АНР Т-объекта с учетом матрицы когнитивных воздействий групп нейроузлов КГМ. На основе гибридных интегральных преобразований Фурье получено высокоскоростное аналитическое векторное решение модели, описывающей элементы траекторий на каждом АНР-сегменте. Предложена новая методика вычисления гибридной спектральной функции, спектральных значений и матрицы когнитивных воздействий нейроузлов КГМ, определяющих гибридное интегральное преобразование построения решения. Сформулированы и решены новые неклассические задачи многопараметрической идентификации нейросистем с обратной связью в неоднородных средах на основе минимизации функционала-невязки между траекториями наблюдения и их модельными аналогами. Построены высокопроизводительные алгоритмы идентификации амплитудно-частотных характеристик систем обратной связи для компонентной оценки влияния когнитивных обратных связей, позволяющих распараллелировать вычисления для многоядерных компьютеров. Выполнено компьютерное моделирование и идентификацию АНР-траекторий нейросистем обратной связи.

Research of Indicators of the Internal and External Environment Influencing the Implementation of the Demand Management System (Demand Side Management) in the Russian Industry

The relevance of the presented research is determined by the need of the Russian economy for the implementation of advanced methods for improving energy efficiency, one of which is the demand management system for electricity and gas consumption. The objective of the article is to identify a set of macro environmental factors that have a limiting effect on the implementation of an integrated demand management system for the consumption of electricity and natural gas in the Russian economy. The research methods are methods of analysis, synthesis and analytical grouping. On the basis of the PESTEL-analysis, the author carried out a classification of the entire spectrum of factors into six categories: political, economic, socio-cultural, technological, environmental and legal. For each factor the degree of influence on the project of introducing a demand management system was determined on the basis of four signs of degree of importance. According to the influence matrix, all the factors were ranked by degree of influence and probability of occurrence and were prioritized as high, medium and low. For the factors of high and medium priority, a complex of preemptive actions was developed, including administrative control, regulatory and innovative measures. The identified factors, as well as their detailed analysis and classification, form the basis for the development of methodological support for an integrated demand management model for electricity and gas consumption in Russia.

On the linkage between influence matrices in the BIEM and BEM to explain the mechanism of degenerate scale for a circular domain

ABSTRACT In this paper, we proposed two ways to understand the rank deficiency in the continuous system (boundary integral equation method, BIEM) and discrete system (boundary element method, BEM) for a circular case. The infinite-dimensional degree of freedom for the continuous system can be reduced to finite-dimensional space using the generalized Fourier coordinates. The property of the second-order tensor for the influence matrix under different observers is also examined. On the other hand, the discrete system in the BEM can be analytically studied, thanks to the spectral property of circulant matrix. We adopt the circulant matrix of odd dimension, (2N + 1) by (2N + 1), instead of the previous even one of 2N by 2N to connect the continuous system by using the Fourier bases. Finally, the linkage of influence matrix in the continuous system (BIE) and discrete system (BEM) is constructed. The equivalence of the influence matrix derived by using the generalized coordinates and the circulant matrix are proved by using the eigen systems (eigenvalue and eigenvector). The mechanism of degenerate scale for a circular domain can be analytically explained in the discrete system.

Procedure for the identification of multiple influential observations in block design for incomplete multi-response experiments in presence of masking

In agricultural experiments, if outliers are present in a data set, inference of experiment may be reversed. The purpose of this article is to develop a method for detection of subset of outlier vectors in block designs for incomplete multiresponse experiments in presence of masking. We defined an influence matrix comprising of Cook-statistics in its diagonal and product of two Cook-statistics in its off-diagonal positions. We then obtained eigenvectors corresponding to large eigenvalues of this matrix which can be used for identification of influential subsets. The proposed procedure has been illustrated with a real life data set.

Formation of Moments Influence Matrix in Frame Based on Graph of its Design Scheme

A procedure is proposed for the automated construction of the bending moments influence matrix in the frame based on the graph of its discrete model. Forming the incidence matrix of the graph characterizing the topological structure of the design scheme of the frame, through matrix transformations of the displacement vectors, at the transition from local coordinate systems to a global system, it is possible to establish the relationship between the nodal displacements and the displacement increments of individual sections in the direction of the axis of the segment and perpendicular to it. The composition of only three initial matrices of the frame structure, the incidence matrix of the graph, the node coordinate matrix and the matrix of the frame model internal rigidity, solves the problem of automatic formation of the bending moments influence matrix with the help of a PC. The procedure proposed for the construction of the influence matrix, makes it possible to find the forces in the frame structure caused by external load, in the matrix form.

Analysis of nonlinear gas turbine models using influence coefficients

The limited availability of gas turbine data, especially faults data and the high costs and risks of using test benches to obtain it,causes that rarely have enough data for form a fault classification. These circumstances have created the need to develop models that can provide simulated data. The quality of the data generated depends on the complexity of the thermodynamic model and the mathematical solution. A method to evaluate the accuracy of the models and their linearization capacity is presented. The method is applied to the models of a turbo shaft and a turbo fan of the commercial software GasTurb 12, as an example. It was simulated a wide database with influence of fault parameters and condition operation, then it calculed the influence matrix ""H"" and ""G"" for prove the influence theirs on behavior of the models. The results show that if the model is sufficiently accuracy, it is possible to find an adequate interval where the linearization errors are not very large and it is just possible the linearization.

Cable optimization of a cable-stayed bridge based on genetic algorithms and the influence matrix method

Structural optimization is an important tool for structural designers that helps them to find innovative design solutions and structural forms with a better exploitation of materials as well as decreased self-weight and minimum material costs. In this article, a design procedure coupling the influence matrix method and genetic algorithms to optimize stay cables in cable-stayed bridges is presented. Following that, the design procedure is utilized in the preliminary design of a twin towers double-cable planes cable-stayed bridge to be located in Ferrara, Italy. The cable cross-sectional areas and corresponding pre-tension forces are optimized simultaneously. The results demonstrate that the proposed procedure is a powerful tool for designing stay cables and predicting the optimum cross-sectional areas of stay cables under certain stress and displacement constraints.

Study on the stress intensity factor and the double-degeneracy mechanism in the BEM/BIEM for anti-plane shear problems

The crack and the rigid-line inclusion problems under the anti-plane shear are the special case of the elliptic hole and elliptic rigid inclusion, respectively. We revisit this kind of problem by using the degenerate kernels in terms of the elliptic coordinates. The stress intensity factor (SIF) is also addressed. Three ways are employed to determine the SIF. One is the extrapolation approach for the boundary or interior displacement near the tip. Another is the extrapolation approach for the boundary stress or interior stress near the tip. The other is the J-integral enclosing the crack tip. It is interesting to find that a rigid-line inclusion case yields a singular influence matrix due to the degenerate scale of length four in the log kernel. However, double-degeneracy including degenerate scale and degenerate boundary may still result in a singular matrix even though the dual BEM/BIEM is employed. The mechanism is well explained thanks to the introduction of degenerate kernel. Without the introduction of degenerate kernel, the mechanism of the double-degeneracy problem in the BIEM can’t be clearly examined. By using the degenerate kernel, the SIF can be easily determined for the crack or the rigid-line inclusion under the anti-plane shear. The path independence of the J-integral can be derived analytically. The reciprocal relation for the SIF between a crack and a rigid-line inclusion with respect to opposite loading is also addressed. In the numerical implementation, the SIF can be determined using the dual BEM. It is worth noting that BEM shows the advantage that the obtained boundary displacement or boundary stress can be directly used to obtain the more accurate SIF for the crack or the rigid inclusion, respectively.

The Modeling of Preference Degree based on Asymmetric Effect

The concept of preference is related favor or support on some opinions or objects. It has potential application values in many social or economic management fields. This paper aims to evolutionary problems of preference of general social economic systems. Preference degree evolutionary dynamics model is proposed by employing ordinary differential equations. The interplay of individuals’ preference is described by this model. Furthermore, numerical results reveal that influence matrix of characterizing individual interactions will conduct essential effects on final distribution of preference.

Learning Influential Cognitive Links in Social Networks by a New Hybrid Model for Opinion Dynamics

A principled approach to modeling sociocognitive networks is fundamental to understanding the network interrelations which in turn can be used in many applications such as human behavior analysis or team performance assessment. More specifically, in the opinion domain, learning the cognitive links and making a proper model for causal relationships between individuals is necessary for both analysis and control purposes. There are several mathematical models for opinion dynamics. However, few of them have been tested to be consistent with real-world data. In this article, a new hybrid model for opinion dynamics is proposed and is put to test with subjective experiments. It is imperative that a realistic model considers two cognitive facts: 1) a person tends to stick to his/her previously shaped opinion and 2) the opinion of a person is affected by others (either reinforced in a positive way or undermined negatively). This article presents a novel mathematical formulation of the proposed opinion dynamics model and proves its stability too. The new model is also extended to support multiple dimensions. In the multidimensional approach, opinions about two or more subjects are considered separately. The rationale behind this is to describe the evolution of agents’ opinions on several topics. To study how the model performs in reality, some real-world experiments are conducted and the influence matrix is learned in each case. In addition, a method is introduced to extract the parameters of the model from the experimental data. It is shown that the new model predictions, after it is trained, chase the real behaviors of participants very well and result in less error compared with the previous models.