scholarly journals Topology Identification of Coupling Map Lattice under Sparsity Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Jiangni Yu ◽  
Lixiang Li ◽  
Yixian Yang
Keyword(s):  
Mathematical Model ◽  
Coupling Coefficient ◽  
Good Accuracy ◽  
Linear Equations ◽  
Identification Problem ◽  
Measurement Time ◽  
High Entropy ◽  
Topology Identification ◽  
Small Coupling ◽  
Sampling Times

Coupling map lattice is an efficient mathematical model for studying complex systems. This paper studies the topology identification of coupled map lattice (CML) under the sparsity condition. We convert the identification problem into the problem of solving the underdetermined linear equations. Thel1norm method is used to solve the underdetermined equations. The requirement of data characters and sampling times are discussed in detail. We find that the high entropy and small coupling coefficient data are suitable for the identification. When the measurement time is more than 2.86 times sparsity, the accuracy of identification can reach an acceptable level. And when the measurement time reaches 4 times sparsity, we can receive a fairly good accuracy.

scholarly journals Introducing a Conditional Ghost Correction Into the Vector Method

1984 ◽  
Vol 6 (2) ◽  
pp. 117-123 ◽  
Author(s):  
H. Schaeben
Keyword(s):  
Mathematical Model ◽  
Quadratic Programming ◽  
Optimization Problem ◽  
Linear Equations ◽  
Singular System ◽  
Orientation Distribution ◽  
Mathematical Approach ◽  
System Of Linear Equations ◽  
Vector Method ◽  
The Mathematical Model

The concept of conditional ghost correction is introduced into the vector method of quantitative texture analysis. The mathematical model actually chosen here reduces the texture problem to one of quadratic programming. Thus, a well defined optimization problem has to be solved, the singular system of linear equations governing the correspondence between pole and orientation distribution being reduced to a set of equality constraints of the restated texture problem. This new mathematical approach in terms of the vector method reveals the modeling character of the solution of the texture problem provided by the vector method completely.

A novel topology identification method based on compressive sensing for multidimensional networks

2020 ◽  
Vol 34 (30) ◽  
pp. 2050294
Author(s):  
Shuheng Fang ◽  
Zhengmin Kong ◽  
Ping Hu ◽  
Li Ding
Keyword(s):  
Compressive Sensing ◽  
Matching Pursuit ◽  
Network Models ◽  
Reconstruction Algorithm ◽  
Identification Problem ◽  
Topology Identification ◽  
Network Recovery ◽  
Threshold Mechanism ◽  
Different Types ◽  
2D Network

In real-world scenarios, it is difficult to know about the complete topology of a huge network with different types of links. In this brief, we propose a method to identify the topology of multidimensional networks from information transmission data. We consider information propagating over edges of a two-dimensional (2D) network, where one type of links is known and the other type is unknown. Given the state of all nodes at each unit time, we can transform the topology identification problem into a compressive sensing framework. A modified reconstruction algorithm, called Sparsity Adaptive Matching Pursuit with Mixed Threshold Mechanism (SAMPMTM), is proposed to tackle the problem. Compared with the classical Sparsity Adaptive Matching Pursuit (SAMP) algorithm, the proposed SAMPMTM algorithm can reduce the conflict rate and improve the accuracy of network recovery. We further demonstrate the performance of this improved algorithm through Monte-Carlo simulations under different network models.

Flow Deflection by Gauze Screens

1969 ◽  
Vol 11 (3) ◽  
pp. 290-294 ◽  
Author(s):  
A. J. Reynolds
Keyword(s):  
Mathematical Model ◽  
Good Accuracy ◽  
Velocity Variations ◽  
Set Up ◽  
Flow Deflection

A mathematical model is set up to predict the deflection of a flow passing obliquely through a plane gauze. It differs from existing descriptions in accounting consistently for velocity variations in the deflecting flow, and in relating the deflection at the gauze to the total deflection in a more realistic way. The deflection at the gauze is specified in two ways, as being half the total, and as equalling the total. These two relations are found to represent the performance of gauzes whose solidities are, respectively, less than and greater than one-half. Formulae are developed which predict the flow deflection with good accuracy for these two régimes.

A MATHEMATICAL MODEL FOR PREDICTING THE OUTCOME OF TREATMENT OF MULTIDRUD-RESISTANT TUBERCULOSIS

2021 ◽  
Vol 74 (7) ◽  
pp. 1649-1654
Author(s):  
Olha S. Shevchenko ◽  
Liliia D. Todoriko ◽  
Iryna A. Ovcharenko ◽  
Olga O. Pogorelova ◽  
Ihor O. Semianiv
Keyword(s):  
Mathematical Model ◽  
Discriminant Analysis ◽  
Treatment Effectiveness ◽  
Linear Equations ◽  
Blood Analysis ◽  
Tissue Destruction ◽  
Additional Criterion ◽  
Resistant Tuberculosis ◽  
Phase Group ◽  
Group 2

The aim: Predicting the effectiveness of treatment for MRI of the lungs by developing a mathematical model to predict treatment outcomes. Materials and methods: 84 patients with MRI of the lungs: group 1 (n = 56) – with signs of effective TB treatment at the end of the intensive phase; group 2 (n = 28) – patients with signs of ineffective treatment. We used the multivariate discriminant analysis method using the statistical environment STATISTICA 13. Results: During the discriminant analysis, the parameters of the clinical blood analysis (monocytes, stab leukocytes, erythrocytes) were selected, which were associated with high (r> 0.5) statistically significant correlations with the levels of MMP-9, TIMP-1, oxyproline and its fractions and aldosterone in the formation of the prognosis. The mathematical model allows, in the form of comparing the results of solving two linear equations and comparing their results, to predict the outcome of treatment: “1” effective treatment, “2” – ineffective treatment. Early prediction of treatment effectiveness is promising, as it allows the use of the developed mathematical model as an additional criterion for the selection of patients for whom surgical treatment is recommended, in order to increase the effectiveness of treatment. Conclusions: An additional criterion for predicting ineffective MRI treatment, along with the criteria provided for by WHO recommendations, is a mathematical model that takes into account probably strong correlation (r = 0.5, p <0.05) between the factors of connective tissue destruction, collagen destruction, aldosterone , and indicators of a clinical blood test (between levels of OBZ and monocytes (r = 0.82, p = 0.00001), OB and monocytes (r = 0.92, p = 0.000001) OB and stab leukocytes (r = – 0.87, p = 0.0003) OBZ and stab leukocytes (r = – 0.53, p = 0.017), aldosterone and ESR.

A mathematical model of psychotherapy: An investigation using dynamic non-linear equations to model the therapeutic relationship

2012 ◽  
Vol 22 (1) ◽  
pp. 40-55 ◽  
Author(s):  
Paul R. Peluso ◽  
Larry S. Liebovitch ◽  
John M. Gottman ◽  
Michael D. Norman ◽  
Jessica Su
Keyword(s):  
Mathematical Model ◽  
Therapeutic Relationship ◽  
Linear Equations ◽  
Non Linear ◽  
Non Linear Equations

scholarly journals A simple mathematical model for the evaluation of the long first wave of the COVID-19 pandemic in Brazil

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yuanji Tang ◽  
Tamires D. A. Serdan ◽  
Amanda L. Alecrim ◽  
Diego R. Souza ◽  
Bruno R. M. Nacano ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Good Accuracy ◽  
Simple Mathematical Model ◽  
Epidemic Curve ◽  
Local Characteristics ◽  
Stable Period ◽  
Long Duration ◽  
Short Period ◽  
The Impact

AbstractWe propose herein a mathematical model to predict the COVID-19 evolution and evaluate the impact of governmental decisions on this evolution, attempting to explain the long duration of the pandemic in the 26 Brazilian states and their capitals well as in the Federative Unit. The prediction was performed based on the growth rate of new cases in a stable period, and the graphics plotted with the significant governmental decisions to evaluate the impact on the epidemic curve in each Brazilian state and city. Analysis of the predicted new cases was correlated with the total number of hospitalizations and deaths related to COVID-19. Because Brazil is a vast country, with high heterogeneity and complexity of the regional/local characteristics and governmental authorities among Brazilian states and cities, we individually predicted the epidemic curve based on a specific stable period with reduced or minimal interference on the growth rate of new cases. We found good accuracy, mainly in a short period (weeks). The most critical governmental decisions had a significant temporal impact on pandemic curve growth. A good relationship was found between the predicted number of new cases and the total number of inpatients and deaths related to COVID-19. In summary, we demonstrated that interventional and preventive measures directly and significantly impact the COVID-19 pandemic using a simple mathematical model. This model can easily be applied, helping, and directing health and governmental authorities to make further decisions to combat the pandemic.

scholarly journals Wireless Power Transfer under Wide Distance Variation Using Dual Impedance Frequency

Electronics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 110
Author(s):  
Woochan Lee ◽  
Dukju Ahn
Keyword(s):  
Output Power ◽  
Coupling Coefficient ◽  
Large Distance ◽  
High Efficiency ◽  
Wireless Power Transfer ◽  
The Other ◽  
Wireless Power ◽  
Frequency Selection ◽  
Small Coupling ◽  
Close Distance

A dual-impedance operation, where coil impedance is controlled by operating frequency selection, is proposed to maintain optimum reflected impedance across coupling variation. More specifically, this work focuses on how high coupling between coils presents excessively high reflected resistance to transmitter (Tx) inverters, degrading the efficiency and output power of the inverter. To overcome this problem, the proposed system is equipped with dual-impedance coil and selects high- or low-impedance coil based on the ability to operate both at 200 kHz and 6.78 MHz frequencies. The reactive impedances of 6.78 MHz coils are designed to be higher than that of 200 kHz coils. Since the reflected resistance is proportional to the coil impedances and coupling squared, at close distance with high coupling coefficient, 200 kHz coils with low coil impedances are activated to prevent an excessive rise in reflected resistance. On the other hand, at large distance spacing with low coupling coefficient, 6.78 MHz coils with high coil impedances are activated so that sufficient reflected resistance is obtained even under the small coupling. The proposed system’s advantages are the high efficiency and the elimination of bulky mechanical relay switches. Measured efficiencies are 88.6–50% across 10 coupling variations.

Effect of Thread Profile Angle and Geometry Clearance on the Loosening Performance of a Preloaded Bolt-Nut System Under Harmonic Transverse Excitation

2011 ◽  
Author(s):  
Xianjie Yang ◽  
Sayed A. Nassar
Keyword(s):  
Mathematical Model ◽  
Analytical Model ◽  
Experimental Verification ◽  
Good Accuracy ◽  
Profile Angle ◽  
Bolt Preload ◽  
Transverse Excitation ◽  
Proposed Model ◽  
Thread Profile ◽  
Number Of Cycles

A mathematical model is proposed for investigating the effect of the thread profile angle, thread and hole clearances on the loosening behavior of a preloaded bolt-nut system that is subjected to cyclic transverse excitation. Experimental verification of the analytical model results is provided for various levels of the initial bolt preload and frictional characteristics. Comparison of the experimental and analytical results on the clamp load decay with the number of cycles verifies that the proposed model predicts the loosening performance with good accuracy.

scholarly journals On a Stochastic Regularization Technique for Ill-Conditioned Linear Systems

2019 ◽  
Vol 9 (1) ◽  
pp. 52-60
Author(s):  
Henrique Gomes Moura ◽  
Edson Costa Junior ◽  
Arcanjo Lenzi ◽  
Vinicius Carvalho Rispoli
Keyword(s):  
Inverse Problems ◽  
Linear Systems ◽  
Regularization Method ◽  
Applied Mathematics ◽  
Linear Equations ◽  
Identification Problem ◽  
Tikhonov Regularization Method ◽  
Input Output ◽  
The Matrix ◽  
Output Only

AbstractKnowledge about the input–output relations of a system can be very important in many practical situations in engineering. Linear systems theory comes from applied mathematics as an efficient and simple modeling technique for input–output systems relations. Many identification problems arise from a set of linear equations, using known outputs only. It is a type of inverse problems, whenever systems inputs are sought by its output only. This work presents a regularization method, called random matrix method, which is able to reduce errors on the solution of ill-conditioned inverse problems by introducing modifications into the matrix operator that rules the problem. The main advantage of this approach is the possibility of reducing the condition number of the matrix using the probability density function that models the noise in the measurements, leading to better regularization performance. The method described was applied in the context of a force identification problem and the results were compared quantitatively and qualitatively with the classical Tikhonov regularization method. Results show the presented technique provides better results than Tikhonov method when dealing with high-level ill-conditioned inverse problems.

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