Minimum Number Of Variables Research Articles

English

In this note, we give an elementary proof of the following classical fact. Any positive definite ternary quadratic form over the rational numbers fails to represent infinitely many positive integers. For any ternary quadratic form (positive definite or indefinite), our method constructs certain congruence classes whose elements, up to a square factor, are the only elements not represented over the rational numbers by that form. In the case of a positive definite ternary form, we show that these classes are non-empty. This shows that the minimum number of variables in a positive definite quadratic form representing all positive integers is four. Our proof is very elementary and only uses quadratic reciprocity of Gauss.

Wind Damage and Temperature Effect on Tree Mortality Caused by Ips typographus L.: Phase Transition Model

The aim of this study was to develop methods for constructing a simple model describing tree mortality caused by Ips typographus L. using a minimum number of variables. We developed a model for areas spanning natural mountain forests in the Tatra National Park (Slovakia) and the Šumava National Park (Czech Republic), and in managed Czech forests located in four areas varying in environmental conditions. The model describes the time series of tree mortality dynamics caused by I.typographus using two submodels: a long-term dynamics submodel, and a short-term dynamics autoregressive distributed lag(ADL) model incorporating a two year delay and temperature variable averaged over the April-May period. The quality of fit for our models (R2 value) ranged from 0.87 to 0.91. The model was formulated to capture the average monthly temperature effect, a key weather factor. We found that for high-elevation stands located at least 1000 ma.s.l., forest damage was predominantly influenced by May temperatures. For lower-elevation managed forests with warmer climates, the weather effect was insignificant.

A stochastic inventory model of COVID-19 and robust, real-time identification of carriers at large and infection rate via asymptotic laws

A critical operations management problem in the ongoing COVID-19 pandemic is cognizance of (a) the number of all carriers at large (CaL) conveying the SARS-CoV-2, including asymptomatic ones and (b) the infection rate (IR). Both are random and unobservable, affecting the spread of the disease, patient arrivals to health care units (HCUs) and the number of deaths. A novel, inventory perspective of COVID-19 is proposed, with random inflow, random losses and retrials (recurrent cases) and delayed/distributed exit, with randomly varying fractions of the exit distribution. A minimal construal, it enables representation of COVID-19 evolution with close fit of national incidence profiles, including single and multiple pattern outbreaks, oscillatory, periodic or non-periodic evolution, followed by retraction, leveling off, or strong resurgence. Furthermore, based on asymptotic laws, the minimum number of variables that must be monitored for identifying CaL and IR is determined and a real-time identification method is presented. The method is data-driven, utilizing the entry rate to HCUs and scaled, or dimensionless variables, including the mean residence time of symptomatic carriers in CaL and the mean residence time in CaL of patients entering HCUs. As manifested by several robust case studies of national COVID-19 incidence profiles, it provides efficient identification in real-time under unbiased monitoring error, without relying on any model. The propagation factor, a stochastic process, is reconstructed from the identified trajectories of CaL and IR, enabling evaluation of control measures. The results are useful towards the design of policies restricting COVID-19 and encumbrance to HCUs and mitigating economic contraction.

A Chemical Analysis of Hybrid Economic Systems—Tokens and Money

With the influence of digital technology in our daily lives continuously growing, we investigate methods with the purpose of assessing the stability, sustainability, and design of systems of token economies that include tokens and conventional currencies. Based on a chemical approach, we model markets with a minimum number of variables and compare the transaction rates, stability, and token design properties at different levels of tokenisation. The kinetic study reveals that in certain conditions, if the price of a product contains both conventional money and tokens, one can treat this combination as one composite currency. The dynamic behaviour of the analysed systems is proven to be dynamically stable for the chosen models. Moreover, by applying the supply and demand law to recalculate the prices of products, the necessity of previous knowledge of certain token attributes—token divisibility and token–money exchange rates—emerges. The chemical framework, along with the analytic methods that we propose, is flexible enough to be adjusted to a variety of conditions and offer valuable information about economic systems.

Метод оптимизации многоступенчатых компрессоров

The paper presents an algorithm for seeking an optimal blade configuration for multistage axial-flow compressors. The primary tool behind the algorithm is 3D CFD simulation, augmented by commercial optimisation software. The core of the algorithm involves feeding an initial data vector to the parametric simulation module so as to form a "new" blade geometry, which is then transferred to 3D computational software. The results obtained are further processed in a program that implements the algorithm for seeking the optimum and forms a new input data vector to achieve the set goal. We present a method of parametrically simulation the blade shape, implemented in a software package, making it possible to describe the shape of the compressor blade profiles using a minimum number of variables and to automatically change the shape in the optimisation cycle. The algorithm developed allows the main parameters of compressor operation (efficiency, pressure ratio, air flow rate, etc.) to be improved by correcting the profile shape and relative position of the blades. The algorithm takes into account various possible constraints. We used the method developed to solve practical problems of optimising multistage axial compressors of gas turbine engines for various purposes, with the number of compressor stages ranging from 3 to 15. As a result, the efficiency, pressure ratio and stability margin of gas turbine engines were increased

Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension

The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the important features of a data set—the intrinsic dimension (Id)—behaves in the vicinity of phase transitions. We employ state-of-the-art nearest-neighbors-based Id estimators to compute the Id of raw Monte Carlo thermal configurations across different phase transitions: first-order, second-order, and Berezinskii-Kosterlitz-Thouless. For all the considered cases, we find that the Id uniquely characterizes the transition regime. The finite-size analysis of the Id allows us to not only identify critical points with an accuracy comparable to methods that rely on a priori identification of order parameters but also to determine the corresponding (critical) exponent ν in the case of continuous transitions. For the case of topological transitions, this analysis overcomes the reported limitations affecting other unsupervised learning methods. Our work reveals how raw data sets display unique signatures of universal behavior in the absence of any dimensional reduction scheme and suggest direct parallelism between conventional order parameters in real space and the intrinsic dimension in the data space.8 MoreReceived 3 July 2020Revised 9 November 2020Accepted 15 December 2020DOI:https://doi.org/10.1103/PhysRevX.11.011040Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasClassical statistical mechanicsPhase transitionsTechniquesData miningMachine learningCondensed Matter, Materials & Applied PhysicsStatistical Physics

Rapid determination of active components in Ginkgo biloba leaves by near infrared spectroscopy combined with genetic algorithm joint extreme learning machine

Near-infrared spectroscopy(NIRS) combined with band screening method and modeling algorithm can be used to achieve the rapid and non-destructive detection of the traditional Chinese medicine(TCM) production process. This paper focused on the ginkgo leaf macroporous resin purification process, which is the key technology of Yinshen Tongluo Capsules, in order to achieve the rapid determination of quercetin, kaempferol and isorhamnetin in effluent. The abnormal spectrum was eliminated by Mahalanobis distance algorithm, and the data set was divided by the sample set partitioning method based on joint X-Y distances(SPXY). The key information bands were selected by synergy interval partial least squares(siPLS); based on that, competitive adaptive reweighted sampling(CARS), successive projections algorithm(SPA) and Monte Carlo uninformative variable(MC-UVE) were used to select wavelengths to obtain less but more critical variable data. With selected key variables as input, the quantitative analysis model was established by genetic algorithm joint extreme learning machine(GA-ELM) algorithm. The performance of the model was compared with that of partial least squares regression(PLSR). The results showed that the combination with siPLS-CARS-GA-ELM could achieve the optimal model performance with the minimum number of variables. The calibration set correlation coefficient R_c and the validation set correlation coefficient R_p of quercetin, kaempferol and isorhamnetin were all above 0.98. The root mean square error of calibration(RMSEC), the root mean square error of prediction(RMSEP) and the relative standard errors of prediction(RSEP) were 0.030 0, 0.029 2 and 8.88%, 0.041 4, 0.034 8 and 8.46%, 0.029 3, 0.027 1 and 10.10%, respectively. Compared with the PLSR me-thod, the performance of the GA-ELM model was greatly improved, which proved that NIRS combined with GA-ELM method has a great potential for rapid determination of effective components of TCM.

DSC-based Generation of Sinusoidal PWM Signals with the Least Number of Variables for Single-, Two- and Three-phase inverters(Dept.E)

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Data segmentation based on the local intrinsic dimension

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data. Contrary to common intuition, there are cases where the ID varies within the same data set. This fact has been highlighted in technical discussions, but seldom exploited to analyze large data sets and obtain insight into their structure. Here we develop a robust approach to discriminate regions with different local IDs and segment the points accordingly. Our approach is computationally efficient and can be proficiently used even on large data sets. We find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded versus unfolded configurations in a protein molecular dynamics trajectory, active versus non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. A simple topological feature, the local ID, is thus sufficient to achieve an unsupervised segmentation of high-dimensional data, complementary to the one given by clustering algorithms.

An efficient isostatic mixed shell element for coarse mesh solution

SummaryA novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger–Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of kinematical parameters minus the number of rigid body motions. We name this new FE MISS‐8. MISS‐8 has generalized displacements and rotations interpolated along its contour and drilling rotation is also considered as degree of freedom. The element is integrated exactly on its contour, it does not suffer from rank defectiveness and it is locking‐free. Furthermore, it is efficient for recovering both stress and displacement fields when coarse meshes are used. The numerical investigation on its performance confirms the suitability, accuracy, and efficiency to recover elastic solutions of thick‐ and thin‐walled beam‐like structures. Numerical results obtained with the proposed FE are also compared with those obtained with isogeometric high‐performance solutions. Finally, numerical results show a rate of convergence between h2 and h4.

Maximally flexible solutions of a random K -satisfiability formula

Random K-satisfiability (K-SAT) is a paradigmatic model system for studying phase transitions in constraint satisfaction problems and for developing empirical algorithms. The statistical properties of the random K-SAT solution space have been extensively investigated, but most earlier efforts focused on solutions that are typical. Here we consider maximally flexible solutions which satisfy all the constraints only using the minimum number of variables. Such atypical solutions have high internal entropy because they contain a maximum number of null variables which are completely free to choose their states. Each maximally flexible solution indicates a dense region of the solution space. We estimate the maximum fraction of null variables by the replica-symmetric cavity method, and implement message-passing algorithms to construct maximally flexible solutions for single K-SAT instances.

Design Simulation System to Simplifying Boolean Equation by using Karnaugh Map

Simulation is one of most important technique used for learning, it makes learning possible without cost and provides best way to improve the practical skills for learners. The purpose of this research was to design program to simulate processing of simplifying Boolean expression by using kranaugh- map depending on rules and procedures applied to Boolean equation in order minimize it to obtain final optimal expression with minimum number of variables ,and reduction in equipment that leads to reduce cost, and this research recommend to use modern methods in education which Simulation programs is one of this method to improve E-learning to keep up with universities which care to use E-learning with traditional education and make student more interactive with education progress.

PRINCIPAL COMPONENTS TO OVERCOME MULTICOLLINEARITY PROBLEM

The impact of ignoring collinearity among predictors is well documented in a statistical literature. An attempt has been made in this study to document application of Principal components as remedial solution to this problem. Using a sample of six hundred participants, linear regression model was fitted and collinearity between predictors was detected using Variance Inflation Factor (VIF). After confirming the existence of high relationship between independent variables, the principal components was utilized to find the possible linear combination of variables that can produce large variance without much loss of information. Thus, the set of correlated variables were reduced into new minimum number of variables which are independent on each other but contained linear combination of the related variables. In order to check the presence of relationship between predictors, dependent variables were regressed on these five principal components. The results show that VIF values for each predictor ranged from 1 to 3 which indicates that multicollinearity problem was eliminated. Finally another linear regression model was fitted using Principal components as predictors. The assessment of relationship between predictors indicated that no any symptoms of multicollinearity were observed. The study revealed that principal component analysis is one of the appropriate methods of solving the collinearity among variables. Therefore this technique produces better estimation and prediction than ordinary least squares when predictors are related. The study concludes that principal component analysis is appropriate method of solving this matter.

GMDH ANN to optimise model development: Prediction of the pressure drop and the heat transfer coefficient during condensation within mini-channels

In this paper, the authors propose the use of Artificial Neural Networks (ANN) coupled with Group of Method Data Handling (GMDH) to develop a new tool to optimise the development of empirical models. Additionally, to show its potential, this technique is applied to a dataset of experimental measurements of condensing two-phase flows within minichannels.Experimental data was obtained in an experimental facility located in the “Technical University of Cartagena”. In this installation, multiple experiments were performed with different parameters such as the saturation pressure, the refrigerant mass flow rate, the vapour quality, tube geometry and refrigerant fluid. The tests presented in this document deal with two different geometries with hydraulic diameters of 1.16 and 0.70 mm and five different refrigerant fluids (R32, R134a, R290, R410A, R1234yf).The Group Method of Data Handling was applied to the experimental data set providing the information about which magnitudes are the minimum required (e.g: mass velocity, fluid properties, tube geometry, hydraulic diameter or vapour quality change) to have the best prediction tool for frictional pressure drop and heat transfer coefficient with the minimum number of variables.

Protocolo de observação de morfologia dentária: sistematização de observações em contexto profissional e de formação académica

Em bioarqueologia, a morfologia dentária centra-se em variáveis da coroa e da raiz que podem estar presentes ou ausentes e, quando presentes, frequentemente exibem variação na expressão, de ligeira a pronunciada (p. ex.: incisivos em pá, carácter de Carabelli). Estudos em gémeos e famílias demonstram que estes caracteres são predominantemente determinados por fatores genéticos. Numerosos estudos de populações demonstraram que os caracteres não-métricos dentários são ferramentas poderosas para ferir afinidade biológica entre amostras ao nível local, regional, continental e global. O objetivo deste trabalho é providenciar a profissionais (p. ex.: quem escreva relatórios de contexto arqueológico) ou estudantes (p. ex.: que preparem projetos de teses) uma lista de 27 caracteres essenciais que constituem o número mínimo de variáveis para caracterizar amostras esqueléticas ou vivas. Recomendações adicionais para além da ‘lista de caracteres não-métricos essenciais’ focam-se em (a) métodos de registo de desgaste oclusal, (b) o formato da base de dados de morfologia dentárias, (c) as bases do método de contagem individual e (d) a importância de avaliar o erro de observador (ou precisão no registo).

A Random Forest approach to predict the spatial distribution of sediment pollution in an estuarine system.

Modeling the magnitude and distribution of sediment-bound pollutants in estuaries is often limited by incomplete knowledge of the site and inadequate sample density. To address these modeling limitations, a decision-support tool framework was conceived that predicts sediment contamination from the sub-estuary to broader estuary extent. For this study, a Random Forest (RF) model was implemented to predict the distribution of a model contaminant, triclosan (5-chloro-2-(2,4-dichlorophenoxy)phenol) (TCS), in Narragansett Bay, Rhode Island, USA. TCS is an unregulated contaminant used in many personal care products. The RF explanatory variables were associated with TCS transport and fate (proxies) and direct and indirect environmental entry. The continuous RF TCS concentration predictions were discretized into three levels of contamination (low, medium, and high) for three different quantile thresholds. The RF model explained 63% of the variance with a minimum number of variables. Total organic carbon (TOC) (transport and fate proxy) was a strong predictor of TCS contamination causing a mean squared error increase of 59% when compared to permutations of randomized values of TOC. Additionally, combined sewer overflow discharge (environmental entry) and sand (transport and fate proxy) were strong predictors. The discretization models identified a TCS area of greatest concern in the northern reach of Narragansett Bay (Providence River sub-estuary), which was validated with independent test samples. This decision-support tool performed well at the sub-estuary extent and provided the means to identify areas of concern and prioritize bay-wide sampling.

A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis

This paper presents a generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates. We exploit a higher-order shear deformation theory in each layer such that the continuity of the displacement and transverse shear stresses at the layer interfaces is ensured. Thanks for enforcing the continuity of the displacement and transverse shear stresses at an inner-laminar layer, the minimum number of variables is retained from the present theory in comparison with other layerwise theories. The method requires only five variables, the same as what obtained from the first- and higher-order shear deformation theories. In comparison with the shear deformation theories based on the equivalent single layer, the present theory is capable of producing a higher accuracy for inner-laminar layer shear stresses. The free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plate are fulfilled without any shear correction factors. The discrete system equations are derived from the Galerkin weak form, and the solution is obtained by isogeometric analysis (IGA). The discrete form requires the C1 continuity of the transverse displacement, and hence NURBS basis functions in IGA naturally ensure this condition. The laminated composite and sandwich plates with various geometries, aspect ratios, stiffness ratios and boundary conditions are studied. The obtained results are compared with the 3D elasticity solution, the analytical as well as numerical solutions based on various plate theories.

Development of an Intelligent Model to Estimate the Probability of having Metabolic Syndrome

Logistic regression has now become an essential part of medical data analysis that uses a binary-response model. The model is frequently used by epidemiologists as a model for the probability (interpreted as the risk) that an individual will acquire a disease during a specified time period, during which he or she is exposed to a condition (called a risk factor) known to be or suspected of being associated with the disease. The objective is to establish a model using a minimum number of variables, and is also able to identify the relationship between the dependent variable and independent variable. Additionally, the study will determine the risk factors that can lead to the development of metabolic syndrome (MetSyn) and will establish an intelligent and biologically acceptable model for estimating the probability of having the condition, based on the NCEP ATP III criteria. In this study, binary logistic regression analysis has been employed in order to specify the risk factors that affect metabolic syndrome. Metabolic syndrome (MetSyn) is a common metabolic disorder that is increasingly caused by the pervasiveness of obesity in society and diagnosed according to the National Cholesterol Education Program (NCEP) Adult Treatment Panel III (ATP III) Identification1. The data has been obtained from the laboratory test results of 321 adult individuals who had consecutively been treated by the Near East University Internal Medicine Department. For this intelligent model, binary logistic regression analysis has been used. The sensitivity, specificity and accuracy rates have been detected as 94.7%, 96.0% and 95.5%, respectively. As a result, homeostatic model assessment (HOMA-IR), uric acid, body mass index (BMI), low-density lipoprotein (LDL) cholesterol, age, smoking, education level (EL) are defined as metabolic syndrome risk factors, the model has been estimated by using those variables in the acquired intelligent model. As a consequence of the research, it has been determined that the key elements that can have an impact are the changeable risk factors, meaning that the illness could be destroyed before it actually occurs, and lifestyle change, that can also prevent the illness.

A Hybrid Formulation for Modelling Multibody Spacecraft

In order to simulate the behavior of a space multibody system, the paper shows the possibility of shifting from a Newton Euler (NE) multibody approach to Lagrange Euler (LE) like formulation of equations of motion. The NE is convenient to understand and to write down the mechanics equations of the system, but the EL based equations of motion show a minimal mathematical complexity and a minimum number of equations in a minimum number of variables. The proposed procedure also allows to swiftly turn back to the NE formulation to calculate the reaction forces and torques among the bodies. The overall revised hybrid formulation, built by mixing both NE and EL approaches, is applied for simulating the deploying phase of spacecraft solar panels.

Quadrupedal bounding with a segmented flexible torso: passive stability and feedback control

In this paper, the implications of torso flexibility on the dynamics of quadrupedal running are examined in a template setting. In the same vein with the spring loaded inverted pendulum, a reductive sagittal-plane model with a segmented flexible torso and compliant legs is introduced to capture the dynamics of bounding in the presence of torso flexibility via a minimum number of variables and parameters. Numerical return map studies of the system in dimensionless setting reveal that a large variety of cyclic bounding motions can be realized passively, through the natural interaction of the model with its environment. Despite the simplicity of the model, the resulting motions correspond to torso bending movements that resemble those in galloping mammals without explicit reliance on the fine structural and morphological details. Furthermore, for certain combinations of the system parameters—in particular the torso and leg relative stiffness—self-stable bounding motions emerge. The implications of the existence of such self-stable bounding orbits to control design are also discussed and a hybrid control law is derived that is capable of stabilizing the system as it encounters significantly large disturbances using only a single actuator located at the torso joint.