Три способи кодування номінальних змінних у регресійному аналізі.

Fingerprint image segmentation heavily influences the performance of automated fingerprint identification systems. We propose a segmentation technique based on the topographic properties of the image surface. The digital image is treated as a noisy sampling of the underlying continuous surface which is approximated by orthogonal Chebyshev polynomials. Ridge and valley regions are discriminated by the sign of the maximum normal curvature of this continuous surface. Different approximation accuracies are used along the orthogonal and parallel directions to the ridge orientation. This determines a lower sensitivity to small irregularities along the ridge direction then along the orthogonal direction, resulting in a high quality segmentation.

If a finite Markov chain (discrete time, discrete states) has a number of absorbing states, one of these will eventually be reached. In this paper are given theoretical formulae for the probability distribution, its generating function and moments of the time taken to first reach an absorbing state, and these formulae are applied to an example taken from genetics. While first passage time problems and their solutions are known for a wide variety of Markov chain processes (e.g., [2], [7], [4]), the theory seems not to have been used in population genetics. Suppose a genetic population consists of a constant number of individuals and the state of the population is defined by the numbers of the various genotypes existing at a given time. Then if mutation is absent, all individuals will eventually become of the same genotype because of random influences such as births, deaths, mating, selection, chromosome breakages and recombinations. The population behavior may in some circumstances be approximated by a Markov chain with absorbing states. In Section 2, two alternative approaches are given for the theoretical determination of absorption time properties, using well known techniques. In Section 3, the consequences of the theoretical results are investigated for a particular population model introduced by Moran [9], [10], and explicit expressions for the distribution of the gene fixation time are obtained in terms of Chebyshev's orthogonal polynomials. The derivation requires finding the pre- and post-eigenvectors of the matrix of transition probabilities, and an incidental by-product is the proof of certain identities for the orthogonal polynomials. The material presented in Section 2 and Section 3 is obtained by exact methods. In Section 4, the Fokker-Planck diffusion equation is used to obtain approximate results, and these are compared with those of the exact theory to ascertain the accuracy of the diffusion approximation.

The ambiguities must be resolved to their correct integer values in order to exploit the high accuracy of the carrier phase double-difference observables. The criterion used by ambiguity resolution technique is the selection of the integer combination that satisfies to the least squares adjustment. Integer ambiguity resolution could be regarded as a kind of global optimization search process. Genetic algorithm (GA) has the advantage to search the global optimum results in the robust and parallel way. Individual encoding is important to improve the efficiency of GA. This paper analyzed two encoding methods, which are binary code and real code, for GPS carrier phase double-difference short baseline ambiguity searching. Then the resolutions of the integer ambiguity using GA with binary and real code were compared. GA with binary code was used to determine the optimum integer estimation after float ambiguity solution resolved. However, due to non-integer nature of baseline vectors values, GA with real code was used to solve baseline vectors and double-difference ambiguity. Real encoding method made up for some deficiencies such as longer code lengthiness, larger solution space and longer time consumed in GA with binary code to non-integer solution. Numerical results showed that GA can be realized to resolve ambiguity resolution of DGPS with whether binary code or real code. The accuracy of both results was basically identical. On the premise of accurate float ambiguity solution, the convergence speed of GA with binary code was faster than that of GA with real code. The resolution of GA with real code was more robust and reliable because it did not depend on the accuracy of initial values.

The Strong Chebyshev Distribution and Orthogonal Laurent Polynomials

BackgroundElectronic medical records (EMR) contain numerical data important for clinical outcomes research, such as vital signs and cardiac ejection fractions (EF), which tend to be embedded in narrative clinical notes. In current practice, this data is often manually extracted for use in research studies. However, due to the large volume of notes in datasets, manually extracting numerical data often becomes infeasible. The objective of this study is to develop and validate a natural language processing (NLP) tool that can efficiently extract numerical clinical data from narrative notes.ResultsTo validate the accuracy of the tool EXTraction of EMR Numerical Data (EXTEND), we developed a reference standard by manually extracting vital signs from 285 notes, EF values from 300 notes, glycated hemoglobin (HbA1C), and serum creatinine from 890 notes. For each parameter of interest, we calculated the sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV) and F1 score of EXTEND using two metrics.(1) completion of data extraction, and (2) accuracy of data extraction compared to the actual values in the note verified by chart review. At the note level, extraction by EXTEND was considered correct only if it accurately detected and extracted all values of interest in a note.Using manually-annotated labels as the gold standard, the note-level accuracy of EXTEND in capturing the numerical vital sign values, EF, HbA1C and creatinine ranged from 0.88 to 0.95 for sensitivity, 0.95 to 1.0 for specificity, 0.95 to 1.0 for PPV, 0.89 to 0.99 for NPV, and 0.92 to 0.96 in F1 scores. Compared to the actual value level, the sensitivity, PPV, and F1 score of EXTEND ranged from 0.91 to 0.95, 0.95 to 1.0 and 0.95 to 0.96.ConclusionsEXTEND is an efficient, flexible tool that uses knowledge-based rules to extract clinical numerical parameters with high accuracy. By increasing dictionary terms and developing new rules, the usage of EXTEND can easily be expanded to extract additional numerical data important in clinical outcomes research.

As a hot fabrication technology for micro scale parts, micro injection molding is receiving increasing market attention. Improving mechanical properties of micro parts should be an important issue in the micro injection molding process. The relation between weld line strength in micro injection molding parts and processing parameters is investigated. A visual mold with variotherm unit is designed and constructed, in which the micro tensile specimen with weld line are prepared. Polypropylene (PP) is used as the research material in this study, and six processing parameters were chosen as investigating factors, which were melt temperature, mold temperature, injection pressure, packing pressure, ejection temperature and injection speed. In order to achieve optimized processing parameters and their order of significance, Taguchi experiment method was applied in this presented study. The prediction formulation of the strength of micro weld line was built up by multiple regression analysis based on Chebyshev orthogonal polynomial. The results showed the influencing significance order of parameters from strong to week separately are mold temperature, melt temperature, injection speed, ejection temperature, packing pressure and injection pressure. And the tolerance of micro weld line prediction formulation was found to be lower than 21% through confirmation experiments.

Chebyshev collocation method for static intrinsic equations of geometrically exact beams

Abstract. Buckling of nonuniform carbon nanotubes are studied with the axial load taken as a combination of concentrated and axially distributed loads. Constitutive modelling of the nanotubes is implemented via nonlocal continuum mechanics. Problem solutions are obtained by employing a weak formulation of the problem and the Rayleigh-Ritz method which is implemented by using orthogonal Chebyshev polynomials. The accuracy of the method of solution is verified against available results. Solutions are obtained for the cases of uniformly distributed and triangularly distributed axial loads. Contour plots are given to assess the effect of nonuniform cross-sections and the small-scale parameter on the buckling load for a combination of simply supported, clamped and free boundary conditions.

Via simulating the contribution of spin-orbit interaction to nuclear masses by orthogonal Chebyshev polynomials, the mass excesses are calculated for a group of atomic nuclei characterized by the isospins of Tz = 51/2, 26, 53/2, 55/2, 28, and 57/2 and by the presence of restored Wigner’s spin-isospin SU(4) symmetry. The root-mean-square deviation of the results of these calculations from their experimental counterparts is σ = 140 keV. The potential of the proposed method is discussed.

Orthogonal Chebyshev Polynomials

Chebyshev collocation method for the free vibration analysis of geometrically exact beams with fully intrinsic formulation

The objective of this paper is to reduce the computational effort in reservoir flooding optimization problems by a combination of different optimization parametrization methods and model order reduction techniques. We compare three different parametrization methods that reduce the cardinality of the original infinite set of control-decision variables to a finite set. The three methods include a traditional piece-wise constant (PWC) approximation, a polynomial approximation by Chebyshev orthogonal polynomials and a piece-wise polynomial approximation by cubic Spline interpolation. The Proper Orthogonal Decomposition with Discrete Empirical Interpolation Method (POD-DEIM) accomplishes the reduced order modeling (ROM).. We compare a gradient-free global stochastic search approach and a gradient-based local search approach. We used Particle Swarm Optimization (PSO) as a gradient-free algorithm and Interior-Point Optimization (IPOPT) with L-BFGS method as a gradient-based algorithm. First, we compare the performances of the three parametrization methods solved by each optimizer, using fine scale simulations for an increasing level of parametrization refinement. Then, in the second part of this paper, we combine the parametrization methods with the reduced modeling workflow. For a given level of parametrization refinement, we compare the performance of each parametrization method coupled with POD-DEIM, and solved by each optimizer. In this part, we introduce an online training procedure, where the first optimization iteration is used to construct the snapshot matrix. The results demonstrate how refining the control approximation with more decision variables per well lead to better NPV values, but with a higher computational cost. The best NPV was achieved using the highest refining level with Chebyshev polynomial approximation. Both polynomial and piece-wise polynomial approximations served as better training sets for POD-DEIM leading to a more accurate and fast reduced model. With the strategy proposed, POD-DEIM showed the best optimization accuracy for Chebyshev polynomial with the gradient-free optimizer, thus permitting the use of the model reduction methodology for global-stochastic search methods. However, the gradient-based approach seems to consistently outperform the gradient-free approach in terms of NPV and number of iterations for the cases shown.

In a Banach space E, we consider the Neumann problem for a second-order homogeneous equation with a constant operator coefficient densely defined in E. Under a weakened strong positivity condition on the operator coefficient (we use the approach due to V.I. Gorbachuk and A.I. Knyazyuk to the study of a-positive operators), we present a criterion for the well-posed solvability of the problem. We obtain a representation of the solution via Chebyshev operator polynomials of the first and second kind.

In this paper, we use maize yield and meteorological data during the period of 1980-2015 in the Yilan County, Heilongjiang Province to study the impact of meteorological factors (rainfall, sunshine hours, temperature) on maize yield. Based on the computer simulation, Fisher integral model and Chebyshev orthogonal polynomials are used to analyze the coefficients between meteorological factors (temperature, precipitation and sunshine hours) and the maize yield so as to establish a mathematics model between the two. Through the coefficients between meteorological factors and maize yield during different periods, it is discovered that meteorological factors have a great effect on maize yield. By fitting degree of maize yield meteorological model, the maize yield can be predicted in an accurate way. It provides a theoretical basis for the information management of maize production in Heilongjiang Province based on the computer simulation. It is of great significance in providing scientific guidance for the sustainable development of Heilongjiang's corn industry.

ABSTRACTA formulation for static and dynamic vibration analysis of composite laminated curved beams is presented by using an efficient domain decomposition method. Multi-segment partitioning strategy is used to accommodate the accurate requirements of responses. The system potential functional is introduced to satisfy the continuity constraints on the segment interfaces. The Chebyshev orthogonal polynomials are used as displacement admissible functions. The theoretical results are verified by comparing with those previously published in literature, and the ones obtained by using the program ABAQUS. Based on the verification, the parametric study of composite laminated curved beam is carried out.