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Articles 1 - 19 of 19
Full-Text Articles in Numerical Analysis and Computation
Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh
Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh
Publications and Research
Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.
Using Statistical Analysis To Examine Weather Variability In New York City, Ryan Chen, Yuhuang Wang, Jiehao Huang
Using Statistical Analysis To Examine Weather Variability In New York City, Ryan Chen, Yuhuang Wang, Jiehao Huang
Publications and Research
As the overall temperature of Earth continues to warm, atmospheric hazards (e.g. heatwaves, cyclones) may be driving increases in climatological trends. This study examines the daily precipitation and temperature record of the greater New York City region during the 1979-2014 period. Daily station observations from three greater New York City airports: John F. Kennedy (JFK), LaGuardia (LGA) and Newark (EWR), are used in this study. Climatological & statistical analyses are performed for the weather variability of New York City metro area to understand the impacts of climate change.The temperature climatology reveals a distinct seasonal cycle, while the precipitation climatology exhibits …
Sensor Data Analysis In Smart Buildings, Manuel A. Mane Penton
Sensor Data Analysis In Smart Buildings, Manuel A. Mane Penton
Publications and Research
Data analysis and Machine Learning are destined to evolve the current technology infrastructure by solving technology and economy demands present mainly in developed cities like New York. This research proposes a machine learning (ML) based solution to alleviate one of the main issues that big buildings such as CUNY campuses have, that is the waste of energy resources. The analysis of data coming from the readings of different deployed sensors such as CO2, humidity and temperature can be used to estimate occupancy in a specific room and building in general. The outcome of this research established a relationship between the …
Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker
Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker
Publications and Research
We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.
Generalized Least-Powers Regressions I: Bivariate Regressions, Nataniel Greene
Generalized Least-Powers Regressions I: Bivariate Regressions, Nataniel Greene
Publications and Research
The bivariate theory of generalized least-squares is extended here to least-powers. The bivariate generalized least-powers problem of order p seeks a line which minimizes the average generalized mean of the absolute pth power deviations between the data and the line. Least-squares regressions utilize second order moments of the data to construct the regression line whereas least-powers regressions use moments of order p to construct the line. The focus is on even values of p, since this case admits analytic solution methods for the regression coefficients. A numerical example shows generalized least-powers methods performing comparably to generalized least-squares methods, …
Generalized Least-Squares Regressions V: Multiple Variables, Nataniel Greene
Generalized Least-Squares Regressions V: Multiple Variables, Nataniel Greene
Publications and Research
The multivariate theory of generalized least-squares is formulated here using the notion of generalized means. The multivariate generalized least-squares problem seeks an m dimensional hyperplane which minimizes the average generalized mean of the square deviations between the data and the hyperplane in m + 1 variables. The numerical examples presented suggest that a multivariate generalized least-squares method can be preferable to ordinary least-squares especially in situations where the data are ill- conditioned.
Generalized Least-Squares Regressions Iv: Theory And Classification Using Generalized Means, Nataniel Greene
Generalized Least-Squares Regressions Iv: Theory And Classification Using Generalized Means, Nataniel Greene
Publications and Research
The theory of generalized least-squares is reformulated here using the notion of generalized means. The generalized least-squares problem seeks a line which minimizes the average generalized mean of the square deviations in x and y. The notion of a generalized mean is equivalent to the generating function concept of the previous papers but allows for a more robust understanding and has an already existing literature. Generalized means are applied to the task of constructing more examples, simplifying the theory, and further classifying generalized least-squares regressions.
Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene
Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene
Publications and Research
This paper continues the work of this series with two results. The first is an exponential equivalence theorem which states that every generalized least-squares regression line can be generated by an equivalent exponential regression. It follows that every generalized least-squares line has an effective normalized exponential parameter between 0 and 1 which classifies the line on the spectrum between ordinary least-squares and the extremal line for a given set of data. The second result is the presentation of fundamental formulas for the generalized least-squares slope and y-intercept.
Stochastic Dea With A Perfect Object And Its Application To Analysis Of Environmental Efficiency, Alexander Vaninsky
Stochastic Dea With A Perfect Object And Its Application To Analysis Of Environmental Efficiency, Alexander Vaninsky
Publications and Research
The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group–related) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional …
Refining Environmental Satellite Data Using A Statistical Approach, Md Zahidur Rahman, Leonid Roytman, Abdelhamid Kadik
Refining Environmental Satellite Data Using A Statistical Approach, Md Zahidur Rahman, Leonid Roytman, Abdelhamid Kadik
Publications and Research
The proposed approach in this article applies an efficient and novel statistical technique to accurately describe radiometric data measured by Advanced Very High Resolution Radiometers (AVHRR) onboard the National Oceanic and Atmospheric Administration’s (NOAA) Polar Orbiting Environmental Satellites (POES). The corrected data set will then be applied to improve the strength of NOAA Global Vegetation Index (GVI) data set for the 1982- 2003 period produced from AVHRR. The GVI is used extensively for studying and monitoring land surface, atmosphere and recently for analyzing climate and environmental changes. The POES AVHRR data, though useful, cannot be directly used in climate change …
Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene
Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene
Publications and Research
In the first paper of this series, a variety of known and new symmetric and weighted least-squares regression methods were presented with efficient derivations. This paper continues and generalizes the previous work with a theory for deriving, analyzing, and classifying all symmetric and weighted least-squares regression methods.
Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene
Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene
Publications and Research
Ordinary least-squares regression suffers from a fundamental lack of symmetry: the regression line of y given x and the regression line of x given y are not inverses of each other. Alternative symmetric regression methods have been developed to address this concern, notably: orthogonal regression and geometric mean regression. This paper presents in detail a variety of least squares regression methods which may not have been known or fully explicated. The derivation of each method is made efficient through the use of Ehrenberg's formula for the ordinary least-squares error and through the extraction of a weight function g(b) which characterizes …
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene
Publications and Research
The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities.In previous work [11,12] we described a numerical procedure for overcoming the Gibbs phenomenon called the Inverse Wavelet Reconstruction method (IWR). The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series. However, we only described the method standard wavelet series and …
Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene
Methods Of Assessing And Ranking Probable Sources Of Error, Nataniel Greene
Publications and Research
A classical method for ranking n potential events as sources of error is Bayes' theorem. However, a ranking based on Bayes' theorem lacks a fundamental symmetry: the ranking in terms of blame for error will not be the reverse of the ranking in terms of credit for lack of error. While this is not a flaw in Bayes' theorem, it does lead one to inquire whether there are related methods which have such symmetry. Related methods explored here include the logical version of Bayes' theorem based on probabilities of conditionals, probabilities of biconditionals, and ratios or differences of credit to …
A Wavelet-Based Method For Overcoming The Gibbs Phenomenon, Nataniel Greene
A Wavelet-Based Method For Overcoming The Gibbs Phenomenon, Nataniel Greene
Publications and Research
The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities. Here we describe a numerical procedure for overcoming the Gibbs phenomenon called the inverse wavelet reconstruction method. The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series.
An Overview Of Conditionals And Biconditionals In Probability, Nataniel Greene
An Overview Of Conditionals And Biconditionals In Probability, Nataniel Greene
Publications and Research
Conditional and biconditional statements are a standard part of symbolic logic but they have only recently begun to be explored in probability for applications in artificial intelligence. Here we give a brief overview of the major theorems involved and illustrate them using two standard model problems from conditional probability.
Fourier Series Of Orthogonal Polynomials, Nataniel Greene
Fourier Series Of Orthogonal Polynomials, Nataniel Greene
Publications and Research
Explicit formulas for the Fourier coefficients of the Legendre polynomials can be found in the Bateman Manuscript Project. However, similar formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials.
Formulas For The Fourier Series Of Orthogonal Polynomials In Terms Of Special Functions, Nataniel Greene
Formulas For The Fourier Series Of Orthogonal Polynomials In Terms Of Special Functions, Nataniel Greene
Publications and Research
An explicit formula for the Fourier coefficient of the Legendre polynomials can be found in the Bateman Manuscript Project. However, formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials. The methods described here apply in principle to a class of polynomials, including non-orthogonal polynomials.
Inverse Wavelet Reconstruction For Resolving The Gibbs Phenomenon, Nataniel Greene
Inverse Wavelet Reconstruction For Resolving The Gibbs Phenomenon, Nataniel Greene
Publications and Research
The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities. Here we describe a numerical procedure for overcoming the Gibbs phenomenon called the inverse wavelet reconstruction method. The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series.