E. P. Miles

Bio: E. P. Miles is an academic researcher from Florida State University. The author has contributed to research in topics: Fibonacci word & Reciprocal Fibonacci constant. The author has an hindex of 2, co-authored 2 publications receiving 207 citations.

Generalized Fibonacci Numbers and Associated Matrices

Abstract: (1960). Generalized Fibonacci Numbers and Associated Matrices. The American Mathematical Monthly: Vol. 67, No. 8, pp. 745-752.

Robust transmission of unbounded strings using Fibonacci representations

Abstract: Families of Fibonacci codes and Fibonacci representations are defined. Their main attributes are robustness, manifesting itself by the local containment of errors; and simple encoding and decoding. The main application explored is the transmission of binary strings in which the length is in an unknown range, using robust Fibonacci representations instead of the conventional error-sensitive logarithmic ramp representation. Though the former is asymptotically longer than the latter, the former is actually shorter for very large initial segments of integers.

Fuzzy time-series based on Fibonacci sequence for stock price forecasting

Abstract: Time-series models have been utilized to make reasonably accurate predictions in the areas of stock price movements, academic enrollments, weather, etc. For promoting the forecasting performance of fuzzy time-series models, this paper proposes a new model, which incorporates the concept of the Fibonacci sequence, the framework of Song and Chissom's model and the weighted method of Yu's model. This paper employs a 5-year period TSMC (Taiwan Semiconductor Manufacturing Company) stock price data and a 13-year period of TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock Index) stock index data as experimental datasets. By comparing our forecasting performances with Chen's (Forecasting enrollments based on fuzzy time-series. Fuzzy Sets Syst. 81 (1996) 311–319), Yu's (Weighted fuzzy time-series models for TAIEX forecasting. Physica A 349 (2004) 609–624) and Huarng's (The application of neural networks to forecast fuzzy time series. Physica A 336 (2006) 481–491) models, we conclude that the proposed model surpasses in accuracy these conventional fuzzy time-series models.

A Simplified Binet Formula for k-Generalized Fibonacci Numbers

Abstract: In this paper, we present a Binet-style formula that can be used to produce the k-generalized Fibonacci numbers (that is, the Tribonaccis, Tetranaccis, etc.). Furthermore, we show that in fact one needs only take the integer closest to the first term of this Binet-style formula in order to generate the desired sequence.

The multidimensional maximum entropy moment problem: a review of numerical methods

Abstract: Recently the author developed a numerical method for the multidimensional momentconstrained maximum entropy problem, which is practically capable of solving maximum entropy problems in the two-dimensional domain with moment constraints of order up to 8, in the threedimensional domain with moment constraints of order up to 6, and in the four-dimensional domain with moment constraints of order up to 4, corresponding to the total number of moment constraints of 44, 83 and 69, respectively. In this work, the author brings together key algorithms and observations from his previous works as well as other literature in an attempt to present a comprehensive exposition of the current methods and results for the multidimensional maximum entropy moment problem.

and Their Applications

Abstract: We consider a family of pseudo dierential operators f + a = 2 ; a2 (0; 1)g on R d that evolves continuously from to + = 2 , where d 1 and 2 (0; 2). It gives rise to a family of L evy processesX a ;a 2 (0; 1)g, where X a is the sum of a Brownian motion and an independent symmetric -stable process with weight a. Using a recently obtained uniform boundary Harnack principle with explicit decay rate, we establish sharp bounds for the Green function of the process X a killed upon exiting a bounded C 1;1 open set D R d . Our estimates are uniform in a2 (0; 1) and taking a! 0 recovers the Green function estimates for Brownian motion inD. As a consequence of the Green function estimates forX a inD, we identify both the Martin boundary and the minimal Martin boundary of D with respect to X a with its Euclidean boundary. Finally, sharp Green function estimates are derived for certain L evy processes which can be obtained as perturbations of X a .