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- research-articleJuly 2022
On the properties of fibotomic polynomials
Advances in Applied Mathematics (AAMA), Volume 138, Issue CJul 2022https://doi.org/10.1016/j.aam.2022.102344AbstractDefine the n-th fibotomic polynomial to be the product of the monic irreducible factors of the n-th Fibonacci polynomial which are not factors of any Fibonacci polynomial of smaller degree. In this paper, we prove a number of ...
- research-articleAugust 2020
Secure image encryption scheme based on fractals key with Fibonacci series and discrete dynamical system
Neural Computing and Applications (NCAA), Volume 32, Issue 15Aug 2020, Pages 11837–11857https://doi.org/10.1007/s00521-019-04667-yAbstractIn this article, our aim is to design a new and efficient digital information confidentiality mechanism. We have offered an encryption scheme which is based on fractals and multiple chaotic iterative maps in order to add more confusion and ...
- research-articleMarch 2020
Fibonacci multi-modal optimization algorithm in noisy environment
AbstractNoises are very common in practical optimization problems. It will cause interference on optimization algorithms and thus makes the algorithms difficult to find a true global extreme point and multiple local extreme points. For the ...
Highlights- A Fibonacci multi-modal optimization (FMO) algorithm in noisy environment is proposed.
- research-articleFebruary 2020
Modified dynamic current mode logic based LFSR for low power applications
Microprocessors & Microsystems (MSYS), Volume 72, Issue CFeb 2020https://doi.org/10.1016/j.micpro.2019.102945AbstractShift Register, which is a cascade of flip flops shares the same clock and the outputs are connected to the data input of the next one in the chain. Linear-feedback shift register or shortly LFSR is one such shift register whose input is a linear ...
- research-articleJanuary 2020
Gapsets and numerical semigroups
Journal of Combinatorial Theory Series A (JCTH), Volume 169, Issue CJan 2020https://doi.org/10.1016/j.jcta.2019.105129AbstractFor g ≥ 0, let n g denote the number of numerical semigroups of genus g. A conjecture by Maria Bras-Amorós in 2008 states that the inequality n g ≥ n g − 1 + n g − 2 holds for all g ≥ 2. Here we show that it holds for the very large ...
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- research-articleFebruary 2020
Comparing Four Important Sorting Algorithms Based on Their Time Complexity
ACAI '19: Proceedings of the 2019 2nd International Conference on Algorithms, Computing and Artificial IntelligenceDecember 2019, Pages 320–327https://doi.org/10.1145/3377713.3377808Time complexity and memory complexity are significant for all algorithms, especially sorting algorithms. Using the right sorting algorithm for our data can possibly decrease time and memory usage. The sorting problem has attracted a great deal of ...
- ArticleOctober 2019
LumiPath – Towards Real-Time Physically-Based Rendering on Embedded Devices
- Laura Fink,
- Sing Chun Lee,
- Jie Ying Wu,
- Xingtong Liu,
- Tianyu Song,
- Yordanka Velikova,
- Marc Stamminger,
- Nassir Navab,
- Mathias Unberath
Medical Image Computing and Computer Assisted Intervention – MICCAI 2019Oct 2019, Pages 673–681https://doi.org/10.1007/978-3-030-32254-0_75AbstractWith the increasing computational power of today’s workstations, real-time physically-based rendering is within reach, rapidly gaining attention across a variety of domains. These have expeditiously applied to medicine, where it is a powerful tool ...
- research-articleJanuary 2019
Verified solving and asymptotics of linear recurrences
CPP 2019: Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and ProofsJanuary 2019, Pages 27–37https://doi.org/10.1145/3293880.3294090Linear recurrences with constant coefficients are an interesting class of recurrence equations that can be solved explicitly. The most famous example are certainly the Fibonacci numbers with the equation f(n) = f(n−1) + f(n−2) and the quite non-obvious ...
- ArticleMarch 2023
Stego Quality Enhancement by Message Size Reduction and Fibonacci Bit-Plane Mapping
Security Standardisation ResearchDec 2014, Pages 151–166https://doi.org/10.1007/978-3-319-14054-4_10AbstractAn efficient 2-step steganography technique is proposed to enhance stego image quality and secret message un-detectability. The first step is a pre-processing algorithm that reduces the size of secret images without losing information. This ...
- articleFebruary 2014
On the linear description of the Huffman trees polytope
Discrete Applied Mathematics (DAMA), Volume 164February, 2014, Pages 225–236https://doi.org/10.1016/j.dam.2012.05.004The Huffman tree is a well known concept in data compression discovered by David Huffman in 1952 [7]. A Huffman tree is a binary tree and represents the most efficient binary code for a given alphabet with respect to a distribution of frequency of its ...
- ArticleSeptember 2013
Elliptic Curve Scalar Multiplication Based on Fibonacci Number
INCOS '13: Proceedings of the 2013 5th International Conference on Intelligent Networking and Collaborative SystemsSeptember 2013, Pages 507–510https://doi.org/10.1109/INCoS.2013.157The paper presents a series algorithms of Elliptic curve scalar multiplication based on Fibonacci numbers. The double free addition chain is used to develop new scalar multiplication. Zeckendorf and Pell representation is analyzed and used to construct ...
- articleApril 2013
Generalized Fibonacci recurrences and the lex-least de Bruijn sequence
Advances in Applied Mathematics (AAMA), Volume 50, Issue 4April, 2013, Pages 465–473https://doi.org/10.1016/j.aam.2012.12.002The skew of a binary string is the difference between the number of zeroes and the number of ones, while the length of the string is the sum of these two numbers. We consider certain suffixes of the lexicographically-least de Bruijn sequence at natural ...
- ArticleJuly 2012
Data Hiding Techniques in Steganography Using Sub-Fibonacci Sequences
IIH-MSP '12: Proceedings of the 2012 Eighth International Conference on Intelligent Information Hiding and Multimedia Signal ProcessingJuly 2012, Pages 89–93https://doi.org/10.1109/IIH-MSP.2012.27Recently, several steganographic methods, based on bitplane analysis have been developed. These methods improve the classical LSB method, generally by increasing the number of bitplanes via sophisticated encodings. In this paper, we show that these ...
- articleJuly 2012
A new optimizing parameter approach of LSSVM multiclass classification model
Neural Computing and Applications (NCAA), Volume 21, Issue 5July 2012, Pages 945–955https://doi.org/10.1007/s00521-011-0673-8The parameter values of kernel function affect classification results to a certain extent. In the paper, a multiclass classification model based on improved least squares support vector machine (LSSVM) is presented. In the model, the non-sensitive loss ...
- ArticleSeptember 2011
New identity of an± bnexpression
AICT'11: Proceedings of the 2nd international conference on Applied informatics and computing theorySeptember 2011, Pages 28–32A polynomial formula depending on a + b and ab arguments of an±bn expression was first put forward. The coefficients in the formula are easily determined from the table written by a special algorithm. The sums of the figures in each row of the triangles ...
- ArticleJune 2010
Enhanced Fibonacci Backoff Algorithm for Mobile Ad-Hoc Network
CIT '10: Proceedings of the 2010 10th IEEE International Conference on Computer and Information TechnologyJune 2010, Pages 749–754https://doi.org/10.1109/CIT.2010.144The most known drawback of IEEE 802.11 MAC is the low performance in terms of throughput in case of congested networks. Backoff time is one of the most important factors that govern the collision probability in Ad-Hoc network. Using backoff algorithm ...
- articleApril 2009
Thermal radiation in quasiperiodic photonic crystals
Microelectronics Journal (MICROJ), Volume 40, Issue 4-5April, 2009, Pages 848–850https://doi.org/10.1016/j.mejo.2008.11.060In this work we investigated the thermal power spectrum of the electromagnetic radiation through one-dimensional stacks of alternating negative and positive refractive index layers, arranged as truncated quasiperiodic photonic structures obeying the ...
- ArticleJanuary 2009
(2,1)-Lagged Fibonacci Generators Using Elliptic Curves over Finite Fields
ICCET '09: Proceedings of the 2009 International Conference on Computer Engineering and Technology - Volume 02January 2009, Pages 456–457https://doi.org/10.1109/ICCET.2009.103A novel pseudorandom sequence generator is presented in this paper. The genesis of this new generator is evolved from the concept of Lagged Fibonacci generator[1] applied to points on elliptic curves over a finite field. It is observed that the ...
- ArticleJune 2007
New Point Addition Formulae for ECC Applications
WAIFI '07: Proceedings of the 1st international workshop on Arithmetic of Finite FieldsJune 2007, Pages 189–201https://doi.org/10.1007/978-3-540-73074-3_15In this paper we propose a new approach to point scalar multiplication on elliptic curves defined over fields of characteristic greater than 3. It is based on new point addition formulae that suit very well to exponentiation algorithms based on ...
- articleFebruary 2004
Tumble, a fast simple iteration algorithm for Fibonacci
Information Processing Letters (IPRL), Volume 89, Issue 428 February 2004, Pages 187–189https://doi.org/10.1016/j.ipl.2003.10.012A faster linear iteration process for Fibonacci (and Lucas) numbers is given. Algorithms are derived for individual numbers and for sequence generation. A general algorithm for generalized Fibonacci numbers is derived from these.