Abstract: A given polynomial, possibly with multiple roots, is
factored into several lower-degree distinct-root polynomials with
natural-order-integer powers. All the roots, including multiplicities,
of the original polynomial may be obtained by solving these lowerdegree
distinct-root polynomials, instead of the original high-degree
multiple-root polynomial directly.
The approach requires polynomial Greatest Common Divisor
(GCD) computation. The very simple and effective process, “Monic
polynomial subtractions" converted trickily from “Longhand
polynomial divisions" of Euclidean algorithm is employed. It
requires only simple elementary arithmetic operations without any
advanced mathematics.
Amazingly, the derived routine gives the expected results for the
test polynomials of very high degree, such as p( x) =(x+1)1000.
Abstract: This paper address the network reliability optimization
problem in the optical access network design for the 3G cellular
systems. We presents a novel 0-1 integer programming model for
designing optical access network topologies comprised of multi-rings
with common-edge in order to guarantee always-on services. The
results show that the proposed model yields access network
topologies with the optimal reliablity and satisfies both network cost
limitations and traffic demand requirements.
Abstract: The Chinese Postman Problem (CPP) is one of the
classical problems in graph theory and is applicable in a wide range
of fields. With the rapid development of hybrid systems and model
based testing, Chinese Postman Problem with Time Dependent Travel
Times (CPPTDT) becomes more realistic than the classical problems.
In the literature, we have proposed the first integer programming
formulation for the CPPTDT problem, namely, circuit formulation,
based on which some polyhedral results are investigated and a cutting
plane algorithm is also designed. However, there exists a main drawback:
the circuit formulation is only available for solving the special
instances with all circuits passing through the origin. Therefore, this
paper proposes a new integer programming formulation for solving
all the general instances of CPPTDT. Moreover, the size of the circuit
formulation is too large, which is reduced dramatically here. Thus, it
is possible to design more efficient algorithm for solving the CPPTDT
in the future research.
Abstract: Wireless Mesh Networking is a promising proposal
for broadband data transmission in a large area with low cost and
acceptable QoS. These features- trade offs in WMNs is a hot research
field nowadays. In this paper a mathematical optimization framework
has been developed to maximize throughput according to upper
bound delay constraints. IEEE 802.11 based infrastructure
backhauling mode of WMNs has been considered to formulate the
MINLP optimization problem. Proposed method gives the full
routing and scheduling procedure in WMN in order to obtain
mentioned goals.
Abstract: Lossless compression schemes with secure
transmission play a key role in telemedicine applications that helps in
accurate diagnosis and research. Traditional cryptographic algorithms
for data security are not fast enough to process vast amount of data.
Hence a novel Secured lossless compression approach proposed in
this paper is based on reversible integer wavelet transform, EZW
algorithm, new modified runlength coding for character
representation and selective bit scrambling. The use of the lifting
scheme allows generating truly lossless integer-to-integer wavelet
transforms. Images are compressed/decompressed by well-known
EZW algorithm. The proposed modified runlength coding greatly
improves the compression performance and also increases the
security level. This work employs scrambling method which is fast,
simple to implement and it provides security. Lossless compression
ratios and distortion performance of this proposed method are found
to be better than other lossless techniques.
Abstract: Traditionally, project scheduling and material planning have been treated independently. In this research, a mixed integer programming model is presented to integrate project scheduling and materials ordering problems. The goal is to minimize the total material holding and ordering costs. In addition, an efficient metaheuristic algorithm is proposed to solve the model. The proposed algorithm is computationally tested, the results are analyzed, and conclusions are given.
Abstract: This research presents a fuzzy multi-objective model
for a machine selection problem in a flexible manufacturing system
of a tire company. Two main objectives are minimization of an
average machine error and minimization of the total setup time.
Conventionally, the working team uses trial and error in selecting a
pressing machine for each task due to the complexity and constraints
of the problem. So, both objectives may not satisfy. Moreover, trial
and error takes a lot of time to get the final decision. Therefore, in
this research preemptive fuzzy goal programming model is developed
for solving this multi-objective problem. The proposed model can
obtain the appropriate results that the Decision Making (DM) is
satisfied for both objectives. Besides, alternative choice can be easily
generated by varying the satisfaction level. Additionally, decision
time can be reduced by using the model, which includes all
constraints of the system to generate the solutions. A numerical
example is also illustrated to show the effectiveness of the proposed
model.
Abstract: We describe a novel method for removing noise (in wavelet domain) of unknown variance from microarrays. The method is based on the following procedure: We apply 1) Bidimentional Discrete Wavelet Transform (DWT-2D) to the Noisy Microarray, 2) scaling and rounding to the coefficients of the highest subbands (to obtain integer and positive coefficients), 3) bit-slicing to the new highest subbands (to obtain bit-planes), 4) then we apply the Systholic Boolean Orthonormalizer Network (SBON) to the input bit-plane set and we obtain two orthonormal otput bit-plane sets (in a Boolean sense), we project a set on the other one, by means of an AND operation, and then, 5) we apply re-assembling, and, 6) rescaling. Finally, 7) we apply Inverse DWT-2D and reconstruct a microarray from the modified wavelet coefficients. Denoising results compare favorably to the most of methods in use at the moment.
Abstract: Over last two decades, due to hostilities of environment
over the internet the concerns about confidentiality of information
have increased at phenomenal rate. Therefore to safeguard the information
from attacks, number of data/information hiding methods have
evolved mostly in spatial and transformation domain.In spatial domain
data hiding techniques,the information is embedded directly on
the image plane itself. In transform domain data hiding techniques the
image is first changed from spatial domain to some other domain and
then the secret information is embedded so that the secret information
remains more secure from any attack. Information hiding algorithms
in time domain or spatial domain have high capacity and relatively
lower robustness. In contrast, the algorithms in transform domain,
such as DCT, DWT have certain robustness against some multimedia
processing.In this work the authors propose a novel steganographic
method for hiding information in the transform domain of the gray
scale image.The proposed approach works by converting the gray
level image in transform domain using discrete integer wavelet
technique through lifting scheme.This approach performs a 2-D
lifting wavelet decomposition through Haar lifted wavelet of the cover
image and computes the approximation coefficients matrix CA and
detail coefficients matrices CH, CV, and CD.Next step is to apply the
PMM technique in those coefficients to form the stego image. The
aim of this paper is to propose a high-capacity image steganography
technique that uses pixel mapping method in integer wavelet domain
with acceptable levels of imperceptibility and distortion in the cover
image and high level of overall security. This solution is independent
of the nature of the data to be hidden and produces a stego image
with minimum degradation.
Abstract: In this work, we study the impact of dynamically
changing link slowdowns on the stability properties of packetswitched
networks under the Adversarial Queueing Theory
framework. Especially, we consider the Adversarial, Quasi-Static
Slowdown Queueing Theory model, where each link slowdown may
take on values in the two-valued set of integers {1, D} with D > 1
which remain fixed for a long time, under a (w, ¤ü)-adversary. In this
framework, we present an innovative systematic construction for the
estimation of adversarial injection rate lower bounds, which, if
exceeded, cause instability in networks that use the LIS (Longest-in-
System) protocol for contention-resolution. In addition, we show that
a network that uses the LIS protocol for contention-resolution may
result in dropping its instability bound at injection rates ¤ü > 0 when
the network size and the high slowdown D take large values. This is
the best ever known instability lower bound for LIS networks.
Abstract: Let F(x, y) = ax2 + bxy + cy2 be a positive definite
binary quadratic form with discriminant Δ whose base points lie on
the line x = -1/m for an integer m ≥ 2, let p be a prime number
and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an
elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be
the cubic congruence corresponding to F. In this work we consider
some properties of positive definite quadratic forms, elliptic curves
and cubic congruences.
Abstract: This paper presents a novel algorithm for path planning of mobile robots in known 3D environments using Binary Integer Programming (BIP). In this approach the problem of path planning is formulated as a BIP with variables taken from 3D Delaunay Triangulation of the Free Configuration Space and solved to obtain an optimal channel made of connected tetrahedrons. The 3D channel is then partitioned into convex fragments which are used to build safe and short paths within from Start to Goal. The algorithm is simple, complete, does not suffer from local minima, and is applicable to different workspaces with convex and concave polyhedral obstacles. The noticeable feature of this algorithm is that it is simply extendable to n-D Configuration spaces.
Abstract: In this research, we study a control method of a multivehicle
system while considering the limitation of communication
range for each vehicles. When we control networked vehicles with
limitation of communication range, it is important to control the
communication network structure of a multi-vehicle system in order
to keep the network-s connectivity. From this, we especially aim to
control the network structure to the target structure. We formulate
the networked multi-vehicle system with some disturbance and the
communication constraints as a hybrid dynamical system, and then
we study the optimal control problems of the system. It is shown
that the system converge to the objective network structure in finite
time when the system is controlled by the receding horizon method.
Additionally, the optimal control probrems are convertible into the
mixed integer problems and these problems are solvable by some
branch and bound algorithm.
Abstract: Let n ≥ 3 be an integer and G2(n) be the subgroup
of square roots of 1 in (Z/nZ)*. In this paper, we give an algorithm
that computes a generating set of this subgroup.
Abstract: Residue Number System (RNS) is a modular representation and is proved to be an instrumental tool in many digital signal processing (DSP) applications which require high-speed computations. RNS is an integer and non weighted number system; it can support parallel, carry-free, high-speed and low power arithmetic. A very interesting correspondence exists between the concepts of Multiple Valued Logic (MVL) and Residue Number Arithmetic. If the number of levels used to represent MVL signals is chosen to be consistent with the moduli which create the finite rings in the RNS, MVL becomes a very natural representation for the RNS. There are two concerns related to the application of this Number System: reaching the most possible speed and the largest dynamic range. There is a conflict when one wants to resolve both these problem. That is augmenting the dynamic range results in reducing the speed in the same time. For achieving the most performance a method is considere named “One-Hot Residue Number System" in this implementation the propagation is only equal to one transistor delay. The problem with this method is the huge increase in the number of transistors they are increased in order m2 . In real application this is practically impossible. In this paper combining the Multiple Valued Logic and One-Hot Residue Number System we represent a new method to resolve both of these two problems. In this paper we represent a novel design of an OHRNS-based adder circuit. This circuit is useable for Multiple Valued Logic moduli, in comparison to other RNS design; this circuit has considerably improved the number of transistors and power consumption.
Abstract: Assume that we have m identical graphs where the
graphs consists of paths with k vertices where k is a positive integer.
In this paper, we discuss certain labelling of the m graphs called
c-Erdösian for some positive integers c. We regard labellings of the
vertices of the graphs by positive integers, which induce the edge
labels for the paths as the sum of the two incident vertex labels.
They have the property that each vertex label and edge label appears
only once in the set of positive integers {c, . . . , c+6m- 1}. Here,
we show how to construct certain c-Erdösian of m paths with 2 and
3 vertices by using Skolem sequences.
Abstract: Let p be a prime number such that p ≡ 1(mod 4), say
p = 1+4k for a positive integer k. Let P = 2k + 1 and Q = k2.
In this paper, we consider the integer solutions of the Pell equation
x2-Py2 = Q over Z and also over finite fields Fp. Also we deduce
some relations on the integer solutions (xn, yn) of it.
Abstract: Attitude Determination (AD) of a spacecraft using the
phase measurements of the Global Navigation Satellite System
(GNSS) is an active area of research. Various attitude determination
algorithms have been developed in yester years for spacecrafts using
different sensors but the last two decades have witnessed a
phenomenal increase in research related with GPS receivers as a
stand-alone sensor for determining the attitude of satellite using the
phase measurements of the signals from GNSS. The GNSS-based
Attitude determination algorithms have been experimented in many
real missions. The problem of AD algorithms using GNSS phase
measurements has two important parts; the ambiguity resolution and
the determining of attitude. Ambiguity resolution is the widely
addressed topic in literature for implementing the AD algorithm
using GNSS phase measurements for achieving the accuracy of
millimeter level. This paper broadly overviews the different
techniques for resolving the integer ambiguities encountered in AD
using GNSS phase measurements.
Abstract: A multicriteria linear programming problem with integer variables and parameterized optimality principle "from lexicographic to Slater" is considered. A situation in which initial coefficients of penalty cost functions are not fixed but may be potentially a subject to variations is studied. For any efficient solution, appropriate measures of the quality are introduced which incorporate information about variations of penalty cost function coefficients. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an efficient solution preserves the property of being efficient are calculated.
Abstract: The objective of this research is to calculate the
optimal inventory lot-sizing for each supplier and minimize the total
inventory cost which includes joint purchase cost of the products,
transaction cost for the suppliers, and holding cost for remaining
inventory. Genetic algorithms (GAs) are applied to the multi-product
and multi-period inventory lot-sizing problems with supplier
selection under storage space. Also a maximum storage space for the
decision maker in each period is considered. The decision maker
needs to determine what products to order in what quantities with
which suppliers in which periods. It is assumed that demand of
multiple products is known over a planning horizon. The problem is
formulated as a mixed integer programming and is solved with the
GAs. The detailed computation results are presented.