Abstract: Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.
Abstract: In this paper, a mathematical model of human immunodeficiency
virus (HIV) is utilized and an optimization problem is
proposed, with the final goal of implementing an optimal 900-day
structured treatment interruption (STI) protocol. Two type of commonly
used drugs in highly active antiretroviral therapy (HAART),
reverse transcriptase inhibitors (RTI) and protease inhibitors (PI), are
considered. In order to solving the proposed optimization problem an
adaptive memetic algorithm with population management (AMAPM)
is proposed. The AMAPM uses a distance measure to control the
diversity of population in genotype space and thus preventing the
stagnation and premature convergence. Moreover, the AMAPM uses
diversity parameter in phenotype space to dynamically set the population
size and the number of crossovers during the search process.
Three crossover operators diversify the population, simultaneously.
The progresses of crossover operators are utilized to set the number
of each crossover per generation. In order to escaping the local optima
and introducing the new search directions toward the global optima,
two local searchers assist the evolutionary process. In contrast to
traditional memetic algorithms, the activation of these local searchers
is not random and depends on both the diversity parameters in
genotype space and phenotype space. The capability of AMAPM in
finding optimal solutions compared with three popular metaheurestics
is introduced.
Abstract: Medical image data hiding has strict constrains such
as high imperceptibility, high capacity and high robustness.
Achieving these three requirements simultaneously is highly
cumbersome. Some works have been reported in the literature on
data hiding, watermarking and stegnography which are suitable for
telemedicine applications. None is reliable in all aspects. Electronic
Patient Report (EPR) data hiding for telemedicine demand it blind
and reversible. This paper proposes a novel approach to blind
reversible data hiding based on integer wavelet transform.
Experimental results shows that this scheme outperforms the prior
arts in terms of zero BER (Bit Error Rate), higher PSNR (Peak Signal
to Noise Ratio), and large EPR data embedding capacity with
WPSNR (Weighted Peak Signal to Noise Ratio) around 53 dB,
compared with the existing reversible data hiding schemes.
Abstract: Cryptographic algorithms play a crucial role in the
information society by providing protection from unauthorized
access to sensitive data. It is clear that information technology will
become increasingly pervasive, Hence we can expect the emergence
of ubiquitous or pervasive computing, ambient intelligence. These
new environments and applications will present new security
challenges, and there is no doubt that cryptographic algorithms and
protocols will form a part of the solution. The efficiency of a public
key cryptosystem is mainly measured in computational overheads,
key size and bandwidth. In particular the RSA algorithm is used in
many applications for providing the security. Although the security
of RSA is beyond doubt, the evolution in computing power has
caused a growth in the necessary key length. The fact that most chips
on smart cards can-t process key extending 1024 bit shows that there
is need for alternative. NTRU is such an alternative and it is a
collection of mathematical algorithm based on manipulating lists of
very small integers and polynomials. This allows NTRU to high
speeds with the use of minimal computing power. NTRU (Nth degree
Truncated Polynomial Ring Unit) is the first secure public key
cryptosystem not based on factorization or discrete logarithm
problem. This means that given sufficient computational resources
and time, an adversary, should not be able to break the key. The
multi-party communication and requirement of optimal resource
utilization necessitated the need for the present day demand of
applications that need security enforcement technique .and can be
enhanced with high-end computing. This has promoted us to develop
high-performance NTRU schemes using approaches such as the use
of high-end computing hardware. Peer-to-peer (P2P) or enterprise
grids are proven as one of the approaches for developing high-end
computing systems. By utilizing them one can improve the
performance of NTRU through parallel execution. In this paper we
propose and develop an application for NTRU using enterprise grid
middleware called Alchemi. An analysis and comparison of its
performance for various text files is presented.
Abstract: Let p be a prime number, Fpbe a finite field and let Qpdenote the set of quadratic residues in Fp. In the first section we givesome notations and preliminaries from elliptic curves. In the secondsection, we consider some properties of rational points on ellipticcurves Ep,b: y2= x3+ b2 over Fp, where b ∈ F*p. Recall that theorder of Ep,bover Fpis p + 1 if p ≡ 5(mod 6). We generalize thisresult to any field Fnp for an integer n≥ 2. Further we obtain someresults concerning the sum Σ[x]Ep,b(Fp) and Σ[y]Ep,b(Fp), thesum of x- and y- coordinates of all points (x, y) on Ep,b, and alsothe the sum Σ(x,0)Ep,b(Fp), the sum of points (x, 0) on Ep,b.
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, p)-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 p > 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 G be a graph of order n, and let a, b and m be positive integers with 1 ≤ a n + a + b − 2 √bn+ 1, then for any subgraph H of G with m edges, G has an [a, b]-factor F such that E(H)∩ E(F) = ∅. This result is an extension of thatof Egawa [2].
Abstract: Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h : E(G) [0, 1] be a function. If e∋x h(e) = k holds for each x V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G) k + m + m k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)} n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.
Abstract: Authentication of multimedia contents has gained much attention in recent times. In this paper, we propose a secure semi-fragile watermarking, with a choice of two watermarks to be embedded. This technique operates in integer wavelet domain and makes use of semi fragile watermarks for achieving better robustness. A self-recovering algorithm is employed, that hides the image digest into some Wavelet subbands to detect possible malevolent object manipulation undergone by the image (object replacing and/or deletion). The Semi-fragility makes the scheme tolerant for JPEG lossy compression as low as quality of 70%, and locate the tempered area accurately. In addition, the system ensures more security because the embedded watermarks are protected with private keys. The computational complexity is reduced using parameterized integer wavelet transform. Experimental results show that the proposed scheme guarantees the safety of watermark, image recovery and location of the tempered area accurately.
Abstract: The problem of estimating time-varying regression is
inevitably concerned with the necessity to choose the appropriate
level of model volatility - ranging from the full stationarity of instant
regression models to their absolute independence of each other. In the
stationary case the number of regression coefficients to be estimated
equals that of regressors, whereas the absence of any smoothness
assumptions augments the dimension of the unknown vector by the
factor of the time-series length. The Akaike Information Criterion
is a commonly adopted means of adjusting a model to the given
data set within a succession of nested parametric model classes,
but its crucial restriction is that the classes are rigidly defined by
the growing integer-valued dimension of the unknown vector. To
make the Kullback information maximization principle underlying the
classical AIC applicable to the problem of time-varying regression
estimation, we extend it onto a wider class of data models in which
the dimension of the parameter is fixed, but the freedom of its values
is softly constrained by a family of continuously nested a priori
probability distributions.
Abstract: The paper proposes an approach for design of modular
systems based on original technique for modeling and formulation of
combinatorial optimization problems. The proposed approach is
described on the example of personal computer configuration design.
It takes into account the existing compatibility restrictions between
the modules and can be extended and modified to reflect different
functional and users- requirements. The developed design modeling
technique is used to formulate single objective nonlinear mixedinteger
optimization tasks. The practical applicability of the
developed approach is numerically tested on the basis of real modules
data. Solutions of the formulated optimization tasks define the
optimal configuration of the system that satisfies all compatibility
restrictions and user requirements.
Abstract: This paper presents the review of past studies
concerning mathematical models for rescheduling passenger railway
services, as part of delay management in the occurrence of railway
disruption. Many past mathematical models highlighted were aimed
at minimizing the service delays experienced by passengers during
service disruptions. Integer programming (IP) and mixed-integer
programming (MIP) models are critically discussed, focusing on the
model approach, decision variables, sets and parameters. Some of
them have been tested on real-life data of railway companies
worldwide, while a few have been validated on fictive data. Based
on selected literatures on train rescheduling, this paper is able to
assist researchers in the model formulation by providing
comprehensive analyses towards the model building. These analyses
would be able to help in the development of new approaches in
rescheduling strategies or perhaps to enhance the existing
rescheduling models and make them more powerful or more
applicable with shorter computing time.
Abstract: In this article an evolutionary technique has been used
for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for
the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been
successfully applied to solve the different forms of Riccati
differential equations. The strength of proposed method has in its
equal applicability for the integer order case, as well as, fractional
order case. Comparison of the method has been made with standard
numerical techniques as well as the analytic solutions. It is found
that the designed method can provide the solution to the equation
with better accuracy than its counterpart deterministic approaches.
Another advantage of the given approach is to provide results on
entire finite continuous domain unlike other numerical methods
which provide solutions only on discrete grid of points.
Abstract: Let R be a ring and n a fixed positive integer, we
investigate the properties of n-strongly Gorenstein projective, injective
and flat modules. Using the homological theory , we prove that
the tensor product of an n-strongly Gorenstein projective (flat) right
R -module and projective (flat) left R-module is also n-strongly
Gorenstein projective (flat). Let R be a coherent ring ,we prove that
the character module of an n -strongly Gorenstein flat left R -module
is an n-strongly Gorenstein injective right R -module . At last, let
R be a commutative ring and S a multiplicatively closed set of R ,
we establish the relation between n -strongly Gorenstein projective
(injective , flat ) R -modules and n-strongly Gorenstein projective
(injective , flat ) S−1R-modules. All conclusions in this paper is
helpful for the research of Gorenstein dimensions in future.
Abstract: The hypercube Qn is one of the most well-known
and popular interconnection networks and the k-ary n-cube Qk
n is
an enlarged family from Qn that keeps many pleasing properties
from hypercubes. In this article, we study the panpositionable
hamiltonicity of Qk
n for k ≥ 3 and n ≥ 2. Let x, y of V (Qk
n)
be two arbitrary vertices and C be a hamiltonian cycle of Qk
n.
We use dC(x, y) to denote the distance between x and y on the
hamiltonian cycle C. Define l as an integer satisfying d(x, y) ≤ l ≤ 1
2 |V (Qk
n)|. We prove the followings:
• When k = 3 and n ≥ 2, there exists a hamiltonian cycle C
of Qk
n such that dC(x, y) = l.
• When k ≥ 5 is odd and n ≥ 2, we request that l /∈ S
where S is a set of specific integers. Then there exists a
hamiltonian cycle C of Qk
n such that dC(x, y) = l.
• When k ≥ 4 is even and n ≥ 2, we request l-d(x, y) to be
even. Then there exists a hamiltonian cycle C of Qk
n such
that dC(x, y) = l.
The result is optimal since the restrictions on l is due to the
structure of Qk
n by definition.
Abstract: Let D = 1 be a positive non-square integer and let δ = √D or 1+√D 2 be a real quadratic irrational with trace t =δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an indefinite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t
2−4n. In the first section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some specific values of Q and P.
Abstract: Bus networks design is an important problem in
public transportation. The main step to this design, is determining the
number of required terminals and their locations. This is an especial
type of facility location problem, a large scale combinatorial
optimization problem that requires a long time to be solved.
The genetic algorithm (GA) is a search and optimization technique
which works based on evolutionary principle of natural
chromosomes. Specifically, the evolution of chromosomes due to the
action of crossover, mutation and natural selection of chromosomes
based on Darwin's survival-of-the-fittest principle, are all artificially
simulated to constitute a robust search and optimization procedure.
In this paper, we first state the problem as a mixed integer
programming (MIP) problem. Then we design a new crossover and
mutation for bus terminal location problem (BTLP). We tested the
different parameters of genetic algorithm (for a sample problem) and
obtained the optimal parameters for solving BTLP with numerical try
and error.
Abstract: In this paper, low end Digital Signal Processors (DSPs)
are applied to accelerate integer neural networks. The use of DSPs
to accelerate neural networks has been a topic of study for some
time, and has demonstrated significant performance improvements.
Recently, work has been done on integer only neural networks, which
greatly reduces hardware requirements, and thus allows for cheaper
hardware implementation. DSPs with Arithmetic Logic Units (ALUs)
that support floating or fixed point arithmetic are generally more
expensive than their integer only counterparts due to increased circuit
complexity. However if the need for floating or fixed point math
operation can be removed, then simpler, lower cost DSPs can be
used. To achieve this, an integer only neural network is created in
this paper, which is then accelerated by using DSP instructions to
improve performance.
Abstract: Main goal of preventive healthcare problems are at
decreasing the likelihood and severity of potentially life-threatening
illnesses by protection and early detection. The levels of
establishment and staffing costs along with summation of the travel
and waiting time that clients spent are considered as objectives
functions of the proposed nonlinear integer programming model. In
this paper, we have proposed a bi-objective mathematical model for
designing a network of preventive healthcare facilities so as to
minimize aforementioned objectives, simultaneously. Moreover, each
facility acts as M/M/1 queuing system. The number of facilities to be
established, the location of each facility, and the level of technology
for each facility to be chosen are provided as the main determinants
of a healthcare facility network. Finally, to demonstrate performance
of the proposed model, four multi-objective decision making
techniques are presented to solve the model.
Abstract: This paper at first presents approximate analytical
solutions for systems of fractional differential equations using the
differential transform method. The application of differential
transform method, developed for differential equations of integer
order, is extended to derive approximate analytical solutions of
systems of fractional differential equations. The solutions of our
model equations are calculated in the form of convergent series with
easily computable components. After that a drive-response
synchronization method with linear output error feedback is
presented for “generalized projective synchronization" for a class of
fractional-order chaotic systems via a scalar transmitted signal.
Genesio_Tesi and Duffing systems are used to illustrate the
effectiveness of the proposed synchronization method.