Abstract: The competitive learning is an adaptive process in
which the neurons in a neural network gradually become sensitive to
different input pattern clusters. The basic idea behind the Kohonen-s
Self-Organizing Feature Maps (SOFM) is competitive learning.
SOFM can generate mappings from high-dimensional signal spaces
to lower dimensional topological structures. The main features of this
kind of mappings are topology preserving, feature mappings and
probability distribution approximation of input patterns. To overcome
some limitations of SOFM, e.g., a fixed number of neural units and a
topology of fixed dimensionality, Growing Self-Organizing Neural
Network (GSONN) can be used. GSONN can change its topological
structure during learning. It grows by learning and shrinks by
forgetting. To speed up the training and convergence, a new variant
of GSONN, twin growing cell structures (TGCS) is presented here.
This paper first gives an introduction to competitive learning, SOFM
and its variants. Then, we discuss some GSONN with fixed
dimensionality, which include growing cell structures, its variants
and the author-s model: TGCS. It is ended with some testing results
comparison and conclusions.
Abstract: The world economic crises and budget constraints
have caused authorities, especially those in developing countries, to
rationalize water quality monitoring activities. Rationalization
consists of reducing the number of monitoring sites, the number of
samples, and/or the number of water quality variables measured. The
reduction in water quality variables is usually based on correlation. If
two variables exhibit high correlation, it is an indication that some of
the information produced may be redundant. Consequently, one
variable can be discontinued, and the other continues to be measured.
Later, the ordinary least squares (OLS) regression technique is
employed to reconstitute information about discontinued variable by
using the continuously measured one as an explanatory variable. In
this paper, two record extension techniques are employed to
reconstitute information about discontinued water quality variables,
the OLS and the Line of Organic Correlation (LOC). An empirical
experiment is conducted using water quality records from the Nile
Delta water quality monitoring network in Egypt. The record
extension techniques are compared for their ability to predict
different statistical parameters of the discontinued variables. Results
show that the OLS is better at estimating individual water quality
records. However, results indicate an underestimation of the variance
in the extended records. The LOC technique is superior in preserving
characteristics of the entire distribution and avoids underestimation
of the variance. It is concluded from this study that the OLS can be
used for the substitution of missing values, while LOC is preferable
for inferring statements about the probability distribution.
Abstract: Most of the real queuing systems include special properties and constraints, which can not be analyzed directly by using the results of solved classical queuing models. Lack of Markov chains features, unexponential patterns and service constraints, are the mentioned conditions. This paper represents an applied general algorithm for analysis and optimizing the queuing systems. The algorithm stages are described through a real case study. It is consisted of an almost completed non-Markov system with limited number of customers and capacities as well as lots of common exception of real queuing networks. Simulation is used for optimizing this system. So introduced stages over the following article include primary modeling, determining queuing system kinds, index defining, statistical analysis and goodness of fit test, validation of model and optimizing methods of system with simulation.
Abstract: In this article we explore the application of a formal
proof system to verification problems in cryptography. Cryptographic
properties concerning correctness or security of some cryptographic
algorithms are of great interest. Beside some basic lemmata, we
explore an implementation of a complex function that is used in
cryptography. More precisely, we describe formal properties of this
implementation that we computer prove. We describe formalized
probability distributions (σ-algebras, probability spaces and conditional
probabilities). These are given in the formal language of the
formal proof system Isabelle/HOL. Moreover, we computer prove
Bayes- Formula. Besides, we describe an application of the presented
formalized probability distributions to cryptography. Furthermore,
this article shows that computer proofs of complex cryptographic
functions are possible by presenting an implementation of the Miller-
Rabin primality test that admits formal verification. Our achievements
are a step towards computer verification of cryptographic primitives.
They describe a basis for computer verification in cryptography.
Computer verification can be applied to further problems in cryptographic
research, if the corresponding basic mathematical knowledge
is available in a database.
Abstract: Reactiondiffusion systems are mathematical models that describe how the concentration of one or more substances distributed in space changes under the influence of local chemical reactions in which the substances are converted into each other, and diffusion which causes the substances to spread out in space. The classical representation of a reaction-diffusion system is given by semi-linear parabolic partial differential equations, whose general form is ÔêétX(x, t) = DΔX(x, t), where X(x, t) is the state vector, D is the matrix of the diffusion coefficients and Δ is the Laplace operator. If the solute move in an homogeneous system in thermal equilibrium, the diffusion coefficients are constants that do not depend on the local concentration of solvent and of solutes and on local temperature of the medium. In this paper a new stochastic reaction-diffusion model in which the diffusion coefficients are function of the local concentration, viscosity and frictional forces of solvent and solute is presented. Such a model provides a more realistic description of the molecular kinetics in non-homogenoeus and highly structured media as the intra- and inter-cellular spaces. The movement of a molecule A from a region i to a region j of the space is described as a first order reaction Ai k- → Aj , where the rate constant k depends on the diffusion coefficient. Representing the diffusional motion as a chemical reaction allows to assimilate a reaction-diffusion system to a pure reaction system and to simulate it with Gillespie-inspired stochastic simulation algorithms. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the specific speed of reaction and diffusion events. Redi is the software tool, developed to implement the model of reaction-diffusion kinetics and dynamics. It is a free software, that can be downloaded from http://www.cosbi.eu. To demonstrate the validity of the new reaction-diffusion model, the simulation results of the chaperone-assisted protein folding in cytoplasm obtained with Redi are reported. This case study is redrawing the attention of the scientific community due to current interests on protein aggregation as a potential cause for neurodegenerative diseases.
Abstract: In large Internet backbones, Service Providers
typically have to explicitly manage the traffic flows in order to
optimize the use of network resources. This process is often referred
to as Traffic Engineering (TE). Common objectives of traffic
engineering include balance traffic distribution across the network
and avoiding congestion hot spots. Raj P H and SVK Raja designed
the Bayesian network approach to identify congestion hors pots in
MPLS. In this approach for every node in the network the
Conditional Probability Distribution (CPD) is specified. Based on
the CPD the congestion hot spots are identified. Then the traffic can
be distributed so that no link in the network is either over utilized or
under utilized. Although the Bayesian network approach has been
implemented in operational networks, it has a number of well known
scaling issues.
This paper proposes a new approach, which we call the Pragati
(means Progress) Node Popularity (PNP) approach to identify the
congestion hot spots with the network topology alone. In the new
Pragati Node Popularity approach, IP routing runs natively over the
physical topology rather than depending on the CPD of each node as
in Bayesian network. We first illustrate our approach with a simple
network, then present a formal analysis of the Pragati Node
Popularity approach. Our PNP approach shows that for any given
network of Bayesian approach, it exactly identifies the same result
with minimum efforts. We further extend the result to a more
generic one: for any network topology and even though the network
is loopy. A theoretical insight of our result is that the optimal routing
is always shortest path routing with respect to some considerations of
hot spots in the networks.
Abstract: Time varying network induced delays in networked
control systems (NCS) are known for degrading control system-s
quality of performance (QoP) and causing stability problems. In
literature, a control method employing modeling of communication
delays as probability distribution, proves to be a better method. This
paper focuses on modeling of network induced delays as probability
distribution.
CAN and MIL-STD-1553B are extensively used to carry periodic
control and monitoring data in networked control systems.
In literature, methods to estimate only the worst-case delays for
these networks are available. In this paper probabilistic network
delay model for CAN and MIL-STD-1553B networks are given.
A systematic method to estimate values to model parameters from
network parameters is given. A method to predict network delay in
next cycle based on the present network delay is presented. Effect of
active network redundancy and redundancy at node level on network
delay and system response-time is also analyzed.
Abstract: Geographic Profiling has successfully assisted investigations for serial crimes. Considering the multi-cluster feature of serial criminal spots, we propose a Multi-point Centrography model as a natural extension of Single-point Centrography for geographic profiling. K-means clustering is first performed on the data samples and then Single-point Centrography is adopted to derive a probability distribution on each cluster. Finally, a weighted combinations of each distribution is formed to make next-crime spot prediction. Experimental study on real cases demonstrates the effectiveness of our proposed model.
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: If a possibility distribution and a probability distribution
are describing values x of one and the same system or process
x(t), can they relate to each other? Though in general the possibility
and probability distributions might be not connected at all, we
can assume that in some particular cases there is an association linked
them.
In the presented paper, we consider distributions of bloodstream
concentrations of physiologically active substances and propose that
the probability to observe a concentration x of a substance X can be
produced from the possibility of the event X = x .
The proposed assumptions and resulted theoretical distributions
are tested against the data obtained from various panel studies of the
bloodstream concentrations of the different physiologically active
substances in patients and healthy adults as well.
Abstract: In this paper we explore the application of a formal proof system to verification problems in cryptography. Cryptographic properties concerning correctness or security of some cryptographic algorithms are of great interest. Beside some basic lemmata, we explore an implementation of a complex function that is used in cryptography. More precisely, we describe formal properties of this implementation that we computer prove. We describe formalized probability distributions (o--algebras, probability spaces and condi¬tional probabilities). These are given in the formal language of the formal proof system Isabelle/HOL. Moreover, we computer prove Bayes' Formula. Besides we describe an application of the presented formalized probability distributions to cryptography. Furthermore, this paper shows that computer proofs of complex cryptographic functions are possible by presenting an implementation of the Miller- Rabin primality test that admits formal verification. Our achievements are a step towards computer verification of cryptographic primitives. They describe a basis for computer verification in cryptography. Computer verification can be applied to further problems in crypto-graphic research, if the corresponding basic mathematical knowledge is available in a database.
Abstract: In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.
Abstract: The present models and simulation algorithms of intracellular stochastic kinetics are usually based on the premise that diffusion is so fast that the concentrations of all the involved species are homogeneous in space. However, recents experimental measurements of intracellular diffusion constants indicate that the assumption of a homogeneous well-stirred cytosol is not necessarily valid even for small prokaryotic cells. In this work a mathematical treatment of diffusion that can be incorporated in a stochastic algorithm simulating the dynamics of a reaction-diffusion system is presented. The movement of a molecule A from a region i to a region j of the space is represented as a first order reaction Ai k- ! Aj , where the rate constant k depends on the diffusion coefficient. The diffusion coefficients are modeled as function of the local concentration of the solutes, their intrinsic viscosities, their frictional coefficients and the temperature of the system. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the intrinsic reaction kinetics and diffusion dynamics. To demonstrate the method the simulation results of the reaction-diffusion system of chaperoneassisted protein folding in cytoplasm are shown.