-
Takeyuki Hida, Si Si
2006 Volume 64 Issue 2 Pages
175-183
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
There are many random phenomena such that their probability distributions
are not Gaussian but other particular distributions with fat tail. They are the
so-called fractional power distributions. We can see that their mathematical models
can, in some favorable cases, be embedded in stable stochastic processes, which are expressed
as superpositions of Poisson processes with various magnitudes of jump. Thus,
our mathematical theory, which characterizes latent traits of Poisson noise, would effectively
be applied to the random phenomena in question, in order to describe their
biological characteristics.
View full abstract
-
Simon Coakley, Rod Smallwood, Mike Holcombe
2006 Volume 64 Issue 2 Pages
185-198
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
Agent-based approaches to modelling biological phenomena are becoming
popular and proving successful in a number of areas. However, the underlying basis of
these techniques is sometimes rather ‘ad-hoc’ and the models are often only applied to
specific systems. This paper describes a general approach that is based on the use of
fully general computational models, using a formal model of an agent and a rigorous
approach to building systems of communicating agents within virtual environments.
A collection of tools has been built which allow for efficient simulation of such systems
and their visualisation. Included in this work is the implementation of the simulations
on parallel clusters of computers to enable large numbers of agents to be simulated.
Application areas where the method has been successfully applied include:
• Signal transduction pathways, specifically the NF-κB pathway. This model has
been validated using single cell data from GFP transvected cells. The model has
enabled the prediction of the possible role of actin filaments in the sequestration
and feedback control of IκB.
• The epitheliome project involves building models of the development of both skin
and urothelial tissue and the investigation of the role of calcium and juxtracrine
signalling in the development and differentiation of tissue. Again, the models
have been validated with ’in vitro’ tissue cultures under a number of important
laboratory conditions.
• Populations of Pharoah’s ants have been simulated and closely compared with
real populations within the laboratory. The role of pheromone signalling has
been studied and the modelling has led to a new understanding of the use of
pheromone trails in foraging behaviour. This has shown that the geometry of the
trails contains vital information that is used in the navigation of the trails by the
insects.
View full abstract
-
Mario Abundo
2006 Volume 64 Issue 2 Pages
199-216
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
We deal with the qualitative behaviour of the first-passage-time density
of a one-dimensional diffusion process X(t) over a moving boundary; in particular, we
study the value that the first-passage time density takes at zero, the distribution of
the maximum process, and the distribution of the first instant at which X(t) attains
the maximum in an interval [0,T]. Our results generalize the analogous ones already
known for Brownian motion. Some examples are reported.
View full abstract
-
Paul Cull
2006 Volume 64 Issue 2 Pages
217-233
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
Difference equations have been used in population biology from Fibonacci
to May and Yorke and to the present day. They have also been used in other biological
fields. Here, we describe a number of fairly well know examples. We give techniques
and results about the analysis of linear and nonlinear difference equations. We also
show that there are practical and theoretical limitations on the analysis of nonlinear
models.
View full abstract
-
Marcello De Giosa, Monica Lazzo
2006 Volume 64 Issue 2 Pages
235-242
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
We state and prove weak and strong laws of large numbers for a product
of random variables. A statistical application to a problem in geometric probability is
also provided.
View full abstract
-
Aldo de Luca
2006 Volume 64 Issue 2 Pages
243-253
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
The scientific research program of Cybernetics, originated by Norbert
Wiener, was mainly concerned with the communication and control whether in living
organisms or machines. The main aim was to get useful and essential information on
the functioning of the brain on which to construct later a science of the mind. This
requires methods and knowledge borrowed from different disciplines including Physics,
Biology, and Humanities. The great novelty of Cybernetics was the introduction of a
new entity called ‘information’ of fundamental importance in the theory of communication.
However, several different formalizations of the intuitive notion of information
exist which depend on the ‘context’, i.e., the characteristic features of the ‘source’,
of the ‘channel’, and of the ‘receiver’. The context is of a particular relevance in the
study of biological systems where there exist sophisticated coding mechanisms which
are essential to the information processing, and underlie the high level functions of
human mind. At present, still lacking is a theory of information and coding that could
be usefully employed for the study of complex biological systems. This was the main
reason for the decline of Cybernetics.
View full abstract
-
Antonio Di Crescenzo, Maria Longobardi
2006 Volume 64 Issue 2 Pages
255-266
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
We consider a “length-biased” shift-dependent information measure, related
to the differential entropy in which higher weight is assigned to large values
of observed random variables. This allows us to introduce the notions of “weighted
residual entropy” and “weighted past entropy”, that are suitable to describe dynamic
information of random lifetimes, in analogy with the entropies of residual and past
lifetimes introduced in [9] and [6], respectively. The obtained results include their
behaviors under monotonic transformations.
View full abstract
-
M. Falconi
2006 Volume 64 Issue 2 Pages
267-275
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
In this paper, we are concerned with the role of the age structure of a prey
in the dynamic of a predator prey model. Specifically, we study the effect of predation
on a non-reproductive class of the prey, when the reproductive class of the prey presents
a group defense mechanism. Three different scenarios are analyzed: (1) Constant
predation rate on the nonreproductive class, no defense mechanism; (2) Predation
of Type II of Holling on the non-reproductive class, no defense mechanism; and (3)
Predation of Type II of Holling on the non-reproductive class, defense mechanism.
View full abstract
-
Virginia Giorno, Amelia G. Nobile, Enrica Pirozzi, Luigi M. Ricciardi
2006 Volume 64 Issue 2 Pages
277-298
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
A new method for constructing first-passage-time probability density functions
in the case of regular one-dimensional time homogeneous diffusion processes
restricted between constant boundaries is proposed. Some diffusion processes of particular
interest in neuronal modeling are considered and thoroughly discusses.
View full abstract
-
Maria Teresa Giraudo, Laura sacerdote
2006 Volume 64 Issue 2 Pages
299-312
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
The response of a neuron to a linear combination of the first two harmonics
of a fundamental frequency is studied by means of a leaky integrate and fire model. A
suitable modification of the classical stochastic model is introduced to consider such
input. The resulting interspike interval distribution exhibits maxima in correspondence
with the fundamental frequency that was absent in the input signal. This fact shows
the ability of the system to recognize the ”ghost” frequency. Resonance-like behavior is
also showed by the model neuron in a set of instances. The simplicity of the considered
model makes also easy to understand the features involved in the ghost resonance
phenomenon and to recognize the parameter the ranges compatible with such behavior.
View full abstract
-
R. Gutiérrez, N. Rico, P. Román, F. Torres
2006 Volume 64 Issue 2 Pages
313-329
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
Approximate and generalized confidence bands for some parametric functions
of the univariate lognormal diffusion process with exogenous factors are obtained.
The procedures to obtain these bands are developed from the suitable adaptation of
the available methods for building confidence intervals for the mean of the lognormal
distribution. The obtained bands are similar to those calculated for the homogeneous
lognormal diffusion process but, in this case it is not possible a general comparative
study in terms of coverage errors, by means of simulation studies, because of the dependence
on the exogenous factors of each particular model. Therefore, in each case
a particular study is necessary. In this sense, in this paper two models are considered
modelling the gross national product of Spain and the global manmade methane
emissions, respectively.
View full abstract
-
José Mira, Ana E. Delgado
2006 Volume 64 Issue 2 Pages
331-349
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
In this work, taking advantage of the fiftieth anniversary of Artificial
Intelligence (AI), we consider the disparity that exist between the excessive initial objectives
of synthesizing general intelligence in machines and the modest results obtained
after half a century of work. We mention some of the possible causes of this disparity
(constitutive differences between man and machines, lack of a theory of computable
knowledge and oblivion of the solid work made by the pioneers of Cybernetics). Then
we go over the history until we arrive to the current AI paradigms (symbolic, situated
and connectionist) in search of its cybernetics roots and conclude with some suggestions
on the strategic decisions that could be adopted to progress in the understanding
of intelligence.
View full abstract
-
A. De Gregorio, Enzo Orsingher
2006 Volume 64 Issue 2 Pages
351-356
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
-
Miguel Lara-Aparicio, Carolina Barriga-Montoya, Beatriz Fuentes-Pardo
2006 Volume 64 Issue 2 Pages
357-370
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
As we know, Arthur Winfree passed away a relatively short time ago. His
memory motived us to investigate his great influence in the biomathematical development
of one of the most important branches of Biological Sciences, i.e. the Chronobiology.
In this paper we present the “giants”, paraphrasing Newton, on whose shoulders
Winfree stood up seeing farther about biological rhythms, as well as some of his contemporaries.
We can appreciate Winfree’s influence in the field observing that when
he decided change his interest towards other fields, there appeared a certain fading
in the number of people working in circadian rhythms from a mathematical point of
view. However, the solid basements built by the founders of this branch of Science
have allowed that nowadays not only high quality papers of biomathematical contents
continue to appear in important journals, but also papers of pure mathematical problems
inspired by circadian rhythms. In fact, the building of the interface of Biology
and Mathematics has been reinforced in such a manner that both disciplines have mutually
benefited. Finally, we present a section in which it is possible to appreciate a
few articles that have appeared after Winfree.
View full abstract
-
Mohiniso Bahromovna Hidirova
2006 Volume 64 Issue 2 Pages
371-379
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
We present some methods to analyze a biological excitable medium. We
provide local-global considerations to describe biological excitable media based on
delay-differential equations. We find that there are the following modes: rest, steady
state, regular oscillations, deterministic chaos and phenomena of oscillation failure.
View full abstract
-
Antonio Di Crescenzo, Barbara Martinucci
2006 Volume 64 Issue 2 Pages
381-394
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
We consider a model for systems perturbed by dichotomous noise, in which
the hazard rate function of a random lifetime is subject to additive time-alternating
perturbations described by the telegraph process. This leads us to define a real-valued
continuous-time stochastic process of alternating type expressed in terms of the integrated
telegraph process for which we obtain the probability distribution, mean and
variance. An application to survival analysis and reliability data sets based on confidence
bands for estimated hazard rate functions is also provided.
View full abstract
-
Roberto Moreno-Díaz jr, Alexis Quesada-Arencibia, José C ...
2006 Volume 64 Issue 2 Pages
395-403
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
We present the results of a computer vision system intended to describe
in real time the trajectories of moving objects in a variety of speeds. The developed
computing mechanism includes channel processing for instant position and velocity
estimation, while trajectory plotting is made by combining direction and speed of
movement. Retinal ganglion cell-like computational elements are randomly distributed
thorough the input image, being direction-selective, allowing lateral interactions among
them to correct peep-hole effects in movement analysis, presenting a variable degree of
overlapping of their receptive fields (RF). We show results and errors of the working
system when all parameters of cells are varied. One unexpected characteristic is that
of the degradation of results in trajectory estimation when the size of receptive fields
or the number of receptive fields, i.e. of computing cells, increase. In order to get good
results for a variety of moving object speeds we have to reach a compromise between
size and number of cells. This effect has interesting implications when translated
back to the biological system which originally inspired the design of the computational
method and could be used as a rationale to explain the distribution, morphological
characteristics and number of movement detecting neurons.
View full abstract
-
Markus Schwaninger
2006 Volume 64 Issue 2 Pages
405-420
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
The purpose of this contribution is to give an overview of the origins and
further developments of Organizational Cybernetics, its transdisciplinary nature and
its links to different areas of science, i.e., both natural sciences and the humanities
View full abstract
-
Amelia G. Nobile, Enrica Pirozzi, Luigi M. Ricciardi
2006 Volume 64 Issue 2 Pages
421-442
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
The first-passage time problem through two time-dependent boundaries
for one-dimensional Gauss-Markov processes is considered, both for fixed and for random
initial states. The first passage time probability density functions are proved to
satisfy a system of continuous-kernel integral equations that can be numerically solved
by an accurate and computationally simple algorithm. A condition on the boundaries
of the process is given such that this system reduces to a single non-singular integral
equation. Closed-form results are also obtained for classes of double boundaries
that are intimately related to certain symmetry properties of the considered processes.
Finally, the double-sided problem is considered.
View full abstract
-
Frank Hoppensteadt, Kevin Lin
2006 Volume 64 Issue 2 Pages
443-448
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
A brain can perform pattern recognition tasks that are not yet possible for
an electronic computer. We continue here our investigation of electronic circuits that
are inspired by knowledge of structures in a brain. These circuits are oscillators that
are motivated by principles of neuroscience, but yet are constructible as micro circuits,
and possibly as nano-circuits. Populations of such oscillators can exhibit patterns
in their output frequencies. This may be in response to an external signal being
applied across the population or in response to internal waves that propagate through
the population. We have investigated the former phenomenon where coalitions of
oscillators, classified by their output frequency, form in response to a common driving
signal. The resulting patterns have been used to characterize the input signal and
they serve as a basis for comparison of signals and other pattern recognition tasks.
In this paper, we investigate pattern formation that results from the propagation of
synchronized activity waves within the population of oscillators. The novelty here is
in the model: We derive a nonlinear wave equation to describe networks of oscillators,
and simulate solutions to demonstrate some basic results.
View full abstract
-
Antonio Di Crescenzo, Elvira Di Nardo, Luigi M. Ricciardi
2006 Volume 64 Issue 2 Pages
449-460
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
We consider the first-crossing-time problem through a constant boundary
for a Wiener process perturbed by random jumps driven by a counting process. On the
base of a sample-path analysis of the jump-diffusion process we obtain explicit lower
bounds for the first-crossing-time density and for the first-crossing-time distribution
function. In the case of the distribution function, the bound is improved by use of
processes comparison based on the usual stochastic order. The special case of constant
jumps driven by a Poisson process is thoroughly discussed.
View full abstract
-
Settimo Termini
2006 Volume 64 Issue 2 Pages
461-468
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
In the present paper a few aspects of the historical development of Cybernetics
will be discussed. The aim is to show that by examining the epistemological
problems behind these aspects of its development, we can acquire some useful tools for
a better understanding of the current state of some of the theories and disciplines, related
to information processing, which evolved out of that explosion of innovative ideas
and which in the 1950s, combined and gave rise to the birth of novel and interesting
paths of investigation.
View full abstract
-
Mahruy Saidalieva
2006 Volume 64 Issue 2 Pages
469-478
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
The age model of cellular communities is considered. Delay-differential
equations and their model systems for cellular communities are constructed and quantitatively
analyzed. It is determined that there are the following states: rest, stationary
state, Poincar´e type limit cycles, dynamic chaos and “black hole” effect. Regularities
for the origin of dynamic chaos, “r-windows” regions and prediction problems for the
determination of destructive changes - “black hole” effect, are investigated. The results
of the developed approaches are applied to the quantitative analysis of cellular
communities and the delay-differential equations of animal and plant organisms are
considered.
View full abstract
-
Paola Tardelli
2006 Volume 64 Issue 2 Pages
479-496
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
A model is given for the evolution of a heterogeneous population of identical
living particles, divided into different classes. The model is dynamic, since the
partition of the population changes as the time goes on. The aim of this paper is to
determine the law of the lifetime of each particle given the number of dead particles up
to time t. This program is achieved by introducing the occupancy numbers, which are
defined as the cardinality of each class. Assuming that the partition is non-observable,
a filtering problem arises and the observation coincides with the cardinality of the class
of dead particles. A discussion is performed about discrete time approximations of the
filter.
View full abstract
-
Bahrom Hidirov
2006 Volume 64 Issue 2 Pages
497-504
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
Using a regulatorika (functioning of regulatory mechanisms) methodology
for dynamical systems, the equations for studying living systems based on the
functional-differential, functional and discrete equations have been developed. From
results of the qualitative analysis of model systems for equations follows, that the
functional state can have a varied nature: stable state, stable limit cycle, deterministic
chaos and break-down of solutions to the trivial attractor (“black hole” effect). It is
shown that there are only seven stable systems, which are in the balance with an external
medium. Control problems for regulatorika systems in areas of dynamical chaos
and “black hole” effect are considered.
View full abstract
-
Shiro Usui
2006 Volume 64 Issue 2 Pages
505-507
Published: 2006
Released on J-STAGE: October 28, 2022
JOURNAL
FREE ACCESS
We provide a brief overview of Lawrence Stark’s fundamental contributions
to Biomedical Engineering.
View full abstract