62 research outputs found
On the Mathematical Modelling of Microbial Growth: Some Computational Aspects
We propose a new approach to the mathematical modelling of
microbial growth. Our approach differs from familiar Monod type models by
considering two phases in the physiological states of the microorganisms and
makes use of basic relations from enzyme kinetics. Such an approach may
be useful in the modelling and control of biotechnological processes, where
microorganisms are used for various biodegradation purposes and are often
put under extreme inhibitory conditions. Some computational experiments
are performed in support of our modelling approach.* The author was partially supported by the Bulgarian NSF Project DO 02-359/2008
On the Arithmetic of Errors
An approximate number is an ordered pair consisting of a (real)
number and an error bound, briefly error, which is a (real) non-negative
number. To compute with approximate numbers the arithmetic operations
on errors should be well-known. To model computations with errors one
should suitably define and study arithmetic operations and order relations
over the set of non-negative numbers. In this work we discuss the algebraic
properties of non-negative numbers starting from familiar properties of real
numbers. We focus on certain operations of errors which seem not to have
been sufficiently studied algebraically. In this work we restrict ourselves to
arithmetic operations for errors related to addition and multiplication by
scalars. We pay special attention to subtractability-like properties of errors
and the induced “distance-like” operation. This operation is implicitly used
under different names in several contemporary fields of applied mathematics
(inner subtraction and inner addition in interval analysis, generalized
Hukuhara difference in fuzzy set theory, etc.) Here we present some new
results related to algebraic properties of this operation.* The first author was partially supported by the Bulgarian NSF Project DO 02-359/2008
and NATO project ICS.EAP.CLG 983334
Towards an Axiomatization of Interval Arithmetic
In this paper intervals are viewed as approximate real numbers. A revised formula for interval multiplication of generalized intervals is given. This formula will be useful for further axiomatization of interval arithmetic and relevant implementations within computer algebra systems. Relations between multiplication of numbers and multiplication of errors are discussed
Analysis of Biochemical Mechanisms using Mathematica with Applications
Biochemical mechanisms with mass action kinetics are usually modeled as
systems of ordinary differential equations (ODE) or bipartite graphs.
We present a software module for the numerical analysis of ODE models of
biochemical mechanisms of chemical species and elementary reactions
(BMCSER) within the programming environment of CAS Mathematica.
The module BMCSER also visualizes the bipartite graph of biochemical
mechanisms. Numerical examples, including a double phosphorylation model,
are presented demonstrating the scientific applications and the visualization
properties of the module.
ACM Computing Classification System (1998): G.4
From the Guest-Editor
The BIOMATH 2012 International Conference on Mathematical Methods and Models in Biosciences was held at the Bulgarian Academy of Sciences in Sofia, in June 17-22, 2012, http://www.biomath.bg/2012/. We were happy to meet more than 70 participants from twenty different countries. More than 40 contributions were submitted for publication in the present BIOMATH proceedings. All submitted papers have been peer-reviewed by at least two independent anonymous reviewers. Twelve selected papers are published in the first issue of this journal. This second issue contains another ten selected contributions which will be published continuously in the electronic version of the journal. . .
From the Guest Editor
The BIOMATH 2012 International Conference on Mathematical Methods and Models in Biosciences was held at the Academy of Sciences in Sofia, Bulgaria, in June 17–22, 2012, http://www.biomath.bg/2012/. We were happy to meet more than 70 participants from twenty different countries. More than 40 contributions were submitted for publication in the present BIOMATH proceedings
Cell Growth Models Using Reaction Schemes: Batch Cultivation
Simple structured mathematical models of bacterial cell growth are proposed. The models involve fractions of bacterial cells related to their physiological phases. Reaction schemes involving the biomass of the cell fractions, the substrate and the product are proposed in analogy to reaction schemes in enzyme kinetics. Applying the mass action law these reaction schemes lead to dynamical models represented by systems of ODE's. All parameters of the models are rate constants with clear biological or biochemical meaning. The proposed models generalize classical bacterial growth models and offer more flexible tools for modelling and control of biotechnological processes. In this paper the study is focused on batch cultivation models
Reaction networks reveal new links between Gompertz and Verhulst growth functions
New reaction network realizations of the Gompertz and logistic growth models are proposed. The proposed reaction networks involve an additional species interpreted as environmental resource. Some natural generalizations and modifications of the Gompertz and the logistic models, induced by the proposed networks, are formulated and discussed. In particular, it is shown that the induced dynamical systems can be reduced to one dimensional differential equations for the growth (resp. decay) species. The reaction network formulation of the proposed models suggest hints for the intrinsic mechanism of the modeled growth process and can be used for analyzing evolutionary measured data when testing various appropriate models, especially when studying growth processes in life sciences
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