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1.
Robert Rosen 《Bulletin of mathematical biology》1964,26(3):239-246
It was previously shown that the abstract biological systems called. (ℳ, ℛ)-systems could be regarded formally as sequential
machines, and that when this was done, the reversibility of environmentally induced structural changes in these systems was
closely related to the strong connectedness of the corresponding machines. In the present work it is shown that the sequential
machines arising in this way are characterized by the property that the size of the input alphabet is very small compared
with the size of the set of states of the machine. It is further shown that machines with this property almost always fail
to be strongly connected. Therefore, it follows that one of the following alternatives holds: either most environmentally
induced structural alterations are not environmentally reversible, or else many mappings in the category from which the (ℳ,
ℛ)-systems are formed must not be physically realizable. 相似文献
2.
Michael Abib 《Bulletin of mathematical biology》1966,28(4):511-517
We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent
states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously
exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding
to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper
presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material
to relational biology. 相似文献
3.
Robert Rosen 《Bulletin of mathematical biology》1965,27(1):11-14
The present note consists of two separate but related parts. In the first, a new graphtheoretic proof is presented that an
(ℳ,R)-system must always contain a nonreestablishable component. The second considers some questions concerning the relation between
re-establishability and the time-lag structure in (ℳ,R)-systems. It is supposed that the reader is familiar with the terminology of the author's previous work on (ℳ,R)-systems, particularly R. Rosen,Bull. Math. Biophysics,20, 245–260, 1958. 相似文献
4.
Lloyd A. Demetrius 《Bulletin of mathematical biology》1966,28(2):153-160
Rosen’s identification of abstract biological systems, called (M,R)-systems, with sequential machines is formally characterized. It is then shown that the determination of environmental alterations
of (M,R)-systems from a knowledge of the response sequence and the structure of the system, which we call behavioral reversibility,
can be interpreted as information-losslessness of sequential machines. Applying this relationship, necessary conditions for
behavioral reversibility are derived. It is further shown that, similar to Rosen’s work on structural reversibility, (M,R)-systems are behaviorally reversible only if the number of physically realizable mappings are restricted. 相似文献
5.
I. Băianu 《Bulletin of mathematical biology》1973,35(1-2):213-217
On the basis of Rosen's representation of (M, R)-systems as sequential machines (Rosen,Bull. Math. Biophys.,26, 103–111, 1964), the existence of projective limits in categories of general (M, R)-systems is proved. 相似文献
6.
B. L. Foster 《Bulletin of mathematical biology》1966,28(3):371-374
It is shown that any (ℳ ℛ) has some component which cannot be re-established after it has been inhibited. If there is only
one such component, it must be central, that is, its inhibition stops the whole system. These results hold even when it is
not assumed that ℳ is connected. 相似文献
7.
N. Rashevsky 《Bulletin of mathematical biology》1960,22(1):73-84
The principle of biotopological mapping (Rashevsky, 1954,Bull. Math. Biophysics,16, 317–48) is given a generalized formulation, as the principle of relational epimorphism in biology. The connection between
this principle and Robert Rosen’s representation of organisms by means of categories (1958,Bull. Math. Biophysics,20, 317–41) is studied. Rosen’s theory of (M,R)-systems, (1958,Bull. Math. Biophysics,20, 245–60) is generalized by dropping the assumption that only terminalM
i
components are sending inputs into theR
i
components. It is shown that, if the primordial organism is an (M,R)-system, then the higher organisms, obtained by a construction well discussed previously (1958,Bull. Math. Biophysics,20, 71–93), are also (M,R)-systems. Several theorems about such derived (M,R)-systems are demonstrated.
It is shown that Rosen’s concept of an organism as a set of mappings throws light on phenomena of synesthesia and also leads
to the conclusion that Gestalt phenomena must occur not only in the fields of visual and auditory perception but in perceptions
of any modality. 相似文献
8.
Miranda I. Teboh-Ewungkem Chandra N. Podder Abba B. Gumel 《Bulletin of mathematical biology》2010,72(1):63-93
A mathematical model is developed to assess the role of gametocytes (the infectious sexual stage of the malaria parasite)
in malaria transmission dynamics in a community. The model is rigorously analysed to gain insights into its dynamical features.
It is shown that, in the absence of disease-induced mortality, the model has a globally-asymptotically stable disease-free
equilibrium whenever a certain epidemiological threshold, known as the basic reproduction number (denoted by ℛ0), is less than unity. Further, it has a unique endemic equilibrium if ℛ0>1. The model is extended to incorporate an imperfect vaccine with some assumed therapeutic characteristics. Theoretical analyses
of the model with vaccination show that an imperfect malaria vaccine could have negative or positive impact (in reducing disease
burden) depending on whether or not a certain threshold (denoted by ∇) is less than unity. Numerical simulations of the vaccination model show that such an imperfect anti-malaria vaccine (with
a modest efficacy and coverage rate) can lead to effective disease control if the reproduction threshold (denoted by ℛvac) of the disease is reasonably small. On the other hand, the disease cannot be effectively controlled using such a vaccine
if ℛvac is high. Finally, it is shown that the average number of days spent in the class of infectious individuals with higher level
of gametocyte is critically important to the malaria burden in the community. 相似文献
9.
Robert Rosen 《Bulletin of mathematical biology》1966,28(2):149-151
The condition which allows the existence of induced replication maps in (M,R)-systems is shown to place strong restrictions on the “richness” of the category from which these systems can be constructed.
This condition also admits of a simple biological interpretation, which can be checked empirically, and which may offer insight
into the physical and biological realizations of these abstract systems. 相似文献
10.
We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment.
Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number
ℛ0 or of the initial fraction of infected people. Moreover, large epidemics can happen even if ℛ0<1. But like in a constant environment, the final epidemic size tends to 0 when ℛ0<1 and the initial fraction of infected people tends to 0. When ℛ0>1, the final epidemic size is bigger than the fraction 1−1/ℛ0 of the initially nonimmune population. In summary, the basic reproduction number ℛ0 keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical
results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or
air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality. 相似文献
11.
Robert Rosen 《Bulletin of mathematical biology》1962,24(1):31-38
It is shown that the class of abstract block diagrams of (M, ℜ)-systems which can be constructed out of the objects and mappings of a particular subcategoryG
0 of the categoryG of all sets depends heavily on the structure ofG
0, and in particular on the number of sets of mappingsH(A, B) which are empty inG
0. In the context ofG
0-systems, there-fore, each particular categoryG
0 gives rise to a different “abstract biology” in the sense of Rashevsky. A number of theorems illustrating the relation between
the structure of a categoryG
0 and the embeddability of an arbitrary mapping αεG
0 into an (M, ℜ)-system are proved, and their biological implication is discussed.
This research was supported by the United States Air Force through the Air Force Office of Scientific Reserch of the Air Research
and Development Command, under Contract No. AF 49(638)-917. 相似文献
12.
Robert Rosen 《Bulletin of mathematical biology》1963,25(1):41-50
The environmentally induced alterations in structure of (M, ℜ) which were described previously (R. Rosen,Bull. Math. Biophysics,23, 165–171, 1961) are examined from the standpoint of determining under what circumstances they can be reversed by further
environmental interactions. For simplicity we consider only the case of (M, ℜ)-systems possessing one “metabolic” and one “genetic” component. In the case of environmentally induced alteration of
the “metabolic” component alone, a necessary and sufficient condition is given for the reversibility of the alteration. In
the case of alteration of the “genetic” component, the situation becomes more complex; several partial results are given,
but a full analysis is not available at this time. Some possible biological implications of this analysis are discussed.
This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air
Research and Development Command, under Contract no. AF-49(638)-917 and Grant no. AF-AFOSR-9-63. 相似文献
13.
N. Rashevsky 《Bulletin of mathematical biology》1971,33(4):555-559
In combining the author's theories of organismic sets (Rashevsky,Bull. Math. Biophysics,31, 159–198, 1969a) and Robert Rosen's theory of (M, R)-systems (Bull. Math. Biophysics,20, 245–265, 1958), a conclusion is reached that the number of either normal or pathological phenomena in organismic sets may
occur. Those phenomena are characterized by occurring spontaneously once in a while but are not exactly periodic. Some epilepsies
are an example of such pathological phenomena in the brain. 相似文献
14.
Robert Rosen 《Bulletin of mathematical biology》1959,21(2):109-128
The general Theory of Categories is applied to the study of the (M, R)-systems previously defined. A set of axioms is provided which characterize “abstract (M, R)-systems”, defined in terms of the Theory of Categories. It is shown that the replication of the repair components of these
systems may be accounted for in a natural way within this framework, thereby obviating the need for anad hoc postulation of a replication mechanism.
A time-lag structure is introduced into these abstract (M, R)-systems. In order to apply this structure to a discussion of the “morphology” of these systems, it is necessary to make
certain assumptions which relate the morphology to the time lags. By so doing, a system of abstract biology is in effect constructed.
In particular, a formulation of a general Principle of Optimal Design is proposed for these systems. It is shown under what
conditions the repair mechanism of the system will be localized into a spherical region, suggestive of the nuclear arrangements
in cells. The possibility of placing an abstract (M, R)-system into optimal form in more than one way is then investigated, and a necessary and sufficient condition for this occurrence
is obtained. Some further implications of the above assumptions are then discussed. 相似文献
15.
M. W. Warner 《Bulletin of mathematical biology》1982,44(5):661-668
Arbib in a paper entitled ‘Categories of (M, R)-Systems' represents both simple (M, R)-systems and those with varying genome
as subcategories of the category of automata. An alternative characterisation of general (M, R)-systems as automata is proposed
and two theorems on (M, R)-automata are proved. The two categories of automata, namely Arbib in a paper entilled ‘Categories
of (M,R)-Systems’ represents both simple (M, R)-systems with variable genetic structure, are compared. 相似文献
16.
Ion C. Baianu 《Bulletin of mathematical biology》1980,42(3):431-446
The mathematical structures underlying the theories of organismic sets, (M, R)-systems and molecular sets are shown to be transformed naturally within the theory of categories and functors. Their natural
transformations allow the comparison of distinct entities, as well as the modelling of dynamics in “organismic” structures. 相似文献
17.
Nicolas Bacaër 《Bulletin of mathematical biology》2009,71(7):1781-1792
This article considers three different aspects of periodic matrix population models. First, a formula for the sensitivity
analysis of the growth rate λ is obtained that is simpler than the one obtained by Caswell and Trevisan. Secondly, the formula for the basic reproduction
number ℛ0 in a constant environment is generalized to the case of a periodic environment. Some inequalities between λ and ℛ0 proved by Cushing and Zhou are also generalized to the periodic case. Finally, we add some remarks on Demetrius’ notion of
evolutionary entropy H and its relationship to the growth rate λ in the periodic case. 相似文献
18.
Robert Rosen 《Bulletin of mathematical biology》1966,28(2):141-148
Using the relationship between (M,R) and sequential machines developed in previous work, it is shown that the totality of (M,R) which can be formed over a given categoryA itself forms a category in a natural fashion. 相似文献
19.
Vaccination and antiviral treatment are two important prevention and control measures for the spread of influenza. However,
the benefit of antiviral use can be compromised if drug-resistant strains arise. In this paper, we develop a mathematical
model to explore the impact of vaccination and antiviral treatment on the transmission dynamics of influenza. The model includes
both drug-sensitive and resistant strains. Analytical results of the model show that the quantities ℛ
SC
and ℛ
RC
, which represent the control reproduction numbers of the sensitive and resistant strains, respectively, provide threshold
conditions that determine the competitive outcomes of the two strains. These threshold conditions can be used to gain important
insights into the effect of vaccination and treatment on the prevention and control of influenza. Numerical simulations are
also conducted to confirm and extend the analytic results. The findings imply that higher levels of treatment may lead to
an increase of epidemic size, and the extent to which this occurs depends on other factors such as the rates of vaccination
and resistance development. This suggests that antiviral treatment should be implemented appropriately. 相似文献
20.
Robert Rosen 《Bulletin of mathematical biology》1961,23(2):165-171
It is shown that a wide variety of structural alterations in both the “metabolic” and “genetic” apparatus of (
, ℜ)-systems can result from specific changes in the environment of such systems. A number of specific examples are investigated
in order to demonstrate the scope of these alterations. Certain biological applications of this discussion are suggested,
including a suggestion for a possible interpretation of the mitotic cycle.
This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air
Research and Development Command, under Contract #AF 49 (638)-917. 相似文献