Outline of a mathematical approach to the cancer problem

The fact that the growth of every organism, as it develops through cell multiplication from the ovum, eventually ceases, makes plausible the hypothesis that each cell of an organism exerts some kind of inhibitory influence upon the growth and multiplication of every other cell through the medium of some factorj. Each cell, however, is considered to possess an amount of a “growth factor”g, the activity of which is inhibited byj. In the course of development, most cells differentiate. A number of them remains relatively undifferentiated, and those are used for repairs of natural tear and wear as well as for healing of wounds. With age either the number of those cells or their “potency” decreases, which accounts for a general decrease in the speed of wound healing. Due to statistical fluctuations, the amount of theg is not uniformly distributed amongst the cells. Some of them have accidentally a greater amount than others. As the number or potency of the undifferentiated cells decreases with age, so does their inhibitory influence upon other cells. Therefore, those cells which do have an accidental dental excess ofg-factor will begin to grow and multiply, producing neoplasms. Putting the above assumptions into mathematical form, it is possible to derive a relation which gives theprobability of cancer incidence as a function of age. The theoretical relation is compared to the rather inadequate empirical data and found in agreement with them. A relation for the speed of wound healing as a function of age is also derived, and also found in general agreement with the rather scant data. Several other conclusions are discussed and possibilities of their practical applications pointed out.     

Relative amounts of sialic acid and fucose of amniotic fluid glycoconjugates in relation to pregnancy age

The present knowledge concerning the glycan structures and role of glycoconjugates derived from amniotic fluid is fragmentary and mainly focuses on the individual glycoproteins. The question has arisen as whether the general glycosylation pattern of amniotic fluid glycoconjugates can change with the progression of a normal pregnancy. In the present work we have described the dynamic, quantitative alterations in relative amounts of sialic acid and fucose linked by a variety of anomeric linkages to subterminal oligosaccharide structures of amniotic fluid glycoconjugates in relation to pregnancy age. The analysis was performed in the following groups of amniotic fluids derived from normal pregnancy by lectin dotting method: “2nd trimester” (14–19 weeks), “3rd trimester” (29–37 weeks), “perinatal period” (38–40 weeks) , “delivery at term” (39–41 weeks) and “post date pregnancy” (41–43 weeks). In the “3rd trimester” the amniotic fluid glycoconjugates contained higher relative amounts of glycans terminated by α2-6-linked sialic acid (p < 0.00002) and by α1-6 innermost fucose (p < 0.000001) than those in the 2nd trimester. In contrast, they showed the lower relative amount of fucose linked α1-3 (p < 0.02). At the perinatal period the relative amount of α2-6-linked sialic acid increased (p < 0.03), and it then decreased during delivery (p < 0.02) to the level found in the “3rd trimester” group. In the post date pregnancy all parameters studied increased. The sialyl- and fucosyl-glycotopes of the amniotic fluid glycoconjugates may play an critical role in growth and tissue remodeling of the foetus, as well as may might reflect maturation of a foetus. Additionally, a determination of the glycotope expressions might be helpful in prenatal diagnosis as predictor factors for well being of mother and child.     

Physics,biology, and sociology: A reappraisal

To the extent that all biological phenomena are perceivable only through their physical manifestations, it may be justified to assume that all biological phenomena will be eventually represented in terms of physics; perhaps not of present day physics, but of some “extended” form of it. However, even if this should be correct, it must be kept in mind that representing individual biological phenomena in terms of physics is not the same as deducing from known physical laws the necessity of biological phenomena. Drawing an analogy from pure mathematics, it is possible that while every biological phenomenon may be represented in terms of physics, yet biological statements represent a class of “undecidable” statements within the framework of physics. Such a conjecture is reinforced by the history of physics itself and illustrated on several examples. The 19th century physicists tried in vain todeduce electromagnetic phenomena from mechanical ones. A similar situation may exist in regard to biological and social sciences. Quite generally, the possibility of representing a class B phenomena in terms of class A phenomena does not imply that the phenomena of class B can be deduced from those of class A. The consequences of the above on the relation between physics, biology, and sociology are studied. A tentative postulational formulation of basic biological principles are given and some consequences are discussed. It is pointed out that not only can the study of biological phenomena throw light on some physical phenomena, but that the study of social phenomena may be of value for the understanding of the structures and functions of living organisms. The possibility of a sort of “socionics” is indicated.     

Contribution to the mathematical theory of contagion and spread of information: I. Spread through a thoroughly mixed population

An equation is derived from the spread of a “state” by contact through a thoroughly mixed population, in which the probability of transmission depends both on the over-all duration of the process and on the time an individual has been in the “state.” Cases in which this probability is a function of only one or the other of the two “times” are worked out. It is shown that in the case of dependence on “private time” alone the asymptotic value of the fraction of the population effected is the same as that derived by the random net approach.     

Physics,biology and sociology: II. Suggestion for a synthesis

In continuation of previous studies (Bull. Math. Biophysics,28, 283–308; 655–661, 1966;29, 139–152, 1967) it is shown that the difference between the “metric” aspects of physics and the “relational” aspects of biological and social sciences disappear by accepting the broader definition of “relation”, such as that given in mathematics and logic. A conceptual superstructure then becomes possible from which all three branches of knowledge may be derived, though none of them can be derived from the others.     

Applications of matrix algebra to communication nets

A “generic” problem amenable to matrix algebraic treatment is outlined. Several examples are given and one, a communication system, is studied in some detail. A typical structure matrix is used to describe the channels of communication and a “status” matrix is used to describe the distribution of information in the system at any time. A theorem is proved relating the status matrix at any timet to thetth power of the structure matrix. The elements of the communication system are interpreted as individuals who can send messages to each other. For the individuals attempting to solve a “group problem” certain relations are derived between the structure and status matrices and time of solution. The structure of the communication system is permitted to vary with time. A general theorem is proved relating the status matrix to the matrix product of the series of structure matrices representing the changing structure of the system. Some suggestions are made for further generalizations. In particular, it is suggested that so-called “higher order” information transmission can be similarly treated.     

Correlations between the psychological peculiarities of an individual and the efficacy of a single neurofeedback session (by the EEG characteristics)

Modifications of different EEG rhythms induced by a single neurofeedback session (by the EEG characteristics) directed toward an increase in the ratio of the spectral powers (SPs) of the α vs θ oscillations were compared with the psychological characteristics of the tested subjects (the group included 30 persons). A generally accepted neurofeedback technique was used; the intensity of acoustic white noise served as the feedback signal. EEG potentials were recorded from the C3 and C4 leads. Psychological testing was carried out using Eysenck’s (EPQ), Rusalov’s (OST), and (16 PF) questionnaires. The directions of changes in the SPs of EEG frequency components were found to significantly correlate with some individuality-related peculiarities of the tested subjects. The SP of the δ rhythm correlated with the EPQ scale “neuroticism,” OST scale “social plasticity,” and 16 PF factors H (“parmia”), I (“premsia”), and Q₃ (“self-control of behavior”). The SP of the θ component demonstrated correlations with the OST scales “ergisity,” “plasticity,” and “social temp” and with 16 PF factors M (“autia”), Q₄ (“frustration”), and Q1 (“exvia”). The SP of the α rhythm correlated with 16 PF factors Q₃ (“self-control of behavior”), G (“strength of superEgo”), O (“hypothymia”), L (“protension”), and N (“shrewdness”). The SP of the β rhythm correlated with the OST scale “emotionality,” while that of the γ rhythm showed correlations with the 16 PF indices L (“protension”) and M (“autia”). Changes in the ratio of the α vs θ SPs correlated with the EPQ scale “neuroticism.” Thus, our data confirm the statement that a high individual variability of the results of a single (first in the series) neurofeedback session is to a great extent related to peculiarities of the individual psychological pattern of the subject. Neirofiziologiya/Neurophysiology, Vol. 38, No. 3, pp. 239–247, May–June, 2006.     

Mathematical biology of social behavior

When an individual grows up in a society, he learns certain behavior patterns which are “accepted” by that society. He may in general have a tendency toward behavior patterns other than those which are “accepted” by the society. This tendency toward such unaccepted behavior may be due to a process of cerebration which results in doubt as to the “correctness” of the accepted behavior. Thus, on the one hand, the individual learns to follow the accepted rules almost automatically; on the other hand, he may tend to consciously break those rules. Using a neural circuit, suggested by H. D. Landahl in his theory of learning, a neurobiophysical interpretation of the above situation is outlined. Mathematical expressions are derived which describe the social behavior of an individual as a function of his age, social status, and some neurobiophysical parameters.     

The charge state of an ion channel controls neutral polymer entry into its pore

Electrostatic potentials created by fixed or induced charges regulate many cellular phenomena including the rate of ion transport through proteinaceous ion channels. Nanometer-scale pores of these channels also play a critical role in the transport of charged and neutral macromolecules. We demonstrate here that, surprisingly, changing the charge state of a channel markedly alters the ability of nonelectrolyte polymers to enter the channel's pore. Specifically, we show that the partitioning of differently-sized linear nonelectrolyte polymers of ethylene glycol into the Staphylococcus aureus α-hemolysin channel is altered by the solution pH. Protonating some of the channel side chains decreases the characteristic polymer size (molecular weight) that can enter the pore by ∼25% but increases the ionic current by ∼15%. Thus, the “steric” and “electric” size of the channel change in opposite directions. The results suggest that effects due to polymer and channel hydration are crucial for polymer transport through such pores. Received: 16 March 1997 / Accepted: 24 April 1997     

Experimental translocation of juvenile water voles in a Scottish lowland metapopulation

Population density affects dispersal success because residents can hinder or facilitate immigration into a new site, via a “social fence effect” or “social attraction” (or “conspecific attraction”), respectively. These mechanisms can affect the dynamics of fragmented populations and the success of translocations. However, information on the settlement behaviour of dispersers is rare. We conducted a manipulative field experiment using wild water voles, which exist in metapopulations along waterways in Scotland. We translocated 17 young of dispersal age into either an occupied site or a vacant site containing good habitat, which had recently become extinct due to a feral predator (American mink) moving through. We monitored the movements of translocated voles using radio telemetry. Translocated voles were less likely to settle in occupied sites with higher densities of residents, suggesting a possible social fence effect at high density. There was evidence of a social attraction mechanism, because voles never remained at new sites unless another individual arrived soon after translocation, and they were more likely to settle in occupied or colonised sites than vacant ones. Voles remained in the transient phase of dispersal for many days, and often followed a “stepping stone” trajectory, stopping for several days at successive sites. We suggest that trajectories followed by dispersing water voles, the time scale and long dispersal distances found in this species are conducive to locating conspecifics at low density and colonising vacant habitat. These results are encouraging for prospects of metapopulation persistence and future translocation success.     

An ant’s eye view of culture: propagation of new traditions through triggering dormant behavioural patterns

We consider a previously unknown way of propagation of behavioural traditions in animal communities using hunting in ants as an example. We experimentally revealed that common litter dwelling ants Myrmica rubra effectively hunt jumping prey and the way the hunting behavioural pattern is distributed within ant colonies is rather sophisticated. Comparison of our results with those obtained on vertebrates enables us to suggest that “distributed social learning” plays an important role in spreading new traditions in animal communities: initial performances by a few carriers of an “at once and entirely” available behavioural pattern propagate this pattern among specimens which have only dormant “sketches” of it. Spread of these behaviours in populations is based on relatively simple forms of social learning such as social facilitation which underlies species’ predisposition to learn certain sequences of behavioural acts. To be triggered, carriers of dormant “sketches” of a relevant behavioural pattern should encounter performances of this pattern with sufficient frequency. We call this strategy triggering of dormant behavioural patterns. Integration of behaviour thus takes place not only at the individual level but at the population level as well.     

Contribution to the mathematical theory of mass behavior: I. The propagation of single acts

The propagation of a single act in a large population is supposed to depend on some external circumstance and on an “imitation component”, where encounters with individuals who are performing or have already performed the act contribute to the tendency of an individual to perform it. The “tendency” to perform is supposed to be measured by the average frequency of stimuli, randomly distributed in time, impinging on the individual. The deduced equation is a relation between the fraction of the population who have performed the act and time, provided the time course of the “external circumstance” and the way in which the imitation component contributes are known. Several special cases are studied, in particular, cases without the imitation component, cases with imitation only, and various mixed cases. Examples are given of social situations in which such factors may operate and general suggestions are made for the systematization of observations and/or experiments to test the assumptions of the theory.     

Defining and explaining culture (comments on Richerson and Boyd, Not by genes alone)

We argue that there is a continuum of cases without any demarcation between more individual and more cultural information, and that therefore “culture” should be viewed as a property that human mental representations and practices exhibit to a varying degree rather than as a type or a subclass of these representations and practices (or of “information”). We discuss the relative role of preservative and constructive processes in transmission. We suggest a revision of Richerson and Boyd’s classification of the forces of cultural evloution.     

Rank and age related feeding strategy observed through field experiments in the Koshima group of Japanese macaques

The feeding process of Japanese monkeys on soy beans which were scattered over a sandy beach on Koshima islet was studied. Younger monkeys were able to pick up more beans when 8 kg of beans were divided and given two times (“two times feeding”) than when the whole amount (8 kg) of beans was given at one time (“one time feeding”). The effect of saturation of the food intake capacity in younger monkeys at the first feeding in “two times feeding” did not appear at the second feeding one hour later. The minutely intake of soy beans (feeding speed) for each age class was analyzed. The decline of feeding speed in adult females after the peak in “one time feeding” was not related to the decline in density of beans on the ground, and this decline was caused by saturation of their food intake capacity. Adult females were divided into four classes according to their dominance rank order: high, lower-high, higher-low, and low classes. The total amount of intake in “one time feeding” was far larger in the high class than in any of the other classes. The total amount of feeding in the first feeding of “two times feeding” increased in accordance with rise in the dominance rank class, and there was no relation to rank and total feeding amount in the second feeding of “two times feeding.” Differences existed in the process of feeding between the rank classes. The feeding speed of the low class was as high as that of the high class on the curve of minutely intake, while the low class stopped feeding much earlier than the high class. The lower-high class displayed a low feeding speed, and stopped feeding the latest. The order of the duration to stay and to feed in the feeding area was lower-high > high > higher-low > low, and this order did not change under the three different feeding conditions, “one time feeding,” and the first and second feedings of “two times feeding.” Adolescent females tended to stay the longest duration in the feeding area among all age classes. Both the lower-high class females and adolescent females had an unstable social status in the Koshima group, and their social status affected their feeding behaviors. The feeding behaviors were similar in attitude depending on social status, and are considered to be maintained for a fairly long time. The feeding strategy of the lower-high class, in staying a longer duration in the artificial feeding area, and departing later, may be effective under the artificial feeding conditions, but it may be a bad strategy in a natural habitat where the food is not so clumped as in artificial feeding, and where choice of other food patches is possible. The above results agree well with previous reports for the Koshima group, indicating that the rank of the lower-high class females was unstable (Mori et al., 1989), and that their reproductive success was low (Watanabe et al., 1992).     

Social influence in manipulations of a capuchin monkey raised in a human environment: A preliminary case study

This preliminary study reports manipulations in an 8-month infant capuchin monkey,Cebus apella, confronted with a variety of objects, during five 2-hour sessions. This subject is raised in a human environment as it participates to the “Aide Simienne aux Personnes Handicapées (Kerpape)” project. Objects have been chosen in order to expose the capuchin to manipulations it will be asked to perform when placed with a quadriplegic. This paper reports the analysis of five hours of video recording. During two sub-sessions within an experimental session, the “human mother” pointed the objects to the monkey, sequentially, either with a vocal designation or not. The results show that the monkey tends to contact more objects and manipulates them more when they have been previously designated by the “mother.” This suggests a form of social facilitation. There is no evidence for imitation.     

On the spread of information with time and distance

The transmission of some information or behavior pattern is treated as a flow of “particles” which execute random motions over a population of individuals and which may multiply or disappear. Equations are derived for the number density of these “particles” and from this is calculated the number of individuals through which the “particles” have passed. The results are applied to a number of situations such as 1) uniform spatial distribution with multiplication factor decreasing with time because of loss of interest or confusion of the information, 2) multiplication factor constant but the rate of spreal decreasing with multiple hearings, 3) one-dimensional region with a small starting region with or without an absorbing barrier 4) two-dimensional region with absorbing barrier, 5) continous sources of information within a small region in one dimension, 6) uniform spatial distribution in which individuals do not respond to more than one hearing.     

Biosemiosis and the Cellular Basis of Mind

The human brain is a complex organ made up of neurons and several other cell types, and whose role is processing information for use in elicitation of behaviors. To accomplish this, the brain requires large amounts of energy, and this energy is obtained by the oxidation of glucose (Glc). However, the question of how the oxidation of Glc by individual neurons in brain results in their collective ability to rapidly generate feats of cognition that allow them to recognize the nature of the universe in which they live and to communicate this information remains unclear. In this article, insights into this process are provided by first considering the brain’ s homeostatic “operating system” for supply of energy to stimulated neurons, and how this system defines the basic unit of brain “structure”. This is followed by consideration of the brain’s “two-cell” neuronal communication mechanism which defines the basic unit of brain “function”. Finally, an analysis of the nature of frequency-encoded “neuronal languages” that enable ensembles of neurons to translate energy derived from the oxidation of Glc into a collective “mind”, the aggregate of all brain processes including those involving perception, thought, insight, foresight, imagination and behavior.     

Gender Victims and Cultural Borders: The Globalization of Prostitution in Italy

In this article I will try to analyse the transformation regarding the italian regulation of prostitution on the grounds of another issue, that is the building up of cultural borders for the definition of “national” and “european” gender identities. The creation of cultural borders allows to outline the differentiation traits between social groups, while escaping plurality and internal contradictions which on the other hand could only show continuity and vicinity traits. In my point of view, the italian current debate on prostitution is a discoursive process that produces a “western” pattern of relation between men and women, while referring internal tensions and contradictions to other cultures. The following analysis will use data and information coming from national official statistics on immigration, estimates on prostitutions and findings from national researchers on prostitution carried out by the research group called “Migration & Prostitutions” based at the Department of Sociology of the Padua University.     

Information-theoretic analysis of de-efferented single muscle spindles

 The information transmission properties of single, de-efferented primary muscle-spindle afferents from the hind limb of the cat were investigated. The gastrocnemius medialis muscle was stretched randomly while recording spike trains from several muscle-spindle afferents in the dorsal root. Two classes of input stimuli were used: (i) Gaussian noise with band-limited flat spectrum, and (ii) Gaussian noise with a more “naturalistic” 1/f ⁿ spectrum. The “reconstruction” method was used to calculate a lower bound to the information rate (in bits per second) between the muscle spindles and the spinal cord. Results show that in response to the flat-spectrum input, primary muscle-spindle afferents transfer information mainly about high frequencies, carrying 2.12 bits/spike. In response to naturalistic-spectrum inputs, primary muscle-spindle afferents transfer information about both low and high frequencies, with “spiking efficiency” increasing to 2.67 bits/spike. A simple muscle-spindle simulation model was analyzed with the same method, emphasizing the important part played by the intrafusal fiber mechanical properties in information transmission. Received: 22 January 2002 / Accepted in revised form: 17 June 2002 Correspondence to: Y. Tock (e-mail: ytock@tx.technion.ac.il, Fax: +972-4-8323041)     

The steady state kinetics of some biological systems: III. Thermodynamic aspects

Some thermodynamic aspects of steady systems are considered. The time rates of changes, “flux”, of various thermodynamic quantities are formulated. In particular the free energy flux in the steady state, the difference between the free energy flux in the steady and time dependent states and the change in free energy flux upon transition between steady states are discussed. Equations are derived which exhibit the formal similarities and differences between the free energy flux and the conventional free energy change. The temperature dependence of the steady state rate is examined and conditions for “mastery” by a single step discussed. A brief discussion of the role ofrate in the coupling of exergonic and endergonic reactions is given.