Some remarks on the mathematical bio-sociology of the relativity of injustice

The author's theory of the adoption of certain types of behavior patterns (Rashevsky, N., 1957, “Contributions to the Theory Initiative Behavior”.Bull. Maths. Biophysics,19, 91–119; 1968,Looking at History through Mathematics, Cambridge, Massachusetts: M.I.T. Press) consisting of elementary behaviors for each of which there is an opposite one and the two are mutually exclusive, is applied to describe the changes in the general type of behavior of a society. The elementary acts of which the whole problem consists may be either overt activities or beliefs or opinions. The general behavior patternsadopted by the society are considered as the “proper” or “just” ones. Any deviation from it in either one or more of the component elementary behaviors is considered as “unjust” and is subject to some punitive action. The total number of possible mutually exclusive behavior patterns is very large but finite. Within this very large range of possible patterns, we find that this notion of justice is relative, because changes from any behavior pattern to any other may occur. It is further shown that the amount of punishment for the deviation from the accepted pattern in order to be effective as well as efficient must be applied in different ways to different individuals even for the same transgression.     

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.     

Automobile driving as psychophysical discrimination

The driver tries to keep the car in the center of the lane. If the car is too near the left edge, this causes the driver to make a “corrective” right turn. If the car is near the right edge, a “corrective” left turn is made. Therefore, a quantity which decreases with increasing distance Δ _L from the left edge may be considered as a stimulusS _R producing the reactionR _R of turning to the right. A similar situation holds for the distance Δ _R from the right edge. When the car is in the center of the lane, Δ _L = Δ _R andS _R =S _L , the stimuli are equal. We thus have here a situation analogous to the one studied by H. D. Landahl in his theory of psychophysical discrimination. In general a reactionR _R (resp.R _L ) will occur only ifR _R −R _L ≥h ^* (resp.R _L −R _R ≥h ^*) whereh ^* is a threshold. Applying Landahl’s theory to this situation, we find thath ^* determines the distance from the edge, at which a corrective turn is made. This distance is not constant, but a function of the speedv of the car. The requirement that a corrective turn should be madebeforre the car runs off the road leads to an expression for the maximum safe speed. Because of the transcendency of the equations involved, closed solutions cannot be obtained. It is, however, shown that the expression for maximum safe speed, given in a previous paper (Bull. Math. Biophysics,21, 299–308, 1959), is a rough first approximation to the expressions found now.     

Salt tolerance in Lycopersicon species VI. Genotype-by-salinity interaction in quantitative trait loci detection: constitutive and response QTLs

 A study of genotype-by-salinity interaction was carried out to compare the behavior of quantitative trait loci (QTLs) in two F₂ populations derived from crosses between the cherry tomato, Lycopersicon esculentum Mill. var. cerasiforme, and two wild relatives Lycopersicon pimpinellifolium (Jusl.) Mill. and Lycopersicon chesmannii f. minor (Hook. f.) Mull., grown at two environmental conditions (optimum and high salinity). QTLs for earliness and fruit yield could be classified into four groups: “response-sensitive”, those detected only under control conditions or whose contribution significantly decreased in salinity; “response-tolerant”, detected only in salinity or in which the direction of their additive effects changed; “constitutive”, detected in both growing conditions; and “altered” QTLs, those where the degree of dominance changed according to the presence or absence of salt. Epistatic interactions were also influenced by the salt treatment. This differential allele effect at some (non-constitutive) QTLs induced by salt stress will make selection under an “optimum environment” unfruitful for the “response-tolerant” QTLs. Similarly, selection under salinity will ignore “response-sensitive” QTLs. Given that salinity is highly variable in the field, marker-assisted selection should take into account not only the “response-tolerant” but also the “response-sensitive” QTLs although there might be cases where selection in some QTLs for both conditions is not feasible. Comparing both populations, very few QTLs showed the same behavior. Received: 5 August 1996 / Accepted: 25 October 1996     

Voiceprint identification and its application to sociological studies of wild Japanese monkeys (Macaca fuscata yakui)

Japanese monkeys often exchange the particular vocal sound, “coo,” especially when they feed or move as a group. It was considered that the “coo” sound had no positive social meaning, perhaps because the “coo” sound network and its function were hidden behind other behavioral observations. For identification of the vocalizer only from hearing the “coo” sound, three phonetic values, i.e., the “fundamental,” “duration,” and “formants,” plus other characteristics were used as indices of voiceprints. The results indicated that these were effective for identifying the vocalizer in two-thirds of the adults in the study troop which was composed of 12 adults and 16 immature members. The “coo” sound exchange network among the troop members (adults) was drawn on the basis of the voiceprint identification. The network showed three characteristics as follows: (1) matriarchs of the kin-groups frequently exchanged “coo” sounds with each other; (2) the other females exchanged “coo” sounds mostly within their own kin-groups; and (3) males seldom participated in the “coo” sound exchange. This suggests that “coo” sound exchange plays a central role for the matriarch of kin-groups in binding each kin-group and, ultimately, in binding all members together into an organized troop.     

Note on psychophysical discrimination with more than two stimuli

H. D. Landahl's well-known theory of psychophysical discrimination between two stimuli (Psychometrica,3, 107–125, 1938) is generalized to the case ofn mutually inhibiting stimuli, such that all the corresponding reactions are mutually incompatible so that only one response at most can occur at a time. It is shown that while in the two-stimulus case a “no-response” situation does not necessarily need to occur, in the case ofn stimuli andn responses a “no-response” situation always occurs with finite probability. Therefore, there is a probabilityP _i of the occurrence of each responsei as well as a probabilityP _e of no response, with . The probabilitiesP _i andP _e are expressed in terms of the intensities of then stimuliS _i and in terms of then distribution functions of the fluctuations at then corresponding connections. The expressions are in the form of sums ofn-tuple integrals of the products of the distribution functions, the limits of integration being determined by the intensities of then stimuli.     

Reward and punishment in learning with possible reference to punishment for crime

On the basis of Landahl's theory of two-choice learning it is shown that application of punishment for wrong responses, without giving award for correct ones, does not lead to complete learning, no matter how many trials are used. If initially a “wrong response” was learned, then an attempt to inhibit it by punishment alone will in a class of cases lead only to a 50% suppression of that wrong response. Possible connection with the problem of effectiveness of punishment as a deterrent for crime is mentioned.     

Further studies of some aspects of a neurobiophysical model of schizophrenia

The neurobiophysical model of schizophrenia discussed previously (Bull. Math. Biophysics,26, 167–185, 1964;27, 21–26, 1965) is generalized further, to include catatonic and stuporous states. It is concluded that the development of schizophrenia will proceed through different stages of catatonic and non-catatonic states, depending on parameters which characterize on one hand the general inhibition of the individual, on the other hand what may be called his “stability.” Suggestions for possible clinical verifications of the conclusions are made.     

Mathematical theory of biological periodicities II. Effect of active transport

A previous study (Bull. Math. Biophysics,30, 735–749) is generalized to the case of active transport, which acts together in general with ordinary diffusion. The basic results obtained are the same except for an additional important conclusion. In principle it is possible to obtain sustained oscillations even when the secretions of the different glands do not affect the rates of formation or decay of each other at all, but affect the “molecular pumps,” which are responsible for the active transports in various parts of the system. Thus no biochemical interactions need necessarily take place between then-metabolites to make sustained oscillations possible in principle. This is an addition to a previous finding (Bull. Math. Biophysics,30, 751–760) that due to effects of the secreted hormones on target organs, non-linearity of biochemical interactions is not needed for production of sustained oscillations.     

On the reversibility of environmentally induced alterations in abstract biological systems

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.     

Materials towards the revision of the genus Triplophysa rendahl, 1933 (Cobitoidea: Balitoridae: Nemacheilinae): A revision of nominal taxa of Herzenstein (1888) described within the species “Nemachilus” stoliczkae and “N.” dorsonotatus, with the description of the new species T. scapanognatha sp. nova

This study reviews the nominal taxa within the species “Nemachilus” stoliczkae and “N.” dorsonotatus, described by Herzenstein (1888). N. dorsonotatus, N. d. retropinnis, and N. plagiognathus are reviewed within the species Triplophysa stoliczkae; it is suggested that this species is represented by at least 5 subspecies. N. stoliczkae brevicauda, N. s. leptosoma (synonym, N. s. productus), and N. s. crassicauda are considered as valid species, the last 2 are related to the group including the species T. tenuis, T. choprai, T. tenuicauda, and T. yasinensis rather than with T. stoliczkae. It was shown that the “stoliczkae” species group (sensu Prokofiev, 2001) should be divided into three species groups: “stoliczkae” (s. str.), “tenuis,” and “robusta”; their diagnoses and the species composition are presented. A new species from the “stoliczkae” group is described (T. scapanognatha sp. nova), related to T. tanggulaensis (Zhu, 1982). Original Russian Text ? A.M. Prokofiev, 2007, published in Voprosy Ikhtiologii, 2007, Vol. 47, No. 1, pp. 5–25.     

A quantum-theoretic approach to enzyme specificity: Proposals for a new type of biochemical control mechanism

A quantum-theoretic approach to the problem of enzymic specificity is presented. The concept of a “measuring system” analogized with the enzyme is utilized. Along these lines a quantum mechanical hypothesis for the mechanism of enzyme reactions was advanced (Enzymologia,35, 117–130, 1968). In the measuring process an ℐ-observable, linked to the proper values of the substrate'sA ₁...A _m observables will indicate the state of the measuring apparatus. On the corresponding Hilbert space of the enzymesubstrate complexH _ES , through the respective statistical operatorU _ES we get a “state” vector [s, a]. Theng:Γ _S xΓ _E →Γ _ES , that is, to an oriented pair 〈s, a〉 ∈Γ _S xΓ _E will correspond a “state” vector [s, a], and to a proper valuei _k of ℐ will correspond, throughg, the respective equivalence classes of Г-spaces. Introducing the concept of enzyme-substrate complex entropyL _ES , a theorem is demonstrated asserting thatL _S =L _ES -L _E + 1/2kn wheren is the number of the degrees of freedom which may fluctuate. The values ofL _ES are denoted “specific values,” and it is demonstrated that a microphysical systemS may be a substrate specific forE, if and only if it can realize one of theL _ES specific values. Along these lines a model of a stochastic process for the enzymic reaction is constructed, and the set of Kolmogorov equations for the respective probabilities is derived. When a “perturbation” is induced in our model, an interesting prediction concerning the fluctuations in the kinetics of the corresponding enzyme is obtained. A relevant experimental proof ensued from these theoretical considerations. When a “gentle perturbation” was induced in a substrate by mild X-ray or UV-irradiations, an interesting oscillatory behavior of enzymic activity was recorded. A biochemical control mechanism is constructed (a simple “flip-flop” type) utilizing nonoverlapping oscillations in the activity of two enzymes at a key metabolic intermediate level. Eventually, a relevant experimental proof for the respective control model is presented.     

Zornia subsessilis (Leguminosae: Papilionoideae: Dalbergieae), a new species from Serra do Cabral, Minas Gerais, Brazil

Zornia subsessilis, a new species from Serra do Cabral, Minas Gerais State, Brazil, is described and illustrated on the basis of field and herbarium studies. It belongs to Zornia section Zornia of subgenus Zornia and it appears to be restricted to “campo rupestre” (rocky fields) within the “cerrado” biome. This new species is characterized by its sessile to subsessile leaves, fruits with articles 4 to 5 mm long and with bristles up to 3.5 mm long.     

Abstract mathematical molecular biology: II some relational consequences of the “one gene-one enzyme” hypothesis

Following the program outlined in a previous paper (Bull. Math. Biophysics,23, 237–260, 1961), a further abstract study is made of some simple relational systems which possess some properties of living organisms. It is shown that the “one gene-one enzyme” hypothesis leads to the conclusion that either all genes are built of the same chemical building blocks, or that at least all genes have a number of building blocks in common. A consistent relational application of the “one gene-one enzyme” hypothesis leads moreover to the conclusion that replication is not an inherent property of a gene. Rather there must be a set of enzymes which “copy” the genes. The number of enzymes in this set must be less than the number of genes and therefore the activity of those “copying” enzymes cannot be absolutely specific.     

Role of secondary metabolites as defense chemicals against ice-ice disease bacteria in biofouler at carrageenophyte farms

Carrageenophyte farming is an expanding economical activity in North Borneo Island, Malaysia. During routine monitoring of “ice-ice” disease and epiphyte outbreak at commercial farms, it was apparent that culture lines were heavily (60–80%) infested with biofoulers, particularly Acanthophora spp. and Laurencia majuscula. However, only L. majuscula showed dominance and flourished even during “ice-ice” disease outbreak. Presence of chemical defense against seaweed pathogens was investigated in two populations of L. majuscula collected from three major carrageenophyte farms in two districts; (A) Lohok Butun, Selakan Island, and Bum-Bum Island, in Semporna district, and (B) Telutuh, Carrington Reef, and Balambangan Island, in Kudat district. The first population contained elatol (1), and iso-obtusol (2), and, second population contained (Z)-10,15-dibromo-9-hydroxy-chamigra-1,3(15),7(14)-triene (3) and (E)-10-15-dibromo-9-hydroxy-chamigra-1,3(15),7(14)-triene (4), as their antibacterial metabolites. All four metabolites showed highly selective inhibition against “ice-ice” disease bacteria compared to human pathogens at 30 μg disk⁻¹. In addition, seasonal variation of these compounds at two representative farms (Selakan Island [P-1] and Balambangan Island [P-2]) revealed a 120–170% increase in concentration during “ice-ice” disease outbreak. Microscopy of fresh specimens showed the presence of corps en cerise, which is the synthesis and storage site of halogenated metabolites at superficial cortical cells, branch tips, and trichoblasts. This suggests the importance of these metabolites as defense chemicals against “ice-ice” disease bacteria in L. majuscula that grows on seaweed culture lines.     

A quasi-steady-state approximation method for diffusion problems: I. Concentration dependent diffusion coefficients

A generalization of Landahl's approximation method (H. D. Landahl,Bull. Math. Biophysics,15, 49–61, 1953) for non-linear diffusion problems is suggested. The method is applied to sorption, desorption, and free diffusion problems involving concentration-dependent diffusion coefficients. With some limitations, the results compare favorably with those obtained by numerical methods.     

Models for reserpine effects on normal and brain-operated animals on a continuous reinforcement bar pressing schedule

Mathematical models are presented for the relationship between changes in the bar pressing rate of albino rats on a continuous reinforcement schedule and alterations of the brain amines norepinephrine and serotonin induced by electrolytic lesions in the hypothalamus and by the drug, reserpine. The discussion utilizes central concepts from some of the more prominent hypotheses on the relation of the amines to behavior and for the potentiation effects of the drug by the lesion (A. Carlsson, 1964. “Functional Significance of Drug-induced Changes in Brain Monoamine Levels.” InBiogenic Amines, eds. H. E. Himwich and W. A. Himwich, New York: Elsevier, 9–27; B. B. Brodie and E. Costa, 1962. “Some Current Views on Brain Monoamines.”Psychopharm. Service Centre Bull.,2, 1–25.) Laboratory data (F. Grabarits and J. Harvey, 1966. “The Effects of Reserpine on Behavior and on Brain Concentrations of Serotonin and Norepinephrine in Control Rats and Rats with Hypothalamic Lesions.”J. Pharm.,153, 403–411) are interpreted, and suggestions for further experimental and theoretical work are made.     

Two types of using of space in the resident common shrews <Emphasis Type="Italic">Sorex araneus</Emphasis> L.

The home range of resident animals is considered as “familiar area” including a “foraging area.” It has been revealed that the activity of an average animal unit in the “foraging area” could be approximated by normal distribution. Estimation of activity distribution in the “familiar area” (beyond the “foraging area”) was impeded by means of marking since it might be difficult to record distant movements, and the method does not provide an essential body of data. In the case of the common shrew Sorex araneus, the “familiar area” was estimated using pitfall as animals evade them in the known areal. The “foraging area” radius of the average shrew was taken to be 30 m (95% of the animal unit activity), the radius of “familiar area” was within the range of 180–240 m. The “foraging area” was expected to provide the animal with vital resources, and the “familiar area” reflects its need for exploratory activity.