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.     

A neurobiophysical model of schizophrenias and of their possible treatment

A neurobiophysical model is proposed for the explanation of some characteristics of schizophrenic behavior. The normal reactions to exogenous stimuli are mediated through a set of centers, while some endogenous stimuli result in abnormal reactions removed from reality, such as dreamlike states, paranoias, hallucinations, etc. The two sets of centers are cross-inhibited and the usual equations for such cross-inhibited systems are applied. In normal life exogenous stimuli as a rule result preponderantly in pleasant reactions, and the corresponding pathways are therefore reinforced. This results in an inhibition of the abnormal reactions. If the life history of an individual is such that a sufficiently large number of ordinarily experienced stimuli leads to unpleasant reactions and, therefore, the corresponding pathways are inhibited, the endogenously stimulated centers for abnormal reactions prevail and various schizophrenic symptoms occur. The same result may be achieved with a normal life history but through organic changes in the system, which differentially affect various thresholds and excitation parameters. The model thus leads to the conclusion that what appears now to be a large array of contradictory findings in the “organic” versus the “psychological” controversy is actually not a contradiction, but is a result of the dependence of normal and abnormal behaviors on a large number of neurobiophysical parameters. Some general comparisons between the conclusions drawn from the model and some known facts are made. The model also provides a first step toward a neurobiophysical interpretation of the mechanism of psychotherapy.     

Contributions to the mathematical biophysics of the central nervous system with special reference to learning

A learning theory based on the lowering of thresholds of neurons under certain conditions is applied to two “random net” models. The first, a so-called “ganglion-brain” is characterized by completely random connections of all afferent tracts except certain ones which form the pathways for unconditioned responses. Certain expressions are derived which measure the learning potentiality of the ganglion— in particular, with respect to the number of responses which can be learned (conditioning potential) and the amount of interference between the learned responses (redundance potential). The second model concerns the progressive refinement of a response. The efficiency of learning in this case is reflected in the eventual specificity of the response which, in turn, depends on the modification of the distribution of thresholds associated with the neurons governing the responses. Expressions are derived relating the initial distribution of thresholds, the relative effectiveness of the various responses, and certain other parameters to the final distribution of thresholds. For a particular choice of the effectiveness distribution of responses the progressive sharpening of the threshold curve (i.e., progressive specificity of response) is demonstrated. Some implications of the model with respect to the evolution of nervous systems are discussed.     

Carbohydrate tolerance,serum albumin and protein values of normal and “waster” marmosets (Callithrix jacchus)

The major objective of this study was to establish standard glucose and lactose tolerance curves for the common marmoset (Callithrix jacchus). These data were utilized to establish criteria for detection of abnormal glucose tolerance and characterization of some aspects of the “marmoset wasting syndrome” which has been observed in this species. Glucose and lactose tolerance tests were performed on healthy animals and typical “marmoset wasters.” Eighteen normal animals were 18 to 36 months old and weighed 194–280 g. Six “wasters” were in the age range of 24 to 84 months and weighed 163–253 g. Seven experiments were carried out for each glucose tolerance test. In each trial it was observed that the serum glucose concentration (SGC) of the healthy animal after 90 min was two times higher than the pre-administration concentrations. The SGC returned to the pre-administration concentration within 150–300 min in animals administered glucose at dosages of 2 g/kg and 1 g/kg of body weight. However, at the dosage level of 5 g/kg body weight, the SGC of the animals tripled after 30 min and required 300 min to return to the pre-administration level. The 2 g/kg dosage level was chosen as typical. When similar experiments were conducted with animals identified as “chronic wasters,” all of the animals except one were observed to be inefficient in the absorption of glucose. When lactose was administered at a level of 4 g/kg, similar results were obtained. Normal and “waster” marmosets were also subjected to serum total protein, albumin and electrophoresis determinations in an effort to establish additional criteria that may be utilized in the identification of the “marmoset wasting” syndrome. Serum albumin was significantly higher in the “waster” marmosets 30 min following an oral administration of glucose than was observed in normal animals. Total protein values were not significantly lower in the “wasters” when subjected to the same tolerance test. The albumin level in normal animals was not affected by similar glucose tolerance tests. The electrophoretic patterns of serum protein for normal animals exhibited more bands than was observed in patterns of serum protein for “waster” marmosets. From these data, it seems logical that these diagnostic tests may be useful in developing a profile for the early detection of the “wasting” syndrome in marmosets.     

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.     

The evolution of magnanimity

Conspicuous consumption associated with status reinforcement behavior can be explained in terms of costly signaling, or strategic handicap theory, first articulated by Zahavi and later formalized by Grafen. A theory is introduced which suggests that the evolutionary raison d’être of status reinforcement behavior lies not only in its effects on lifetime reproductive success, but in its positive effects on the probability of survival through infrequent, unpredictable demographic bottlenecks. Under some circumstances, such “wasteful” displays may take the form of displays of altruistic behavior and generosity on the part of high status individuals, in that is signals the ability to bear the short-term costs of being generous or “cooperative,” while at the same time reinforcing the long-term benefits of higher status. James L. Boone is an associate professor in the Department of Anthropology at the University of New Mexico, where he carries out research in behavioral ecology and the archaeology of complex societies. His current interests are in the evolution of social status reinforcement behavior and variation in patterns of conspicuous consumption in human history.     

Design optimization of a helical endothelial cell culture device

The specific roles of mass transfer and fluid dynamic stresses on endothelial function, important in atherogenesis, are not known. Further, the effects of mass transfer and fluid dynamic stresses are difficult to separate because areas of “abnormal” mass transfer and “abnormal” wall shear stress tend to co-localize (where abnormal is defined as any deviation from the mass transfer rate or wall shear stress present in a long straight artery with the same flow rate and diameter). Our goal was to design a cell culture device which gives maximum separation between areas of abnormal shear stress and areas of abnormal mass transfer. We used design optimization principles to design a helical cell culture device. Using shear stress and mass transfer fields predicted by solving the governing equations, the area of the device which was exposed to low rates of mass transfer and normal levels of wall shear stress was determined. The design optimization method then maximized this area by varying the design variables, resulting in the optimum design. The optimum design had Reynolds number = 50, helical radius = 3.23 and helical pitch = 3.82. The area of the device which was exposed to low rates of mass transfer and regular levels of wall shear stress was about 4.5 times the inlet cross-sectional area of the device or about 5% of the device total internal surface area. An optimum design was successfully determined and the methodology used was shown to be robust. The area of the device which was exposed to low rates of mass transfer and regular levels of wall shear stress occurred in a defined region which should aid further experimental work.     

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.     

The perfect learner

As a “base line” of memorization performance, the behavior of a “perfect learner” is considered. He is characterized by a perfect memory and by the ability to choose the best search procedure in problems where the correct response from a given repertoire is to be found to each of several stimuli under the condition of “right” and “wroing” promptings by the experimenter. Expected learning curves are derived for the case of disjoint response repertoires associated with the stimuli under cyclic and random presentation of the stimuli and for the case of a single response repertoire (a one-to-one matching problem) under cyclic presentation.     

Recognition of facial expressions in a Japanese monkey (Macaca fuscata) and humans (Homo sapiens)

Recognition of facial expressions by a Japanese monkey and two humans was studied. The monkey subject matched 20 photographs of monkey facial expressions and 20 photographs of human facial expressions. Humans sorted the same pictures. Matching accuracy by the monkey was about 80% correct for both human and monkey facial expressions. The confusion matrices of those facial expressions were analyzed by a multi-dimensional scaling procedure (MDSCAL). The resulting MDS plots suggested that the important cues in recognizing facial expressions of monkeys were “thrusting the mouth” and ‘raising the eyebrows.” Comparison of the MDS plots by the monkey subject with those by human subjects suggested that the monkey categorized the human “happiness” faces. This may suggest that the monkey has an ability to recognize human smile face even though it is learned. However, the monkey did not differentiate the human “anger/disgust” faces from the human “sad” faces, while human subjects clearly did. This may correlate with the lack of eyebrow movement in monkeys.     

Generalization and categorization of spectral colors in goldfish. II. Experiments with two and six training wavelengths

In part I of this study (Kitschmann and Neumeyer 2005), goldfish categorized spectral colors only in the sense that wavelengths in a range of about twice as large as the just noticeable difference were treated as similar to a given training wavelength. Now, we trained goldfish on more than one wavelength to prevent very accurate learning. In one experiment goldfish were trained on six adjacent wavelengths with equal numbers of rewards, and, thus, equal numbers of learning events. Generalization tests showed that some wavelengths were chosen more often than others. This indicated that certain spectral ranges are either more attractive or more easily remembered than others. As this is a characteristic of the “focal” colors or centers of color categories in human color vision, we interpret the findings in goldfish accordingly. We conclude (Figs. 5 and 6) that there are four categories in spectral ranges approximately coinciding with the maximal sensitivities of the four cone types, and three categories in-between. Experiments with two training colors indicate that there is no direct transition between categories analogous to human “green” and “red”, but that there is a color analogous to human “yellow” in-between (Figs. 2, 3; Table 1).     

Abnormal births and other “ill omens”

We summarize the ethnographic literature illustrating that “abnormal birth” circumstances and “ill omens” operate as cues to terminate parental investment. A review of the medical literature provides evidence to support our assertion that ill omens serve as markers of biological conditions that will threaten the survival of infants. Daly and Wilson (1984) tested the prediction that children of demonstrably poor phenotypic quality will be common victims of infanticide. We take this hypothesis one stage further and argue that some children will be poor vehicles for parental investment yet are not of demonstrably poor quality at birth. We conclude that when people dispose of infants due to “superstitious beliefs” they are pursuing an adaptive strategy in eliminating infants who are poor vehicles for parental investment. Catherine Hill lectures in biological anthropology/human sciences at Durham University’s University College, Stockton. She trained in biological anthropology at University College, London. Her current research interests include human and nonhuman primate socioecology and human resource ecology and development issues. Helen Ball lectures in biological anthropology/human sciences at Durham University’s University College, Stockton. She trained in biological anthropology at the University of Massachusetts at Amherst. Her current research interests include nonhuman primate behavior and socioecology, reproductive biology, and evolutionary issues.     

Human neuropsychology and the concept of culture

American anthropology is distinguished by a four-fields approach in which biological, cultural, archaeological, and linguistic dimensions of behavior are examined in evolutionary and cross-cultural perspective. Nevertheless, assumptions of mind-body dualism pervade scholarly thinking in anthropology and have prevented the development of a truly integrated science of human experience. This dualism is most exemplified by the lack of consideration of the role of the brain in both “physical” and “mental” processes, including phenomena labeled as cultural. In this paper, I review neural mechanisms of learning, communication, and emotion, and discuss the implications of these findings for culture theory. Lee Xenakis Blonder is an assistant professor in the Department of Behavioral Science and the Sanders-Brown Center on Aging, University of Kentucky Medical School, Lexington. She is currently examining the effects of stroke in different regions of the brain on language, nonverbal communication, and emotional processing in an attempt to better understand human brain and behavior relations. Recent publications include “Neuropsychological Functioning in Hemiparkinsonism” (with R. E. Gur, R. C. Gur, A. J. Saykin, and H. I. Hurtig),Brain and Cognition 9:244–257 (1989).     

Markers for human placental trophoblasts in two-dimensional gel electrophoresis

Summary Primary cultures of trophoblasts established from human term placentae showed high viability and reproducibility. Two-dimensional gel patterns obtained by metabolically labeling the trophoblasts with [³⁵S]-methionine demonstrated that their pattern of gene expression was stable during the 6-d period investigated. Gel analysis demonstrated the keratins 7, 8, 14, 17, 18, and 19. Analysis of the gel pattern confirmed the presence of a small proportion of contaminating fibroblasts and lymphocytes. The gel patterns were compared with that of skin fibroblasts, peripheral lymphocytes, and epithelial cells to identify a group of proteins that are enriched in the trophoblasts and thus may be used as marker for these cells. This work was supported by the Danish Cancer Society, the Lundbeck Foundation, the Danish Medical Research Council, “Pedersholmlegatet,” and by “Anna og Jakob Jakobsens Legat.”     

Heat shock proteins HSP70 and GP96: structural insights

Several heat shock proteins (HSPs) act as potent adjuvants for eliciting anti-tumor immunity. HSP-based tumor vaccine strategies have been highly successful in animal models and are undergoing testing in clinical trials. It is generally accepted that HSPs, functioning as chaperones for tumor antigens, elicit tumor-specific adaptive immune responses. HSPs also appear to induce innate immune responses in an antigen-independent fashion. Innate responses generated by HSPs may contribute to anti-tumor immunity. Immunologically active chaperones with anti-tumor activity are referred to as “immunochaperones”. Here, we review the studies that address the role of structural domains or regions of the immunochaperones HSP70 and GP96 that may be involved in the induction of adaptive or innate immune responses. This article forms part of the Symposium in Writing “Thermal stress-related modulation of tumor cell physiology and immune responses”, edited by Elfriede Noessner.     

A quantum model for controlled enzymic reactions: II. Controlled biochemical networks

Two control units, the switching and the two factor discriminating net are described. They are derived as a consequence of the enzymic oscillatory behavior induced by substrate “perturbation”. A complex network encompassing long sequences of metabolic reactions is constructed and the organization of cellular metabolic activities in well defined “regimes” and “states” inferred.     

Development of sexual and protective behavior of female crickets <Emphasis Type="Italic">Gryllus argentinus</Emphasis> Sauss. at the prereproductive and reproductive periods of imaginal ontogenesis

Data are presented about the development of reproductive and defense behavior of noncopulated female crickets Gryllus argentinus Sauss. in the beginning of the imaginal ontogeny. The character of interaction of females with “virtual” males (the “supporting ball” method-“trackball”) was studied. The forms of female motor reactions to models of intraspecies male sound signals-the calling and aggressive songs-are described and analyzed. The character of the development of female acoustic behavior is described as judged by change in the forms of motor reactions in the course of the imaginal ontogeny. It is shown that immediately after the imaginal molt the reproductive behavior is not formed yet but it matures gradually within a few days. At the early stages of the imaginal ontogeny passive defense behavior is found to be most clearly expressed.     

Decrease in Alarm Call Response Among Tufted Capuchins in Competitive Feeding Contexts: Possible Evidence for Counterdeception

Animal signals function to elicit behaviors in receivers that ultimately benefit the signaler, while receivers should respond in a way that maximizes their own fitness. However, the best response may be difficult for receivers to determine when unreliable signaling is common. “Deceptive” alarm calling is common among tufted capuchins (Cebus apella nigritus) in competitive feeding contexts, and responding to these calls is costly. Receivers should thus vary their responses based on whether a call is likely to be reliable. If capuchins are indeed able to assess reliability, I predicted that receivers will be less likely to respond to alarms that are given during competitive feeding contexts than in noncompetitive contexts, and, within feeding contexts, that individuals inside or adjacent to a food patch will be less likely to respond to alarms than those further from the resource. I tested these predictions in a group of wild capuchins by observing the reactions of focal animals to alarm calls in both noncompetitive contexts and experimental feeding contexts. Antipredator escape reactions, but not vigilance reactions, occurred significantly less often in competitive feeding contexts than in noncompetitive contexts and individuals adjacent to food patches were more likely to respond to alarm calls than were those inside or further from food patches. Although not all predictions were fully supported, the findings demonstrate that receivers vary their behavior in a way that minimizes the costs associated with “deceptive” alarms, but further research is needed to determine whether or not this can be attributed to counterdeception.     

Medicinal Flora of the Popoluca, Mexico: A botanical systematical perspective

We studied the medicinal plants used by the Popoluca of the Sierra de Santa Marta (eastern Mexico). Using Moerman’s method of regression analysis we determined which ethnomedically used taxa are over-represented in the Popolucan pharmacopoeia (e.g., Asteraceae) and which are underrepresented (e.g., Orchidaceae). Moerman et al. (1999) found high correlation between the holarctic pharmacopoeias and assumed that apart from the relatedness of the northern floras a “global pattern of human knowledge“ may account for this finding. Although the Popoluca dwell in a habitat dominated by a neotropical flora but intermixed with important holarctic elements, they include considerably fewer neotropical taxa in their pharmacopoeia as one would expect if the historical transmitted knowledge were influencing their selection. This finding confirms the theory stated by Moerman et al. However, the Popoluca include some neotropical taxa in their pharmacopoeia and thus a moderate correlation exists between the Popolucan pharmacopoeia and the neotropical pharmacopoeia analysed by Moerman et al. We therefore conclude that apart from historically transmitted knowledge about specific taxa the “global pattern of human knowledge” addressed by Moerman et al. is largely based on “common selection criteria.”