A logical calculus of the ideas immanent in nervous activity

Because of the “all-or-none” character of nervous activity, neural events and the relations among them can be treated by means of propositional logic. It is found that the behavior of every net can be described in these terms, with the addition of more complicated logical means for nets containing circles; and that for any logical expression satisfying certain conditions, one can find a net behaving in the fashion it describes. It is shown that many particular choices among possible neurophysiological assumptions are equivalent, in the sense that for every net behaving under one assumption, there exists another net which behaves under the other and gives the same results, although perhaps not in the same time. Various applications of the calculus are discussed. Reprinted from theBulletin of Mathematical Biophysics, Vol. 5, pp. 115–133 (1943).     

Logical identification of all steady states: The concept of feedback loop characteristic states

Biological regulatory systems can be described in terms of non-linear differential equations or in logical terms (using an “infinitely non-linear” approximation). Until recently, only part of the steady states of a system could be identified on logical grounds. The reason was that steady states frequently have one or more variable located on a threshold (see below); those steady states were not detected because so far no logical status was assigned to threshold values. This is why we introduced logical scales with values 0,¹θ, 1²θ, 2, ..., in which¹θ,²θ, ... are the logical values assigned to the successive thresholds of the scale. We thus have, in addition to the regular logical states,singular states in which one or more variables is located on a threshold. This permits identifyingall the steady states on logical grounds. It was noticed that each feedback loop (or reunion of disjointed loops) can be characterized by a logical state located at the thresholds at which the variables of the loop operate. This led to the concept ofloop-characteristic state, which, as we will see, enormously simplifies the analysis.The core of this paper is a formal demonstration that among the singular states of a system, only loop-characteristic states can be steady. Reciprocally, given a loop-characteristic state, there are parameter values for which this state is steady; in this case, the loop is effective (i.e. it generates multistationarity if it is a positive loop, homeostasis if it is a negative loop). This not only results in the above-mentioned radical simplification of the identification of the steady states, but in an entirely new view of the relation between feedback loops and steady states.     

The inconsistencies of present-day mathematical-physical methods pertaining to current generators in volume conductors used in electrocardiography

The present-day practices of electrocardiography and vectorardiography are based upon the theory that the surface potential differences can be assumed to be due to a single dipole inside the body. It is shown in this paper that a dipole cannot account for all the surface potentials due to realistic current generators, and hence the determination of the current generator from surface potential measurements based upon such a theory will lead to inconsistent representations of the heart for one and the same subject. To demonstrate this point two eccentric dipoles of different strengths and locations representing two muscle fibers are taken to be the current generator in a homogeneous spherical conductor. The exact surface potentials are then expressed by means of the “interior sphere theorem” of the authors. With these expressions the magnitude, direction, and location of the resultant dipole are determined by the method of D. Gabor and C. V. Nelson (J. App. Physics,25, 413–16, 1954). The surface potentials due to this resultant dipole are again exactly expressed by means of the “interior sphere theorem” and compared with those due to the eccentric dipoles assumed. It can be seen that the differences can be considerable. It is suggested that the multipole model of the authors (Bull. Math. Biophysics,20, 203–16, 1958) be used as a more accurate and the only unique representation of the heart. This investigation was supported by the National Heart Institute under a research grant H-2263(c).     

Logic in a Dynamic Brain

The ability of the human brain to carry out logical reasoning can be interpreted, in general, as a by-product of adaptive capacities of complex neural networks. Thus, we seek to base abstract logical operations in the general properties of neural networks designed as learning modules. We show that logical operations executable by McCulloch–Pitts binary networks can also be programmed in analog neural networks built with associative memory modules that process inputs as logical gates. These modules can interact among themselves to generate dynamical systems that extend the repertoire of logical operations. We demonstrate how the operations of the exclusive-OR or the implication appear as outputs of these interacting modules. In particular, we provide a model of the exclusive-OR that succeeds in evaluating an odd number of options (the exclusive-OR of classical logic fails in his case), thus paving the way for a more reasonable biological model of this important logical operator. We propose that a brain trained to compute can associate a complex logical operation to an orderly structured but temporary contingent episode by establishing a codified association among memory modules. This explanation offers an interpretation of complex logical processes (eventually learned) as associations of contingent events in memorized episodes. We suggest, as an example, a cognitive model that describes these “logical episodes”.     

Variables influencing one-zero and instantaneous time sampling outcomes

Previous studies have shown that instantaneous time sampling results are more highly correlated with true duration than are one-zero sampling results. One-zero results, however, reflected a composite of both duration and frequency better than did instantaneous results. It is shown in this analysis that these outcomes are the logical result of the definitions of the two sampling modes. When interval lengths meet specific requirements, correct frequency counts can be obtained with either mode and systematic duration error with one-zero sampling can be eliminated by subtracting frequency from the number of intervals scored ‘one.’     

Modifications des comportements liés au SIDA

Since the seropositivity declaration, a certain number of assests appears and express a psychic distress in man. This psychic “shock” doesnt always show itself directly. When it appears it’s often as form of “signifiant “having said that phoneme, word, representing, symbolizing what spring up without some one knowing, a truth of his desire. The first of these assests is the word Revelation This term means not as the surprise as the time lag between a “fashion of life” and its results. As a matter of fact, they must be less surprised than witness of their life always in danger. This word of “revelation” lays us in a sacred country, but also in the dark, the mysterious and experience; saying always “testing something” Other meaning, Aesthetisation Current events media supplies evenly gushing examples of Estheticism. By estheticism, we must understand as much documents where the body is left to the others. Stain and guilt, last stand, “dramatic exist”, taking fligth, so much examples of “desecration” or “redemption”. Other assest, Convocation It’s an experience of the request. Often the person life is marked out a succession of invocations and/or provocations before than the virus intervenes who, in the psychic representations that it conveys, changes the status of requests. It’s in this change of status that people are affected and the doctor can look for an application who arouse changes of behaviours. Revelation, aesthetisation, convocation, these three words part of method where the person works by oscillation between, first time a position of subject, it means a psychic work of hesitations, withdrawal, desire, and also a position of being, it means acting, an act where all sense is vacant. The notions of “risk behaving” and “ordalic behaving” help us to better understand and separate all these behaviours which some people will be infected. To take a risk is the behaviour of “human condition”, like the venial sin defins the human being, only the ordalic behaving shows a desperate endeavour with a meeting of a sort of sovereignty, a next world not defined. The work of this whole on the modifications tie up the AIDS, can give us a reflection about the S.C.D. where the notion of risk is rarely absent.     

A canonical form for neural nets without circles

By “neural net” will be meant “neural net without circles.” Every neural net effects a transformation from inputs (i.e., firing patterns of the input neurons) to outputs (firing patterns of the output neurons). Two neural nets will be calledequivalent if they effect the same transformation from inputs to outputs. A canonical form is found for neural nets with respect to equivalence; i.e., a class of neural nets is defined, no two of which are equivalent, and which contains a neural net equivalent to any given neural net. This research was supported by the U.S. Air Force under Contract AF 49(638)-414 monitored by the Air Force Office of Scientific Research.     

Conditions Under Which Nitrogen Can Limit Steady-State Net Primary Production in a General Class of Ecosystem Models

Human activity is drastically altering global nitrogen (N) availability. The extent to which ecosystems absorb additional N—and with it, additional CO₂—depends on whether net primary production (NPP) is N-limited, so it is important to understand conditions under which N can limit NPP. Here I use a general dynamical model to show that N limitation at steady-state—such as in old-growth forests—depends on the balance of biotically controllable versus uncontrollable N inputs and losses. Steady-state N limitation is only possible when uncontrollable inputs (for example, atmospheric deposition) exceed controllable losses (for example, leaching of plant-available soil N), which is the same as when uncontrollable losses (for example, leaching of plant-unavailable soil N) exceed controllable inputs (biological N fixation). These basic results are robust to many model details, such as the number of plant-unavailable soil N pools and the number and type of N fixers. Empirical data from old-growth tropical (Hawai’i) and temperate (Oregon, Washington, Chile) forests support the model insights. Practically, this means that any N fixer—symbiotic or not—could overcome ecosystem N limitation, so understanding N limitation requires understanding controls on all N fixers. Further, comparing losses of plant-available N to abiotic inputs could offer a rapid diagnosis of whether ecosystems can be N-limited, although the applicability of this result is constrained to ecosystems with a steady-state N cycle such as old-growth forests largely devoid of disturbance.     

Variation in the outcome of population interactions: bifurcations and catastrophes

 The nature of the association between two species may vary depending on population abundances, age or size of individuals, or environmental conditions. Interactions may switch between beneficial and detrimental depending on the net balance of costs and benefits involved for each species. We study the repercussion of the ecological setting on the outcomes of conditional or variable interactions by means of a model that incorporates density-dependent interaction coefficients; that is, interaction α-functions. These characterize the responsiveness and sensitivity of the association to changes in partner's abundance, and can take positive and negative values. Variable outcomes – and transitions between them – are categorized as homeo- or allo-environmental, that is, occurring under the same ecological setting, or not, respectively. Bifurcation analyses show that these dynamics are moulded by ecological factors that are: intrinsic to the nature of the association (concerning the sensitivity of the interaction), and extrinsic to the association itself (the quality of the environment referred to each species alone). The influence of these factors may be conflicting; consequently, the dynamics involve catastrophic events. In a facultative variable association, stable coexistence is expected when environmental conditions are adverse; otherwise, the exclusion of one species is the likely outcome. Remarkable situations as the switching of victim-exploiter roles illustrate the theoretical perspective. Received: 15 December 2001 / Revised version: 18 November 2002 / Published online: 28 February 2003 Key words or phrases: Variable population interactions – Conditional interactions – Costs and benefits – Density dependent interaction coefficient – Hysteresis – Symbiosis – Mutualism – Parasitism     

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.     

Some bio-sociological aspects of the mathematical theory of communication

In the first part of the paper a general discussion of the transmission of information through neural chains is given in terms of the Shannon-Weaver theory. It is pointed out that with the all-or-none law a single chain of neurons connected in series transmits one bit of information per signal. A set ofN independent parallel chains transmitsN bits per signal. If, however, the chains are interconnected, the amount of information is reduced. At the same time, however, the degree of coordination of the final neuromuscular reaction is increased. A relation between the maximum possible speed of a reaction and its degree of coordination is derived, and possible applications to spoken language are suggested. A general quantitative discussion of the relation between amount of information and amount of knowledge which an individual may obtain when confronted with the external world is made and a possible connection with new trends in logical thinking is pointed out. In the second part transmission of information through “social chains” is discussed under certain special assumptions. An expression for the “social channel noise” in terms of the length of the channel is derived. Finally an expression is given for the amount of information transmitted from one individual to another in a social group of uniform density as a function of the physical distance between the two individuals.     

Molecular computing revisited: a Moore's Law?

Moore's Law states that the processing power of microchips doubles every one to two years. This observation might apply to the nascent field of molecular computing, in which biomolecules carry out logical operations. Incorporation of new technologies that improve sensitivity and throughput has increased the complexity of problems that can be addressed. It is an ultimate goal for molecular computers to use the full potential of massive parallelism.     

Usefulness of the analysis of links among dream sources in therapy.

A study of the links among the memory sources of dreams can be carried out by means of an automatic analysis of text files including dream reports and associations. Heuristic criteria can provide plausible explanations for the existence of these links, which generally present a logical and at the same time emotional significance. The aim of this paper is to support the idea that the study of the link patterns among dream sources, in addition to being interesting from the cognitive viewpoint can be also useful for the therapeutic process. An interaction schema is described including four operators: the dreamer (patient), the therapist, the detector of possible links, and the proposer of plausible explanations. Two examples are given of application of this schema. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Design and Fabrication of Ultralight Weight,Adjustable Multi-electrode Probes for Electrophysiological Recordings in Mice

The number of physiological investigations in the mouse, mus musculus, has experienced a recent surge, paralleling the growth in methods of genetic targeting for microcircuit dissection and disease modeling. The introduction of optogenetics, for example, has allowed for bidirectional manipulation of genetically-identified neurons, at an unprecedented temporal resolution. To capitalize on these tools and gain insight into dynamic interactions among brain microcircuits, it is essential that one has the ability to record from ensembles of neurons deep within the brain of this small rodent, in both head-fixed and freely behaving preparations. To record from deep structures and distinct cell layers requires a preparation that allows precise advancement of electrodes towards desired brain regions. To record neural ensembles, it is necessary that each electrode be independently movable, allowing the experimenter to resolve individual cells while leaving neighboring electrodes undisturbed. To do both in a freely behaving mouse requires an electrode drive that is lightweight, resilient, and highly customizable for targeting specific brain structures.A technique for designing and fabricating miniature, ultralight weight, microdrive electrode arrays that are individually customizable and easily assembled from commercially available parts is presented. These devices are easily scalable and can be customized to the structure being targeted; it has been used successfully to record from thalamic and cortical regions in a freely behaving animal during natural behavior.     

Response time and threshold of a random net

The response time of a random net is defined as the expected time (measured in the number of synaptic delays) required for the excitation in the net (measured by the fraction of neurons firing per unit time) to reach a certain level. The response time is calculated in terms of the net parameters as a function of the intensity of the outside stimulation. Two principal types of cases are studied, 1) an instantaneous initial stimulation, and 2) continuously applied stimulation. It is shown that for a certain type of net where the required level of excitation is small, the response time-intensity equation reduces to the one derived on the basis of the “one-factor” theory applied to a neural connection. More general assumptions, however, give different types of equations. The concept of the “net threshold” is defined, and its calculation indicated. The net threshold for instantaneous stimulation is, in general, greater than that for continuous stimulation. The results are discussed with reference to existing theories of reaction times.     

Effects of Temperature on the Growth and Development of Lemna minor, under Conditions of Natural Daylight

The effects of temperature on the growth and development ofLemna minor in the open have been studied in the east of Scotlandby means of four water baths constructed to maintain constantwater temperatures of 12.5, 17.5, 22.5, and 27.5 °C whensubjected to natural insolation. Experiments were conductedat weekly intervals between August and November in 1958 andMay and July in 1959. At the beginning of every experiment,for all temperature treatments, 134 fronds were placed in eachof six containers. From the initial and final samples, the weightsof roots and fronds together with frond (leaf) area were measured,so that weekly values for net assimilation rate, leaf-area ratio,and relative growth-rate could be calculated. Daily solar radiationwas recorded by means of bimetallic radiation recorder. In 1958 linear regressions of a satisfactory fit were obtainedwhen the data for net assimilation rate, leaf-area ratio, andrelative growth-rate were calculated on the logarithms of theradiation for each temperature. Since radiation remained relativelyconstant in 1959 it was not possible to evaluate very reliablythe effects of radiation on the growth parameters but only occasionally,notably for the final leaf-area ratio (12.5 °C) were thelines for 1958 and 1959 significantly different. Single lineswere fitted to the points for both years. In all the regressions,apart from that for final leaf-area ratio (12.5°C) the proportionof the variation accounted for ranged from 87 to 97 per cent. The results showed that the net assimilation rate was positivelylinked with radiation and was optimal at 17.5 °C, thoughthe rise from 12.5 to 17.5 °C was not significant. At thehigher temperatures (22.5 and 27.5 °C) there was a significantnegative effect of temperature on the net assimilation rate.The leaf-area ratio and relative growth-rate were positivelydependent on radiation and reached the highest values at thehighest temperatures. The maximum growth-rate recorded amountedto no less than 0.39 g.g^–1 day^–1. The results are discussed in relation to those for other aquaticand terrestrial plants.     

Mathematical biosociology of beliefs and prejudices

Following a suggestion made previously (Bull. Math. Biophysics,13, 61, 1951), it is assumed that every individual has both a tendency to behavearationally, by accepting everything on faith, and rationally, by subjecting everything to rational analysis. Arational behavior is characterized by various beliefs, prejudices, etc., which are considered to be conditioned reactions, learned by the individual before he completely develops his faculties for rational thinking. The two tendencies are assumed to be due to excitations of two different regions of the central nervous system, and are measured by the intensities ɛ _f and ɛ _r of those excitations. Those intensities are further assumed to increase linearly with time, the increases of the two beginning, in general, at different ages. The rates of increase are considered as normally distributed in the population. The relative frequency of arational and rational behavior is determined by the difference φ=ɛ _f =ɛ _r according to equations 0 developed previously (Bull. Math. Biophysics,11, 255, 1949). It is shown that with the above assumptions the majority of the population, which starts with arational behavior, will, within two or three of generations, either change to rational behavior or continue indefinitely to behave arationally. This will hold as long as imitative factors are present. Expressions for the numbers of individuals who behave rationally and arationally are derived. If the intensity of conditioning toward an arational behavior decreases with increasing size of the rationally behaving minority, or, if the rationally behaving individuals are not influenced by imitation, then a slow secular trend toward rational behavior may be present. An expression is also derived for the fraction of individuals who behave rationally as a function of age. This fraction increases with increase of the age at which the beginning conditioning toward any beliefs or prejudices begins.     

Allometric Relationships in Field-grown Soybean

Allometric relationships in plants uncover size-correlated variationsin form and development and characterize the relative growthof a part of a plant in comparison with a whole. Stable allometricrelationships in ontogeny can be used as components of cropmodels and to estimate plant parameters that are difficult tomeasure. Our objective was to discover whether stable allometricrelations exist in ontogeny of field-grown soybeans (GlycinemaxL.). We used field data on vegetative stages, plant height,stem weight, and leaf weight of 16 soybean cultivars measuredon farms and on the experiment station of Mississippi StateUniversity during 1993–1995 growing seasons. The numberof observed crops for each cultivar ranged from one to 14. Stemheights displayed linear log-log dependencies on the vegetativestage, before and after the breakpoint stage, which typicallywas between the ‘fourth node’ and ‘sixth node’vegetative stages. Slopes of the log-log dependencies afterthe breakpoint stage were similar in all cultivars. Stem masshad log-log linear dependencies on stem height. Slopes of thesedependencies differed among cultivars grown under the same conditions,and among crops of the same cultivar grown under different conditions.Water stress could be a modifier of these relationships. Theproportion of leaf weights in the total weight of leaves andstems decreased linearly as the vegetative development progressed.Since allometric relations are stable for a specific crop, theycan be used to forecast vegetative development as soon as theyare established.Copyright 1998 Annals of Botany Soybean,Glycine maxL., allometry, vegetative development.     

Enhanced Synonymous Site Divergence in Positively Selected VertebrateAntimicrobial Peptide Genes

Nonrandom patterns associated with adaptively evolving genes can shed light on how selection and mutation produce rapid changes in sequences. I examine such patterns in two independent families of antimicrobial peptide genes: those in frogs, which are known to have evolved under positive selection, and those in flatfishes, which I show have also evolved under positive selection. I address two recently proposed hypotheses about the molecular evolution of antimicrobial peptide genes. The first is that the mature peptide region is replicated by an error-prone polymerase that increases the mutation rate and the transversion/transition ratio compared to the signal sequence of the same genes. The second is that mature peptides evolve in a coordinated fashion with their propieces, such that a change in net charge in one molecular region prompts an opposite change in charge in the other region. I test these hypotheses using alternative methods that minimize alignment errors, correct for phylogenetic nonindependence, reduce sequence saturation, and account for differing selection pressures on different regions of the gene. In both gene families I show that divergence at both synonymous and nonsynonymous sites within the mature peptide region is enhanced. However, in neither gene family is there evidence of an increased mutational transversion/transition ratio or coordinated evolution. My observations are consistent with either an elevated mutation rate in an adaptively evolving gene region or widespread selection on “silent” sites. These hypotheses challenge the assumption that mutations are random and can be measured by the synonymous substitution rate. [Reviewing Editor: Dr. Willie J. Swanson]     

Ungulate stimulation of nitrogen cycling and retention in Yellowstone Park grasslands

We studied how ungulates and a large variation in site conditions influenced grassland nitrogen (N) dynamics in Yellowstone National Park. In contrast to most grassland N studies that have examined one or two soil N processes, we investigated four rates, net N mineralization, nitrification, denitrification, and inorganic N leaching, at seven paired sites inside and outside long-term (33+ year) exclosures. Our focus was how N fluxes were related to one another among highly variable grasslands and how grazers influenced those relationships. In addition, we examined variation in soil δ¹⁵N among grasslands and the relationships between soil ¹⁵N abundance and N processes. Previously, ungulates were reported to facilitate net N mineralization across variable Yellowstone grasslands and denitrification at mesic sites. In this study, we found that herbivores also promoted nitrification among diverse grasslands. Furthermore, net N mineralization, nitrification, and denitrification (kg N ha^–1 year^–1, each variable) were postively and linearly related to one another among all grasslands (grazed and fenced), and grazers reduced the nitrification/net N mineralization and denitrification/net N mineralization ratios, indicating that ungulates inhibited the proportion of available NH₄ ⁺ that was nitrified and denitrified. There was no relationship between net N mineralization or nitrification with leaching (indexed by inorganic N adsorbed to resin buried at the bottom of rooting zones) and leaching was unaffected by grazers. Soil δ¹⁵N was positively and linearly related to in situ net N mineralization and nitrification in ungrazed grasslands; however, there was no relationship between isotopic composition of N and those rates among grazed grasslands. The results suggested that grazers simultaneously increased N availability (stimulated net N mineralization and nitrification per unit area) and N conservation (reduced N loss from the soil per unit net N mineralization) in Yellowstone grasslands. Grazers promoted N retention by stimulating microbial productivity, probably caused by herbivores promoting labile soil C. Process-level evidence for N retention by grazers was supported by soil δ¹⁵N data. Grazed grassland with high rates of N cycling had substantially lower soil δ¹⁵N relative to values expected for ungrazed grassland with comparable net N mineralization and nitrification rates. These soil ¹⁵N results suggest that ungulates inhibited N loss at those sites. Such documented evidence for consumer control of N availability to plants, microbial productivity, and N retention in Yellowstone Park is further testimony for the widespread regulation of grassland processes by large herbivores. Received: 5 May 1999 / Accepted: 1 November 1999