Contribution to the probabilistic theory of neural nets: II. Facilitation and threshold phenomena

The output curve of a single neuron with a threshold of response with respect to the frequency of the stimuli is derived. If the stimuli are regularly spaced in time, the output curve has discontinuities. If the threshold and/or refractory period are sufficiently large, the output curve approaches the “all-or-none” curve. In the case of completely randomized stimuli, the output curve is sigmoid. The equation of this curve is derived and some properties are studied. Threshold and “all-or-none” effects can be achieved by “pyramiding” neurons of this type to converge on neurons of higher order.     

“Addition” and “multiplication” theorems for the inputs of two neurons converging on a third

The output of a neuron innervated by two other neurons which, in turn, are subjected to two independent Poisson showers of stimuli, is derived as a function of the frequencies of the Poisson showers under two distinct assumptions, 1) where either of the two neurons can fire the third, and 2) where the stimuli from both neurons must impinge within a certain time interval to fire the third. For very small frequencies, the output of the third neuron is very nearly the sum of the input frequencies in the first case and proportional to the product of the input frequencies in the second case. Hence the designation “addition” and “multiplication” theorems. This treatment is a generalization of a previous treatment where the Poisson shower was assumed identical for the two outer neurons.     

A preliminary study of vocal communication in wild long-tailed macaques (Macaca fascicularis). I. Vocal repertoire and call emission

Vocal communication in wild long-tailed macaques (Macaca fascicularis) is described in terms of (1) a preliminary vocal repertoire and the situations in which calls occur in the natural habitat of this species and (2) quantitative measurement of the natural occurrence of calls in the field. Although a number of calls are relatively discrete (e.g., a male loud call), gradation is pronounced for both wide-spectrum (“harsh”) and narrow-spectrum (“clear”) vocal signals. Thirteen general types of harsh calls are identified provisionally as elements of the vocal repertoire. The exact number of discrete clear calls contributing to the vocal repertoire could not be ascertained precisely, but these calls were classified operationally into six broadly acoustically different classes in order to measure natural vocal behavior. Vocalizations tended to occur in temporal “clusters” during sample, periods. Narrow-band clear or “coo” calls were more frequently performed by macaques than wide-band harsh calls. The possible functional implications of the correlated occurrence of multiple vocal signals are discussed.     

Transduction mechanism(s) of Na-saccharin in the blowfly <Emphasis Type="Italic">Protophormia terraenovae</Emphasis>: evidence for potassium and calcium conductance involvement

The study on transduction mechanisms underlying bitter stimuli is a particularly intriguing challenge for taste researchers. The present study investigates, in the labellar chemosensilla of the blowfly Protophormia terraenovae, the transduction mechanism by which saccharin evokes the response of the “deterrent” cell, with particular attention to the contribution of K⁺ and Ca²⁺ current and the role of cyclic nucleotides, since second messengers modulate Ca²⁺, Cl⁻ and K⁺ currents to different extents. As assessed by extracellular single-sensillum recordings, our results show that the addition of a Ca²⁺ chelator such as EGTA or the Ca²⁺ current blockers SK&F-96365, Mibefradil, Nifedipine and W-7 decrease the response of the “deterrent” cell to saccharin. A similar decreasing effect was also obtained following the addition of 4-aminopyridine, a K⁺ current blocker. On the contrary, the membrane-permeable cyclic nucleotide 8-bromoguanosine 3′,5′-cyclic monophosphate (8Br-cGMP) activates this cell and shows an additive effect when presented mixed with saccharin. Our results are consistent with the hypothesis that in the labellar chemosensilla of the blowfly both Ca²⁺ and K⁺ ions are involved in the transduction mechanism of the “deterrent” cell in response to saccharin. Our results also suggest a possible pathway common to saccharin and 8Br-cGMP.     

Dynamics of heart rate response in sleeping infants exposed to tone stimuli

Heart rate, EEG, and motor responses were recorded following presentation of a series of 6–10 sound stimuli (2.5-s tones of 1000, 4000, and 250 Hz, 70 dB, interstimulus intervals 18–25 s) in neonates aged 9 to 22 weeks during stage 2–3 sleep. The infants (17 of 19) revealed heart rate (HR) changes in response to tone stimuli that consisted in an expanded form of three phases: (1) short-latency (at 1 s after tone presentation) HR deceleration, (2) HR acceleration with a maximum at 3–5 s, and (3) late HR deceleration at 6–9 s of the poststimulus interval. The occurrence rate of the first two phases of cardiac response is relatively constant during a series of stimuli, whereas the likelihood of late HR deceleration is the highest following the first tone presentation and decreases significantly when the stimulus is repeated. Differences in the dynamics and statistical analysis allow a relative independence of all the three response phases to be suggested. The HR acceleration phase is dramatically enhanced in association with the motor response elicited by the sound stimulus. The late HR deceleration phase occurs not only after the first presentation of stimuli, but also when they are repeated if they evoke EEG reaction (vertex potentials) in response to both the beginning and end of the tone sound. Possible mechanisms of the three phases of poststimulus HR changes are: the vagal cardiac reflex associated with the acoustic (adaptive) reflex, activation of sympathetic efferents in combination with the startle reflex, and secondary vagal deceleration of sinus rhythm likely to be associated with the processes of perception (detection) of a “novel” stimulus and to serve as an indirect sign of an orienting reaction.     

Receptive Fields of Visually Sensitive Neurons of the Extrastriate Associative Area 21b of the Cat Cerebral Cortex

Organization of the receptive fields (RFs) of neurons of the extrastriate associative region 21b of the cerebral cortex was studied in cats. Most neurons under study (63%) were “monocular,” while 37% of the cells were “binocular” units. Among 178 neurons examined in detail, heterogeneous RF functional organization was typical of about 76% of the units; point-to-point testing of the entire RF area by stationary stimuli resulted in the generation of various types of responses (on, off, or on-off). The rest of the neurons (24%) generated homogeneous responses. The dimension, form, and functional organization of RFs of the neurons under study depended to a certain extent on the parameters of visual stimuli used for the measurements. Examination of the influence of the visual space, which surrounded the RF, on responses of the neurons evoked by stimulation of the RF per se showed that darkening of the visual space adjacent to the RF inhibited neuronal responses to moving stimuli; in some cases the responses were totally suppressed. Analysis of spatial overlapping of the RF sequentially recorded in the course of each insertion of the electrode showed that the density of distribution of the overlapping RF areas of neighboring neurons with the RF of the examined neuron is irregular, and that the RF is of a mosaic nature. We hypothesize that the visual space surrounding the RF plays a significant role in the formation of responses of visually sensitive neurons to presentation of moving stimuli. Neirofiziologiya/Neurophysiology, Vol. 37, No. 3, pp. 223–234, May–June, 2005.     

How songbirds deal with large amounts of serial information: retrieval rules suggest a hierarchical song memory

Many songbirds develop remarkably large vocal repertoires, and this has prompted questions about how birds are able to successfully learn and use the often enormous amounts of information encoded in their various signal patterns. We have studied these questions in nightingales (Luscinia megarhynchos), a species that performs more than 200 different types of songs (strophen), or more than 1000 phonetically different elements composing the songs. In particular, we investigated whether and how both song repertoires and song performance rules of nightingales were coded by auditory stimuli presented in serial learning experiments. Evaluation of singing episodes produced by our trained birds revealed that nightingales cope well with an exposure to even long strings of master song-types. They can readily acquire information encoded within and between the different master songs, and they memorize, for example, which master song-types they have experienced in the same learning context. Imitations of such song-types form distinct sequential associations that are termed “context groups”. Additionally, nightingales develop other song-type associations that are smaller in size and termed “package groups”. Package formation results from constraints of the acquisition mechanisms which obviously lead to a segmentation of auditorily perceived master song sequences. Further experimentation validated that the song memory of nightingales is organized in a hierarchical manner and holding information about “context groups” composed of packages, “package groups” composed of songs, and songs composed of song elements. The evidence suggests that implementation of such a hierarchical organization facilitates a quick retrieval of particular songs, and thereby provides an essential prerequisite for a functionally appropriate use of large vocal repertoire is in songbirds. Received: 4 October 1997 / Accepted in revised form: 26 August 1998     

Responses of recurrent nets of asymmetric ON and OFF cells

A neural field model of ON and OFF cells with all-to-all inhibitory feedback is investigated. External spatiotemporal stimuli drive the ON and OFF cells with, respectively, direct and inverted polarity. The dynamic differences between networks built of ON and OFF cells (“ON/OFF”) and those having only ON cells (“ON/ON”) are described for the general case where ON and OFF cells can have different spontaneous firing rates; this asymmetric case is generic. Neural responses to nonhomogeneous static and time-periodic inputs are analyzed in regimes close to and away from self-oscillation. Static stimuli can cause oscillatory behavior for certain asymmetry levels. Time-periodic stimuli expose dynamical differences between ON/OFF and ON/ON nets. Outside the stimulated region, we show that ON/OFF nets exhibit frequency doubling, while ON/ON nets cannot. On the other hand, ON/ON networks show antiphase responses between stimulated and unstimulated regions, an effect that does not rely on specific receptive field circuitry. An analysis of the resonance properties of both net types reveals that ON/OFF nets exhibit larger response amplitude. Numerical simulations of the neural field models agree with theoretical predictions for localized static and time-periodic forcing. This is also the case for simulations of a network of noisy integrate-and-fire neurons. We finally discuss the application of the model to the electrosensory system and to frequency-doubling effects in retina.     

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.     

Wavelet entropy in event-related potentials: a new method shows ordering of EEG oscillations

 In this work we show the application of a measure of entropy defined from the wavelet transform, namely the wavelet entropy (WS), to the study of event-related potentials (ERPs). WS was computed for ERPs recorded from nine healthy subjects with three different types of stimuli, among them target stimuli in a cognitive task. A significant decrease of entropy was correlated with the responses to target stimuli (P300), thus showing that these responses correspond to a more “ordered” state than the spontaneous EEG. Furthermore, we propose the WS as a quantitative measure for such transitions between EEG (“disordered state”) and ERP (“ordered state”). Received: 12 April 2000 / Accepted in revised form: 11 September 2000     

A contribution to the mathematical biology of automobile driving: II. Passing as a case of psychophysical discrimination

The decision to pass or not to pass in view of an oncoming car is considered as a case of comparative judgment in which it is to be decided whether the time it will take to pass safely is greater or less than the time it will take to collide with the oncoming car. H. D. Landahl's well-known theory of psychophysical discrimination is used, and it is assumed that the “distracting stimuli” considered previously (Rashevsky, 1959,Bull. Math. Biophysics,21, 375–85) tend to increase the standard deviation of Landahl's fluctuation function. Effects of the “distracting stimuli” on the threshold of the neuroelements in Landahl's circuit are also considered. On this basis an expression is derived which gives the probability of a collision accident in passing as a function of the “distracting stimuli.”     

An innovative LC/MS approach applied to the determination of zeralenone in maize: Alternate Isotope-coded Derivatization Assay (AIDA)

Zearalenone is a mycotoxin mainly produced by severalFusarium species, which are known to colonize grains in temperate climates. The purpose of the study is to provide a reliable isotope dilution method for the quantification of this mycotoxin. A derivative of the analyte to be used as standard is obtained by reaction with acetic anhydride, which is available in two pure isotopic forms, a protonated (“light”) and a hexadeuterated (“heavy”). The derivatized standards are added to the matrix split intwo parts. Then, the derivatization procedure is repeated on both matrices derivatizing the part containing the “heavy” labelled standard with the “light” acetic anhydride and the part containing the “light” labelled standard with the “heavy” acetic anhydride. Both extracted mixtures are analyzed by LC/MS, monitoring the “light” and the “heavy” labelled analytes and using the former as standard for the latter in one case and viceversa in the other case. The method allowed to obtain very good results, without the need of IAC purification. Presented at the 27^th Mykotoxin-Workshop, Dortmund, Germany, June 13–15, 2005. Financial support: The Italian Ministry of Health     

The probabilistic approach to the effects of radiations and variability of sensitivity

The calculation of the size of the “sensitive volume” or “control center” in biological effects of radiations is discussed from the viewpoint of the probabilistic theory of these phenomena based on the concept of random “effective events”. On the bases of that theory, the resistivity of a microorganism to radiation is defined as its “mean life” under a radiation of one roentgen per minute. This mean is calculated for processes with and without recovery. The case of variable sensitivity, as it occurs for instance during mitosis, is discussed in detail. Methods are given to calculate this variability from survival curves or similar experimental data. The theory is applied to experiments of A. Zuppinger on irradiation ofAscaris eggs with X-rays.     

A mathematical model of decision-making neural circuits controlling behavioral model selection

Mathematical models of mutually interacting reverberatory neural circuits exhibit decision-making properties that can account for behavioral mode selection in terms of identifiable neural subsystems and measurable variables, without the need for invoking concepts such as “drive,” “motivation,” or “instinct”. The models can account for an animal's ability to persist in a given behavioral mode under appropriate stimulus conditions and to rapidly switch modes in response to significant stimulus changes via the properties of stable steady states, thresholds for steady-state transitions, and the lack of intrinsic oscillations.     

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.     

An analysis of the 2o and 10o field color-matching functions

The 2^o and 10^o field color-matching functions are independent: one specification is not a linear transformation of the other, even after correcting for macular pigment effects. Therefore, the “true” color-matching functions which directly describe the linear responses of the eye must be different for the two field sizes. This means that a given stimulus will, in general, have a different chromaticity depending upon the field size, regardless of the choice of any one colorimetric co-ordinate system for all field sizes. However, in spite of these chromaticity differences, a large uniform field usually appears nearly uniform. Such color uniformity implies that even though chromatic differences occur as a function of retinal position or field size, these differences are small. If this is the case, then the underling “true” color-matching functions determining the observed color-matching functions must be nearly, but not quite, identical. These differences vanish as identity between the sets of color-matching functions is approached. This property suggests a method of calculating the “true” color-matching functions. The “true” color-matching functions must approximate those obtained by minimizing the chromaticity differences between two independent sets of data. This can be done by assuming that the coefficients of transformation should be adjusted so as to produce as nearly identical chromaticities for spectrum stimuli as possible. In this paper, it is also assumed that the “true” color-matching functions have no negative values, as if they were based on actual absorption spectra. This article describes the calculation of the “true” 2^o and 10^o field color-matching functions satisfying these two conditions. For both field sizes, the maxima of the three functions are near 435, 540, and 585 mμ, after correcting for the filtering effects of the ocular media and macular pigment.     

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.     

“Ignition” phenomena in random nets

The spread of excitation in a “random net” is investigated. It is shown that if the thresholds of individual neurons in the net are equal to unity, a positive steady state of excitation will be reached equal to γ, which previously had been computed as the weak connectivity of the net. If, however, the individual thresholds are greater than unity, either no positive steady state exists, or two such states depending on the magnitude of the axone density. In the latter case the smaller of the two steady states is unstable and hence resembles an “ignition point” of the net. If the initial stimulation (assumed instantaneous) exceeds the “ignition point,” the excitation of the net eventually assumes the greater steady state. Possible connections between this model and the phenomenon of the “preset” response are discussed.     

Mating system and stigmatic behaviour during flowering of Alpinia kwangsiensis (Zingiberaceae)

 Little is known about the breeding systems of tropical perennial ginger species. In this paper, we provide information about the breeding system of Alpinia kwangsiensis in Yunnan, Southwest China, specifically self-compatibility, mechanisms promoting outcrossing, and the visitation characteristics of pollinators. Populations of A. kwangsiensis have two specific phenotypes that differ in flowering behaviour: 1) “cataflexistyle” individuals in which the stigma is held erect above the dehiscent anther when anthesis begins in the morning and becomes decurved under the anther at noon and 2) “anaflexistyle” individuals in which the receptive stigma is decurved under the indehiscent anther first and moves into a reflexed superior position above the anther as it begins to shed pollen at mid-day. The stigmatic movements in the two floral phenotypes, which occur in a ratio of 1:1 in natural populations, are synchronous and correlate with the foraging behaviour of floral visitors; pollination is effected only between floral forms. Field experiments indicate that A. kwangsiensis is self-compatible and dependent upon insects for fertilization. This newly reported floral mechanism, which we have named “flexistyly,” adds to the repertoire of devices that have evolved in flowering plants to insure outcrossing. Received November 29, 2001 Accepted January 8, 2002