CASCADES OF BEHAVIORAL PHASE TRANSITIONS

Carlos H. von der Becke, Oscar García,

Universidad Nacional de Luján, Provincia de Buenos Aires, Argentina.

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a. INTRODUCTION AND STATE OF ART

1. "Neuroethological engineering or robotics" is a new description refered to a new field of applied knowledge. By ethology Lorentz refers to the study of normal animal behaviors in natural environments. By neuroethology Camhi refers to the neuronal mechanisms which give a causal explanation to the natural behaviors already mentioned. By computational neuroethology, Beer (1991) refers to the computer simulations of control systems involving those neural mechanisms. By neuroethological robotics or engineering, one refers to the branch of control engineering and robotics which studies the design of artificial managers with autonomous and flexible actions, using in a practical way, the novelties discovered by computational neuroethology. The present study makes a comparison between two selforganized behavior-producing (neuroethological) neural nets. One is a rather simple insect model with some hundred neurons and a slightly higher number of interconnections between them, proposed by RB Beer and programmed in C++ by P. and G. Williams, and the other is a "parliament of the mind" (M. Minsky) very schematic model of some superior human brain activities (Barral and von der Becke, 1991/5), in which the manager shows a theorem- proving capability.

LORENZ KZ: The Foundations of Ethology - Simon and Shuster (1961) CAMHI JM: Neuroethology, Sinauer Associates (1984) BEER R,McKENNA T - Invertebrate Neuroethology and Robotics - Academic Press (1992) BARRAL R, BECKE CH von der: Cerebro, Imprenta de Universidad N. de Luján, Luján, Argentina, (1991) BARRAL R, BECKE CH von der: Biotermodinámica del Cerebro, Imprenta de Universidad N. de Luján, Luján, Argentina, 2a. ed. (1995)

2. Randall Beer's book explains a computer simulated bug with obvious behavioral sequences. This bug is pure artificial brain and includes inputs (sensors) and outputs (locomotion legs and mandibular motors), but no metabolism. It reduces the bug's activities to 48 neurons with 88 main links between them (Fig. 1). - - - - - - - - - - - - - - - - - - - - - - - - - Everything in this map is in accordance with physics. Therefore everything the bug "does" on the screen, has in principle a sufficient explanation with no mysteries. The 48 neurons have specific numerical values (around 10 for each) which appear in the book's appendix. The whole project is condensed by the PC C++ version of the whole neuron map, due to P and G Williams. Some other publications show the advancement of the idea of using all the knowledge developed by neural net groups of investigators to the particular field of invertebrate neuroethology. (Beer and McKenna)

b. OBJECTIVES

The two goals are:

1. To apply careful direct visual analysis as well as ANOVA and multiple correlation techniques, to discover and characterise behavioral subcascades and cascades on a typical computer neuroethological engineering program.

2. To discuss the generalized conclusions derived from results, especially when compared with previous models (Barral and von der Becke) made with respect to human intellectual superior mental behavioral cascades.

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c. METHODS

1. The Analysis of variance and the Multiple correlations methods, both related and unified by previous work of one of us (vdB), are the tools used to interpret a binary digital characterization of behavioral cascades, as frequently used in all kinds of multivariable factorial Box Wilson experimental designs.

BECKE CH von der -Puesta en Marcha Optima de una Planta, Publ. 11002/7, Universidad Tecnológica Nacional, FRBA, (1989)

2. The commercial shareware program developed by P. and G. Williams was run using the same Beer's 480 numerical values, recorded and analized.

3. During the analysis, the specific locomotion neuron subsystems (Fig. 2) were disregarded. The emphasis is in the relation of the main five behaviour marker neurons, and the visual behaviors shown. Both appear simultaneously at the PC monitor.

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PL1 inhibits PR1 and PL2 .................... PR1 inhibits PL1 and PR2
PL2 inhibits PL1, PL3 and PR2............PR2 inhibits PL2, PR1 and PR3
PL3 inhibits PL2 and PR3......................PR3 inhibits PL3 and PR3
-----------------------------------

Fig.2- Six pacemakers for leg movements, left outside the 48 neuron list. They self-organize different gaits according to environmental conditions.There is a inhibitory coupling between the six legs. P means Pacemaker, L means Left and R Right.

4. It is possible to select the computer program's last and most ambitious development, called APP3, among the ones which Beer engineered. Based on it, different behaviors of walking and eating characteristics can be studied.

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d. DISCUSSION OF RESULTS

d.1. GENERALITIES

1. Considered in detail, the initial behaviors of the hundreds of runs recorded by the authors, sometimes with initial conditions intentionally modified, were soon spontaneously changed to other behaviors because of the vagaries of early random bursts. They modify the trajectory of each of the runs: no two are the same. The two-dimensional bug walks either towards the screen's two-dimensional external limits (the external border) and generally starves (because the edge-following gait traps it stronger than what the food odor can arouse it), or towards a long rectangular obstacle on the upper half, also with (internal) borders and generally survives for a longer time. The mentioned obstacle interferes on the way to the food patch, centered almost in the middle of the screen. The best case appears when the bursts conduct the bug towards the inner obstacle.

2. The bug's neuroethological net offers a neat computer "experimental" demonstration of the interplay of different neural subsystems contributing in a series-parallel fashion to mixed behaviors. To arrive to any specific non-initial behavior, the prerequisite behaviors should in general be present, depending on the environment (presence of obstacles and food patches) and the initial conditions (location and angle of bug and bioenergetic level). The initial behavior appears again after the bug exits the food patch. This produces a cyclic cascade of behaviors.

d.2. REDUCTION IN THE NUMBER OF TYPICAL NEURONS TO BE ANALYSED

1. The locomotion subsystem is excluded, as previously said. After a visual inspection of correlations between on/off conditions and simultaneous exhibition of behaviors, the remaining universe of 48 neurons was carefully analysed so as to reduce the number to seven, without losing the scope of the main bug behaviors visually recognized. Among those seven there were two left-right pairs with easily deduced relations among them, so that finally the selection settled down.

2. The remainig five b e h a v i o r m a r k e r s are the black nodes of Fig. 1, and the possible states in an ordered list are:

  • 1st.digit 0 means NFCL is off (the possibility of some free body angles when walking along obstacle edges), and 1 means NFCL is not off (the inhibition of the freedom).

  • 2nd.digit 0 means FO is off (the body angle is independent of the food odor signals, saving energy), and 1 otherwise.

  • 3rd.digit 0 means SC off (saving energy due to a high serotonine level), and 1 otherwise

  • 4th.digit 0 means a single non-wandering (another peculiar walking gait) command off and no change in the body angle (saving energy), and 1 otherwise

  • 5th.digit 0 means a couple of random buster neurons off, and 1, which in standard operation turn the body direction counterclockwise, or clockwise, with rather low RBL frequencies. This happens because the right symmetric neuron RBR (not shown) bursts with stronger discharges.

  • 3. During the runs, when the burst fequency was zero, the level of the neuron was also considered zero (rest). In any other case its value is indicated by one (activated). The five neurons will be called for standardising purposes, X1, X2, X3, X4 and X5, in the same order as the previous list. X1 is either 0 or 1, if NFCL is either inhibited or firing. The same rule applies to the other cases. The initial behavior is always 00000, meaning that the five listed neurons, are off. It walks because of neurons not listed.

    d.3. MATHEMATICAL DEDUCTION OF THE MAIN BEHAVIORAL CASCADES.

    1. Some runs showed a behavior that conducted directly to death. The remaining runs exhibited a main sequence of behaviors. The decision to use a list of five neurons presupposes that the behaviors observed visually when those neurons are on or off will be the only analysed. No prediction a priori can be made to determine in which moment the behavior sequence is passing through a significative non-equilibrium phase transition.

    2. So the main sequence observed was

                                    <-------------------------------
                                   00000 (START; STRAIGHT WALK)      |
    (1)                                                              |
                                   00001 (CW OR CCW TURN)            |
     (2)                                                             |
                                   00000 (STRAIGHT WALK)             |
     (3)                                                             |
                                   00010 (TRAPPED BY EDGE-FOLLOWING) |
    (4)                                                              |
                                   00110 (ODOR AROUSED + EDGE TRAP)  |
    (5)                                                              |
              DEATH<--(9)--------- 01110 (PATCH-IN or PATCH-BORDERING)                |
    (6)                                                              |
                                   11010 (PATCH-IN)                 (8)
     (7)                                                             |
                                   10010 (PATCH-OUT)>----------------                          

    Fig. 3 - Main behavioral sequence, which cycles like a biological clock. The actual list has 8 main steps among 7 main behaviors, one of them repeated twice (behavior 00000). The step (8) cycles back. There is a possibility of death as a consequence of Patch-Bordering.

    3. Fig. 3 has the resemblance of a biological clock, when conditions help to the repetition of the cycle: enough food left, internal but not external borders followed during the edge-following gait when the bug exits the food patch.

    SELVERSTON AI, MOULINS M-Oscillatory neural networks, Ann. Rev. Physiol. (1985), p. 29.

    4. Ocassionally some other short secondary behaviors were observed. Seventeen combinations were impossible to find. The probability to find a particular behavior during the runs appears on column C.

    A Behavior?
    B On the main sequence or cascade of behaviors?Yes or No
    C Frequency on the real list of behavors, including rare behaviors?
    D Probable main precessor?
    E Probable main succesor?
    F Fluctuations detected?Yes or No
    G Type?
    A B C D E F G
    00000 Y 0.1604 00001 00001 Y START
    00001 Y 0.0755 00000 00000 Y CCWCW
    00010 Y 0.1132 0000x 00000 N EDGE1
    00100 N 0.0566 00000 00000 Y WANDG
    00110 Y 0.0755 00010 01110 N ODOR
    01010 N 0.0660 11010 00000 N TRAP1
    01110 Y 0.1509 11110 11110 Y IN
    10000 N 0.0189 10XX0 0000X N WANDG
    10010 Y 0.0660 11010 11110 N OUT
    10100 N 0.0094 10110 10000 N WANDG
    10110 N 0.0283 11110 10010 N TRAP
    11010 Y 0.0945 X1110 10010 N IN
    11110 N 0.0849 11010 000X0 Y ODOR

    5.The tabulated frequencies are modified in the case of fluctuations, mostly in the neighborhood of an important phase transition, generally because of body angle fine adjustments.

    6. In order to treat statistically the data, an ANOVA test was made on the interactions of two, three, four and five Xi, with emphasis on the higher order interactions according to the general interpretation rules of any factorial test analysis. The possible significance of a high order interaction means the existence of non-linearities, and, as usual, the implications of the non-linearities are much more important than the linearities. The linear effects were excluded.

    d.5. ENERGETICS

    1. At the same time it is possible to analyse the cascade energetics, with antienthropic and enthropic branches, some characterising better energy saving behaviors. This is also related to selforganized serial subcascades at the whole cycle of behaviors. It is not always so. There appear environmental situations in which the bug is condemned to starving if it follows the minimal energy policy.

    2. The bug begins with a free behavior, 00000, a straight linear gait with no random bursts whatsoever. The behavioral sequence, afterwards, starts mainly with 00001, which imply the appearance of a wandering gait, with small incomplete clockwise and counterclockwise turns, interrupted when one of the bug's antennae tactile sensors detects an obstacle. So this triggers an edge-following gait, 00010, enslaving half of the previous wandering gait. The random bursts appear and show only if the body angle goes towards the edge, and the normal 00010 behavior is given priority. If the environment presents a convex obstacle, the bug recoils and follows the previous general orientation. This recoil is not detected by any of the five selected neurons. Nevertheless, it certainly is a distinct behavior which should be added outside of the main list.

    3. Simulating evolutive inherited behaviors, with some exceptions, the bug does not remain in the food patch zone for a long time. On the contrary, when the bug "feels satisfied" or senses the neural correlate of this situation, there is an energy saving switch and it runs away, including situations in which food is below its mouth. The arousal to exit subcascade is, in this last case, 11010/01010/11010, a locomotion slow/fast phase transition, nothing to do with the main sequence, Fig. 3. The most frequent slow/fast exiting subcascade means just 11010/10010/0000x series, with 10010 as a short happening, sometimes unseen. What one sees at the screen is that the two bug's antennae emerge out of the food patch as a signal that the locomotion phase transition will show during the next seconds.

    4. The arousal to exit subcascade is related to the energy sensor (name for a chemical detector of high/low serotonine internal levels if the bug shold have metabolism). As is, each mouth movement increases energy and each single leg movement cycle decreases it. The alarm condition, when the level falls below a threshold value, connects again the command to search for food (neuron SC triggers to frecuency 1): the behavior is now 00110. When bioenergy decays, it justifies a new odor oriented 01110 behavior, which drags the bug towards the food patch when no obstacles interfere (this is one of the much studied m o t i v a t e d behaviors, when the bug feels hunger and exhibits at the same time an arousal subcascade of behaviors, with an energetic driving force strongly related to survival [Beer, p. 126]). If there is an obstacle, the bug circles it, as previously explained.

    5. This often means that the bug is walking in the same direction as the negative odor gradient, instead of following the normal, but now left behind, positive odor gradient. This, studied a posteriori, suggests a distinct adaptive behavior, specifically related to the environment. On other environments and with some of the 480 parameters differently valued, this strange behavior does not show up. It may seem strange, but a posteriori it appears as the best way to delay death. If all its bioenergy is lost in a two way pendular motion among both sides of the place of maximum odor, no other fate happens.

    6. Afterwards, with the obstacle left at the side, the bug's chemical sensors at both antennae activate the FO neuron and now the behavior is 01110. The bug, with SC firing, searches for food with his pair of antennae odor sensors.

    d.4. RANKING OF THE 2,3,4 and 5 TERM INTERACTIONS WITH AND WITHOUT STATISTICAL SIGNIFICANCE

    1. Here is the list of the findings, discarding the principal linear effects:

    TABLE WITH INDEX OF SIGNIFICANCE

    It shows the six principal non linear components of a behavioral cascade, three of them triple interactions (less probable a priori) and three double interactions.

    1 x2x4 76 included significant
    2 x1x2 70    
    3 x2x4x5 68    
    4.5 x1x3x4 67    
    4.5 x1x2x3 67    
    6 x4x5 67    
    7 x1x5 66 excluded not significant
    8 x2x3 65 excluded  
    9.5 x1x4x5 64 excluded  
    9.5 x1x2x4 64 excluded  
    11.5 x2x3x5 63 excluded  
    11.5 x3x4 63 excluded  

    The highest four-term interaction gives an index of 59 (excluded) and the only five-term one, gives 57 (excluded)

    2. The 6 main non-linear interactions are studied in Fig. 4 to 9. There are at the top of the non-linear interactions list. The figures show the interactions opened, so as to reveal in which sense they were statistically significant.

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