Proceedings of the 2006 WSEAS Int. Conf. on Cellular & Molecular Biology, Biophysics & Bioengineering, Athens, Greece, July 14-16, 2006 (pp91-94)
Scale Free Dynamics Involved in the Ant Locomotion
KAZUMITSU HANAI1, MAMIKO OZAKI2, DAIGO YAMAUCHI2, YASUHIRO NAKATOMI3, CHIHIRO YOKOYAMA3 and KENJI FUKUI3

1Department

of Physics, Kyoto Prefectural University of Medicine, Taishogun, Kita-ku, Kyoto 603-8334; 2Kyoto Institute of Technology, Medicine, Kajii-cho 465, Kamigyo-ku, Kyoto 602-8566, JAPAN.
Department of Applied Biology, Faculty of Textile Science, Matsugasaki, Sakyo-ku, Kyoto 606-8585; 3Kyoto Prefectural University of
Abstract: Ant locomotor activity was carefully examined. We obtained the ordinates of the center of the gravity from sequential images of 1/30 sec intervals from a video movie of 160 min walk of an ant on a plain glass dish. The displacements during a unit time showed large variances and the distribution was different from the Gaussian statistics. The durations of move and rest state were determined from these ordinate data. The histogram for the occurrence of move events at specified duration was in accord with a Poisson statistics, and that of rest events was that of a power law.
Keywords: Ant, locomotor activity, move and rest events, Poisson distribution, power law

1 Introduction

Ants have developed a sophisticated chemical communication system that enables them to reject non-nestmate conspecifics and to accept nestmates [1, 2]. Recently there are considerable evidences that hydrocarbons from the cuticular surface are responsible for the nestmate recognition from behavioral [3, 4] and electrophysiological studies [4]. The hydrocarbons may affect many aspects of ant behaviors because the nestmate recognition is so crucial for their social lives [1]. For example, the hydrocarbons may play a role as a marking substance on their journey for the foods or other useful objects in the field [5]. On the way of detailed analyses of the effect of the hydrocarbons on the locomotor activities [6], we have noticed a simple rule on the ant locomotion, that is, the histogram of the occurrence of duration of the moving phase is consistent with a Poisson process and that of stop phase is consistent with a power law.
boxes (20x30x5 cm3). An ant walked freely on a glass dish of 6 cm diameter, which had been rinsed and wiped with n-hexane to clean possible hydrocarbons which might affect the ant behavior [4]. The activity was recorded by a digital video camera (DCR-TRV70K, Sony, Tokyo, Japan) for 160 min (two 80 min mini DV tapes), then the images were imported into a computer, Power Macintosh G5 (Apple, Qupertino, Cal.) as
movie files. The movie was converted into sequential image files (TIFF file format) at a rate 29.97 frames per sec with use of Quick Time Player. We got the ordinates of the center of gravity from the images after extracting the target animal images in each frame with use of glana on Linux, a program developed by ourselves with the C language [6]. The program discriminated the target image from the background and automatically removed the background from the image frame. It extracted the target image precisely making use of the difference in brightness variances between the background and the target image. Though the differences of the brightness levels of the target image and that of the background is large in the vicinity

2 Materials and Methods

Recording the locomotor activity: the carpenter ants, Camponotus japonicus were collected from the local field and kept in the laboratory until experiments by feeding on 20% sucrose and water in the plastic
A Fig. 1A Ant, Camponotus japonicus, on a plain dish of 6 cm diameter.

Fig. 1B

Track of the ant during first 10 min of walk. The outer dashed circle is the border of the dish.
of the target, some parts of the background may be of similar brightness levels to the target image. Such places of the background can be discriminated by the variances of the brightness levels at each pixel of the frame, which were calculated at every pixels for 10 images at different time. The variance of the brightness of the background, where the ant was not present, was small, even though the brightness itself varied considerably because of the presence of a dish or other things. On the other hand, the pixels occupied by the ant exhibited the large variance in the brightness because the ant moved from a location to another when several images at different times are averaged. But it would be easy to make the variance of the brightness level to be small by counterchanging the images at different time in which the ant occupied different pixels. Then correct background was estimated by extending regions where the variance of the brightness levels were small. The threshold value to make binary images was determined for each image by an algorism making use of lateral inhibition (the Gaussian filter) to sharpen the border of the target image to make the detection of the border more easy [7]. The locally minimum brightness levels on the border which was stressed after the image processing, were determined as candidates for the threshold value. The most suitable level was selected as a threshold to make binary image, which gave the most similar target image to the actual target from the image frame. Glana was operated on a Fedora Core 4-installed personal computer (Precision 450, Dell, Round Rock, TX). Then we had sequential ordinate data of the center of gravity of the animal for 2.5 hours at a time resolution of 1/30 secs. Though they are not utilized in the present study, glana calculates other image quantities such as image moments [8]. Figure 1 shows a trace of an ant during first 10 min after walk Data processing: The ordinate data of the center of gravity were processed with perl scripts. The duration of move and rest state, which were calculated from the ant positions in every frames, were analyzed as follows: If the distance between the adjacent two positions < 0.8 pixels, the ant was considered to be in the rest state.

On the contrary, if the distance > 0.8 pixels, the ant was in the state of move. The distance of 0.8 pixels is far smaller than the image size of an ant (usually pixels). Small change in the ant positions may be due to an artifact of a subtle threshold change to calculate the binary image. All events of the specified duration during the whole observation period were counted. Then the distribution histogram was fitted to an exponential function or power function after linear conversion by the logarithmic conversion.

3 Results

Our glana software made it possible to obtain the binary images of the target ant with high precision automatically and the position ordinates of the center of gravity and other image quantities from more than 99 % of the large amount of the input image frames in a relatively short time. It processed 18000 image frames in less than 3 hr. The velocity data were easily calculated from the ant positions, because the position data were obtained at the same time interval. The velocity of the ant during walk varied in a short time and its variance was large. Figure 2 shows that the mean displacements and the standard deviations in 0.1 sec (3 frames, average was calculated adjacent 50 data) during the whole observing time of the ant. The histogram of the same data shows that the events of the smaller displacements occur more often, and its distribution is not Gaussian (Fig. 3). The mean value of the displacements in a time interval does not make sense in this situation. As the displacements in a unit time appeared to be of large variance, we examined to analyze the position data after converting them to move and rest events. If the displacement between adjacent times is > 0.8 pixels, the ant is defined to be in the move state: On the contrary, the displacement < 0.8 pixels, in the rest state. The threshold value 0.8 itself was not important. Similar results were obtained even with other threshold values. Then the whole

displacements (mm)

counts

Time (sec)

Fig. 2 Mean displacements during 0.1 sec as a function of time. The displacements are averaged in the adjacent 50 blocks. Bar is the SD.

Fig. 3

Displacement histogram. The occurrence of the displacements during 0.1 sec is plotted. The distribution is not a Gaussian, rather in accord with an exponential curve.
sequential position data are converted to sequential event (move and rest) data. Duration of move and rest state was obtained from these data by checking the events sequentially, and occurrence of the specified duration of the specified state was counted. The event occurrence data obtained by the above procedure were plotted after conversion to cumulative data of the events. The logarithm of the cumulative occurrences of the move duration showed linear relationships with duration, that is, the move events showed the Poisson distribution (Fig. 4). There appear several Poisson processes with different time constants because the data show steeper line in the shorter time region. The rate constant for the slower process is estimated to be 1.15 sec-1 from the linear portion of the graph. As for the rest state, the logarithm of the cumulative occurrences of the rest duration showed linear relationships with the logarithms of the duration, that is, the rest events agreed with a power law (Fig. 5). The exponent is calculated to be 0.93.

gradient in the short time range. On the contrary, the distribution of rest event duration appears to agree with a power law. Similar rule was also observed for the mouse locomotion, suggesting that this may be due to a common mechanism in a wide range of animals (unpublished observation). The Poisson statistics of the move events suggests that a few steps with constant rate processes are involved in the control of the moving state of the locomotion. On the contrary, duration histogram of the rest events appeared to be more appropriate to express a nonPoisson statistics. It is noted that at the time when the rest state is over, the animal start to move motivated by something internal or external of which we do not know the exact reason. Human activities such as e-mail communications or letter correspondences have been reported to follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity [9, 10]. In e-mail communication, exponents about 1 (with exponential decay [11, 12]) or 1.5 were reported for the event probability. This is considerably smaller than our observed value 0.93 for the cumulative occurrence of the duration of the rest state, because the exponent value for the cumulative event probability is expected to be smaller by 1 than that for the noncumulative occurrence distribution. Barabasi has proposed a priority model to explain their exponents [9-12]. Poisson statistics and power laws are seen in many fields such as physics, biology and sociology, and they are often related to complex networks [13, 14]. The nervous system is one of such complex networks, and likely to be involved in the control of locomotion. Considering that the power law in the rest state of the locomotion is seen in broad range of animals, it is conceivable that this trait is related to the control system of the locomotion. Then

4 Discussion

The velocities (the displacement in a unit time) calculated from the position data of the ant locomotion showed large variance. This is sharp contrast to movement of an artificial vehicle that moves smoothly at a constant mean velocity with small variance. The distribution of displacements in a unit time appeared to be like an exponential curve, which was different from a Gaussian distribution expected for the mean constant velocity. When we paid attention to the duration of the move and rest state in the locomotion, we observed a remarkable rule in contrast to large variation of a displacement in a unit time. The distribution of move event duration appears to be that of a Poisson statistics. There appear to be several Poisson processes because of the steeper

log_frames

log_log_events
duration (frames) Fig. 4 Cumulative occurrence of move events. The plot of the log cumulative occurrences vs duration (arrows indicate the relevant horizontal axes, respectively) showed a linear portion (the dashed line) in the tail, showing that the move events are in accord with the Poisson statistics. The steeper gradient in the shorter time region suggests several Poisson processes.

log_cum_events

duration (frames) Fig. 5 Cumulative occurrence of rest events is plotted similarly to the move events of Fig. 4. For the rest events, the plot of the log cumulative occurrences vs log duration (arrows indicate the relevant horizontal axes, respectively) shows a linear line (dashed line) in the almost all range, showing this is in accord with a power law distribution.
it would be interesting to analyze the locomotion in relation to the nervous network. Neuronal networks of Caenorhabditis elegance [15] or that of the vertebrate brainstem reticular formation [16] have been reported to be small-world type. Even a simple topology of neuronal networks may produce complex dynamic behaviors [17-19]. Current our observations may be understood as one of such complex dynamic behaviors of a simple neuronal network connection.
[7] Tsukata, A., Aikawa, H., Sasaki, K., Hanai, K.: Selection method of the threshold to make binary image for Hydra. The Transactions of the Institute of Electronics, Information and Communication Engineers J83-D-II, 1841-1845, 2000 [8] i, Y.: Reforming the theory of invariant moments for pattern L recognition. Pattern Recognition 25, 723-730, 1992 [9] Barabasi, A.-L.; Origin of bursts and heavy tails in human dynamics. Nature 435, 207-211, 2005 [10] Oliveira, J.G., Barabsi, A.-L.: Darwin and Einstein correspondence patterns. Nature London 437, 1251, 2005 [11] Vazquez, A.: Exact results for the Barabasi model of human dynamics. Phys. Rev. Lett. 95, 248701-1-4, 2005 [12] Vzquez, A., Oliveira, J.G., Dezs, Z., Goh, K.-I., Kondor, I., Barabsi,A.-L.: Modeling bursts and heavy tails in human dynamics Phys. Rev. E 73, 036127, 2006 [13] Watts, D.J., Strogatz, S.H.; Collective dynamics of small-world networks. Nature 393, 440-442, 1998 [14] Barabasi, A.-L., Albert, R.; Emergence of Scaling in Random Networks. Science 286, 509-512, 1999 [15] Amaral, L.A.N., Scala, A., Barthelemy, M., Stanley, H.E.: Classes of small-world networks PNAS 97: 11149-11152, 2000 [16] Humphries, M.D., Gurney, K., Prescott, T.J.: The brainstem reticular formation is a small-world, not scale-free, network. Proc. Roy. Acad. Sci. B 273: 503-511, 2006 [17] Lago-Fermandez, L. F., Huerta, R., Corbacho, F., Siguenza J. A.; Fast response and temporal coherent oscillations in small-world networks. Phys. Rev. Lett. 84, 2758-2761, 2000 [18] Roxin A, Riecke H, Solla S.A.: Self-sustained activity in a small-world net work of excitable neurons. Phys Rev Lett. 2004 92:198901 [19] Roxin A, Brunel N, Hansel D.: Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks.

Acknowledgements

This work was supported by grants from KAKENHI 15570069 (K.H.) and 17207003 (M.O.).

References:

[1] Vander Meer, R.K., Morel L.: Nestmate recognition in ants. In: Vander Meer, R.K., Breed, M., Winston, M., Epselie, K.E. (eds) Pheromone communication in social insects. Westview, Boulder, Colo., pp 79103, 1998 [2] Obin, M.S., Vander Meer, R.K.: Mechanism of templatelabel matching in fire ant, Solenopsis invicta Buren, nestmate recognition. Anim. Behav. 38, 430-435, 1989 [3] Lahav, S., Soroker, V., Hefetz, Z., Vander Meer, R.K.: Direct behavioral evidence for hydrocarbons as ant recognition discriminators. Naturwissenschaften 86, 246-249, 1999 [4] Ozaki, M., Wada-Katsumata, A., Fujikawa, K., Iwasaki, M., Yokohari, F., Satoji, Y., Nisimura, T., Yamaoka, R.: Ant nestmate and non-nestmate discrimination by a chemosensory sensillum. Science 309: 311-314, 2005 [5] Yamaoka, R.: Chemical approach to understanding interactions among organisms. Physiolo. Ecol. Jpn. 27, [6] Hanai, K. Nakagawa, E., Ohashi, O., Ozaki, M., Yamaoka, R.: Video analysis of ant behavior in the presence of colony discrimination substance. The Japanese Journal of Taste and Smell Research, 10: 577 580, 2003

PR Log - Global Press Release Distribution
DCR-TRV740 Battery, Sony DCR-TRV740 Battery, Sony DCR-TRV740 Camcorder Battery
By batteryreplacement Dated: Aug 07, 2010
provides DCR-TRV740 Battery, Sony Camcorder Battery. We carry huge range of Sony replacement batteries, chargers and power adapter at very competitive price to save you money. Sony dcr-trv740 battery replacement (li-polymer 1250mah) Sony dcr-trv740 battery Model no.: dcr-trv740 Battery type: li-polymer Battery volt: 7.2v Battery capacity: 1250mah Battery color: dark grey Battery weight: 105g Battery dimension: 55.50x38.60x20.50mm Battery category: sony camcorder battery This info comes from: http:// www.battery-replacement.com/sony-dcr-trv740-battery-pack-2788-56090.html This camcorder battery can replace the following part numbers: Sony Np-fm30 Np-fm50 Np-fm51 Np-qm50 Np-qm51 This camcorder battery is also compatible with the following models: Sony Ccd-tr108 Ccd-tr208 Ccd-tr408 Ccd-tr748 Ccd-tr748e Ccd-trv106k Ccd-trv107 Ccd-trv108 Ccd-trv108e Ccd-trv116 Ccd-trv118 Ccd-trv126 Ccd-trv128 Ccd-trv138

Page 1/6

Ccd-trv208 Ccd-trv208e Ccd-trv218 Ccd-trv218e Ccd-trv228 Ccd-trv228e Ccd-trv238 Ccd-trv238e Ccd-trv308 Ccd-trv318 Ccd-trv328 Ccd-trv338 Ccd-trv408 Ccd-trv408e Ccd-trv418 Ccd-trv418e Ccd-trv428 Ccd-trv428e Ccd-trv438e Ccd-trv608 Ccd-trv730 Ccd-trv740 Ccd-trv96k Cyber-shot dsc-f707 Cyber-shot dsc-f717 Cyber-shot dsc-f828 Cyber-shot dsc-r1 Cyber-shot dsc-s30 Cyber-shot dsc-s50 Cyber-shot dsc-s70 Cyber-shot dsc-s75 Cyber-shot dsc-s85 Dcr-dvd100 Dcr-dvd100e Dcr-dvd101 Dcr-dvd101e Dcr-dvd200 Dcr-dvd200e Dcr-dvd201 Dcr-dvd201e Dcr-dvd300 Dcr-dvd301 Dcr-dvd91 Dcr-dvd91e Dcr-hc1 Dcr-hc14 Dcr-hc14e Dcr-hc15 Dcr-hc15e Dcr-hc88

Page 2/6

Dcr-pc100 Dcr-pc101 Dcr-pc101e Dcr-pc101k Dcr-pc103 Dcr-pc103e Dcr-pc104 Dcr-pc104e Dcr-pc105 Dcr-pc105e Dcr-pc105k Dcr-pc110 Dcr-pc110e Dcr-pc115 Dcr-pc115e Dcr-pc120 Dcr-pc120bt Dcr-pc120e Dcr-pc300k Dcr-pc330 Dcr-pc330e Dcr-pc6 Dcr-pc6e Dcr-pc8 Dcr-pc8e Dcr-pc9 Dcr-pc9e Dcr-trv10 Dcr-trv10e Dcr-trv11 Dcr-trv116 Dcr-trv116e Dcr-trv118e Dcr-trv11e Dcr-trv12e Dcr-trv14 Dcr-trv140 Dcr-trv140e Dcr-trv140u Dcr-trv145 Dcr-trv145e Dcr-trv14e Dcr-trv15 Dcr-trv150 Dcr-trv15e Dcr-trv16 Dcr-trv16e Dcr-trv17 Dcr-trv17e Dcr-trv17k

Page 3/6

Dcr-trv18 Dcr-trv18e Dcr-trv18k Dcr-trv19 Dcr-trv19e Dcr-trv20 Dcr-trv20e Dcr-trv22 Dcr-trv22e Dcr-trv22k Dcr-trv230 Dcr-trv230e Dcr-trv235 Dcr-trv235e Dcr-trv238 Dcr-trv238e Dcr-trv239 Dcr-trv239e Dcr-trv24 Dcr-trv240 Dcr-trv240e Dcr-trv240k Dcr-trv245 Dcr-trv245e Dcr-trv24e Dcr-trv25 Dcr-trv250 Dcr-trv250e Dcr-trv255 Dcr-trv255e Dcr-trv25e Dcr-trv260 Dcr-trv265 Dcr-trv265e Dcr-trv27 Dcr-trv270e Dcr-trv27e Dcr-trv280 Dcr-trv285e Dcr-trv30 Dcr-trv300k Dcr-trv30e Dcr-trv325 Dcr-trv33 Dcr-trv330 Dcr-trv330e Dcr-trv33e Dcr-trv33k Dcr-trv340 Dcr-trv340e

Page 4/6

Dcr-trv345 Dcr-trv345e Dcr-trv350 Dcr-trv351 Dcr-trv355 Dcr-trv355e Dcr-trv360 Dcr-trv361 Dcr-trv38 Dcr-trv39 Dcr-trv40 Dcr-trv40e Dcr-trv430 Dcr-trv430e Dcr-trv460 Dcr-trv460e Dcr-trv480 Dcr-trv480e Dcr-trv50 Dcr-trv50e Dcr-trv530 Dcr-trv530e Dcr-trv6 Dcr-trv60 Dcr-trv60e Dcr-trv6e Dcr-trv70 Dcr-trv70k Dcr-trv725 Dcr-trv730 Dcr-trv730e Dcr-trv738 Dcr-trv738e Dcr-trv740 Dcr-trv740e Dcr-trv75 Dcr-trv75e Dcr-trv8 Dcr-trv80 Dcr-trv80e Dcr-trv828 Dcr-trv828e Dcr-trv830 Dcr-trv830e Dcr-trv840 Dcr-trv8k Dcr-trv940 Dcr-trv940e Dcr-trv950 Dcr-trv950e

Page 5/6

Dcr-tv480 Dsr-pdx10 Dsr-pdx10p Gv-d1000(video walkman) Hdr-hc1 Hdr-hc1&hvr-a1 Hdr-hc1e Hdr-sr1 Hdr-sr1e Hdr-ux1 Hdr-ux1e Hvl-irm(infrared light) Hvl-ml20m (underwater video light) Hvr-a1 Hvr-a1e Hvr-a1j Hvr-a1n Hvr-a1p Hvr-a1u Mvc-cd200 Mvc-cd250 Mvc-cd300 Mvc-cd350 Mvc-cd400 Mvc-cd500 We also stock many different capacity battery replacement for sony dcr-trv740 http://www.battery-replacement.com/sony-camcorder-battery/sony-dcr-trv740-battery-56090.html We also sale sony dcr-trv740 battery charger, you can look at it via the following link: http://www.battery-replacement.com/sony-battery-charger/sony-dcr-trv740-charger-62202.html ### We specialize in all kind of Battery Replacewment and Battery Charger, Power Adapter. Our store carry the most Replacement Battery cover Laptop Battery, Camcorder Battery, Digital Camera Battery, Power Tool Battery to fulfill need of the market.

Category Tags Email City/Town State/Province Zip Country Shopping sony camcorder battery Click to email author Fremont California 94538 United States

Page 6/6