As discussed elesewhere (Chino, 2019a, 2020a,b,c), increasing attention has been paid to mutual interactions among
objects, especially in the medical and biological literature recently (Imai et al., 2014; Park & Greenberg, 2005;
Sato et al., 2002; Tian et al., 2016; Vega et al., 2013; Yamada et al., 2000). Interactions among objects in the
literature are generally asymmetric in contrast to those in the physical world. For example, Imai et al.
(2014) report biosynthetic pathways of nicotinamide adenine dinucleotide (NAD^{+}). Such a pathway can be
converted into an asymmetric matrix, elements of which are binary, since it can be expressed as a certain directed
graph (digraph) in graph theory (e.g., Bang-Jensen & Guttin, 2007; Christofides, 1975). In quorum sensing, some
bacteria secrete a signaling molecule called autoinducer to their host environment and detect their number, and if
it reaches a threshold they respond again to the environment by secreting some special substance (e.g., Parsek &
Greenberg, 2005; Vega et al., 2013). Tian et al. (2016) studies the midbrain dopamine system, in which dopamine
neurons in the ventral tegmental area (VTA) are thought to compute reward prediction error (RPE) (e.g., Schultz et
al., 1997). They demonstrate that even simple arithmetic computations such as RPE are not localized in specific
brain areas but, rather, are distributed across multiple nodes in a global brain network. Such a network might
also be described by a complicated digraph whose corresponding weight matrix is generally asymmetric.
Asymmetry can be observed in the other literature such as in the social and behavioral sciences (e.g., Chino,
2012). Close (2000) summarizes various asymmetric phenomena in the various disciplines of science and discusses
the meaning of asymmetry. Chino (2020a) analyzes the trade imbalance data between 4 nations using HFM which was
proposed by Chino and Shiraiwa (1993). Chino (1978) analyzes a similar trade data between 10 nations and depicts
their asymmetric relations graphically using one of the asymmetric multidimensional scaling (asymmetric MDS) methods
in psychometrics developed by the author. Asymmetry can be analyzed using hypothesized asymmetric matrices in some
literature. For example, Sato et al. (2002) assume a hypothetical asymmetric matrix in investigating the problem of
learning to play the game of rock-paper-scissors based on the theory of games and the notion of evolutionally stable
strategy ESS introduced by Maynard and Price (1973).
In response to such a great deal of attention, Chino Institute for the Studies of
Asymmetry and Chaos (abbreviated as Chino ISAC) was established in 2020. Our mission is twofold. One is to develop
mathematical theories and statistical methods for the analysis of
asymmetric data which are observed ubiquitously as asymmetric similarity matrices (abbreviated as ASMs) among
objects in the various disciplines of sciences varying from the social and behavioral sciences to natural sciences.
For example, one-sided love and hate among members of any informal group constitute such an ASM in psychology.
Amount of migration from one region to another gives rise to ASMs in geography. Trade imbalance forms another
example. We may observe various pathways among voxels of neurons, biosynthetic pathways of nicotinamide adenine
dinucleotide in research laboratories (e.g., Imai & Guarente,2014). Sometimes, ASMs are not observed but
hypothesized. For example, payoff matrices hypothesized in the game of rock-paper-scissors are examples of ASM's
(e.g., Sato et al., 2002).
In developing these theories and methods, it will be appropriate and natural in general
to distinguish between the holistic structure and the dynamics among objects, although in the
relativity theory it is known that the gravity exerted on stars determines their space-time structure (Einstein, A.,
1916). One of the promising theories and methods for the analysis of the former might be to utilize the asymmetric
multidimensional scaling (abbreviated as asymmetric MDS) developed in psychometrics (e.g., Chino, 2012; Cox & Cox,
2001; Saburi & Chino, 2008), especially the Hermitian Form Model (abbreviated as HFM) by Chino and Shiraiwa (1993).
According to the Chino-Shiraiwa theorem proved in that paper, objects can be embedded in a finite-dimensional Hilbert
space under a mild condition. As regards the manual of HFM, see, for example, Chino (2020b). As for the relation
between the Hilbert space in HFM and that in quantum mechanics, see Chino (2020c). As regards the analysis of the
latter, we may utilize dynamical system theories developed in mathematics, especially complex dynamical system
theories (e.g., Alexander, 1994; Milner, 2000; Ueda et al., 1995).
The other mission is to apply our theories and methods to various ASM's, and is to show their effectiveness.
We shall attach MATLAB codes for these methods.
Alexander, D. S. (1994). A History of Complex Dynamics - From Schroeder to Fatou and Julia.
Wiesbaden: Vieweg.
Bang-Jensen, J. & Guttin, G. (2007) Digraphs - Theory, Algorithms and Applications. New York:
Springer Verlag.
Chino, N. (2020c). Hermitian symmetry in Hilbert space - Its applications to
some asymmetric phenomena. Natural Science, 12, 221-236.
Chino, N. (2020b). How to use the Hermitian form model for asymmetric MDS.
In T. Imaizumi, A. Nakayama, and S. Yokoyama (Eds), Advanced Studies in
Behaviometrics and Data Science, Essays in Honor of Akinori Okada (pp. 19-41).
Tokyo: Springer.
Chino, N. (2020a).
Psychological and physical science, today and tomorrow (2).
Journal of the Institute for Psychological and Physical Science, 12,
1-11. (in Japanese with English abstract)
Chino, N. (2019a).
Psychological and physical science, today and tomorrow (1).
Bulletin of The Faculty of Psychological & Physical Science of Aichi Gakuin
University, 15 31-39. (in Japanese with English
abstract)
Chino, N. (2012). A brief survey of asymmetric MDS and some open problems. Behaviormetrika39,127-165.
Chino, N. & Shiraiwa, K. (1993). Geometrical structures of some non-distance models for
asymmetric MDS. Behaviormetrika, 20, 35-47.
Christofides, N. (1975). Graph Theory - An Algorithmic Approach. New York: Academic Press.
Close, F. (2000). Lucifer's Legacy: The Meaning of Asymmetry. Oxford University Press, Oxford.
Cox, T. F., & Cox, M. A. A. (2001). Multidimensional Scaling, 2nd ed., London: Chapman &
Hall/CRC.
Einstein, A. (1916). Die Grundlage der allgemeinen Relatititaetstheorie [The foundation of the generalized
theory of relativity]. Annalen der Physik, 49, 284-539, translated by S. N. Bose,
https://en.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity.
Guckenheimer, J., & Holmes, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations
of Vector Fields. New York: Springer-Verlag.
Imai, S. & Guarente, L. (2014). NAD+ and sirtuins in aging and disease. Trends in Cell Biology,
24, 464-471.
Maynard S., and Price, G. R. (1973). The logic of animal conflict. Nature, 246, 15-18.
Milnor, J. (2000). Dynamics in One Complex Variable, Introductory Lectures, 2nd ed.,
Wiebaden: Wieweg.
Parsek, M. R. and Greenberg, E. P. (2005). Sociomicrobiology: the Connections between Quorum Sensing and
Biofilms. Trends in Microbiology, 13, 27-33.
Saburi, S., & Chino, N. (2008). A maximum likelihood method for an asymmetric MDS model. Computational
Statistics and Data Analysis, 52, 4673-4684.
Sato, Yl, Akiyama, E., & Farmer, J. D. (2002). Chaos in learning a simple two-person game. Proceedings
of the Natural Academy of Science of the United States of Amerika, 99, 4748-4751.
Schultz, W., Dayan, P., and Montague, P. R. (1997). A Neural Substrate of Prediction and Reward. Science,
275, 1593-1599.
Tian, Ju, Huang, R., Osakada, F., Kobak, D., Machens, C. K., Callaway, E. M., Uchida, H., and Watanabe, M.
(2016) Distributed and Mixed Information in Monosynaptic Inputs to Dopamine Neurons. Neuron,
91,1-16.
Ueda, T., Taniguchi, M., & Morozawa, S. (1995). Introduction to Complex Dynamical System -
Fractal and Complex Analysis, Tokyo: Baihukan. (in Japanese)
Vega, N. M., Allison, K. R., Samuels, A. N., Klempner, M. S., and Collins, J. J. (2013) Salmonella
Typhimurium intercepts Escherichia Coli Signaling to Enhance Antibiotic Tolerance. Proceedings of the
National Academy of Sciences, 110, 14420-14425.
Yamada, H., Toth, A., and Nakagaki, T. (2000) Intelligence: Maze-solving by an Amoeboid Organism.
Nature, 407, 470.
Dr. (Educational Psychology)
Emeritus Professor of Aichi Gakuin University
E-mail Address
chino@dpc.agu.ac.jp
Education
Mar 1970 BA in Educational Psycholgy, Nagoya University
Mar 1972 MA in Educational Psychology, Nagoya University
Nov 1994 PhD in Educational Psycholgy, Nagoya University
Chino, N. (2020b).
Hermitian symmetry in Hilbert space - Its applications to
some asymmetric phenomena. Natural Science, 12, 221-236.
Chino, N. (2020a). How to use the Hermitian form model for asymmetric MDS.
In T. Imaizumi, A. Nakayama, and S. Yokoyama (Eds), Advanced Studies in
Behaviometrics and Data Science, Essays in Honor of Akinori Okada (pp. 19-41).
Tokyo: Springer.
Chino, N. (2012).
A brief survey of asymmetric MDS and some open problems.
Behaviormetrika,39,127-165.
Ohsuka, K., Chino, N., Nakagaki, H., Kataoka, I., Oshida, Y., Ohsawa, I., &
Sato, Y. (2009). Analysis of risk factors for dental caries in infants:
a comparison between urban and rural areas. Environmental Health and
Preventive Medicine, 14, 103-110.
Chino, N. (2008). Tests for symmetry in asymmetric MDS. In Shigemasu, K., Okada, A.,
Imaizumi, T., and Hoshino, T. (Eds.) New Trends in Psychometrics Tokyo:
Universal Academy Press.
Saburi, S. and Chino, N. (2008). A maximum likelihood method for an
asymmetric MDS model. Computational Statistics and Data Analysis,
52, 4673-4684.
Chino, N. (2003). Complex difference system models for the analysis
of asymmetry. In Yanai, H., Okada, A., Shigemasu, K., Kano, Y.,
& Meulman, J. J. (Eds.), New Developments in Psychometrics
(pp. 479-486). Tokyo: Springer-Verlag.
Chino, N. (2002). Complex space models for the analysis of asymmetry.
In S. Nishisato, Y. Baba, H. Bozdogan, & K. Kanefuji (Eds.),
Measurement and multivariate analysis (pp. 107-114).
Tokyo: Springer-Verlag.
Chino, N. and Shiraiwa, K.
(1993). Geometrical structures of some non-distance models for
asymmetric MDS. Behaviormetrika, 20, 35-47.
Chino, N. and Nakagawa, M.
(1990). A bifurcation model of change in group structure. The
Japanese Journal of Experimental Social Psychology, 29, No.3,
25-38.
Chino, N. (1990).
A generalized inner product model for the analysis of asymmetry.
Behaviormetrika. 27, 25-46.
Chino, N. (2020).
Psychological and physical science, today and tomorrow (2).
Journal of the Institute for Psychological and Physical Science, 12,
1-11. (in Japanese with English abstract)
Chino, N. (2019a).
Psychological and physical science, today and tomorrow (1).
Bulletin of The Faculty of Psychological & Physical Science of Aichi Gakuin
University, 15 31-39. (in Japanese with English
abstract)
Chino, N. (2019b). An elementary theory of a dynamic weighted digraph (2).
Journal of the Institute for The Faculty of Psychological and Physical Science
of Aichi Gakuin University, 11, 1-7.
Chino, N. (2018a). An elementary theory of a dynamic weighted digraph (1).
Bulletin of The Faculty of Psychological & Physical Science of Aichi
Gakuin University, 14, 23-31.
Chino, N. (2018b). Dynamical scenarios of changes in asymmetric relationships
over time (2). Journal of the Institute for The Faculty of Psychological and
Physical Science of Aichi Gakuin University, 10, 7-14.
Chino, N. (2017). Dynamical
scenarios of changes in asymmetric relationships over time (1).Bulletin
of The Faculty of Psychological & Physical Science of Aichi Gakuin
University, 13, 23-31.
Chino, N. (2011). Asymmetric Multidimentional
Scaling - 1.Introduction. Journal of the Institute for Psychological and
Physical Science, 3, 101-107.
Chino, N. & Saburi, S.(2010).
Controlling the two kinds of error rate in selecting an appropriate asymmetric
MDS model. Journal of the Institute for Psychological and
Physical Science, 2, 37-42.
Chino, N. (2005).
Abnormal behaviors of members predicted by a complex difference system
model. Bulletin of The Faculty of Psychological & Physical
Science of Aichi Gakuin University, 1, 69-73.
Chino, N. (2000). Complex difference
system models of social interaction. - (1) Preliminary considerations
and a simulation study.
Bulletin of The Faculty of Letters of Aichi Gakuin University,
30, 43-53.
Chino, N. (1999). EFASID - an
asymmetric MDS for interval data.
Bulletin of The Faculty of Letters of Aichi Gakuin University,
29, 25-34.
Chino, N. (1998). Hilbert space theory
in psychology (1) - Basic concepts and possible applications.
Bulletin of The Faculty of Letters of Aichi Gakuin University,
28, 45-65.
Chino, N. (1995). The continuing problems in applying ANOVA, MANOVA,
GMANOVA to repeated measures design data in psychology and education.
Bulletin of the Faculty of Letters of Aichi Gakuin University,
25, 71-96. (in Japanese with English
abstract)
Chino, N. (1994). A critical review on and around sphericity tests.
Bulletin of the Faculty of Letters of Aichi Gakuin University,
24, 103-119. (in Japanese with English
abstract)
Chino, N. (1993). An overview of repeated measures designs. Bulletin
of the Faculty of Letters of Aichi Gakuin University, 23,
223-236. (in Japanese)
Chino, N. (1992). Family of scalar
product models. In T. Saito (Ed.), Data Analyses of Asymmetrical
Relationships (pp.8-28). Hokkaido Behavioral Science Report,
Series M, No. 20.
Chino, N. (2016).
A general non-Newtonian n-body problem and dynamical scenarios of
solutions. Handout presented at the 31th International Congress of
Psychology, Yokohama, Japan.
Chino, N. (2014a). A
Hilbert state space model for the formation and dissolution of affinities
among members in informal groups. Supplement of the paper presented
at the workshop on The Problem Solving through the Applications of
Mathematics to Human Behaviors by the aid of The Ministry of Education,
Culture, Sports, Science and Technology in Japan (pp.1-24).
Chino, N. (2014b). A general non-Newtonian n-body problem and dynamical
scenarios of solutions. Proceedings of the 42th annual meeting of The
Behaviormetric Society of Japan (pp.48-51). Tokyo, Japan. Chino, N. (2014b).
A general non-Newtonian n-body problem and dynamical scenarios of solutions.
Handout presented at the 42th annual meeting of The Behaviormetric
Society of Japan, September 3, Sendai, Japan. (partly in Japanese)
Chino, N. (2006).
Asymmetric multidimensional scaling and related topics. Invited
lecture at the Weierstrass Institute for Applied Analysis and
Stochastics. Berlin, Germany.
(Additional figures
and tables)
Chino, N., & Saburi, S. (2006). Tests of symmetry in asymmetric MDS.
Paper presented at the 2nd German Japan Symposium on Classification
- Advances in data analysis and related new techniques &
applications. Berlin, Germany.
Saburi, S., & Chino, N. (2005). A maximum likelihood method for
asymmetric MDS (2). Proceedings of the 33rd annual meeting of The
Behaviormetric Society of Japan (pp.404-407). Nagaoka, Japan.
Chino, N. (2004). Behaviors of
members predicted by a special case of a complex difference system
model. Proceedings of the 32nd annual meeting of The Behaviormetric
Society of Japan (pp.256-259). Yokohama, Japan.
Saburi, S., and Chino, N.
(2004). A maximum likelihood method for asymmetric MDS.
Proceedings of the 32th annual meeting of The Behaviormetric Society
of Japan (pp.24-27). Yokohama, Japan.
Chino, N. (2000). Complex space models for the analysis of asymmetry.
Paper to be presented at the International Conference on Measurement
and Multivariate Analysis. Banff, Canada.
Chino, N. (1999a). A Hermitian form asymmetric MDS for interval datta.
Proceedings of the 27th annual meeting of The Behaviormetric Society
of Japan (pp. 325-328). Kurashiki, Japan.
Chino, N. (1999b). Implications of HFM for the analysis of asymmetry.
Proceedings of the 27th annual meeting of The Behaviormetric Society
of Japan (pp. 329-332). Kurashiki, Japan.
Chino, N. (1998). Hilbert space theory
in psychology (1) - Basic concepts and possible applications.
Bulletin of The Faculty of Letters of Aichi Gakuin University,
28, (in print). Paper presented at a workshop of the 62th
annual meeting of The Japanese Psychological Association. Tokyo.
Japan.
Chino, N., and Yoshino, R. (1998). Relation between HFM and Sato's
asymmetric Minkowski metric model. Proceedings of the 26th annual
meeting of The Behaviormetric Society of Japan (pp. 405-408). Tokyo,
Japan.
Chino, N., Grorud, A., and Yoshino, R. (1998). A revised version of
GSTATIS. Proceedings of the 26th annual meeting of The Behaviormetric
Society of Japan (pp. 409-412). Tokyo, Japan.
Chino, N., Grorud, A., and Yoshino, R. (1996). A complex analysis for
two-mode three-way asymmetric relational data.
Handout presented at the Fifth Conference of the International
Federation of Classification Societies, Kobe Japan.
Chino, N. (1995). Analysis of repeated measures design in education
and psychology (2). Proceedings of the 59th annual meeting of the
Japanese Psychological Association. Okinawa, Japan. 440.
(in Japanese).
Grorud, A., Chino, N., and Yoshino, R. (1995). A complex analysis
for three-way asymmetric relational data. Proceedings of the 23th
annual meeting of the Behaviormetric Society of Japan. 292-295.
Osaka, Japan.