Evolution and Time Horizons in an Agent Based Stock Market, Working Paper
This paper presents initial results from a new agent
based artificial stock market. The market is populated with
heterogeneous boundedly rational agents maximizing lifetime
utility. Heterogeneity is introduced through the agents'
perception of the past, or memory. They each view the market in
different ways in terms of how much past price data is useful for
decision making. Long horizon agents, using information from the
distant past, compete with short horizon agents in an evolutionary
struggle endogenously driving the price of an asset paying a risky
dividend. Selection removes agents with less wealth over time.
Trading strategies are determined by a common set of fixed rules
loosely modeling mutual fund managers, or investment newsletters.
The managers recommend a dynamic allocation between equity and
cash given past information. Managers also evolve over time, and
only survive when they have customers following their investment
advice. The selection of advisors allows for some pooling of
strategy information across traders. It also makes the ability to
trade an endogenous feature of the market since it is easier to
find someone to trade with when heterogeneity is larger and
strategy use is more diverse.
The market setup has a well defined homogeneous rational expectations equilibrium. It is shown that restricting strategies to be long horizon enables convergence to this equilibrium where agents agree on the appropriate pricing function, and trading volume goes to zero. Allowing a broad range of trader horizons to enter the market stops this convergence, and causes the market to converge to something that more closely resembles real markets with high trading volume, price volatility well above what it should be due to fundamentals, fat tailed return distributions, and persistence in both volume and volatility.
Experiments are performed to explore situations that might drive the market to the homogenous equilibrium. Implementing a transaction cost for changing strategies slows down the exploration of the individual agents enough for the market to converge. Also, seeding a market with a large number of long horizon agents initially can cause convergence to the equilibrium which then is relatively impervious to invasions of short horizon traders.
This framework suggests many further explorations both in calibrating time series, and in policy related examinations of the heterogeneous agent populations. Basically, it emphasizes the importance of learning about time and the relevance of how agents use past data in real financial markets.
- Evolution and Time Horizons in an Agent Based Stock Market, Blake LeBaron, Working Paper, Brandeis Univeristy, Rev. 4/00, (Contributed by the author)
Scalar Turbulence, Nature
Fluid turbulence is one of the problems that scientists
have been actively working on for more than a century and where
they agree that it still eludes a satisfactory theory. The
challenge is to predict the properties of a fluid flow knowing the
velocities of the fluid particles at every location of the flow.
The hope was that once this basic problem is solved then one could
also predict how things that move with the flow will change over
space and time. For instance the temperature of a volume of air
will be transported along with the wind. But we know that the
temperature distribution itself will influence the flow pattern of
air for instance in the form of thermals.
Shraiman and Siggia give a review of recent progress of "passive scalar" turbulence i.e. the more simple case where the transported quantity will not influence the flow patterns. Some of the most important examples are the spread of pollutants in air and water. While in non-turbulent spreading of pollutants one would expect that the concentration decreases smoothly with the distance from the source, the situation is much more complex in the case of turbulence: The spreading can be much more rapid and highly non-uniform or "intermittent" in both space and time. That means for instance that radioactive particles from a reactor accident could arrive at a distant location at a very short time and at a concentration that is much higher than what one would expect from simple, uniform diffusion assumptions.
The researchers point out that theoretical progress for scalar turbulence was possible even without the corresponding in progress in understanding the turbulent velocity field. One could show that probability distributions of concentration values in scalar turbulence have similar properties -such as "fat tails"- to those observed in financial markets.
Furthermore mathematical progress could be made by shifting from an Eulerian viewpoint (observation from the laboratory as reference system) to an Lagrangian perspective (the observation point moves along with the flow). Also it turned out that it was important to go beyond that traditional description of pair-wise correlations to "multi-point correlators".
These new theoretical insights together with the steady increase in available computational power give rise to hope that the understanding of turbulence fluid-flow will dramatically increase during this century even if the turbulence problem will not be "solved" in a traditional sense.
- Scalar Turbulence , Boris I. Shraiman And Eric D. Siggia, Nature 405, 639 - 646 (2000)
How Soft Is a Protein?, Science
The qualitative behavior of complex, non-linear systems
typically can be dramatically changed ("bifurcate") under very
small changes of intrinsic systems parameters. This parametric
sensitivity is different from the widely publicized "butterfly
effect" but maybe even more important for understanding and
eventually controlling complex systems. For large bio-molecules,
like DNA for instance, it is more and more realized that the
chemical composition does not play that a dominant role for
determining the functional outcome of the molecule. Other factors
like the molecule's shape and maybe vibrational states seem to
play a much more important role than originally anticipated. One
of the microscopic parameters that has a profound impact on both
the shape and vibrational properties is the "stiffness" (or
"softness") of the elastic components of the molecule. Zaccai
describes some new results how these parameters can be measured
with the help of neutron-scattering experiments.
Abstract: An effective environmental force constant is introduced to quantify the molecular resilience (or its opposite, "softness") of a protein structure and relate it to biological function and activity. Specific resilience-function relations were found in neutron-scattering experiments on purple membranes containing bacteriorhodopsin, the light-activated proton pump of halobacteria; the connection between resilience and stability is illustrated by a study of myoglobin in different environments. Important advantages of the neutron method are that it can characterize the dynamics of any type of biological sample--which need not be crystalline or monodisperse--and that it enables researchers to focus on the dynamics of specific parts of a complex structure with deuterium labeling.
- How Soft Is a Protein? A Protein Dynamics Force Constant Measured by Neutron Scattering, G. Zaccai, Science 2000 June 2; 288(5471): p. 1604-1607
Quantum Chaos for the Radially Vibrating Spherical Billiard, Chaos
The title of our project in general is "Quantum Chaos in
Vibrating Billiard Systems." This is an example of a phenomenon
known as semi-quantum chaos (genuinely chaotic behavior in a
system that consists of the coupling of a quantum system with a
classical one), which differs from the quantum chaos normally
studied (which some term 'quantized chaos' or 'quantum chaology')
that looks for quantum signatures of classical chaos, and usually
goes to the semi-classical or high quantum-number limits in this
analysis. (Martin Gutzwiller, in his well-known book, _Chaos in
Classical and Quantum Mechanics_ even writes that one must go to
one of these limits in order to obtain a meaningful study of
quantum chaos.) A nice thing about this my project is that---as
you'll see in the paper---this limit is not required here. One may
observed chaotic behavior even in some eigenstate superpositions
that include the ground state. In terms of applications, the most
promising one is as a toy model of quantum-well nanostructures.
Since I have begun working on this project, I have heard several
other people claim that quantum billiards are models for these
nanostructures, so that I believe there is _some_ credence to this
claim. (It is a toy model after all.)
This claim has been made for stationary billiards, and as quantum-well nanostructures do experience vibrations, perhaps this can help claim them a bit. The radially vibrating spherical billiard, for example, models quantum dots that are termed 'ballistic' to describe the Dirichlet boundary conditions. Despite this, the major import of this project is theoretical---as is true for nearly all studies of toy models.
- Quantum Chaos for the Radially Vibrating Spherical Billiard, Liboff, R. L., Porter, M.A., Chaos Vol. 10, No. 2: 366-370.
- See also: M.A. Porter's Research Website
Neural Synchrony And Perception of Surfaces, Nature
The last decade of the last millennium was
dedicated to the research about how the brain works. Maybe the
most important general principle that found increasing support
from a vast number of different experiments during that time was
that the brain does not work like a computer. Instead it seems to
learn to do what it does through the self-organized activation of
neuronal cell-assemblies. Singer's group was one of the first who
could experimentally observe in the brains of cats the
synchronized neuronal activity during visual perception of shapes.
Now they report a careful refinement of their original experiment where they produce composite patterns of lines with variable transparency. The result of this arrangement is that the apparent visual pattern can be continuously tuned so that the lines seem to belong to two different surfaces or to the same identical surface. This arrangement is important because it allows to keep the average activity of the neurons constant while the visual patterns make a transition between the two different perceptions. This observation rules out that neuronal activity or firing rate actually encodes the information about the nature of the observed surfaces. On the other hand, the synchronization between neurons that respond to the two different stripe patterns is only present when the transparency is tune so that a coherent surface is perceived. This clever experimental arrangement therefore provides further evidence that the timing of the neuronal spikes does indeed carry important information.
- Neural Synchrony Correlates With Surface Segregation Rules, Miguel Castelo-Branco, Rainer Goebel, Sergio Neuenschwander & Wolf Singer, Nature 405, 685 - 689 (2000)
Black Holes Shed Light On Galaxy Formation, Science Daily News
Excerpt: "Astronomers are concluding that
monstrous black holes weren't simply born big but instead grew on
a measured diet of gas and stars controlled by their host galaxies
in the formative years of the universe. These results, gleaned
from a NASA Hubble Space Telescope census of more than 30 galaxies
with its powerful "black hole hunting" spectrograph, are painting
a broad picture of a galaxy's evolution and its long and intimate
relationship with its giant central black hole.
Though much more analysis remains, an initial look at Hubble evidence favors the idea that titanic black holes did not precede a galaxy's birth but instead evolved with the galaxy by trapping an amazingly exact percentage (0.2 percent) of the mass of the bulbous hub of stars and gas in a galaxy.
This means that black holes in small galaxies went relatively undernourished, weighing in at a mere few million solar masses. Black holes in the centers of giant galaxies, some tipping the scale at over one billion solar masses, were so engorged with infalling gas they once blazed as quasars, the brightest objects in the cosmos.
The bottom line is that the final mass of a black hole is not primordial; it is determined during the galaxy formation process. "This supports the original theory of why black holes are important and how they got their masses. It suggests that the major events that made a galaxy and the ones that made its black hole shine as a quasar were the same events," says John Kormendy of the University of Texas at Austin. "These results are a catalyst that helps to tie together many lines of investigation." (…)
The results also explain why galaxies with small bulges, like our Milky Way, have diminutive central black holes of a few million solar masses, while giant elliptical galaxies house billion-solar-mass black holes, some still smoldering from their days as quasars. Disk galaxies without a central bulge of stars either have no black hole or have only tiny black holes that are well below Hubble's detection limit.
The findings are based on two types of Hubble observations. Several teams measured the black holes' masses by recording the whirling speeds of disks of gas trapped around the black holes, like water swirling around a drain. Other teams measured the motions of stars around the galaxies' hubs like a swarm of bees hovering around a beehive. The more massive the bulge, the greater the speed of the stars. (…) "
- Black Holes Shed Light On Galaxy Formation, Science Daily News, Posted 6/7/2000,
- See also: Space Telescope Science Institute
New Theory On The Mystery Of The Origin Of Life, Weizmann Institute/Science Daily
Excerpt: "One of the greatest mysteries, which
continuously fascinates many scientists worldwide, concerns the
way by which life emerged on primeval Earth. The accepted notion
is that prior to the appearance of living organisms, there was a
stage of chemical evolution, which involved selection within
inanimate chemical mixtures. This is thought to have eventually
led to the crucial moment, when self-replicating molecules arose.
As self-replication is a most fundamental characteristic of living
entities, such an event is often defined as the birth of life.
Self-replication of molecular systems is often viewed in the context of information content. Many scientists believe that life began with the spontaneous emergence of biopolymers, such as proteins or RNA, where information is stored in the sequence of chemical units. Experiments mimicking the conditions on Earth billions of years ago have shown how such chemical units, e.g. some of the building blocks of proteins and RNA, could appear spontaneously. Yet, the emergence of proteins or self-replicating RNA molecules remained enigmatic.
This started Prof. Doron Lancet of the Crown Human Genome Center in the Weizmann Institute of Science, and his students, Daniel Segre and Dafna Ben-Eli, on a journey leading to alternatives to proteins and RNA. They have developed a model, suggesting a new route for the origin of life, based on lipid molecules. This model is described in an article published in a recent issue of the Proceedings of the National Academy of Science, USA. (…)
The model proposed by Lancet and colleagues offers a solution. They surmise that early on, lipid-like compounds existed in a very large diversity of shapes and forms. They show mathematically that under such conditions, lipid assemblies could contain almost as much information as an RNA strand or a protein chain. Information would be stored in the assembly's composition, i.e. in the exact amount of each of its compounds, rather than in a sequence of molecular "beads" on a string. (…)
Thus, the authors argue, heterogeneous lipid assemblies may be thought of as having a "compositional genome". They further demonstrate how a droplet-like lipid assembly, when growing and splitting, could manifest a form of inheritance. Their computer simulations show how a compositional genome would be handed down with some fidelity to the offspring assemblies. A crucial aspect of the model is how such molecular inheritance is made possible. In present-day cells, the replication of information-containing DNA is facilitated by protein enzyme catalysts. In the early prebiological era, catalysis could be performed by the same lipid-like substances that carry the information. Molecules already present inside a droplet would function as a molecular selection committee, enhancing the rate of entry for some, and rejecting others. (…)"
- New Theory On The Mystery Of The Origin Of Life Proposed By Weizmann Institute Scientists, Science Daily, Posted 6/8/2000
- News Release Weizmann Institute
Searching For Genes In Complex Diseases, Clin Invest
Excerpt: "(...) Although positional cloning has
been highly successful in identifying the loci underlying
Mendelian diseases, it has been much less so for identifying genes
for common, complex disorders. The reason is that Mendelian
disorders are genetically simple: they feature a strong
correspondence between the presence of a predisposing genotype at
a single genetic locus and the phenotypic outcome. This
correspondence produces a strong linkage signal in families and
allows for localizing a disease gene by recombination events. The
more common familial but complex disorders involve numerous loci,
which may interact with each other to predispose to disease.
Because the total genetic effect is partitioned among several or
many loci, the correspondence between a predisposing genotype at
one such locus and the disease outcome is weaker, greatly reducing
the power of linkage analysis.
The power of linkage analysis to locate susceptibility loci for complex diseases is much greater in animal models than in humans, for a variety of reasons. First, inbred strains are used, which tends to reduce the genetic complexity and limit genetic effects to the loci that differentiate the original strains used in the breeding experiments. Second, by design, all matings are informative (e.g., all parents are heterozygous in an intercross). Third, all matings have the same phase (i.e., the genotypes at a presumed disease locus are known), and offspring from all matings can be combined into a single analysis. (...)
- Searching For Genes In Complex Diseases: Lessons From Systemic Lupus Erythematosus, Neil Risch, Clin Invest, June 2000, Volume 105, Number 11, 1503-1506
Heart Rate Analysis With Approximate Entropy And Sample Entropy, AJP Heart Online
Abstract: Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.
- Physiological Time-Series Analysis Using Approximate Entropy And Sample Entropy, J. S. Richman, J. R. Moorman, AJP Heart Online Vol. 278, Issue 6, H2039-H2049, June 2000
Entropies Of Binary Sequences In Heart Rhythms, AJP Heart Online
Abstract: Dynamic aspects of R-R intervals have often
been analyzed by means of linear and nonlinear measures. The goal
of this study was to analyze binary sequences, in which only the
dynamic information is retained, by means of two different aspects
of regularity. R-R interval sequences derived from 24-h
electrocardiogram (ECG) recordings of 118 healthy subjects were
converted to symbolic binary sequences that coded the beat-to-beat
increase or decrease in the R-R interval. Shannon entropy was used
to quantify the occurrence of short binary patterns (length N = 5)
in binary sequences derived from 10-min intervals. The regularity
of the short binary patterns was analyzed on the basis of
approximate entropy (ApEn). ApEn had a linear dependence on mean
R-R interval length, with increasing irregularity occurring at
longer R-R interval length. Shannon entropy of the same sequences
showed that the increase in irregularity is accompanied by a
decrease in occurrence of some patterns. Taken together, these
data indicate that irregular binary patterns are more probable
when the mean R-R interval increases. The use of surrogate data
confirmed a nonlinear component in the binary sequence. Analysis
of two consecutive 24-h ECG recordings for each subject
demonstrated good intraindividual reproducibility of the results.
In conclusion, quantification of binary sequences derived from ECG
recordings reveals properties that cannot be found using the full
information of R-R interval sequences.
- Entropies Of Short Binary Sequences In Heart Period Dynamics, D. Cysarz, H. Bettermann, P. van Leeuwen, AJP Heart Online Vol. 278, Issue 6, H2163-H2172, June 2000
Links & Snippets
1 Editor's Notes, #11.1
- There have been a number of inquiries about transcripts and copies of the video clips in Complexity Digest 2000.20. They were taken of the talks given at the 3rd International Conference on Complex Systems. We have a CD with the basic video clips but for full video coverage and proceedings please contact the conference organizer Yaneer Bar Yam.
- Reminder: During the conference we started taking a ballot about the most important topics in complexity for the coming century. Because of the very positive response we want to continue this ballot electronically until June 15, 2000. Please download the form from our website and e-mail your votes to editor@comdig.org. The winners who predict the topic that will be elected as most important will receive a special award.
2 Three Billion Year Old Microbe Fossils, Nature
Excerpt: The record of Archaean microfossils is sparse. (…) Here, I report the discovery of pyritic filaments, the probable fossil remains of thread-like microorganisms, in a 3,235-million-year-old deep-sea volcanogenic massive sulphide deposit from the Pilbara Craton of Australia. (…) They represent the first fossil evidence for microbial life in a Precambrian submarine thermal spring system, and extend the known range of submarine hydrothermal biota by more than 2,700 million years. Such environments may have hosted the first living systems on Earth, consistent with proposals for a thermophilic origin of life.
- Filamentous
Microfossils In A 3,235-Million-Year-Old Volcanogenic
Massive Sulphide Deposit,
Birger Rasmussen, Nature 405, 676 - 679 (2000)
- Filamentous
Microfossils In A 3,235-Million-Year-Old Volcanogenic
Massive Sulphide Deposit,
Birger Rasmussen, Nature 405, 676 - 679 (2000)
3 A Chemical Bio-Compass
Excerpt: Here we assess whether reactions whose rates are affected by the orientation of reactants in magnetic fields could form the basis of a biological compass. We use a general model, incorporating biological components and design criteria, to calculate realistic constraints for such a compass. This model compares a chemical signal produced owing to magnetic field effects with stochastic noise and with changes due to physiological temperature variation. Our analysis shows that a chemically based biological compass is feasible with its size, for any given detection limit, being dependent on the magnetic sensitivity of the rate constant of the chemical reaction.
Note: I have asked some experts in animal navigation and they claim there is no experimental evidence that this mechanism is actually used by animals. (gmk)
- Biological
Sensing Of Small Field Differences By Magnetically
Sensitive Chemical
Reactions, J.C.
Weaver, T.E. Vaughan, R. D. Astumian, Nature 405, 707 -
709 (2000)
- Biological
Sensing Of Small Field Differences By Magnetically
Sensitive Chemical
Reactions, J.C.
Weaver, T.E. Vaughan, R. D. Astumian, Nature 405, 707 -
709 (2000)
4 Music On The Brain, New York Academy of Sciences/Time
Excerpt: What is it that makes humans unique among animals? Most philosophers point to language. Others are pinpointing music as another means of communication. When paired with lyrics, music is one of the most powerful and emotional means of communicating. So, what is music? How does music interact with our brain? In other words, what are the biological correlates of music? And what are its broader implications for understanding brain structure? Unlike other complex, rule-governed activities such as language, why is musical proficiency heavily influenced by tutoring? (...)
The conference will cover such topics as: Musical Predispositions in Infancy; Universals of Temporal Processing; Music, Cognition, Culture and Evolution; The Brain of Musicians: A Model for Functional and Structural Adaptation; Similarity, Invariance and Musical Variation; Tonal Cognition; Tonality and the Brain; Cerebral Substrates for Musical Temporal Processes; Neural Specialization for Tonal Processing; Functional Neuroanatomy of Musical Listening, Discrimination, and Performance; and Rhythm and Contour in Music and Poetry.
- New York Academy of Sciences Press Release: The Biological Foundations Of Music, Conference, May 20-22
- See also: Music On The Brain, Experts still don't know how and why tunes tickle our fancy--but new research offers intriguing clues, M.D. Lemonick , Time, June 5, 2000 Vol. 155 No. 23