The amount of text stored on the Internet, and in our libraries, continues to expand at an exponential
rate. There is a great practical need to locate relevant content. This requires quick automated methods
for classifying textual information, according to subject. We propose a quick statistical approach, which
can distinguish between 'keywords' and 'noisewords', like 'the' and 'a', without the need to parse the text
into its parts of speech. Our classification is based on an F-statistic, which compares the observed Word
Recurrence Interval (WRI) with a simple null hypothesis. We also propose a model to account for the
observed distribution of WRI statistics and we subject this model to a number of tests.
It is a well observed fact that markets follow both positive and/or negative trends, crashes and bubble effects. In general a strong positive trend is followed by a crash--a famous example of these effects was seen in the recent crash on the NASDAQ (April 2000) and prior to the crash in the Hong Kong market, which was associated with the Asian crisis in the early 1994. In this paper we use real market data coupled into a minority game with different payoff functions
to study the dynamics and the location of financial bubbles.
It is well established that volatility has a memory of the past, moreover it is found that volatility correlations are long ranged. As a consequence the volatility cannot be characterized by a single correlation time. Recent empirical work suggests that the volatility correlation functions of various assets actually decay as a power law. In this paper we show that it is possible to derive the path integral for a non-Gaussian option pricing model that can capture fat-tails. We aim to find the most probable path that contributes to the action functional, that describes the dynamics of the entire system, by finding local minima. We obtain a second order differential equation for the functional return. This paper reviews our current progress and the remaining open questions.
Electroencephalograph (EEG) analysis enables the dynamic behavior of the brain to be examined. If the behavior is nonlinear then
nonlinear tools can be used to glean information on brain behavior, and aid in the diagnosis of sleep abnormalities such as obstructive sleep apnea syndrome (OSAS). In this paper the sleep EEGs of a set of normal children and children with mild OSAS are evaluated for nonlinear brain behaviour. We found that there were differences in the nonlinearity of the brain behaviour between different sleep stages, and between the two groups of children.
Gene networks are composed of many different interacting genes and gene products (RNAs and proteins). They can be thought of as switching regions in n-dimensional space or as mass-balanced signaling networks. Both approaches allow for describing gene networks with the limited quantitative or even qualitative data available. We show how these approaches can be used in modeling the apoptosis gene network that has a vital role in tumor development. The open question is whether engineering changes to this network could be used as a possible cancer treatment.
We apply the technique of the calculus of stochastic differential equations to the problem of noise in an electronic circuit with positive feedback. We argue that this is a very natural approach to the more general problem of noise in electronic circuits of all types. We apply the standard small-signal analysis to the circuit, incorporating the standard high-frequency small-signal model for the field effect transistor. This allows us to derive a state-variable
model for the system, which is essentially a coupled system of Ordinary Differential Equations. If we then incorporate a standard noise model for the field effect transistor, we obtain a coupled system of Stochastic Differential Equations, or SDEs. We apply the stochastic differential calculus of Ito to this problem and compare
the results with simulations. We examine the dependence of phase-noise on the system parameters. We also simulate the case where the oscillations become large and use this to investigate the limits of the small-signal approximation.
This paper explores fluctuations and noise in various facets of cancer development. The three areas of particular focus are the stochastic progression of cells to cancer, fluctuations of the tumor size during treatment, and noise in cancer cell signalling. We explore the stochastic dynamics of tumor growth and response to treatment using a Markov model, and fluctutions in tumor size in response to treatment using partial differential equations. We also explore noise within gene networks in cancer cells, and noise in inter-cell signalling.
This paper explores the use of genetic algorithms for the design of networks, where the demands on the network fluctuate in time. For varying network constraints, we find the best network using the standard genetic algorithm operators such as inversion, mutation and crossover. We also examine how the choice of genetic algorithm operators affects the quality of the best network found. Such networks typically contain redundancy in servers, where several servers perform the same task and pleiotropy, where servers perform multiple tasks. We explore this trade-off between pleiotropy versus redundancy on the cost versus reliability as a measure of the quality of the network.
Proc. SPIE. 5471, Noise in Complex Systems and Stochastic Dynamics II
KEYWORDS: Probability theory, Stochastic processes, Data modeling, Differential equations, Motion models, Partial differential equations, Signal processing, Statistical analysis, Monte Carlo methods, Numerical analysis
In this short note we propose an approach for calculating option prices in financial markets in the framework of path integrals. We review various techniques from engineering and physics applied
to the theory of financial risks. We explore how the path integral methods may be used to study financial markets quantitatively and we also suggest a method in calculating transition probabilities for option pricing using real data in that framework.
Noise is present in the wide variety of signals obtained from sleep patients. This noise comes from a number of sources, from presence of extraneous signals to adjustments in signal amplification and shot noise in the circuits used for data collection. The noise needs to be removed in order to maximize the information gained about the patient using both manual and automatic analysis of the signals. Here we evaluate a number of new techniques for removal of that noise, and the associated problem of separating the original signal sources.
This paper investigates the different effects of chaotic switching
on Parrondo's games, as compared to random and periodic switching.
The rate of winning of Parrondo's games with chaotic switching
depends on coefficient(s) defining the chaotic generator, initial
conditions of the chaotic sequence and the proportion of Game A
played. Maximum rate of winning can be obtained with all the above
mentioned factors properly set, and this occurs when chaotic
switching approaches periodic behavior.
We review various techniques from engineering and physics applied to the theory of financial risks. We also explore at an introductory level how the quantum aspects of physics may be used to study the dynamics of financial markets. In particular we explore how the path integral methods may be used to study financial markets quantitatively.
Evolutionary computation algorithms are increasingly being used to solve optimization problems as they have many advantages over traditional optimization algorithms. In this paper we use evolutionary computation to study the trade-off between pleiotropy and redundancy in a client-server based network. Pleiotropy is a term
used to describe components that perform multiple tasks, while redundancy refers to multiple components performing one same task. Pleiotropy reduces cost but lacks robustness, while redundancy increases network reliability but is more costly, as together, pleiotropy and redundancy build flexibility and robustness into
systems. Therefore it is desirable to have a network that contains a balance between pleiotropy and redundancy. We explore how factors such as link failure probability, repair rates, and the size of the network influence the design choices that we explore using genetic algorithms.
In this paper we present a 3D cellular automaton for exploring gene interactions in segmentation of Drosophila larvae. Beginning with the expression levels of maternally expressed genes such as bicoid, our simple model successfully produces the distinctive expression pattern of the even-skipped gene in the developing larvae. This work highlights how complex gene interactions in developing organism can nonetheless be accurately modeled using simple rules.
Discrete games of chance can be used to illustrate principles of stochastic processes. For example, most readers are familiar with the use of discrete random walks to model the microscopic phenomenon of Brownian motion. We show that discrete games of chance, such as those of Parrondo and Astumian, can be used to quantitatively model stochastic transport processes. Discrete games can be used as “toy” models for pedagogic purposes but they can be much more than “toys”. In principle we could perform accurate simulations and we could reduce the errors of approximation to any desired level, provided that we were prepared to pay the computational cost. We consider some different approaches to discrete games, in the literature, and we use partial differential equations to model the particle densities inside a Brownian Ratchet. We apply a finite difference approach and obtain finite difference equations, which are equivalent to the games of Parrondo. The new games generalize Parrondo's original games, in the context of stochastic transport problems. We provide a practical method for constructing sets of discrete games, which can be used to simulate stochastic transport processes. We also attempt to place discrete games, such as those of Parrondo and Astumian, on a more sound philosophical basis.
The rectification of thermal motion can give rise to a steady state
flow of particles. This process is believed to occur in nature and to
be of central importance for intra-cellular transport. Ajdari and
Prost have proposed an "on-off" or "flashing" ratchet and Magnasco
has proposed a similar "tilting" or "rocking" ratchet mechanism. These developments led to new and active fields of research in statistical physics and physical chemistry. Recent work by Gillespie and Eisenberg suggests that the effectiveness of the natural transport process, in biological ion channels, depends strongly on how we model the effect of ion to ion interactions. At high local ion concentrations the effect of the crowding of charge is
significant. It is necessary to include this effect in the models. If
we are interested in average ion currents then we can replace the
complicated many-body problem with a time-average mean-field for the
distribution of charge.
To date, all analyses of artificial, human-made, ratchets require us
to neglect the effect of distributed charge. This means that the
analysis is only strictly valid for dilute solutions. The purpose of
our present paper is to include the effect of distributed charge in
the analysis of artificial Brownian ratchets.
We formulate the Brownian ratchet problem for the case where distributed charge is significant. We investigate methods of solution
and find that the finite difference approach is not adequate because
the governing equations are very "stiff." We propose an alternative
approach based on Fourier series.
We introduce a model for simulating mutation of prokaryote DNA sequences. Using that model we can then evaluated traditional techniques like parsimony and maximum likelihood methods for computing phylogenetic relationships. We also use the model to mimic large scale genomic changes, and use this to evaluate multifractal and related information theory techniques which take into account these large changes in determining phylogenetic relationships.
A number of signal processing and statistical methods can be used in analyzing either pieces of text or DNA sequences. These techniques can be used in a number of ways, such as determining authorship of documents, finding genes in DNA, and determining phylogenetic and linguistic trees. Signal processing methods such as spectrograms provide useful new tools in the area of genomic information science. In particular, fractal analysis of DNA "signals" has provided a new way of classifying organisms.
Redundancy is where multiple agents perform one task. On the other hand, pleiotropy is the inverse of redundancy- that is, where one agent multitasks. In real systems it is usual to find a mixture of both pleiotropic and redundant agents. In engineered systems we may see this in communication networks, computer systems, smart structures, nano-self-assembled systems etc. In biological systems, we can also observe the interplay of pleiotropy and redundancy from neural networks through to DNA coding. The open question is how to design a given complex system with the correct trade-off between redundancy and pleiotropy, in order to confer maximum robustness for lowest cost. Here we propose an evolutionary computational approach for exploring this trade-off in a toy model cellular automation, dubbed Real Life.
A Brownian Ratchet is a device that can rectify the random Brownian
motion of particles to yield a directed steady-state flow.
We can imagine a thermo-fluid field of particles which
interact with the ratchet. The laws of thermodynamics imply that the
ratchet must use energy from some other source.
The dynamics of continuous-time Brownian ratchets are determined by a
stochastic partial differential equation. We have used a simplified
discrete-time model of a Brownian ratchet called ``Parrondo's games''
which are governed by a difference equation. In their original form,
Parrondo's games are a finite set of simple games of chance. An
indefinite pure sequence of any single game is neutral or even
losing. A periodic or randomised sequence of mixed games can be
winning. There is a steady state flow of probability in the preferred
We have been able to design a feasible and consistent device, by
mapping the conservation law of total probability onto the law of
conservation of charge. This device can absorb energy from a
mechanical field to produce a directed flow of charge. The fundamental
architecture is based on a ``bucket-brigade'' device. The capacitors
are 2-port MEMS devices. We use CMOS transmission gates to connect the
capacitors in the required topology.
We present an analysis and simulation of the MEMS Brownian ratchet and
suggest some possible applications.
Power electronics has made great advances since the introduction of the thyristor in 1958. Even a casual study of consumer electronics have steadily replaced passive circuits. Switched mode circuits can accommodate higher power densities, they are lighter, cheaper and easier to control. The use of microprocessors and microcontrollers can make switched mode circuits even more versatile. Unfortunately, there are some problems with switched mode circuits. The higher power densities handled by these circuits can cause catastrophic failure. Periodic switching can give rise to acoustic noise or undesirable electromagnetic radiation. These problems can be reduced through the use of random switching policies. One theoretical disadvantage of random switching policies is that the time averaged switched system is not strictly equivalent to the classical system with the same average parameters. The stability limits for the randomly switched and classical system are different. This is a possible area for concern, given the high power densities and the possibility of catastrophic failure. In this paper we examine the stability of randomly switched control systems. We provide simulations, some analysis and derive some practical rules for stability. We show that some randomness can be beneficial from the point of view of minimizing power spectral density of the noise waveforms in the output current.