Interpersonal pattern dynamics and adaptive behavior in multiagent neurobiological systems : conceptual model and data

Ecological dynamics characterizes adaptive behavior as an emergent, self-organizing property of interpersonal interactions in complex social systems. The authors conceptualize and investigate constraints on dynamics of decisions and actions in the multiagent system of team sports. They studied coadaptive interpersonal dynamics in rugby union to model potential control parameter and collective variable relations in attacker–defender dyads. A videogrammetry analysis revealed how some agents generated fluctuations by adapting displacement velocity to create phase transitions and destabilize dyadic subsystems near the try line. Agent interpersonal dynamics exhibited characteristics of chaotic attractors and informational constraints of rugby union boxed dyadic systems into a low dimensional attractor. Data suggests that decisions and actions of agents in sports teams may be characterized as emergent, self-organizing properties, governed by laws of dynamical systems at the ecological scale. Further research needs to generalize this conceptual model of adaptive behavior in performance to other multiagent populations.

Power law distributions in pattern dynamics of attacker-defender dyads in the team sport of Rugby Union : phenomena in a region of self-organized criticality?

In the region of self-organized criticality (SOC) interdependency between multi-agent system components exists and slight changes in near-neighbor interactions can break the balance of equally poised options leading to transitions in system order. In this region, frequency of events of differing magnitudes exhibits a power law distribution. The aim of this paper was to investigate whether a power law distribution characterized attacker-defender interactions in team sports. For this purpose we observed attacker and defender in a dyadic sub-phase of rugby union near the try line. Videogrammetry was used to capture players’ motion over time as player locations were digitized. Power laws were calculated for the rate of change of players’ relative position. Data revealed that three emergent patterns from dyadic system interactions (i.e., try; unsuccessful tackle; effective tackle) displayed a power law distribution. Results suggested that pattern forming dynamics dyads in rugby union exhibited SOC. It was concluded that rugby union dyads evolve in SOC regions suggesting that players’ decisions and actions are governed by local interactions rules.

Human cortical processing of colour and pattern

Investigated human visual processing of simple two-colour patterns using a delayed match to sample paradigm with positron emission tomography (PET). This study is unique in that the authors specifically designed the visual stimuli to be the same for both pattern and colour recognition with all patterns being abstract shapes not easily verbally coded composed of two-colour combinations. The authors did this to explore those brain regions required for both colour and pattern processing and to separate those areas of activation required for one or the other. 10 right-handed male volunteers aged 18–35 yrs were recruited. The authors found that both tasks activated similar occipital regions, the major difference being more extensive activation in pattern recognition. A right-sided network that involved the inferior parietal lobule, the head of the caudate nucleus, and the pulvinar nucleus of the thalamus was common to both paradigms. Pattern recognition also activated the left temporal pole and right lateral orbital gyrus, whereas colour recognition activated the left fusiform gyrus and several right frontal regions.

Rough set-based reasoning and pattern mining for information filtering

An information filtering (IF) system monitors an incoming document stream to find the documents that match the information needs specified by the user profiles. To learn to use the user profiles effectively is one of the most challenging tasks when developing an IF system. With the document selection criteria better defined based on the users’ needs, filtering large streams of information can be more efficient and effective. To learn the user profiles, term-based approaches have been widely used in the IF community because of their simplicity and directness. Term-based approaches are relatively well established. However, these approaches have problems when dealing with polysemy and synonymy, which often lead to an information overload problem. Recently, pattern-based approaches (or Pattern Taxonomy Models (PTM) [160]) have been proposed for IF by the data mining community. These approaches are better at capturing sematic information and have shown encouraging results for improving the effectiveness of the IF system. On the other hand, pattern discovery from large data streams is not computationally efficient. Also, these approaches had to deal with low frequency pattern issues. The measures used by the data mining technique (for example, “support” and “confidences”) to learn the profile have turned out to be not suitable for filtering. They can lead to a mismatch problem. This thesis uses the rough set-based reasoning (term-based) and pattern mining approach as a unified framework for information filtering to overcome the aforementioned problems. This system consists of two stages - topic filtering and pattern mining stages. The topic filtering stage is intended to minimize information overloading by filtering out the most likely irrelevant information based on the user profiles. A novel user-profiles learning method and a theoretical model of the threshold setting have been developed by using rough set decision theory. The second stage (pattern mining) aims at solving the problem of the information mismatch. This stage is precision-oriented. A new document-ranking function has been derived by exploiting the patterns in the pattern taxonomy. The most likely relevant documents were assigned higher scores by the ranking function. Because there is a relatively small amount of documents left after the first stage, the computational cost is markedly reduced; at the same time, pattern discoveries yield more accurate results. The overall performance of the system was improved significantly. The new two-stage information filtering model has been evaluated by extensive experiments. Tests were based on the well-known IR bench-marking processes, using the latest version of the Reuters dataset, namely, the Reuters Corpus Volume 1 (RCV1). The performance of the new two-stage model was compared with both the term-based and data mining-based IF models. The results demonstrate that the proposed information filtering system outperforms significantly the other IF systems, such as the traditional Rocchio IF model, the state-of-the-art term-based models, including the BM25, Support Vector Machines (SVM), and Pattern Taxonomy Model (PTM).

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation

In this paper, we consider the variable-order nonlinear fractional diffusion equation View the MathML source where xRα(x,t) is a generalized Riesz fractional derivative of variable order View the MathML source and the nonlinear reaction term f(u,x,t) satisfies the Lipschitz condition |f(u1,x,t)-f(u2,x,t)|less-than-or-equals, slantL|u1-u2|. A new explicit finite-difference approximation is introduced. The convergence and stability of this approximation are proved. Finally, some numerical examples are provided to show that this method is computationally efficient. The proposed method and techniques are applicable to other variable-order nonlinear fractional differential equations.

Theoretical investigation of thermal tweezers for parallel manipulation of atoms and nanoparticles on surfaces

A major focus of research in nanotechnology is the development of novel, high throughput techniques for fabrication of arbitrarily shaped surface nanostructures of sub 100 nm to atomic scale. A related pursuit is the development of simple and efficient means for parallel manipulation and redistribution of adsorbed atoms, molecules and nanoparticles on surfaces – adparticle manipulation. These techniques will be used for the manufacture of nanoscale surface supported functional devices in nanotechnologies such as quantum computing, molecular electronics and lab-on-achip, as well as for modifying surfaces to obtain novel optical, electronic, chemical, or mechanical properties. A favourable approach to formation of surface nanostructures is self-assembly. In self-assembly, nanostructures are grown by aggregation of individual adparticles that diffuse by thermally activated processes on the surface. The passive nature of this process means it is generally not suited to formation of arbitrarily shaped structures. The self-assembly of nanostructures at arbitrary positions has been demonstrated, though these have typically required a pre-patterning treatment of the surface using sophisticated techniques such as electron beam lithography. On the other hand, a parallel adparticle manipulation technique would be suited for directing the selfassembly process to occur at arbitrary positions, without the need for pre-patterning the surface. There is at present a lack of techniques for parallel manipulation and redistribution of adparticles to arbitrary positions on the surface. This is an issue that needs to be addressed since these techniques can play an important role in nanotechnology. In this thesis, we propose such a technique – thermal tweezers. In thermal tweezers, adparticles are redistributed by localised heating of the surface. This locally enhances surface diffusion of adparticles so that they rapidly diffuse away from the heated regions. Using this technique, the redistribution of adparticles to form a desired pattern is achieved by heating the surface at specific regions. In this project, we have focussed on the holographic implementation of this approach, where the surface is heated by holographic patterns of interfering pulsed laser beams. This implementation is suitable for the formation of arbitrarily shaped structures; the only condition is that the shape can be produced by holographic means. In the simplest case, the laser pulses are linearly polarised and intersect to form an interference pattern that is a modulation of intensity along a single direction. Strong optical absorption at the intensity maxima of the interference pattern results in approximately a sinusoidal variation of the surface temperature along one direction. The main aim of this research project is to investigate the feasibility of the holographic implementation of thermal tweezers as an adparticle manipulation technique. Firstly, we investigate theoretically the surface diffusion of adparticles in the presence of sinusoidal modulation of the surface temperature. Very strong redistribution of adparticles is predicted when there is strong interaction between the adparticle and the surface, and the amplitude of the temperature modulation is ~100 K. We have proposed a thin metallic film deposited on a glass substrate heated by interfering laser beams (optical wavelengths) as a means of generating very large amplitude of surface temperature modulation. Indeed, we predict theoretically by numerical solution of the thermal conduction equation that amplitude of the temperature modulation on the metallic film can be much greater than 100 K when heated by nanosecond pulses with an energy ~1 mJ. The formation of surface nanostructures of less than 100 nm in width is predicted at optical wavelengths in this implementation of thermal tweezers. Furthermore, we propose a simple extension to this technique where spatial phase shift of the temperature modulation effectively doubles or triples the resolution. At the same time, increased resolution is predicted by reducing the wavelength of the laser pulses. In addition, we present two distinctly different, computationally efficient numerical approaches for theoretical investigation of surface diffusion of interacting adparticles – the Monte Carlo Interaction Method (MCIM) and the random potential well method (RPWM). Using each of these approaches we have investigated thermal tweezers for redistribution of both strongly and weakly interacting adparticles. We have predicted that strong interactions between adparticles can increase the effectiveness of thermal tweezers, by demonstrating practically complete adparticle redistribution into the low temperature regions of the surface. This is promising from the point of view of thermal tweezers applied to directed self-assembly of nanostructures. Finally, we present a new and more efficient numerical approach to theoretical investigation of thermal tweezers of non-interacting adparticles. In this approach, the local diffusion coefficient is determined from solution of the Fokker-Planck equation. The diffusion equation is then solved numerically using the finite volume method (FVM) to directly obtain the probability density of adparticle position. We compare predictions of this approach to those of the Ermak algorithm solution of the Langevin equation, and relatively good agreement is shown at intermediate and high friction. In the low friction regime, we predict and investigate the phenomenon of ‘optimal’ friction and describe its occurrence due to very long jumps of adparticles as they diffuse from the hot regions of the surface. Future research directions, both theoretical and experimental are also discussed.

Effective pattern taxonomy mining in text documents

Many data mining techniques have been proposed for mining useful patterns in databases. However, how to effectively utilize discovered patterns is still an open research issue, especially in the domain of text mining. Most existing methods adopt term-based approaches. However, they all suffer from the problems of polysemy and synonymy. This paper presents an innovative technique, pattern taxonomy mining, to improve the effectiveness of using discovered patterns for finding useful information. Substantial experiments on RCV1 demonstrate that the proposed solution achieves encouraging performance.

Bit-pattern based integral attack

Integral attacks are well-known to be effective against byte-based block ciphers. In this document, we outline how to launch integral attacks against bit-based block ciphers. This new type of integral attack traces the propagation of the plaintext structure at bit-level by incorporating bit-pattern based notations. The new notation gives the attacker more details about the properties of a structure of cipher blocks. The main difference from ordinary integral attacks is that we look at the pattern the bits in a specific position in the cipher block has through the structure. The bit-pattern based integral attack is applied to Noekeon, Serpent and present reduced up to 5, 6 and 7 rounds, respectively. This includes the first attacks on Noekeon and present using integral cryptanalysis. All attacks manage to recover the full subkey of the final round.

Thermal tweezers for manipulation of adatoms and nanoparticles on surfaces heated by interfering laser pulses

We conduct the detailed numerical investigation of a nanomanipulation and nanofabrication technique—thermal tweezers with dynamic evolution of surface temperature, caused by absorption of interfering laser pulses in a thin metalfilm or any other absorbing surface. This technique uses random Brownian forces in the presence of strong temperature modulation (surfacethermophoresis) for effective manipulation of particles/adatoms with nanoscale resolution. Substantial redistribution of particles on the surface is shown to occur with the typical size of the obtained pattern elements of ∼100 nm, which is significantly smaller than the wavelength of the incident pulses used (532 nm). It is also demonstrated that thermal tweezers based on surfacethermophoresis of particles/adatoms are much more effective in achieving permanent high maximum-to-minimum concentration ratios than bulk thermophoresis, which is explained by the interaction of diffusing particles with the periodic lattice potential on the surface. Typically required pulse regimes including pulse lengths and energies are also determined. The approach is applicable for reproducing any holographically achievable surfacepatterns, and can thus be used for engineering properties of surfaces including nanopatterning and design of surface metamaterials.