Results

**11 - 20**of**20**### Modeling of Topologically-disordered Tetrahedral Network Structures Using Local Rules

"... A method for modeling tetrahedral network structures is presented by which local rules are applied to the successive assembly of tetrahedral units which share elements (corners,edges, faces). In this way, even comparatively complex crystalline structures are easily assembled with surprisingly simple ..."

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A method for modeling tetrahedral network structures is presented by which local rules are applied to the successive assembly of tetrahedral units which share elements (corners,edges, faces). In this way, even comparatively complex crystalline structures are easily assembled with surprisingly simple rule sets, but also topologically disordered structures may be generated by application of deviant rules in order to model the topologically-possible structures of network glasses. Optimization of aperiodic networks is accomplished by representation as spring-mass models. The advantage over hand modeling is that the adjacency matrix is immediately available from which we can extract topological parameters such as ring statistics. Furthermore, the atom coordinates are recorded during assembly so that obtaining information such as bond angle statistics is simple. The approach has been applied initially to SiO 2 , SiC and Si 3 N 4 tetrahedral networks in their several polymorphic crystalline m...

### THE INFLUENCE OF SYMMETRY ON THE PROBABILITY OF ASSEMBLY PATHWAYS FOR ICOSAHEDRAL VIRAL SHELLS

"... This paper motivates and sets up the mathematical framework for a new program of investigation: to isolate and clarify the precise influence of symmetry on the probability space of assembly pathways that successfully lead to icosahedral viral shells. Several tractable open questions are posed. Besid ..."

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This paper motivates and sets up the mathematical framework for a new program of investigation: to isolate and clarify the precise influence of symmetry on the probability space of assembly pathways that successfully lead to icosahedral viral shells. Several tractable open questions are posed. Besides its virology motivation, the topic is of independent mathematical interest for studying constructions of symmetric polyhedra. Preliminary results are presented: a natural, structural classification of subsets of facets of T = 1 polyhedra, based on their stabilizing subgroups of the icosahedral group; and a theorem that uses symmetry to formalize why increasing depth increases the numeracy (and hence probability) of an assembly pathway type (or symmetry class) for a T = 1 viral shell. 1.

### COUNTING AND ENUMERATION OF SELF-ASSEMBLY PATHWAYS FOR SYMMETRIC MACROMOLECULAR STRUCTURES

"... We consider the problem of explicitly enumerating and counting the assembly pathways by which an icosahedral viral shell forms from identical constituent protein monomers. This poorly understood assembly process is a remarkable example of symmetric macromolecular self-assembly occuring in nature and ..."

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We consider the problem of explicitly enumerating and counting the assembly pathways by which an icosahedral viral shell forms from identical constituent protein monomers. This poorly understood assembly process is a remarkable example of symmetric macromolecular self-assembly occuring in nature and possesses many features that are desirable while engineering self-assembly at the nanoscale. We use the new model of���that employs a static geometric constraint graph to represent the driving (weak) forces that cause a viral shell to assemble and hold it together. The model was developed to answer focused questions about the structural properties of the most probable types of successful assembly pathways. Specifically, the model reduces the study of pathway types and their probabilities to the study of the orbits of the automorphism group of the underlying geometric constraint graph, acting on the set of pathways. Since these are highly symmetric polyhedral graphs, it seems a viable approach to explicitly enumerate these orbits and count their sizes. The contribution of this paper is to isolate and simplify the core combinatorial questions, list related work and indicate the advantages of an explicit enumerative approach. 1.

### Modeling Virus Self-Assembly Pathways Using Computational Algebra and Geometry

- APPLICATIONS OF COMPUTER ALGEBRA (ACA-2004)
, 2004

"... We develop a tractable model for elucidating the assembly pathways by which an icosahedral viral shell forms from 60 identical constituent protein monomers. This poorly understood process a remarkable example of macromolecular self-assembly occuring in nature and possesses many features that are d ..."

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We develop a tractable model for elucidating the assembly pathways by which an icosahedral viral shell forms from 60 identical constituent protein monomers. This poorly understood process a remarkable example of macromolecular self-assembly occuring in nature and possesses many features that are desirable while engineering self-assembly at the nanoscale. The model uses static geometric constraints to represent the driving (weak) forces that cause a viral shell to assemble and hold it together. The goal is to answer focused questions about the structural properties of a successful assembly pathway. Pathways and their

### The Double-Helix Pattern of Prime Number Growth

"... Abstract—This paper is the result of analyzing the growth pattern of the first 500 prime numbers. The growth rate was found to be related to two characteristics – two parallel threads and the almost viral impact of the multiples of 6 on these two threads. When corresponding cause and effect of these ..."

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Abstract—This paper is the result of analyzing the growth pattern of the first 500 prime numbers. The growth rate was found to be related to two characteristics – two parallel threads and the almost viral impact of the multiples of 6 on these two threads. When corresponding cause and effect of these impacts are overlaid, a double-helix structure is the result. This concept and modeling approach is submitted with the hope of providing a model that helps connect the research benefits of bioinformatics and the potential impact of the prime number structure of the Riemann Hypothesis when applied by professionals in their scientific computing fields. Index Terms—Double-helix, gap, growth, prime numbers. I.

### New Ideas in Psychology] (]]]])]]]–]]]

"... Hints of beauty in social cognition: Broken symmetries in mental dynamics ..."

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Hints of beauty in social cognition: Broken symmetries in mental dynamics

### Tree Orbits under Permutation Group Action: Algorithm, Enumeration and Application to Viral Assembly

, 2009

"... This paper uses combinatorics and group theory to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the capsid (shell) is fairly well understood in terms of its constituent subunits, the assembly process is not. For the purpose of this paper, the ca ..."

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This paper uses combinatorics and group theory to answer questions about the assembly of icosahedral viral shells. Although the geometric structure of the capsid (shell) is fairly well understood in terms of its constituent subunits, the assembly process is not. For the purpose of this paper, the capsid is modeled by a polyhedron whose facets represent the monomers. The assembly process is modeled by a rooted tree, the leaves representing the facets of the polyhedron, the root representing the assembled polyhedron, and the internal vertices representing intermediate stages of assembly (subsets of facets). Besides its virological motivation, the enumeration of orbits of trees under the action of a finite group is of independent mathematical interest. If G is a finite group acting on a finite set X, then there is a natural induced action of G on the set TX of trees whose leaves are bijectively labeled by the elements of X. If G acts simply on X, then |X |: = |Xn | = n · |G|, where n is the number of G-orbits in X. The basic combinatorial results in this paper are (1) a formula for the number of orbits of each size in the action of G on TXn, for every n, and (2) a simple algorithm to find the stabilizer of a tree τ ∈ TX in G that runs in linear time and does not need memory in addition to its input tree.

### Hybrid Reaction Modeling for Top-Down . . .

, 2008

"... We propose a new modeling framework inspired by chemical reaction processes. Our approach consists in defining the processes and the interactions within the system in term of reactions. Such a definition can be applied to many systems, ranging from biochemical systems to swarm robotics. In particula ..."

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We propose a new modeling framework inspired by chemical reaction processes. Our approach consists in defining the processes and the interactions within the system in term of reactions. Such a definition can be applied to many systems, ranging from biochemical systems to swarm robotics. In particular, we aim at exploiting the toolbox developed in the context of hybrid system modeling and simulation. The concept of extended self-assembly is the following: given a set of passive building blocks A, B, C, and D, how to obtain, with a maximal yield, the products X, Y, and Z using a set of N active transporters? What is the smallest set of reactions leading to these products? More importantly, how shall we design the building blocks and their transporters in order to fit this set of reactions? The reaction set may also involve intermediate products and be influenced by external factors. We draw inspiration from the DNA

### Dynamic Pathways for Viral Capsid Assembly

, 2006

"... ABSTRACT We develop a class of models with which we simulate the assembly of particles into T1 capsidlike objects using Newtonian dynamics. By simulating assembly for many different values of system parameters, we vary the forces that drive assembly. For some ranges of parameters, assembly is facile ..."

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ABSTRACT We develop a class of models with which we simulate the assembly of particles into T1 capsidlike objects using Newtonian dynamics. By simulating assembly for many different values of system parameters, we vary the forces that drive assembly. For some ranges of parameters, assembly is facile; for others, assembly is dynamically frustrated by kinetic traps corresponding to malformed or incompletely formed capsids. Our simulations sample many independent trajectories at various capsomer concentrations, allowing for statistically meaningful conclusions. Depending on subunit (i.e., capsomer) geometries, successful assembly proceeds by several mechanisms involving binding of intermediates of various sizes. We discuss the relationship between these mechanisms and experimental evaluations of capsid assembly processes.

### Automated Evolutionary Design of Self-Assembly and Self-Organising Systems

"... Self-assembly and self-organisation are natural construction processes where the spontaneous formation of aggregates emerges throughout the progressive interplay of local interactions among its constituents. Made upon cooperative self-reliant components, selfassembly and self-organising systems are ..."

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Self-assembly and self-organisation are natural construction processes where the spontaneous formation of aggregates emerges throughout the progressive interplay of local interactions among its constituents. Made upon cooperative self-reliant components, selfassembly and self-organising systems are seen as distributed, not necessarily synchronous, autopoietic mechanisms for the bottom-up fabrication of supra-structures. The systematic understanding of how nature endows these autonomous components with sufficient “intelligence” to combine themselves to form useful aggregates brings challenging questions to science, answers to which have many potential applications in matters of life and technological advances. It is for this reason that the investigation to be presented along this thesis focuses on the automated design of self-assembly and self-organizing systems by means of artificial evolution. Towards this goal, this dissertation embodies research on evolutionary algorithms applied to the parameters design of a computational model of self-organisation and the components design of a computational model of self-assembly. In addition, an analytical assessment combining correlation metrics and clustering, as well as the exploration of emergent patterns of cooperativity and the measurement of activity across evolution, is made. The results support the research hypothesis that an adaptive process such as artificial evolution is indeed a suitable strategy for the automated design of self-assembly and self-organising systems where local interactions, homogeneity and both stochastic and discrete models of execution play a crucial role in emergent complex structures. ii Acknowledgements I would like to thank my academic supervisors Dr. Natalio Krasnogor and Prof. Graham Kendall for all the support, guidance, discussions, ideas and advice during my Ph.D. career. I also thank Prof. Edmund Burke for providing the opportunity to study in the ASAP Group. I am specially grateful to my financial sponsors Universities UK for the Overseas