719 research outputs found
Self-Assembly of 4-sided Fractals in the Two-handed Tile Assembly Model
We consider the self-assembly of fractals in one of the most well-studied
models of tile based self-assembling systems known as the Two-handed Tile
Assembly Model (2HAM). In particular, we focus our attention on a class of
fractals called discrete self-similar fractals (a class of fractals that
includes the discrete Sierpi\'nski carpet). We present a 2HAM system that
finitely self-assembles the discrete Sierpi\'nski carpet with scale factor 1.
Moreover, the 2HAM system that we give lends itself to being generalized and we
describe how this system can be modified to obtain a 2HAM system that finitely
self-assembles one of any fractal from an infinite set of fractals which we
call 4-sided fractals. The 2HAM systems we give in this paper are the first
examples of systems that finitely self-assemble discrete self-similar fractals
at scale factor 1 in a purely growth model of self-assembly. Finally, we show
that there exists a 3-sided fractal (which is not a tree fractal) that cannot
be finitely self-assembled by any 2HAM system
Fractals, Randomization, Optimal Constructions, and Replication in Algorithmic Self-Assembly
The problem of the strict self-assembly of infinite fractals within tile self-assembly is considered. In particular, tile assembly algorithms are provided for the assembly of the discrete Sierpinski triangle and the discrete Sierpinski carpet.
The robust random number generation problem in the abstract tile assembly model is introduced. First, it is shown this is possible for a robust fair coin flip within the aTAM, and that such systems guarantee a worst case O(1) space usage. This primary construction is accompanied with variants that show trade-offs in space complexity, initial seed size, temperature, tile complexity, bias, and extensibility.
This work analyzes the number of tile types t, bins b, and stages necessary and sufficient to assemble n Ă n squares and scaled shapes in the staged tile assembly model.
Further, this work shows how to design a universal shape replicator in a 2-HAM self-assembly system with both attractive and repulsive forces
Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience
This essay is presented with two principal objectives in mind: first, to
document the prevalence of fractals at all levels of the nervous system, giving
credence to the notion of their functional relevance; and second, to draw
attention to the as yet still unresolved issues of the detailed relationships
among power law scaling, self-similarity, and self-organized criticality. As
regards criticality, I will document that it has become a pivotal reference
point in Neurodynamics. Furthermore, I will emphasize the not yet fully
appreciated significance of allometric control processes. For dynamic fractals,
I will assemble reasons for attributing to them the capacity to adapt task
execution to contextual changes across a range of scales. The final Section
consists of general reflections on the implications of the reviewed data, and
identifies what appear to be issues of fundamental importance for future
research in the rapidly evolving topic of this review
Complex systems approach to natural language
The review summarizes the main methodological concepts used in studying
natural language from the perspective of complexity science and documents their
applicability in identifying both universal and system-specific features of
language in its written representation. Three main complexity-related research
trends in quantitative linguistics are covered. The first part addresses the
issue of word frequencies in texts and demonstrates that taking punctuation
into consideration restores scaling whose violation in the Zipf's law is often
observed for the most frequent words. The second part introduces methods
inspired by time series analysis, used in studying various kinds of
correlations in written texts. The related time series are generated on the
basis of text partition into sentences or into phrases between consecutive
punctuation marks. It turns out that these series develop features often found
in signals generated by complex systems, like long-range correlations or
(multi)fractal structures. Moreover, it appears that the distances between
punctuation marks comply with the discrete variant of the Weibull distribution.
In the third part, the application of the network formalism to natural language
is reviewed, particularly in the context of the so-called word-adjacency
networks. Parameters characterizing topology of such networks can be used for
classification of texts, for example, from a stylometric perspective. Network
approach can also be applied to represent the organization of word
associations. Structure of word-association networks turns out to be
significantly different from that observed in random networks, revealing
genuine properties of language. Finally, punctuation seems to have a
significant impact not only on the language's information-carrying ability but
also on its key statistical properties, hence it is recommended to consider
punctuation marks on a par with words.Comment: 113 pages, 49 figure
Non-Standard Sound Synthesis with Dynamic Models
Full version unavailable due to 3rd party copyright restrictions.This Thesis proposes three main objectives: (i) to provide the concept of a new generalized non-standard synthesis model that would provide the framework for incorporating other non-standard synthesis approaches; (ii) to explore dynamic sound modeling through the application of new non-standard synthesis techniques and procedures; and (iii) to experiment with dynamic sound synthesis for the creation of novel sound objects.
In order to achieve these objectives, this Thesis introduces a new paradigm for non-standard synthesis that is based in the algorithmic assemblage of minute wave segments to form sound waveforms. This paradigm is called Extended Waveform Segment Synthesis (EWSS) and incorporates a hierarchy of algorithmic models for the generation of microsound structures.
The concepts of EWSS are illustrated with the development and presentation of a novel non-standard synthesis system, the Dynamic Waveform Segment Synthesis (DWSS). DWSS features and combines a variety of algorithmic models for direct synthesis generation: list generation and permutation, tendency masks, trigonometric functions, stochastic functions, chaotic functions and grammars. The core mechanism of DWSS is based in an extended application of Cellular Automata.
The potential of the synthetic capabilities of DWSS is explored in a series of Case Studies where a number of sound object were generated revealing (i) the capabilities of the system to generate sound morphologies belonging to other non-standard synthesis approaches and, (ii) the capabilities of the system of generating novel sound objects with dynamic morphologies.
The introduction of EWSS and DWSS is preceded by an extensive and critical overview on the concepts of microsound synthesis, algorithmic composition, the two cultures of computer music, the heretical approach in composition, non- standard synthesis and sonic emergence along with the thorough examination of algorithmic models and their application in sound synthesis and electroacoustic composition.
This Thesis also proposes (i) a new definition for âalgorithmic compositionâ, (ii) the term âtotalistic algorithmic compositionâ, and (iii) four discrete aspects of non-standard synthesis
Proceedings of the ECCS 2005 satellite workshop: embracing complexity in design - Paris 17 November 2005
Embracing complexity in design is one of the critical issues and challenges of the 21st century. As the realization grows that design activities and artefacts display properties associated with complex adaptive systems, so grows the need to use complexity concepts and methods to understand these properties and inform the design of better artifacts. It is a great challenge because complexity science represents an epistemological and methodological swift that promises a holistic approach in the understanding and operational support of design. But design is also a major contributor in complexity research. Design science is concerned with problems that are fundamental in the sciences in general and complexity sciences in particular. For instance, design has been perceived and studied as a ubiquitous activity inherent in every human activity, as the art of generating hypotheses, as a type of experiment, or as a creative co-evolutionary process. Design science and its established approaches and practices can be a great source for advancement and innovation in complexity science. These proceedings are the result of a workshop organized as part of the activities of a UK government AHRB/EPSRC funded research cluster called Embracing Complexity in Design (www.complexityanddesign.net) and the European Conference in Complex Systems (complexsystems.lri.fr). Embracing complexity in design is one of the critical issues and challenges of the 21st century. As the realization grows that design activities and artefacts display properties associated with complex adaptive systems, so grows the need to use complexity concepts and methods to understand these properties and inform the design of better artifacts. It is a great challenge because complexity science represents an epistemological and methodological swift that promises a holistic approach in the understanding and operational support of design. But design is also a major contributor in complexity research. Design science is concerned with problems that are fundamental in the sciences in general and complexity sciences in particular. For instance, design has been perceived and studied as a ubiquitous activity inherent in every human activity, as the art of generating hypotheses, as a type of experiment, or as a creative co-evolutionary process. Design science and its established approaches and practices can be a great source for advancement and innovation in complexity science. These proceedings are the result of a workshop organized as part of the activities of a UK government AHRB/EPSRC funded research cluster called Embracing Complexity in Design (www.complexityanddesign.net) and the European Conference in Complex Systems (complexsystems.lri.fr)
Connecting theory and simulation with experiment for the study of diffusion in nanoporous solids
Nanoporous solids are ubiquitous in chemical, energy, and environmental processes, where controlled transport of molecules through the pores plays a crucial role. They are used as sorbents, chromatographic or membrane materials for separations, and as catalysts and catalyst supports. Defined as materials where confinement effects lead to substantial deviations from bulk diffusion, nanoporous materials include crystalline microporous zeotypes and metalâorganic frameworks (MOFs), and a number of semi-crystalline and amorphous mesoporous solids, as well as hierarchically structured materials, containing both nanopores and wider meso- or macropores to facilitate transport over macroscopic distances. The ranges of pore sizes, shapes, and topologies spanned by these materials represent a considerable challenge for predicting molecular diffusivities, but fundamental understanding also provides an opportunity to guide the design of new nanoporous materials to increase the performance of transport limited processes. Remarkable progress in synthesis increasingly allows these designs to be put into practice. Molecular simulation techniques have been used in conjunction with experimental measurements to examine in detail the fundamental diffusion processes within nanoporous solids, to provide insight into the free energy landscape navigated by adsorbates, and to better understand nano-confinement effects. Pore network models, discrete particle models and synthesis-mimicking atomistic models allow to tackle diffusion in mesoporous and hierarchically structured porous materials, where multiscale approaches benefit from ever cheaper parallel computing and higher resolution imaging. Here, we discuss synergistic combinations of simulation and experiment to showcase theoretical progress and computational techniques that have been successful in predicting guest diffusion and providing insights. We also outline where new fundamental developments and experimental techniques are needed to enable more accurate predictions for complex systems
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