The Omega Number: Irreducible Complexity in Pure Math

2006 ◽  
pp. 1-1
Author(s):  
Gregory J. Chaitin
Keyword(s):  
Irreducible Complexity ◽  
Pure Math

scholarly journals Irreducible complexity of iterated symmetric bimodal maps

2005 ◽  
Vol 2005 (1) ◽  
pp. 69-85 ◽  
Author(s):  
J. P. Lampreia ◽  
R. Severino ◽  
J. Sousa Ramos
Keyword(s):  
Tree Structure ◽  
Unimodal Maps ◽  
Markov Shifts ◽  
Irreducible Complexity ◽  
The Family

We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a∗-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the∗-product induced on the associated Markov shifts.

Semiotics

2020 ◽  
Author(s):  
Bob Hodge
Keyword(s):  
Literary Theory ◽  
Modern World ◽  
Intellectual Tradition ◽  
Founding Fathers ◽  
21St Century Literature ◽  
Irreducible Complexity ◽  
The Social ◽  
Intellectual Revolution ◽  
Modern Era

Semiotics refers to an intellectual tradition that deals with processes of making and interpreting meaning in all kinds of text, in all modes. However, semiotics was never integrated into mainstream disciplinary structures. Because of this marginal status semiotic tendencies flourished outside and between the major disciplines. As a discipline semiotics seems small, vulnerable and out-of-date. But as a broad intellectual tradition semiotics can be seen as a meta-theory which encompasses literary theory. This second perspective makes semiotics more useful for literary readers, and hence is emphasized in this chapter. Semiotics’ value is enhanced when it is seen as a complex, heterogeneous field with fuzzy boundaries and productive entanglements with literary objects and theories. “Semiotics” comes from Greek semeion (sign, omen, or trace), something that points towards important, often hidden meanings. Signs in this sense go beyond words and verbal media. This scope gives “semiotics” a radically disruptive quality. Western culture in the modern era has been based on the primacy of words as carriers of all meaning and thought. Semiotics is the site of a radical challenge to this dominance. Semiotics sees signs and meanings everywhere, in every mode, not just in words. The changing media of literature in the present and past raise many semiotic issues for literary theory. Poetry always carried meanings through sound as well as words. Drama needs to be performed. Film and multimedia carry the role of print fiction in new contexts. In the multimedia 21st century, literature has gone beyond writing, and its theories need a semiotic dimension. Semiotics has a divided history, with two founding fathers. Peirce emphasized complexity and flow, and Saussure emphasized structure. Before 1960 structuralism dominated, but by the end of the 20th century post-structuralism prevailed. Semiotics went underground, but left traces everywhere of the intellectual revolution it participated in. It helped to trigger the turn to meaning across the social sciences and celebrated the irreducible complexity and diversity of forms and meanings in literature and life in the modern world.

scholarly journals NIELSEN EQUIVALENCE OF GENERATING PAIRS OF SL(2,q)

2013 ◽  
Vol 55 (3) ◽  
pp. 481-509 ◽  
Author(s):  
DARRYL MCCULLOUGH ◽  
MARCUS WANDERLEY
Keyword(s):  
Number Theory ◽  
American Mathematical Society ◽  
Equivalence Classes ◽  
Conjugacy Classes ◽  
Mathematical Society ◽  
Additional Work ◽  
Pure Math ◽  
Infinite Set

AbstractWe present several conjectures which would describe the Nielsen equivalence classes of generating pairs for the groups SL(2,q) and PSL(2,q). The Higman invariant, which is the union of the conjugacy classes of the commutator of a generating pair and its inverse, and the trace of the commutator play key roles. Combining known results with additional work, we clarify the relationships between the conjectures, and obtain various partial results concerning them. Motivated by the work of Macbeath (A. M. Macbeath, Generators of the linear fractional groups, in Number theory (Proc. Sympos. Pure Math., vol. XII, Houston, TX, 1967) (American Mathematical Society, Providence, RI, 1969), 14–32), we use another invariant defined using traces to develop algorithms that enable us to verify the conjectures computationally for all q up to 101, and to prove the conjectures for a highly restricted but possibly infinite set of q.

scholarly journals Remark on quasi-ideals of ordered semigroups

2015 ◽  
Vol 25 (2) ◽  
pp. 144-150
Author(s):  
Niovi Kehayopulu
Keyword(s):  
Ordered Semigroups ◽  
Pure Math

Abstract The aim is to correct part of the Remark 3 of my paper “On regular, intra-regular ordered semigroups” in Pure Math. Appl. (PU.M.A.) 4, no. 4 (1993), 447-461. On this occasion, some further results and the similarity between the po-semigroups and the le-semigroups are discussed.

scholarly journals Biological Algorithms for Digital Manufacture

2021 ◽  
Author(s):  
◽  
Louise Wotton
Keyword(s):  
Computational Design ◽  
Digital Fabrication ◽  
Free Form ◽  
Research Approach ◽  
Design Intent ◽  
Agent Based ◽  
Spatial Design ◽  
Irreducible Complexity ◽  
Agent Based Simulations ◽  
Rule Sets

<p>Computational simulations are generally built upon a form or design that is near or mostly complete. Agent-based simulations are ones where the rules and behaviours are designed, creating an unpredictable output. In this research, these rules are derived from the complex systems in nature, utilising cross-disciplinary principles between architecture and biology. The abstraction of data and rules from biological structures are used to inform computational rule-sets for modelling 3D printed structures.  The simulations in this paper explore the concept of emergence: where systems have an irreducible complexity and adaptability - a series of smaller parts combined acting as a whole. The concept of agent-based simulations as a form of emergence is a tool used greatly within many areas of research as a speculative method to build form and space.  Computation rule-sets define a design intent for each simulation, demonstrating the ability to use agent-based systems and a spatial design driver. Informing the agents with design intent, allows them to adapt to their environment and to the ability and limitations of a freeform 3D printer.  The focus in this project is the design of emergent principles in nature and how they can be applied to optimize structures for use with digital fabrication methods, thus producing a new approach to designing fabricated forms.  Using a design by research approach, this research demonstrates the potential of free-form 3D printing as a technique for an integrated fabrication system. It outlines computational design techniques including the simulation of emergent phenomena to define a digital workflow that supports the integration of both emergent structures and free-form printing.</p>

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