1,403 research outputs found
Random Subgroups of Rationals
This paper introduces and studies a notion of algorithmic randomness for subgroups of rationals. Given a randomly generated additive subgroup (G,+) of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of (G,+); second, what learnability properties can one extract from G and its subclass of finitely generated subgroups? For the first question, it is shown that the theory of (G,+) coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for G with respect to any generating sequence for G is not even semi-decidable, one can build a generating sequence beta such that the word problem for G with respect to beta is co-recursively enumerable (assuming that the set of generators of G is limit-recursive). In regard to the second question, it is proven that there is a generating sequence beta for G such that every non-trivial finitely generated subgroup of G is recursively enumerable and the class of all such subgroups of G is behaviourally correctly learnable, that is, every non-trivial finitely generated subgroup can be semantically identified in the limit (again assuming that the set of generators of G is limit-recursive). On the other hand, the class of non-trivial finitely generated subgroups of G cannot be syntactically identified in the limit with respect to any generating sequence for G. The present work thus contributes to a recent line of research studying algorithmically random infinite structures and uncovers an interesting connection between the arithmetical complexity of the set of generators of a randomly generated subgroup of rationals and the learnability of its finitely generated subgroups
Artificial and Natural Genetic Information Processing
Conventional methods of genetic engineering and more recent genome editing techniques focus on identifying genetic target sequences for manipulation. This is a result of historical concept of the gene which was also the main assumption of the ENCODE project designed to identify all functional elements in the human genome sequence.
However, the theoretical core concept changed dramatically. The old concept of genetic sequences which can be assembled and manipulated like molecular bricks has problems in explaining the natural genome-editing competences of viruses and RNA consortia that are able to insert or delete, combine and recombine genetic sequences
more precisely than random-like into cellular host organisms according to adaptational needs or even generate sequences de novo. Increasing knowledge about natural genome editing questions the traditional narrative of mutations (error replications) as essential for generating genetic diversity and genetic content arrangements in biological systems. This may have far-reaching consequences for our understanding
of artificial genome editing
Discovering the Harmony of Reason and Faith in the Symphony of Eternal Creation
Tensions between the domain of reason and the domain of faith have been one of the most controversial issues in the history of our civilization for over three hundred years. They have contributed to many divisions, conflicts, and even wars. Contributions that have sought to reconcile the two domains have largely used the cultural approach in trying to solve this problem. The approach used in this essay views faith and reason from the perspective of cognitive operations. It shows that viewed from this perspective, faith and reason emerge as two aspects of the process of creation of new levels of organization that takes place in the human mind. The essay correlates faith and reason with such cognitive operations as equilibration and the production of disequilibrium. This approach shows that there is no fundamental ontological contradiction between faith and reason, and that cooperation between them is not only possible but is actually essential for sustaining our mental work and the survival of our civilization
Discovering the Harmony of Reason and Faith in the Symphony of Eternal Creation
Tensions between the domain of reason and the domain of faith have been one of the most controversial issues in the history of our civilization for over three hundred years. They have contributed to many divisions, conflicts, and even wars. Contributions that have sought to reconcile the two domains have largely used the cultural approach in trying to solve this problem. The approach used in this essay views faith and reason from the perspective of cognitive operations. It shows that viewed from this perspective, faith and reason emerge as two aspects of the process of creation of new levels of organization that takes place in the human mind. The essay correlates faith and reason with such cognitive operations as equilibration and the production of disequilibrium. This approach shows that there is no fundamental ontological contradiction between faith and reason, and that cooperation between them is not only possible but is actually essential for sustaining our mental work and the survival of our civilization
DNA Computing by Self-Assembly
Information and algorithms appear to be central to biological organization
and processes, from the storage and reproduction of genetic information to
the control of developmental processes to the sophisticated computations
performed by the nervous system. Much as human technology uses electronic
microprocessors to control electromechanical devices, biological
organisms use biochemical circuits to control molecular and chemical events.
The engineering and programming of biochemical circuits, in vivo and in
vitro, would transform industries that use chemical and nanostructured
materials. Although the construction of biochemical circuits has been
explored theoretically since the birth of molecular biology, our practical
experience with the capabilities and possible programming of biochemical
algorithms is still very young
Computational universes
Suspicions that the world might be some sort of a machine or algorithm
existing ``in the mind'' of some symbolic number cruncher have lingered from
antiquity. Although popular at times, the most radical forms of this idea never
reached mainstream. Modern developments in physics and computer science have
lent support to the thesis, but empirical evidence is needed before it can
begin to replace our contemporary world view.Comment: Several corrections of typos and smaller revisions, final versio
The Relativity of Existence
Despite the success of modern physics in formulating mathematical theories
that can predict the outcome of experiments, we have made remarkably little
progress towards answering the most fundamental question of: why is there a
universe at all, as opposed to nothingness? In this paper, it is shown that
this seemingly mind-boggling question has a simple logical answer if we accept
that existence in the universe is nothing more than mathematical existence
relative to the axioms of our universe. This premise is not baseless; it is
shown here that there are indeed several independent strong logical arguments
for why we should believe that mathematical existence is the only kind of
existence. Moreover, it is shown that, under this premise, the answers to many
other puzzling questions about our universe come almost immediately. Among
these questions are: why is the universe apparently fine-tuned to be able to
support life? Why are the laws of physics so elegant? Why do we have three
dimensions of space and one of time, with approximate locality and causality at
macroscopic scales? How can the universe be non-local and non-causal at the
quantum scale? How can the laws of quantum mechanics rely on true randomness
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