6,590 research outputs found
Erwin Schroedinger, Francis Crick and epigenetic stability
Schroedinger's book 'What is Life?' is widely credited for having played a
crucial role in development of molecular and cellular biology. My essay
revisits the issues raised by this book from the modern perspective of
epigenetics and systems biology. I contrast two classes of potential mechanisms
of epigenetic stability: 'epigenetic templating' and 'systems biology'
approaches, and consider them from the point of view expressed by Schroedinger.
I also discuss how quantum entanglement, a nonclassical feature of quantum
mechanics, can help to address the 'problem of small numbers' that lead
Schroedinger to promote the idea of molecular code-script for explanation of
stability of biological order.Comment: New and improved version of the essay, now published in the online
journal 'Biology Direct'. Contains more expanded discussion on entanglement.
18 pages, 2 figures. The file includes open reviews by E.Koonin, V.Vedral and
E.Karsent
Termination of Original F5
The original F5 algorithm introduced by Faug\`ere is formulated for any
homogeneous polynomial set input. The correctness of output is shown for any
input that terminates the algorithm, but the termination itself is proved only
for the case of input being regular polynomial sequence. This article shows
that algorithm correctly terminates for any homogeneous input without any
reference to regularity. The scheme contains two steps: first it is shown that
if the algorithm does not terminate it eventually generates two polynomials
where first is a reductor for the second. But first step does not show that
this reduction is permitted by criteria introduced in F5. The second step shows
that if such pair exists then there exists another pair for which the reduction
is permitted by all criteria. Existence of such pair leads to contradiction.
Version v3 fixes the bibliography
Exhausting formal quantization procedures
In paper arXiv:1109.6031 the author introduced stable formality
quasi-isomorphisms and described the set of its homotopy classes. This result
can be interpreted as a complete description of formal quantization procedures.
In this note we give a brief exposition of stable formality quasi-isomorphisms
and prove that every homotopy class of stable formality quasi-isomorphisms
contains a representative which admits globalization. This note is loosely
based on the talk given by the author at the XXX Workshop on Geometric Methods
in Physics in Bialowieza, Poland.Comment: 10 pages. The paper is submitted to Proceedings of the XXX Workshop
on Geometric Methods in Physic
- …