534 research outputs found
Downward transference of mice and universality of local core models
If M is a proper class inner model of ZFC and omega_2^M=omega_2, then every
sound mouse projecting to omega and not past 0-pistol belongs to M. In fact,
under the assumption that 0-pistol does not belong to M, K^M \| omega_2 is
universal for all countable mice in V.
Similarly, if M is a proper class inner model of ZFC, delta>omega_1 is
regular, (delta^+)^M = delta^+, and in V there is no proper class inner model
with a Woodin cardinal, then K^M \| delta is universal for all mice in V of
cardinality less than delta.Comment: Revised version, incorporating the referee's suggestion
On sets of numbers rationally represented in a rational base number system
In this work, it is proved that a set of numbers closed under addition and
whose representations in a rational base numeration system is a rational
language is not a finitely generated additive monoid.
A key to the proof is the definition of a strong combinatorial property on
languages : the bounded left iteration property. It is both an unnatural
property in usual formal language theory (as it contradicts any kind of pumping
lemma) and an ideal fit to the languages defined through rational base number
systems
An Introduction to Programming for Bioscientists: A Python-based Primer
Computing has revolutionized the biological sciences over the past several
decades, such that virtually all contemporary research in the biosciences
utilizes computer programs. The computational advances have come on many
fronts, spurred by fundamental developments in hardware, software, and
algorithms. These advances have influenced, and even engendered, a phenomenal
array of bioscience fields, including molecular evolution and bioinformatics;
genome-, proteome-, transcriptome- and metabolome-wide experimental studies;
structural genomics; and atomistic simulations of cellular-scale molecular
assemblies as large as ribosomes and intact viruses. In short, much of
post-genomic biology is increasingly becoming a form of computational biology.
The ability to design and write computer programs is among the most
indispensable skills that a modern researcher can cultivate. Python has become
a popular programming language in the biosciences, largely because (i) its
straightforward semantics and clean syntax make it a readily accessible first
language; (ii) it is expressive and well-suited to object-oriented programming,
as well as other modern paradigms; and (iii) the many available libraries and
third-party toolkits extend the functionality of the core language into
virtually every biological domain (sequence and structure analyses,
phylogenomics, workflow management systems, etc.). This primer offers a basic
introduction to coding, via Python, and it includes concrete examples and
exercises to illustrate the language's usage and capabilities; the main text
culminates with a final project in structural bioinformatics. A suite of
Supplemental Chapters is also provided. Starting with basic concepts, such as
that of a 'variable', the Chapters methodically advance the reader to the point
of writing a graphical user interface to compute the Hamming distance between
two DNA sequences.Comment: 65 pages total, including 45 pages text, 3 figures, 4 tables,
numerous exercises, and 19 pages of Supporting Information; currently in
press at PLOS Computational Biolog
Local Definability of in
We show that in , assuming large cardinals, is locally definable from for all -cardinals . This is a further elaboration of the
statement " is a core model below " made
by John Steel
- …