43 research outputs found
Algebra of differential operators associated with Young diagrams
We establish a correspondence between Young diagrams and differential
operators of infinitely many variables. These operators form a commutative
associative algebra isomorphic to the algebra of the conjugated classes of
finite permutations of the set of natural numbers. The Schur functions form a
complete system of common eigenfunctions of these differential operators, and
their eigenvalues are expressed through the characters of symmetric groups. The
structure constants of the algebra are expressed through the Hurwitz numbers.Comment: 11 page
New words in human mutagenesis
<p>Abstract</p> <p>Background</p> <p>The substitution rates within different nucleotide contexts are subject to varying levels of bias. The most well known example of such bias is the excess of C to T (C > T) mutations in CpG (CG) dinucleotides. The molecular mechanisms underlying this bias are important factors in human genome evolution and cancer development. The discovery of other nucleotide contexts that have profound effects on substitution rates can improve our understanding of how mutations are acquired, and why mutation hotspots exist.</p> <p>Results</p> <p>We compared rates of inherited mutations in 1-4 bp nucleotide contexts using reconstructed ancestral states of human single nucleotide polymorphisms (SNPs) from intergenic regions. Chimp and orangutan genomic sequences were used as outgroups. We uncovered 3.5 and 3.3-fold excesses of T > C mutations in the second position of ATTG and ATAG words, respectively, and a 3.4-fold excess of A > C mutations in the first position of the ACAA word.</p> <p>Conclusions</p> <p>Although all the observed biases are less pronounced than the 5.1-fold excess of C > T mutations in CG dinucleotides, the three 4 bp mutation contexts mentioned above (and their complementary contexts) are well distinguished from all other mutation contexts. This provides a challenge to discover the underlying mechanisms responsible for the observed excesses of mutations.</p
BGWM as Second Constituent of Complex Matrix Model
Earlier we explained that partition functions of various matrix models can be
constructed from that of the cubic Kontsevich model, which, therefore, becomes
a basic elementary building block in "M-theory" of matrix models. However, the
less topical complex matrix model appeared to be an exception: its
decomposition involved not only the Kontsevich tau-function but also another
constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition
function. The BGW tau-function can be represented either as a generating
function of all unitary-matrix integrals or as a Kontsevich-Penner model with
potential 1/X (instead of X^3 in the cubic Kontsevich model).Comment: 42 page
Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations
Correlators in topological theories are given by the values of a linear form
on the products of operators from a commutative associative algebra (CAA). As a
corollary, partition functions of topological theory always satisfy the
generalized WDVV equations. We consider the Hurwitz partition functions,
associated in this way with the CAA of cut-and-join operators. The ordinary
Hurwitz numbers for a given number of sheets in the covering provide trivial
(sums of exponentials) solutions to the WDVV equations, with finite number of
time-variables. The generalized Hurwitz numbers from arXiv:0904.4227 provide a
non-trivial solution with infinite number of times. The simplest solution of
this type is associated with a subring, generated by the dilatation operators
tr X(d/dX).Comment: 24 page
Homothetic perfect fluid space-times
A brief summary of results on homotheties in General Relativity is given,
including general information about space-times admitting an r-parameter group
of homothetic transformations for r>2, as well as some specific results on
perfect fluids. Attention is then focussed on inhomogeneous models, in
particular on those with a homothetic group (acting multiply
transitively) and . A classification of all possible Lie algebra
structures along with (local) coordinate expressions for the metric and
homothetic vectors is then provided (irrespectively of the matter content), and
some new perfect fluid solutions are given and briefly discussed.Comment: 27 pages, Latex file, Submitted to Class. Quantum Gra
Small Cofactors May Assist Protein Emergence from RNA World: Clues from RNA-Protein Complexes
It is now widely accepted that at an early stage in the evolution of life an RNA world arose, in which RNAs both served as the genetic material and catalyzed diverse biochemical reactions. Then, proteins have gradually replaced RNAs because of their superior catalytic properties in catalysis over time. Therefore, it is important to investigate how primitive functional proteins emerged from RNA world, which can shed light on the evolutionary pathway of life from RNA world to the modern world. In this work, we proposed that the emergence of most primitive functional proteins are assisted by the early primitive nucleotide cofactors, while only a minority are induced directly by RNAs based on the analysis of RNA-protein complexes. Furthermore, the present findings have significant implication for exploring the composition of primitive RNA, i.e., adenine base as principal building blocks
Cardy condition for open-closed field algebras
Let be a vertex operator algebra satisfying certain reductivity and
finiteness conditions such that , the category of V-modules, is
a modular tensor category. We study open-closed field algebras over V equipped
with nondegenerate invariant bilinear forms for both open and closed sectors.
We show that they give algebras over certain \C-extension of the Swiss-cheese
partial dioperad, and we obtain Ishibashi states easily in such algebras. We
formulate Cardy condition algebraically in terms of the action of the modular
transformation on the space of intertwining
operators. We then derive a graphical representation of S in the modular tensor
category . This result enables us to give a categorical
formulation of Cardy condition and modular invariant conformal full field
algebra over . Then we incorporate the modular invariance condition
for genus-one closed theory, Cardy condition and the axioms for open-closed
field algebra over V equipped with nondegenerate invariant bilinear forms into
a tensor-categorical notion called Cardy -algebra. We also give a categorical construction of Cardy
-algebra in Cardy case.Comment: 70 page, 105 figures, references are updated. less typos, to appear
in Comm. Math. Phy