6,935 research outputs found
A steepest descent calculation of RNA pseudoknots
We enumerate possible topologies of pseudoknots in single-stranded RNA
molecules. We use a steepest-descent approximation in the large N matrix field
theory, and a Feynman diagram formalism to describe the resulting pseudoknot
structure
An Algorithmic Approach to Limit Cycles of Nonlinear Differential Systems: the Averaging Method Revisited
This paper introduces an algorithmic approach to the analysis of bifurcation
of limit cycles from the centers of nonlinear continuous differential systems
via the averaging method. We develop three algorithms to implement the
averaging method. The first algorithm allows to transform the considered
differential systems to the normal formal of averaging. Here, we restricted the
unperturbed term of the normal form of averaging to be identically zero. The
second algorithm is used to derive the computational formulae of the averaged
functions at any order. The third algorithm is based on the first two
algorithms that determines the exact expressions of the averaged functions for
the considered differential systems. The proposed approach is implemented in
Maple and its effectiveness is shown by several examples. Moreover, we report
some incorrect results in published papers on the averaging method.Comment: Proc. 44th ISSAC, July 15--18, 2019, Beijing, Chin
Manning condensation in two dimensions
We consider a macroion confined to a cylindrical cell and neutralized by
oppositely charged counterions. Exact results are obtained for the
two-dimensional version of this problem, in which ion-ion and ion-macroion
interactions are logarithmic. In particular, the threshold for counterion
condensation is found to be the same as predicted by mean-field theory. With
further increase of the macroion charge, a series of single-ion condensation
transitions takes place. Our analytical results are expected to be exact in the
vicinity of these transitions and are in very good agreement with recent
Monte-Carlo simulation data.Comment: 4 pages, 4 figure
The me in memory:the role of the self in autobiographical memory development
This paper tests the hypothesis that self development plays a role in the offset of childhood amnesia; assessing the importance of both the capacity to anchor a memory to the self-concept, and the strength of the self-concept as an anchor. We demonstrate for the first time that the volume of 3- to 6-year-oldâs specific autobiographical memories is predicted by both the volume of their self-knowledge, and their capacity for self-source monitoring within self-referencing paradigms (N =186). Moreover, there is a bidirectional relationship between self and memory, such that autobiographical memory mediates the link between self-source monitoring and self-knowledge. These predictive relationships suggests that the self memory system is active in early childhood
Real symmetric random matrices and replicas
Various ensembles of random matrices with independent entries are analyzed by
the replica formalism in the large-N limit. A result on the Laplacian random
matrix with Wigner-rescaling is generalized to arbitrary probability
distribution.Comment: 17 page
Enumeration of RNA structures by Matrix Models
We enumerate the number of RNA contact structures according to their genus,
i.e. the topological character of their pseudoknots. By using a recently
proposed matrix model formulation for the RNA folding problem, we obtain exact
results for the simple case of an RNA molecule with an infinitely flexible
backbone, in which any arbitrary pair of bases is allowed. We analyze the
distribution of the genus of pseudoknots as a function of the total number of
nucleotides along the phosphate-sugar backbone.Comment: RevTeX, 4 pages, 2 figure
Are better conducting molecules more rigid?
We investigate the electronic origin of the bending stiffness of conducting
molecules. It is found that the bending stiffness associated with electronic
motion, which we refer to as electro-stiffness, , is governed by
the molecular orbital overlap and the gap width between HOMO and LUMO
levels, and behaves as . To study the
effect of doping, we analyze the electron filling-fraction dependence on
and show that doped molecules are more flexible. In addition, to
estimate the contribution of to the total stiffness, we consider
molecules under a voltage bias, and study the length contraction ratio as a
function of the voltage. The molecules are shown to be contracted or dilated,
with increasing nonlinearly with the applied bias
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