230,495 research outputs found
An Efficient Algorithm for Upper Bound on the Partition Function of Nucleic Acids
It has been shown that minimum free energy structure for RNAs and RNA-RNA
interaction is often incorrect due to inaccuracies in the energy parameters and
inherent limitations of the energy model. In contrast, ensemble based
quantities such as melting temperature and equilibrium concentrations can be
more reliably predicted. Even structure prediction by sampling from the
ensemble and clustering those structures by Sfold [7] has proven to be more
reliable than minimum free energy structure prediction. The main obstacle for
ensemble based approaches is the computational complexity of the partition
function and base pairing probabilities. For instance, the space complexity of
the partition function for RNA-RNA interaction is and the time
complexity is which are prohibitively large [4,12]. Our goal in this
paper is to give a fast algorithm, based on sparse folding, to calculate an
upper bound on the partition function. Our work is based on the recent
algorithm of Hazan and Jaakkola [10]. The space complexity of our algorithm is
the same as that of sparse folding algorithms, and the time complexity of our
algorithm is for single RNA and for RNA-RNA
interaction in practice, in which is the running time of sparse folding
and () is a sequence dependent parameter
Metrics for Graph Comparison: A Practitioner's Guide
Comparison of graph structure is a ubiquitous task in data analysis and
machine learning, with diverse applications in fields such as neuroscience,
cyber security, social network analysis, and bioinformatics, among others.
Discovery and comparison of structures such as modular communities, rich clubs,
hubs, and trees in data in these fields yields insight into the generative
mechanisms and functional properties of the graph.
Often, two graphs are compared via a pairwise distance measure, with a small
distance indicating structural similarity and vice versa. Common choices
include spectral distances (also known as distances) and distances
based on node affinities. However, there has of yet been no comparative study
of the efficacy of these distance measures in discerning between common graph
topologies and different structural scales.
In this work, we compare commonly used graph metrics and distance measures,
and demonstrate their ability to discern between common topological features
found in both random graph models and empirical datasets. We put forward a
multi-scale picture of graph structure, in which the effect of global and local
structure upon the distance measures is considered. We make recommendations on
the applicability of different distance measures to empirical graph data
problem based on this multi-scale view. Finally, we introduce the Python
library NetComp which implements the graph distances used in this work
Is Random Close Packing of Spheres Well Defined?
Despite its long history, there are many fundamental issues concerning random
packings of spheres that remain elusive, including a precise definition of
random close packing (RCP). We argue that the current picture of RCP cannot be
made mathematically precise and support this conclusion via a molecular
dynamics study of hard spheres using the Lubachevsky-Stillinger compression
algorithm. We suggest that this impasse can be broken by introducing the new
concept of a maximally random jammed state, which can be made precise.Comment: 6 pages total, 2 figure
On the enumeration of closures and environments with an application to random generation
Environments and closures are two of the main ingredients of evaluation in
lambda-calculus. A closure is a pair consisting of a lambda-term and an
environment, whereas an environment is a list of lambda-terms assigned to free
variables. In this paper we investigate some dynamic aspects of evaluation in
lambda-calculus considering the quantitative, combinatorial properties of
environments and closures. Focusing on two classes of environments and
closures, namely the so-called plain and closed ones, we consider the problem
of their asymptotic counting and effective random generation. We provide an
asymptotic approximation of the number of both plain environments and closures
of size . Using the associated generating functions, we construct effective
samplers for both classes of combinatorial structures. Finally, we discuss the
related problem of asymptotic counting and random generation of closed
environemnts and closures
Software for Exact Integration of Polynomials over Polyhedra
We are interested in the fast computation of the exact value of integrals of
polynomial functions over convex polyhedra. We present speed ups and extensions
of the algorithms presented in previous work. We present the new software
implementation and provide benchmark computations. The computation of integrals
of polynomials over polyhedral regions has many applications; here we
demonstrate our algorithmic tools solving a challenge from combinatorial voting
theory.Comment: Major updat
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