432 research outputs found
Protected percolation: a new universality class pertaining to quantum critical systems
We describe a new universality class - dubbed protected percolation - that we show to be relevant to quantum critical systems. Percolation theory describes phase transitions where long-range order is lost when parts of a system become disconnected from other parts; in the vicinity of the transition, critical behavior is observed, captured by universal power laws. Protected percolation has the added restriction that only sites from the system spanning connection can be removed. We developed a new technique to simulate protected percolation, and we used it to determine the critical exponents of this new universality class in 2, 3, and 4 dimensions. We relate the exponents analytically to those of standard percolation. The Harris criterion predicts whether a phase transition is stable against impurities. We prove that protected percolation violates this criterion in 3 dimensions and higher, implying that impurities result in the loss of universal behavior in systems governed by protected percolation. We investigated the change in critical exponents for various types of impurities, focusing on the case for three dimensions where protected percolation models quantum critical systems. We detail how our simulations can be used for direct comparison to experimental results on such quantum critical systems
Fixed-parameter algorithms for some combinatorial problems in bioinformatics
Fixed-parameterized algorithmics has been developed in 1990s as an approach to solve NP-hard problem optimally in a guaranteed running time. It offers a new opportunity to solve NP-hard problems exactly even on large problem instances.
In this thesis, we apply fixed-parameter algorithms to cope with three NP-hard problems in bioinformatics:
Flip Consensus Tree Problem is a combinatorial problem arising in computational phylogenetics. Using the formulation of the Flip Consensus Tree Problem as a graph-modification problem, we present a set of data reduction rules and two fixed-parameter algorithms with respect to the number of modifications. Additionally, we discuss several heuristic improvements to accelerate the running time of our algorithms in practice. We also report computational results on phylogenetic data.
Weighted Cluster Editing Problem is a graph-modification problem, that arises in computational biology when clustering objects with respect to a given similarity or distance measure. We present one of our fixed-parameter algorithms with respect to the minimum modification cost and describe the idea of our fastest algorithm for this problem and its unweighted counterpart.
Bond Order Assignment Problem asks for a bond order assignment of a molecule graph that minimizes a penalty function. We prove several complexity results on this problem and give two exact fixed-parameter algorithms for the problem. Our algorithms base on the dynamic programming approach on a tree decomposition of the molecule graph. Our algorithms are fixed-parameter with respect to the treewidth of the molecule graph and the maximum atom valence. We implemented one of our algorithms with several heuristic improvements and evaluate our algorithm on a set of real molecule graphs. It turns out that our algorithm is very fast on this dataset and even outperforms a heuristic algorithm that is usually used in practice
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
Symmetry in Graph Theory
This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view
Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
A quantum many-body system whose dynamics includes local measurements at a
nonzero rate can be in distinct dynamical phases, with differing entanglement
properties. We introduce theoretical approaches to measurement-induced phase
transitions (MPT) and also to entanglement transitions in random tensor
networks. Many of our results are for "all-to-all" quantum circuits with
unitaries and measurements, in which any qubit can couple to any other, and
related settings where some of the complications of low-dimensional models are
reduced. We also propose field theory descriptions for spatially local systems
of any finite dimensionality. To build intuition, we first solve the simplest
"minimal cut" toy model for entanglement dynamics in all-to-all circuits,
finding scaling forms and exponents within this approximation. We then show
that certain all-to-all measurement circuits allow exact results by exploiting
local tree-like structure in the circuit geometry. For this reason, we make a
detour to give general universal results for entanglement phase transitions
random tree tensor networks, making a connection with classical directed
polymers on a tree. We then compare these results with numerics in all-to-all
circuits, both for the MPT and for the simpler "Forced Measurement Phase
Transition" (FMPT). We characterize the two different phases in all-to-all
circuits using observables sensitive to the amount of information propagated
between initial and final time. We demonstrate signatures of the two phases
that can be understood from simple models. Finally we propose
Landau-Ginsburg-Wilson-like field theories for the MPT, the FMPT, and
entanglement transitions in random tensor networks. This analysis shows a
surprising difference between the MPT and the other cases. We discuss
measurement dynamics with additional structure (e.g. free-fermion structure),
and questions for the future.Comment: 67 pages, 41 figures; minor modifications to text and updated
references; abstract shortened to meet arxiv requirements, see pdf for full
abstrac
Automated de novo metabolite identification with mass spectrometry and cheminformatics
In this thesis new algorithms and methods that enable the de novo identification of metabolites have been developed. The aim was to find methods to propose candidate structures for unknown metabolites using MSn data as starting point. These methods have been integrated into a semi-automated pipeline to identify new human metabolites. The discovery of new metabolites will improve our capability to understand disease via its metabolic fingerprint, to develop personalized treatments and to discover new drugs. In addition, the cheminformatics methods presented in this thesis increase our understanding on the properties of human metabolites. The research described in this thesis has shown that the success of de novo metabolite identification relies on the synergy between analytical chemistry methods (i.e. LC-MSn) and cheminformatics tools.Netherlands Organization for Applied Scientific Research (TNO) Netherlands Metabolomics CentreUBL - phd migration 201
- …