On the threshold-width of graphs

The GG-width of a class of graphs GG is defined as follows. A graph G has GG-width k if there are k independent sets N1,...,Nk in G such that G can be embedded into a graph H in GG such that for every edge e in H which is not an edge in G, there exists an i such that both endpoints of e are in Ni. For the class TH of threshold graphs we show that TH-width is NP-complete and we present fixed-parameter algorithms. We also show that for each k, graphs of TH-width at most k are characterized by a finite collection of forbidden induced subgraphs

Dynamic representation of consecutive-ones matrices and interval graphs

2015 Spring.Includes bibliographical references.We give an algorithm for updating a consecutive-ones ordering of a consecutive-ones matrix when a row or column is added or deleted. When the addition of the row or column would result in a matrix that does not have the consecutive-ones property, we return a well-known minimal forbidden submatrix for the consecutive-ones property, known as a Tucker submatrix, which serves as a certificate of correctness of the output in this case, in O(n log n) time. The ability to return such a certificate within this time bound is one of the new contributions of this work. Using this result, we obtain an O(n) algorithm for updating an interval model of an interval graph when an edge or vertex is added or deleted. This matches the bounds obtained by a previous dynamic interval-graph recognition algorithm due to Crespelle. We improve on Crespelle's result by producing an easy-to-check certificate, known as a Lekkerkerker-Boland subgraph, when a proposed change to the graph results in a graph that is not an interval graph. Our algorithm takes O(n log n) time to produce this certificate. The ability to return such a certificate within this time bound is the second main contribution of this work

Probing the (H3-H4)(2) histone tetramer structure using pulsed EPR spectroscopy combined with site-directed spin labelling

The (H3-H4)2 histone tetramer forms the central core of nucleosomes and, as such, plays a prominent role in assembly, disassembly and positioning of nucleosomes. Despite its fundamental role in chromatin, the tetramer has received little structural investigation. Here, through the use of pulsed electron-electron double resonance spectroscopy coupled with site-directed spin labelling, we survey the structure of the tetramer in solution. We find that tetramer is structurally more heterogeneous on its own than when sequestered in the octamer or nucleosome. In particular, while the central region including the H3-H3′ interface retains a structure similar to that observed in nucleosomes, other regions such as the H3 αN helix display increased structural heterogeneity. Flexibility of the H3 αN helix in the free tetramer also illustrates the potential for post-translational modifications to alter the structure of this region and mediate interactions with histone chaperones. The approach described here promises to prove a powerful system for investigating the structure of additional assemblies of histones with other important factors in chromatin assembly/fluidity

Recognition Algorithm for Probe Interval 2-Trees

Recognition of probe interval graphs has been studied extensively. Recognition algorithms of probe interval graphs can be broken down into two types of problems: partitioned and non-partitioned. A partitioned recognition algorithm includes the probe and nonprobe partition of the vertices as part of the input, where a non-partitioned algorithm does not include the partition. Partitioned probe interval graphs can be recognized in linear-time in the edges, whereas non-partitioned probe interval graphs can be recognized in polynomial-time. Here we present a non-partitioned recognition algorithm for 2-trees, an extension of trees, that are probe interval graphs. We show that this algorithm runs in O(m) time, where m is the number of edges of a 2-tree. Currently there is no algorithm that performs as well for this problem

07211 Abstracts Collection -- Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes

From May 20 to May 25, 2007, the Dagstuhl Seminar 07211 ``Exact, Approximative, Robust and Certifying Algorithms on Particular Graph Classes\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Specialized Named Entity Recognition For Breast Cancer Subtyping

The amount of data and analysis being published and archived in the biomedical research community is more than can feasibly be sifted through manually, which limits the information an individual or small group can synthesize and integrate into their own research. This presents an opportunity for using automated methods, including Natural Language Processing (NLP), to extract important information from text on various topics. Named Entity Recognition (NER), is one way to automate knowledge extraction of raw text. NER is defined as the task of identifying named entities from text using labels such as people, dates, locations, diseases, and proteins. There are several NLP tools that are designed for entity recognition, but rely on large established corpus for training data. Biomedical research has the potential to guide diagnostic and therapeutic decisions, yet the overwhelming density of publications acts as a barrier to getting these results into a clinical setting. An exceptional example of this is the field of breast cancer biology where over 2 million people are diagnosed worldwide every year and billions of dollars are spent on research. Breast cancer biology literature and research relies on a highly specific domain with unique language and vocabulary, and therefore requires specialized NLP tools which can generate biologically meaningful results. This thesis presents a novel annotation tool, that is optimized for quickly creating training data for spaCy pipelines as well as exploring the viability of said data for analyzing papers with automated processing. Custom pipelines trained on these annotations are shown to be able to recognize custom entities at levels comparable to large corpus based recognition

Binding of a Pyrene-Based Fluorescent Amyloid Ligand to Transthyretin: A Combined Crystallographic and Molecular Dynamics Study

Misfolding and aggregation of transthyretin (TTR) cause several amyloid diseases. Besides being an amyloidogenic protein, TTR has an affinity for bicyclic small-molecule ligands in its thyroxine (T4) binding site. One class of TTR ligands are trans-stilbenes. The trans-stilbene scaffold is also widely applied for amyloid fibril-specific ligands used as fluorescence probes and as positron emission tomography tracers for amyloid detection and diagnosis of amyloidosis. We have shown that native tetrameric TTR binds to amyloid ligands based on the trans-stilbene scaffold providing a platform for the determination of high-resolution structures of these important molecules bound to protein. In this study, we provide spectroscopic evidence of binding and X-ray crystallographic structure data on tetrameric TTR complex with the fluorescent salicylic acid-based pyrene amyloid ligand (Py1SA), an analogue of the Congo red analogue X-34. The ambiguous electron density from the X-ray diffraction, however, did not permit Py1SA placement with enough confidence likely due to partial ligand occupancy. Instead, the preferred orientation of the Py1SA ligand in the binding pocket was determined by molecular dynamics and umbrella sampling approaches. We find a distinct preference for the binding modes with the salicylic acid group pointing into the pocket and the pyrene moiety outward to the opening of the T4 binding site. Our work provides insight into TTR binding mode preference for trans-stilbene salicylic acid derivatives as well as a framework for determining structures of TTR-ligand complexes

Simultaneous Graph Representation Problems

Many graphs arising in practice can be represented in a concise and intuitive way that conveys their structure. For example: A planar graph can be represented in the plane with points for vertices and non-crossing curves for edges. An interval graph can be represented on the real line with intervals for vertices and intersection of intervals representing edges. The concept of ``simultaneity'' applies for several types of graphs: the idea is to find representations for two graphs that share some common vertices and edges, and ensure that the common vertices and edges are represented the same way. Simultaneous representation problems arise in any situation where two related graphs should be represented consistently. A main instance is for temporal relationships, where an old graph and a new graph share some common parts. Pairs of related graphs arise in many other situations. For example, two social networks that share some members; two schedules that share some events, overlap graphs of DNA fragments of two similar organisms, circuit graphs of two adjacent layers on a computer chip etc. In this thesis, we study the simultaneous representation problem for several graph classes. For planar graphs the problem is defined as follows. Let G1 and G2 be two graphs sharing some vertices and edges. The simultaneous planar embedding problem asks whether there exist planar embeddings (or drawings) for G1 and G2 such that every vertex shared by the two graphs is mapped to the same point and every shared edge is mapped to the same curve in both embeddings. Over the last few years there has been a lot of work on simultaneous planar embeddings, which have been called `simultaneous embeddings with fixed edges'. A major open question is whether simultaneous planarity for two graphs can be tested in polynomial time. We give a linear-time algorithm for testing the simultaneous planarity of any two graphs that share a 2-connected subgraph. Our algorithm also extends to the case of k planar graphs, where each vertex [edge] is either common to all graphs or belongs to exactly one of them. Next we introduce a new notion of simultaneity for intersection graph classes (interval graphs, chordal graphs etc.) and for comparability graphs. For interval graphs, the problem is defined as follows. Let G1 and G2 be two interval graphs sharing some vertices I and the edges induced by I. G1 and G2 are said to be `simultaneous interval graphs' if there exist interval representations of G1 and G2 such that any vertex of I is assigned to the same interval in both the representations. The `simultaneous representation problem' for interval graphs asks whether G1 and G2 are simultaneous interval graphs. The problem is defined in a similar way for other intersection graph classes. For comparability graphs and any intersection graph class, we show that the simultaneous representation problem for the graph class is equivalent to a graph augmentation problem: given graphs G1 and G2, sharing vertices I and the corresponding induced edges, do there exist edges E' between G1-I and G2-I such that the graph G1 U G_2 U E' belongs to the graph class. This equivalence implies that the simultaneous representation problem is closely related to other well-studied classes in the literature, namely, sandwich graphs and probe graphs. We give efficient algorithms for solving the simultaneous representation problem for interval graphs, chordal graphs, comparability graphs and permutation graphs. Further, our algorithms for comparability and permutation graphs solve a more general version of the problem when there are multiple graphs, any two of which share the same common graph. This version of the problem also generalizes probe graphs