6,125 research outputs found
Interval-Like Graphs and Digraphs
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all, broadly speaking, different generalizations of interval graphs, and include, in addition to interval graphs, adjusted interval digraphs, threshold graphs, complements of threshold tolerance graphs (known as `co-TT\u27 graphs), bipartite interval containment graphs, bipartite co-circular arc graphs, and two-directional orthogonal ray graphs. (The last three classes coincide, but have been investigated in different contexts.) This common view is made possible by introducing reflexive relationships (loops) into the analysis. We also show that all the above classes are united by a common ordering characterization, the existence of a min ordering. We propose a common generalization of all these graph and digraph classes, namely signed-interval digraphs, and show that they are precisely the digraphs that are characterized by the existence of a min ordering. We also offer an alternative geometric characterization of these digraphs. For most of the above graph and digraph classes, we show that they are exactly those signed-interval digraphs that satisfy a suitable natural restriction on the digraph, like having a loop on every vertex, or having a symmetric edge-set, or being bipartite. For instance, co-TT graphs are precisely those signed-interval digraphs that have each edge symmetric. We also offer some discussion of future work on recognition algorithms and characterizations
Obstruction characterization of co-TT graphs
Threshold tolerance graphs and their complement graphs ( known as co-TT
graphs) were introduced by Monma, Reed and Trotter[24]. Introducing the concept
of negative interval Hell et al.[19] defined signed-interval bigraphs/digraphs
and have shown that they are equivalent to several seemingly different classes
of bigraphs/digraphs. They have also shown that co-TT graphs are equivalent to
symmetric signed-interval digraphs. In this paper we characterize
signed-interval bigraphs and signed-interval graphs respectively in terms of
their biadjacency matrices and adjacency matrices. Finally, based on the
geometric representation of signed-interval graphs we have setteled the open
problem of forbidden induced subgraph characterization of co-TT graphs posed by
Monma, Reed and Trotter in the same paper.Comment: arXiv admin note: substantial text overlap with arXiv:2206.0591
Canonical, Stable, General Mapping using Context Schemes
Motivation: Sequence mapping is the cornerstone of modern genomics. However,
most existing sequence mapping algorithms are insufficiently general.
Results: We introduce context schemes: a method that allows the unambiguous
recognition of a reference base in a query sequence by testing the query for
substrings from an algorithmically defined set. Context schemes only map when
there is a unique best mapping, and define this criterion uniformly for all
reference bases. Mappings under context schemes can also be made stable, so
that extension of the query string (e.g. by increasing read length) will not
alter the mapping of previously mapped positions. Context schemes are general
in several senses. They natively support the detection of arbitrary complex,
novel rearrangements relative to the reference. They can scale over orders of
magnitude in query sequence length. Finally, they are trivially extensible to
more complex reference structures, such as graphs, that incorporate additional
variation. We demonstrate empirically the existence of high performance context
schemes, and present efficient context scheme mapping algorithms.
Availability and Implementation: The software test framework created for this
work is available from
https://registry.hub.docker.com/u/adamnovak/sequence-graphs/.
Contact: [email protected]
Supplementary Information: Six supplementary figures and one supplementary
section are available with the online version of this article.Comment: Submission for Bioinformatic
Anti-CD20 Therapy Acts via FcĪ³RIIIA to Diminish Responsiveness of Human Natural Killer Cells
Natural killer (NK) immune cells mediate antibody-dependent cellular cytotoxicity (ADCC) by aggregating FcĪ³RIIIA/CD16, contributing significantly to the therapeutic effect of CD20 monoclonal antibodies (mAb). In this study, we show that CD16 ligation on primary human NK cells by the anti-CD20 mAb rituximab or ofatumumab stably impairs the spontaneous cytotoxic response attributable to cross-tolerance of several unrelated NK-activating receptors (including NKG2D, DNAM-1, NKp46, and 2B4). Similar effects were obtained from NK cells isolated from patients with chronic lymphocytic leukemia in an autologous setting. NK cells rendered hyporesponsive in this manner were deficient in the ability of these cross-tolerized receptors to phosphorylate effector signaling molecules critical for NK cytotoxicity, including SLP-76, PLCĪ³2, and Vav1. These effects were associated with long-lasting recruitment of the tyrosine phosphatase SHP-1 to the CD16 receptor complex. Notably, pharmacologic inhibition of SHP-1 with sodium stibogluconate counteracted CD20 mAb-induced NK hyporesponsiveness, unveiling an unrecognized role for CD16 as a bifunctional receptor capable of engendering long-lasting NK cell inhibitory signals. Our work defines a novel mechanism of immune exhaustion induced by CD20 mAb in human NK cells, with potentially negative implications in CD20 mAb-treated patients where NK cells are partly responsible for clinical efficacy. Cancer Res; 75(19); 1-12. Ā©2015 AACR
Isomorphisms in co-TT graphs
2019 Spring.Includes bibliographical references.A threshold tolerance graph is a graph where each vertex v is assigned a weight wv and a tolerance tv, and there is an edge between two vertices vx and vy if and only if wx + wy ā„ min(tx,ty). A co-TT graph is the complement of a threshold tolerance graph. Recognition of these graphs can be done in O(n2) time; however no polynomial-time algorithm to identify isomorphisms between pairs of TT or co-TT graphs was previously known. We give an algorithm to identify these isomorphisms, which takes O(n2) time
Linear-Time Recognition of Double-Threshold Graphs
A graph G=(V, E) is a double-threshold graph if there exist a vertex-weight function w:Vāā and two real numbers lb, ub ā ā such that uv ā E if and only if lb ā¤ w(u)+w(v) ā¤ ub. In the literature, those graphs are studied also as the pairwise compatibility graphs that have stars as their underlying trees. We give a new characterization of double-threshold graphs that relates them to bipartite permutation graphs. Using the new characterization, we present a linear-time algorithm for recognizing double-threshold graphs. Prior to our work, the fastest known algorithm by Xiao and Nagamochi [Algorithmica 2020] ran in O(nĀ³ m) time, where n and m are the numbers of vertices and edges, respectively
Fast Approximate Spectral Clustering for Dynamic Networks
Spectral clustering is a widely studied problem, yet its complexity is
prohibitive for dynamic graphs of even modest size. We claim that it is
possible to reuse information of past cluster assignments to expedite
computation. Our approach builds on a recent idea of sidestepping the main
bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by
using fast Chebyshev graph filtering of random signals. We show that the
proposed algorithm achieves clustering assignments with quality approximating
that of spectral clustering and that it can yield significant complexity
benefits when the graph dynamics are appropriately bounded
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