Unit Interval Editing is Fixed-Parameter Tractable

Given a graph~$G$ and integers $k_1$, $k_2$, and~$k_3$, the unit interval editing problem asks whether $G$ can be transformed into a unit interval graph by at most $k_1$ vertex deletions, $k_2$ edge deletions, and $k_3$ edge additions. We give an algorithm solving this problem in time $2^{O(k\log k)}\cdot (n+m)$, where $k := k_1 + k_2 + k_3$, and $n, m$ denote respectively the numbers of vertices and edges of $G$. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time $O(4^k \cdot (n + m))$. Another result is an $O(6^k \cdot (n + m))$-time algorithm for the unit interval vertex deletion problem, significantly improving the algorithm of van 't Hof and Villanger, which runs in time $O(6^k \cdot n^6)$.Comment: An extended abstract of this paper has appeared in the proceedings of ICALP 2015. Update: The proof of Lemma 4.2 has been completely rewritten; an appendix is provided for a brief overview of related graph classe

Methods of Isolation and Analysis of TREG Immune Infiltrates from Injured and Dystrophic Skeletal Muscle

The immune infiltrate present in acutely injured or dystrophic skeletal muscle has been shown to play an important role in the process of muscle regeneration. Our work has described, for the first time, muscle regulatory T cells (Tregs), a unique population in phenotype and function capable of promoting skeletal muscle repair. Herein, we describe the methods we have optimized to study muscle Tregs, including their isolation from injured muscle, immuno-labeling for analysis/separation by flow cytometry, and measurement of their proliferation status

On the Threshold of Intractability

We study the computational complexity of the graph modification problems Threshold Editing and Chain Editing, adding and deleting as few edges as possible to transform the input into a threshold (or chain) graph. In this article, we show that both problems are NP-complete, resolving a conjecture by Natanzon, Shamir, and Sharan (Discrete Applied Mathematics, 113(1):109--128, 2001). On the positive side, we show the problem admits a quadratic vertex kernel. Furthermore, we give a subexponential time parameterized algorithm solving Threshold Editing in $2^{O(\surd k \log k)} + \text{poly}(n)$ time, making it one of relatively few natural problems in this complexity class on general graphs. These results are of broader interest to the field of social network analysis, where recent work of Brandes (ISAAC, 2014) posits that the minimum edit distance to a threshold graph gives a good measure of consistency for node centralities. Finally, we show that all our positive results extend to the related problem of Chain Editing, as well as the completion and deletion variants of both problems

Plasticity of the Muscle Stem Cell Microenvironment

Satellite cells (SCs) are adult muscle stem cells capable of repairing damaged and creating new muscle tissue throughout life. Their functionality is tightly controlled by a microenvironment composed of a wide variety of factors, such as numerous secreted molecules and different cell types, including blood vessels, oxygen, hormones, motor neurons, immune cells, cytokines, fibroblasts, growth factors, myofibers, myofiber metabolism, the extracellular matrix and tissue stiffness. This complex niche controls SC biology-quiescence, activation, proliferation, differentiation or renewal and return to quiescence. In this review, we attempt to give a brief overview of the most important players in the niche and their mutual interaction with SCs. We address the importance of the niche to SC behavior under physiological and pathological conditions, and finally survey the significance of an artificial niche both for basic and translational research purposes

Mechanisms of T cell organotropism

F.M.M.-B. is supported by the British Heart Foundation, the Medical Research Council of the UK and the Gates Foundation