Parameterized Complexity of Maximum Happy Set and Densest k-Subgraph

We present fixed-parameter tractable (FPT) algorithms for two problems, Maximum Happy Set (MaxHS) and Maximum Edge Happy Set (MaxEHS)--also known as Densest k-Subgraph. Given a graph $G$ and an integer $k$, MaxHS asks for a set $S$ of $k$ vertices such that the number of $\textit{happy vertices}$ with respect to $S$ is maximized, where a vertex $v$ is happy if $v$ and all its neighbors are in $S$. We show that MaxHS can be solved in time $\mathcal{O}\left(2^\textsf{mw} \cdot \textsf{mw} \cdot k^2 \cdot |V(G)|\right)$ and $\mathcal{O}\left(8^\textsf{cw} \cdot k^2 \cdot |V(G)|\right)$, where $\textsf{mw}$ and $\textsf{cw}$ denote the $\textit{modular-width}$ and the $\textit{clique-width}$ of $G$, respectively. This resolves the open questions posed in literature. The MaxEHS problem is an edge-variant of MaxHS, where we maximize the number of $\textit{happy edges}$, the edges whose endpoints are in $S$. In this paper we show that MaxEHS can be solved in time $f(\textsf{nd})\cdot|V(G)|^{\mathcal{O}(1)}$ and $\mathcal{O}\left(2^{\textsf{cd}}\cdot k^2 \cdot |V(G)|\right)$, where $\textsf{nd}$ and $\textsf{cd}$ denote the $\textit{neighborhood diversity}$ and the $\textit{cluster deletion number}$ of $G$, respectively, and $f$ is some computable function. This result implies that MaxEHS is also fixed-parameter tractable by $\textit{twin cover number}$

Numerical Simulation of Water Quality Structure in Ise Bay at Tokai Heavy Rain Using Atmosphere-Ocean-Wave-Water Quality Coupled Model

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

DNA Lesions Induced by Replication Stress Trigger Mitotic Aberration and Tetraploidy Development

During tumorigenesis, cells acquire immortality in association with the development of genomic instability. However, it is still elusive how genomic instability spontaneously generates during the process of tumorigenesis. Here, we show that precancerous DNA lesions induced by oncogene acceleration, which induce situations identical to the initial stages of cancer development, trigger tetraploidy/aneuploidy generation in association with mitotic aberration. Although oncogene acceleration primarily induces DNA replication stress and the resulting lesions in the S phase, these lesions are carried over into the M phase and cause cytokinesis failure and genomic instability. Unlike directly induced DNA double-strand breaks, DNA replication stress-associated lesions are cryptogenic and pass through cell-cycle checkpoints due to limited and ineffective activation of checkpoint factors. Furthermore, since damaged M-phase cells still progress in mitotic steps, these cells result in chromosomal mis-segregation, cytokinesis failure and the resulting tetraploidy generation. Thus, our results reveal a process of genomic instability generation triggered by precancerous DNA replication stress

Impact of cystatin C-derived glomerular filtration rate in patients undergoing transcatheter aortic valve implantation

BackgroundChronic kidney disease (CKD) impacts prognosis in patients undergoing transcatheter aortic valve implantation (TAVI). While estimated glomerular filtration rate (eGFR) calculated from serum creatinine [eGFR (creatinine)] is affected by body muscle mass which reflects frailty, eGFR calculated from serum cystatin C [eGFR (cystatin C)] is independent of body composition, resulting in better renal function assessment.MethodsThis study included 390 consecutive patients with symptomatic severe aortic stenosis (AS) who underwent TAVI, and measured cystatin C-based eGFR at discharge. Patients were divided into two groups, with or without CKD estimated with eGFR (cystatin C). The primary endpoint of this study was the 3-year all-cause mortality after TAVI.ResultsThe median patient age was 84 years, and 32.8% patients were men. Multivariate Cox regression analysis indicated that eGFR (cystatin C), diabetes mellitus, and liver disease were independently associated with 3-year all-cause mortality. In the receiver-operating characteristic (ROC) curve, the predictive value of eGFR (cystatin C) was significantly higher than that of eGFR (creatinine). Furthermore, Kaplan–Meier estimates revealed that 3-year all-cause mortality was higher in the CKD (cystatin C) group than that in the non-CKD (cystatin C) group with log-rank p = 0.009. In contrast, there was no significant difference between the CKD (creatinine) and non-CKD (creatinine) groups with log-rank p = 0.94.ConclusionseGFR (cystatin C) was associated with 3-year all-cause mortality in patients who underwent TAVI, and it was superior to eGFR (creatinine) as a prognostic biomarker

Open Problems in (Hyper)Graph Decomposition

Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gain new insights about our surroundings. Even if the final application concerns a different problem (such as traversal, finding paths, trees, and flows), decomposing large graphs is often an important subproblem for complexity reduction or parallelization. This report is a summary of discussions that happened at Dagstuhl seminar 23331 on "Recent Trends in Graph Decomposition" and presents currently open problems and future directions in the area of (hyper)graph decomposition

Insights into Land Plant Evolution Garnered from the Marchantia polymorpha Genome.

The evolution of land flora transformed the terrestrial environment. Land plants evolved from an ancestral charophycean alga from which they inherited developmental, biochemical, and cell biological attributes. Additional biochemical and physiological adaptations to land, and a life cycle with an alternation between multicellular haploid and diploid generations that facilitated efficient dispersal of desiccation tolerant spores, evolved in the ancestral land plant. We analyzed the genome of the liverwort Marchantia polymorpha, a member of a basal land plant lineage. Relative to charophycean algae, land plant genomes are characterized by genes encoding novel biochemical pathways, new phytohormone signaling pathways (notably auxin), expanded repertoires of signaling pathways, and increased diversity in some transcription factor families. Compared with other sequenced land plants, M. polymorpha exhibits low genetic redundancy in most regulatory pathways, with this portion of its genome resembling that predicted for the ancestral land plant. PAPERCLIP

Minimizing Congestion for Balanced Dominators

A primary challenge in metagenomics is reconstructing individual microbial genomes from the mixture of short fragments created by sequencing. Recent work leverages the sparsity of the assembly graph to find $r$-dominating sets which enable rapid approximate queries through a dominator-centric graph partition. In this paper, we consider two problems related to reducing uncertainty and improving scalability in this setting. First, we observe that nodes with multiple closest dominators necessitate arbitrary tie-breaking in the existing pipeline. As such, we propose finding $\textit{sparse}$ dominating sets which minimize this effect via a new $\textit{congestion}$ parameter. We prove minimizing congestion is NP-hard, and give an $\mathcal{O}(\sqrt{\Delta^r})$ approximation algorithm, where $\Delta$ is the max degree. To improve scalability, the graph should be partitioned into uniformly sized pieces, subject to placing vertices with a closest dominator. This leads to $\textit{balanced neighborhood partitioning}$: given an $r$-dominating set, find a partition into connected subgraphs with optimal uniformity so that each vertex is co-assigned with some closest dominator. Using variance of piece sizes to measure uniformity, we show this problem is NP-hard iff $r$ is greater than $1$. We design and analyze several algorithms, including a polynomial-time approach which is exact when $r=1$ (and heuristic otherwise). We complement our theoretical results with computational experiments on a corpus of real-world networks showing sparse dominating sets lead to more balanced neighborhood partitionings. Further, on the metagenome $\textsf{HuSB1}$, our approach maintains high query containment and similarity while reducing piece size variance