Equitable partition of graphs into induced forests

An equitable partition of a graph $G$ is a partition of the vertex-set of $G$ such that the sizes of any two parts differ by at most one. We show that every graph with an acyclic coloring with at most $k$ colors can be equitably partitioned into $k-1$ induced forests. We also prove that for any integers $d\ge 1$ and $k\ge 3^{d-1}$, any $d$-degenerate graph can be equitably partitioned into $k$ induced forests. Each of these results implies the existence of a constant $c$ such that for any $k \ge c$, any planar graph has an equitable partition into $k$ induced forests. This was conjectured by Wu, Zhang, and Li in 2013.Comment: 4 pages, final versio

Long induced paths in graphs

We prove that every 3-connected planar graph on $n$ vertices contains an induced path on $\Omega(\log n)$ vertices, which is best possible and improves the best known lower bound by a multiplicative factor of $\log \log n$. We deduce that any planar graph (or more generally, any graph embeddable on a fixed surface) with a path on $n$ vertices, also contains an induced path on $\Omega(\sqrt{\log n})$ vertices. We conjecture that for any $k$, there is a contant $c(k)$ such that any $k$-degenerate graph with a path on $n$ vertices also contains an induced path on $\Omega((\log n)^{c(k)})$ vertices. We provide examples showing that this order of magnitude would be best possible (already for chordal graphs), and prove the conjecture in the case of interval graphs.Comment: 20 pages, 5 figures - revised versio

Small feedback vertex sets in planar digraphs

Let $G$ be a directed planar graph on $n$ vertices, with no directed cycle of length less than $g\ge 4$. We prove that $G$ contains a set $X$ of vertices such that $G-X$ has no directed cycle, and $|X|\le \tfrac{5n-5}9$ if $g=4$, $|X|\le \tfrac{2n-5}4$ if $g=5$, and $|X|\le \tfrac{2n-6}{g}$ if $g\ge 6$. This improves recent results of Golowich and Rolnick.Comment: 5 pages, 1 figure - v3 final versio

The effect of religion and religiosity on contraception decisions among emerging adults

Emerging adults (age 18-25) are at high risk for unplanned pregnancy because of their relatively low use of contraception. The purpose of this paper is to examine the role of religion and religiosity on contraceptive behaviors among emerging adults. Using different search criteria and databases, thirteen studies were selected for review. Overall, there appears to be negligible influence of religion on contraceptive use among emerging adults. Religiosity had an effect to a certain extent, but there is not enough evidence to make any firm conclusions. None of the studies examined emerging adults who were not enrolled in college, which was an important limitation. Yet, the findings have implications for religious communities and for providers who offer birth control counseling. Further research is urged.Master of Public Healt

Tau PET imaging: present and future directions.

Abnormal aggregation of tau in the brain is a major contributing factor in various neurodegenerative diseases. The role of tau phosphorylation in the pathophysiology of tauopathies remains unclear. Consequently, it is important to be able to accurately and specifically target tau deposits in vivo in the brains of patients. The advances of molecular imaging in the recent years have now led to the recent development of promising tau-specific tracers for positron emission tomography (PET), such as THK5317, THK5351, AV-1451, and PBB3. These tracers are now available for clinical assessment in patients with various tauopathies, including Alzheimer's disease, as well as in healthy subjects. Exploring the patterns of tau deposition in vivo for different pathologies will allow discrimination between neurodegenerative diseases, including different tauopathies, and monitoring of disease progression. The variety and complexity of the different types of tau deposits in the different diseases, however, has resulted in quite a challenge for the development of tau PET tracers. Extensive work remains in order to fully characterize the binding properties of the tau PET tracers, and to assess their usefulness as an early biomarker of the underlying pathology. In this review, we summarize recent findings on the most promising tau PET tracers to date, discuss what has been learnt from these findings, and offer some suggestions for the next steps that need to be achieved in a near future

Nano-Engineered Scaffold for Osteoarticular Regenerative Medicine

In the last decade, regenerative medicine has benefited from the exponential development of nanomaterial sciences, tissue engineering and cell-based therapies. More and more sophisticated designed structures and surface topologies are being developed to basically mimic the extracellular matrix of native tissues such as cartilage and bone. Here we give an overview of the progress made in osteochondral lesion repair, with nano-engineered scaffolds comprising building blocks such as nanoparticles, nanotubes, layer-by-layer nano-assemblies, molecular self-assembly, nanopatterned surfaces…. This nano-engineering technology is coupled with bio-functionalization, by the use of adhesion peptides, growth factors, or deoxyribonucleic acid, to drive cell adhesion, proliferation and behavior towards tissue regeneration. In osteochondral regeneration, the challenge is the simultaneous development of chondrocytes and cartilage extracellular matrix on the one side and a well vascularized bone tissue with osteoblasts on the other sid

The evolving SARS-CoV-2 epidemic in Africa: Insights from rapidly expanding genomic surveillance

INTRODUCTION Investment in Africa over the past year with regard to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sequencing has led to a massive increase in the number of sequences, which, to date, exceeds 100,000 sequences generated to track the pandemic on the continent. These sequences have profoundly affected how public health officials in Africa have navigated the COVID-19 pandemic. RATIONALE We demonstrate how the first 100,000 SARS-CoV-2 sequences from Africa have helped monitor the epidemic on the continent, how genomic surveillance expanded over the course of the pandemic, and how we adapted our sequencing methods to deal with an evolving virus. Finally, we also examine how viral lineages have spread across the continent in a phylogeographic framework to gain insights into the underlying temporal and spatial transmission dynamics for several variants of concern (VOCs). RESULTS Our results indicate that the number of countries in Africa that can sequence the virus within their own borders is growing and that this is coupled with a shorter turnaround time from the time of sampling to sequence submission. Ongoing evolution necessitated the continual updating of primer sets, and, as a result, eight primer sets were designed in tandem with viral evolution and used to ensure effective sequencing of the virus. The pandemic unfolded through multiple waves of infection that were each driven by distinct genetic lineages, with B.1-like ancestral strains associated with the first pandemic wave of infections in 2020. Successive waves on the continent were fueled by different VOCs, with Alpha and Beta cocirculating in distinct spatial patterns during the second wave and Delta and Omicron affecting the whole continent during the third and fourth waves, respectively. Phylogeographic reconstruction points toward distinct differences in viral importation and exportation patterns associated with the Alpha, Beta, Delta, and Omicron variants and subvariants, when considering both Africa versus the rest of the world and viral dissemination within the continent. Our epidemiological and phylogenetic inferences therefore underscore the heterogeneous nature of the pandemic on the continent and highlight key insights and challenges, for instance, recognizing the limitations of low testing proportions. We also highlight the early warning capacity that genomic surveillance in Africa has had for the rest of the world with the detection of new lineages and variants, the most recent being the characterization of various Omicron subvariants. CONCLUSION Sustained investment for diagnostics and genomic surveillance in Africa is needed as the virus continues to evolve. This is important not only to help combat SARS-CoV-2 on the continent but also because it can be used as a platform to help address the many emerging and reemerging infectious disease threats in Africa. In particular, capacity building for local sequencing within countries or within the continent should be prioritized because this is generally associated with shorter turnaround times, providing the most benefit to local public health authorities tasked with pandemic response and mitigation and allowing for the fastest reaction to localized outbreaks. These investments are crucial for pandemic preparedness and response and will serve the health of the continent well into the 21st century

Small feedback vertex sets in planar digraphs

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