Superpatterns and Universal Point Sets

An old open problem in graph drawing asks for the size of a universal point set, a set of points that can be used as vertices for straight-line drawings of all n-vertex planar graphs. We connect this problem to the theory of permutation patterns, where another open problem concerns the size of superpatterns, permutations that contain all patterns of a given size. We generalize superpatterns to classes of permutations determined by forbidden patterns, and we construct superpatterns of size n^2/4 + Theta(n) for the 213-avoiding permutations, half the size of known superpatterns for unconstrained permutations. We use our superpatterns to construct universal point sets of size n^2/4 - Theta(n), smaller than the previous bound by a 9/16 factor. We prove that every proper subclass of the 213-avoiding permutations has superpatterns of size O(n log^O(1) n), which we use to prove that the planar graphs of bounded pathwidth have near-linear universal point sets.Comment: GD 2013 special issue of JGA

Q2Q_2-free families in the Boolean lattice

For a family $\mathcal{F}$ of subsets of [n]=\{1, 2, ..., n} ordered by inclusion, and a partially ordered set P, we say that $\mathcal{F}$ is P-free if it does not contain a subposet isomorphic to P. Let $ex(n, P)$ be the largest size of a P-free family of subsets of [n]. Let $Q_2$ be the poset with distinct elements a, b, c, d, a<b, c<d; i.e., the 2-dimensional Boolean lattice. We show that $2N -o(N) \leq ex(n, Q_2)\leq 2.283261N +o(N),$ where $N = \binom{n}{\lfloor n/2 \rfloor}$. We also prove that the largest $Q_2$-free family of subsets of [n] having at most three different sizes has at most 2.20711N members.Comment: 18 pages, 2 figure

Tur\'an numbers for Ks,tK_{s,t}-free graphs: topological obstructions and algebraic constructions

We show that every hypersurface in $\R^s\times \R^s$ contains a large grid, i.e., the set of the form $S\times T$, with $S,T\subset \R^s$. We use this to deduce that the known constructions of extremal $K_{2,2}$-free and $K_{3,3}$-free graphs cannot be generalized to a similar construction of $K_{s,s}$-free graphs for any $s\geq 4$. We also give new constructions of extremal $K_{s,t}$-free graphs for large $t$.Comment: Fixed a small mistake in the application of Proposition

In vitro efficacy of artemisinin-based treatments against SARS-CoV-2

Effective and affordable treatments for patients suffering from coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), are needed. We report in vitro efficacy of Artemisia annua extracts as well as artemisinin, artesunate, and artemether against SARS-CoV-2. The latter two are approved active pharmaceutical ingredients of anti-malarial drugs. Concentration–response antiviral treatment assays, based on immunostaining of SARS-CoV-2 spike glycoprotein, revealed that treatment with all studied extracts and compounds inhibited SARS-CoV-2 infection of VeroE6 cells, human hepatoma Huh7.5 cells and human lung cancer A549-hACE2 cells, without obvious influence of the cell type on antiviral efficacy. In treatment assays, artesunate proved most potent (range of 50% effective concentrations (EC50) in different cell types: 7–12 µg/mL), followed by artemether (53–98 µg/mL), A. annua extracts (83–260 µg/mL) and artemisinin (151 to at least 208 µg/mL). The selectivity indices (SI), calculated based on treatment and cell viability assays, were mostly below 10 (range 2 to 54), suggesting a small therapeutic window. Time-of-addition experiments in A549-hACE2 cells revealed that artesunate targeted SARS-CoV-2 at the post-entry level. Peak plasma concentrations of artesunate exceeding EC50 values can be achieved. Clinical studies are required to further evaluate the utility of these compounds as COVID-19 treatment

Universal Geometric Graphs

We introduce and study the problem of constructing geometric graphs that have few vertices and edges and that are universal for planar graphs or for some sub-class of planar graphs; a geometric graph is \emph{universal} for a class $\mathcal H$ of planar graphs if it contains an embedding, i.e., a crossing-free drawing, of every graph in $\mathcal H$. Our main result is that there exists a geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex forests; this extends to the geometric setting a well-known graph-theoretic result by Chung and Graham, which states that there exists an $n$-vertex graph with $O(n \log n)$ edges that contains every $n$-vertex forest as a subgraph. Our $O(n \log n)$ bound on the number of edges cannot be improved, even if more than $n$ vertices are allowed. We also prove that, for every positive integer $h$, every $n$-vertex convex geometric graph that is universal for $n$-vertex outerplanar graphs has a near-quadratic number of edges, namely $\Omega_h(n^{2-1/h})$; this almost matches the trivial $O(n^2)$ upper bound given by the $n$-vertex complete convex geometric graph. Finally, we prove that there exists an $n$-vertex convex geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex caterpillars.Comment: 20 pages, 8 figures; a 12-page extended abstracts of this paper will appear in the Proceedings of the 46th Workshop on Graph-Theoretic Concepts in Computer Science (WG 2020

Governance tools for board members : adapting strategy maps and balanced scorecards for directorial action

The accountability of members of the board of directors of publicly traded companies has increased over years. Corresponding to these developments, there has been an inadequate advancement of tools and frameworks to help directorial functioning. This paper provides an argument for design of the Balanced Scorecard and Strategy Maps made available to the directors as a means of influencing, monitoring, controlling and assisting managerial action. This paper examines how the Balanced Scorecard and Strategy Maps could be modified and used for this purpose. The paper suggests incorporating Balanced Scorecards in the Internal Process perspective, ‘internal’ implying here not just ‘internal to the firm’, but also ‘internal to the inter-organizational system’. We recommend that other such factors be introduced separately under a new ‘perspective’ depending upon what the board wants to emphasize without creating any unwieldy proliferation of measures. Tracking the Strategy Map over time by the board of directors is a way for the board to take responsibility for the firm’s performance. The paper makes a distinction between action variables and monitoring variables. Monitoring variables are further divided on the basis of two considerations: a) whether results have been met or not and b) whether causative factors have met the expected levels of performance or not. Based on directorial responsibilities and accountability, we take another look at how the variables could be specified more completely and accurately with directorial recommendations for executives

HCV IRES manipulates the ribosome to promote the switch from translation initiation to elongation.

The internal ribosome entry site (IRES) of the hepatitis C virus (HCV) drives noncanonical initiation of protein synthesis necessary for viral replication. Functional studies of the HCV IRES have focused on 80S ribosome formation but have not explored its role after the 80S ribosome is poised at the start codon. Here, we report that mutations of an IRES domain that docks in the 40S subunit's decoding groove cause only a local perturbation in IRES structure and result in conformational changes in the IRES-rabbit 40S subunit complex. Functionally, the mutations decrease IRES activity by inhibiting the first ribosomal translocation event, and modeling results suggest that this effect occurs through an interaction with a single ribosomal protein. The ability of the HCV IRES to manipulate the ribosome provides insight into how the ribosome's structure and function can be altered by bound RNAs, including those derived from cellular invaders

In-vitro model systems to study Hepatitis C Virus

Hepatitis C virus (HCV) is a major cause of chronic liver diseases including steatosis, cirrhosis and hepatocellular carcinoma. Currently, there is no vaccine available for prevention of HCV infection due to high degree of strain variation. The current treatment of care, Pegylated interferon α in combination with ribavirin is costly, has significant side effects and fails to cure about half of all infections. The development of in-vitro models such as HCV infection system, HCV sub-genomic replicon, HCV producing pseudoparticles (HCVpp) and infectious HCV virion provide an important tool to develop new antiviral drugs of different targets against HCV. These models also play an important role to study virus lifecycle such as virus entry, endocytosis, replication, release and HCV induced pathogenesis. This review summarizes the most important in-vitro models currently used to study future HCV research as well as drug design