Overlap properties of geometric expanders

The {\em overlap number} of a finite $(d+1)$-uniform hypergraph $H$ is defined as the largest constant $c(H)\in (0,1]$ such that no matter how we map the vertices of $H$ into $\R^d$, there is a point covered by at least a $c(H)$-fraction of the simplices induced by the images of its hyperedges. In~\cite{Gro2}, motivated by the search for an analogue of the notion of graph expansion for higher dimensional simplicial complexes, it was asked whether or not there exists a sequence $\{H_n\}_{n=1}^\infty$ of arbitrarily large $(d+1)$-uniform hypergraphs with bounded degree, for which $\inf_{n\ge 1} c(H_n)>0$. Using both random methods and explicit constructions, we answer this question positively by constructing infinite families of $(d+1)$-uniform hypergraphs with bounded degree such that their overlap numbers are bounded from below by a positive constant $c=c(d)$. We also show that, for every $d$, the best value of the constant $c=c(d)$ that can be achieved by such a construction is asymptotically equal to the limit of the overlap numbers of the complete $(d+1)$-uniform hypergraphs with $n$ vertices, as $n\rightarrow\infty$. For the proof of the latter statement, we establish the following geometric partitioning result of independent interest. For any $d$ and any $\epsilon>0$, there exists $K=K(\epsilon,d)\ge d+1$ satisfying the following condition. For any $k\ge K$, for any point $q \in \mathbb{R}^d$ and for any finite Borel measure $\mu$ on $\mathbb{R}^d$ with respect to which every hyperplane has measure $0$, there is a partition $\mathbb{R}^d=A_1 \cup \ldots \cup A_{k}$ into $k$ measurable parts of equal measure such that all but at most an $\epsilon$-fraction of the $(d+1)$-tuples $A_{i_1},\ldots,A_{i_{d+1}}$ have the property that either all simplices with one vertex in each $A_{i_j}$ contain $q$ or none of these simplices contain $q$

Insights into the unique characteristics of hepatitis C virus genotype 3 revealed by development of a robust sub-genomic DBN3a replicon

Hepatitis C virus (HCV) is an important human pathogen causing 400 000 chronic liver disease-related deaths annually. Until recently, the majority of laboratory-based investigations into the biology of HCV have focused on the genotype 2 isolate, JFH-1, involving replicons and infectious cell culture systems. However, genotype 2 is one of eight major genotypes of HCV and there is great sequence variation among these genotypes (>30 % nucleotide divergence). In this regard, genotype 3 is the second most common genotype and accounts for 30 % of global HCV cases. Further, genotype 3 is associated with both high levels of inherent resistance to direct-acting antiviral (DAA) therapy, and a more rapid progression to chronic liver diseases. Neither of these two attributes are fully understood, thus robust genotype 3 culture systems to unravel viral replication are required. Here we describe the generation of robust genotype 3 sub-genomic replicons (SGRs) based on the adapted HCV NS3-NS5B replicase from the DBN3a cell culture infectious clone. Such infectious cell culture-adaptive mutations could potentially promote the development of robust SGRs for other HCV strains and genotypes. The novel genotype 3 SGRs have been used both transiently and to establish stable SGR-harbouring cell lines. We show that these resources can be used to investigate aspects of genotype 3 biology, including NS5A function and DAA resistance. They will be useful tools for these studies, circumventing the need to work under the biosafety level 3 (BSL3) containment required in many countries

Global and local envelope protein dynamics of hepatitis C virus determine broad antibody sensitivity

Broad antibody sensitivity differences of hepatitis C virus (HCV) isolates and their ability to persist in the presence of neutralizing antibodies (NAbs) remain poorly understood. Here, we show that polymorphisms within glycoprotein E2, including hypervariable region 1 (HVR1) and antigenic site 412 (AS412), broadly affect NAb sensitivity by shifting global envelope protein conformation dynamics between theoretical “closed,” neutralizationresistant and “open,” neutralization-sensitive states. The conformational space of AS412 was skewed toward -hairpin–like conformations in closed states, which also depended on HVR1, assigning function to these enigmatic E2 regions. Scavenger receptor class B, type I entry dependency of HCV was associated with NAb resistance and correlated perfectly with decreased virus propensity to interact with HCV co-receptor CD81, indicating that decreased NAb sensitivity resulted in a more complex entry pathway. This link between global E1/E2 states and functionally distinct AS412 conformations has important implications for targeting AS412 in rational HCV vaccine design

Virus adaptation and selection following challenge of animals vaccinated against classical swine fever virus

Vaccines against classical swine fever have proven very effective in protecting pigs from this deadly disease. However, little is known about how vaccination impacts the selective pressures acting on the classical swine fever virus (CSFV). Here we use high-throughput sequencing of viral genomes to investigate evolutionary changes in virus populations following the challenge of naïve and vaccinated pigs with the highly virulent CSFV strain “Koslov”. The challenge inoculum contained an ensemble of closely related viral sequences, with three major haplotypes being present, termed A, B, and C. After the challenge, the viral haplotype A was preferentially located within the tonsils of naïve animals but was highly prevalent in the sera of all vaccinated animals. We find that the viral population structure in naïve pigs after infection is very similar to that in the original inoculum. In contrast, the viral population in vaccinated pigs, which only underwent transient low-level viremia, displayed several distinct changes including the emergence of 16 unique non-synonymous single nucleotide polymorphisms (SNPs) that were not detectable in the challenge inoculum. Further analysis showed a significant loss of heterogeneity and an increasing positive selection acting on the virus populations in the vaccinated pigs. We conclude that vaccination imposes a strong selective pressure on viruses that subsequently replicate within the vaccinated animal

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

A twist in the tail : SHAPE mapping of long-range interactions and structural rearrangements of RNA elements involved in HCV replication

The RNA structure and long-range interactions of the SL9266 cis-acting replication element located within the NS5B coding region of hepatitis C virus (HCV) were determined using selective 2′-hydroxyl acylation analysed by primer extension. Marked differences were found in the long-range interactions of SL9266 when the two widely used genotype 2a JFH-1 (HCVcc) and genotype 1b Con1b sub-genomic replicon systems were compared. In both genomes, there was evidence for interaction of the sub-terminal bulge loop of SL9266 and sequences around nucleotide 9110, though the replication phenotype of genomes bearing mutations that disrupted this interaction was fundamentally different. In contrast, a ‘kissing loop’ interaction between the terminal loop of SL9266 and sequences in the 3′-untranslated X-tail was only detectable in JFH-1-based genomes. In the latter, where both long-range interactions are present, they were independent, implying that SL9266 forms the core of an extended pseudoknot. The presence of the ‘kissing loop’ interaction inhibited the formation of SL9571 in the 3′-X-tail, an RNA structure implicated in genome replication. We propose that, SL9266 may contribute a switch function that modulates the mutually incompatible translation and replication events that must occur for replication of the positive-strand RNA genome of HCV

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

A core-particle model for periodically focused ion beams withintense space-charge

A core-particle model is derived to analyze transverse orbits of test particles evolving in the presence of a core ion beam that has uniform density within an elliptical cross-section. The model can be applied to both quadrupole and solenoidal focused beams in periodic or aperiodic lattices. Efficient analytical descriptions of electrostatic space-charge fields external to the beam core are derived to simplify model equations. Image charge effects are analyzed for an elliptical beam centered in a round, conducting pipe to estimate model corrections resulting from image charge nonlinearities. Transformations are employed to remove coherent flutter motion associated with oscillations of the ion beam core due to rapidly varying, linear applied focusing forces. Diagnostics for particle trajectories, Poincare phase-space projections, and single-particle emittances based on these transformations better illustrate the effects of nonlinear forces acting on particles evolving outside the core. A numerical code has been written based on this model. Example applications illustrate model characteristics. The core-particle model described has recently been applied to identify physical processes leading to space-charge transport limits for an rms matched beam in a periodic quadrupole focusing channel. Further characteristics of these processes are presented here