A generating set for a finite group G is minimal if no proper subset generates G, and
$m(G)$
denotes the maximal size of a minimal generating set for G. We prove a conjecture of Lucchini, Moscatiello ...and Spiga by showing that there exist
$a,b> 0$
such that any finite group G satisfies
$m(G) \leqslant a \cdot \delta (G)^b$
, for
$\delta (G) = \sum _{p \text { prime}} m(G_p)$
, where
$G_p$
is a Sylow p-subgroup of G. To do this, we first bound
$m(G)$
for all almost simple groups of Lie type (until now, no nontrivial bounds were known except for groups of rank
$1$
or
$2$
). In particular, we prove that there exist
$a,b> 0$
such that any finite simple group G of Lie type of rank r over the field
$\mathbb {F}_{p^f}$
satisfies
$r + \omega (f) \leqslant m(G) \leqslant a(r + \omega (f))^b$
, where
$\omega (f)$
denotes the number of distinct prime divisors of f. In the process, we confirm a conjecture of Gill and Liebeck that there exist
$a,b> 0$
such that a minimal base for a faithful primitive action of an almost simple group of Lie type of rank r over
$\mathbb {F}_{p^f}$
has size at most
$ar^b + \omega (f)$
.
Apple decline in Washington state has been increasing in incidence, particularly on Honeycrisp trees grown on G.935 rootstock. In this disease the trees exhibit dieback with necrosis at the graft ...union and in the rootstock. The cause of this disease remains unknown. To identify viral candidates, RNA-seq was performed on six trees: four trees exhibiting decline and two healthy trees. Across the samples, eight known viruses and Apple hammerhead viroid were detected, however none appear to be specifically associated with the disease. A BLASTx analysis of the RNA-seq data was performed to identify novel viruses that might be associated with apple decline. Seventeen novel putative viruses were detected, including an ilarvirus, two tombus-like viruses, a barna-like virus, a picorna-like virus, three ourmia-like viruses, three partiti-like viruses, and two narna-like viruses. Four additional viruses could not be classified. Three of the viruses appeared to be missing key genes, suggesting they may be dependent upon helper viruses for their function. Others showed a specific tropism, being detected only in the roots or only in the leaves. While, like the known apple viruses, none were consistently associated with diseased trees, it is possible these viruses may have a synergistic effect when co-infecting that could contribute to disease. Or the presence of these viruses may weaken the trees for some other factor that ultimately causes decline. Additional research will be needed to determine how these novel viruses contribute to apple decline.
The transcription factor REST silences neuronal gene expression in non-neuronal cells. In neurons, the protein is sequestered in the cytoplasm in part through binding to huntingtin. Polyglutamine ...expansions in huntingtin, which causes Huntington's disease (HD), abrogates REST-huntingtin binding. Consequently, REST translocates to the nucleus, occupies RE1 repressor sequences and decreases neuronal gene expression. In this work, we found that levels of several microRNAs (miRNAs) with upstream RE1 sites are decreased in HD patient cortices relative to healthy controls. Interestingly, one of these, the bifunctional brain enriched miR-9/miR-9*, targets two components of the REST complex: miR-9 targets REST and miR-9* targets CoREST. These data provide evidence for a double negative feedback loop between the REST silencing complex and the miRNAs it regulates.
Facioscapulohumeral muscular dystrophy (FSHD) is a potentially devastating myopathy caused by de-repression of the DUX4 gene in skeletal muscles. Effective therapies will likely involve DUX4 ...inhibition. RNA interference (RNAi) is one powerful approach to inhibit DUX4, and we previously described a RNAi gene therapy to achieve DUX4 silencing in FSHD cells and mice using engineered microRNAs. Here we report a strategy to direct RNAi against DUX4 using the natural microRNA miR-675, which is derived from the lncRNA H19. Human miR-675 inhibits DUX4 expression and associated outcomes in FSHD cell models. In addition, miR-675 delivery using gene therapy protects muscles from DUX4-associated death in mice. Finally, we show that three known miR-675-upregulating small molecules inhibit DUX4 and DUX4-activated FSHD biomarkers in FSHD patient-derived myotubes. To our knowledge, this is the first study demonstrating the use of small molecules to suppress a dominant disease gene using an RNAi mechanism.
Let G be a finite simple group. By a theorem of Guralnick and Kantor, G contains a conjugacy class C such that for each nonidentity element x \in G, there exists y \in C with G = \langle x,y\rangle . ...Building on this deep result, we introduce a new invariant \gamma _u(G), which we call the uniform domination number of G. This is the minimal size of a subset S of conjugate elements such that for each 1 \ne x \in G, there exists s \in S with G = \langle x, s\rangle . (This invariant is closely related to the total domination number of the generating graph of G, which explains our choice of terminology.) By the result of Guralnick and Kantor, we have \gamma _u(G) \leqslant \vert C\vert for some conjugacy class C of G, and the aim of this paper is to determine close to best possible bounds on \gamma _u(G) for each family of simple groups. For example, we will prove that there are infinitely many nonabelian simple groups G with \gamma _u(G) = 2. To do this, we develop a probabilistic approach based on fixed point ratio estimates. We also establish a connection to the theory of bases for permutation groups, which allows us to apply recent results on base sizes for primitive actions of simple groups.
Modernism is both a contested aesthetic category and a powerful political statement. Modernist music was condemned as degenerate by the Nazis and forcibly replaced by socialist realism under the ...Soviets. Sympathetic philosophers and critics have interpreted it as a vital intellectual defence against totalitarianism, yet some American critics consider it elitist, undemocratic and even unnatural. Drawing extensively on the philosophy of Heidegger and Badiou, The Quilting Points of Musical Modernism proposes a new dialectical theory of faithful, reactive and obscure subjective responses to musical modernism, which embraces all the music of Western modernity. This systematic definition of musical modernism introduces readers to theory by Badiou, Žižek and Agamben. Basing his analyses on the music of William Walton, Harper-Scott explores connections between the revolutionary politics of the nineteenth and twentieth centuries and responses to the event of modernism in order to challenge accepted narratives of music history in the twentieth century.
Societal and environmental pressures demand high-quality and resilient cropping plants and plant-based foods grown with the use of low or no synthetic chemical inputs. Mild strain cross-protection ...(MSCP), the pre-immunization of a plant using a mild strain of a virus to protect against subsequent infection by a severe strain of the virus, fits with future-proofing of production systems. New examples of MSCP use have occurred recently. New technologies are converging to support the discovery and mechanism(s) of action of MSCP strains thereby accelerating the popularity of their use.
Facioscapulohumeral muscular dystrophy (FSHD) is among the most common forms of muscular dystrophy. FSHD is caused by aberrant expression of the toxic
gene in muscle. Detecting endogenous
in patient ...tissue using conventional methods can be challenging, due to the low level of
expression. Therefore, developing simple and trustworthy
detection methods is an important need in the FSHD field. Here, we describe such a method, which uses the RNAscope assay, an RNA in situ hybridization (ISH) technology. We show that a custom-designed RNAscope assay can detect overexpressed
mRNA in transfected HEK293 cells and endogenous
mRNA in FSHD patient-derived myotubes. The RNAscope assay was highly sensitive for tracking reductions in
mRNA following treatment with our therapeutic mi405 microRNA, suggesting that RNAscope-based
expression assays could be developed as a prospective outcome measure in therapy trials. This study could set the stage for optimizing and developing a new, rapid RNA ISH-based molecular diagnostic assay for future clinical use in the FSHD field.
Charcot-Marie-Tooth disease type 1A (CMT1A), the most common inherited demyelinating peripheral neuropathy, is caused by PMP22 gene duplication. Over-expression of wild-type PMP22 in Schwann cells ...destabilizes the myelin sheath, leading to demyelination and ultimately to secondary axonal loss and disability. No treatments currently exist that modify the disease course. The most direct route to CMT1A therapy will involve reducing PMP22 to normal levels. To accomplish this, we developed a gene therapy strategy to reduce PMP22 using novel artificial microRNAs targeting human and mouse PMP22/Pmp22 mRNAs. Our lead therapeutic microRNA, miR871, was packaged into an AAV9 vector and delivered by lumbar intrathecal injection into C61-het mice, a model of CMT1A. AAV9-miR871 efficiently transduced Schwann cells in C61-het peripheral nerves and reduced human and mouse PMP22/Pmp22 mRNA and protein levels. Treatment at early and late stages of the disease significantly improved multiple functional outcome measures and nerve conduction velocities. Furthermore, myelin pathology in lumbar roots and femoral motor nerves was ameliorated. Treated mice also showed reductions in circulating biomarkers of CMT1A. Taken together, our data demonstrate that AAV9-miR871-driven silencing of PMP22 rescues a CMT1A model and provides proof of principle for treating CMT1A using a translatable gene therapy approach.
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