Search results for " Regular"
showing 10 items of 197 documents
Constant sign and nodal solutions for nonlinear robin equations with locally defined source term
2020
We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood of zero). Using suitable cut-off techniques together with variational tools and comparison principles, we show that for all big values of the parameter, the problem has at least three nontrivial smooth solutions, all with sign information (positive, negative and nodal).
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
CRISPR-mediated strand displacement logic circuits with toehold-free DNA
2021
DNA nanotechnology, and DNA computing in particular, has grown extensively over the past decade to end with a variety of functional stable structures and dynamic circuits. However, the use as designer elements of regular DNA pieces, perfectly complementary double strands, has remained elusive. Here, we report the exploitation of CRISPR-Cas systems to engineer logic circuits based on isothermal strand displacement that perform with toehold-free double-stranded DNA. We designed and implemented molecular converters for signal detection and amplification, showing good interoperability between enzymatic and nonenzymatic processes. Overall, these results contribute to enlarge the repertoire of su…
Engineering CRISPR guide RNA riboswitches for in vivo applications
2019
CRISPR-based genome editing provides a simple and scalable toolbox for a variety of therapeutic and biotechnology applications. Whilst the fundamental properties of CRISPR proved easily transferable from the native prokaryotic hosts to eukaryotic and multicellular organisms, the tight control of the CRISPR-editing activity remains a major challenge. Here we summarise recent developments of CRISPR and riboswitch technologies and recommend novel functionalised synthetic-gRNA (sgRNA) designs to achieve inducible and spatiotemporal regulation of CRISPR-based genetic editors in response to cellular or extracellular stimuli. We believe that future advances of these tools will have major implicati…
Comparison of CRISPR and Marker-Based Methods for the Engineering of Phage T7
2020
This article belongs to the Section Bacterial Viruses.
Long-term genomic coevolution of host-parasite interaction in the natural environment
2017
Antagonistic coevolution of parasite infectivity and host resistance may alter the biological functionality of species, yet these dynamics in nature are still poorly understood. Here we show the molecular details of a long-term phage–bacterium arms race in the environment. Bacteria (Flavobacterium columnare) are generally resistant to phages from the past and susceptible to phages isolated in years after bacterial isolation. Bacterial resistance selects for increased phage infectivity and host range, which is also associated with expansion of phage genome size. We identified two CRISPR loci in the bacterial host: a type II-C locus and a type VI-B locus. While maintaining a core set of conse…
New insights about the putative role of myokines in the context of cardiac rehabilitation and secondary cardiovascular prevention.
2017
Exercise training prevents the onset and the development of many chronic diseases, acting as an effective tool both for primary and for secondary prevention. Various mechanisms that may be the effectors of these beneficial effects have been proposed during the past decades: some of these are well recognized, others less. Muscular myokines, released during and after muscular contraction, have been proposed as key mediators of the systemic effects of the exercise. Nevertheless the availability of an impressive amount of evidence regarding the systemic effects of muscle-derived factors, few studies have examined key issues: (I) if skeletal muscle cells themselves are the main source of cytokin…
A posteriori modelling-discretization error estimate for elliptic problems with L ∞-Coefficients
2017
We consider elliptic problems with complicated, discontinuous diffusion tensor A0. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say Aϵ, and to use standard finite elements. In [19] a combined modelling-discretization strategy has been proposed which estimates the discretization and modelling errors by a posteriori estimates of functional type. This strategy allows to balance these two errors in a problem adapted way. However, the estimate of the modelling error was derived under the assumption that the difference A0 - Aϵ becomes small with respect to the L∞-norm. This implies in particular that interfaces/discontinui…
Facilitation of Insulin Effects by Ranolazine in Astrocytes in Primary Culture
2022
Ranolazine (Rn) is a drug used to treat persistent chronic coronary ischemia. It has also been shown to have therapeutic benefits on the central nervous system and an anti-diabetic effect by lowering blood glucose levels and however, no effects of Rn on cellular sensitivity to insulin (Ins) have been demonstrated yet. The present study aimed to investigate the permissive effects of Rn on the actions of Ins in astrocytes in primary culture. Ins at 10-8 M, Rn (10-6 M) and Ins+Rn (10-8 M and 10−6 M respectively) were added to astrocytes during 24 h. In comparison to control cells, Rn and/or Ins caused modifications in cell viability and proliferation. p-AKT, p-ERK, p-eNOS, Mn-SOD, COX-2, and t…
Uniqueness of diffusion on domains with rough boundaries
2016
Let $\Omega$ be a domain in $\mathbf R^d$ and $h(\varphi)=\sum^d_{k,l=1}(\partial_k\varphi, c_{kl}\partial_l\varphi)$ a quadratic form on $L_2(\Omega)$ with domain $C_c^\infty(\Omega)$ where the $c_{kl}$ are real symmetric $L_\infty(\Omega)$-functions with $C(x)=(c_{kl}(x))>0$ for almost all $x\in \Omega$. Further assume there are $a, \delta>0$ such that $a^{-1}d_\Gamma^{\delta}\,I\le C\le a\,d_\Gamma^{\delta}\,I$ for $d_\Gamma\le 1$ where $d_\Gamma$ is the Euclidean distance to the boundary $\Gamma$ of $\Omega$. We assume that $\Gamma$ is Ahlfors $s$-regular and if $s$, the Hausdorff dimension of $\Gamma$, is larger or equal to $d-1$ we also assume a mild uniformity property for $\Omega$ i…