Search results for "5C"
showing 10 items of 72 documents
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, …
Expression of miR159 Is Altered in Tomato Plants Undergoing Drought Stress.
2019
In a scenario of global climate change, water scarcity is a major threat for agriculture, severely limiting crop yields. Therefore, alternatives are urgently needed for improving plant adaptation to drought stress. Among them, gene expression reprogramming by microRNAs (miRNAs) might offer a biotechnologically sound strategy. Drought-responsive miRNAs have been reported in many plant species, and some of them are known to participate in complex regulatory networks via their regulation of transcription factors involved in water stress signaling. We explored the role of miR159 in the response of Solanum lycopersicum Mill. plants to drought stress by analyzing the expression of sly-miR159 and …
Mycobacterium tuberculosis Rv2145c Promotes Intracellular Survival by STAT3 and IL-10 Receptor Signaling
2021
Although Mycobacterium tuberculosis (Mtb) is an intracellular pathogen in phagocytic cells, the factors and mechanisms by which they invade and persist in host cells are still not well understood. Characterization of the bacterial proteins modulating macrophage function is essential for understanding tuberculosis pathogenesis and bacterial virulence. Here we investigated the pathogenic role of the Rv2145c protein in stimulating IL-10 production. We first found that recombinant Rv2145c stimulated bone marrow-derived macrophages (BMDMs) to secrete IL-10, IL-6 and TNF-α but not IL-12p70 and to increase the expression of surface molecules through the MAPK, NF-κB, and TLR4 pathways and enhanced …
Statistically robust methylation calling for whole-transcriptome bisulfite sequencing reveals distinct methylation patterns for mouse RNAs
2017
AbstractCytosine-5 RNA methylation plays an important role in several biologically and pathologically relevant processes. However, owing to methodological limitations, the transcriptome-wide distribution of this mark has remained largely unknown. We previously established RNA bisulfite sequencing as a method for the analysis of RNA cytosine-5 methylation patterns at single-base resolution. More recently, next-generation sequencing has provided opportunities to establish transcriptome-wide maps of this modification. Here we present a computational approach that integrates tailored filtering and data-driven statistical modeling to eliminate many of the artifacts that are known to be associate…
Packing colorings of subcubic outerplanar graphs
2018
Given a graph $G$ and a nondecreasing sequence $S=(s_1,\ldots,s_k)$ of positive integers, the mapping $c:V(G)\longrightarrow \{1,\ldots,k\}$ is called an $S$-packing coloring of $G$ if for any two distinct vertices $x$ and $y$ in $c^{-1}(i)$, the distance between $x$ and $y$ is greater than $s_i$. The smallest integer $k$ such that there exists a $(1,2,\ldots,k)$-packing coloring of a graph $G$ is called the packing chromatic number of $G$, denoted $\chi_{\rho}(G)$. The question of boundedness of the packing chromatic number in the class of subcubic (planar) graphs was investigated in several earlier papers; recently it was established that the invariant is unbounded in the class of all sub…
Inhomogeneous long-range percolation in the weak decay regime
2023
We study a general class of percolation models in Euclidean space including long-range percolation, scale-free percolation, the weight-dependent random connection model and several other previously investigated models. Our focus is on the weak decay regime, in which inter-cluster long-range connection probabilities fall off polynomially with small exponent, and for which we establish several structural properties. Chief among them are the continuity of the bond percolation function and the transience of infinite clusters.
Miscellaneous Graph Preliminaries
2020
Summary This article contains many auxiliary theorems which were missing in the Mizar Mathematical Library [2] to the best of the author’s knowledge. Most of them regard graph theory as formalized in the GLIB series (cf. [8]) and most of them are preliminaries needed in [7] or other forthcoming articles.
Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering
2021
Motivated by the challenge of incorporating data into misspecified and multiscale dynamical models, we study a McKean-Vlasov equation that contains the data stream as a common driving rough path. This setting allows us to prove well-posedness as well as continuity with respect to the driver in an appropriate rough-path topology. The latter property is key in our subsequent development of a robust data assimilation methodology: We establish propagation of chaos for the associated interacting particle system, which in turn is suggestive of a numerical scheme that can be viewed as an extension of the ensemble Kalman filter to a rough-path framework. Finally, we discuss a data-driven method bas…
On the stability of some controlled Markov chains and its applications to stochastic approximation with Markovian dynamic
2015
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical methods. We show in particular how individual Lyapunov functions and associated drift conditions for the parametrized family of Markov transition probabilities and the parameter update can be combined to form Lyapunov functions for the joint process, leading to the proof of the desired stability property. Of particular interest is the fact that the approach applies even in situations where the two components of the process present a time-scale separation, w…
Coupled conditional backward sampling particle filter
2020
The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous theoretical results have not been able to demonstrate the improvement brought by backward sampling, whereas we provide rates showing that CBPF can remain effective with a fixed number of particles independent of the time horizon. Our result is based on analysis of a new coupling of two CBPFs, the coupled conditional backward sampling particle filter (CCBPF). We show that CCBPF has good stability properties in the sense that with fixed number of particles, …