5-hydroxymethylcytosine is a key epigenetic regulator of keratinocyte stem cells during psoriasis pathogenesis

Epigenetic regulation is now known to play an important role in determining stem cell fate during normal tissue development and disease pathogenesis. In this study, we report loss of 5-hydroxymethylcytosine (5-hmC) mediated by ten-eleven translocation (TET) methylcytosine dioxygenases in keratinocyte stem cells (KSCs) and in their progenitor transit-amplifying (TA) cells of psoriatic lesions. We establish the DNA hydroxymethylation profile in both human psoriasis as well as in the imiquimod (IMQ)-induced mouse psoriasis model. Genome-wide mapping of 5-hmC in IMQ-treated mice epithelium revealed a loci-specific reduction of 5-hmC in genes associated with maintaining stem cell homeostasis including those involved in the RAR and Wnt/β-catenin signaling pathways. Restoration of TET expression in human KSC cultures via vitamin C treatment increased 5-hmC levels and induced more normal KSC differentiation. We found that by modulating 5-hmC levels in vitro, we could alter downstream expression of genes important in regulating stem cell homeostasis like nestin as well as IL-17R known to promote the psoriatic phenotype. Our findings demonstrate that loss of 5-hmC is a critical epigenomic phenomenon in KSCs and TA cells during psoriasis pathogenesis.2019-12-17T00:00:00

On the Convergence of Decentralized Gradient Descent

Consider the consensus problem of minimizing $f(x)=\sum_{i=1}^n f_i(x)$ where each $f_i$ is only known to one individual agent $i$ out of a connected network of $n$ agents. All the agents shall collaboratively solve this problem and obtain the solution subject to data exchanges restricted to between neighboring agents. Such algorithms avoid the need of a fusion center, offer better network load balance, and improve data privacy. We study the decentralized gradient descent method in which each agent $i$ updates its variable $x_{(i)}$, which is a local approximate to the unknown variable $x$, by combining the average of its neighbors' with the negative gradient step $-\alpha \nabla f_i(x_{(i)})$. The iteration is $$x_{(i)}(k+1) \gets \sum_{\text{neighbor} j \text{of} i} w_{ij} x_{(j)}(k) - \alpha \nabla f_i(x_{(i)}(k)),\quad\text{for each agent} i,$$ where the averaging coefficients form a symmetric doubly stochastic matrix $W=[w_{ij}] \in \mathbb{R}^{n \times n}$. We analyze the convergence of this iteration and derive its converge rate, assuming that each $f_i$ is proper closed convex and lower bounded, $\nabla f_i$ is Lipschitz continuous with constant $L_{f_i}$, and stepsize $\alpha$ is fixed. Provided that $\alpha < O(1/L_h)$ where $L_h=\max_i\{L_{f_i}\}$, the objective error at the averaged solution, $f(\frac{1}{n}\sum_i x_{(i)}(k))-f^*$, reduces at a speed of $O(1/k)$ until it reaches $O(\alpha)$. If $f_i$ are further (restricted) strongly convex, then both $\frac{1}{n}\sum_i x_{(i)}(k)$ and each $x_{(i)}(k)$ converge to the global minimizer $x^*$ at a linear rate until reaching an $O(\alpha)$-neighborhood of $x^*$. We also develop an iteration for decentralized basis pursuit and establish its linear convergence to an $O(\alpha)$-neighborhood of the true unknown sparse signal

Stationary Distributions for Retarded Stochastic Differential Equations without Dissipativity

Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems in which both the drift and the diffusion coefficients depend only on the arguments with delays, the existing results become not applicable. This work uses a variation-of-constants formula to overcome the difficulties due to the lack of the information at the current time. This paper establishes existence and uniqueness of stationary distributions for retarded SDEs that need not satisfy dissipative conditions. The retarded SDEs considered in this paper also cover SDEs of neutral type and SDEs driven by L\'{e}vy processes that might not admit finite second moments.Comment: page 2