373 research outputs found
On commuting Tonelli Hamiltonians: Autonomous case
We show that the Aubry sets, the Ma\~{n}\'{e} sets, Mather's barrier
functions are the same for two commuting autonomous Tonelli Hamiltonians. We
also show the quasi-linearity of -functions from the dynamical point of
view and the existence of common critical subsolution for their
associated Hamilton-Jacobi equations.Comment: 15 page
Achieving Optimal Throughput and Near-Optimal Asymptotic Delay Performance in Multi-Channel Wireless Networks with Low Complexity: A Practical Greedy Scheduling Policy
In this paper, we focus on the scheduling problem in multi-channel wireless
networks, e.g., the downlink of a single cell in fourth generation (4G)
OFDM-based cellular networks. Our goal is to design practical scheduling
policies that can achieve provably good performance in terms of both throughput
and delay, at a low complexity. While a class of -complexity
hybrid scheduling policies are recently developed to guarantee both
rate-function delay optimality (in the many-channel many-user asymptotic
regime) and throughput optimality (in the general non-asymptotic setting),
their practical complexity is typically high. To address this issue, we develop
a simple greedy policy called Delay-based Server-Side-Greedy (D-SSG) with a
\lower complexity , and rigorously prove that D-SSG not only achieves
throughput optimality, but also guarantees near-optimal asymptotic delay
performance. Specifically, we show that the rate-function attained by D-SSG for
any delay-violation threshold , is no smaller than the maximum achievable
rate-function by any scheduling policy for threshold . Thus, we are able
to achieve a reduction in complexity (from of the hybrid
policies to ) with a minimal drop in the delay performance. More
importantly, in practice, D-SSG generally has a substantially lower complexity
than the hybrid policies that typically have a large constant factor hidden in
the notation. Finally, we conduct numerical simulations to validate
our theoretical results in various scenarios. The simulation results show that
D-SSG not only guarantees a near-optimal rate-function, but also empirically is
virtually indistinguishable from delay-optimal policies.Comment: Accepted for publication by the IEEE/ACM Transactions on Networking,
February 2014. A preliminary version of this work was presented at IEEE
INFOCOM 2013, Turin, Italy, April 201
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HNRNPK maintains epidermal progenitor function through transcription of proliferation genes and degrading differentiation promoting mRNAs.
Maintenance of high-turnover tissues such as the epidermis requires a balance between stem cell proliferation and differentiation. The molecular mechanisms governing this process are an area of investigation. Here we show that HNRNPK, a multifunctional protein, is necessary to prevent premature differentiation and sustains the proliferative capacity of epidermal stem and progenitor cells. To prevent premature differentiation of progenitor cells, HNRNPK is necessary for DDX6 to bind a subset of mRNAs that code for transcription factors that promote differentiation. Upon binding, these mRNAs such as GRHL3, KLF4, and ZNF750 are degraded through the mRNA degradation pathway, which prevents premature differentiation. To sustain the proliferative capacity of the epidermis, HNRNPK is necessary for RNA Polymerase II binding to proliferation/self-renewal genes such as MYC, CYR61, FGFBP1, EGFR, and cyclins to promote their expression. Our study establishes a prominent role for HNRNPK in maintaining adult tissue self-renewal through both transcriptional and post-transcriptional mechanisms
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