Small RNA(sRNA)-mediated post-transcriptional regulation differs from protein-mediated regulation. Through basepairing, sRNA can regulate the target m RNA in a catalytic or stoichiometric manner. Some theoretical models were built for comparison of the protein-mediated and sRNA-mediated modes in the steady-state behaviors and noise properties. Many experiments demonstrated that a single sRNA can regulate several m RNAs, which causes crosstalk between the targets.Here, we focus on some models in which two target mRNAs are silenced by the same sRNA to discuss their crosstalk features. Additionally, the sequence-function relationship of sRNA and its role in the kinetic process of base-pairing have been highlighted in model building.
This paper first shows the exact boundary controllability for a coupled system of wave equations with Neumann boundary controls. In order to establish the corresponding observability inequality, the authors introduce a compact perturbation method which does not depend on the Riesz basis property, but depends only on the continuity of projection with respect to a weaker norm, which is obviously true in many cases of application. Next,in the case of fewer Neumann boundary controls, the non-exact boundary controllability for the initial data with the same level of energy is shown.
Studies on heat conduction are so far mainly focused on regular systems such as the one-dimensional(1D) and twodimensional(2D) lattices where atoms are regularly connected and temperatures of atoms are homogeneously distributed.However, realistic systems such as the nanotube/nanowire networks are not regular but heterogeneously structured, and their heat conduction remains largely unknown. We present a model of quasi-physical networks to study heat conduction in such physical networks and focus on how the network structure influences the heat conduction coefficient κ. In this model,we for the first time consider each link as a 1D chain of atoms instead of a spring in the previous studies. We find that κ is different from link to link in the network, in contrast to the same constant in a regular 1D or 2D lattice. Moreover, for each specific link, we present a formula to show how κ depends on both its link length and the temperatures on its two ends.These findings show that the heat conduction in physical networks is not a straightforward extension of 1D and 2D lattices but seriously influenced by the network structure.
It is proved that if a nonlinear system possesses some group-symmetry, then under certain transversality it admits solutions with the corresponding symmetry. The method is due to Mawhin's guiding function one.
Let G be a countable discrete infinite amenable group which acts continuously on a compact metric space X and let μ be an ergodic G-invariant Borel probability measure on X. For a fixed tempered F?lner sequence {Fn} in G with limn→+∞|Fn|/log n= ∞, we prove the following result:h_top^B(G_μ, {F_n}) = h_μ(X, G),where G_μ is the set of generic points for μ with respect to {F_n} and h_top^B(G_μ, {F_n}) is the Bowen topological entropy(along {F_n}) on G_μ. This generalizes the classical result of Bowen(1973).
This is the first of the two papers devoted to the study of global regularity of the 3+1 dimensional Einstein-Klein-Gordon system with a U(1)×R isometry group.In this first part,the authors reduce the Cauchy problem of the Einstein-Klein-Gordon system to a 2+1 dimensional system.Then,the authors will give energy estimates and construct the null coordinate system,under which the authors finally show that the first possible singularity can only occur at the axis.
