Absolute co-supplement and absolute co-coclosed modules

A module M is called an absolute co-coclosed (absolute co-supplement) module if whenever M ≅ T/X the submodule X of T is a coclosed (supplement) submodule of T. Rings for which all modules are absolute co-coclosed (absolute co-supplement) are precisely determined. We also investigate the rings whose (finitely generated) absolute co-supplement modules are projective. We show that a commutative domain R is a Dedekind domain if and only if every submodule of an absolute co-supplement R-module is absolute co-supplement. We also prove that the class Coclosed of all short exact sequences 0→A→B→C→0 such that A is a coclosed submodule of B is a proper class and every extension of an absolute co-coclosed module by an absolute co-coclosed module is absolute co-coclosed.Scientific and Technical Research Council of Turke

The pseudo-code of CLIMP.

<p>The pseudo-code of CLIMP.</p

Evaluation of the three clustering algorithms in a phylogenetic foot-printing dataset.

<p>Cumulative numbers of recovered known motifs (A) and putative motifs (B) of the yeast phylogenetic foot-printing dataset in the top-ranked clusters produced by MCL, AP, and CLIMP, respectively.</p

Running time statistics.

<p>The running times of CLIMP and MCL on graphs with different densities with either one or four threads.</p

Pipeline of space-time diagram.

<p>Pipeline of space-time diagram.</p

ARI values.

<p>The adjusted Rand index values at different motif similarity cutoffs for the three clustering algorithms.</p

An illustration of merging cliques.

<p>An illustration of merging cliques.</p

An example of finding a maximal clique associated with node <i>v</i> in <i>N</i>(<i>v</i>).

<p>(a) Sort the neighbor nodes to get an array {<i>C</i>, <i>D</i>, <i>E</i>, <i>B</i>, <i>A</i>}. (b) Successively delete the nodes <i>C</i>, <i>D</i>, and <i>E</i> as well as their incident edges from <i>N</i>(<i>v</i>) to get <i>C</i>_<i>v</i> until <i>v</i> and the remaining nodes have the same degree. (c) For <i>D</i> and <i>C</i>, determine if they can be expanded to <i>C</i>_<i>v</i>.</p

Evaluation of the three clustering algorithms in a ChIP dataset.

<p>Cumulative numbers of recovered known motifs (A) and putative motifs (B) of the ChIP datasets in the top-ranked clusters produced by MCL, AP, and CLIMP, respectively.</p

Noise Propagation in Gene Regulation Networks Involving Interlinked Positive and Negative Feedback Loops

<div><p>It is well known that noise is inevitable in gene regulatory networks due to the low-copy numbers of molecules and local environmental fluctuations. The prediction of noise effects is a key issue in ensuring reliable transmission of information. Interlinked positive and negative feedback loops are essential signal transduction motifs in biological networks. Positive feedback loops are generally believed to induce a switch-like behavior, whereas negative feedback loops are thought to suppress noise effects. Here, by using the signal sensitivity (susceptibility) and noise amplification to quantify noise propagation, we analyze an abstract model of the Myc/E2F/MiR-17-92 network that is composed of a coupling between the E2F/Myc positive feedback loop and the E2F/Myc/miR-17-92 negative feedback loop. The role of the feedback loop on noise effects is found to depend on the dynamic properties of the system. When the system is in monostability or bistability with high protein concentrations, noise is consistently suppressed. However, the negative feedback loop reduces this suppression ability (or improves the noise propagation) and enhances signal sensitivity. In the case of excitability, bistability, or monostability, noise is enhanced at low protein concentrations. The negative feedback loop reduces this noise enhancement as well as the signal sensitivity. In all cases, the positive feedback loop acts contrary to the negative feedback loop. We also found that increasing the time scale of the protein module or decreasing the noise autocorrelation time can enhance noise suppression; however, the systems sensitivity remains unchanged. Taken together, our results suggest that the negative/positive feedback mechanisms in coupled feedback loop dynamically buffer noise effects rather than only suppressing or amplifying the noise.</p> </div