Geometric partitioning of cohesin and condensin is a consequence of chromatin loops

SMC (structural maintenance of chromosomes) complexes condensin and cohesin are crucial for proper chromosome organization. Condensin has been reported to be a mechanochemical motor capable of forming chromatin loops, while cohesin passively diffuses along chromatin to tether sister chromatids. In budding yeast, the pericentric region is enriched in both condensin and cohesin. As in higher-eukaryotic chromosomes, condensin is localized to the axial chromatin of the pericentric region, while cohesin is enriched in the radial chromatin. Thus, the pericentric region serves as an ideal model for deducing the role of SMC complexes in chromosome organization. We find condensin-mediated chromatin loops establish a robust chromatin organization, while cohesin limits the area that chromatin loops can explore. Upon biorientation, extensional force from the mitotic spindle aggregates condensin-bound chromatin from its equilibrium position to the axial core of pericentric chromatin, resulting in amplified axial tension. The axial localization of condensin depends on condensin’s ability to bind to chromatin to form loops, while the radial localization of cohesin depends on cohesin’s ability to diffuse along chromatin. The different chromatin-tethering modalities of condensin and cohesin result in their geometric partitioning in the presence of an extensional force on chromatin.

Optimizing the Formation of DMAs in a Water Distribution Network Applying Geometric Partitioning (GP) and Gaussian Mixture Models (GMMs)

In the last three decades, the need of achieving a reliable water distribution system has become more eminent for both the consumer’s satisfaction and the efficient management of water sources. The purpose of this paper is to provide an optimal separation of a water distribution network (WDN) into District Metered Areas (DMAs) in order to ensure that the delivered water is of proper age and pressure. At first, the water distribution network is divided into smaller areas via the method of Geometric Partitioning, which is based on Recursive Coordinate Bisection (RCB). Subsequently, Gaussian Mixture Modelling (GMM) solution is applied, obtaining an optimal placement of isolation valves and separation of the WDN into DMAs. The performance of the proposed system is evaluated on two different networks and is compared against the Genetic Algorithm (GA) tool, constituting a very promising approach, especially for sizeable water distribution networks due to the diminished running time and the noteworthy reduction of pressure and water age.