Connected regions

From the manner in which 7ra-7rb overlap in 1 arises primarily from the region of the connecting atoms C2 and C3, it is apparent that polarity changes that amplify the orbitals in this connecting region will enhance the conjugative interaction. 

The network of crude oil pipelines in the U.S. is extensive. There are approximately 55,000 miles of crude oil trunk lines (usually 8-24 inches in diameter) in the U.S. that connect regional markets. The map below shows some of the major crude oil trunk lines in the U.S. (Figure 1). 

For k 1 (1 -NN), a new object would always get the same class membership as its next neighbor. Thus, for small values of k, it is easily possible that classes do no longer form connected regions in the data space, but they can consist of isolated clouds. The classification of new objects can thus be poor if k is chosen too small or too large. In the former case, we are concerned with overfitting, and in the latter case with underfitting. 

It was known that large organic cations such as the tetraethylammonium (TEA) ion and large inactivation peptides (part of the p subunit—T1 assembly) enter the transmembrane pore and the question arises as to how that would take place given the T1 domain s narrow central core. These researchers answer the question in reference 16 through their analysis of the structure and function at the cytoplasmic interface (the connection region between the a and P subunits). 

The confirmed recombinant plasmid is sequenced in the connecting region or in all regions. 

Connected Region. A region of space enclosed within the boundaries of a closed surface is described as a connected region if it is possible to skip from one point to an other using an infinite number of paths, all of them located within this specific region of space. For example, each region located inside and outside a closed surface is, individually, a connected region. 

Reconcilable Circuits. Whether closed or open, two circuits are mutually reconcilable if they can be brought to match one another by continuous distortion, without leaving the connected region of space. If not, these circuits are described as irreconcilable. 

Loops or Reducible Surfaces. Any loop or closed surface located within a connected region of space is described as reducible if it can be continuously contracted into a point without leaving the aforementioned region of space, as illustrated by loop C in Fig. 2. In the opposite case,... 

Simply Connected Region. A region of space is described as simply connected when all circuits joining any two points are reconcilable or any loop drawn within the region is reducible. For instance, regions located inside or outside a finite surface are individually, simply connected spaces. 

Doubly Connected Region. A region of space is called doubly connected when there exists only two irreconcilable paths in this region. In this case, a single irreducible loop can be identified in this region. 

In the case of an infinitely long solenoid, space is halved and dissociated into two distinct regions (1) a simply connected region inside the solenoid and (2) a doubly connected region outside the solenoid. 

Figure 10. The molecular quasispecies and its support in sequence space. Due to unavoidable non-zero mutation rates, replicating populations form distributions of genotypes or polynucleotide sequences. As shown in the sketch these distributions are centered around a most frequent genotype called the master sequence. A population thus occupies a connected region in sequence space which, according to usual mathematical terminology, is called the support of the population.

NSG that connect regions of low and high SAR discontinuity). Such SAR pathways represent a set of compounds that when ordered appropriately exhibit a continuous series of SAR changes. While network-based analyses of landscapes have seen much activity, an alternative visualization approach described by Seebeck et al. (42) abstracted the idea of the SALI metric and extended it to include the receptor. Using this technique they were able to highlight specific regions within protein-binding sites that are most likely to lead to activity cliffs. 

Shape space covering by small connected regions in sequence space shows that only a relatively small fraction of all sequences has to be searched in order to find any of the common structure. 

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