# Novel Graphical Representation and Numerical Characterization of DNA Sequences
## 3 Results and Discussion  
In this section, we will illustrate the use of the proposed cell-based descriptor \(V_{tp}\) of a DNA sequence. For any two sequences \(S_{a}\) and \(S_{b}\), suppose their descriptor vectors are \(a=(a_{1},a_{2},\cdots,a_{3k})\) and \(b=(b_{1},b_{2},\cdots,b_{3k})\), respectively. Then, their similarity can be examined by the following Euclidean distance. Clearly, the smaller the Euclidean distance is, the more similar the two DNA sequences are. \[d\left(a,b\right)=\sqrt{\sum\limits_{j=1}^{3k}\left(a_{j}-b_{j}\right)^{2}} \tag{7}\]  
Firstly, we give a comparison for CDS (Coding DNA Sequence) of \(\beta\)-globin gene of 18 species listed in Table 3. The lengths of the 18 sequences are about 434 bp. Thus \(K\) is taken to be 4, and each of these sequences is converted into a 12-D vector. According to Equation (7), we calculate the distance between any two of the 18 DNA sequences. Then an \(18\times\ 18\) real symmetric matrix \(D_{18}\) is obtained. On the basis of \(D_{18}\), a phylogenetic tree (see Figure 3) is constructed using UPGMA (Unweighted Pair Group Method with Arithmetic Mean) program included in MEGA4 [34]. Observing Figure 3, we find that the CDS are more similar for Primate group (_Gorilla, Chimpanzee, Human, Homo, CebusaPella, LagothrixLagotricha, Lemur_), Cetariodactyla group {_bovine, sheep, goat, mouflon_}, Lagomorpha group {_Rabbit, European hare_}, and Rodentia group {_mouse, rat_}, respectively. On the other hand, CDS of the two kinds of non-mammals {_Gallus, Muscoy duck_} are very dissimilar to the mammals because they are grouped into an independent branch. This is analogous to that reported in the literature [8; 12; 14; 31], and the relationship of these species detected by their graphical representations as well. From this result, a conclusion one can draw is that the cell-based descriptors of the new graphical representation may suffice to characterize DNA sequences. In order to further illustrate the effectiveness of our method, we test it by phylogenetic analysis on other three datasets: one consists of mitochondrial cytochrome oxidase subunit I (COI) genes of nine butterflies, another includes S segments of 32 hantaviruses (HVs), and the last is composed of 70  complete mitogenomes (mitochondrial genomes). For convenience, we denote the three datasets by COI, HV and mitogenome, respectively. In the COI dataset (see Table 4), which is taken from [PERSON] _et al._[12], eight belong to the _Catopsisia_ genus and one belongs to _Appias_ genus, which is used as the out-group. The average length of these COI gene sequences is 661 bp, and thus \(K\), the number of cells, is calculated as 4. According to the method mentioned above, a distance matrix is constructed, and then a phylogenetic tree (see Figure 4) is generated. Figure 4 shows that the five _pomona_ sub-species have relatively high similarity with each other, while the two _pyranthe_ sub-species cluster together  
The hantavirus (HV), which is named for the Hantan River area in South Korea, is a relatively newly discovered RNA virus in the family _Bunyaviridae_. This kind of virus normally infects rodents and does not cause disease in these hosts. Humans may be infected with HV, and some HV strains could cause severe, sometimes fatal, diseases in humans, such as HFRS (hantavirus hemorrhagic fever with renal syndrome) and HPS (hantavirus pulmonary syndrome). The later occurred in North and South America, while the former mainly in Eurasia [12; 36]. In Eastern Asia, particularly in China and Korea, the viruses that cause HFRS mainly include Hantaa (HTN) and Seoul (SEO) viruses, while Puumala (PUU) virus is found in Western Europe, Russia and northeastern China. The HV dataset analyzed in this paper includes 32 HV sequences. Phlebovirus (PV) is another genus of the family _Bunyaviridae_. Here, two PV strains KF297911 and KF297914 are used as the out-group. The name, accession number, type, and region of the 34 sequences are described in Table 5. The lengths of these sequences are in the range of 1.30-1.88 kbp.