q

q

on. Therefore, some more advanced sequence comparison

ms were developed more than a decade ago, i.e., comparing

s based on the sequence statistics such as the word library or the

rary [Gao and Qi, 2007; Sims, et al., 2009; Wang, et al., 2009;

d Kim, 2011; Kolekar, et al., 2012; Hatje and Kollmar, 2012;

er, et al., 2014]. This type of algorithms is named as the

t-free sequence comparison approaches and has played a very

t role in many modern whole-genome pattern discovery projects.

ddition, the quantum computing technique has also been

ed for sequence homology alignment [Huo, et al., 2008; Prousalis

ofaos, 2019] and whole-genome de novo sequence assembly

d Nam, 2018].

global optimisation pattern discovery problem

achine learning algorithms are originally based on the Newton’s

which is also called the greatest descent method or the greedy

ethod. To estimate model parameters for a machine learning

numerical objective function, which is differentiable, needs to be

ed at first. The basic principle is to find a saddle point on the

function curve. At the saddle point, the objection function is

d. The most useful method of detecting a saddle point within an

function curve is based on the derivative function of the

function. This is why an objective function must be

able. A saddle point is always residing at the point in which the

vative function is zeroed and the objective function value at a

int is minimised.

arch for a saddle point within an objective function curve to

the parameters for a complicated model is called the Newton’s

Fletcher, 1987; Nocedal and Wright, 1999]. With this method, no

here the initial point is, the method will lead the move to a saddle

the objective function curve very quickly and efficiently. The

rs of a model which have been mapped to a saddle point are called