## 1 Introduction  
Schizophrenia (SZ) is a mental condition in which individuals experience hallucinations [1], delusions, and profoundly disorganized thinking and behavior as a result of their erroneous interpretation of reality. Positive symptoms such as hallucinations, delusions, and flight of ideas are common in SZ patients, as are negative symptoms such as apathy, emotionlessness, lack of social functioning, and cognitive symptoms such as difficulties concentrating and paying attention, as well as memory deficits [2]. Literature suggests that a person's risk of developing the illness is increased by a mix of physical, genetic, psychological, and environmental variables. A stressful or emotional life experience may precipitate a psychotic episode in some persons who are predisposed to SZ. Approximately half of SZ patients have a history of drug abuse disorders [3], and nearly all of them smoke [4]. An Omega-3 polyunsaturated fatty acids (PUFAs) dietary imbalance could aggravate its course while also raising the risk of metabolic complications [5]. Despite the availability of effective pharmacological treatments for HC, up to 50% of patients experience poor illness outcomes [6; 7]. Many possible outcome factors have been revealed in group-level research, including disease-course characteristics, treatment adherence and response, comorbidity, and cognitive impairments [8]. It is yet unclear which of these features should be used for prediction, or whether findings at the group-level can be utilized to make meaningful predictions for individuals with SZ [9]. We can now use neuroimaging technologies, such as MRI, computed tomography, and positron emission tomography (PET), to research brain structure and function, thanks to advances in neuroimaging technology. Through the measurement of the blood oxygenation level-dependent (BOLD) signal, functional MRI (fMRI) can provide information about the properties of FC--that is, collections of brain regions that are coactivated to support shared functions--during task or at rest (i.e., in the absence of stimuli) [10; 11; 12]. Different task-based studies of functional magnetic resonance imaging (fMRI) [13; 14] unveiled changes between SZ and HC groups, but they have faced the challenge of difficulty in interpretation since subjects perform different scanning tasks [15]. Resting-state fMRI (rfMRI) examines behavioral characteristics such as personality, psychological states, temperament traits, sustained attention, and creative capacity, and cognitive abilities such as working memory and motor function [16; 17; 18; 19]. The majority of fMRI studies that have looked into FC in SZ have used static functional connectivity (sFC) methods, which involve averaging FC across the scanning time. These methods are based on the premise that the FC between brain regions does not change significantly during the course of the scanning session, which lasts about 5-15 min. However, in light of mounting evidence suggesting significant changes in fMRI FC across time, this assumption does not appear to be correct [20; 21]. As a result, current sfMRI research has increasingly focused on time-varying FC or dynamic FC (dFC) [22; 23]. The goal of these studies is to find connection patterns that can be seen across individuals at different times during the scanning period [24; 25]. When it comes to categorizing SZ patients, dFC has been demonstrated to outperform sFC measurements [26; 27]. Although there is substantial evidence that the brain FC of patients with SZ is abnormal [28; 29; 30; 31] the differences in functional connectivity observed in SZ are inconsistent across different studies. For instance, some works have revealed increased FC in the default mode region in patients with SZ [32], and increased connectivity involving default mode region nodes and cortical and subcortical domain nodes [33], whilst reduced or mixed FC was seen between cortical regions and default mode regions [34].