## 4 Problem Formulation and Brief System Architecture
### Primary Layer
#### 4.1.2 Data Acquisition  
Our primary data sources are patient and hospital. A patient generates data through the visiting frequency to a doctor in a hospital or through some wearable device. The data source of a hospital is their doctor and patient information, medical billing information, and biomedical research and medical test results. In our proposed system, we analyze the data generated by a patient to provide a better outcome in the hospital and make a functional interaction between doctor and patient.  
**Definition 1**.: _An individual patient generates at least \(\sigma=\sum_{v=1}^{v}\left(D_{v}+Dp_{v}\right)+w+g\) amount of data in a visiting frequency to a hospital._  
Proof.: Suppose a patient generates w amount of data through some wearable device. As biomedical factors of a human change in the time domain, thus we take the latest data of the wearable device. The frequency visit of a patient \(P_{ij}^{k}\) is v in time interval t to the \(\mathit{i}^{th}\) department of \(k^{th}\) hospital, where \(\forall i\in Dp\) and \(\forall k\in H\). In each visit, a patient generates some data through the doctor's note which is generated when a patient consults a doctor D and some medical test and patient information which are kept in the department's server. We take the union set of doctors and department, represented respectively as \(D_{ij}^{k}=\{D_{1j}^{k}\cup D_{2j}^{k}\cup D_{3j}^{k}.....\}\) and \(Dp_{i}=\{Dp_{1}\cup Dp_{2}\cup Dp_{3}......\}\).  
Thus, a patient generates \(\sum_{v=1}^{v}\left(D_{v}+Dp_{v}\right)+w\) amount of data at a hospital. The genomic sequence g of a patient changes very slowly, thus we assume that any genomic sequence is constant. So, the equation can be expressed as Equation (1).  
\[\sigma=\sum_{v=1}^{v}\left(D_{v}+Dp_{v}\right)+w+g \tag{1}\]  
It is noted that the data generation of a patient increases very sharply when the visiting frequency is increased to a hospital.  
**Definition 2**.: _Data generated by a hospital for all patients is at least \(\beta=\sum_{i=1}^{p}\alpha_{i}\)._  
Proof.: A hospital consists of various departments. Those departments generate a lot of medical data. Two types of patients generate data for a hospital. The first type consults with a doctor, but they do not stay overnight, and their generation of data is at least \(\sigma=\sum_{v=1}^{v}\left(D_{v}+Dp_{v}\right)+w+g\), proved in Definition 1. The other type of patient stays overnight in the hospital and generates more data. In a hospital, data consists of both text data such as a doctor's note and some medical test reports, and image data such as X-rays and signal data, e.g., ECG or heart rate. The patient who stay overnight in the hospital generates s, t, and u megabytes of data from text, image, and signal, respectively. The data made by a patient in a hospital is f(TD), f(ID), and f(SD), where TD refers to text data, ID means image data, and SD is signal data. A patient generates \(\Phi(P)\) amount of data in a hospital, which can be expressed by Equation (2).  
\[\Phi(P)=\sum f(TD)*s+\sum f(ID)*t+\sum f(SD)*u \tag{2}\]  
Total medical data generation for a patient is \(\alpha\) shown in Equation (3).  
\[\alpha=\sigma*\Phi(P) \tag{3}\]  
Thus, the data generated by a hospital for all patients is at least \(\beta\) in Equation (4).  
\[\beta=\sum_{i=1}^{p}\alpha_{i} \tag{4}\]