Creation of Formula to Predict Time and Cost Benefit by Using 5D BIM Rather than Traditional Method of Construction

Building Information Modeling (BIM) is becoming a well-known established collaboration process in the construction industry. Owners are increasingly requiring BIM services from construction managers, architects and engineering firms. Many international construction firms are now investing in “BIM” technologies during bidding, preconstruction, construction and post construction. The goal of this research is to understand and examine the uses and benefits of 5D BIM for construction project of Pakistan. There are three objectives to this research. First is to make comparative analysis of an existing high rise building with reference to scheduling and cost as done by traditional method. Second is to develop 5D model of high rise building with help of autodesk revit and autodesk navisworks. Third is to make 3D models of 20 and 30 storey building on autodesk revit and navisworks by making 10 storey building as reference to overview the comparative benefits of schedule and cost with help of 5D BIM and development of formula with reference to schedule and cost for any number of stories of building. First an existing commercial building was selected for comparative study between 5D BIM analysis and traditional CAD methods. 5D Building information model was created and analyzed. Furthermore, the BIM-based schedule and cost was integrated to 5D model. Finally, the project concluded with an analysis on the advantages of 5D BIM and its implementation barriers in construction industry of Pakistan. The study concludes that despite of few shortcomings and barriers in 5D BIM implementation, BIM and 5D construction processes are concluded as a promising tool for construction planning. 5D BIM modeling helps to reduce time and cost of a project and provide efficient planning by better visualization of construction work, better communication among project teams, detailed and accurate work plans and quantity takeoffs. Also, with increase in number of stories time and cost benefits also increase in 5D BIM.

Introduction
The Construction industry has a greater impact on the economy of all countries. It is one of the sectors that provide crucial ingredients for the development of economy. Due to poor cost and time management these days, the construction industry is facing a huge amount of cost overrun. This has become quite a problem for the construction industry. Poor cost management and overrun are huge problem and very serious issue when it comes to project cost in both developed and emerging countries. The increasing complexity of infrastructure projects and the environment within which they are constructed place greater demand on construction managers to deliver projects on time, within the planned budget and with high quality [1].
There is still a great difference between execution and plan despite the fact that a huge number of planning methodologies have been adopted and implemented. But these are not enough to improve the construction process. Hence an competent and operative planning method is needed to increase project performance at different levels of project to minimize the risks of cost overruns and time delays [2]. The adoption of BIM for complex high-rise buildings gives innovative structure engineering and improved construction technology. Among such innovative engineering and technologies, structural analysis in construction process, automated clash detecting technology, real time construction sequence simulation and 3D measurement technology is obtained. Also, sophistication of collaboration environment, promotion of technology and construction innovation is obtained by implementing BIM to high rise buildings [3]. a series of activities for estimating, allocating, and controlling costs within the project. It allows determining and approving budget for the project and controlling spending. For example, in construction project cost management it is vital to estimate cost of materials, equipment, salary of workers, etc. In IT project cost management, it is critical to estimate cost of software development, salary of IT staff, etc. Effective project cost management allows each project to be specific and unique because that project entails costs and requires specific funding. However, no matter whether you lead a software development project (IT project cost management) or construction project (construction project cost management), you should consider project cost management as a process that consists of the three key steps (get more info at the PM guidelines).

Traditional project cost estimation processes
The process of managing project costs is an activity for estimating costs, developing project budget and controlling spending. The project cost management process includes the following key steps: Resource planning: In the initial phase of a project the required resources to complete the project activities need to be defined. Work Breakdown Structures (WBS) and historical information of comparable projects can be used to define which physical resources are needed. You can think of the required time, material, labor, equipment, etc. Once the resource types and quantities are known the associated costs can be determined.
Cost estimation: It is the project cost management process step when the project manager cooperates with the financial department to estimate costs required for purchasing all necessary good/services and undertaking necessary activities to deliver the project. Project Cost Estimation is conducted at the planning phase. The project manager uses project cost management software to develop spreadsheets and make calculations.
Budget determination: At this step of the cost management process, cost spreadsheets are used to develop the budget framework and determine the budget. The project manager can use project cost management software to work in collaboration with the financial department to determine items of the budget and sources of funding and then to allocate the budget. The step entails close cooperation with the project sponsor.
Spending control: It is the step of the project cost management process when the allocated budget is reviewed, and spending is tracked. The project manager takes responsibility for control spending and to ensure that the budget allocation is optimized, and costs are fully covered with the planned and allocated budget.

Limits of traditional approaches when planning resource and cost in complex projects
Ambiguity: First, the resource allocation process is even more complex when information about the required skills or the skills possessed by potential project team members are unclear or ambiguous. Moreover, role conflict and role ambiguity have a direct influence on the creativity of a project team. When project team members face unclear or ambiguous specifications of what they are meant to do, this makes it all he more difficult to execute and coordinate the project.

Uncertainty:
The inherent uncertainty of cost estimates makes it all the more difficult to establish a robust project cost baseline. Even though some advanced methods try to build up cost envelopes for each part of a single project, they remain not widely used by industrial practitioners.
Propagation: In terms of resource allocation, "a resource is a relative concept, rather than an element in itself because it is heterogeneous and interdependent with other resources it is combined with" Limits of Traditional Project Management Approaches. Resource allocation approaches, however, do not generally use this interdependence as a parameter, which may not facilitate resource coordination in the end. Moreover, to the best of our knowledge, there is no reputed approach which directly introduces the interconnection of activities in terms of cost and the potential propagation and consequences of a possible overcost during the execution of the project. One could however anticipate more the possibilities of cost reduction of other activities if a specific activity faces overcost. An interesting research perspective would be to facilitate the anticipation of cost monitoring and control through the introduction of possible cost decisions due to the complexity of the project networks [4].

Project cost management with 5D BIM
Building information modelling (BIM) provides both opportunities and challenges for the project cost management profession. As quantification increasingly becomes automated and BIM models develop the role of the project cost manager will need to adapt accordingly to provide more sophisticated cost management services that incorporate 4D time and 5D cost modelling and sharing cost information/data with the project team as part of the BIM integrated project delivery approach. The RICS (2014) contend that BIM provides project cost managers with the opportunity to spend more time on providing knowledge and expertise intensive advice to the project team-the automation of processes such as quantification will substantially reduce time spent on technical processes and will provide more time and the digital tools for higher value-added and more sophisticated cost management services. Mitchell (2012) describes the importance for the project cost management professional to embrace the 5th dimension and become key players in the BIM environmentthe '5D Project Cost Manager'. Muzvimwe (2011) supports this notion and describes the value of the cost manager in being able to simulate and explore various design and construction scenarios for the client in real time through having their cost data and quantities integrally linked in the live BIM model. This certainly raises the value of the cost management service but is dependent on the cost manager having BIM capability/expertise, sharing their cost data in the model and having the experience, expertise and intuition to analyze and critique the information that is being generated by the model [5].

Autodesk Revit
After introducing the most popular building information modeling software and autodesk as company that develops Revit, the spotlight will move now to Revit itself. In 1997 Reonid Raiz and Irwin Jungreis founded the company Charles River Software, which started building Revit. Their main goal was to include parametric modelling to existing idea of CAD, and to allow the user to determine the parametric components graphically, instead of having to use a programming language. This idea of bidirectional associativity is the concept that distinguished Revit from other Building information modeling software platforms for a certain period of time, until the competition caught up. Bidirectional associativity means that when u change a certain component of your model (for example wall) all components in relation with the modified one will automatically adjust themselves to applied changes. This concept of bi-directional associativity makes the software more intuitive and therefore easier to work with for the user. It also saves enormous amount of time when applying changes to an existing model.

Microsoft project
Using this software, we can get the actual cash flow, planned cash flow and achieved cash flow. Microsoft project is a project management software program, developed and sold by Microsoft, which is designed to assist a project manager in developing a plan, assigning resources to tasks, tracking progress, managing the budget, and analyzing workloads. Project creates budgets based on assignment work and resource rates. As resources are assigned to tasks and assignment work estimated, the program calculates the cost, equal to the work times the rate, which rolls up to the task level and then to any summary tasks and finally to the project level. Resource includes people, equipment and materials can be shared between projects using a shared resource pool. Each resource can have its own calendar, which defines what days and shifts a resource is available. Resource rates are used to calculate resource assignment costs which are rolled up and summarized at the resource level. Each resource can be assigned to multiple tasks in multiple plans and each task can be assigned multiple resources, and the application schedules task work based on the resource availability as defined in the resource calendars.

Autodesk naviswork
Autodesk navisworks manage is a software application providing a comprehensive project review solution which supports coordination, analysis, and communication of design intent and constructability. It allows integration of multidisciplinary design data created in different BIM design applications to a single project model. It also provides the interference management and clash detection functions to anticipate and avoid potential problems in the project which can eventually minimize delays and reworks. In addition, it supports 4D and 5D simulation and analysis by combining parametric models with the project schedule and costs.

5D Bim Implementation Studies
Case study 1

5D BIM analysis on an existing local project
Introduction-b-type apartment building, sector i-16/3 islamabad: An existing small-scale commercial building was selected to illustrate the process of visualization, scheduling and cost estimation in BIM. The building selected for this purpose was "B-type apartments sector I-16/3 ISLAMABAD ". This was selected because it has simple architectural and structural designs, data was easily available, relevant to research, and traditional tools were used for designing and construction process. Figure 1 shows the perspective view of building ( Table 1). The building is basically a framed structure residential flats building having two staircases and two lifts. The estimated project duration was calculated to be 2.6 years, but it actually got completed in 3.5 years. Total project cost was estimated to be 175M, but its actual cost was about 218M.  Traditional tools-design and construction process: The traditional tools used for the design and construction process of this building are described below. These tools are commonly used traditional tools in the construction industry of Pakistan.

B.
Project Scheduling-MS Project

C. Quantities and Cost Estimation-Microsoft Excel
Time analysis of b-type apartment building: On the basis of data collected, time analysis on B-Type apartment building was performed. The graphical representation of analysis is shown below in Figure 2. The blue bar shows the planned duration of the project and orange bar shows the actual duration of project. The estimated project duration was calculated to be 2.6 years but it actually got completed in 3.2 years. The major difference in actual and planned duration of the project occurs during the construction phase i.e. 83%. The construction phase was planned to be complete in 2 years, but it got completed actually in 2.6 years. In construction phase it can also be seen that major difference occurs in civil works i.e. 80%. Whereas design phase duration contains 9% difference of actual and estimated project time. According to lean construction institute, a well-managed project has PPC (percentage plan complete) value greater than 60%. It is the ratio between actual and estimated project duration. B-Type apartment building project has a PPC value calculated as 12% which shows it was a poorly managed project. Cost analysis of b-type apartment building: It is observed during project time analysis of B-Type apartment building, the major difference of time occurred during the construction phase of the project. Therefore, cost analysis of project during construction phase was conducted. The cost analysis is shown in Figure 3. The bar in blue shows planned or 5D BIM cost and bar in orange shows the estimated cost. Total project cost was estimated to be 175M, but its actual cost was about 218M. It means 42M is the difference in estimated and actual cost of the project. So major increase in cost was occurred in structure, finishes and electrical works. The estimated cost of structure work was 138M while its actual cost came out to be 168M.

Case Study 2
5d Bim Analysis on A 20 And 30-Storey Building with Reference To 10-Storey Building Introduction-analysis on 20 storey building: A 5D BIM model of 20 storey building was created by taking the case study one's 10 storey apartment building as reference and making these assumptions that 20 storey building has: a.
Same storey height as of 10 storey building.

b.
Same building area as of 10 storey building.
c. Same type of unexpected time and cost overruns occur as of 10 storey building.
Time analysis of 20 storey building: On the basis of data collected from analysis of ten storey B-Type Apartment Building, time analysis on 20 storey building was performed by taking ten storey building as reference. The graphical representation of analysis is shown below in Figure 4. The blue bar shows the planned duration of the project and orange bar shows the actual duration of project. The estimated project duration was calculated to be 3.4 years, but it actually got completed in 4 years. The major difference in actual and planned duration of the project occurs during the construction phase i.e. 80%. The construction phase was planned to be complete in 2.7 years, but it got completed actually in 3.3 years. In construction phase it can also be seen that major difference occurs in civil works i.e. 84%. Whereas design phase duration contains 11% difference of actual and estimated project time. According to lean construction institute, a well-managed project has PPC (percentage plan complete) value greater than 60%. It is the ratio between actual and estimated project duration. B-Type apartment building project has a PPC value calculated as 12% which shows it was a poorly managed project. Cost analysis of 20 storey building: It is observed during project time analysis of 20 Storey Building, the major difference of time occurred during the construction phase of the project. Therefore, cost analysis of project during construction phase was conducted. The cost analysis is shown in Figure 5. The bar in blue shows planned or 5D BIM cost and bar in orange shows the estimated cost. Total project cost was estimated to be 419M, but its actual cost was about 521M. It means 102M is the difference in estimated and actual cost of the project. So major increase in cost was occurred in structure, finishes and electrical works. The estimated cost of structure work was 331M while its actual cost came out to be 390M.

Introduction-analysis on 30 storey building
A 5D BIM model of 30 storey building was created by taking the case study one's 10 storey apartment building as reference and making these assumptions that 30 storey building has: A. Same storey height as of 10 storey building.

B.
Same building area as of 10 storey building.

C.
Same type of unexpected time and cost overruns occur as of 10 storey building.

Time analysis of 30 storey building:
On the basis of data collected from analysis of ten storey B-Type apartment building, time analysis on 30 storey building was performed by taking ten storey building as reference. The graphical representation of analysis is shown below in Figure 6. The blue bar shows the planned duration of the project and orange bar shows the actual duration of project. The estimated project duration was calculated to be 4.1years but it actually got completed in 5 years. The major difference in actual and planned duration of the project occurs during the construction phase i.e. 85%. The construction phase was planned to be complete in 3.4 years but it got completed actually in 4.2 years. In construction phase it can also be seen that major difference occurs in civil works i.e. 82%. Whereas design phase duration contains 11% difference of actual and estimated project time. According to lean construction institute, a well-managed project has PPC (percentage plan complete) value greater than 60%. It is the ratio between actual and estimated project duration.
B-Type apartment building project has a PPC value calculated as 12% which shows it was a poorly managed project.

Cost Analysis of 30 Storey Building:
It is observed during project time analysis of 30 Storey Building, the major difference of time occurred during the construction phase of the project. Therefore, cost analysis of project during construction phase was conducted. The cost analysis is shown in Figure 7. The bar in blue shows planned or 5D BIM cost and bar in orange shows the estimated cost. Total project cost was estimated to be 706M, but its actual cost was about 890M. It means 184M is the difference in estimated and actual cost of the project. So major increase in cost was occurred in structure, finishes and electrical works. The estimated cost of structure work was 582M while its actual cost came out to be 702M.

Results and Recommendation
In this section, the results extracted from case studies will be discussed. On the basis of 5D BIM analysis of B-Type apartment building with building design from traditional method and by making it reference doing 5D BIM analysis of 20 and 30 storey building, time analysis was conducted. As shown in Figure 8, time in days are mentioned along y axis and storeys are mentioned along x axis. It can be clearly seen that by the use of 5D BIM technology, the project could have been completed as per the estimated time or even less if worked as per plan. The difference in planned and actual duration could have been reduced using 5D BIM. On the basis of 5D BIM analysis of ten, twenty and thirty storey building, cost analysis was evaluated. As shown in Figure 9, cost in millions are mentioned along y axis and building stories are mentioned along x axis. It can be observed that by the use of 5D BIM technology, the project could have been completed as per the estimated cost or even less if worked as per the plan. The difference in planned and actual cost could have been reduced using 5D BIM. On the basis of 5D BIM analysis of ten, twenty and thirty storey building, analysis of civil works is done. As shown in Figure 10, cost in millions are mentioned along y axis and building stories are mentioned along x axis. It can be observed that by the use of 5D BIM technology, the major factor of cost overrun is civil works. The difference in planned and actual cost could have been reduced using 5D BIM. Also, with increase in storey height more benefit in cost is achieved like in case of 30 storey building 120M can be saved if 5D BIM is used rather than traditional method of construction. As compared to traditional CAD method, BIM based detailed project design documentation can improve the visualization of the project, so design changes are reduced during construction phase. Quantity take-off and cost estimation taken by BIM is faster and more accurate as compared to traditional methods. When plans are created elevations, sections and even schedules are created automatically. So, time is not wasted on drafting and there are less chances of errors. An insight review of these case studies clearly shows that 5D BIM has brought many advanced construction management skills to project scheduling and cost estimation and also project controls for contractors. Since the quantities of building components are read by Autodesk Revit Architecture from BIM model directly. This will save contractors substantial amount of time on cost estimating. Also, the changes in design of building model can be updated in minutes in quantity take-off. It means that owner can get a faster cost feedback on changes in design using 5D BIM. In these case studies, the tasks defined with planned and actual dates in Gantt chart view. By comparison of planned and actual dates, the status bars can tell the contactor the progress of project in a simple way. The model of the progress can also help contractor to adjust the project schedule according to design change in building model.

Result from case studies
With the help of 5D BIM, fresh engineer with less experience of management of project can produce a well-managed project. Knowledge and visualization are basic components of project management. An experienced project manager based on his experience can visualize 2D CAD drawings and can manage the project. But visualization of 5D BIM can enable fresh engineer to manage a project effectively. Construction of high-rise building projects can be managed well at fast tracks by planning and visualizing multiple tasking at pre-construction phase of project using 5D BIM. Better visualization of various construction process can help to improve the process of planning and improve the project team collaboration. If each and every project team member will be able to understand the design and construction process of the project, then collaboration among themselves will be increased.

Creation of formulas for estimation of time and cost of various storey heights
Formula of cost for N number of heights of building: As result of total cost estimation of 10, 20 and 30 storey building a comparison of their total costs is done. By comparing the difference in estimated and 5D BIM cost of ten, twenty and thirty storey building, a common value in their differences is obtained by making 10 storey building as reference (Table 2). By using this formula of number of storey, cost benefit of any number of storey can be done if it is built on 5D BIM rather than traditional method. For example, if any owner wants to build 100 storey building by 5D BIM and he/she wants to know overall cost benefit, it can be seen easily by putting number of storey as 100 in above formula. Cost benefit of (100 no of storey) by 5D BIM = 600M From the above formula it can also be said that with increase in stories of a building, cost benefit also increases. More the number of stories more are the losses in cost that can be avoided.

Formula of schedule for N number of heights of building:
Similar procedure can be done in case of schedule of a building by making ten storey building as a reference and taking differences between actual and 5D BIM schedule. By comparing the values of differences of ten, twenty and thirty storey building a formula is devised that can tell what benefit in form of days is obtained if 5D BIM is used rather than traditional method (Table 3). By using this formula of number of storey, schedule benefit of any number of storey can be done if it is built on 5D BIM rather than traditional method. For example, if any owner wants to build 100 storey building by 5D BIM and he/she wants to know overall schedule benefit, it can be seen easily by putting number of storey as 100 in above formula. Schedule benefit of (100 no of storey) by 5D BIM = 1098 Days

Conclusion
With the help of analysis of time and cost of ten, twenty and thirty storey building by traditional and 5D BIM method. It can be seen that with increase in storey height due to increase in complexity of projects time delays and cost overruns are very common. Also, in civil works both these delays have their major part. With help of 5D BIM it is seen that time and cost benefits are obtained and with increase in storey height these benefits in terms of days and cost also increases.
By the assistance formula devised to see the 5D benefits in terms of time and cost. By only putting storey height in the formula one can easily find out that how much saving in terms of days and in terms of cost one can obtain. So, it will be easier for future owners to decide rather to use older methods of construction or to switch on new methods. In comparison to traditional construction method by using 5D BIM the productivity of project can be increased. There are many positive impacts of 5D BIM that cannot be achieved through traditional planning methods. The most significant benefits of 5D BIM are found to be better visualization of construction process, better communication among project members and increased planning efficiency.
In addition to it, 5D BIM helps in achieving detailed and accurate work plans, quantity take-offs and cost estimates. 5D BIM enhances the efficiency of project schedule and also helps in increasing constructability and site safety. The research also conducted that 5D BIM can help the project manager in delivering a successful project. The project manager can make better decisions in the project process. With 5D BIM, a better depiction of reality is obtained, which makes it easier to see the consequences of their decisions. Hence a better basis of decisions is obtained through 5D BIM in comparison with traditional method and project manager can do a better job. In a nutshell, it is concluded that implementing 5D BIM can be a milestone development for construction firms and it can help mitigating the most common problems in the construction projects by controlling time and cost overruns with enhanced planning efficiency.

Recommendation
In future more dimensions of BIM like 6D BIM that tells the energy efficiency estimate of a building must be explored and research work should be done on it. In this way BIM can become a common construction tool of Pakistan industry. A company specialized in BIM must be devised to produce effective links between different companies and it should also provide training to the staff. In this way companies can be shifted towards 5D BIM. Seminars in universities and offices should be conducted to create awareness of benefits of 5D BIM in construction industry. In addition to it, software of 5D BIM should also be teach to civil and architecture students.
If the barriers in implementation of 5D BIM can be overcome, a large amount of BIM benefits can be extracted. This thing can bring drastic changes in construction industry of Pakistan. So, efforts should be done to overcome these barriers. Moreover, by application of 5D modeling on runtime projects of construction firm's actual data and information that determines the effectiveness of 5D modeling can be obtained. It will develop a broader perception of 5D BIM.
Steps should be taken to increase the contribution of construction industry in economy of Pakistan that can only be possible if delays in schedule and cost over runs are controlled. For this, 5D BIM is a best choice that will help in boosting up our economy.


Detecting bursty terms in computer science research

Research topics rise and fall in popularity over time, some more swiftly than others. The fastest rising topics are typically called bursts; for example “deep learning”, “internet of things” and “big data”. Being able to automatically detect and track bursty terms in the literature could give insight into how scientific thought evolves over time. In this paper, we take a trend detection algorithm from stock market analysis and apply it to over 30 years of computer science research abstracts, treating the prevalence of each term in the dataset like the price of a stock. Unlike previous work in this domain, we use the free text of abstracts and titles, resulting in a finer-grained analysis. We report a list of bursty terms, and then use historical data to build a classifier to predict whether they will rise or fall in popularity in the future, obtaining accuracy in the region of 80%. The proposed methodology can be applied to any time-ordered collection of text to yield past and present bursty terms and predict their probable fate.

Introduction
In 2012, a group of scientists from the University of Toronto built a convolutional neural network (CNN) and applied it to a well-known image classification task. Their paper (Krizhevsky et al. 2017) sparked a revolution in the field of deep learning; an explosion of popularity and interest that is still continuing today. CNNs have since spread outwards from their original domain and can be found in diverse fields, such as biomedicine (Chen et al. 2018) and astronomy (Dambre et al. 2015).
If we were to imagine the trajectory of the phrase "convolutional neural network" in terms of its popularity over time, we might imagine an exponential curve upwards. And indeed, when we search for it in a large database of computer science abstracts (DBLP 1 3 2019), that is what we see (Fig. 1). This behaviour-a sudden and sustained rise in popularity relative to some historical baseline level-is referred to as a burst in most of the literature (Kleinberg 2002).
Being able to detect bursty terms automatically in scientific literature would have a number of applications. Firstly, early detection might allow funding agencies and publishers to take note of the most promising new ideas and channel new support that way. For newcomers to a field and researchers in the sociology of science, automatically listing the hottest topics over time would give an instant snapshot of the evolution of the field. Finally, compiling a corpus of historical bursty terms over time might make it possible to characterise the life cycles that new ideas go through as they develop.
In this paper, we explore a burst detection methodology that requires little tuning and can be used on a large dataset. We build on work by He and Parker (2010), who used a technique from stock market analysis to detect bursty keywords in PubMed, a very large online bibliography of biomedical citations.
This work has three main research objectives: -To adapt an existing burst detection methodology to the free text of a large corpus of computer science abstracts. To our knowledge, this is the first use of this method on free text rather than a controlled vocabulary of keywords. -To report a list of historical and current bursts in the computer science literature.
-To predict the future prevalence of existing bursty terms using machine learning.

Burst detection
The problem of tracking topics in time-ordered corpora was formalised by a DARPAsponsored initiative under the name Topic Detection and Tracking (TDT). Early research Fig. 1 Number of abstracts containing the term "Convolutional neural network(s)" over time  in DBLP. While there were isolated mentions of CNNs in the 90s and 00s, the topic underwent exponential growth in popularity beginning in the year 2012, which continues to the present focused on segmenting a corpus into topics, finding the first mention of each topic and then tracking and plotting their popularity over time (Allan et al. 1998). As computer hardware improved, it became common to use Latent Dirichlet Allocation (LDA) for this kind of topic modelling (Blei et al. 2003). A typical method involves splitting the corpus into time steps, finding topics in each chunk and then linking them together across time steps based on some measure of similarity Steyvers et al. 2004;Mei and Zhai 2005). The prevalence of each topic can then be tracked over time and bursty periods identified. However, this comes with a number of disadvantages, such as the lack of interpretability of the results and the difficulty in coherently linking LDA topics together between subsequent time-steps.
The opposite approach is to first identify the bursty terms in a dataset, and then cluster them together into topics, using, for instance, Kleinberg (2002)'s burst detection algorithm. Originally developed to detect topics in email chains, Kleinberg's method assumes that terms in documents are emitted by a two-state automaton. The automaton may spontaneously transition from a non-bursty state to a bursty state, or vice versa. Variants of this have been applied across several domains: Diao et al. (2012) and Mathioudakis and Koudas (2010) used it to detect bursty topics in Twitter data, the latter in real time, while Fung et al. (2005) and Takahashi et al. (2012) applied it to news streams.
However, when it comes to scientific literature, there are a few reasons why Kleinberg's method is a less natural fit. He and Parker (2010) point out that, unlike Tweets and news articles, scientific papers tend to enter the world in batches, such as when a new edition of a journal or the proceedings of a conference is published. This violates Kleinberg's underlying assumption that new items enter the dataset in a continuous fashion. It also forces us to impose longer time steps, such as years rather than seconds. This causes a second problem: the quantity of data available.
While there are several large open-access corpora of scientific abstracts, such as Pub-Med (biomedicine), arXiv (physics and computer science), Semantic Scholar (assorted) and DBLP (computer science), all of them cover short intervals, relative to the size of the time steps. Even in the best case scenario, we are likely to have less than a hundred years worth of usable data-which means approximately a hundred time steps. There has also been a vast change in the underlying landscape over the span of the dataset, because science in general (Bornmann and Mutz 2015) and computer science in particular (Wu et al. 2018), have both seen strong and sustained growth in the last century. By contrast, unless one collects many years of Twitter data, the size and characteristics of the dataset do not change substantially over time.
Several burst detection methods from other domains have been proposed for use on scientific documents. For instance, Stroup et al. (1989) take inspiration from epidemiology, and Zhang and Shasha (2006) take inspiration from gamma rays. However, of particular interest to us is He and Parker (2010)'s work that takes a popular technique from stock market analysis and applies it to PubMed data. This is an attractive idea: a great deal of work has been done in analysing stocks, because some people are highly motivated to predict what prices will do in later time steps.

Moving average convergence divergence
The basic item in the toolkit of the stock market analyst is the moving average. While a moving average necessarily lags behind real time data, it can smooth out random fluctuations to reveal underlying trends. The simple moving average (SMA) of a time series is the sum of its values in a set interval (called the span of the SMA), divided by the width of that interval. More advanced methods use exponential moving averages (EMAs), which assign more weight to more recent data.
For a given span, n, the exponential moving average of a time series, y(t), is (Investopedia 2019): Buy and sell signals for stocks can be generated by taking two EMAs with different spans and seeing where they cross. The moving average with the longer span responds more slowly to new data, so when there is a sudden change in the price of the stock, the shorter moving average will cross it in an upwards or downwards direction (Murphy 1999) (Fig. 2b). Moving Average Convergence Divergence (MACD) takes this idea a step further (Appel 2005). The long EMA is subtracted from the short EMA to give the MACD line. This MACD line is then itself averaged, to create a fourth time series called the signal line (Fig. 2c). The difference between the MACD and signal lines is called the histogram of the data, and can be thought of as an approximate measure of curve acceleration. When the histogram is positive, the price of the stock is accelerating upwards. When it is negative, the reverse is happening.
Here we introduce these notions more formally. For two moving averages with spans n 1 and n 2 : The signal line is the MACD line, smoothed with an EMA with span n 3 ;

And the histogram is:
This is the technique that He and Parker (2010) applied to PubMed data between 1950-2008. Instead of stock prices, they looked at the frequency of MeSH terms assigned to scientific papers over time [MeSH terms, or Medical Subject Headings, are a hierarchically-ordered taxonomy maintained by the National Library of Medicine (National Library of Medicine 2019)]. Their model was evaluated by comparing their detected bursts to real events; for instance, they found that "Morphine" was a popular keyword during the Vietnam war, and "Sexually Transmitted Diseases" was a popular keyword during the AIDS crisis. They also compared several of their bursts to the results reported by Mane and Borner (2004) in a similar burst detection study. He and Parker found that both methods identified the same bursty periods for the terms.
Using a controlled vocabulary rather than free text has advantages in that it ensures the terms in the vocabulary will be meaningful, unique and free of spelling errors. However, a controlled vocabulary will necessarily lag behind the forefront of scientific development because new terms can only be added after they have risen to prominance. Additionally, keywords are not available for all datasets, limiting the scope of the method. For this reason, we use the free text of abstracts and titles. (1) (3) Signal[n 1 , n 2 , n 3 ] = EMA[n 3 ](MACD[n 1 , n 2 ]) (4) Histogram[n 1 , n 2 , n 3 ] = MACD[n 1 , n 2 ] − Signal[n 1 , n 2 , n 3 ]

Prediction
As well as detecting historically bursty terms, we would like to be able to predict whether they will become more or less prevalent in the future. Some related work has been done on this task. Prabhakaran et al. (2016) took 2.4 million abstracts from Web of Science and used an implementation of LDA to identify 500 topics. They then used a logistic regression classifier to predict whether their topics would rise or fall in popularity over subsequent time steps, yielding an accuracy of 70%. Balili et al. (2017) looked at a slightly different task; they took 21.2 million PubMed abstracts, clustered their MeSH keywords based on Fig. 2 Illustration showing how moving averages can be used to detect changepoints. a Shows how the crossover of two simple moving averages, one with a span of 12 and another with a span of 6, can generate a sell signal, b shows the same phenomenon, but with exponential moving averages, c shows the MACD graph of the time-series; note how the sell signal comes earlier than in (a) and (b) co-occurrence in article annotations and then trained a gradient-boosted trees classifier to predict whether individual clusters would survive or dissolve. Finally, in their 2011 paper, He and Parker took a database of approximately 100,000 Californian grant abstracts which were pre-labelled with "project terms" (keywords from a defined vocabulary of biomedical concepts (RePORT 2018) that were automatically assigned to grant applications) (He and Parker 2011). They calculated the MACD and histogram values for each term, then used various classifiers to predict whether the histogram itself would rise or fall in the future. While this is not exactly the same as predicting whether term prevalence would increase, their best classifier had an accuracy of 88%.

Materials and method
The code used in this section can be found on GitHub at https ://githu b.com/etatt ersha ll/ burst -detec tion

Dataset
We use a corpus gathered from DBLP, which is a large computer science bibliography hosted by Trier University in Germany. DBLP is considered to be reasonably comprehensive in its coverage of the field: Cavacini (2015) compared a number of bibliographies and found that DBLP had the greatest number of unique computer science articles indexed. It is freely available to download, either directly (DBLP 2019), or via Semantic Scholar (Allen Institute for Artificial Intelligence 2015).
After downloading, cleaning, and filtering out foreign language abstracts, we had a dataset of 2.6 million articles spanning the years 1988-2017. For each article, we combined title and abstract to form a document, then used Python's Natural Language Toolkit (NLTK) (Bird et al. 2009) to tokenise, lemmatise and remove a short list of standard English stopwords.
From there, we read in the dataset year by year and formed a vocabulary of uni-, bi-and tri-gram terms. We calculated the document frequency of each term in each year, which left us with a 31 (year) × 4.1 million (term) matrix. We filtered again, removing the terms that did not occur in more than 0.02% of abstracts for at least three consecutive years. This substantially reduced the amount of noise in the dataset from digitization errors and very rare bi-and tri-gram terms. The final size of our vocabulary was approximately 70,000 terms.

Normalisation
Over the 31 year span of the dataset, the number of documents published each year has risen substantially (Fig. 3). The mean length of titles has increased, while the mean length of abstracts has fluctuated (Fig. 4). This presents a problem; terms later in the dataset will be more likely to be flagged as bursts because of the underlying increase of size of the dataset. Therefore, we normalised the document frequency counts twice, first by dividing the data for each year by the total number of documents in that year, and then dividing by the mean number of tokens per document. This means that each element in the year-term matrix can be viewed as a normalised measure of prevalence.

Applying MACD
The first parameter we chose was the length of the moving average spans, ( n 1 , n 2 , n 3 ). In stock market analysis, it is common to use (12,26,9) months (Murphy 1999). However, our dataset has just 31 time steps, so moving averages of this length would leave us with too little data with which to work. Therefore, after some experimentation, we used (6, 12, 3) years. He and Parker (2010) used the raw value of the histogram as their metric for burstiness. However, when we attempted to apply it to our dataset, we discovered that there were some  issues with scale. Common terms, such as "data", often showed large numerical shifts on the histogram that are still insignificant when compared to their historical baseline level. Therefore, we introduced a scaling factor.
Initially, we experimented with using the mean or median value of each term's historical prevalence. However, this biased the metric in favour of new terms which did not exist in the dataset before becoming popular. Then we tried the historical maximum, but found that this produced variable results; the prevalence over time is not generally smooth, so anomalous spikes occur frequently. Finally, we decided on the square root of the historical maximum since this produces more consistent results than the other metrics.
Therefore, for the prevalence p(w, t) of term w over time, we have:

Predicting the future prevalence of terms using MACD features
In order to train a supervised classifier, we need to create a training set, (X, Y), where X is a matrix of terms and features and Y is a binary class indicating whether each term rose or fell in prevalence after a number of years. First, we choose how far in the future we wanted to predict (e.g. 3 years) and call this the prediction interval I. Then, for each year, y i , we: 1. Take the last 20 years of data ( D(y i−20 , y i )).
2. Apply our burst detection method to D(y i−20 , y i ) . Select all terms above a burstiness threshold. 3. Extract time series features such as the MACD and histogram values, the standard deviation, min and max. This forms the X part of our dataset (Fig. 5). 4. Take a smoothed value of term prevalence during y i+I and calculate whether it is above or below prevalence during y i . This forms the Y part of our dataset. 5. Append X and Y onto the data for the previous year.
Both He and Parker (2011) and Balili et al. (2017) used a tree-based method to predict whether their clusters or terms would rise or fall in popularity. We follow them, using a random forest classifier, tested via 10-fold cross validation. A process diagram for the full methodology can be found in Fig. 6.

Burst detection
As an initial evaluation, we applied the burst detection method to our dataset and sorted the burstiness scores in descending order. Some terms with high burstiness were surprising, such as "novel" and "state [of the] art". However, when we plotted them on a graph over time, we found that they have indeed become more popular over the span of the dataset (Fig. 7).
Social media is another interesting example (Fig. 8). "Social network" began to climb in popularity around 1998, with a growth curve that mirrors "social media", 5 years later. "Twitter" and "facebook" climb together, but "facebook" reaches a plateau earlier. We also find some cases where the orthography of words has changed over time. For instance, "web site", peaked in 2001, then was gradually replaced by "website" (Fig. 9).
There are, however, some issues with the terms detected. For example, the top 30 bursty terms over the span of the dataset are: deep, neural network, neural, convolutional, reserved, right reserved, science bv right, bv right, bv right reserved, convolutional neural, convolutional neural network, elsevier bv, deep learning, elsevier bv right, right, elsevier science bv, science bv, elsevier science, spl, bv, elsevier, cnn, iot, learning, deep neural, deep neural network, elsevier ltd, xml, internet thing, elsevier ltd right This list contains terms that refer to the same idea, such as "convolutional neural" and "convolutional neural network". It also contains publishing artefacts such as "elsevier bv right". This is part of a copyright declaration that was often included at the end of abstracts-e.g. "©1999 Elsevier Science B.V. All rights reserved". In order to remove these and merge duplicates, we cluster the top 500 bursty terms based on their co-occurrence in abstracts using SciPy's hierarchical clustering algorithm (SciPy 2019), then The feature extraction process. For instance, for the year 2008, we take data in the range 1998-2008 and extract features to form the X part of our dataset. We then take the prevalence for each term during 2011 as our Y 1 3 manually remove the clusters containing publishing artefacts. This leaves 114 clusters, which are displayed in Table 1.
To investigate how bursty terms have developed over time, we sort the clusters by year, based on when the bulk of the activity occurred, then manually choose a sample that is fairly evenly spread over the span of the dataset. For each of the 52 chosen clusters, we Process diagram for the methodology choose a single representative term, or a term and an acronym, such as [recurrent neural, rnn] for [recurrent neural network, recurrent neural, recurrent, network rnn, rnn, neural network rnn], then track the term over time and display it on a graph (Fig. 10).
In Fig. 10, we notice that many of the later bursts seem to involve deep learning in some way. The earlier ones are more diverse. There are a number of different growth patterns. "Security" undergoes a nearly linear increase, as does "dataset". Others peak twice, such as "neural networks" and "virtual reality". This ties in neatly with what we know of the history of these two ideas: the first consumer VR headsets were in the headlines in the 90s (Kahaner 1994), and a number of neural network breakthroughs happened in a similar time period (Rumelhart et al. 1986). Some of the terms reach peak popularity, then persist, such as "data mining" and "gene expression". Others fall out of favour fairly swiftly, such as "intranet" and "web 2.0". We note that this does not mean Fig. 7 The terms "novel" and "state [of the] art" have increased substantially in popularity over the last 30 years Fig. 8 The prevalence of the terms "social network", "social media", "twitter" and "facebook" over time that these concepts are no longer used, only that these particular terms no longer find their way into titles and abstracts.

Prediction
As described in "Predicting the future prevalence of terms using MACD features" section, we aim to predict whether a given term will rise or fall in popularity after a time interval I. Since the classes (rise, fall) are unbalanced, we subsampled the majority class, and trained a random forest classifier on the data. We chose the number of trees and the maximum depth by considering the training/testing error, then experimented with a range of prediction intervals (1-5 years) and burstiness thresholds (0.0006-0.0016).
The results are shown in Fig. 11, while the effect of the burstiness threshold on dataset size is shown in more detail in Table 2.
Increasing the burstiness threshold increases the performance of the classifier substantially. However, thresholding this way comes at the cost of the amount of data available. At the highest threshold, there are just over 3000 terms, some of which describe the same concept (e.g. "convolutional neural", "convolutional neural network"). The prediction interval also matters. When we vary both parameters together, we see that performance is highest when the prediction is made 3 years into the future.

Prediction of term prevalence in 2020
To predict the future prevalence of the discovered bursty terms we chose parameters I = 3 and B pred = 0.0012 and trained our classifier on data from 1988-2014. Given the results in Table 2, we expect this classifier to achieve 81% accuracy. We then selected terms that were above a significance threshold in 2017 and generated predictions of whether their prevalence in abstracts will rise or fall in 2020. Table 3 shows the results.
Most machine learning terms are expected to rise, while some web, networking and social media terms are expected to fall. Encouragingly, the only overlap between the two groups was "5g" and "fifth generation" in the rising group, and "5g network" in the falling group.

Fig. 9
Changing word use over time as "web site" is replaced with "website"  papers, as they are seen as more mature technologies that can be used as tools-e.g. "cloud computing", "xml", "java". When abstracts alone are used, there is no way to distinguish between these terms and ideas that have genuinely fallen out of use. -Validation It is not trivial to validate the list of bursty terms in Fig. 10. So far as we are aware, there is no gold standard list of "hot topics" that covers the last thirty years of computer science. The scope of the dataset is also quite large; validation by a domain expert would be likely to have low coverage over the different sub-disciplines. -Historical data The burst detection method we have used requires a span of historical data to detect bursts. This means that it cannot effectively detect bursts in the earliest years of the dataset. -The trade-off between accuracy and dataset size We can have high accuracy (in the region of 84%) at the cost of most of our data, by choosing a higher burstiness threshold. -Scientific progress can happen without warning There is no way to predict the future prevalence of terms that have not even appeared in our dataset. Some trends grow swiftly and suddenly; see "big data", "Kinect" and "smart grid".

Fig. 11
Choosing a prediction interval. We vary the interval, I and measure the F1 score of the classifier (in terms of how often it correctly predicted whether terms would rise or fall), for a number of different burstiness thresholds (see legend). What we find is that optimal performance is reached when the prediction is made 3-4 years in the future. The error bars represent standard deviation over 10 folds However, despite these limitations, this method has a number of strengths. It can be applied to datasets for which the authors have little domain knowledge to create a snapshot of the history of the field. It also has an obvious use to funding agencies and researchers exploring the research landscape.

Conclusion
We have explored a stock market-inspired burst detection algorithm, and used it to find bursty terms in over thirty years of computer science abstracts. These terms represent a snapshot of computer science research over the years, from Java, e-commerce and peer-topeer networking, to fog computing, 5G, word embeddings and deep learning. We see terms that have peaked twice, such as neural networks and virtual reality, and terms which have experienced a linear increase in popularity, such as "novel". Most interestingly though, we find that many of our terms display a characteristic life cycle in their popularity over time, and note that it shares some similarities with the famous Gartner hype cycle (Fenn and Raskino 2008). Our classifier, which is, to our knowledge, the first built using only bursty terms, is able to predict whether terms will rise or fall in popularity with accuracy in the region of 80%.


extfieldsofstudy:
Mathematics
Physics
Computer Science

text:
Estimation of exciton diffusion lengths of organic semiconductors in random domains

Exciton diffusion length plays a vital role in the function of opto-electronic devices. Oftentimes, the domain occupied by an organic semiconductor is subject to surface measurement error. In many experiments, photoluminescence over the domain is measured and used as the observation data to estimate this length parameter in an inverse manner based on the least square method. However, the result is sometimes found to be sensitive to the surface geometry of the domain. In this paper, we employ a random function representation for the uncertain surface of the domain. After non-dimensionalization, the forward model becomes a diffusion-type equation over the domain whose geometric boundary is subject to small random perturbations. We propose an asymptotic-based method as an approximate forward solver whose accuracy is justified both theoretically and numerically. It only requires solving several deterministic problems over a fixed domain. Therefore, for the same accuracy requirements we tested here, the running time of our approach is more than one order of magnitude smaller than that of directly solving the original stochastic boundary-value problem by the stochastic collocation method. In addition, from numerical results, we find that the correlation length of randomness is important to determine whether a 1D reduced model is a good surrogate for the 2D model.

Introduction
From a practical perspective, measurement error or insufficient data in many problems inevitably introduces uncertainty, which however has been overlooked for a long time. In materials science, recent adventure in manufacturing has reduced the device dimension from macroscropic/mesoscropic scales to nanoscale, in which the uncertainty becomes important [4]. In the field of organic opto-electronics, such as organic light-emitting diodes (LEDs) and organic photovoltaics, a surge of interest has occurred over the past few decades, due to major advancements in material design, which led to a significant boost in the materials performance [28,24,31]. These materials are carbon-based compounds with other elements like N, O, H, S, and P, and can be classified into small molecules, oligomers, and polymers with atomic mass units ranging from several hundreds to at least several thousands and conjugation length ranging from a few nanometers to hundreds of nanometers [13,24].
At the electronic level, exciton, a bound electron-hole pair, is the elementary energy carrier, which does not carry net electric charge. The characteristic distance that an exciton travels during its lifetime is defined as the exciton diffusion length, which plays a critical role in the function of opto-electronical devices. A small diffusion length in organic photovoltaics limits the dissociation of excitons into free charges [33,22], while a large diffusion length in organic LEDs may limit luminous efficiency if excitons diffuse to non-radiative quenching sites [1]. Generally, there are two types of experimental methods to measure exciton diffusion length: photoluminescence quenching measurement, including steady-state and time-resolved photoluminescence surface quenching, time-resolved photoluminescence bulk quenching, and exciton-exciton annihilation [20], and photocurrent spectrum measurement [27]. Exciton generation, diffusion, dissociation, recombination, exciton-exciton annihilation, and exciton-environment interaction, are the typical underlying processes. Accordingly, two types of models are used to describe exciton diffusion, either differential equation based or stochastic process based. The connections between these models are systematically discussed in [9].
We focus on the differential equation model in this paper. Accordingly, the device used in the experiment includes two layers of organic materials. One layer of material is called donor and the other is called acceptor or quencher due to the difference of their chemical properties. A typical bilayer structure is illustrated in Figure 1. These materials are thin films with thicknesses ranging from tens of nanometers to hundreds of nanometers along the x direction and in-plane dimensions up to the macroscopic scale. Under the illumination of solar lights, excitons are generated in the donor layer, and then diffuse. Due to the exciton-environment interaction, some excitons die out and emit photons which contribute to the photoluminescence. The donor-acceptor interface serves as the absorbing boundary while other boundaries serve as reflecting boundaries due to the tailored properties of the donor and the acceptor. As derived in [9], such a problem can be modeled by a diffusion-type equation with appropriate boundary conditions, which will be introduced in §2. Since the donor-acceptor interface is not exposed to the air/vacuum and the resolution of the surface morphology is limited by the resolution of atomic force microscopy, this interface is subject to an uncertainty with amplitude around 1 nm. At a first glance, this uncertainty does not seem to affect the observation very much since its amplitude is much smaller than the film thickness. However, in some scenarios [20], the fitted exciton diffusion lengths are sensitive to the uncertainty, which may affect a chemist to determine which material should be used for a specific device. Therefore, it is desirable to understand the quantitative effect of such an uncertainty on the exciton diffusion length and provide a reliable estimation method to select appropriate models for organic materials with different crystalline orders.
Uncertainty quantification is an emerging research field that addressing these issues [35,19,30]. Due to the complex nature of the problems considered here, finding analytical solutions is almost impossible, so numerical methods are very important to study these solutions. Here we give a briefly introduction of existing numerical methods, which can be classified into nonintrusive sampling methods and intrusive methods.
Monte Carlo (MC) method is the most popular non-intrusive method [16]. For the randomness in the partial differential equations (PDEs), one first generates N random samples, and then solves the corresponding deterministic problem to obtain solution samples. Finally, one estimates the statistical information by ensemble averaging. The MC method is easy to implement, but the convergence rate is merely O( 1 √ N ). Later on, quasi-Monte Carlo methods [7] and multilevel Monte Carlo methods [15] have been developed to speed up the MC method. Stochastic collocation (SC) methods explore the smoothness of PDE solutions with respect to random variables and use certain quadrature points and weights to compute solution realizations [36,2,25]. Exponential convergence can be achieved for smooth solutions, but the quadrature points increase exponentially fast as the number of random variables increases, known as the curse of dimensionality. Sparse grids were introduced to reduce the quadrature points to some extent [6]. For high-dimensional PDEs with randomness, however, the sparse grid method is still very expensive.
In intrusive methods, solutions of the random PDEs are represented by certain basis functions, e.g., orthogonal polynomials. Typical examples are the Wiener chaos expansion (WCE) and polynomial chaos expansion (PCE) method. Then, Galerkin method is used to derive a coupled deterministic PDE system to compute the expansion coefficients. The WCE was introduced by Wiener in [34]. However, it did not receive much attention until Cameron provided the convergence analysis in [8]. In the past two decades, many efficient methods have been developed based on WCE or PCE; see [14,37,38,3,18] and references therein.
When dealing with relatively small input variability and outputs that do not express high nonlinearity, perturbation type methods are most frequently used, where the random solutions are expanded via Taylor series around their mean and truncated at a certain order [21,11]. Typically, at most second-order expansion is used because the resulting system of equations are typically complicated beyond the second order. An intrinsic limitation of the perturbation methods is that the magnitude of the uncertainties should be small. Similarly, one also chooses the operator expansion method to solve random PDEs. In the Neumann expansion method, we expand inverse of the stochastic operator in a Neumann series and truncate it at a certain order. This type of method often strongly depends on the underlying operator and is typically limited to static problems [39,35].
In this paper, we employ a diffusion-type equation with appropriate boundary conditions as the forward model and the exciton diffusion length is extracted in an inverse manner. Surface roughness is treated as a random function. After nondimensionalization, the forward model becomes a diffusion-type equation on the domain whose geometric boundary is subject to small perturbations. Therefore, we propose an asymptotic-based method as the forward solver with its accuracy justified both analytically and numerically. It only requires solving several deterministic problems over the regular domain without randomness. The efficiency of our approach is demonstrated by comparing with the SC method as the forward solver. Of experimental interest, we find that the correlation length of randomness is the key parameter to determine whether a 1D surrogate is sufficient for the forward modeling. Precisely, the larger the correlation length, the more accurate the 1D surrogate. This explains why the 1D surrogate works well for organic semiconductors with high crystalline order.
The rest of the paper is organized as follows. In §2, a diffusion-type equation is introduced as the forward model and the exciton diffusion length is extracted by solving an inverse problem. Domain mapping method and the asymptotic-based method are introduced in §3 with simulation results presented in §4. Conclusion is drawn in §5.

Model
In this section, we introduce a diffusion-type equation over the random domain as the forward model and the extraction of exciton diffusion length is done by solving an inverse problem.
Refer to Figure 1. The donnor-acceptor interface, Γ, is described by x = h(z, ω), a random field with period L: where {θ k } are i.i.d. random variables, φ k (z) = sin(2kπ z L ), and λ k > 0 are eigenvalues that control the decay speed of physical mode φ k (z). In principle, one could also add the cosine modes in the basis functions {φ k }. We here only use the sine modes for simplicity. In the experiment,h ∼ 1 nm due to the surface roughness limited by the resolution of atomic force microscopy. The thickness d varys between 10 ∼ 100 nm in a series of devices. Therefore, the dimensionless parameter characterizing the ratio between measurement uncertainty and film thickness =h/d, ranges around [0.01, 0.1]. So, it is assume that the amplitudeh d in our models. The in-plane dimensions of the donor layer are of centimeters in the experiment, but we choose L ∼ 100 nm and set up the periodic boundary condition along the z direction based on the following two reasons. First, the current work treats exciton diffusion length as a homogeneous macroscopic quantity, which is a good approximation for ordered structures. For example, small molecules are the simplest and can form crystal structures under careful fabrication conditions [12,29]. Second, the light intensity and hence the exciton generation density is a single variable function depending on x only.
Define the domain D : Here σ is the exciton diffusion length which is an unknown parameter, and the σ 2 term in (2a) describes the exciton diffusion. Exciton-environment interaction makes some excitons emit phonons and die out, which is described by the term −u in (2a). The normalized exciton generation function G is R + -valued, and is smooth on R + ∪{0}. By solving the Maxwell equation over the layered device, one can find that G(x) is a combination of exponential functions which decay away from 0 [5]. x = d is served as the reflexive boundary and homogeneous Neumann boundary condition is thus used there, while x = h(z, ω) is served as the absorbing boundary and homogeneous Dirichlet boundary condition is used in (2b). Periodic boundary condition is imposed along the z direction in (2c). It is not difficult to see that the solution u to (2) is strictly positive in D by the maximum principle. The (normalized) photoluminescence is computed by the formula If the interface Γ is random but entirely flat, i.e., h(x, ω) = ξ(ω) for some random variable ξ, then the domain is a rectangle (ξ(ω), d) × (0, L). Notice that in (2), G is a function of x only. Then, (2) actually reduces to the following 1D problem For the 1D model (4), when L → 0, the photoluminescence defined by (3) reduces to This is why the normalized factor 1/L is used in (3). Due to the simple analytical formula, the 1D model given by (4) and (5) has been widely used to fit experimental data for photoluminescence measurement [20] and photocurrent measurement [17].
Since the roughness of the interface is taken into account, problem (2) with the random interface Γ is viewed as a generalized and more realistic model. The 1D model (4) still has the uncertainty of the boundary but fails to include the spatial variety of the donor-interface interfacial layer. We are interested in identifying under which condition the 1D model can be viewed as a good surrogate for the 2D model and how this condition can be related to the property of organic semiconductors.

2.2.
Inverse problem: Extraction of exciton diffusion length. In the experiment, photoluminescence data { I i } N i=1 are measured for a series of bilayer devices with different thicknesses Here i denotes the i-th observation in the experiment with d i the thickness of the donor layer. σ is the unknown parameter, and the optimal σ is expected to reproduce the experimental in a proper sense. To achieve this, we propose the following minimization problem in the sense of mean square error We use the Newton's method to solve (6) for σ. Given σ (0) , for n = 1, 2, . . . , until convergence, we have Here α n ∈ (0, 1] is given by a line search [26]. Details are given in Appendix A.

Methods for solving the forward model
In the photoluminescence experiment, the surface roughness is very small compared to the film thickness, i.e.,h ∼ 1 nm and 10 ≤ d ≤ 100 nm. Based on this observation, we propose an asymptotic-based method for solving the diffusion-type equation over the random domain. For comparison, we first describe the domain mapping approach [38].

Domain mapping method.
To handle the random domain D , we introduce the following transformationỹ so that D becomes the unit square D s = (0, 1) × (0, 1). Under this change of variables, Eq.
(2) becomes the following PDE with random coefficients (still use y and z to represent y and z, respectively) where the spatial differentiation operator is defined for a random element ω in the probability space and g(y, z, ω) The boundary condition is The photoluminescence defined in (3) is then transformed into Remark 3.1. In 1D, changing of variable y = x−ξ d−ξ also transforms (4) to a differential equation with random coefficients over the unit interval.
with (14) and the boundary condition Accordingly, the photoluminescence can be written as Remark 3.2. The generation term in (10) depends on both y and z after changing of variables. We expect some dimensional effect on the estimation of σ, which will be carefully examined in §4.

3.2.
Finite difference method for the model problem. We use finite difference method to discretize the forward model (8) .., N y + 1 and j = 1, ..., N z + 1, respectively. For the discretization in space, we use a second-order, centereddifference scheme [23]. We introduce the difference operators The operators D z 0 , D z − , and D z + are defined similarly. For each ω ∈ Ω and each interior mesh point (i, j) with 2 i N y , 2 j N z , we discretize the forward model (8) as where h, h , and h are evaluated at (y i , z j ). We then discretize the boundary conditions (11) on ∂D s . The Dirichlet boundary condition on y = 0 gives u 1,j = 0, 1 j N z + 1. For the Neumann boundary condition on y = 1, we introduce ghost nodes at (y −1 , z j ) and obtain a second order accurate finite difference approximation = 0. Then, the values of the u −1,j at the ghosts nodes are eliminated by combining with Eq. (17). Finally, the periodic boundary condition along the z direction gives u i,Nz+1 = u i,1 . We solve a system of N y (N z + 1) linear equations for {u i,j } with 2 i N y + 1 and 1 j N z + 1.
The equations have a regular structure, each equation involving at most nine unknowns. Thus the corresponding matrix of the system is sparse and can be solved efficiently using existing numerical solvers. After obtaining {u i,j }, we use the 2D trapezoidal quadrature rule to compute the photoluminescence I(σ, d) defined in (12).
In this paper, we choose the sparse-grid based SC method [6,25] to discretize the stochastic dimension in Eq. (8). As such the expectation of u(y, z, ω) is computed by where s q are sparse-grid quadrature points, w q are the corresponding weights, and Q is the number of sparse-grid points. Other functionals of u(y, z, ω) can be computed in the same way. When the solution u(y, z, ω) is smooth in the stochastic dimension, the SC method provides very accurate results.

3.
3. An asymptotic-based method. If we rewrite Eq. (2) in the nondimensionalized form with the change of variablesx = x/d andz = z/L, the domain D becomes where K is the mode number in the interface modeling. As discussed in §2, ∼ 0.01 − 0.1. Therefore, it is meaningful to derive the asymptotic equations when → 0. For ease of description, we list the main results below. The main idea is: (1) we rewrite Eq. (2) over D s, ; (2) with appropriate extension/restriction of solutions on the fixed domain D s , we obtain a Taylor series with each term satisfying a PDE of the same type with the boundary condition involving lower order terms; (3) we apply the inverse transform for each term and change the domain D s back to D 0 = (0, d) × (0, L). Detailed derivation can be found in Appendix B for self-consistency.
The interested readers can find the systematic study on asymptotic expansions for more general problems in [10]. The asymptotic expansion over the fixed domain D 0 is of the form The equation for each w n can be derived in a sequential manner. Only the first three terms are listed here. More details are included in Appendix B.
The leading term w 0 (x, z) is the solution to the boundary value problem and w 2 (x, z, ω) is the solution to the following boundary value problem Remark 3.3. As demonstrated in Eqs. (20), (21), and (22), the asymptotic expansion in (19) requires a sequential construction from lower order terms to high order terms and the partial derivatives of lower terms appear in the boundary condition for high terms. Numerically, we use the second-order finite difference scheme for (20), (21), and (22). For boundary conditions, we use the one-sided beam warming scheme to discretize ∂ x w 0 (0, z) and ∂ x w 1 (0, z, ω) so the overall numerical schemes are still of second order accuracy.
Define v [n] = n k=0 k w k . Note that w 0 is a function of (x, z) only. The zeroth order approximation of the photoluminescence is and so For k = 1, 2, . . . , K, let w 1,k (x, z) be the solution to (21) with φ k (z) in place ofh(z, ω) Then by linearity, the solution w 1 to (21) withh given by (18) can be expressed as Hence the first order approximation of the photoluminescence becomes and so Next, we consider the second order approximation of the photoluminescence. Sinceh and w 1 are given by (18) and (26), the boundary condition for w 2 at x = 0 can be written as Introduce w 2,j,k (x, z) as the solution to the boundary value problem (22) with the boundary condition at x = 0 replaced by Then and consequently, the second order approximation of the photoluminescence is and we have In general, w n can be written as the sum of K n functions, each of which solves a deterministic problem.
The approximation accuracy of a finite series in (19) is given by the following theorem. Proof can be found in [10].
where u is the solution to (2) and v [n] = n k=0 k w k .
To proceed, let us recall the definition of Bochner spaces.

Proof. From Theorem 3.4, for
Since w n , n 0 satisfies the same elliptic equation (20) with a boundary condition depending on w k , k n − 1. By the Lax-Milgram's theorem, we have w n ∈ L 2 P (Ω, H 1 (D 0 )), n 0. Therefore, v [n] ∈ L 2 P (Ω, H 1 (D 0 )), n 0 and the desired result is obtained. A direct consequence of Proposition 3.6 is Based on the above assertions, we have Corollary 3.7. For (24), (28), and (30), we have the following approximation errors In summary, by using the asymptotic expansion solution, we circumvent the difficulty of sampling the random function and solving PDEs on irregular domains for each sample. In our approach, there is no statistical error or errors from numerical quadratures as in MC method, SC method, and PCE method. However, our method is applicable only for small perturbation of the random interface, where a small n is sufficient in practice. The computational cost depends on the approximation order n and the number of modes K used to represent the random interface, and increases proportionally to K n .

Numerical Results
In this section, we numerically investigate the accuracy and efficiency of the asymptotic-based method in computing photoluminescence and the efficiency in estimating the exciton diffusion length. In addition, we study of the validation of the diffusion-type model, i.e., under which condition the 1D model can be viewed as a good surrogate for the 2D model.  , ω), d), z ∈ (0, L)}. Recall that the random interface h(z, ω) between the donor and the acceptor is parameterized by h(z, ω) = h K k=1 λ k θ k (ω) sin(2kπ z L ), where θ k (ω) are i.i.d. uniform random variables and K is the number of random variables in the model.
We first solve (8) over the fixed domain D s = (0, 1) × (0, 1) in the domain mapping method using the SC method. Note that the spatial differentiation operator in (9) depends on the random variables in a highly nonlinear fashion, which makes the WCE method and PCE method extremely difficult. In the asymptotic-based method, we solve deterministic boundary value problems (20), (21), and (22) over the fixed domain D 0 = (0, d) × (0, L), respectively. Recall that in the asymptotic-based method, =h/d and the random interface becomesh(z, ω) = K k=1 λ k θ k (ω) sin(2kπz). In our simulation, the random interface h(z, ω) is parameterized by K = 5 random variables. The accuracy of the asymptotic-based method is verified by two numerical tests. In the first test, θ k ∼ U (0, 1), while in the second one θ k ∼ U (−1, 1).
To compute the reference solution, we employ the finite difference method to discretize the spatial dimension of Eq. (8) with a mesh size H = 1 128 , and use the sparse-grid based SC method to discretize the stochastic dimension. We choose level six sparse grids with 903 quadrature points. After obtaining solutions at all quadrature points, we compute the expectation of the photoluminescence, which provides a very accurate reference solution. In the asymptotic-based method, we use the finite difference method to discretize the spatial dimension of boundary value problems (20), (25), and (22) for w 2,j,k with a mesh size H = 1 64 . Expectations E[θ k ] in (28) and E[θ j θ k ] in (30) can be easily computed beforehand. Therefore, given the approximate solutions w 0 , w 1,k , and w 2,j,k , we immediately obtain different order approximations of the expectation of the photoluminescence. This provides the significant computational saving over the SC method. For = 2 −i , i = 2, ..., 7, Figure 2 shows the approximation accuracy of the asymptotic-based method. In Figure 2(a), θ k ∼ U (0, 1). The approximated expectation of the photoluminescence obtained by using the zeroth, first and second order approximations are shown in the lines with circle, star, and triangle, with convergence rates 1.21, 1.99, and 3.81, respectively. In Figure  2 We conclude this subsection with a discussion on the computational time of our method. In these two tests, on average it takes 164.5 seconds to compute one reference expectation of the photoluminescence. If we choose a low level SC method to compute the expectation of the photoluminescence, it takes 27.3 seconds to compute one reference expectation of the photoluminescence that gives a comparable approximation result to our asymptotic-based method. However, our method with the second order approximation only takes 1.56 seconds to obtain one result. We achieve a 18X speedup over the SC method. Generally, the ratio of the speedup is problem-dependent. It is expected that higher ratio of speedup can be achieved it one solves a problem where the random interface is parameterized by high-dimensional random variables.

4.2.
Estimation of the exciton diffusion length. In this section, we estimate the exciton diffusion length in an inverse manner with the asymptotic-based method as the forward solver. Since only limited photoluminescence data from experiments are available, we solve the forward model (2) to generate data in our numerical tests. Specifically, given the exciton diffusion length σ, the exciton generation function G, the in-plane dimension L, and the parametrization of the random interface h(z, ω), we solve Eq. (2) for a series of thicknesses {d i }, and calculate the corresponding expectations of the photoluminescence data p{Ĩ i } according to Eq. (3). Therefore, {d i ,Ĩ i } serves as the "experimental" data. We then solve the minimization problem (6) based on our numerically generated data {d i ,Ĩ i } to estimate the "exact" exciton diffusion length σ in the presence of randomness, denoted by σ exact and will be used for comparison later.
We fix L = 4 in all our numerical tests since it is found that this minimizer is not sensitive to the in-plane dimension L. We show the convergence history of exciton diffusion lengths for various in Figure 3, where the photoluminescence data are generated with σ = 5, σ = 10, and σ = 20, respectively. Here the relative error is defined as E n, = | σexact−σ n, σexact |, where n is the iteration number, σ exact is the "exact" exciton diffusion length, and σ n, is the numerical result defined in Eq. (7). To show more details about the accuracy of our asymptotic-based method, in Tables 1, 2, and 3, we list the relative errors of our method for plotting Figures 3(a), 3(b), and 3(c). In all numerical tests, we choose the same termination criteria |σ (n) − σ (n−1) | < 10 −4 in the Newton's method. Our asymptotic-based method performs well in estimating the exciton diffusion length. In general, the smaller amplitudes the random interface, the more accurate the exciton diffusion length and the smaller the iteration number. Additionally, for larger exciton diffusion lengths σ exact , a faster convergence in the optimization approach is observed.   Table 3. Relative errors E n, = | σexact−σ n, σexact | for iteration number n = 1, 2, 3, ..., and various . The prescribed σ is 20.
Again, only limited photoluminescence data from experiments are available and we have to solve the forward model to generate data in our numerical tests. Specifically, given the exciton diffusion length σ, the exciton generation function G, and the parametrization of the random interface h(ω), we solve Eq. (4) for a series of thicknesses {d i }, and calculate the corresponding expectations of the photoluminescence data {Ĩ i } according to Eq. (5). Therefore, {d i ,Ĩ i } serves as the "experimental" data generated by the 1D model. We then solve the minimization problem (6) based on our numerically generated data {d i ,Ĩ i } to estimate the "exact" exciton diffusion length σ in the presence of randomness, denoted by σ exact and will be used for comparison.
In our numerical tests, we use the 1D model (4) with σ = 5 and σ = 10 to generate photoluminescence data. d i = 10i, i = 1, ..., 10,h = 1, and =h/d i . We use K = 10 random variables to parameterize the random interface. We set λ k = k β , where β 0 controls the decay rate of λ k . The random interface therefore takes the form 1]. Figure 4 plots the covariance function of the random interface defined by Eq. (36) for β = 0 and β = −2. It is clear that the smaller the β, the larger the correlation length.  The convergence history of the exciton diffusion length for various β is plotted in Figure 5, where the photoluminescence data is generated by the 1D model (Eqs. (4) and (5)) with σ = 5 and σ = 10. Again, the relative error is defined as E n,β = | σexact−σ n,β σexact |, where n is the iteration number, σ exact is the "exact" exciton diffusion length, and σ n,β is the numerical result defined in Eq. (7). Note that σ n,β depends also on implicitly but we omit its dependence for convenience. Tables 4 and 5 list the relative errors of our method for plotting Figure 5. The same criteria |σ (n) − σ (n−1) | < 10 −4 is used here. The numerical exciton diffusion length obtained by our method converges to the reference one with the relative error less than 1% when β −1.
Our numerical results show that a faster decay of the eigenvalues λ k leads to a better agreement between the results of the 1D model and the 2D model. The smaller the β, the better the agreement. On the other hand, the smaller the β, the larger the correlation length. Therefore, the larger the correlation length, the better the agreement. Our study sheds some light on how to select a model as simple as possible without loss of accuracy for describing exciton diffusion in organic materials. In the chemistry community, it is known that under careful fabrication conditions [12,29], organic semiconductors, including small molecules and polymers, can form crystal structures, which have large correlation lengths. As a consequence, exciton diffusion in these materials can be well described by the 1D model [27,20,32]. For organic materials with  Table 4. Relative errors E n,β = | σexact−σ n,β σexact | for iteration number n = 1, 2, 3, ..., and various β. The prescribed σ is 5. low crystalline order, i.e., small correlation length, however, our result suggests that the 1D model is not a good surrogate of the high dimensional models.

Conclusion
In this paper, we model the exciton diffusion by a diffusion-type equation with appropriate boundary conditions over a random domain. The exciton diffusion length is extracted via minimizing the mean square error between the experimental data and the model-generated data. Since the measurement uncertainty for the domain boundary is much smaller compared to the  Table 5. Relative errors E n, = | σexact−σ n,β σexact | for iteration number n = 1, 2, 3, ..., and various β. The prescribed σ is 10. device thickness, we propose an asymptotic-based method as the forward solver. Its accuracy is justified both analytically and numerically and its efficiency is demonstrated by comparing with the SC method as the forward solver. Moreover, we find that the correlation length of randomness is the key parameter to determine whether a 1D surrogate is sufficient for the forward modeling.
The discussion here focuses on the photoluminescence experiment. For the photocurrent experiment, from the modeling perspective, the forward model is the same but the objective function is different. An exciton either contributes to the photoluminescence or the photocurrent, so the photocurrent is defined as the difference between a constant (total exciton contribution) and the photoluminescence [9]. Therefore, the proposed method can be applied straightforwardly with very little modification.
, (37) where α k ∈ (0, 1] is given by the line search technique. For example, we take (6) as the minimization problem and the domain mapping formulation in §3.1 as the forward problem. Other combinations can be worked out similarly. In 2D, for the first derivatives, we have and Denote the derivatives of u(y, z) with respective to the parameter σ by u 1 (y, z) := ∂u ∂σ (y, z), and u 2 (y, z) := ∂ 2 u ∂σ 2 (y, z). Differentiating (8) with respect to σ directly, we have and u 1 shares the same boundary condition as u.
For the second derivatives, we have and and u 2 satisfies Again, the same boundary condition applies for u 2 .
Note that Eq. (42) is in fact a Cauchy problem of the time evolution equation not a boundaryvalue problem of the elliptic PDE. The velocity is specified on the interface Γ by ∂ n u and the wave travels along the normal n. So, the solution of (42) exists for 0 x h (z, ω) [10].
Particularly, we have the existence of the value of u lay at x = 0.
B.1. The solution on regular domain and its asymptotic expansion. Now the solutions u and u lay are both well-defined on D s, and L by (41) and (42), respectively. In the next, we introduce a function piecewisely defined by these two functions on the regular domain D and want to find the correct equation for this function on D in order to carry our asymptotic method. Let w be defined on D = D s, ∪ L as follows This definition is justified by (42) and immediately implies the following obvious but important fact which arises from the boundary condition on the interface Γ of u : w (x, z) = 0 on Γ .
It is easy to see that w is the unique solution to the following problem where u lay at x = 0 is given a prior : w (0, z) = u lay (0, z), for 0 z 1, ∂ x w (1, z) = 0, for 0 z 1, w (x, z + 1) = w (x, z), for (x, z) ∈ D. (45) We start with the following ansätz for w , w (x, z) = ∞ n=0 n w n (x, z) for (x, z) ∈ D.
Plug this ansätz into the equation (45), and match the terms at the same order of , then we obtain the following equations for w n in D: L w 0 + g(x) = 0, Lw n = 0, n 1.
Next, we discuss the boundary conditions for these PDEs. The two of the boundary conditions in (45), ∂ x w (1, z) = 0 and w (x, z + 1) = w (x, z), do not depend on u lay . Thus, the ansätz (46) simply gives us the same boundary conditions for each w n : ∂ x w n (1, z) = 0, and w n (x, z + 1) = w n (x, z).
The boundary condition of (45) at x = 0, i.e., on Γ 0 , depends on the data u lay on this boundary. If one works on this boundary condition, it is possible to solve the Cauchy problem (42) for small analytically so that u lay (x = 0, z) can be obtained in terms of u (i.e., w ), and eventually certain connections for w n can be built. But the use of the very original boundary condition (44) on Γ ⊂ ∂D s, , not on ∂D, actually significantly simplifies the calculations and finally offers more friendly results. The details follow below.


Design and Development of Online Mobile Phone Sales System Based On Java

With the rise of a new economic form named “Internet +”, the traditional mobile phone sales industry is also seeking the new cooperation opportunity, hoping to find cross-border integration and use Internet information to improve sales levels. Mobile phone sales industry will integrate efficient and optimization information which obtained from the Internet, then put forward more market-oriented sales program in order to access to consumers’ recognition and thus make a high sales record. In order to meet the needs of mobile phone sales industry, this paper has designed and developed the Java-based system, and developed the online mobile phone sales system with iPhone as an example. Firstly, the demand analysis and feasibility analysis of the system were carried out. After the feasibility of the system was analyzed, the overall design and function design of the system were carried out. The system use Java, servlet,. Net and other technologies, combined with oracle database, and use object-oriented approach to the preparation of procedures to achieve the function, including the users’ login and registration, purchasing of mobile phones, paying orders and the administrator’s mobile phones’ model management, mobile phones’ information management, users’ information management and modifying administrator’s information.

Design background
"Design and development of mobile phone sales system based on Java" is a set of system to make users use the Internet to shop online and improve shopping and sales efficiency. Currently, there are two main ways to sell mobile phones in the market, namely, online and offline. Although offline sales can provide users with intuitive feelings and better experience of goods, so as to compare goods. On the one hand, the seller needs to spend manpower and material resources to increase the cost of sales. On the other hand, users also need to devote special time and energy to purchase, causing some unnecessary waste of time. Taking the form of online sales, it not only saves the cost of sales, but also provides all kinds of convenience to customers, so the idea of designing this system has come into being. At the same time, through the more rigorous and real market research with the majority of middle-aged and young people as the main body, the author makes a survey of the more inclined consumption patterns of the vast number of consumers, and finds that consumers emphasize optimistic and supportive attitude towards online shopping. And are willing to trust the reliability of online goods. In addition, at a time when Apple's phones are being updated so quickly, the system has a promising future because consumers are in increasing demand for it. In order to better provide time and space convenience for this kind of mobile phone consumers, through the simple and easy-to-understand operation interface, we can really enjoy the convenience of the first time to get the mobile phone without leaving home. Compared with the traditional offline mobile phone sales mode, the system can reduce the workload of employees, carry out unified and standardized operation, and can ensure the privacy and high efficiency, so that the buyers are more comfortable and less worried.

Demand analysis
The users of this system are the marketing managers of Apple and those who are about to buy Apple's mobile phone products. The general goal is to provide marketing managers with timely and effective sales information, develop corresponding sales plans, and obtain better economic benefits. And to provide users with a new way to buy products without leaving home, save uses' time and energy, select the most satisfied mobile phone in the shortest time. By analyzing the needs of users, two types of users are summarized: administrators and users. The main functions of the administrator are mobile phone model management, mobile phone information management and users' information management. The mobile phone information management includes the addition, modification and deletion of the model, color, price and other information. Users' information management mainly includes query user information and other operations. The main functions of users are to login and purchase products. According to the analysis of the two types of users in the system, the process that the mobile sales system should have is as follows: first, the user registers the login account, and after the user logs in, the mobile phone commodity information is queried. Next，the user chooses the phone according to the preference for the model and storage. Finally, the purchase is completed after the user pays successfully.
Therefore, it can be analyzed that the main functions of the entire online sales system of Apple mobile phone are as follows: 1. Users sign up and log in 2. Users buy goods 3. Users pay orders 4. The administrator manages the categories of goods 5. The administrator manages the details of goods 6. The administrator manages user's information 7. The administrator revises information Therefore, it is imperative to establish a mobile phone sales system that meets all the above requirements. We need to solve the problem caused by traditional retail stores with modern methods and give users real enjoyment of shopping.

Feasibility analysis
The adoption of information systems can help managers sell mobile phones and satisfy buyers' desire to buy ideal products. It can also establish long-term relationship between the company and customers and provide convenience for shopping. The feasibility study of the system is as follows: Technical Feasibility: technical conditions are the key conditions for the successful completion of the development work. This system adopts .NET and Oracle database, which are convenient for users to develop the system. At the same time, the use of Oracle database reduces the cost of managing commodity and all users' information, which is characterized by high efficiency, high reliability and high intelligence. The operation feasibility: the system adopts a simple and generous interface design, and the interface operation is humanized. The system not only provides convenience for consumers to quickly select their favorite products, but also provides convenience for managers to collect sales information.
Economic feasibility: with the rapid development of hardware, the price is becoming more and more affordable to meet the needs of users. Compared with the way of offline sales, the online mobile phone sales system reduces operating costs and saves resources such as manpower and material resources. In addition, the system development and later maintenance cost less.
Management feasibility: on the one hand, the technology adopted by the system is convenient for system management and system maintenance. On the other hand, the management can update and modify the model, color, price and other information of the mobile phone through the system.

The overall design
This system uses B/S (browser/server) structure for distributed management. The overall network structure of the system is shown in figure1 below: