A third example is to draw n balls from an urn containing balls of various colours. In spite of the simplicity of this experiment, a thorough understanding gives the theoretical basis for opinion polls and sample surveys. For example, individuals in a population favouring a particular candidate in an election may be identified with balls of a particular colour, those favouring a different candidate may be identified with a different colour, and so on. Probability theory provides the basis for learning about the contents of the urn from the sample of balls drawn from the urn; an application is to learn about the electoral preferences of a population on the basis of a sample drawn from that population.
Another application of simple urn models is to use clinical trials designed to determine whether a new treatment for a disease, a new drug, or a new surgical procedure is better than a standard treatment. In the simple case in which treatment can be regarded as either success or failure, the goal of the clinical trial is to discover whether the new treatment more frequently leads to success than does the standard treatment. Patients with the disease can be identified with balls in an urn. The red balls are those patients who are cured by the new treatment, and the black balls are those not cured.
Usually there is a control group , who receive the standard treatment. They are represented by a second urn with a possibly different fraction of red balls. The goal of the experiment of drawing some number of balls from each urn is to discover on the basis of the sample which urn has the larger fraction of red balls. A variation of this idea can be used to test the efficacy of a new vaccine. Perhaps the largest and most famous example was the test of the Salk vaccine for poliomyelitis conducted in It was organized by the U. Public Health Service and involved almost two million children.
Its success has led to the almost complete elimination of polio as a health problem in the industrialized parts of the world.
Strictly speaking, these applications are problems of statistics, for which the foundations are provided by probability theory. In contrast to the experiments described above, many experiments have infinitely many possible outcomes. Another example is to twirl a spinner. Many measurements in the natural and social sciences, such as volume, voltage, temperature, reaction time, marginal income, and so on, are made on continuous scales and at least in theory involve infinitely many possible values.
If the repeated measurements on different subjects or at different times on the same subject can lead to different outcomes, probability theory is a possible tool to study this variability. Because of their comparative simplicity, experiments with finite sample spaces are discussed first.
The probability of an event is defined to be the ratio of the number of cases favourable to the event—i. An outcome of the experiment is an n -tuple, the k th entry of which identifies the result of the k th toss. Since there are two possible outcomes for each toss, the number of elements in the sample space is 2 n. You are using an outdated browser. Please upgrade your browser to improve your experience and security.
Space (mathematics) - Wikipedia
Studies that employed quantitative analyses for open space use are also rare. The differences in user patterns between open spaces in Eastern and Western societies are worth exploring. The current study regarded the community open space as the specific study subject. Considering that several studies pointed out that distance to a green space accessibility is not a limiting factor for most residents [ 18 , 19 ], we focused on other important influencing factors, such as the attractiveness of a space.
On the other hand, community open spaces are often small in scale [ 18 , 31 ]. Controlling the influence of the size of the space is possible to some extent. Therefore, we focused on the characteristics of an open space itself.
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To date, the factors that affect the use patterns of community open spaces are still unclear. Thus the goals of the current study are twofold: 1 to analyze the specific characteristics of community open spaces that are associated with the use of open spaces in a typical community in China and 2 to explore landscape design strategies through which community open space utilization can be strengthened. We systematically investigated the large communities in the Nanshan District of Shenzhen, which is a pioneering area in China, to look for a mature community with multiple open spaces, good accessibility, and environmental diversity characteristics as a case for our research.
It is a typical, high-density, mixed community. The entire community is separated from other communities by urban streets in the north, east, and south and by a high wall with an urban village in the west. High-class residential groups are located in the northwest and the southeast, middle-class and low-class residential groups are located in the south and the southwest, and collective dormitory groups exist in the middle. The open space in this community is composed of several community parks, a hilly country park, several lakes, several pedestrian-only commercial zones, and other types of greenery.
The distribution of green space in this community is relatively reasonable, and its landscape is ranked as first class in Shenzhen City.
The access of residents to open spaces is very high, given that Therefore, this community with high-quality, high-accessibility open spaces is an appropriate case to study the characteristics that influence the use of open spaces. Before the specific data acquisition process, interviews were conducted with staff members of the OCT administration, the security department, and security guards to obtain a general overview of the community, the management and maintenance of the open spaces, and the public security situation.
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Through the interviews, we found that the open spaces in the OCT community were planned and developed with high-level standards and are maintained by the OCT Enterprise itself. Therefore, it has high utilization and good public security. The OCT community was developed and constructed in It was built and is administrated by a state-owned enterprise, the OCT Group, and has excellent internal facilities and a carefully planned environment [ 33 ].
Over the years, the OCT community has become a modernized seashore community that integrates tourism, housing, commercial offices, creative cultural industries, and other functions. The community is divided into two parts by Shennan Avenue. The northern part is mainly composed of residential and commercial venues. The northern part of the community, with a total land area of To establish a theoretical model, three instances of data collection were implemented.
First, all the open spaces were identified and then divided into independent units.
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Second, an environmental scan was conducted to obtain the environmental characteristics of each open space unit. Finally, a systematic four-day observation was carried out to determine the number of users and their activity engagements in each open space unit. In this study, open spaces refer to areas left open for public use in urban communities, whether green or not, such as a plaza, park, playground, or courtyard. The open spaces located in high-class residential communities and villas are not included in this research because they are not open to the general public.
In addition, streets, water surfaces, inaccessible hilly areas, and courtyards inside building blocks are excluded. Thus, in this study, open spaces mainly include community parks, outdoor playgrounds, public-access courtyards, water fronts, and small squares around commercial and public buildings. All open spaces in the OCT community were surveyed, particularly those where visitors can enter and stay to a certain extent.
To explore the environmental elements that affect the use of open spaces and control the influence of open space size, large-scale open spaces were divided into space units based on spatial configuration and environmental characteristics. This process was also conducted to maintain the basic conformity or continuity of landscape elements inside the units and simultaneously achieve a large difference or obvious spatial separation between adjacent open space units.
Moreover, to guarantee the size comparability of the basic space units, we ensured that the area of each unit is not less than m 2 and not greater than 20, m 2. The original largest open space in the community is Yanhanshan Hilly Country Park with long wandering walking paths and large woodlands; it was difficult to divide into units. Thus, several user-gathering squares and rest areas were recognized as space units.
According to these principles, all open spaces in the research area were divided into space units with an average area of approximately m 2. The composition and functions of each unit differed. Among the space units, 68 were individual land units and 44 belonged to a continuous network of open space or large public parks.
Their accessibility had no significant differences [ 32 ]; most units were located inside residential or commercial areas, whereas others were located among residential areas. However, the use of the units differed significantly. Several units were always crowded, whereas many others were seldom visited. Full investigation and documentation of the environmental characteristics of all the space units were conducted. Existing evidence suggests that the characteristics that influence the use of urban public open spaces include the configuration of a place e.
Referring to previous studies, the audit content in the current study mainly included three aspects spatial configuration, facilities, and landscape features with 17 characteristic variables. For spatial configuration, the total site area S1 , accessible lawn area S2 , woodland area S3 , footpath length S4 , and hard pavement S5 were measured.
The site facilities comprised eight types, namely, fitness facilities F1 , commercial facility sites located within the open space units and surrounding the open space units, F2 , total number of regular seats F3 , auxiliary seats F4 , rain and sun-shading devices F5 , bicycle parking facilities F6 , trash cans F7 , and lighting facilities F8.
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The landscape setting surveys included the number of water landscapes L1 , mammal and bird biological habitat types L2 , sculptures L3 , and motor vehicle parking volume L4. Site investigation of the use of all community open space units was conducted in four days in November Table 1. A total of 17 trained researchers observed the visitors in the open space units on two weekdays 5 and 13 November and on two weekends 9 and 16 November. The observation time in each day was from 9 am to 10 pm, and documentation was performed every hour. Each observer was assigned to a residential group, a commercial area, or a park to systematically observe and record the number of visitors to these space units.
Each space or space unit was subjected to a 6 min continuous visual scan every hour. Thus, we recorded a sufficient number of visitors, including those who stayed for a long time and those who only stayed for a short period or merely passed by. All visitors to a particular space observed within the 6 min visual scan were recorded as point data on a detailed map of the site. The average activity population number in each open space unit was During the day 9 am to 6 pm , 27, headcounts were observed, and during the evening 7 pm to 10 pm , headcounts were observed.
In total, 14, headcounts were observed during weekdays, and 20, headcounts were observed during weekends. The number of headcounts utilized in the subsequent text analysis comprises the summary of headcounts observed during the four-day site investigation. The data confirmed that the open spaces had the most number of visitors from 3 pm to 5 pm; the smallest number was recorded during lunch time and dinner time.
In the other time periods within a day, the stream of visitors was relatively stable. After 9 pm, a rapid decrease in the number of visitors was observed Figure 2. In the environment scanning process, 17 variables representing the characteristics of each space unit were scanned. These variables are potential factors that could affect the attractiveness of open spaces and physical activities. However, the initial data analysis showed that several variables should be excluded from the regression model.