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# Dilution effect of the building area on energy intensity in urban residential buildings

## Abstract

Urban residential buildings make large contributions to energy consumption. Energy consumption per square meter is most widely used to measure energy efficiency in urban residential buildings. This study aims to explore whether it is an appropriate indicator. An extended STIRPAT model was used based on the survey data from 867 households. Here we present that building area per household has a dilution effect on energy consumption per square meter. Neglecting this dilution effect leads to a significant overestimation of the effectiveness of building energy savings standards. Further analysis suggests that the peak of energy consumption per square meter in China’s urban residential buildings occurred in 2012 when accounting for the dilution effect, which is 11 years later than it would have occurred without considering the dilution effect. Overall, overlooking the dilution effect may lead to misleading judgments of crucial energy-saving policy tools, as well as the ongoing trend of residential energy consumption in China.

## Introduction

Human activities are influencing the process of global climate change by emitting large amounts of greenhouse gases into the air, and global warming has become the most significant environmental problem facing humankind so far1,2. Approximately one-third of global greenhouse gas emissions and 40% of energy consumption is associated with the building sector3. As the largest carbon emitter, China accounts for over one-quarter of the world’s total carbon emissions, and the global carbon reduction trend is highly correlated with China’s emission reduction4. Although China’s economic growth has entered a new normal stage, the urbanization process will undoubtedly continue after decades of vigorous development5. As a result, the number and scale of Chinese cities have increased dramatically, encouraging the rapid expansion of buildings and its attendant surging energy consumption. The urban residential building energy consumption (URBEC) has increased from 309 Million ton coal equivalent (Mtce) in 2001 to 857 Mtce in 2015 in China. At the same time, with the deepening of the industrialization process, industrial energy savings potential has been declining. Therefore, the building sector has to assume more energy-saving and emission-reduction tasks. Currently, China’s building energy consumption mainly comes from industrial buildings, public buildings and residential buildings6. Although the energy consumption per square meter for urban residential buildings (URBEC) is much lower than that of public buildings, the total floor area of residential buildings in China occupies a very high proportion of the total construction area. In addition, the demand for energy consumption caused by the improvement of housing conditions is also increasing with the continuous improvement of people’s living standards7. Therefore, the residential sector has a very large potential for decreasing energy consumption and environmental impact.

Improving the residential building energy efficiency plays an essential role in reducing the URBEC. Therefore, it is of great importance to measure energy efficiency effectively, which may facilitate energy conversation policy-making. Two methods are being applied extensively for the URBEC efficiency evaluation. The first method is to directly compare the URBEC of similar buildings at a project level. The other method is to employ the URBEC per square meter as the indicator of energy efficiency, an approach which is mainly used at the industry level. Due to its ease of use and relatively low cost, the URBEC per square meter has been widely applied in most studies, research reports, energy efficiency design standards, and other relevant documents issued by universities, scientific research institutes and governments8,9,10.

Previous literature took the URBEC per square meter as an important efficiency indicator to analyze the driving factors of energy consumption11,12,13,14,15,16,17,18,19, measure energy use performance11,14,20, and evaluate the effect of policy tools and make projections16,18,21. China Building Energy Use, a widely used annual report published by the Building Energy Research Center of Tsinghua University, explores the energy use status, energy-saving potential, as well as sustainable development paths in the building sector in China, taking the energy use per square meter as an efficiency index22. The national building energy saving design standard (BESD) for residential buildings and a number of local BESDs also adopt energy consumption per square meter as the criterion for judging the energy use performance of building operation23,24,25,26. In addition, the American Council for an Energy Efficient Economy (ACEEE) also evaluates the energy conservation achievements of the building sector in global regions (including China) with the indicator kilojoules per square meter.

These studies, reports, and standards play important roles in facilitating government policy-making and efforts to upgrade building performance, which directly affect the progress of energy conservation and environmental protection. Therefore, whether it is reasonable to use the URBEC per square meter as the benchmark indicator for changing energy use efficiency is critical to energy-saving work and conducting further studies. However, to date, little or no attention has been placed on the rationality of using URBEC per square meter to measure the change in building energy consumption performance.

Here, we propose the dilution effect of building area per household on URBEC per square meter. Data from 867 Chinese households were collected to validate the dilution effect based on an extended STIRPAT model we developed. In brief, the growing floor area per household reduced the URBEC per square meter because of rapid urban sprawl. In other words, the decreasing URBEC per square meter fails to represent the real change in energy use efficiency of building operation without accounting for the dilution effect. We then introduced the interaction term of the BESD and the building area per household into the model. The empirical results show that overlooking the dilution effect leads to significant overvaluation of the effectiveness of implementing BESD in residential buildings, especially those in rapidly urbanized areas. Further analysis finds that the inflection point in the China URBEC is delayed from 2001 to 2012 if the expansion of building area per household is taken into consideration. The full details of models and data sources are available in the Methods section. In addition, we also discuss why the dilution effect phenomenon happens in China, but not everywhere, and how conditions can vary among different economies.

## Results

### The dilution effect of the building area per household

To untangle the impacts of the expansion of the building area per household on the URBEC per square meter, a multivariate linear regression (MLR) model was employed. Based on the survey data, the coefficients of all variables except the Building Floor number passed the 10% significance test.

As shown in Fig. 1, the influence coefficients of the variables Household size (x3), Household income (x4), Number of air conditioning units (x5), and Number of other household appliances (x6) are positive, indicating that the URBEC per square meter grows in step with the household size, household income, number of air conditionings, and other household appliances. In contrast, the building floor area per household (x1) is the only variable negatively affecting the URBEC per square meter, and its influence coefficient is −0.450. Thus, the URBEC per square meter will decline as the building area per household increases. In other words, the URBEC per square meter is diluted by the building area per household. Therefore, the survey data in this research validates the dilution effect.

The URBEC per household (y2) is the product of the URBEC per square meter (y1) and the building area per household (x1), as shown in Eq. (1).

$${\mathrm{The}}\,{\mathrm{URBEC}}\,{\mathrm{per}}\,{\mathrm{household}}(y_2)\, {\mathrm{ = the}}\,{\mathrm{URBEC}}\,{\mathrm{per}}\,{\mathrm{square}}\,{\mathrm{meter}}(y_1) \qquad \\ \times {\mathrm{the}}\,{\mathrm{building}}\,{\mathrm{area}}\,{\mathrm{per}}\,{\mathrm{household}}(x_1)$$
(1)

To intuitively understand how strongly the URBEC per square meter is influenced by the increase of the building area per household, we further explored the impact of the building area per household on the URBEC per household. The results show that the influence coefficient of the building area per household on the URBEC per household is positive (0.133). This finding indicates that the URBEC per household increases with the expansion of the building area per household when other factors are ruled out. Based on Eq. (1), this means that when the building area per household increases and the URBEC per square meter decreases, their product also increases. In other words, the decrease rate of the URBEC per square meter drops in the interval from 0 to the increase rate of the building area per household. The extent of this decrease depends on the gap between the rates of increase of living space and energy consumption per household (see below for further discussion). In regions where the building area per household is expanding rapidly, the dilution effect can be very significant and thus should be carefully considered.

### The overestimation of the BESD effectiveness

As a widely applied policy tool, the building energy saving standard (BESD) plays a crucial role in improving the energy saving performance of urban buildings in China. However, to date, the evaluation of the BESD effectiveness has generally omitted any discussion of being influenced by the rapid expansion of building area per household. To explore how the effectiveness of BESD differs when the dilution effect is accounted for or not, indicating the impacts of the fast-growing building area per household, the interaction term of building area per household (x1) and BESD is introduced into the MLR model.

The results show that the influence coefficients of BESD and building area per household on the URBEC per square meter are −1.409 and −0.67 respectively, reflecting that both factors have a positive effect on reducing energy intensity (Fig. 2). However, the coefficient of the interaction term of BESD and building area per square meter is 0.309, which shows a negative effect opposite to their single influence. With this interaction term introduced into the model, the effect coefficients of BESD and building area per square meter decreased by 21.9% and 46.1% to −1.1 and −0.361, respectively. This finding indicates that when the increase of building area per square meter is considered, the degree of reduction in the URBEC per square meter attributed to BESD implementation decreases significantly. For those regions where floor area per household is expanding rapidly, the effectiveness of BESD adoption on energy savings should be reevaluated properly to account for the dilution effect.

### The BESD moderates the dilution effect

The results also show that the adoption of the BESD in buildings can weaken the dilution effect caused by the increase in building area per household. Figure 3 demonstrates the differences in the URBEC per square meter between two groups of buildings. Buildings in group (a) adopted the BESD, while buildings in group (b) did not adopt the BESD. In both cases, the gap between the energy intensity of large-area buildings and smaller ones is obvious, which is consistent with the dilution effect. However, for buildings that meet the BESD, the reduction of the URBEC per square meter aroused by the expansion of floor area per household is less noticeable. In fact, the BESD is better implemented in more developed regions, where the pursuit of higher indoor comfort level eases the gap between the growth of the URBEC and building area per household. In general, the dilution effect could be more significant in emerging economies.

### Delayed inflection point of the China URBEC

The inflection point of the URBEC per square meter is widely considered an important indicator to predict the evolution trend and the temporal peak of the URBEC in China27. As indicated by the IPAT model and Kuznets curve theory, the occurrence of the inflection point of energy intensity signifies that the urban population, economic growth, and technological level have reached a certain level, at which point further development would lead to a reduction in the increment in the energy consumption.

Here, we estimated the inflection point of the URBEC per square meter of China with and without considering the dilution effect. Figure 4 shows the change patterns of the URBEC per square meter in China from 2000 to 2016. The inflection point of URBEC intensity occurred in 2001 without considering the dilution effect. If the dilution effect is taken into account, the inflection point occurred in 2012, 11 years later than it would have occurred if the dilution effect was not considered. Thus, from 2001 to 2012, the energy intensity was still increasing (rather than decreasing) as the growth of the population, the economy, and technology increased. Only after 2012 has the URBEC per square meter truly reversed its rising trend. Since China is still undergoing a rapid expansion of urban building area, neglecting the dilution effect may cause misleading judgments about the ongoing trend of the URBEC in China.

## Discussion

The past decades have witnessed a dramatic increase in the living space of urban residents, and this growth trend is expected to continue in the future. As a result, the building area per household has also been increasing, especially in many emerging economies. In the meantime, economic development contributes to the pursuit of better indoor comfort levels and living conditions in urban areas, thus leading to a higher energy demand per household. Against such a background, energy efficiency improvement is important to save energy resources and reduce the environmental impact.

The URBEC per square meter is widely considered as a benchmark indicator of energy intensity to measure energy use performance, estimate the effectiveness of policy tools, and understand trends. While it is obvious that the energy use per household directly affects the energy intensity, the impacts of growing building area per household on the URBEC per square meter have been overlooked. Here, we analyze the socioeconomic background of the dilution effect in China, as well as how this differs from other economies. In general, how the URBEC per square meter varies with increasing floor area per household depends on the gap between the growth rates of building area and energy use per household.

Energy consumption of residential buildings mainly result from the operation of household appliances (including heating, air conditioning, and other appliances)28. The number and the use intensity of these appliances are closely related to the number of residents and the building area29. According to the design standard of residential buildings in China, the volume of energy consumption of one building can be expressed as: Et = e1A + e2N. Et represents the energy consumption of the entire building at time t. e1 is the energy consumption per square meter consumed by the appliances (heating, for example) associated with the floor area. e2 is the energy consumption per capita consumed by the appliances (cooking, for example) associated with the number of residents. A denotes the total living area of the entire building. N is the number of the residents living in the building. Therefore, the energy consumption per square meter of the entire building can be given as:

$$e_t = \frac{{e_1 \ast A + e_2 \ast N}}{A} = e_1 + e_2 \ast N/A = e_1 + e_2/(A/N)$$
(2)

where et represents the URBEC per square meter. In modern China, the household size has steadily declined since 198230 and then gradually leveled off in recent years31. Meanwhile, there are no obvious differences in household size from family to family. In 2015, the State Health Planning Commission released China’s Household Development Report (2015). The report shows that the household size has been decreasing, and families of two and three members has become the mainstream type32. By contrast, the building area per household has shown an increasing trend since 1950. Therefore, this paper proposes two hypotheses: first, the household size has changed little in recent years; second, the building area per household has been increasing continuously33. Under the first hypothesis, the building area per capita can be expressed by formula (3).

$$A/N = a/n$$
(3)

a is the building area per household, and n is the household size. The energy consumption per square meter can be expressed by formula (4).

$$e_t = e_1 + e_2/(a/n)$$
(4)

For most regions, e1 and e2 are increasing at certain speeds depending on a number of economic, social, and environmental factors. With both the energy consumption (e1 and e2) and the building area per household (a) growing, the change pattern of et can vary significantly. In rapidly urbanized areas of China (Chongqing for example), the floor area per household has increased dramatically, overwhelming the growth pace of energy consumption (e1, and e2). This can be attributed to the following reasons. First, an aging population and a migration from rural to urban areas squeezed living space for urban residents, leading to a rigid housing demand years ago. Second, with economic development, wealthier urban residents have a strong desire for larger living spaces, which has been nurtured by the booming real estate construction in recent years. The National Bureau of Statistics reported that floor area per household in urban China more than quintupled from 6.7 m2 in 1978 to 36.6 m2 in 201634. Third, although people have been pursing more comfortable indoor environments, leading to higher residential energy consumption demands, the continuous improvement in building energy-saving performance moderates the upward trend of the URBEC per household.

The market-oriented reform of the Chinese real estate industry launched in the 1980s has made remarkable achievements. In the meantime, several problems have also been created in this booming industry. First, the faulty market mechanism in the real estate industry has failed to guide normal investment, resulting in a large number of speculative actions. Second, due to the imbalance between supply and demand, the market demand is huge, while the effective supply is insufficient. Moreover, the housing price-income ratio in some cities is exorbitant, thus boosting the rental market in China. As a result, both multi-house families (families owing more than one house) and renters account for a large proportion of the population in urban China, which is highly correlated with the data collection and findings of our research. In general, the reasons why people purchase more houses than they need are, to avoid summer heat or winter cold, for investment, and for earning rental income.

To illustrate how these different phenomena influence the dilution effect, a scenario analysis is conducted in this paper (see Fig. 5).

To eliminate the influences of these disturbing factors and maintain consistency of the climate zone, customs, living habits and other uncontrollable factors, we followed three criteria to collect the samples which includes that the actual residence time in the house is more than 8 months during one year; the households are owners of the houses or family tenants; and the houses are located in the main urban area of Chongqing.

Overall, our results show that the growing building area per household significantly affects the urban residential energy use per square meter in rapidly urbanized regions. Overlooking the dilution effect may lead to misleading judgments of energy conservation progress, as well as the effectiveness of sustainable policy tools. Under a 2 °C warming target, options to manage residential energy use play increasingly important roles in global carbon emission reductions. Efforts to promote residential building energy use performance must be enhanced to align with the sustainable environmental goals, and whether policy actions are truly effective highly depends upon the rationality of energy use estimation.

## Methods

### Extended STIRPAT model

Accompanied by the progress of industrialization, environmental problems are becoming increasingly severe. American biologists proposed the theory of technical determinism, indicating that the expansion of industrial production is the main cause of environmental problems35. Ehrlich et al.35,36 argued that the main cause of environmental problems was population growth. In follow-up studies, scholars realized that environmental issues are not shaped by a single factor. Therefore, Ellic and Holton proposed the famous IPAT model:37

$${I} = {P} \times {A} \times {T}$$
(5)

where I represents the environmental impact. P denotes the population factor. A is the affluence level. T is the technical level. However, the premise of the IPAT model is that the effects each variable on the dependent variable are the same38. To overcome this limitation, Dietz et al39. proposed the STIRPAT model.

$${I} = {\alpha P}_{it}^{\beta _1}{A}_{it}^{\beta _2}{T}_{it}^{\beta _3}e_{it}$$
(6)

where α is a constant. β1, β2, and β3 are the parameters to be estimated, and e represents the random error. To address the heteroscedasticity of the model, we took the natural logarithm of I in formula (10) to obtain the following equation:

$${\mathrm{ln}}I_{it} = \alpha + \beta _1{\mathrm{ln}}P_{it} + \beta _2{\mathrm{ln}}A_{it} + \beta _3{\mathrm{ln}}T_{it} + e_{it}$$
(7)

The STIRPAT model is more extensible, and overcomes the limitations of the IPAT model, allowing variables to be added or removed according to research purposes. Considering previous literature (see Supplementary Table 1), the household size (x3) and the household income (x4) were selected as indicators of the population (variable P in the IPAT model) and affluence (variable A in the IPAT model), respectively. However, the technology indicator is an important, but difficult-to-quantify, variable. In this research, the technologies to promote the URBEC efficiency include improvements in the overall heat transfer coefficient of the building envelope, the shape coefficient of the building, the window-to-wall ratio, the heating system and so on. Therefore, the BESD of urban residential buildings, which embodies the performance of these improvement interventions, was selected as the indicator of technology level (variable T in the IPAT model). In addition, the number of floors was introduced into the STIRPAT model as variable x2, since it significantly impacts lighting and ventilation. The number of the air conditioning units (x5) was particularly employed as a key variable in this model, as Chongqing is typically hot in summer and cold in winter. Other household appliances were denoted as x6. Therefore, formulas (8) and (9) were established as follows.

$${\mathrm{ln}}y_2 = \alpha _0 + \alpha _1{\mathrm{ln}}x_1 + \alpha _2{\mathrm{ln}}x_2 + \alpha _3{\mathrm{ln}}x_3 + \alpha _4{\mathrm{ln}}x_4 + \alpha _5{\mathrm{ln}}x_5 + \alpha _6{\mathrm{ln}}x_6 + \alpha _7D + e_{it}$$
(8)
$${\mathrm{ln}}y_2 = \alpha _0 + \alpha _1{\mathrm{ln}}x_1 + \alpha _2{\mathrm{ln}}x_2 + \alpha _3{\mathrm{ln}}x_3 + \alpha _4{\mathrm{ln}}x_4 + \alpha _5{\mathrm{ln}}x_5 + \alpha _6{\mathrm{ln}}x_6 + \alpha _7D + e_{it}$$
(9)

A MLR model was then employed for parameter estimation to explore the impact of growing building area per household on the URBEC per square meter.

### Impacts on BESD effectiveness

To explore how the growing building area per square meter influences the evaluation of the effectiveness of adopting BESD in residential buildings, the interaction term of BESD and x1 (D x1) was introduced into formula (8). We then obtain formula (10) as follows.

$${\mathrm{ln}}y_1 = \alpha + \beta _0D + \beta _1{\mathrm{ln}}x_1 + \mu D \ast {\mathrm{ln}}x_1 + \beta _2{\mathrm{ln}}x_2 + \beta _3{\mathrm{ln}}x_3 + \beta _4{\mathrm{ln}}x_4 + \beta _5{\mathrm{ln}}x_5 \\ + \beta _6{\mathrm{ln}}x_6 + e_{it}$$
(10)

where μ is the coefficient of the interaction term Dx1. If the results show that β0 is negative while μ is positive, then the effectiveness of adopting BESD has been overestimated with the dilution effect neglected. If both β0 and μ are negative, then the impacts go in the opposite direction. With the growing building area per household considered, the real effect of BESD is represented by μ + β0.

### Impacts of adopting the BESD on the dilution effect

The PSM (Propensity Score Matching) model, as a rigorous method to overcome selection bias, uses nonexperimental data or observation data to analyze the intervention effect40,41,42. The law of its extrapolation is as follows: if there is no A, what is the result of B? It uses the scores for sample matching and makes comparisons in order to estimate the value of the Average Treatment Effect on the Treated (ATT)43,44.

$${\mathrm{ATT}} = {\mathrm{E}}\left[ {Y_1 - Y_0|T = 1} \right]$$
(11)
$${\mathrm{T}} = \left\{ {\begin{array}{*{20}{l}} {1\quad \mathrm{accept}\,\mathrm{the}\,\mathrm{intervention}} \hfill \\ {0\quad \mathrm{not}\,\mathrm{accept}\,\mathrm{the}\,\mathrm{intervention}} \hfill \end{array}} \right.$$
(12)

In formula (11) and (12), Y1 is the experimental group, and Y0 is the control group. T is selected as the key indicator variable to identify the experimental group and the control group. Here, we take variable x1 as the key indicator T. Then, the formula (13) is obtained.

$${\mathrm{ATT}} = {\mathrm{E}}\left[ {y_2|\left( {x_1 = 1} \right)} \right] - {\mathrm{E}}\left[ {y_2|\left( {x_1 = 0} \right)} \right]$$
(13)

Because x1 is either 0 or 1 in formula (13), we need to dichotomize the variable x1 from a continuous variable to a 0–1 variable. First, the data were categorized into group (a) (BESD = 1) and group (b) (BESD = 0) according to the value of the variable BESD. Second, the average values of x1 were calculated in group (a) and group (b), respectively. The variables x1 less than the average value were set to 0, and those above the average value were set to 1. Then, the dichotomized value of x1 was stored in the x11 variable. Finally, the data were paired by the nearest neighbor matching method.

### Impacts on URBEC inflection point estimation

To eliminate the distorted influence of the dilution effect on the URBEC inflection point prediction, we introduce the area correction index (ACI) referring to the principle of the consumer price index (CPI). Given the time period concerned, the urban residential building area per capita in 2000 was selected as the base year. Therefore, the area correction index (ACI) can be expressed as

$${\mathrm{ACI}}_i = \frac{{\mathrm{URBAPC}}_i}{{\mathrm{URBAPC}_{2000}}}$$
(14)

where URBAPC2000 and URBAPCi denote the urban residential building area per capital in the year 2000 and year i, respectively. The adjusted URBEC per square meter (AURBECP) is

$${\mathrm{AURBECP}}_i = {\mathrm{URBAPC}}_i \ast {\mathrm{ACI}}_i$$
(15)

### Variable selection

A number of factors affect the URBEC per square meter, including macroeconomic factors (economy, culture, and society) and microeconomic factors45,46. Based on a review of previous literature, the key factors were classified into two types: area-related factors and residents-related factors47,48,49,50,51,52,53,54,55,56,57,58,59 (Supplementary Table 1).

The value of variable BESD is 1 when the energy efficiency design standard is adopted. Otherwise, its value is 0.

$${\mathrm{BESD}} = \left\{ {\begin{array}{*{20}{l}} {1,\mathrm{the}\,\mathrm{energy}\,\mathrm{efficiency}\,\mathrm{design}\,\mathrm{standard}\,\mathrm{is}\,\mathrm{adopted}} \hfill \\ {0,\mathrm{the}\,\mathrm{energy}\,\mathrm{efficiency}\,\mathrm{design}\,\mathrm{standard}\,\mathrm{is}\,\mathrm{notadopted}} \hfill \end{array}} \right.$$
(16)

As the major source of final energy consumed by residential building operation in urban China, electricity consumption was taken to be representative of the URBEC60. In this research, the URBEC per square meter (y1) and the URBEC per household (y2) are defined as two dependent variables.

The design standard for the energy efficiency of residential buildings (BESD) was released to improve buildings’ energy use performance to reduce energy waste and carbon generation. As a major part of energy-saving efforts, the Chongqing Building Energy Conservation Association Green Building Professional Committee, the Chongqing Construction Technology Development Center, and other related departments have jointly developed the design standard for the energy efficiency of residential buildings61,62. Here, we select the building area per household (x1) as the key explanatory variable and the BESD as the auxiliary variable.

### Data sources

Data for this study were collected in three ways. First, the data for the physical characteristics of the residential buildings, including name, age, and other basic information was obtained from the Chongqing Municipal Commission of Urban-Rural Development (CMCURD). Considering accessibility and convenience, multilevel random sampling techniques and the probability proportional to size (PPS) were applied to select optimal samples. Second, the data for variable values, including building area per household, number of floors, household size, household income, number of air conditioning units, and number of other appliances were collected from a survey conducted by the China Association of Building Energy Efficiency (CABEE) in 2016. A team of 40 undergraduates, 10 graduate students and 4 Ph.D. students completed this survey over almost two months. To guarantee the quality of the survey, all the team members were trained for a week in advance. During the survey, all the team members were required to record all the interviewees’ telephone numbers for follow-up confirmation. The selected families met three criteria. First, the household selected had to provide the electricity billing number or the ID of the electric meter for finding the electricity consumption data from the State Grid Chongqing Electric Power Company (SGCEPC). Second, the households used the energy for consumption purposes rather than production purposes. Third, the households had been living in the building for more than one year, so that the incomparability of the energy consumption data caused by seasonal weather changes over the year can be eliminated. Third, the household electricity consumption data were collected from the SGCEPC. Based on the obtained survey data and monthly electricity consumption data for 867 households, the basic statistical characteristics of the variables are shown in Supplementary Table 2.

### Collinearity test

To avoid the result deviation caused by the collinearity of variables, the variance inflation factor (VIF) was calculated. As shown in Supplementary Table 3, the VIF for all variables is between 1.02 and 1.36. The closer the VIF is to 1, the smaller the collinearity of variables will be. Therefore, the results demonstrate that there is no collinearity among the variables selected in this paper.

## Data availability

The data for the physical characteristics of the residential buildings, the household electricity consumption and variable values, including building area per household, number of floors, household size, household income, number of air conditioning units, and number of other appliances are in Supplementary data 1. The data for the PSM (Propensity Score Matching) model is in Supplementary data 2. The source data for the Fig. 3 is in Supplementary data 3 and 4. The source data for the Fig. 4 is in Supplementary data 5. Supplementary Table 1 is the factors influencing the URBEC per square meter. Supplementary Table 2 is the statistical characteristics of the variables. Supplementary Table 3 is variance inflation factor of variables.

## Code availability

All the computer code generated during this study is available from the corresponding authors and provided in the Supplementary Data 6.

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## Acknowledgements

This study was supported by the National Social Science Fund of China (19BJY065), the Fundamental Research Funds for the Central Universities (No. 2019 CDJSK 03 XK 04) and National Natural Science Foundation of China (Grant No. 71902053).

## Author information

Authors

### Contributions

J.G. and W.C. designed the study. J.G. performed the analysis and prepared the manuscript. J.G. and W.C. assembled input data, implemented the model and analyzed output data and results. X.W. conducted data collection and preliminary analysis. H.R. and T.H. revised the original manuscript. Z.M. and X.Z. validated modelling results and discussed the results and implications. All authors (J.G., X.Z., W.C., H.R., T.H., X.W., and Z.M.) participated in the writing of the manuscript. W.C. coordinated and supervised the project.

### Corresponding authors

Correspondence to Weiguang Cai or Zhifu Mi.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Gao, J., Zhong, X., Cai, W. et al. Dilution effect of the building area on energy intensity in urban residential buildings. Nat Commun 10, 4944 (2019). https://doi.org/10.1038/s41467-019-12852-9

• Accepted:

• Published:

• DOI: https://doi.org/10.1038/s41467-019-12852-9


text:
# Chapter 22 - Electric Charges and Forces - Exercises and Problems: 40

(a) The force on object A is 0.45 N (b) $q_A = 1.0\times 10^{-6}$ $q_B = 5.0\times 10^{-7}~C$

#### Work Step by Step

(a) Since both objects experience the same magnitude of electric force, the force on object A is also 0.45 N (b) Let $q$ be the charge on object B. Then the charge on object A is $2q$. We can find the charge $q$. $F = \frac{k~q_A~q_B}{r^2}$ $F = \frac{k~(2q)~q}{r^2}$ $2q^2 = \frac{F~r^2}{k}$ $q^2 = \frac{F~r^2}{2k}$ $q = \sqrt{\frac{F}{2k}}~r$ $q = \sqrt{\frac{0.45~N}{(2)(9.0\times 10^9~N~m^2/C^2)}}~(0.10~m)$ $q = 5.0\times 10^{-7}~C$ Since $q_A = 2q$, then $q_A = 1.0\times 10^{-6}$ and $q_B = 5.0\times 10^{-7}~C$.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.

format: plain


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Chain Rule Questions Answers (MCQ) listings with explanations includes questions on calculating costs, time etc by using chain rule which are important for many competitive exams and also save time while getting answers.

1) If 16 toys cost 240, then what do 40 toys cost

• 1) Rs. 600
• 2) Rs. 620
• 3) Rs. 640
• 4) Rs. 660
Ans.   C
Explanation :
Although we can first calculate the cost of one toy and then can multiply it with 40 to get the result. but we will solve it with chain rule so that we can prepare ourself for other complex problems which we can solve easily by applying this rule. Let the required cost be Rs. x More toys means More Cost. (Direct Proportion) \begin{aligned} 15:40 :: 240:x \=> x = \frac{240*40}{15} \=> x = 640 \end{aligned} So 40 toys will cost Rs 640

2) If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate

• 1) xd
• 2) yd
• 3) yd/x
• 4) x/yd
Ans.   C
Explanation :

3) If the price of 23 toys is 276, then what will the price of 12 toys

• 1) 144
• 2) 148
• 3) 156
• 4) 186
Ans.   A
Explanation :
Less toys, Less Price (Direct Proportion) So, let the price be Rs. x then, \begin{aligned} 23:12 :: 276:x => x = \frac{276*12}{23} \=> x = 144 \end{aligned} So price of 12 toys will be Rs. 144

4) If a quarter kg of potato costs 60 paise, how many paise will 200gm cost

• 1) 45 paise
• 2) 46 paise
• 3) 47 paise
• 4) 48 paise
Ans.   D
Explanation :
Quarter of Kg means 250 gm Less weight, less price (Direct Proportion) So, \begin{aligned} 250:200 :: 60:x \=> x = \frac{200*60}{250} \=> x = 48 \end{aligned} So 200 gm will cost 48 paise.

5) An industrial loom weaves 0.128 metres of cloth every second. Approximately, how many seconds will it take for the loom to weave 25 metre of cloth

• 1) 194 seconds
• 2) 195 seconds
• 3) 196 seconds
• 4) 197 seconds
Ans.   B
Explanation :
Let the time required by x seconds. Then, More cloth means More time (Direct Proportion) So, \begin{aligned} 0.128 : 1 :: 25 : x => x = \frac{25*1}{0.128} \=> x = 195.31 \end{aligned} So time will be approx 195 seconds

6) A flagstaff 17.5 metre high casts a shadow of length 40.25 metre. The height of building, which casts a shadow of length 28.75 metre under similar conditions will be

• 1) 12 metre
• 2) 12.5 metre
• 3) 13.5 metre
• 4) 14 metre
Ans.   B
Explanation :
Less shadow, Less Height (Direct Proportion) So, let height of building be x metre then, \begin{aligned} 40.25 : 17.5 :: 28.75 : x \ => x = \frac{17.5*28.75}{40.25} \=> x = 12.5 \end{aligned} So height of building should be 12.5 metre

7) 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work

• 1) 24 days
• 2) 28 days
• 3) 34 days
• 4) 35 days


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# Can wing-tip vortices be reduced/eliminated with a rear-facing propeller near the wing-tip?

Let's say we have a propeller-driven aircraft in the pusher configuration (rear-facing propellers). If we could somehow put an engine at the wing tip (ignoring structural concerns), and maybe make the propeller rotate in the opposite direction of the way the wing-tip vortex wants to spin, would this eliminate or at least drastically reduce the wing-tip vortex?

• It's been tried before.
– fooot
Jan 22, 2016 at 4:05
• @fooot a fascinating aircraft that seems to imply the answer is yes. However I envisioned the propellers to be a little proportionally smaller and the wing shape to be much more conventional. Hopefully the vortex-cancelling effect will be the same. Jan 22, 2016 at 4:29
• Vmca on that aircraft had to be pretty high! Jan 22, 2016 at 6:22
• @RalphJ I think the idea was specifically to have more lift and control at low speeds by using the propellers to boost the wing efficiency. The article suggests that was actually achieved. Jan 22, 2016 at 7:05
• That might actually be an interesting design to revive for hobbyists. It looks to me that it was designed to optimize space usage (hangar and deck) and robustness for carrier operations. I think there are people who'd like to have a compact and robust design. Although I kind of wonder what happens if you have engine or propeller problems... Jan 22, 2016 at 7:10

Yes. From an aerodynamic standpoint it makes some sense to use the wingtip vortex in combination with a propeller.

In this article by Sinnige et al., the researchers modeled and tested a propeller in various positions along a semispan, concluding that there were real gains to be had due to the increased span efficiency. Up to 15% less drag was measured when the propeller was positioned at the wingtip compared to a conventional mounting:

By positioning the propeller at the tip of the wing, the slipstream interacts with the flow around the wingtip, thus affecting the roll-up and downstream behavior of the wingtip vortex. PIV measurements downstream of a propeller–wing model showed that this leads to a reduction in overall swirl with inboard-up rotation, for which the swirl in the slipstream is opposite to that associated with the wingtip vortex. At the same time, the system performance was found to improve due to a reduction of the wing induced drag, leading to the conclusion that the decrease in swirl causes a reduction in downwash experienced by the wing.

Apart from the change in drag, the interaction of the wing with the propeller slipstream also modifies the wing lift. The locally enhanced dynamic pressure increases the lift over the spanwise part of the wing washed by the slipstream, which is amplified by the induced swirl for the case with inboard-up rotation. As a result, a strong spanwise variation in lift occurs with the propeller on. The induced velocities caused by this lift gradient lead to a spanwise shearing of the slipstream. With outboard-up rotation, the swirl in the slipstream acts to locally oppose the increase in wing lift due to the propeller-induced dynamic-pressure rise. Compared to the inboard-up rotation case, this leads to a reduction in wing lift at a given angle of attack, thus also a reduction in maximum lift coefficient. Furthermore, the direction of the spanwise shearing of the propeller slipstream is inverted on both sides of the wing.

To quantify the potential aerodynamic benefits of the wingtip-mounted configuration, a direct comparison was made with a conventional configuration, with the propeller mounted on the inboard part of the wing. The increase in wing lift due to the interaction with the propeller was 1 - 4% smaller for the wingtip-mounted configuration than for the conventional configuration. For the latter, the enhanced dynamic pressure and swirl in the slipstream acts over double the spanwise extent, and on a part of the wing where the section lift is higher than for the wingtip-mounted configuration. At higher angles of attack, the lift advantage for the conventional configuration could be further enhanced by the local angle-of-attack increase in proximity of both sides of the nacelle.

In terms of drag performance, on the other hand, the wingtip-mounted configuration showed superior performance. At a wing lift coefficient of $$C_L = 0.5$$ and a thrust coefficient of $$0.09 < C_T < 0.13$$, the drag reduction amounted to about 15 - 40 counts (5 - 15%) compared to the conventional configuration. The aerodynamic benefit of the wingtip-mounted configuration further increases with increasing wing lift coefficient and propeller thrust coefficient, leading to a drag reduction of 100 - 170 counts (25 - 50%) at $$C_L = 0.7$$ and $$0.14 < C_T < 0.17$$. An analysis of the wing performance confirmed that this drag benefit is mostly due to a reduction of the wing-induced drag. Compared to the conventional configuration, a relative increase in span efficiency of up to 40% was measured for the wingtip-mounted configuration. Although the exact drag benefit will be specific to vehicle design and operating conditions, it is concluded that the interaction between the propeller slipstream and the wingtip vortex leads to a clear drag reduction for the wingtip-mounted configuration.

Keep in mind this is purely aerodynamical, of course, and from a structural standpoint things might not be so clear-cut. While weight in the wings helps alleviate the bending stresses generated by lift, a large mass at the tip can lower the first bending eigenfrequency to unacceptable levels, risking a coupling of the wing oscillations with some other mode in flight or on the ground.

As far as I am aware wingtip fuel tanks have mostly been used on relatively low aspect ratio wings, which lends some credence to the magnitude of this problem.

• Well done for spotting that paper! Also, putting the propeller before the wing makes a ton of sense. An additional problem with having this weight at the wing tip: Landing. Passenger aircraft must be able to land at constant 3° glide slope (in case the pilot doesn't pull up in time) -- with nice slender wings, that means unless your engine is very light, you have a problem. So I would still not expect to see this in practice, at least not without a host of other smart ideas to make it work.
– Zak
Aug 13, 2019 at 1:05
• That paper had been sitting in my "to read" pile for half a year, this was more of a happy coincidence. Also, good point about wingtip clearance; there is also the issue of FOD damage for engines hanging outside the paved width of a runway. Aug 13, 2019 at 14:37

Eliminate, no. The wingtip vortices are inherent part of lift generation. There is no lift without wingtip vortices. The wake vortices are carrying the momentum that was given to the air to produce the lift, and to cancel them, you'd have to give the air the opposite momentum, which would negate the produced lift. See How does an aircraft form wake turbulence?

Improve efficiency, yes, a little bit. The propellers would cause downwash in their span outside of the wing tips, effectively extending the wing span and longer wing span means, slightly, less induced drag.

However, such design would have extremely poor single-engine handling, not only because the thrust would become very asymmetric, but also because the lift would partially depend on the engines and therefore the side with stopped engine would also loose some lift, and deflecting aileron to compensate would generate more drag to make the thrust even more asymmetric. And it would have poor all-engine-out performance too due to the loss of lift. Does not sound like optimal approach when similar benefits can be obtained without all these problems by using longer wings.

• "The wingtip vortices is what generates the lift." Wrong, wingtip vortices are a by-product of lift generated by the wings, but they generate drag by themselves. Otherwise why add winglets? Aug 5, 2019 at 21:33
• I agree with Micheal Hall. Otherwise, why not put some vortex generators on the wingtip to increase vorticity? Would putting propellers behind the wingtips to cancel the vortex out destroy the lift? The wingtip vortices are a side effect of having a lifting vortex in your wing (precisly: spanwise change of strength of the lifting vortex) -- which itself is as much a mathematical construct than an actual thing.
– Zak
Aug 5, 2019 at 23:22
• Correct: single-engine handling would be horrible (and also putting such masses at the wingtips is a recipe for aerolastic catastrophes), and ailerons interacting with propellers must be a nightmare in terms of stability and control (and the propeller, too) -- but the propellers wouldn't generate very much lift. Also: making the wings longer isn't always an option.
– Zak
Aug 5, 2019 at 23:27
• @JanHudec You are correct in saying lift cannot exist without vortices. Michael and Zak are also correct in saying wingtip vortices do not contribute to additional lift. Wingtip vortices are what contribute to the induced drag, a finite-span 3D phenomenon. In infinite span, induced drag would disappear and you would get the 2D result, and you will still have bound vortices.
– JZYL
Aug 7, 2019 at 12:47
• This thread is becoming ricidulously long. I suggest you look at @AEhere's answer and the linked paper there: Fig 24 nicely shows how lift is almost unaffacted by moving the prop to the wingtip, but drag is nicely reduced. There's more figures showing how the vortex is weaker if the prop is turned on. I'm tapping out now.
– Zak
Aug 13, 2019 at 1:10

Doug MacLean has a great synopsis of wingtip devices that is worth reading, and gives a good intuition as to why propellers could reduce, but likely not eliminate, the wingtip vortex.

To summarize: the wingtip vortex (really, the rolled-up vortex wake sheet), creates a downwash at the wing which effectively reduces the angle of attack of the wing relative to the freestream. This downwash increases with the strength of the wingtip vortex, which is proportional to the lift of the wing. The induced downwash angle $$\alpha_i$$ can be compactly given as $$\alpha_i = \frac{C_L}{\pi e AR}$$.

To compensate for this downwash, the plane has to fly at a higher angle of attack to achieve some amount of lift. A component of the lift ($$C_L\sin\alpha_i$$) is now pointing in the streamwise direction. This is induced drag, and if the $$\alpha_i$$ is small you get the conventional induced drag expression $$C_{D_i} = C_L\sin\alpha_i = \frac{C_L^2}{\pi e AR}$$.

So how does this change if we add another source of vorticity? It won't reduce the lift of the wing; the vorticity generated by lifting surface will still be present. To remove the induced drag ideally our new source of vorticity will have opposite sign and equal magnitude, so as to create a corresponding upwash at the wing, which would rotate the lift vector back towards the freestream direction.

Can the propeller do that? It's worth thinking about where the vorticity (swirl) comes from in the propeller wake. Swirl is the tangential velocity imparted to the wake; it's essentially due to viscous losses in the blades. Well-designed propellers try to, among other things, minimize this type of loss. If you had a propeller well-designed to provide forward thrust, you would need to put in a huge amount of energy that the viscous losses counteract the entirety of the wingtip vortex; likely much more than you need for forward thrust. In a typical jetliner wing, the lifting force in cruise is something like 20x the propulsive force. Swirl losses, like tip vorticity, are proportional to the thrust produced by the propeller, which is an order of magnitude smaller than the wing lift.

In theory you could design a propeller to add more swirl to the wake, counteracting the tip vortex more efficiently. But this would reduce the efficiency of the propeller at creating forward thrust, so is unlikely to give a net benefit.

As the testing shows there is some benefit to wingtip mounting. You can't design a propeller with no swirl, so you might as well get some credit for it by putting it at the wingtips (if you can accept the weight and OEI tradeoffs associated with it). But it's not going to entirely (or even substantially) eliminate induced drag.

TL:DR Propeller swirl and wingtip vorticies are both due to inefficiencies in the two systems. These inefficiencies can cancel to some extent, but they are both proportional to the amount of force being produced by the wing/propeller. Since the wing is producing ~20x the force of the propeller in cruise, the effect of its inefficiency will dominate.

• Welcome to Av.SE! Aug 7, 2019 at 18:46

The wingtip vortices carry some energy, and not leaving it behind seems like a good idea. That's why winglets are a thing, after all.

So, what if you put a propeller at the wingtip, aligning the axis with the vortex core? The propeller would "see" the incoming vorticity, and the blades would get accordingly larger local incidences, thus generate more forwards force -- a little like putting guide vanes in front of it. Alternatively, the propeller could rotate a little slower or reduce blade incidence a little to get thrust back to where it was. The swirl which the propeller produces would be accordingly reduced, so there'd be overall less vorticity and swirl in the flow behind the aircraft.

That all sounds pretty good so far.

However, there are a few drawbacks, from least to most severe:

1: The wintip vortex is pretty strong at its core, but angular velocity reduces quickly as you move away -- this means that the innermost section of your propeller gains most additional incidence, but since it's also moving slowest and the blades are thickest, it doesn't produce a lot of thrust anyway. The outer bits won't see much of an effect, as their own circumferential speed will be much higher than the vortex at that position

2: When mounting the propeller directly behind the wing, the blades will pass through the wing profile wake on the inboard side, where airflow is significantly slower. In the worst case, if the flow on the wing separates, propeller blades could go through a significant zone of "dead water", which means less thrust, and more mechanical load on the blades. Also more noise. Most existing pusher configurations have the propeller mounted at some distance from the wing to reduce this effect. But if you did that with wingtip pusher propellers, it would just make reinforce an even worse problem...

3: The wingtip vortex doesn't align nicely with the trailing edge of the wingtip, let alone the propeller axis. Depending on flight condition, the vortex will be stronger or weaker, and at large incidence, it becomes more of a smeared-out vortex sheet -- imagine lots of small vortices released from points along the outer wing edge, propagating in downstream direction. This means at many flight conditions you'd have the vortex not really matching with the propeller, this diminishing the desired effect, but in some other conditions, you'd have a strong, well-focussed vortex hitting the propeller somewhere off-center, and having your propeller blades rotate through that causes bad vibrations, and might also separations on the blades, which means lost thrust and horrible noise, coupled with either having to reinforce the entire drive train (or facing much higher wear and tear). You could make a propeller aerodynamically more robust to such things, but that will always come at the expense of efficiency, and that's what we set out to gain in the first place...

Pusher propellers are not very efficient to begin with (because putting the whole aircraft into the swirl coming from the propeller is still more efficient than exposing the propeller to the wake of the aircraft), and mostly used for stability reasons (This has to do with the pitching and yawing moment produced by a propeller in inclined flow) -- so although aligning a propeller with a vortex, in isolation does indeed make sense, there are too many real effects keep this from improving efficiency over a regular old front-mounted prop.

So, can't we do anything with that vortex? Oh yes, you can! You could place a little wing inside the upwash just outside the wingspan, also known as "increase the wingspan" -- more wing makes more lift, but the vortex does not get stronger. This is why sailplanes have such long, thin wings. Or, if you can't make the wing any longer (wing root bending moment too large, size restrictions...), add the little bit at an angle! The classical vertical winglet works like this: It redirects the inwards-headed flow above the wingtip to go straight downstream, and this produces mostly an inwards-facing force but also a forward facing component ==> this means it does exactly what the propeller can't do efficiently, which is weakening the vortex and deriving a little forwards force from it. These days, most winglets are some sort of blend between a wingspan extension and the classical winglet.

• How would a turbine engine placed on the wing tip to receive the tip vortex in its entirety?
– Muze
Aug 5, 2019 at 23:24
• @Muze: I typed "Turbofan vortex ingestion" into duckduckgo, and wouldn't you know it, this is the first result: ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19750018896.pdf -- somebody testing what happens when a wingtip vortex gets into an engine. It's not good. Stall and surge margin are reduced, and so is efficiency -- unless you hit exactly straight on, but you virtually cannot. Ground vortex ingestion is also a longstanding problem for turbofan engines: aviation.stackexchange.com/questions/21219/…
– Zak
Aug 5, 2019 at 23:35
• "Pusher propellers are not very efficient to begin with" – are you sure? Most evidence points to the contrary. Aug 7, 2019 at 18:42
• @Peter -- I have no proper literature to hand right now, but the fact that very few aircraft use pusher props (and that most pusher props are seen in photos from the Age of Experimentation) does point that way. The way I learned it: Pusher props avoid penalties for having the fuselage sit in the accelerated, swirling air from the prop, but degrade prop performance, which is (usually) worse. They're also audibly louder (can confirm from personal experience). If they are used, it's mostly due to stability reasons or to clean up the flow on the rear. Reality is likeley more complex than that ...
– Zak
Aug 8, 2019 at 14:08

You can't stop them from forming, but in the case of rotor blades you can reduce the tip vortices to the point that they are almost gone by the time the next blade arrives.


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# How to make a temporary collision?

I have a key and door system working, the character(ball) picks up the key and when it is within the collider it sets the text("press E to open") on the screen to active so that they can open the door. This only needs to be there while the door is closed. How Would I fix this. Thank you so much in advance.

    //GameObject E is the canvas text to instruct the player to press E to open the door.
public GameObject E;
//Door is the door itself, I assigned this manually because the door consists of the doorframe and door.
public GameObject Door;
private bool Unlock;
// Use this for initialization
void Start ()
{
E.SetActive(false);
Unlock = false;
}

// Update is called once per frame
void Update ()
{
if (Unlock)
{
if (Input.GetKeyDown("e"))
{
Door.GetComponent<Animation>().Play();
E.SetActive(false);
CodeManager.GotKey = false;
}
}
}
void OnTriggerEnter(Collider other)
{
if (CodeManager.GotKey)
{
if(other.gameObject.CompareTag("Player"))
{
E.SetActive(true);
Unlock = true;
}
}
}

if(ohter.gameObject.CompareTag("Player") && Door.isClosed)


text:
## Elementary Algebra

We need to convert 0.25 miles per 6 seconds into miles per hour. To do this, we multiply 0.25 miles per 6 seconds by the ratio that converts seconds to hours. The ratio that converts seconds to hours is $\frac{3600\ seconds}{1\ hour}$. So, $\frac{0.25\ mile}{6\ seconds}$ $\times$ $\frac{3600\ seconds}{1\ hour}$ = $\frac{900\ miles}{6\ hours}$ = 150 miles per hour.


text:
# Axis of a parabola lies along x-axis. If its vertex and focus are at distance 2 and 4 respectively from the origin,

more_vert
Axis of a parabola lies along x-axis. If its vertex and focus are at distance 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it ?

(1) $(4,\ -4)$

(2) $(5,\ 2\sqrt6)$

(3) $(8,\ 6)$

(4) $(6,\ 4\sqrt2)$


text:
# How to use the discriminant to find out how many real number roots an equation has for x^2 - 5x + 7 = 0?

${x}^{2} - 5 x + 7$ is of the form $a {x}^{2} + b x + c$, with $a = 1$, $b = - 5$ and $c = 7$.
$\Delta = {b}^{2} - 4 a c$
$= {\left(- 5\right)}^{2} - \left(4 \times 1 \times 7\right) = 25 - 28 = - 3$
Being negative, we can deduce that ${x}^{2} - 5 x + 7 = 0$ has no real roots (it has two distinct complex roots).


text:
×

# NMTC Results Declared

PARTY TIME AS AMTI RESULTS ARE DECLARED. also share your results too. and also how to prepare for second level. This lists shows the result of students qualified from Nagpur for second level of AMTI

2 years, 1 month ago

Sort by:

@Shivam Jadhav How do I see the Delhi results?

- 2 years, 1 month ago

We both gave the same paper. How much are you expecting?

- 2 years, 1 month ago

Actually, I didn't give the paper. Idk why my Fiitjee didn't let me give it. I saw the paper though.

I just wanted to see the results f some friends of mine. :)

- 2 years, 1 month ago

Your result will be delivered to the institution through which you gave the exam. Contact them:)

- 2 years, 1 month ago

plz tell the results of this year of sub junior and cutoff

- 1 year, 1 month ago

HELLO How did you the second level exam?

- 1 year, 11 months ago

I am still waitiiiiiiing for my results..neverthless congrats SHIVAM JADHAV....Best of luck for 2nd lvl

- 2 years, 1 month ago

I also cleared the junior level this year how should I prepare for the final?

- 2 years, 1 month ago

How can I participate in NMTC?

- 2 years, 1 month ago

Congrats! @Shivam Jadhav btw, is this list exhaustive? I mean, that are these the only ones who got selected?

- 2 years, 1 month ago

Congrats! I couldn't give NMTC neither previous year nor this year. If I am not wrong if you clear the second round you will be able to give INMO right? And Is this list of your state?

- 2 years, 1 month ago

Where is it declared?

- 2 years, 1 month ago

Congrats @Shivam Jadhav . BTW What is NMTC? Never heard of such exam :/

- 2 years, 1 month ago

NMTC is National Mathematics Talent Competition. It is conducted by FIITJEE.

- 2 years, 1 month ago

It is not conducted by FIITJEE. It is conducted by AMTI.

- 2 years, 1 month ago

NMTC is same as AMTI.

- 2 years, 1 month ago

Oh , that's why I don't know about it. Is it a private exam , or it has some relation with RMO?

- 2 years, 1 month ago

There is some relation like you have to clear the second level and then you will be able to give inmo probably. I'm not sure inmo or rmo but there is a connection for sure.

- 2 years, 1 month ago

I don't think so.

- 2 years, 1 month ago

Congrats!

- 2 years, 1 month ago

- 2 years, 1 month ago

Hey! Congrats, I'm online about after 2 months or so, and I can see that Brilliant has changed a lot... BTW I didn't take the NMTC this year but I took it last year, and the second level paper was too annoying.. :(

- 2 years, 1 month ago

Why was it annoying?

- 2 years, 1 month ago

Congrats @Shivam Jadhav your name as one of the rare XI student looks great in the list. Hope you do even better in the second level :)

By the way how much did you get?

- 2 years, 1 month ago

@Shivam Jadhav : I can't see any link for result on AMTI website. Congrats though!

- 2 years, 1 month ago

It is not given in AMTI site but your institution will be given the names of selected students. Then your institution will provide the names.

- 2 years, 1 month ago

They seem to have changed the format of the competition. Earlier (3-4 years back) , they used to put up the results for the prelims also on their own website.

- 2 years, 1 month ago


text:
# Deducting period-density law

1. Oct 19, 2011

### sl2382

1. The problem statement, all variables and given/known data

Consider a start of mass M and radius R.
1.It can be modeled as a single shell in hydrostatic equilibrium
The star's pressure is given by P(core)/2
The star's density is average density a
2.Period=star's diameter/speed
3.Speed=sqrt(γP/a)
γ=5/3
P is the average pressure

T=Ka^(-1/2) where K is a constant you should be able to calculate.

2. Relevant equations

hydrostatic equilibrium

so that's
ΔP=GMa/R

3. The attempt at a solution

I've been trying it for numerous times but just can't get the right answer. I assume that:
according to hydrostatic equilibirum rule
P(core)/2=(GMa)/R
and
T=2R/speed = 2R/sqrt((5/4)P/a) since average pressure should be (P/2 + P)/2

So from the first equation, I get that P=(2GMa)/R so plug this into the second equation

It's too complicated to put here but I just can't get the right answer.. is any of those steps wrong so I can make corrections?? Thanks a lot!!


text:
# How to model a dice pool with re-rolls mechanic? [closed]

I have a dice mechanic where players roll a number of D10s and have a different number of re-rolls they can use to maximize the total.

For example: The player has 3D10 and 2 re-rolls.
They roll 9,6,3 and choose to keep the 9 and re-roll the 6,3
The first re-roll gives 7,5. They choose to keep the 7.
The second re-roll gives a 4.

The total is therefore: 9+7+4 = 20.

I would like to be able to model this is something like AnyDice but I can't get my head around it.

To clarify a few points from the comments. The re-rolls are optional and the player can choose to stop at any time. They are trying to maximize their result because it represents the amount of money they earn from an exchange.

Based on this question on Math.SE and the answer by @theoza the optimal strategy is:

• 1 re-roll : keep 6+
• 2 re-rolls: keep 7+
• 3-4 re-rolls: keep 8+
• 5-8 re-rolls: keep 9+
• 10+ re-rolls: keep 10

## closed as unclear what you're asking by Miniman, doppelgreener♦, Tritium21, Pulsehead, MaximillianMay 26 '15 at 13:58

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• How do they choose what to keep? Could you articulate the logic flow here? – Brian Ballsun-Stanton May 26 '15 at 4:37
• I'm going to let my vote to close stick: you don't know what you want to model, so we can't really help you model it. That is probably the part you're having trouble getting your head around. The model for chances of reaching a particular number differ and involve strategy as well as statistics. The model for odds of getting various numbers is not meaningful, because of player decision making involved in rerolls. – doppelgreener May 26 '15 at 5:24
• @Ben Yes, but you don't know how your player will decide whether to reroll. I can write a function to model whichever strategy your player is using, but I can't include all of the functions for every single possible strategy your player might use in a single answer. – Miniman May 26 '15 at 5:46
• @Ben The way to get the biggest score is to reroll & risk everything until you get 30, but that's not useful to examine. Working out the optimum strategy is a whole other ballpark to working out how to model it, and there are different optimum strategies when engaging in different situations. In-game you'll never be trying to get the biggest number (too unlikely): you might be simply trying to beat an opposition of 14, or you might be trying to get a reasonably high number (but it's okay if you don't get "the biggest"). It's kinda jumping the gun to try to model a strategy we don't know yet. – doppelgreener May 26 '15 at 5:53
• Even if we assume the goal of just trying to maximise your expected value, a) as doppelgreener points out, this isn't actually what that players will want to be doing most of the time and b) this is sadly not a trivial problem. The interaction between the amount of value you lose by rerolling a die and having it come out lower, and the amount of expected value you gain by rerolling a die and having it come out lower, are... awkward. That said if you want to make a question about what the optimal strategy is for MD10 and N rerolls, it would probably fit in fairly well on Math.SE – a computing pun May 26 '15 at 6:03

Let's assume that we are simply trying to maximize the expected value of our roll. (As discussed this might not be a realistic representation of actual gameplay, but we can work it out anyway.) Then the rolls on any of the dice don't affect our decisions to reroll for other dice - that is, any one die's rolls and strategy is independent of other dice and we can work out expected value as the expected value for one die times the number of dice.

Now for the expected value of a N-sided die with R rerolls, we can establish a recurrence relation.

Starting with 0 rerolls, this is the normal expected value for a single die:

$$E = \dfrac{1+N}{2}$$

Given $E$ as the expected value for R rerolls, we calculate $E'$ for R+1 rerolls:

$$E' = P(reroll) \cdot E + P(keep) \cdot (average keep)$$

Now the decision to reroll is based on whether our expected value with R rerolls is higher than our current roll. Let $\lfloor{E}\rfloor$ be the floor of $E'$ (i.e. $E'$ rounded down to the nearest whole number - the highest number we will want to reroll), then:

$$P(reroll) = \dfrac{\lfloor{E}\rfloor}{N} \\ P(keep) = \dfrac{N-\lfloor{E}\rfloor}{N} \\ \text{Average keep} = \dfrac{\lfloor{E}\rfloor+1 + N}{2}$$

This gives us a formula for R+1 rerolls:

\begin{align} E' &= \dfrac{E\lfloor{E}\rfloor}{N} + \dfrac{(N-\lfloor{E}\rfloor)(N+\lfloor{E}\rfloor+1)}{2N} \\ &= \dfrac{2E\lfloor{E}\rfloor + (N-\lfloor{E}\rfloor)(N+\lfloor{E}\rfloor+1)}{2N} \end{align}

With an $\lfloor{E}\rfloor$ in our final formula, we can't get a nice closed form for any number of rerolls, but we can just calculate the values from the recurrence relation. For example, for your example with $N=10$:

\begin{align} E[\text{0 rerolls}] &= 5.5 & (\lfloor{E}\rfloor=5) \\ E[\text{1 reroll}] &= \dfrac{55 + 80}{20} = 6.75 & (\lfloor{E}\rfloor=6) \\ E[\text{2 rerolls}] &= \dfrac{81 + 68}{20} = 7.45 \end{align}

For 3D10 with 2 rerolls our expected value is $(3 \times 7.45) = 22.35$. Our strategy is to reroll all values 1-6 on our first roll, reroll all values 1-5 on our second roll.

• I am not sure by what measure you determine this method to be maximizing the expected value of a roll. Mind explaining? What does it mean to maximize the expected roll (considering you tolerate 7's instead of shooting for 9's and 10's), and how can you tell that this strategy does that? – doppelgreener May 27 '15 at 3:02

## This cannot be nicely modeled purely as probability

The issue with this system is that it's not purely a matter of randomness, it's (as you seem to be presenting it) a matter of both randomness and decision-making. A dice rolling program can model the randomness, but not the decision-making (at least, not in a manner that is of much use).

Basically, using a reroll can sometimes improve your total and sometimes reduce your total. The question of whether or not to use a reroll depends upon what the player wants. If we make an assumption about the player's goal, then we can write an expression that assumes they make certain decisions.

If our goal is to get a result of 21 or higher (on 3d10), then the optimal strategy is to always reroll our lowest die until our total is 21 or higher.

This actually produces quite a different curve from the curve where the goal is to get a result of 22 or higher. For example, if we need a 22, we have 7,7,7, and we have 1 reroll, we need to reroll, even though we are likely to end up with a worse result than just keeping.

If our goal is just to get the highest possible score at all times, then the optimal strategy is probably¹ to always reroll your lowest die if it's a 5s or less, otherwise stop rerolling.

(¹Sadly, this isn't actually true, but it's a good approximation when number of rerolls is close to 0. The truth is even more complex!)

• The lesson here might be: work out what result you're trying to get first before you try to do statistical modelling, or it's going to be really hard to model anything meaningful. – doppelgreener May 26 '15 at 5:21
• I wrote such a beautiful function, but I'm going to have to toss it - you're right on all counts. – Miniman May 26 '15 at 5:29
• I will accept that this beyond me and go on, diminished, into the west. – Ben May 26 '15 at 5:51
• This is not true. Game theory (rational choice theory) beautifully meshes in the probability of utility and choice. By utilizing expected values and probability it can optimally determine if you should reroll a die or keep it. Since you must take the result even if its worse, the notion of a reroll provides no extra utility gain. The expected value of d10 is always 5.5. Game theory would then dictate that you should keep any roll above and reroll anything below 5.5. (balances risk vs. reward). Rerolling die above it is too risky. Don't reroll die below it and you're playing it too safe. – Spoo Sep 30 '16 at 15:43


text:
Model Counting

# On the Size of XORs and Randomization in Approximate Model Counters

Note:

1. This post is based on our (Kuldeep and yours truly ) paper submitted in TACAS2019 and is currently a work in progress.

2. Currently some of the repositories might not be publicly available.

## Prelude: What is (approximate) Model Counting?1

Given a Boolean formula, say $\phi$, to to compute the number of solutions of $\phi$ is called (Exact) Model Counting. But it turns out it’s NP-hard ( Actual it’s #P, which is a class of counting problems associated with decision problems, and therefore is harder than NP-complete problems because counting the solutions is definitely harder than identifying one ).

So theoretically we can’t even approximate a solution in general, but it turns out we can still approximate reasonable sized( with over 1000 variables) problems with present day SAT solvers, hence the name Approximate Model Counting.

The basic idea is this: Suppose you were to calculate the number of people in a large room. How would you do it as efficiently as possible. One obvious way is to simply count each person but that’s too costly ( $O(n)$ where $n$ is exponentially large ), it turns out there is a clever way to count by exploiting randomness( ask each person to get a coin ). Consider the following algorithm,

Every person starts with a hand up.

Everyone tosses a coin
Else bring it down
Repeat till all hands are down.

Report  2^(number_of_rounds)  as the estimate.

Observe that the above algorithm takes $O(\log(n))$ steps in expectation and returns the correct count with a high probability.

Now in practice this is achievedi(with some extra details) using a powerful mathematical tool called 2-Univerasal Hash Family , which is very good at dividing the solution space in small cells( each with a small number of elements), and a SAT solver which can (somewhat majically) count the number of cells with elements greater than some number (called the pivot, we usually set it to 72 ).

Now pivot $\times$ #number_of_cells gives the approximate count.

Approximate Counting

## A word on XORs

XOR function

Now hash function is actually implemented by adding XORs with density $p=\frac{1}{2}$. Thus on average XOR constraint size is $n/2$ where $n$ is number of variables.

Constraints with smaller size are friendlier to SAT solvers hence Zhao et al proposed a family of sparse hash functions with $p\le1/2$ (actually $\log(n)/n$ asymptotically)) to decrease the size of XOR constraints and hence make it easy for the SAT solver and hence decreasing the runtime of counter( they proposed an algorithm SparseCount, you can check out our implementation here ).

But it turns out if we use sparse families then we loose the gurantees on the count. So to achieve the same guarantees we end up increasing the number of iterations (by a factor $>100$ ) and thereby the runtime.

After seeing Zhao et al paper we did some calculations and ran some simulations suggesting that sparse-XORs won’t work in practice. In the next section we describe major results from the paper.

Other popular belief in SAT community was that sparse constraints could be used directly with ApproxMC. We show that’s not the case atleast from the analysis of Zhao et al.

## Major Results

### 1.) Spaesecount2: A better version of Sparsecount based on prefix-slicing

Prefix-slicing is a technique that uses prefixes of previous hash functions, thereby making them dependent. This dependence creates a ordering which could to perform Galloping Search( similar to Binary Search). Thus reducing the number of SAT oracle calls from linear to logarithmic.

$n \rightarrow \log(n)$

This was the idea that made ApproxMC3 much faster than ApproxMC. We applied to SparseCount and obtained significant speedups(> 2.5x).

Code:

Release: Contains a prebuilt static binary

Github Repo: Contains the SourceCode

### 2.) Argument for why sparse XORs cannot be used with ApproxMC

It turns out the properties of sparse hash families proposed by Zhao et al are not sufficient for proofs of ApproxMC3 to go through. The proofs of ApproxMC3 depend on the relationship between variance($\sigma^{2}$) and mean($\mu$), specifically for proofs to work out $\sigma^{2} \leq \mu^{2}$. But with proposed family of hash functions it could be shown that $\sigma^{2} \leq \eta$ where $\eta$ $\in$ $\Omega(\mu^{2})$.

### 3.) Empirical results supporting our arguments

All four algorithms, SparseCount, SparseCount2, ApproxMC, and Toeplitz-ApproxMC implemented in C++ and use the same underlying SAT solver, CryptoMiniSAT.

• Our algorithm SparseCount2 is 2.5x faster than Zhao et’al’s SparseCount.
SparseCount vis-a-vis SparseCount2

• Also the usual ApproxMC3 (with p = 12) is 118x faster than SparseCount.
ApproxMC3 vis-a-vis SparseCount2

### Effect of Randomness

It was proposed by Ermon et al that usage of Toeplitz matrix where all the entries are not independent leads to more deterministic and stable behavior in their hashing-based algorithm for approximate weighted model counting, also known as discrete integration. We tried an implementation based on Toeplitz matrix to see if it has any effect. Note that usage of Toeplitz matrices bring down requirement of random bits from $O(mn)$ to $O(m+n)$.

## We observe that there is no visible effect.

ApproxMC3 vs Toeplitz-ApproxMC3 comparison

## Conclusions

• Hashing-based techniques have emerged as a promising paradigm to attain scalability and rigorous guarantees in the context of approximate model counting.

• The core idea of a hashing-based framework is a combination of SAT solving and usage of random XOR constraints to partition the solution space.

• Since the performance of SAT solvers was observed to degrade with increase in the size of XORs, efforts have focused on the design of sparse hash functions .

• Our conclusions are surprising and stand in stark contrast to widely believed beliefs that current construction of sparse XORs (by Zhao et al. and Ermon et al. ) lead to runtime improvement specifically we observe that

1. Sparse constraints do not work with ApproxMC3.
2. Sparsecount2 performs better than SparseCount
3. ApproxMC3 performs much better than both SparseCount and Spaesecount2
4. Toeplitz matrices have no effect on run-time

[1] You can find a nice blogpost , with much more SAT solver internal details, on the same here.


text:
# Find the bias for the Maximum-likelihood estimator

Let $X_1,...,X_n$ be a random sample from the pdf $$f(x|\theta) = \theta x^{\theta-1} , 0 \leq x \leq 1, \theta >0.$$

I found the Maximum-likelihood estimator of $\theta$ is $$\hat{\theta} = \frac{-n}{\sum_{i=1}^N \ln(X_i)}.$$ Can anyone confirm that this is right?

Then, I want to determine whether $\hat{\theta}$ has bias. My approach is to calculate ${\bf E}[\hat{\theta}] = {\bf E}\left[\frac{-n}{\sum_{i=1}^N \ln(X_i)}\right]$...Then I am stuck. Could someone help me with this?

-

You got the right answer for the MLE. To find the expectation of $\hat{\theta}$, it will help to first find the distribution of the transformation $Y=-log(X_i)$. It's a well known distribution, and so will be $-\sum log(X_i)$ as well as $-1/\sum log(X_i)$.

You have already found that the distribution of $Y_i=-log(X_i)$ is exponential($1/\theta$).

According to section 4.2 of Pitman, "Probability", the sum of n iid exponential($1/\theta$) distributions is gamma(n, $1/\theta$). Thus, Z=\sum$Y_i=-\sum log(X_i)$ is distributed gamma(n,$1/\theta$) where the pdf of Z is

$\dfrac{\theta^n}{\Gamma(n)}z^{n-1}e^{-z\theta}$ with mean $E(Z)=n/\theta$.

Notice that since a pdf must integrate to 1, it is straightforward to show

$\int_0^{\infty}z^{n-1}e^{-z\theta}dz = \dfrac{\Gamma(n)}{\theta^n}$. Call this result 1.

This will be useful in the following step to find $E(1/Z)$.

$E(1/Z) = \int_0^{\infty}1/z\dfrac{\theta^n}{\Gamma(n)}z^{n-1}e^{-z\theta}dz$

$= \dfrac{\theta^n}{\Gamma(n)} \int_0^{\infty}z^{(n-1)-1}e^{-z\theta}$

$= \dfrac{\theta^n}{\Gamma(n)} \dfrac{\Gamma(n-1)}{\theta^{n-1}}$ by result 1.

$=\dfrac{\theta\Gamma(n-1)}{\Gamma(n)}$

Now, according to Casella and Berger, Statistical Inference pg 99, a useful property of the gamma function is that

$\Gamma(\alpha+1) = \alpha\Gamma(\alpha)$, thus

$\Gamma(n) = \Gamma((n-1)+1) = (n-1)\Gamma(n-1)$ and

$E(1/Z) = \dfrac{\theta\Gamma(n-1)}{\Gamma(n)} =\dfrac{\theta\Gamma(n-1)}{(n-1)\Gamma(n-1)}= \theta/(n-1)$

It's now straightforward to find $E(n/Z) = n*E(1/Z) = n\theta/(n-1)$.

-
I found that $log(X_i)$ has an exponential distribution with mean $1/\theta$. How does this help? –  afsdf dfsaf May 13 '14 at 14:51
Do you know what the distribution is of a sum of exponential distributions? –  jsk May 13 '14 at 14:54
is it going to be gamma distribution? –  afsdf dfsaf May 13 '14 at 14:58
whoa, wait a sec. You have to pay attention to the details. $E(1/X)$ DOES NOT EQUAL $1/E(X)$!!!! –  jsk May 14 '14 at 4:23
YOU CAN USE THE GAMMA APPROACH, but you CANNOT claim that $E(-1/\sum log(X_i)) = 1/E(-\sum log(X_i))$ THIS IS NOT TRUE BECAUSE OF JENSEN'S INEQUALITY –  jsk May 14 '14 at 4:28


text:
# Injective and Surjective

• September 29th 2010, 12:59 AM
ineedyourhelp
Injective and Surjective
I need help! can someone help me with this?

Prove or disprove the following statements:
(a) There exists an injection from
N to N^2.
(b) There exists a surjection from
N to N^2.
(c) There exists an injection from
N to N^3.

(d) There exists a surjection from
N to N^3.

where N is the set of natural numbers.

Thanks
• September 29th 2010, 05:22 AM
HallsofIvy
What exactly is your difficulty? Do you know what "injection" and "surjection" mean? It should be very easy to do part (a) or part (c). Parts (b) and (d) are a little harder. Can you use the fact that $N$, $N^2$, and $N^3$ are all "countable" sets?
• September 29th 2010, 06:57 AM
ineedyourhelp
Quote:

Originally Posted by HallsofIvy
What exactly is your difficulty? Do you know what "injection" and "surjection" mean? It should be very easy to do part (a) or part (c). Parts (b) and (d) are a little harder. Can you use the fact that $N$, $N^2$, and $N^3$ are all "countable" sets?

I know the definition of injectivity and surjectivity and I know the proof for N--->N. My problem is I don't know how to prove for N^2 and N^3. Thanks.
• September 29th 2010, 07:46 AM
undefined
Quote:

Originally Posted by ineedyourhelp
I know the definition of injectivity and surjectivity and I know the proof for N--->N. My problem is I don't know how to prove for N^2 and N^3. Thanks.

You didn't anaswer HallsofIvy's last question.

Have you seen this before?

http://personal.maths.surrey.ac.uk/s...ntable.svg.png
• September 29th 2010, 01:27 PM
ineedyourhelp
Quote:

Originally Posted by undefined
You didn't anaswer HallsofIvy's last question.

Have you seen this before?

http://personal.maths.surrey.ac.uk/s...ntable.svg.png

Yes i made used of countability and also the picture. I solve for N^2 already. Is there a shortcut on N^3 such that we can make use of N^2? instead of using 3D space and come up with a general formula for the function? For example let F: N--> N^2 and G: N^2--->N3? so that f(x)=(x,y) and gf(x)=(x,y,z)?
• September 29th 2010, 01:37 PM
undefined
Quote:

Originally Posted by ineedyourhelp
Yes i made used of countability and also the picture. I solve for N^2 already. Is there a shortcut on N^3 such that we can make use of N^2? instead of using 3D space and come up with a general formula for the function? For example let F: N--> N^2 and G: N^2--->N3? so that f(x)=(x,y) and gf(x)=(x,y,z)?

Well the image gives a bijection between N and N^2. You can repeat the exact same procedure, looking at N^3 as Nx(N^2). See how that works?
• September 29th 2010, 01:41 PM
ineedyourhelp
Quote:

Originally Posted by undefined
Well the image gives a bijection between N and N^2. You can repeat the exact same procedure, looking at N^3 as Nx(N^2). See how that works?

yes i am seeing it as N X N^2 but how to show it on paper? I need to submit it as a graded assignmentT.T
• September 29th 2010, 01:45 PM
Plato
Quote:

Originally Posted by ineedyourhelp
yes i am seeing it as N X N^2 but how to show it on paper? I need to submit it as a graded assignmentT

If it is a graded assignment, then the rules of this forum do not allow us to do any more on this for you.

Sorry.
• September 29th 2010, 01:49 PM
ineedyourhelp
Quote:

Originally Posted by Plato
If it is a graded assignment, then the rules of this forum do not allow us to do any more on this for you.

Sorry.

OMG ok. the grade is basically as long as you write something you will get the marks but I dont know what to write. but I understand the rules. Thanks!
• September 29th 2010, 01:51 PM
undefined
Quote:

Originally Posted by ineedyourhelp
OMG ok. the grade is basically as long as you write something you will get the marks but I dont know what to write. but I understand the rules. Thanks!

Clearly this can't be the case, otherwise you could just write 1+1=3 and get full marks. Perhaps a mod should close this thread.
• September 29th 2010, 02:00 PM
ineedyourhelp
Quote:

Originally Posted by undefined
Clearly this can't be the case, otherwise you could just write 1+1=3 and get full marks. Perhaps a mod should close this thread.

Precisely my teacher marks for effort marks and he doesnt explain after that because he expects us to know it by learning from the internet ourselves and I'm here to learn from you guys=)
• September 29th 2010, 02:16 PM
Plato
Quote:

Originally Posted by ineedyourhelp
Precisely my teacher marks for effort marks and he doesnt explain after that because he expects us to know it by learning from the internet ourselves and I'm here to learn from you guys=)

We are not here to give tutorials. It is also in the forum rules.
Are you sure that you did read the rules?


text:
# Random thoughts on Swift

·  by Alex Polozov  ·  Read in about 2 min  ·  321 Words

Based on my quick skimming session through the language guide.

Kind of expected from a modern language, would be surprised if it wasn’t included:

• Closures
• Type inference
• First-class collections and tuples
• Generics with all kinds of boundary restrictions
• Interoperability with existing libraries (in this case with C and Obj-C).

Surprisingly included, and it’s nice:

• First-class Maybe monad
• Bret Victor-style interactive IDE (let me make a sincere bow to Apple folks at this point)
• Opt-in mutability
• Lots of small inspirations from D, C#, Scala, etc.

However…

• Reference counting instead of garbage collection. Cannot detect reference cycles, ergo manual weakref management.
• I’m not quite sure how to combine “protocols” (read: interfaces) and “extensions” (read: mixins) into full-fledged traits and typeclasses. For example, how do I define a default method implementation for an interface a protocol?

(Also, why the heck do you need so many new names for existing concepts?!)

• Optional types are not quite Maybe, you can force the “unwrapping” with a ! operator (naturally, with a possible runtime exception). I foresee every single iOS developer just blindly doing it with every external optional they get.

• Extremely closed infrastructure: iOS/MacOS only, proprietary compiler, etc. Hell, you need an iTunes account to even read language documentation.

• Absolutely no first-class concurrency treatment. Moreover, there’s even no library treatment for concurrency (even though it is not enough).

• No stream processing sugar (read: comprehensions/LINQ). Well, at least they have map and reduce in the standard library, but that’s about it.

• No private members.

Not sure how I feel about:

• No exceptions. If you gave us some other monadic alternative, I might’ve put it in the “nice” section.
• Some magic in interoperability. Apparently, they wrote “external parameters names” for many standard library functions and forgot to show them to the legacy Objective-C programmers.
• The fact that their compiler cannot resolve recursive ADT definitions, even though it supposedly should.

Interesting. Let’s see how it flies.