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# The Impact of Future Fuel Consumption on Regional Air Quality in Southeast Asia

## Abstract

Aerosols emitted from fossil fuel burning can cause air quality and human health issues. In this sensitivity study, we examine the impact of fossil fuel aerosols on air quality in Southeast Asia under five different hypothetical fuel consumption scenarios. These scenarios reflect air pollutant outcomes of implementations of certain idealized policies in the power generation, industry, and residential sectors. Analyses based on comparison among the modeling results from these scenarios reveal the sectors that should be targeted by air pollution mitigation policy. The results reveal that in Southeast Asia, sulfate could be decreased by 25% if coal were to be replaced by natural gas in the power generation and industry sectors. Black carbon concentration would reduce 42% overall if biofuel were replaced by natural gas in the residential sector. Shipping emissions are especially critical for the urban air quality in Singapore: fine particular matters (PM2.5) could be dramatically cut by 69% in Singapore by merely eliminating shipping emissions.

## Introduction

Since the industrial revolution, fossil-fuel consumption has been systematically increasing worldwide. In recent years, the rise of energy demands in Southeast Asian countries is higher than most developed counties due to increasing population and fast-growing economies1. Such expansion in energy use causes an increase in fossil fuel consumption and associated emissions of pollutants, resulting in air quality and human health issues in the region2,3,4. In our previous study, fossil fuel burning aerosols were found to be responsible for the occurrence of 82% of the low visibility days (visibility <10 km), whereas biomass burning aerosols only contributed to 18% of the low visibility days in Southeast Asia5. Our result thus suggests that it is necessary to drastically reduce fossil fuel emissions in order to improve the air quality in Southeast Asia.

The awareness of climate change and associated problems has been gradually increasing within the general public and governments globally, resulting in the commitment of most countries to cut their emissions to a certain level (e.g., the Paris Agreement). Southeast Asian countries have also shown a strong willingness to work together on energy issues and to tackle environmental problems within the Association of Southeast Asian Nations (ASEAN). With a rapid economic growth of 5% from 2000 to 20131 and an estimated increase in the population from 525 million in 2000 to 728 million in 20306, Southeast Asian countries will have to face the challenge of increasing their energy consumption without increasing emissions. However, according to the International Energy Agency (IEA), with the current policies in the region regarding fuel consumptions, the energy demands of Southeast Asian countries would have to be mainly satisfied by burning fossil fuels, in particular coal, which is likely to become the primary fossil fuel in the energy mix of the region by 20401. Therefore, ASEAN countries will need a change in their energy policies in order to be consistent with their environmental commitments.

In addition to coal usage, shipping is also an important emission source in Southeast Asia. Even in 20 years ago, annual emissions of sulfur dioxide (SO2) from international shipping in Asian waters were already estimated to be 0.236 Tg, representing about 11.7% of emissions in Southeast Asia7. In a recent study, Johansson et al.8 used Automatic Identification System (AIS) ship data for the year 2015 to investigate the global emissions from shipping. Their study shows that Singapore has the highest density of shipping emissions in the world. Besides that, the highest PM2.5 and SOx emissions per unit area occurred in the eastern and southern South China Sea as well as over waters close to Southeast and South Asia. Ship-emitted nitrogen oxides (NOx) also enhances ozone (O3) production, leading to adverse effects on both human health9 and agricultural production10. However, despite a growing concern about the impact of atmospheric pollutants from ships on air quality in many ASEAN coastal cities, the regulation of air pollution in marine transport in the region remains unclear.

In fact, the impacts of current or alternative fuel consumption practices in the region on air quality have never been quantitatively analyzed, likely due to the complexity of such a task that requires the use of sophisticated weather and atmospheric chemistry models supported by emissions and measurement data.

Here we conduct a sensitivity study to examine the air quality outcomes over Southeast Asia in two selected years with sufficient data support, as results of five different hypothetic scenarios of fuel consumptions in the power generation, industry, and residential sectors. By exploiting a state-of-the-science regional weather and atmospheric chemistry model to simulate atmospheric concentrations of atmospheric pollutants including particulate matter, we examine the effects of these idealized emission-mitigation policies in altering atmospheric levels of several key air pollutants. In the paper, we first describe methodologies adopted in the study, followed by the results and findings from our assessment of the different hypothetical fuel consumption scenarios on the degradation of air quality over Southeast Asia. We then discuss the impact of trans-boundary pollution from surrounding countries on the air quality in Southeast Asia under these different scenarios in the discussion section. The last section summarizes and concludes our work.

## Methodology

### Model and emission inventories

The Weather Research and Forecasting model coupled with a chemistry module (WRF-Chem) version 3.6.1 is used in this study. We choose the Regional Acid Deposition Model, version 2 (RADM2) photochemical mechanism11 coupled with the Modal Aerosol Dynamics Model for Europe (MADE) and the Secondary Organic Aerosol Model (SORGAM)12,13 to simulate atmospheric chemistry and anthropogenic aerosol evolutions. The domain, as shown in Fig. 1, is designed to have a horizontal resolution of 36 km and 31 vertically staggered layers based on a terrain-following pressure coordinate system, and to include the tropical Indian Ocean on the west side in order to capture the path of Madden-Julian Oscillation (MJO), and to have a northern boundary confined within 23°N in latitude to avoid potential numerical instability from the terrain of Tibetan Plateau. The National Center for Environment Prediction FiNaL (NCEP-FNL) reanalysis data14 are selected for providing initial and boundary meteorological conditions, and for performing four-dimensional data assimilation (FDDA) to nudge model temperature, water vapor, and zonal and meridional wind speeds above the planetary boundary layer (PBL). The Mellor-Yamada-Nakanishi-Niino level 2.5 (MYNN)15 is chosen as the planetary boundary scheme in this study. The physics schemes in the simulations include Morrison (2 moments) microphysics scheme16, RRTMG longwave and shortwave radiation schemes17,18, unified Noah land-surface scheme19, and Grell-Freitas ensemble cumulus scheme20. The simulation periods are 2006 and 2008, representing a high year and an average year regarding precipitation, respectively (Fig. S1). The simulation of each year starts on 1 November of the previous year and runs for 14 months. The first two months are used for spin-up.

We notice that the default chemical profile in the lateral boundary condition is higher than the background concentration in our study region, and thus equivalent to provide additional aerosol sources from boundaries. Hence, we have set NO, NO2, SO2 and all primary aerosol levels to zero in the lateral boundary condition. We have also adjusted the ozone profile as shown in Fig. S2. The surface background mixing ratio of ozone from the World Meteorological Organization (WMO) Global Atmosphere Watch (GAW) station in Bukit Kototabang, Indonesia is 13.4 ppbv. We have thus adopted this value as the initial surface ozone level in the model and also scaled the tropospheric profile of ozone based on this new surface value.

Regional Emission inventory in ASia (REAS) version 2.121 is a regional emission inventory for Asia including most primary air pollutants and greenhouse gases, and covering each month from 2000 to 2008. Due to the limited spatial coverage of REAS, we have used Emissions Database for Global Atmospheric Research (EDGAR) version 4.2 (2005 emission) (http://edgar.jrc.ec.europa.eu) for regions that are not covered by REAS within the domain (Fig. 1). In our pervious work5, we have compared the modeled results using REAS versus EDGAR emission inventories in a set of 1-year paired simulations. The differences between these two model runs are rather limited regarding aerosol-related variables.

### The design of fossil fuel emissions for various scenarios

Based on the current fossil fuel consumption and associated emissions in Southeast Asia, we have designed four policy scenarios and a reference scenario in the study. These scenarios are described in the following paragraphs.

The Reference Scenario is based on the original REAS fossil fuel emissions and complementary EDGAR emissions. This scenario provides a reference case for the real atmospheric concentrations of various pollutants that are not influenced by any hypothetical fossil fuel consumption changes during the period of simulation, and for analyzing the outcome associated with four other scenarios.

The Gas Scenario and the Coal Scenario: the former intends to mimic the implementation of a policy favoring the usage of natural gas in power generation and industrial sectors, while the latter intends to represent an opposite approach that is to enhance coal usage in these sectors. Specifically, in design, we assume that in the Gas Scenario, coal is no longer used in industry and power generation. Instead, all the energy produced by coal in these two sectors is replaced by the same amount of energy coming from burning of natural gas. Whereas in the Coal Scenario, we assume that natural gas is no longer used in industry and power generation, and all the energy produced in these two sectors comes from coal and existing oil burning (Fig. 2).

The Modern Scenario is designed to highlight the impact of policies that would favor the usage of gas and electricity in the residential sector (e.g., for cooking and heating) instead of the traditional biofuels. In this scenario, we assume that all biofuel energy of the residential sector is replaced by energy coming from natural gas rather than biofuel (Fig. 2).

Note that the emission modification domain in the Gas Scenario, Coal Scenario, and Modern Scenario is limited to the Southeast Asia region (10°S–23°N in latitude, 90–150°E in longitude; the red box in Fig. 1). The emission modification domain is referred to as the SEA domain in this paper. For convenience, the SEA domain includes a part of Southern China.

The Shipping Scenario is designed to highlight the contribution of pollutants emitted from marine traffic to worsening of regional air quality in Southeast Asia. We remove all aerosol and gas emissions from the shipping sector within the model domain to compare with the Reference Scenario.

The relevant calculations of all the above scenarios are done based on data of IEA1, and the fuel usages in each emission sector for various scenarios are shown in Fig. 2. Note that road transportation is an important pollution source in many major cities in Southeast Asia. However, due to the difficulty in obtaining the emission data that could represent the fuel usage, road conditions and distributions for Southeast Asia, we choose to focus on the above-described sectors in our study. Due to the availability of emission inventories, our simulations are limited to the year 2006 and 2008; therefore, the results of these simulations might not fully represent most current atmospheric concentrations. Nevertheless, such a selection in designing our simulations should not affect the relative changes of each hypothetical fossil fuel consumption in relate to the Reference Scenario.

Designing each one of these scenarios requires the modification of emissions in order to fit the assumption of each scenario. The emissions of five pollutants in the fossil fuel emission inventory – black carbon (BC), organic carbon (OC), nitrogen oxides (NOx), carbon monoxide (CO), and sulfur dioxide (SO2) – are adjusted by using different coefficients for the selected fuel in each sector. These coefficients are calculated using the share of each fuel in the energy sector given by IEA1 and also using emission factors from Ohara, et al.22.

Equation (1) is an example of the calculation of the coefficient related to SO2 emissions in the power generation sector for Gas Scenario.

$$c=\frac{{m}_{SO2}-\mathop{\overbrace{(\frac{{m}_{SO2}}{E{F}_{PG.REGIONAL}}\times { \% }_{PG.COAL}\times E{F}_{PG.COAL})}}\limits^{T1}+\mathop{\overbrace{(\frac{{m}_{SO2}}{E{F}_{PG.REGIONAL}}\times { \% }_{PG.COAL}\times E{F}_{PG.GAS})}}\limits^{T2}}{{m}_{SO2}},$$
(1)

where T1 is the total mass of SO2 that is emitted by coal power plants, and T2 is the mass of SO2 that would be emitted if the energy produced by coal in power generation were produced by natural gas. Indeed, we first divide the mass of SO2 $$({m}_{SO2})$$ by the average emission factor of power generation $$(E{F}_{PG.REGIONAL})$$ in order to get the energy used in power plants. We then multiply by the share of coal in power generation sector $$({ \% }_{PG.COAL})$$ (Fig. 2) and the energy factor of coal in power generation $$(E{F}_{PG.COAL})$$ (Table 1). The coefficients for the five pollutants in each one of the three sectors are presented in Table 2. Figure 3 shows the monthly BC, OC, CO, SO2, and NOx emissions in 2006 and 2008 in five scenarios. Compared with 2006, emissions of all species have been increased in 2008.

We also have designed another pair of simulations of the Gas, Coal and Modern Scenarios, which extend the emission modification region from the SEA domain to the whole model domain including a very large part of South Asia (referred to as _ALL in Sect. 4). The purpose of this design is to investigate whether air quality in Southeast Asia would be further affected by transboundary transport of pollutants if the different hypothetical fuel consumption policies were applied to other counties outside of Southeast Asia, especially India. The emission modification outside of the SEA domain also uses the same coefficients shown in Table 2.

## Results

### Model evaluation

Meteorological conditions, particularly wind fields and precipitation, could substantially influence the life cycle and transport path of aerosols. Hence, a rainfall comparison between observation and modeled results is conducted to evaluate the model’s performance in simulating meteorological features. The WRF simulation driven by NCEP-FNL reanalysis data produced a time series of monthly mean precipitation over 2006 and 2008 that closely followed that of satellite-retrievals from the Tropical Rainfall Measuring Mission (TRMM) 3B43 (V7) dataset23 despite a systematic overestimate (6.62 ± 0.48 mm day−1 versus 4.67 ± 0.32 mm day−1). Based on the sensitivity tests for FDDA grid nudging, the wet bias in the model results mainly comes from water vapor nudging. In our previous study24, we demonstrated a long term precipitation comparison with TRMM data using the same domain configuration but different aerosol emissions. The comparison showed that despite the model overestimate in average total precipitation, the temporal and spatial correlation of monthly rainfall between TRMM and modeled results are 0.68 and 0.86, respectively.

To evaluate the model’s performance in simulating the atmospheric abundance of several key pollutants, we have used surface PM10 concentrations derived from the Air Quality Index (AQI) in Kuala Lumpur, Malaysia and the observed CO and O3 levels from the World Meteorological Organization (WMO) Global Atmosphere Watch (GAW) station in Bukit Kototabang, which is located on the island of Sumatra, Indonesia. Note that in this study, we exclude biomass burning emissions to focus on the chemical concentration differences between each fuel consumption scenario. Therefore, we have also included in this comparison the results from our previous study5, where the same model configuration was used, but with both fossil fuel and biomass burning emissions included, referred to as FFBB.

The results show that the model simulated time evolution of PM10 is very close to that of observations, including peaks during the fire seasons (Fig. S3a). In comparison, as expected, the Reference Scenario results are very similar to those of FFBB except during the fire seasons. The background PM10 concentration produces by both FFBB and Reference Scenario, however, exhibits a systematic negative bias of 20 μg m−3 from the observations. As discussed previously in Lee et al.5, this discrepancy is likely due to the relatively coarse resolution of the model or an underestimation of aerosol and aerosol precursor emissions, or both. In Lee et al.5, we referred to Philip et al.25 study and highlighted that most global emission inventories do not include anthropogenic fugitive, combustion, and industrial dust (AFCID) from urban sources, e.g., fly ash from coal combustion and industrial processes such as iron, steel production and cement production, resuspension from paved and unpaved roads, mining, quarrying, and agricultural operations, and road-residential–commercial construction. In their study, they estimated a 2–16 μg m−3 increase in fine particulate matter (PM2.5) concentration across East and South Asia simply by including AFCID emission. A bigger gap for PM10 concentration is expected. Overall, the temporal correlation of daily PM10 between modeled PM10 in FFBB and observations is 0.55.

For gaseous species, the model has accurately captured observed CO including both peaks and background levels (Fig. S3b). Since the primary source of CO in Bukit Kototabang is from biomass burning, all high CO levels occurred during fire seasons as reflected in FFBB results. In comparison, the Reference Scenario well captured CO evolutions during all the other periods. Additionally, the model has successfully simulated the evolution of surface O3 levels during the two simulated years. Nevertheless, the model indeed produced a positive bias of about 13 ppbv between observations (12.8 ± 5.1 ppbv) and the Reference Scenario (26.1 ± 5.1 ppbv), as well as about 23 ppbv between observations and FFBB (35.3 ± 11.0 ppbv) (Fig. S3c). The correlations for FFBB to observations in O3 and CO are 0.61 and 0.52, respectively. We notice that NOx emission is higher in REAS emission inventory compared with several other emission inventories and estimates21. This could lead to the overestimate of background ozone in the model. High NOx emissions in the REAS emission inventory could also have caused an overestimate of nitrate (NO3) in our simulation (Fig. 4) as suggested by the filter samples from the Surface PARTiculate mAtter Network (SPARTAN; http://spartan-network.weebly.com/), which show that the ratio of nitrate in PM2.5 concentration is much lower than that of sulfate (SO4) at all observational sites within the domain including Hanoi (Vietnam), Singapore (Singapore), Bandung (Indonesia), and Manila (Philippines) (Fig. S4). Observations from SPARTAN also indicate that there are missing anthropogenic aerosol components, mainly organic matter25,26, in the emission inventory. This could largely explain the underestimate of PM10 by the model.

### Spatial distributions and relative changes of indicative pollutants under different fuel consumption scenarios

Fine particular matter (PM2.5) is one of the target air pollutants in our analyses because long-term exposure to PM2.5 may lead to chronic obstructive pulmonary disease, ischemic heart disease, lung cancer, and stroke27,28. In the Reference Scenario, high PM2.5 concentrations are found in major cities across Southeast Asia as well as India, including Hanoi, Bangkok, Jakarta, Kolkata, and Mumbai (Fig. 5a). The monthly mean PM2.5 in the SEA domain is 0.79 ± 0.13 μg m−3 averaged over 2006 and 2008 (Table 3). In general, the model underestimates PM2.5 concentration due to the 36-km model resolution used in this study and the missing anthropogenic fugitive, combustion and industrial dust emissions in the emission inventory5,25. The modeled chemical components of PM2.5 in the SEA domain suggest that nitrate aerosol is the major component of PM2.5 particles in Southeast Asia (Fig. 4). As mentioned above, it could come from high NOx emissions in the REAS emission inventory. Under different hypothetical scenarios of fuel consumption in the SEA domain, the changes of PM2.5 concentration mainly occur locally (Fig. 5b–d); however, removing shipping emissions in the study domain reduces PM2.5 concentration significantly (Fig. 5e). Since chemical species come from various emission sectors, the spatial and temporal change patterns of these species also vary under different fuel consumption scenarios. Here, we focus on the changes of major PM2.5 components under different hypothetical scenarios.

In the Reference Scenario, high monthly-mean concentrations of BC mainly occur both in the cities of Southeast Asia and widely across India (Fig. 6a). The mean concentration of BC in the SEA domain is 0.05 ± 0.00 μg m−3 (Table 3). In the Gas and Coal Scenarios, the change of BC concentration compared to the Reference Scenario is minor (Fig. 6b,c), less than 2% in the SEA domain (Table 4). However, BC concentration has a significant reduction in the Modern Scenario from its level in the Reference Scenario, especially in mainland Southeast Asia, Sumatra, and Java Island (Table 4; Fig. 6d). Substantial BC reductions in these major cities and their suburbs in the Modern Scenario, on the other hand, indicate high biofuel consumptions in these areas and the effectiveness in cutting BC concentration by replacing biofuel with natural gas in the residential sector. In other words, if the ASEAN governments want to regulate BC emissions, focusing on the residential sector would be more effective than focusing on the industry and power generation sectors. It is worth highlighting a relatively small BC reduction in the Malay Peninsula in the Modern Scenario compared with other major cities in Southeast Asia. This is because the primary BC emissions in this region come from road transportation; therefore, the changes of BC concentration in the Gas, Coal, and Modern Scenarios are all small. In the Shipping Scenario, most BC reductions happen in the coastal area, leading to a 21.6% decrease across the SEA domain (Table 4; Fig. 6e). Because diesel is widely used to fuel ocean-going ships, reducing shipping emissions can effectively reduce concentrations of several major pollutants.

In the Reference Scenario, the monthly mean OC in the SEA domain is 0.19 ± 0.01 μg m−3 averaged over 2006 and 2008 (Table 3). High OC concentrations also mainly occur in the major cities in Southeast Asia and India (Fig. 7a). Compared with the Reference Scenario, the emission coefficient of OC in the industry sector is higher in the Gas Scenario while lower in the Coal Scenario (Table 2) so that OC concentration increases by 0.4% in the Gas Scenario and decreases by 0.7% in the Coal Scenario in the SEA domain (Table 4; Fig. 7b,c). This is because we refer the OC emission factor for “other” fuel combustion from Ohara, et al.22, which is higher than that of coal and oil combustion (Table 1). This setup also introduces higher OC emission in the Gas Scenario than the Reference Scenario (Fig. 3b). The spatial distribution of OC reduction in the Modern Scenario is similar to that in the Coal Scenario (Fig. 7d). However, the decrease in OC concentration in the Modern Scenario can be as high as 8.2% in the SEA domain, suggesting that reducing biofuel combustion in the residential sector is much more effective in reducing OC concentration in Southeast Asia than other emission mitigation measures in the power generation and industry sectors. The spatial distribution and percentage of OC decreases in the Shipping Scenario are similar to BC (Fig. 7e). The concentrations are reduced by 19.9% in the SEA domain (Table 4).

SO2 is the predominant anthropogenic sulfur-containing air pollutant, and its oxidation produces sulfate. SO2 is primarily emitted from fossil fuel combustion in the power generation and industry sectors. Hence, high SO2 mixing ratio usually appears in high population areas and industrial cities, such as the northwest coast of India, Southern China, Bangkok, Manila, and Jakarta (Fig. 8a). In our simulations, high SO4 concentrations from the northwest coast of India and Southern China can even be transported downwind to the Arabian Sea and Bay of Bengal (Fig. 9a). In the Reference Scenario, the monthly mean SO4 is 0.06 ± 0.02 μg m−3 in the SEA domain averaged over 2006 and 2008 (Table 3). Both SO2 and SO4 have a significant reduction in the Gas Scenario by 36.1% and 25.0% in the SEA domain, respectively (Table 4; Figs 8b and 9b). Our result shows that the gas-favorite policy can effectively lower SO2 mixing ratio and SO4 concentration in the region. On the other hand, a coal-favorite policy can worsen air quality by elevating sulfate abundance. In the Coal Scenario, SO2 and SO4 in the SEA domain increase by 69.7% and 48.0%, respectively (Table 4). The impact areas of air quality due to sulfate particles are not only seen in the source but also in wider regions (Fig. 9c). Differing from the reduction of BC and OC in the Modern Scenario, SO2 mixing ratio increases in some major cities in Southeast Asia because natural gas combustion emits more sulfur-containing air pollutants than biofuel combustion. Therefore, the concentration of SO4 has been increasing by 2.8% in the SEA domain (Figs 8d and 9d). Our result in the Shipping Scenario shows removing shipping emission can effectively cut down SO2 emission. The reduction of SO2 mixing ratio happens not only at harbor areas but also along the shipping tracks, so does the reduction of SO4 concentration (Figs 8e and 9e). In the Shipping Scenario, SO2 and SO4 in the SEA domain decrease by 27.3% and 27.7%, respectively (Table 4).

NO3 aerosol is an important air pollutant and mainly produced from the reactions involving anthropogenic NOx and O3. In the Reference Scenario, the monthly mean NO3 in the SEA domain is 0.32 ± 0.08 μg m−3 averaged over 2006 and 2008 (Table 3). High concentrations of NO3 mainly occur in Southern China, Thailand, the east coast of Malaysia, Java Island, and the offshore area of India (Fig. 10a). The main reduction zones in the Gas Scenario also correspond to the high NO3 concentration regions in the Reference Scenario, and the reduction of NO3 in the SEA domain is about 4.1% (Table 4; Fig. 10b). Compared with the growth of SO4 concentration in the Coal Scenario, the increase of NO3 is relatively small, only 6.9% in the SEA domain (Table 4). This is because that in our simulation, NO3 is the main component of PM2.5 and the substantial emissions of NOx from road vehicles in the cities. Such a result explains the relatively minor changes of NO3 concentration in the Gas and Coal Scenarios compared with the changes of SO4. NO3 concentration does not have a significant change in the Modern Scenario except a decrease in southern China (Fig. 10d). Although the reduction of NO3 concentration is not substantial in the Gas and Modern Scenarios, it can be reduced by more than 30% in the Shipping Scenario in the SEA domain (Table 4). Furthermore, the reduction area covers not only ocean but also land (Fig. 10e).

In this study, we have also modified CO emissions based on different energy use scenarios (Fig. 3). CO is mainly from fossil fuel combustion, industrial processes, and biomass burning. In the Reference Scenario, high CO mixing ratio occurs mostly in the major cities in Southeast Asia and India, such as Hanoi, Bangkok, Jakarta, and Kolkata. The change of CO in the Gas and Coal Scenarios is relatively small, less than 0.4%; however, the change is substantial in the Modern Scenario (Table 4; Fig. 11b–d). As we mentioned above, CO comes from the combustion process, and biofuel combustion usually occurs under incomplete burning conditions. Therefore, replacing biofuel with natural gas can reduce CO mixing ratio by 2.9% in the SEA domain (Table 4). CO reduction also can be seen in the coastal regions in the Shipping Scenario, but the decreases over the open ocean are small (Fig. 11e).

O3 production is mainly from photochemical reactions of precursors such as nitrogen oxides, volatile organic compounds, and CO, all mainly from anthropogenic emissions. A high level of near-surface O3 can cause public health issues9. In the Reference Scenario, the monthly mean O3 mixing ratio in the SEA domain is 23.3 ± 0.9 ppbv averaged over 2006 and 2008. The spatial distribution of high O3 mixing ratio is similar to CO (Fig. 12). The change of O3 in each scenario is rather minor, less than 0.3%, owing to the small change of precursors as well (Table 4; Fig. 12b–d). However, the reduction of O3 mixing ratio in the Shipping Scenario is substantial, −12.9% in the SEA domain (Table 4). It is due to the reduction of the major precursor nitrogen oxides in the region.

### Air quality impacts in five selected ASEAN cities under different fuel consumption scenarios

Population in Southeast Asia was about 634 million in 2015, with more than 100 million living in the major cities6. Owing to different industrial and urban infrastructures, air pollution sources are quite different from city to city. For those cities highly dependent on manufacturing as well as trading (in particular via shipping), our study provides a useful reference for making air pollution mitigation policies regarding future fuel consumption. In this section, we focus on five selected cities across Southeast Asia: Jakarta (Indonesia), Bangkok (Thailand), Hanoi (Vietnam), Singapore (Singapore), and Kuala Lumpur (Malaysia) (ordered according to population), and discuss their current air pollution issues and potential air quality adjustment under different hypothetical fuel consumption policies.

Jakarta is the largest capital city in Southeast Asia, with a population exceeding 10 million. The emissions are mainly from the residential, transportation, and industry sectors1. The mean PM2.5 concentration in the Reference Scenario is 14.7 ± 4.7 μg m−3 and about 60% of that is nitrate. The precursor of NO3, NOx, is also a major pollutant in Jakarta and causes severe smog and acid rain problems. In the Gas and Coal Scenarios, the change of NO3 concentration is about −4.5% and 7.2%, respectively. However, the most substantial changes in the aerosol composition come from SO4, −46.3% in the Gas Scenario and 85.6% in the Coal Scenario (Table 5). On the other hand, because BC and OC in Jakarta are not primarily emitted from industry and power generation, their changes in the Gas and Coal Scenarios are hence relatively small. Overall, the PM2.5 concentration decreases by 4.7% in the Gas Scenario and 8.0% in the Coal Scenario (Table 6). In the Modern Scenario, BC reduction can reach 56.9%, however, the concentrations of NO3 and SO4 increase by 1.1% and 6.1%, respectively. All these changes in opposite directions somewhat cancel out each other. As a result, the PM2.5 concentration would only experience a slight decrease (<1%) in the end if natural gas were chosen to replace biofuel in the residential sector. In fact, we find that targeting shipping emissions can lead to a significant improvement regarding PM2.5 concentration in Jakarta. Our result shows that removing shipping emissions can reduce NO3 by 25.4%, SO4 by 15.9%, OC by 16.6%, BC by 15.1%, and PM2.5 by 23.2% (Table 5).

In Bangkok, the monthly mean PM2.5 concentration in the Reference Scenario is 10.0 ± 3.6 μg m−3. NO3 and OC are the dominant components of PM2.5 with 50.4% and 25.7%, respectively. Besides BC, the relative change of each species in the Gas and Coal Scenarios in Bangkok is similar to that in Jakarta. BC decreases 2.9% in the Gas Scenario in Bangkok and increases 6.3% in the Coal Scenario. Similar to the case of Jakarta, the significant BC reduction comes from the Modern Scenario, by 22.9%; nevertheless, this still cannot compensate the increase of SO4 and NO3. Hence, PM2.5 concentration in Bangkok slightly increases in the Modern scenario (Table 5). Shipping emission is not the most crucial pollution source in Bangkok to total PM2.5 (only contributing about 10%); however, shipping is a substantial source for SO4 concentration (22.1%), and thus a good target for sulfate aerosols mitigation policies in Bangkok.

The primary emission sectors in Hanoi are road transportation and residential. The mean PM2.5 concentration in Hanoi in the Reference Scenario is 9.8 ± 1.7 μg m−3. NO3 and OC are still the dominant components of PM2.5 with 39.7% and 29.4%, respectively. However, the proportion of BC to PM2.5 in Hanoi is 12.8%, 4~5 times higher than the BC percentage in Jakarta or Bangkok. Because the major pollutants do not come from industry and power generation, the changes of various aerosol species in the Gas or Coal Scenario in Hanoi are relatively small (Table 5). In the Modern Scenario, however, the massive hypothetical reduction in biofuel combustion would reduce BC concentration by 70.5%, and OC by 5.7%. It could result in a significant improvement of PM2.5 concentration in Hanoi by reducing it nearly 11%. We also would like to highlight an abundant CO reduction, about 35% in the Modern Scenario. All these results suggest that replacing biofuel by natural gas as a combustion fuel in the residential sector in Hanoi could efficiently reduce PM2.5 concentration by 11% and CO mixing ratio by 35%. In addition, shipping emissions also play an important role in causing air pollution in Hanoi. Removing shipping emissions in the Shipping Scenario lowers NO3 and SO4 concentrations by 16.5% and 16.3%, respectively, and PM2.5 by 10.7%, comparable to the effect of the Modern Scenario (Table 5).

Singapore has an active and dynamic industrial sector including chemical and metallurgic industries as well as a major petroleum-refining center in Southeast Asia. Additionally, power plants generate electricity by burning natural gas and, to a lesser extent, oil. Waste incinerators, busy seaport traffic, and a major airport in the region also make the emission map more complicated29. In the Reference Scenario, the mean PM2.5 concentration in Singapore is 2.5 ± 2.4 μg m−3 averaged over 2006 and 2008, and 60.9% of PM2.5 comes from nitrate aerosols. The most substantial change in aerosol composition in the Gas and Coal Scenarios occurs to SO4 with −28.0% and 54.8%, respectively. Based on the report published by Energy Market Authority, the proportion of natural gas burning in Singapore’s power generation is 95.2%30, much higher than other countries in Southeast Asia. Pollutants generated by coal burning in Singapore hence come mainly from transboundary atmospheric transport. On the other hand, shipping emission is a large pollution source in Singapore, though the government has not paid much attention to it until recently. In 2017, the International Maritime Organization (IMO) has set a 0.5% global cap on SO2 content in marine fuels, a significant reduction from the current limit of 3.5%, in order to achieve the 2020 target of reducing air pollutions due to international shipping31. In our simulation, at about 78.7%, shipping emissions make the most significant contribution to NO3 concentration in Singapore. Besides that, removing shipping emissions also reduces SO2 mixing ratio dramatically by 51.1%, SO4 concentration by 42.0%, and overall PM2.5 concentration by 68.7%. We also see a substantial reduction of O3 as high as 21.9% in the Shipping Scenario (Table 5).

Kuala Lumpur is a city of 1.76 million people in Southeast Asia, with an annual mean PM2.5 concentration derived in the Reference Scenario of 6.8 ± 3.2 μg m−3. Compared with the other cities discussed previously, the proportion of BC and OC to PM2.5 concentration is high in Kuala Lumpur, at 18.6%, and 25.5%, respectively. On the other hand, the proportion of NO3 component is relatively low, only 38.2%. Somewhat uniquely, the concentration of BC and OC are barely changed in the Gas, Coal, and Modern Scenarios compared to the Reference Scenario (Table 5). This indicates that the major emission source of BC and OC is road transportation, not the industry, power generation, or residential sectors. Shipping emissions have a significant contribution to NO3 and SO4 by 35.5% and 29.7%, respectively. Furthermore, as demonstrated in the Shipping Scenario, reducing shipping emissions could result in a 19.8% reduction in PM2.5 concentration, and this appears to be the most effective target for air quality improvement than other energy use scenarios.

### A discussion of the sensitivity of chemical concentration in Southeast Asia to transboundary pollution

The considerably high concentration of air pollution in India within the model domain makes it hard to overlook its potential impact on air quality in Southeast Asia. Hence, we have estimated the impact of transboundary pollution from India on each chemical concentration in Southeast Asia under different hypothetical fuel consumption scenarios. This has been done by comparing the results from simulations with emission modifications applied only to the Southeast Asia subdomain with results from simulations with emission modifications applied to the who model domain, including the South Asia subdomain (referred to as _ALL below).

Compared with the reduction of PM2.5 concentration in the Gas Scenario, the reduction of PM2.5 concentration in Gas_ALL (the Gas Scenario with emission modification in the whole model domain) is 1.0% more, which mainly comes from the reduction of SO4 by 11.3% (25.0% in Table 4 versus 36.3% in Table 6). In other words, if all countries in the model domain would use gas to replace coal in the power generation and industry sectors, it could further reduce SO4 concentration by 11.3% in Southeast Asia (from −25.0% to −36.3%). On the other hand, the substantial increases of SO4 and PM2.5 concentration in Coal_ALL are expected based on the high SO4 concentration observed in India in the Reference Scenario (Fig. 9a). If the coal-favorite policy in industry and power generation were also applied in India, it could worsen air quality not only in India locally but also neighboring countries in Southeast Asia. Compared with the Coal Scenario, Coal_ALL indeed adds an additional 21% of SO4 in Southeast Asia (in terms of increase from the Reference Scenario, 48.0% in Table 4 versus 69.0% in Tables 6), and 2.8% in PM2.5 (from 8.6% to 11.4%). Our results show that the simulations with the gas-favorite and coal-favorite emission modifications in the whole domain do not change the concentrations of chemical species other than SO4 significantly in Southeast Asia (<1%), implying that the abundance of these species in Southeast Asia is less affected by transboundary pollution.

High BC and OC concentration in India are also observed in the Reference Scenario (Figs 6a and 7a). As discussed previously, BC and OC are both reduced significantly in the Modern Scenario. We find that by reducing biofuel consumption and using natural gas and electricity in the residential sector in both Southeast and South Asia, BC and OC abundances in the SEA domain can be reduced 43.3% and 10.5%, respectively (Table 6). On the other hand, compared with the Modern Scenario with the Modern_ALL Scenario shows that the major contributors of BC and OC concentration in Southeast Asia are primarily the local sources: transboundary BC and OC only affect 1.6% (from 41.7% to 43.3%) and 2.3% (from 8.2% to 10.5%) of BC and OC concentration in the SEA domain, respectively.

### Summary and conclusions

In this study, we have designed five hypothetical fuel consumption scenarios: the Reference, Gas, Coal, Modern, and Shipping Scenarios. By applying pollutant emissions resulting from these scenarios in a regional weather-atmospheric chemistry model, we have examined the outcomes in air quality over Southeast Asia in response to different fuel usage policies in the power generation, industry, or residential sector. Through the analyses based on the comparison of the results from these scenarios, we demonstrate that a practice favoring the dominant usage of coal in the energy mix (the Coal Scenario) could lead to a significant increase in the aerosol and gas emissions and a worsening of air quality in the region. On the other hand, a practice of shifting fuels in the energy mix from coal to natural gas (the Gas Scenario) would effectively lower the abundance of air pollutants. Besides potential policies regarding the fuel consumptions in the industrial and energy generation sectors, we have also investigated the consequences in air quality by either reducing the use of traditional biofuels in the residential sector (the Modern Scenario) or the emissions from shipping (the Shipping Scenario).

Sulfate aerosols (SO4) are the primary pollutant produced by coal burning in the power generation and industry sectors. In the Gas Scenario, the reduction of SO4 concentration can reach 25% in Southeast Asia by shifting fuels in energy mix from coal to natural gas, resulting in a decrease in PM2.5 concentration by 4.8% compared to the Reference Scenario. On the other hand, in the Coal Scenario, shifting fuels from natural gas to coal in the energy mix could make air quality much worse by increasing SO4 concentration by 48% and PM2.5 concentration by 8.6%. In the Modern Scenario, substantial reduction of BC and OC concentration by 41.7% and 8.2%, respectively, in Southeast Asia, results in a 5.0% decrease of PM2.5 concentration, even more than the reduction of PM2.5 in the Gas Scenario. This result shows that people in Southeast Asia still commonly use biofuel in their daily activities. Specifically, based on our analyses, shipping emission affects air quality in Southeast Asia significantly, responsible for more than 26% of PM2.5 concentration. Our results suggest that mitigation policies targeting total PM2.5 concentration in Southeast Asia should focus not only on the coal and biofuel consumption sectors but also on shipping emissions.

We find the impacts of various policies on key pollutants vary across 5 selected cities. In the Gas Scenario, all five cities show a substantial reduction in sulfate aerosols varying from 28.0% to 46.3%. Jakarta and Bangkok can reduce even more than half of SO2 mixing ratio in the Gas Scenario. However, if the regulation policy aims to target BC concentration, replacing biofuel by natural gas in the residential sector can reduce BC concentration in Jakarta and Hanoi more substantially than others by 57.0% and 70.6%, respectively. On the other hand, shipping emission has a significant impact on the air quality in the selected cities, especially in Singapore. By eliminating shipping emissions, the PM2.5 concentration in Singapore can be reduced by 68.7%. We also see that the substantial reduction of O3 mixing ratio in the Shipping Scenario can be as high as 21.9% in Singapore. In our study, we did not include road transportation in Southeast Asia in making our hypothetical scenarios. Nevertheless, our results actually imply the potential importance of road transportation in mitigating PM2.5 in several major cities in the region. Future studies should directly address the roles of various policies regarding road transportation sector in the mitigation of air pollution for Southeast Asia.

We have investigated the impact of transboundary pollution from outside of Southeast Asia on air quality in Southeast Asia by designing another set of the Gas, Coal, and Modern Scenarios with emission modification applied to the entire model domain including South Asia. Our results show that SO4 concentration in Southeast Asia can be influenced by 11.3% by transboundary pollution. Whereas, all other key pollutants are much dependent on local emissions, transboundary transport only accounts less than 1% of their changes.

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

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## Acknowledgements

This research was supported by the National Research Foundation Singapore through the Singapore-MIT Alliance for Research and Technology, the interdisciplinary research program of Center for Environmental Sensing and Modeling. It was also supported by the U.S. National Science Foundation (AGS-1339264), the U.S. Department of Energy (DE-FG02-94ER61937), and L’Agence National de la Recherche (ANR) of France through the Make-Our-Planet-Great-Again Initiative, ANR-18-MPGA-003 EUROACE. The authors would like to acknowledge WMO AGW, SPARTAN, NCEP-FNL, and NCAR FINN working groups for releasing their data to the research communities; and the NCAR WRF developing team for providing the numerical model for this study. The computational work for this article was performed on resources of the National Supercomputing Centre, Singapore (https://www.nscc.sg).

## Author information

### Author notes

• Chien Wang

Present address: Laboratoire d’Aerologie/CNRS/University of Toulouse, Toulouse, France

### Affiliations

1. #### Center for Environmental Sensing and Modeling, Singapore-MIT Alliance for Research and Technology, Singapore, Singapore

• Hsiang-He Lee
•  & Chien Wang
2. #### Energy and Environmental Engineering Department, National Institute of Applied Science of Lyon (INSA Lyon), Villeurbanne, France

• Oussama Iraqui

• Chien Wang

### Contributions

Hsiang-He Lee designed the experiment, performed the simulations, analyzed the data, and wrote the manuscript. Oussama Iraqui calculated and produced emissions of various fuel consumption scenarios. Chien Wang contributed to the experimental design, analysis methodology, and redrafting of the manuscript.

### Competing Interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Hsiang-He Lee.


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# American Institute of Mathematical Sciences

December  2018, 38(12): i-iii. doi: 10.3934/dcds.201812i

## Preface of Llavefest: A broad perspective on finite and infinite dimensional dynamical systems

 1 ICREA and Universitat Politècnica de Catalunya, Departament de Matemàtiques, Diagonal 647, 08028 Barcelona, Spain 2 Departament de Matemàtiques and Lab of Geometry and Dynamical Systems, Universitat Politècnica de Catalunya, Av. Doctor Marañón, 44-50, Barcelona, 08028, Spain 3 Mathematics at Stern College, Department of Mathematical Sciences, Yeshiva University, New York, USA 4 School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332, USA

Published  September 2018

Citation: Xavier Cabré, Amadeu Delshams, Marian Gidea, Chongchun Zeng. Preface of Llavefest: A broad perspective on finite and infinite dimensional dynamical systems. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : i-iii. doi: 10.3934/dcds.201812i
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Measuring the independence between the components of a stochastic process

In a context of blind source separation (e.g. you want to extract the voice of a singer from a song), many approaches consist in maximizing the independence between the components of a certain decomposition of an input signal. However, the signals are often considered only as random variables, although their temporal structure is often strong. I am interested in reading / learning / developing about an appropriate generalization of this approach where the signal is now modeled as a stochastic process (and even a diffusion process is it makes things simpler). So first I need a manageable definition and measure of the independence between the components of a stochastic process.

For a random variable $X$ on $\mathbb{R}^n$, the Kullback-Leibler divergence between the joint and the product of the marginal distributions of $X$ is often used to measure the degree of independence between the components of $X$. It is written $$I = \int p(X) log \frac{p(X)}{\prod_{a=1}^n p_a(X_a)}dX$$ where $p_a(X_a)$ is a marginal probability function. If $I=0$, the components are completely independent.

How can I generalize it to stochastic processes? On this link http://planetmath.org/IndependentStochasticProcesses.html, is given the definition of the independence between two stochastic processes. I guess this could lead to a formal generalization but I do not manage to write it. Can anyone do it?

Besides, I am afraid it would lead to unpractical computations. So I am thinking that maybe with sufficient strong conditions on the stochastic process (which will not be worse than the usual ergodic random variable approach), one could simplify this expression up to a practical one. For instance, assuming that the process is solution to a stochastic differential equation, I am dreaming of the power of Girsanov theorem to compute the fraction in the above equation...

Do you have the answers to my questions? Do you know any litterature on this topic? Any advice about the direction I should take?

Thanks for your help.

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2 Answers

For the Kullback-Leibler divergence to be finite you need (at the very least) the joint distribution of the components to be absolutely continuous with respect to the product. For stochastic processes this seems to be a very strong condition: for example, for continuous semimartingales this implies zero quadratic covariation, and indeed much more.

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This has been addressed to some extent in the machine learning literature, though I'm not sure how helpful it will be for your problem. One way of defining the KL divergence between two distributions P and Q is the expectation (under P) of the log of the Radon-Nikodym derivative of Q with respect to P.

This definition works nicely for diffusion processes. The Radon-Nikodym derivative is known from Girsanov's theorem, so everything can be computed as long as the two diffusions of interest have the same (constant) diffusion coefficient.

The work of Archambeau et al covers a lot of this stuff: http://www.cs.ucl.ac.uk/staff/c.archambeau/publ/nips_ca07.pdf

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# Gas station without pumps

## 2013 August 8

### Hard Math for Elementary School

Filed under: Uncategorized — gasstationwithoutpumps @ 20:34
Tags: , , , , ,

Hard Math for Elementary School by Glenn Ellison: (ISBN 9781489507174) looks like a book I could have used with my son about 8 years ago (too bad it was just published a couple of months ago).

The premise is simple: it is a math enrichment textbook, intended to take the topics of elementary school math deeper for gifted students.

The presentation is good, but the students will have to be reading at the 4th grade level as well as doing math at that level to get much out of the book.  This is not a flashy book with lots of illustrations and stories—it is just cool math, presented as cool math.

Disclaimer: I don’t have a copy of the book, and I haven’t read much of it. I used Amazon’s “Look Inside” feature to look at the table of contents and a couple of pages, and saw such gems as calculation tricks for computing some squares (like 552=3025) quickly.  (The trick is based on $(x+y)(x-y)=x^2-y^2$, but the author wisely avoids algebraic notation.)

Reviews from people who have looked at it in more detail can be found at http://albanyareamathcircle.blogspot.com/2013/05/recommended-summer-reading-for-young.html and http://blog.supplysideliberal.com/post/53817714552/glenn-ellisons-new-book-hard-math-for-elementary

Glenn also has a book for middle school students: Hard Math for Middle School

## 2012 October 13

### When is a line graph not a line graph?

Filed under: Uncategorized — gasstationwithoutpumps @ 21:39
Tags: , , ,

I recently discovered that elementary school teachers have taken to calling histograms “line plots”, and that this definition has gotten quite widespread:

A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer then 25 numbers. It is a quick, simple way to organize data. [http://ellerbruch.nmu.edu/classes/cs255w03/cs255students/nsovey/p5/p5.html]

A line plot shows data on a number line with x or other marks to show frequency. [http://www.icoachmath.com/math_dictionary/Line_Plot.html]

A line plot is a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer than 25 numbers. It is a quick, simple way to organize data. [http://www.mathplanet.com/education/algebra-2/equations-and-inequalities/line-plots-and-stem-and-leaf-plots]

This page contains worksheets with line plots, a type of graph that shows frequency of data along a number line. [http://www.superteacherworksheets.com/line-plots.html]

Of course, no one outside the elementary school teachers uses that term, which is confusingly similar to the standard term “line graphs”.  Even the superteacherworksheets site acknowledges the terrible confusion that the “line plot” term generates:

Line Graph Worksheets Line graphs (not to be confused with line plots) have plotted points connected by straight lines.

“Line graph” is a common term, even among educators:

Line graph is a graph that uses line segments to connect data points and shows changes in data over time. [http://www.icoachmath.com/math_dictionary/line_graph.html]

Line graph: A graph that uses points connected by lines to show how something changes in value (as time goes by, or as something else happens). [http://www.mathsisfun.com/definitions/line-graph.html]

line graph definition: a diagram of lines made by connected data points which represent successive changes in the value of a variable quantity or quantities. [http://dictionary.reference.com/browse/line+graph]

Was it just because they couldn’t spell “histogram” that elementary school teachers had to invent a new term confusingly close to an existing standard term?  I feel sorry for the kids subjected to this poor choice of nomenclature, as they will have to do more unlearning before taking high school or college tests, where they will be expected to know what a histogram and a line graph are, but not anything about “line plots”.

## 2012 April 16

### Squishy Circuits, for family science night

Mylène recently posted a good description of an electrical building project suitable for young kids (she did it with a Brownie troop): K-12 Engineering: Squishy Circuits Tips and Tricks.

A few years ago, when my son was in 5th and 6th grade, I helped run a Family Science Night at his school.  We did a lot of fun activities, but never tried squishy circuits.  I did keep on-line notes about what we did do and web resources we found at that time.  Perhaps these notes may be useful to someone planning a family science night at an elementary or middle school.

## 2011 June 5

### Analysis of Common Core Standards

Filed under: Uncategorized — gasstationwithoutpumps @ 09:59
Tags: , , , ,

The article

Common Core Standards: The New U.S. Intended Curriculum by Andrew Porter, Jennifer McMaken, Jun Hwang, and Rui Yang
doi: 10.3102/0013189X11405038 Educational Researcher 40(3):103–116, May 5, 2011.

has an analysis of the new Common Core Standards, comparing them to existing state standards, standards in other countries, and a few well-known assessments or standards documents. (I’ve blogged about a different comparison almost a year ago in California standards vs. Common Core.)

The method published in Educational Researcher attempts to reduce the complexity of comparing huge, complex documents down to single numbers measuring similarity, which loses a lot of the information. Saying that California shares 0.27 similarity (on a scale of 0 to 1) with the Common Core for kindergarten math standards, or 0.31 for high-school math, does not tell me whether the Common Core is better or worse, just that it is different.

The similarity measure is computed from comparing the weights given to each of 1085 cells of an array in math (815 for language arts). The arrays are 2-dimensional, crossing topics with cognitive demand. The projections onto the cognitive demand axis are shown for “state” standards (which I assume are the sum over all grades and states for which they have data) and the Common Core.  Later on in the paper, they imply that the tables are just for grades 3–6, but they failed to have any caption on the table (so much for “Data displays” being taught to educational researchers).

level state CC
Memorize  12.11%  9.50%
Perform Procedures  48.82%  43.74%
Demonstrate understanding  28.66%  35.65%
Conjecture  7.78%  5.96%
Solve non-routine problems  2.63%  5.16%

Of course, this comparison is for all states and some subset of grades, not specifically for any one state, which is where the comparison might be useful. Still, I’m glad to see an increase in “demonstrate understanding” and “solve non-routine problems”, and a decrease in “memorize” and “conjecture”. (Note: conjecturing is a useful thing, but grade schools and high schools confuse it with guessing, so students are better off not being taught to do it wrong.)

A more informative table is the one that breaks things down by major topic area:

Topic state CC
Number sense 13.84% 32.75%
Operations 15.08% 22.72%
Measurement 0.00% 17.79%
Consumer applications 11.58% 0.05%
Basic algebra 0.03% 13.40%
Geometric concepts 0.24% 5.73%
Data displays 2.83% 2.76%
Statistics 4.72% 3.16%
Probability 0.15% 0.00%
Analysis 0.03% 0.00%
Trigonometry 0.64% 0.00%
Special topics 0.32% 0.00%
Functions 1.09% 0.00%
Instructional technology 25.71% 0.00%

This table tells me more about the weaknesses of their method than it does about the standards, though.  I see no way that one set of standards can be all “basic algebra” and no “advanced algebra” while the other is all “advanced” and no “basic”.  I also have no idea what they mean by “analysis”, but it is almost certainly not the topic that mathematicians call “analysis”, which is a more advanced form of calculus.  The numbers in both columns look ludicrous (25.7% on “instructional technology”, which probably means use of calculators?  32.75% on number sense?).  Quite frankly, after seeing this table, I do not believe anything the authors have to say about the standards—the numbers look cooked to make their point, rather than being a dispassionate analysis of the data.  Looking further in their paper, I see that this is just incompetent proof-reading, as their graphs show low “advanced algebra” content in both  columns, and do not show  huge bump for “instructional technology” in the state column

So, the one interesting table in their paper is clearly garbage.  What a waste of effort, doing all that work then failing to proofread the paper and printing trash. Other incompetent editing: some tables have states labeled with names, others have “State A”, “State G”, … .

I think that Educational Researcher needs to retract the paper and have the authors redo the paper with proper proofreading and captioning of their tables and figures—this is unacceptably bad work for an academic publisher.

## 2010 November 18

### Math game competition

Filed under: Uncategorized — gasstationwithoutpumps @ 00:10
Tags: , , , , , , ,

The Games for Learning Institute have announced a contest for games that teach 5 of the New York State geometry standards for 6th grade. There is a flier at if you want something to post on the wall.

Register by: December 12, 2010
Game Submission Deadline: January 12, 2011

Unlike many game designers, the organizers here seem to be aware that schools don’t have cutting-edge equipment. The game has to run in a browser on a commodity PC or Mac (no special hardware or special plug-ins). I believe that Scratch games should qualify, via the Scratch Player (a Java applet), so beginning programmers (even 6th graders!) can get in on the action.

I’ve posted about Scratch before (Computer Languages for Kids) and the Build-Your-Own-Blocks extension to Scratch.  I don’t know whether BYOB has a Java applet player, which would be necessary for entering this contest.

Next Page »


text:
# Server Mode¶

With --major-mode server Artemis runs an ‘analysis server’ with a JSON interface for controlling it externally and reporting what it finds.

In this mode all other arguments except those prefixed by analysis-server-* are ignored, including the URL.

There is a debug view which shows the internal browser, which is shown when the option --analysis-server-debug-view is given.

The concolic advice mode is documented at Server Mode - Concolic Advice.

## The API¶

The server runs on port 8008 by default. This can be changed with the --analysis-server-port option.

Calls to the server are expected to POST a JSON message with the following format:

{
"url": "http://www.example.com"
}

We do not use REST-style URLs to avoid the complications of URL-encoding complex strings like URLs or XPaths.

The command property must always be set, and the rest of the properties depend on which command was used.

There is an echo command which can be used to check the server is running:

curl -w "\n" --data '{"command":"echo","message":"Hello, World"}' localhost:8008

This should return:

{
"message": "Hello, World"
{

Only one command can be sent per request. The server is designed to be blocking; any requests sent while another is still being processed will return an error.

## Commands¶

• echo

Used for testing. Returns the text provided in the message field. The optional delay field is the number of seconds to delay before sending back the response (integers 0–30 are valid).

Send:

{
"command": "echo",
"message": "Hello, World",
"delay": 1
}

Receive: {"message": "Hello, World"}

• exit

Shuts down the server.

Send: {"command": "exit"}

Receive: {"message", "Server is shutting down"}

• pageload

Loads a URL in the Artemis browser. The final URL we end up on after redirects etc. is returned.

The optional timeout parameter is the number of milliseconds to wait before cancelling the load and returning an error (integers 0–3600000 accepted), 0 implies no timeout.

Send:

{
"url": "http://www.example.com",
"timeout": 5000
}

{
"url": "http://www.example.com"
}

• backbutton

Uses the browser history to go back one page.

It is an error to call this command before there are at least two pages in the history. Due to an implementation issue, “about:blank” is never accessible via this command.

Send: {"command": "backbutton"}

{
"backbutton": "done",
"url": "http://www.example.com"
}

• handlers

Lists the event handlers registered on the current page. The list returned shows XPath expressions identifying the DOM elements with events, and a list of events attached to each. The special cases “document” or “window” may also be given as an identifier for events registered on those objects.

Send: {"command": "handlers"}

Receive: (e.g for the handlers.html test case)

{
"handlers": [
{
"element": "//a[@id='dom-attr']",
"events": ["click"]
},
{
"element": "//a[@id='js-attr']",
"events": ["click"]
},
{
"element": "//a[@id='listener']",
"events": ["click", "focus"]
}
]
}

It is also possible to specify a filter (by XPath) and receive only the handlers registered on matching elements.

Send:

{
"command": "handlers",
"filter": "id('listener')"
}

Receive: (e.g for the handlers.html test case)

{
"handlers": [
{
"element": "//a[@id='listener']",
"events": ["click", "focus"]
}
]
}

The XPath identifiers returned are Artemis’ internally generated ones and may not match the filter, even if it selects a single element.

• click

Clicks on an element specified by XPath.

For now then only type of click is a JavaScript-level click, with no option for a GUI click.

N.B. This is now just a special case of the newer event command.

Send:

{
"command": "click",
"element": "id(\"clickable\")"
}

Receive: {"click": "done"}

There is an optional method field, which allows you to choose the type of click performed. Possible values are:

simple (default)

Just generates a click event, in the saem way as the event command would.

simulate-js

Uses JavaScript events to simulate a user click.

simulate-gui

Uses GUI events to simulate a click.

N.B. This click is done by clicking the coordinates at the centre of the element. If the element is behind another element or the element bounding box is larger than the clickable/visible area, this command can miss and click the wrong thing.

Send:

{
"command": "click",
"element": "id(\"clickable\")",
"method": "simulate-js"
}

Receive: {"click": "done"}

• event

Triggers a JavaScript event on the element at the specified XPath. (Or custom event; see below.)

N.B. Event names are given as “change” or “focus, not “onchange”, “onfocus”, etc.

Send (e.g. on handlers.html):

{
"command": "event",
"element": "id(\"listener\")",
"event": "focus"
}

Receive: {"event": "done"}

There are also some custom Artemis event types which are not the standard JavaScript events. These are handled separately by Artemis and are not triggered as JavaScript events directly.

So far there is only one implemented: for pressing Enter on a form field (e.g. to submit the form).

Send (e.g. on form-submission.html):

{
"command": "event",
"element": "id(\"input-text\")",
"event": "ARTEMIS-press-enter"
}

Receive: {"event": "done"}

• page

Returns information about the current page (the URL, page title, and DOM statistics).

Send: {"command": "page"}

{
"url": "http://www.example.com",
"title": "Example Domain",
"elements": 12,
"characters": 1262
}

The optional “dom” parameter can be set to True to include the entire DOM dump.

Send:

{
"command": "page",
"dom": true
}

{
"url": "http://www.example.com",
"title": "Example Domain",
"dom": " ... ",
"elements": 12,
"characters": 1262
}

• element

Returns the string representation of each element (if any) matching a given XPath.

Send: (e.g. for the click.html test page)

{
"command": "element",
"element": "id(\"clickable\")"
}

{
}

There is also an optional property field which will return the string representation of that object property instead.

Send:

{
"command": "element",
"element": "id(\"clickable\")",
"property": "nodeName"
}

{
"elements": [ "A" ]
}

• fieldsread

Returns a list of the form fields which have been read by different events since the last page load.

Send: {"command": "fieldsread"}

Receive: (e.g. from form.html test page)

{
{
"element": "//button[1]",
"event": "click",
{
"count": 2,
"field": "//input[@id='first']"
}
]
},
{
"element": "//button[2]",
"event": "click",
{
"count": 1,
"field": "//input[@id='second']"
}
]
},
{
"element": "//button[3]",
"event": "click",
{
"count": 3,
"field": "//input[@id='first']"
},
{
"count": 3,
"field": "//input[@id='second']"
}
]
}
]
}

Each “event object” contains the event type triggered and target element (XPath as passed in via the click command), and a list of the form fields which were read by the handler for that event. Each of these “read objects” contains an XPath to the field and a count of the number of times the field value was read (at a low level in the JavaScript interpreter).

• forminput

Injects values into form fields and triggers their change handlers. The method of injection can be changed with the optional method parameter (see below).

Send:

{
"command": "forminput",
"field": "id('input-text')",
"value": "Hello, world."
}

Receive: {"forminput": "done"}

The valid element types for field are input and select.

The value property can be set to a string (as above), integer, or bool. Strings are used when injecting into text fields or select boxes. Integers can be used to inject into a select box by index (sets the selectedIndex property to the given value). Booleans are used to inject into inputs with type checkbox or radio.

The allowable combinations of field and value are:

input (not checkbox or radio) input with type checkbox or radio select
String Sets .value Invalid Sets .value
Int Invalid Invalid Sets .selectedIndex
Bool Invalid Sets .checked Invalid

For example, the following commands are all valid on the form-injections.html test case:

{
"command": "forminput",
"field": "id('input-text')",
"value": "Hello, world."
}

This one sets the checkbox to ticked:

{
"command": "forminput",
"field": "id('input-checkbox')",
"value": true
}

When injecting into a select box, the value attribute of the appropriate option element must be given, which is not necessarily the text which appears in the UI.:

<select id="input-select" >
<option value="first" >First Option</option>
<option value="second" >Second Option</option>
<option value="third" >Third Option</option>
</select>

This one selects “Third Option” in the UI:

{
"command": "forminput",
"field": "id('input-select')",
"value": "third"
}

This one also selects “Third Option”, by using the index:

{
"command": "forminput",
"field": "id('input-select')",
"value": 2
}

The form-injections.html example includes a ‘marker’ element so you can confirm the form input worked:

{
"command": "element",
"element": "id('status')"
}

{
"elements": [ "#input-text set to 'Hello, World'" ]
}

There is a method field, which allows you to choose the type of injection performed. Possible values are:

inject

Inject the value into the .value property (depending on the input type; see above).

onchange (default)

Inject the value and trigger the onchange handler for the form field.

simulate-js

Uses JavaScript events to simulate a user filling the form field as closely as possible. The support for text inputs is currently much more sophisticated than for checkboxes, radio buttons, and select boxes.

When simulate-js is used, an extra optional property noblur can be set to boolean true to stop the ‘blur’ (de-focus) event being triggered on this element once the injection is complete. This can be useful (for example) to stop auto-complete boxes being hidden when the field is deselected.

simulate-gui

Not yet implemented.

Send:

{
"command": "forminput",
"field": "id('input-text')",
"value": "Hello, world.",
"method": "inject"
}

Receive: {"forminput": "done"}

• xpath

Evaluates an XPath query and returns the result.

The result may be a String, Number, Boolean or Node-Set. Node-sets are represented as an array of the string representations of the nodes.

Node-set (all examples on the click.html test case):

{
"command": "xpath",
"xpath": "//h1"
}

{
"result": [ "
Clickable elements
" ]
}

String:

{
"command": "xpath",
"xpath": "string(//h1)"
}

{
"result": "Clickable elements"
}

Number:

{
"command": "xpath",
"xpath": "string-length(string(//h1))"
}

{
"result": 18
}

Boolean:

{
"command": "xpath",
"xpath": "string-length(string(//h1)) > 10"
}

{
"result": true
}

It is also possible to provide a list of XPaths to evaluate. The result will be a list of the results of each XPath as above:

{
"command": "xpath",
"xpath": [
"//h1",
"string(//h1)",
"string-length(string(//h1))",
"string-length(string(//h1)) > 10"
]
}

{
"result": [
[ "
Clickable elements
" ],
"Clickable elements",
18,
true
]
}

N.B. Non-matching queries are handled as normal in a browser’s XPath evaluation:

//does-not-exist => []
string(//does-not-exist) => ""
boolean(//does-not-exist) => false

An XPath which cannot be evaluated (because it is invalid) will return an error.

• windowsize

Set the size of the browser window.

Send:

{
"command": "windowsize",
"width": 1024,
"height": 768
}

Receive: { "windowsize": "done" }

• concolicadvice

Allows the server to record traces nito a concolic execution tree and return advice about new form field values which can lead to new exploration.

See the Server Mode - Concolic Advice documentation for details.

• evaluate-js

Evaluates a JavaScript string on the current page.

Send:

{
"command": "evaluatejs",
"js": "document.getElementById('clickable').click()"
}

Receive: { "evaluatejs": "done" }

• setsymbolicvalues

Sets the internal symbolic values of variables accessed via artemisInputBoolean(), artemisInputInteger(), and artemisInputString(). This can be used for testing the internal concolic engine of the platform. For normal testing of web pages the forminput command should be used instead for concolic testing.

The values parameter is a mapping from variable names (strings) to values, which may be strings, integers or booleans.

The reset parameter is optional, and if set to true, the internal symbolic value table will be cleared before setting these replacement values.

Send:

{
"command": "setsymbolicvalues",
"values": {
"X": "Hello",
"Y": 123,
"Z": true
},
"reset": true
}

Receive: { "setsymbolicvalues": "done" }

Now a call like the following would update the DOM with the injected symbolic values:

{
"command": "evaluatejs",
"js": "document.getElementById('status').textContent = artemisInputString('X') + ' ' + artemisInputInteger('Y') + ' ' + artemisInputBoolean('Z');"
}

• coverage

Returns a report of the line coverage from the executed commands. The line coverage is taken since the server was started, and cannot be reset.

The report is a list of reports for each distinct JavaScript source (web page, JS file, etc.). The line-by-line coverage report is human-readable, not in a good machine-readable format. It can be parsed with analyse-coverage.py.

The linescovered parameter is a list of line numbers which were covered.

N.B. A line is considered covered if some interpretation was done on that line. So the close-braces of if statements, else statements, blank lines, and so on will never be considered covered.

Send:

{
"command": "coverage"
}

{
"coverage": [
{
"url": "...",
"line": "...",
"linescovered": [...]
"report": "..."
},
{
...
}
]
}


text:
## Abstract

Arguments to the effect that Church's thesis is intrinsically unprovable because proof cannot relate an informal, intuitive concept to a mathematically defined one are unconvincing, since other 'theses' of this kind have indeed been proved, and Church's thesis has been proved in one direction. However, though evidence for the truth of the thesis in the other direction is overwhelming, it does not yet amount to proof.


text:
# MPMusicPlayerController Track Length

Using an MPMusicPlayerController is there a way to query the tracks length?

Using .currentPlaybackTime I can figure out how far I am into the track but I have no way of knowing how long the track is.

My [MPMediaItem valueForProperty:MPMediaItemPropertyAssetURL] returns null for some tracks so using the AVAsset won't work for me.

   NSNumber *duration=[item valueForProperty:MPMediaItemPropertyPlaybackDuration];


text:
# Chapter 14 - Graph Theory - 14.2 Euler Paths and Euler Circuits - Exercise Set 14.2: 22

(a) This connected graph has exactly two odd vertices. Therefore, by Euler's theorem, the graph has at least one Euler path. (b) C,A,E,C,D,B,F,D is an Euler path.

#### Work Step by Step

(a) Vertex C and vertex D are odd vertices. The other vertices are even vertices. This connected graph has exactly two odd vertices. Therefore, by Euler's theorem, the graph has at least one Euler path. (b) If a graph has exactly two odd vertices, then any Euler path starts at one odd vertex and ends at the other odd vertex. Let's start at vertex C. From there, let's travel around the triangle to vertex A, then to vertex E, and then back to vertex C. From there, let's travel to vertex D, then to vertex B, then to vertex F, and then back to vertex D. This path is C,A,E,C,D,B,F,D. This path travels through every edge of the graph exactly once, so it is an Euler path.

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.


text:
# How long is needed to clear the area of robots?

This question has been written in order to help answer Fastest way to collect an arbitrary army.

There is a 1 x 1 square area with corners labelled clockwise A, B, C and D. A finite number of stationary robots are spread out across the area. Every robot knows where every other robot is at any time. A robot may only pass a message to another robot by touch. All robots travel with speed 1.

Robot Zero is at point A and receives the following message from an off grid source:

"Ensure that all robots leave the area as quickly as possible, through point C".

Given that we do not know how many robots there are or where they are:

What is the longest time it could take to clear the area of robots?

and

How can you prove it?

You can assume the following:

• Robots have negligible area, so when they touch in order to relay the message, they are occupying the same point on the square.
• Message is transferred in negligible time
• When faced with two options of equal efficiency a robot is able to make a decision (in collaboration with another robot where necessary) in negligible time. So, if there are two robots at B and there is only one other robot on the grid, at D, the two robots at B are able to send one robot to D to relay the message, while the other robot goes straight from B to C.
• The robots are all able to calculate the most efficient way of relaying the message to all robots.
• This is very similar to puzzling.stackexchange.com/questions/548/… Jun 30 '14 at 0:00
• My answer to that question argues that the answer to this should be 2 but not quite as there could be one at ABC and D. This would require $1+\sqrt 2$ Jun 30 '14 at 1:51
• $2 + sqrt{2}$ ? I agree. My theory is that Robot Zero should be able to go from A to C along the critical path and always be increasing its direct distance to A, but I can't prove it...
– Ali
Jun 30 '14 at 8:54
• @Ali I believe you could probably prove that $2 + sqrt(2)$ is indeed sufficient, but that doesn't guarantee that it couldn't be shorter still. I suppose the best approach would be to assume a different configuration would take longer, and prove otherwise. Once you have the worst case scenario, you also know the minimum amount of time to clear that area.
– Neil
Jun 30 '14 at 12:32
• i meant 1 not 2 but that did not include going to C at the end Jun 30 '14 at 13:37

Although the question is for one answer the comments are slightly confused about the minimum so below are the minimum and maximum times for all robots to exit the square:

Minimum time: √2
If all robots are on the line that joins A to C then the initial robot can travel directly to C in the shortest time/distance. Every other robot would join with the first and also travel directly to C.

Maximum time: 2 + √2
The worst scenario is where there are only three robots at A, B and D.The first robot has to travel to either B or D, then travel diagonally across the square to direct the final robot.

Justification:
The scenario presented in the maximum time represents the configuration where the robots and the exit are all as far away from each other as possible, hence each corner of the square has a robot or the exit. Adding more robots to the play-field cannot increase this maximum distance due to two reasons:

1. Each new robot can travel in a different direction to the first robot which can reduce the overall time needed for all robots to leave the square. For instance if there are four robots and the fifth is at the centre of the square the first robot would travel to the robot at the centre then it could travel to B and then directly to C. This would give a travel time of 1+√2. The robot at the centre would travel to D and then on to C. The travel to B and D happens at the same time and do reduces the overall cost.

2. A mathematician could probably phrase this better so my apologies if it is not concise. If you imagine that there are at least three robots at A, B and D and lets imagine that the robot at A travels to B. From that point the longest distance to D and then C is diagonally across the square which divides the square into two triangles. Now assume that there are no robots in the triangle ABD but there is one somewhere in BCD. In order to increase the maximum length of robot A's journey this distance must be greater than the two legs B->D and D->C but there are no triangles that can fit within BCD with a greater total of side lengths. This means that the greatest distance the robot has to travel is BDC. If this is the case for a journey going from A to C through a triangle at BCD then it would also be true if we travelled in the opposite direction from C to A through triangle ABD.

When there are robots at A, B and D then there is a better chance of achieving 1+√2.

Hope that explains it well enough but the following pictures describe the minimum, maximum and explanation of maximum in, hopefully, a clearer way:

• Sorry there are two questions but I believe I answered both.
– Alan
Jul 31 '14 at 16:57
• Well I 100% agree that that is the answer but don't have a good way to prove it. Thank you. Aug 1 '14 at 12:53
• I'm not entirely Sure - in your last picture you are always assuming, there is a free robot, which can just get the new point without having to go back to D afterwards. But couldn't there be two new targets, so both robots from B have to deviate from the diagonal course? One would then have to go to D and C afterwards, which is longer than the original course... Can you prove there is no such constellation ? Aug 5 '14 at 11:58
• Your "proof" doesn't take into account the possibility that certain layouts with robots on B and D would not allow B to be on the path to D. For example, add robot E at the midpoint of AD, and F at the midpoint of BC. If B is visited first, then one robot would have to head straight toward D, and could play no part in waking E and F. Once D was awake, it and the robot that woke it would have to head immediately for C. The shortest sequence of events that would start by having Robot Zero wake B would thus have length ABEFC or ABFEC. Sep 22 '14 at 20:57
• Obviously in the indicated scenario, Robot Zero could simply proceed AEDBFC waking every robot it touches (and things could be even faster using paths AEBC and AEDFC) but the fact that one may have to vary the sequence of robot visits would suggest a need to enumerate more cases. Sep 22 '14 at 21:01


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# Change the values of a measurable function on a negligible set

If $f$ is a $\mu$-measurable function and I change its values on a $\mu$-negligible set, i.e. on $Y \subset Z$ with $\mu (Z) = 0$, why is $f$ still measurable?

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This is not true if the measure is not complete. Simply take a non-measurable subset $Y$ of a measurable null-set $Z$ and look at the characteristic function of $Y$, which is clearly not measurable but agrees with the (measurable) zero function outside of $Y$.
However, your modified $f$ will be measurable with respect to the completion $\tilde{\mu}$ of the measure and agree with $f$ outside of a $\tilde{\mu}$-null set, so the $\tilde{\mu}$-integral will remain unchanged by such a modification and that's enough for most purposes.
To make this more precise, let $g$ be the modified function and $Y = \{x\,:f(x) \neq g(x)\}$. By hypothesis, $Y \subset Z$ with $Z$ measurable and $\mu(Z) = 0$. Observe that $g = [X \smallsetminus Y] \cdot f + [Y] \cdot (g - f)$. With respect to the completion $Y$ and $X \smallsetminus Y$ are measurable because $\tilde{\mu}(Y) = 0$. Note that on a complete space every function which is nonzero only inside a null-set is measurable. Therefore $g$ is the sum of two $\tilde{\mu}$-measurable functions and hence measurable.
Theo, many thanks, it took me a while to understand. In other words: if $f$ is the constant function $f(x) = 0$ and $Z$ is a non-measurable, negligible set then changing $f$ to $1$ on $Z$ makes it a non-measurable function. On the other hand, if I make my space complete by defining the standard extension (all unions $\hat{Y} = Y \cup Y_0$, $Y$ measurable, $Y_0$ negligible and $\mu^\prime (\hat{Y}) := \mu(Y)$) then there are no non-measurable, negligible sets anymore, so changing any $f$ on a negligible set leaves it measurable. –  Rudy the Reindeer Jan 16 '11 at 20:05
@Matt: To connect all this back to your previous question about $L^{1}$-spaces it is an illuminating exercise to prove that the obvious map $L^{1}(\mu) \to L^{1}(\tilde{\mu})$ is an isometric isomorphism, i.e., it is well-defined, linear, onto and $\|f\|_{L^{1}(\mu)} = \|f\|_{L^{1}(\tilde{\mu})}$ for all $f \in L^{1}{(\mu)}$. –  t.b. Jan 16 '11 at 20:28
Taking the obvious map $\varphi: f \mapsto f$, linear and surjective are "obvious". It's well-defined: Let $f \neq f^\prime$ on $U$ with $\mu(U) = 0$. Then $\tilde{\mu}(U) = 0$ and so $f = f^\prime$ $\tilde{\mu}$-a-e. Finally, $$\| f \|_{L^1 (\mu)} = \int_X |f| d \mu = \sup \{ \int_X s d \mu \mid s \text{ step function }, s \leq |f| \} =$$ $$\sup \{ \sum_{i=1}^n \alpha_i \mu(Y_i) \mid \text{ for some } \alpha_i \} = \sup \{ \sum_{i=1}^n \alpha_i \tilde{\mu} \mid \text{ for some } \alpha_i \} = \| f \|_{L^1(\tilde{\mu})}$$. –  Rudy the Reindeer Nov 22 '11 at 22:20