text:
Open access peer-reviewed chapter

# Towards Energy Security for the Twenty-First Century

By Collins Ayoo

Submitted: September 12th 2018Reviewed: December 17th 2019Published: May 15th 2020

DOI: 10.5772/intechopen.90872

## Abstract

Energy security is a goal that many countries are pursuing to ensure that their economies function without interruption and that their people have access to adequate, reliable and affordable supplies of modern and clean energy. It is a pressing concern because the demand for energy is growing rapidly due to robust economic expansion, population growth, new uses of energy and income growth, and yet the supplies of energy resources required to power these needs are finite and in most cases non-renewable. Furthermore, the production, transportation and utilization of energy are a major source of greenhouse gases that cause global warming and climate change. This chapter examines the multidimensional nature of energy security, presents some indicators that can be used to assess changes in energy security and outlines a range of policy measures that can be used to improve energy security. These include more investments in energy production and transmission; promotion of energy efficiency in various end-use sectors; modernization of the grid to enable the integration of renewables such as wind, solar and geothermal energy into the energy system; undertaking reforms in energy markets to attract private sector investment in energy production, increase competition, reduce wastage and lower costs to energy users and fostering greater international collaboration on energy issues and regional energy trade.

### Keywords

• energy security
• energy security indicators
• energy efficiency
• renewable energy
• energy demand
• energy market reforms

## 1. Introduction

Energy is a critical resource that all economies require to produce goods and services and to enhance human, social, and economic wellbeing [1, 2, 3, 4]. It is needed by various industries as an input into the production of goods and services, for transportation, and by households for heating, cooking, lighting and powering domestic appliances. Empirical studies show that energy consumption is positively correlated with indices of economic growth and wellbeing [3]. This is why the provision of energy to most of the world’s population has been identified as a criterion for assessing progress towards sustainable development. Both developed and developing countries, however, face a myriad of energy challenges that include inadequate and unsuitable supplies of energy sources, energy supply uncertainties, high and fluctuating prices of energy, and environmental pollution and degradation as a result of the production, distribution, and use of energy. For countries that rely heavily on energy imports from politically unstable regions, additional risks stem from the threats of disruption to energy supplies and the destabilizing effects of such disruptions to their economies and energy markets [5, 6]. Examples of such disruption include the 1973 and 1979 oil crises, the disruption of world oil supplies during the Persian Gulf wars, and the disruption of natural gas supplies to Ukraine in 2014 due to disagreements with Russia [7]. More recently concerns have emerged from energy supply and storage infrastructure due to natural disasters and terrorism. For countries such as the United States, these challenges are intricately linked to their national security. For poor countries, these challenges have undermined their prospects of economic development and constrained their efforts to alleviate poverty and improve the standards of living of their peoples. They have also had an adverse impact on the balance of payments. Addressing these challenges has therefore increasingly become the centrepiece of the energy policies of many countries where the issue is being framed as one of enhancing energy security. This chapter examines energy security with a focus on its nature and meaning, its multiple dimensions, the indicators currently being used to measure energy security, and some policy measures that can be used to enhance energy security.

## 2. Meaning of energy security

A clear conceptualization of energy security is essential for an efficient and effective pursuit of this policy goal. The literature on energy security is however characterized by widely differing and sometimes inconsistent definitions of the concept. This is partly because various authors on the subject have tended to focus on different sources of risk and conducted studies that differ in the scope of the impacts of the various risks. The International Energy Agency (IEA) that was formed in the 1970s to coordinate a robust response to disruptions to oil supplies defines energy security as the uninterrupted availability of energy sources at an affordable price. Bohi and Toman [8, 9] define energy insecurity as the loss of welfare that may occur as a result of a change in the price or availability of energy. Cherp and Jewell [10] assert that energy security is an instance of security in general and define energy security as “low vulnerability of vital energy systems”. Winzer [11] notes that energy security is commonly defined by incorporating the context. Thus, in the United States, the focus of energy security has traditionally been on the reduction of vulnerability to political extortion following the economic hardships experienced in the aftermath of the oil embargo by the Organization of Petroleum Exporting Countries (OPEC) in the 1970s. This is also the reason why policy makers in the United States strongly support the goals of energy independence and raising the shares of renewable energy. Winzer [11] further notes that in several developing countries, the goal of energy security has been to protect the poor against commodity price volatility. He defines energy security as continuity of energy supplies relative to energy demand. According to Andrews [12] and Jun et al. [13], energy security means assuring adequate, reliable supplies of energy at reasonable prices and in ways that do not jeopardize major national values and objectives. Intharak et al. [14] define energy security as the ability of an economy to guarantee the availability of energy supply in a sustainable and timely manner with the energy price being at a level that will not adversely affect economic performance. Their definition thus embodies three fundamental aspects, namely, physical energy security which is the availability and accessibility of energy supply sources; economic energy security which is the affordability of resource acquisition and energy infrastructure development; and, environmental sustainability which entails using energy resources in ways that meet the needs of the present without compromising the ability of future generations to meet their own needs [15]. According to Grubb et al. [16] and Kruyt et al. [17], security of supply is a system’s ability to provide a flow of energy to meet demand in an economy in a manner and price that does not disrupt the course of the economy. They further point out that non-secure energy systems are characterized by sharp energy price increases, reduction in quality, sudden supply interruptions, and long-term disruptions of supply. Sovacool [18, 19, 20, 21], Sovacool and Brown [22], Sovacool and Mukherjee [23], Sovacool et al. [24], Brown and Sovacool [25], and Badea et al. [26] define energy security as equitably providing available, affordable, reliable, efficient, and environmentally benign energy services to end users. Brown et al. [27] opine that energy security has to do with questions of reliable energy supplies, regional concentration of energy resources, and the implications of strategic withholding of energy. They point out specific aspects of energy security such as electricity reliability, natural gas and petroleum security, and the vulnerability of the entire energy supply chain. They also maintain that robust global coordination of responses to energy supply shock is critical to energy security. According to APERC [28], energy security consists of 4A’s namely, availability, accessibility, acceptability, and affordability.

Although the definitions of energy security provided above are not exhaustive, they all illustrate the importance of energy security, its multi-dimensional nature, and why many countries regard it as a policy priority. In the short-term, energy security concerns focus on the ability of the energy system to react promptly to sudden changes in the supply–demand balance. In the long-term, energy security concerns have to do with timely investments in energy supply in line with economic developments and environmental needs. At the multilateral and global levels, energy security has continued to receive increasing attention as evidenced by Sustainable Development Goal 7 of the United Nations that requires countries to ensure access to affordable, reliable, sustainable, and modern energy for all.

## 3. Indicators of energy security

Several indicators have been proposed for assessing the energy security risks that various countries face, how the energy security situations have been changing over time, and how energy security is impacted by the energy policies of these countries. Estimates of these indicators are valuable in developing energy security strategies that take into account countries’ energy resource endowments, market conditions, vulnerabilities to energy supply shocks, and technological progress. In what follows I present some energy security indicators, explain their use in assessing energy security, and provide energy security metrics for selected countries.

### 3.1 Energy reserves

Energy reserves refer to the estimated quantity of energy sources (e.g. coal, gas, or oil) known to exist with reasonable certainty, and which can be recovered with presently available technology at an economically viable cost. A country’s energy resources and the extent to which they are developed is an important determinant of energy security. In general, countries with vast energy resources are more energy secure compared to those with meagre energy resources. Over time, however, changes can occur that alter a country’s energy resources and thus improve or worsen its energy security. For example, the discovery of vast oil and gas resources in the North Sea had a significant impact on Norway’s economy and energy security and made Norway a rich oil-exporting country [29]. This is also the case with countries which have recently discovered new energy reserves. Table 1 presents estimates for the proved oil reserves for various geographic regions for selected years from 1980 to 2017. Estimates for natural gas are presented in Table 2.

19801990200020102017
North America123.3125.4232.1221.5226.1
South and Central America26.971.597.9325.2330.1
CIS67.058.4120.5144.5144.9
Europe16.617.520.613.413.4
Middle East362.4659.6696.7765.9807.7
Africa53.458.793.0124.5126.5
Asia Pacific33.936.340.148.048.0
World683.51027.51300.91643.11696.6

### Table 1.

Proved oil reserves in thousand million barrels 1980–2017 [30].

19801990200020102017
North America9.69.27.210.510.8
South and Central America2.85.57.38.18.2
CIS20.534.940.350.059.2
Europe4.25.24.74.43.0
Middle East24.237.258.378.279.1
Africa5.79.011.914.013.8
Asia Pacific4.59.011.114.919.3
World71.6109.3140.9180.1193.5

### Table 2.

Proved natural gas reserves in trillions of cubic metres [30].

Table 1 shows that the Middle East has the greatest quantity of proven oil reserves followed by North America. Although these two regions account for more than 50% of the world’s total proven oil reserves, this fact alone own does not confer on the regions the greatest energy security. Assessing oil security requires a consideration of additional factors such as oil production and consumption and how these are evolving over time. Table 1 also shows that over time, with the exception of Europe, several regions of the world have reported an increase in their proven oil reserves thus suggesting an improvement in oil security. The case of the United States is particularly significant given that it has in recent years considerably expanded its production and reduced its dependence on oil imports. This has been possible through the shale revolution and also through changes to regulations to permit the drilling and extraction of oil in previously proscribed areas.

Table 2 shows that the Middle East has the largest proven natural gas reserves followed by the CIS. Like the case of oil, most regions of the world have reported an increase in proven natural gas reserves from 1980 to 2017. The exception is Europe whose proven natural gas reserves have declined. The proven reserves of oil and natural gas are a good indicator of the existence or otherwise of potential that can be developed to improve the energy security.

Table 3 shows the proven reserves of coal and the reserve-to-production ratios (R/P ratios) for the various regions at the end of 2017. R/P ratios estimate the time period remaining for the different regions to exhaust their known coal stocks given the current rates of extraction, assuming no changes in existing stocks, technologies, or other policies. At the world level, the existing coal reserves can last for about 134 years. The existing coal stocks can last for periods ranging from 53 years for the Middle East and Africa to about 335 years for North America. Based on these results it can be inferred that in the short to medium term, there will be continued energy security with respect to coal availability and utilization. Although concerted efforts are currently being made to reduce the use of coal as part of measures to mitigate climate change, the use of coal will continue to be significant for certain regions of the world. It however implies that coal will play an increasingly smaller role in energy security in the coming years. This could change if significant progress in the carbon capture and storage technologies results in greater use of coal.

End of 2017R/P ratio
North America258,709335
South & Central America14,016141
CIS223,228397
Europe100,405159
Middle East and Africa14,42053
Asia Pacific424,23479
World1,035,012134

### Table 3.

Proved coal reserves in millions of tonnes and reserves to production ratio [30].

### 3.2 Energy production and consumption

Being the predominant source of energy in most of the world, the production and consumption of oil can serve as a valuable indicator of energy security. The production and consumption of oil for various regions from 1980 to 2017 is shown in Table 4 and depicted in Figures 18. At the global scale, both the production and consumption of oil have been growing over time with the oil production consistently matching the oil consumption. This implies that the world has the potential to be energy secure if robust mechanisms are implemented to facilitate the flow of oil from regions with oil surpluses to those with oil deficits. For North America, Europe and Asia Pacific, the oil consumption has consistently exceeded the oil production while for Africa, the Middle East, the CIS, and Central and South America, the oil production has over time been greater than the oil consumption. The United States has for several decades been the largest consumer of oil in the world and has relied considerably on oil imports to bridge the gap between its production and consumption of oil. This has been a major policy concern in the US and partly explains the country’s preoccupation with the goal of energy independence since the oil crises of the 1970s.

19801990200020102017
North AmericaProduction670.7654.5642.5638.6916.8
Consumption928.4923.21060.61040.51056.4
South and Central AmericaProduction194.7234.0345.0378.5368.3
Consumption170.9176.2235.1299.4317.0
EuropeProduction143.4217.9332.5196.7162.6
Consumption779.2729.4762.5734.2708.3
CISProduction603.2570.3396.4663.1699.6
Consumption421.5399.1169.1178.6196.3
Middle EastProduction934.0837.41146.91220.01481.1
Consumption93.7166.5239.0356.9404.4
AfricaProduction300.5317.0371.6481.5383.3
Consumption69.695.6118.4164.4189.3
Asia PacificProduction244.8325.9381.3403.0375.5
Consumption515.4664.2998.31302.11598.0
WorldProduction3091.33157.03616.23981.44387.1
Consumption2978.73154.13583.14076.04469.7

### Table 4.

Oil production and consumption in millions of tonnes from 1980 to 2017 [30].

The data in Table 4 also shows that the Middle East and the CIS have had the greatest oil surpluses while Europe has had the greatest oil deficit. From this broad picture that is based on aggregated regional data, we can infer that relative to other regions, Europe and Asia Pacific have the greatest oil insecurity, while the Middle East, Africa, and the CIS are the least oil insecure. In the recent past, the oil consumption in the Asia Pacific has grown rapidly due to its high population and economic growth rates.

Natural gas constitutes a significant share of the energy mix of several countries and contributes critically to their energy security. It is used for heating buildings and water, to cook, to operate refrigeration and cooling equipment, to dry clothes, to provide outdoor lighting, as a fuel in combined heat and power systems, as a fuel to operate compressors that move natural gas through pipelines, to generate electricity, and as a vehicle fuel in the form of compressed natural gas and liquified natural gas. Natural gas is also used as a raw material to produce chemicals, fertilizers and hydrogen.

Table 5 presents data on the production and consumption of natural gas in various world regions from 1970 to 2017. Figure 9 depicts the global production and consumption of natural gas over the same period. Overall, both the production and consumption of natural gas have been increasing over time with the production increasing to match the consumption.

197019801990200020102017
North AmericaProduction636.5621.4613.2728.3775.9951.5
Consumption619.5605.8607.6753.5803.0942.8
South & Central AmericaProduction18.735.360.3103.1163.8179.0
Consumption18.836.159.697.8150.1173.4
EuropeProduction104.5229.5215.5293.5289.5241.9
Consumption108.5280.7360.8484.0567.7531.7
CISProduction187.5412.2764.1661.6755.9815.5
Consumption189.5377.1632.1527.2588.7574.6
Middle EastProduction10.534.4101.8206.5481.6659.9
Consumption9.431.996.7185.6385.6536.5
AfricaProduction3.024.872.2135.1206.1225.0
Consumption1.618.739.955.7102.5141.8
Asia PacificProduction15.171.9149.3277.4496.5607.5
Consumption14.273.6152.0298.2578.3769.6
WorldProduction975.81429.61976.32405.53169.33680.4
Consumption961.41423.81948.72402.03175.93670.4

### Table 5.

Natural gas production and consumption in billions of cubic metres from 1970 to 2017 [30].

According to the data in Table 5 and Figures 10 and 11, North America, the CIS, the Middle East and Africa produced at least as much natural gas as they consumed in 2017. For the Middle East and the CIS, the natural gas production was significantly higher than the consumption making these regions important global exporters of natural gas. For Europe and Asia Pacific, the production of natural gas has tended to be significantly less than the consumption necessitating the heavy reliance of these regions on large natural gas imports to meet their demands. For the Asia Pacific region, the consumption of natural gas has in recent years been rising rapidly due to robust economic growth and the high population in the region. The situation in Europe is considerably tighter as evidenced by the fact that in 2017 the production of natural gas was less than half the amount consumed in the region thus implying a high dependence on natural gas imports. In the foreseeable future, natural gas security in Europe and the Asia Pacific region will depend on stable, well-integrated efficient natural gas markets that can ensure adequate, reliable and affordable supplies.

The shortage of natural gas in China in the winter of 2017 is a recent example of how the demand and supply of natural gas can impact energy security. The primary cause of the shortage was China’s decision to curb reliance on dirty coal so as to reduce urban air pollution and improve the overall quality of the environment. This shift in policy triggered an increase in the demand for natural gas and a rise in its price not only to consumers in China but also for other natural gas importers [31, 32]. The shortage of natural gas in China and the spike in its price occurred despite a glut in global supply and was due to infrastructure and logistical constraints. Achieving natural gas security therefore requires not only initiatives aimed at boosting natural gas production, but also complementary measures such as increased investments in distribution infrastructure and improving LNG shipping capacity.

Electricity is critically important to most economies around the world and its role is expected to increase in the future as countries pursue the goal of decarbonizing their power sectors. Electricity is also important in efforts to eliminate poverty and transform the world into a safe, equitable and environmentally sustainable place [33]. Today, however, many countries are facing massive challenges in electricity security due to rapidly increasing demand and supply constraints. Table 6 shows the production and consumption of electricity for various regions from 1990 to 2017. With the exception of the CIS where the electricity production fell by about 7% between 1990 and 2017, in all other regions electricity production increased with the greatest percentage increase being in Asia (400%) and the Middle East (387.7%).

1990200020102017% Change
North AmericaProduction370146584982496334.1
Consumption314640934415437939.2
Latin AmericaProduction60598213751590162.8
Consumption50678811291312159.3
EuropeProduction290034383865388634.0
Consumption251629523377337734.2
CISProduction1676125014831566−6.6
Consumption1417100012031257−11.3
Middle EastProduction2444728921190387.7
Consumption213400742977358.7
AfricaProduction319446675818156.4
Consumption263379554663152.1
AsiaProduction22594024798311,274399.1
Consumption1923336968699777408.4
PacificProduction19025330230460.0
Consumption16521826527365.5

### Table 6.

Electricity production and consumption in terawatt Hours (TWH) from 1970 to 2017 [30].

The consumption of electricity has been increasing rapidly in most part of the world with the main drivers being industrial and economic growth, and population increase. Figure 12 depicts the consumption of electricity for the various regions in 1990 and 2017. It is evident from Figure 12 that the greatest absolute increase in electricity consumption over this period occurred in Asia where electricity consumption increased by 408.4% from 1923 TWH to 9777 TWH. Most of the growth in electricity consumption in Asia occurred in China, India, and Japan. Over the 1990–2017 period, the electricity consumption in China increased from 534 TWH to 5683 TWH; that in India increased from 215 TWH to 1156 TWH; and, that in Japan increased from 781 TWH to 1019 TWH. These increases in electricity consumption occurred despite strong energy efficiency improvements.

The electricity production and consumption data for the various regions for 2017 that is plotted in Figure 13, shows that although both electricity production and consumption have been increasing over time, the production of electricity exceeded its consumption. Therefore, the inference can be made that at the regional level, potential exists for achieving electricity security in the short to medium term. The broad picture presented in Figure 13 masks the electricity supply and demand conditions in specific countries and how the electricity is produced and consumed in those countries. It also masks the fact that due to grid and storage losses, not all of the electricity produced is available for consumption.

At particular times, specific countries or regions often have imbalances in their demand and supply of energy that are met through imports and exports. Whether a country is a net importer or exporter of energy is indicated by their energy trade balance that is computed as the difference between energy imports and exports. Countries that are net energy exporters have negative energy trade balances while net energy importers have positive energy trade balances. Based on energy trade balances, it can be inferred that regions with positive energy trade balances are more energy insecure compared to those with negative energy trade balances. Figure 14 depicts the energy trade balances for various regions for 2017 and shows that the largest energy net importers were Asia and Europe and the largest net exporters were the Middle East and the CIS. Europe’s energy security situation is precarious because of dwindling energy supplies that have necessitated increasing reliance on energy imports. Importation of less expensive energy into Europe from regions such as the Middle East is a more attractive option compared to more costly efforts to develop the region’s own energy resources. As producers of large quantities of cheap energy, the Middle East and the CIS will continue to play a significant role in the global energy scene in the short to medium term. It is worth noting that several major changes are currently occurring in global energy markets and that these changes will have profound implications on energy security in the coming years. An example of such a change is the increase in energy production in the United States that has changed the country’s status from a net energy importer to a net energy exporter.

### 3.4 Energy prices

In general, energy prices are determined by the supply and demand conditions in energy markets and also by the policies and regulations such as taxes and subsidies that governments may make to regulate these markets and achieve particular outcomes. Energy prices are an important indicator of energy security to the extent that they embody information about energy scarcity and energy affordability and also play a central role in energy investment decisions. The crude oil prices from 1970 to 2017 are depicted in Figure 15. Although the crude oil prices have fluctuated widely over this period, the general trend has been upward. In 1973 the world oil market was significantly impacted by the oil embargo by the Organization of Petroleum Exporting Arab Countries (OPEC) that drastically reduced the supply of oil at a time when the demand for oil was increasing. This action resulted in the price of oil rising from US$3 to US$ 12 globally. World oil supplies were again adversely affected in 1979 in the aftermath of the Iranian Revolution and oil prices increased rapidly from $13 per barrel in mid-1979 to about$34 per barrel in mid-1980. Both these oil shocks threated the energy security of oil-importing countries, reduced economic activity, and increased inflation.

In several developing countries, a significant fraction of the population cannot access modern energy due to the high energy prices. In Kenya, for example, where the majority of the population use Kerosene for cooking and lighting, the price of kerosene has recently risen rapidly thus inducing low income households to reduce their use of kerosene and shift towards wood fuel. Although liquefied natural gas is available, its high price has limited its use to medium and high-income households. Further energy price increases can be expected as energy markets are increasingly deregulated and energy subsidies eliminated. To the extent that these measures reduce energy affordability, they have an adverse effect on household energy security. This brief discussion of energy prices underscores the fact that a strong correlation exists between energy prices and energy security and that, in general, energy security will be compromised when energy prices are rising rapidly. These broad conclusions can be extended to other energy sources such as electricity and natural gas.

### 3.5 Energy diversity

All else equal, economies that depend on a limited portfolio of non-renewable energy sources are less energy secure compared to those endowed with an abundance of diverse energy supplies [34]. Energy systems that are diverse are more resilient and adaptable to shocks in energy supplies. The Russian-Ukrainian gas crisis is an example of the vulnerability that can result from dependence on a single supplier of energy. In January 2006 following disagreements about the price of natural gas and the cost of transit, Russia cut off all gas supplies passing through Ukraine thus adversely affecting several European nations. In January 2009, disagreements about natural gas price again resulted in the disruption of natural gas supplies from Russia to 18 European nations. The severity of this threat to Europe’s energy security stems from the fact that Russia provides about 25% of the natural gas consumed in the European Union and that approximately 80% of natural gas exports from Russia to the European Union are through pipelines across Ukraine. The Southern Gas Corridor (SGC) was started as a response to the overdependence of many countries in Central and South East Europe on Russia to meet most or all of their natural gas requirements. The overarching goal of the SGC was to enhance EU’s energy security by diversifying the routes and sources of gas supplies to the EU [35, 36]. This strategic objective has been achieved through the construction of a system of pipelines that can bring natural gas from the Caspian Basin, Central Asia, the Middle East, and the Eastern Mediterranean Basin into Europe thus reducing the dependence on Russian natural gas supplies [35].

The contribution of diversity to energy security also applies to other domains such as transportation fuels and the generation of electricity. In the transportation sector, the fuels that are mostly used are gasoline and diesel due to their high energy content. Some measures that are currently being undertaken to enhance transportation energy security are developing and promoting the use of alternative fuels such as ethanol, natural gas, biodiesel, hydrogen, propane, methanol and electricity (as in the case of battery-powered electric and fuel-cell vehicles). In addition to reducing dependence on fossil fuels, the use of these alternative fuels has been cited as having the potential to drastically lower the emissions of greenhouse gases and thus mitigate the risk climate change. There are however several controversies associated with the increased use of alternative transportation fuels as a strategy for diversifying the energy mix. For example, the simulation model developed by Chen et al. [37] shows that although promoting greater production of food-based biofuels reduces overall fossil fuel use, it leads to a marginal reduction in the global greenhouse emissions, and a large increase in food prices. Flynn [38] noted that the adoption of compressed natural gas as an alternative transportation fuel in Canada and the United States had been slow and below the critical level which would enable suppliers to survive in a competitive market. The reasons for this outcome include the high cost of hybrid cars relative to conventional cars, the lack of infrastructure to support converted vehicles, lack of refuelling facilities, and the failure of existing refuelling stations to achieve profitability.

Diversifying electric power generation is an area that several countries are increasingly focusing on to enhance their overall energy security. It is driven by the increase in the demand for electricity due to factors such as population growth, greater use of electrical appliances and equipment, and the need reduce emissions of greenhouse gases. In a country such as the United States, the main energy sources for electric power generation are coal, natural gas, nuclear power and hydro. The amounts of electricity produced from these sources are shown in Figure 16. Although coal and nuclear power have dominated electricity production, a significant change has occurred leading to reduced use of these fuels for electricity production and greater use of natural gas that is cheaper, cleaner, and more abundant.

### 3.6 Share of renewable energy

In general, economies that depend on a limited portfolio of non-renewable energy sources are less energy secure than those that are endowed with abundant renewable energy sources. Renewable energy resources are attractive because their supplies are unlimited and inexhaustible so that, unlike non-renewable sources, their consumption today does not reduce the flows available in the future. If adequately developed, they can substitute for non-renewable energy and underpin the transition needed in the energy system to sustainably power economic growth and ameliorate the threat of climate change. Some of the common renewable energy resources that can be harnessed to improve energy security are biomass, hydropower, solar, wind, and geothermal energy. Presently, increasing the share of renewables in the final energy consumption is a policy priority of many countries as evidenced by the European Union’s goal of generating 20% of its electricity from renewables by 2020 [39]. Similarly, the United States has regulations (known as the renewable portfolio standard or renewable electricity standard) obligating electricity supply companies to produce a specific fraction of their electricity from renewable energy sources [40]. In Germany, the Renewable Energy Act mandates that 35% of electricity be produced from renewable sources in 2020 and that this share be increased to 80% by 2050. Table 7 presents data on the consumption of renewables in the US electric power sector from 1984 to 2018. Over this period, the US electric power sector experienced a significant increase in the use of renewables with wind and solar playing a dominant role. The data in Table 7, shows that in 2000, the share of wind and solar in the renewables used to produce electricity was only 2% and that this increased to 49% in 2018. The combined use of wind and solar in electricity production in the US is shown in Figure 17 and the combined share of wind and solar in the total renewable energy used in the electric power sector is shown in Figure 18. The increased use of wind and solar energy has been facilitated by technological innovation and has not only contributed to the diversification of the energy system but also provided several other benefits such improvement in health, savings from reduced fossil use, reduced emissions of greenhouse gases, industrial growth, and the creation of thousands of clean manufacturing jobs. Further growth in the use of wind and solar power can be expected in the future as the market costs of these technologies continue to fall and as progress is made to overcome the challenges of intermittency.

HydroGeothermalSolarWindWoodWasteBiomassTotal renewable
19843352.8180.810.060.074.824.439.253442.99
19903014.01160.553.8229.01128.52187.99316.513523.89
19953149.39137.965.1232.63125.41296.25421.663746.77
20002767.92143.765.0357.06134.32318.43452.753426.52
20052670.13146.905.50178.09184.97220.72405.703406.32
20102521.49148.4811.76923.27195.60263.78459.374064.37
20152307.72148.34227.901775.71243.86281.02524.884984.54
20182672.51153.81606.972530.41215.11280.03495.146458.83

### Table 7.

Renewable energy use in US electric power sector in trillion of Btu [30].

## 4. Policy instruments for improving long-term energy security

Energy resources are indispensable to all economies where they are used to power economic growth and to provide households with critical services such as heating, lighting, cooking, and operating equipment and appliances. A secure energy system is vital in averting the economic, social, and political disruptions that can occur if supplies are interrupted [41]. Energy insecurity can precipitate a loss in welfare as a result of the physical unavailability of energy or prices that are volatile and not competitive [41, 42]. Due to the interdependence that characterizes today’s energy markets, considerable scope exists for countries to coordinate their energy strategies to reduce their vulnerabilities to energy shocks and improve their overall energy security. Some measures that are currently being used to improve energy security include:

1. Investments in energy resources and infrastructure: Countries and/or regions can improve their energy security by undertaking investments that promote exploration, extraction, processing, transportation, and marketing of energy resources. One of the objectives of these initiatives is to upgrade existing energy infrastructure and develop new transmission infrastructure that is crucial to energy security. This is occurring in several regions such as the United States, Africa, and the Caspian Basin. In the United States, for example, previously restrictive regulations have been amended to allow offshore drilling in the Gulf of Mexico, horizontal drilling, hydraulic fracturing, and the drilling for oil and natural gas in the Arctic National Wildlife Refuge in Alaska. These measures have resulted in a substantial increase in oil and natural gas production in the United States and reduced the country’s dependence on energy imports. Pipeline projects from the Caspian Basin have also contributed to increasing the supply of oil and natural gas to Europe and Asia. In Africa, the energy infrastructure projects that have recently been commissioned include the Grand Inga Dam in the Democratic Republic of Congo that will produce about 40,000 MW of electricity when completed; the Rusumo Falls Hydroelectric Project in Rwanda that aims to supply about 80 MW of power to Rwanda, Tanzania and Burundi; the Lake Turkana wind power project in Kenya that will provide the country’s national grid with about 300 MW of clean power; and, the Jasper Power project in the Northern Cape of South Africa that aims to generate 18 GW of clean energy by 2030. The successful completion of these and similar projects will increase the overall energy supply and enhance energy security.

2. Investments in energy efficiency: Energy efficiency is an important instrument for stemming the growth in energy demand, providing households and firms with cost savings due to reduced energy use, and reducing the emissions of greenhouse gases [43, 44]. According to the International Energy Agency, energy efficiency is the world’s most available, secure and affordable energy resource that every government has the power to exploit for widespread benefit [44]. To the extent that energy efficiency actions such as retrofitting homes, adopting more stringent building codes, increasing the fuel economy of vehicles, and adopting more productive technologies in industries reduce energy demand and consumption, they contribute towards the goal of energy security [45]. It is estimated that between 2000 and 2017, improvements in energy efficiency saved an additional 37 exajoules of final energy use in the IEA countries and other major economies and that globally, over this period, efficiency improvements prevented about 12% more energy use [46]. The fact that energy efficiency potential is vast and has not been fully utilized in many countries implies that it is a strategy that can be cost-effectively used to improve energy security. This will entail identifying the barriers to the implementation of energy efficiency programs and addressing these barriers through appropriate policy actions [43].

3. Energy diversification: Countries can enhance their energy security by diversifying the types of energy carriers that their economies depend on and also the sources of their energy supply. Kruyt et al. [17] regard diversification as critical to energy security because the increasing global demand for energy can over time lead to the depletion of currently known energy resources. Yergin [6] notes that energy diversification enhances energy security by allowing societies to absorb shocks in one energy input by increasing the use of other energy inputs. Li [47] asserts that diversifying a country’s energy system is vital not only for mitigating the risks that arise from over-reliance on fossil fuels, but also for achieving the goal of sustainable development. Trinidad and Tobago are an example of a country whose primary energy supply is not diverse and consists of 72.3% natural gas and 27.7% crude oil. Canada, in contrast, has a diverse energy mix consisting of natural gas, oil, coal, hydropower, nuclear and others and is therefore much less prone to shortages and price shocks because it is unlikely that these systems would all fail at the same time. Having multiple sources of energy enables countries to continue without disruption if one of the energy sources failed. Over the medium to long-term, Trinidad and Tobago can diversify their energy mix by developing and harnessing their vast potential for wind and solar power.

4. Technological innovation: Technological innovation, like energy efficiency, is a valuable instrument that countries can use to mitigate climate change and enhance their overall energy security. Kim [48] cites Germany and Japan as examples of countries that are not well endowed with vast oil reserves, but which have invested heavily in alternative energy technologies especially in the transportation sector. These technologies include fuel cells and electric and hybrid vehicles that are increasingly being adopted as a response to the high gasoline prices. Lin and Chen [49] and Lin and Zhu [50] argue that technological innovation is key in developing renewable energy and promoting the transition to a low-carbon economy. Denholm and Hand [51] advance a similar argument and assert that increased grid flexibility and energy storage are critical innovations that are required to achieve high penetration of wind and solar energy. They further claim that in the United States, the limits of wind and solar energy are not resource based; that wind and solar resources are significantly greater than the total electric demand; and, that the primary technical challenge is the resource intermittency that can be addressed through technical innovations that enable energy storage.

The availability of vast supplies of fossil energy resources implies that their increased utilization is a viable strategy that can be used to meet the rising demand for energy and enhance energy security. This option is however not favoured by policy makers who claim that it is likely to increase emissions of carbon dioxide and undermine efforts to mitigate climate change [52]. Carbon capture and storage is a technological innovation that can permit an increase in the use of fossil fuels but curtail the release of stationary carbon dioxide emissions into the atmosphere [53]. According to the IEA [54], more investment needs to be made in carbon capture and storage that has been demonstrated to be a low-cost technological pathway that can help achieve deep decarbonization, promote greater energy security, support diversity of power generation and enhance economic prosperity and employment.

5. Market and institutional reforms: Several countries are currently reforming their energy markets to improve security of supply by incentivising investments in secure, low-carbon energy sources; improving efficiency and productivity; supporting cost-effective integration of renewable energy sources; and, improving affordability for consumers [55, 56, 57]. Some of the issues that these reforms aim to address are: inadequate electricity generation and distribution infrastructure when electricity demand is growing rapidly [55, 57]; underutilization of cheap resources and overutilization of expensive resources; unnecessary curtailment of renewable energy; existence of barriers to minimizing the cost of power due to inability of energy distribution companies to access all available power generation and the associated marginal costs; lack of flexibility in the energy system; heavy and restrictive regulations that impose costs and hinder innovation; and distortions in energy markets. Examples of reforms that various countries have implemented to address these issues include: liberalization of the downstream gas market in Egypt to end government monopoly, increase competition, and attract foreign direct investment to the energy sector [58]; deregulation of energy prices in China to optimize energy allocation, improve energy efficiency, promote the penetration of renewable energy, and induce energy-saving technologies and innovations [59]; and, expansion of cross-border electricity cooperation and trade through establishment of regional electricity grids in South Asia [60]. Where reforms have been properly designed and implemented, they have increased competition in energy markets, reduced energy prices to consumers, stimulated technological and structural change, increased the share of renewable energy in the energy mix, increased the reliability of the energy system, reduced power outages, increased investment in the energy sector, and improved energy security [16].

## 5. Conclusions and implications

Energy resources play a critical role in economic growth and human wellbeing and will continue to be a key concern to policy makers in both developed and developing countries. How energy is produced and used will also continue to be of national and global concern because greenhouse gas emissions from these processes are the primary cause of global warming and climate change. The rapid growth in the demand for energy in recent years due to robust economic expansion, population growth, and new uses of energy is a major challenge that requires policy actions to ensure that energy users have access to reliable, affordable, and secure energy supplies. It is a problematic situation to countries that are not endowed with abundant energy resources and must rely on energy imports. There are however several strategies that countries can implement individually or jointly to improve their energy security. First, agricultural by-products and crop residues such as maize stalks, rice straw, cattle dung, molasses and bagasse can be harnessed and used to produce energy products such as methane which can be used for cooking, heating and lighting [61]. These processes can also be used to produce alcohol which can be used to blend automotive fossil fuels. Energy security can be positively impacted by these measures because they expand the supplies of available energy resources and reduce the demand for conventional energy. Second, countries can increase their energy security by harnessing renewable energy such as wind, solar, and geothermal energy and integrating them into the energy system. This alternative holds considerable promise particularly in regions such as North Africa and the Middle East. Third, through investments in energy efficiency, countries can reduce their demand for energy and enhance their energy security. This can be accomplished through more stringent building codes, market penetration of hybrid and electric cars that have greater fuel economy, and real-time pricing of electricity. Fourth, energy security can be greatly enhanced by improving the performance of energy markets through deep reforms and institutional changes. If properly designed and implemented, the reforms can reduce wastage, incentivise private sector investment in energy generation, increase competition in energy markets reducing the prices to consumers, and improve overall efficiency. Fifth, global energy security can be enhanced through international cooperation on energy issues and the promotion of regional energy trade. Such trade will be a win-win outcome for both exporters and importers of energy.

chapter PDF
Citations in RIS format
Citations in bibtex format

## More

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## How to cite and reference

### Cite this chapter Copy to clipboard

Collins Ayoo (May 15th 2020). Towards Energy Security for the Twenty-First Century, Energy Policy, Tolga Taner, IntechOpen, DOI: 10.5772/intechopen.90872. Available from:

### Related Content

#### Energy Policy

Edited by Tolga Taner

Next chapter

#### Proton Exchange Membrane Fuel Cell

Edited by Tolga Taner

First chapter

#### Introductory Chapter: An Overview of PEM Fuel Cell Technology

By Tolga Taner

We are IntechOpen, the world's leading publisher of Open Access books. Built by scientists, for scientists. Our readership spans scientists, professors, researchers, librarians, and students, as well as business professionals. We share our knowledge and peer-reveiwed research papers with libraries, scientific and engineering societies, and also work with corporate R&D departments and government entities.

View all Books


text:
### Efficient Zero-Knowledge Proof of Algebraic and Non-Algebraic Statements with Applications to Privacy Preserving Credentials

Melissa Chase, Chaya Ganesh, and Payman Mohassel

##### Abstract

Practical anonymous credential systems are generally built around sigma-protocol ZK proofs. This requires that credentials be based on specially formed signatures. Here we ask whether we can instead use a standard (say, RSA, or (EC)DSA) signature that includes formatting and hashing messages, as a credential, and still provide privacy. Existing techniques do not provide efficient solutions for proving knowledge of such a signature: On the one hand, ZK proofs based on garbled circuits (Jawurek et al. 2013) give efficient proofs for checking formatting of messages and evaluating hash functions. On the other hand they are expensive for checking algebraic relations such as RSA or discrete-log, which can be done efficiently with sigma protocols. We design new constructions obtaining the best of both worlds: combining the efficiency of the garbled circuit approach for non-algebraic statements and that of sigma protocols for algebraic ones. We then discuss how to use these as building-blocks to construct privacy-preserving credential systems based on standard RSA and (EC)DSA signatures. Other applications of our techniques include anonymous credentials with more complex policies, the ability to efficiently switch between commitments (and signatures) in different groups, and secure two-party computation on committed/signed inputs.

Available format(s)
Publication info
Keywords
zero knowledgegarbled circuitsanonymous credentials
Contact author(s)
melissac @ microsoft com
chaya ganesh @ gmail com
payman mohassel @ gmail com
History
Short URL
https://ia.cr/2016/583

CC BY

BibTeX

@misc{cryptoeprint:2016/583,
author = {Melissa Chase and Chaya Ganesh and Payman Mohassel},
title = {Efficient Zero-Knowledge Proof of Algebraic and Non-Algebraic Statements with Applications to Privacy Preserving Credentials},
howpublished = {Cryptology ePrint Archive, Paper 2016/583},
year = {2016},
note = {\url{https://eprint.iacr.org/2016/583}},
url = {https://eprint.iacr.org/2016/583}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.

format: plain


text:
## Sunday, December 28, 2008

### Windows Movie Maker: unspecified error

I couldn't run Movie Maker 2.1. It immediately gave me an "Unspecified Error" popup message. Movie Maker 2.6 behaved in the same way. I learned that it worked fine for other users.

It turned out that the temporary directory got wrong read-only file permissions - who knows why.

A fix: Go to Start / Accessories / Command Prompt, right-click this program, Run [it] as administrator. Get to your user directory and change the attributes by the attrib command:
cd c:\users\lubos\appdata\local
attrib -r +a -s -h Temp
The path is designed for Vista: replace "lubos" by your user name. For XP, "Users" becomes "Documents and Settings" while "Local" becomes "Local Settings". If the tip works for you, leave a comment here.

1. Worked perfectly, thank you

2. hi... can u teach me how to do it...
my windows player have some files are missing... n d movie maker -- unspecified error... email me please... yingyin86@yahoo.com thanks....

3. Worked great!! I tried and tried to fix it and nothing worked!

4. what is the meaning of attrb -r +a... in ur post above?I still don't know how to solve the prob...can u explain?

5. Dear Azmir, attrb is a DOS command. But you didn't even need to know that. I am afraid that if the instructions above are not clear to you, the answer to your question is No. Please ask someone who has already used a computer before to help you.


text:
# Chapter 9 - Impulse and Momentum - Conceptual Questions: 9

After the impulse, the object's speed is 3 m/s to the right.

#### Work Step by Step

The change in momentum of an object is equal to the impulse exerted on the object. The final momentum is equal to the initial momentum plus the impulse $J$. $p_f = p_0+J$ $p_f = m~v_0+J$ $p_f = (2~kg)(1~m/s)+4~N~s$ $p_f = 6~N~s$ We can find the final velocity of the object. $p_f = 6~N~s$ $m~v_f = 6~N~s$ $v_f = \frac{6~N~s}{m}$ $v_f = \frac{6~N~s}{2~kg}$ $v_f = 3~m/s$ After the impulse, the object's speed is 3 m/s to the right.

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:
# Adding and Subtracting Polynomials Worksheet

• Page 1
1.
Simplify the expression (4$x$2 - 3$x$) - (2$x$2 + 2$x$), using algebra tiles to model the expression.
 a. 2$x$2 - $x$ b. 2$x$2 - 5$x$ c. 2$x$2 + 5$x$ d. 3$x$2 + 5$x$

2.
Simplify the expression (2$x$2 + 3$x$) - ($x$2 + 2$x$) using algebra tiles.
 a. 2$x$2 + 3$x$ b. 3$x$2 + 5$x$ c. $x$2 - $x$ d. $x$2 + $x$

3.
Simplify the expression (4$x$2 - 3$x$) - (2$x$2 + 2$x$), using algebra tiles to model the expressions.
 a. 2$x$2 - $x$ b. 2$x$2 + 5$x$ c. 2$x$2 - 5$x$ d. 3$x$2 + 5$x$

4.
Simplify ($x$2 - 5) + (3$x$2 + 2$x$) using algebra tiles.
 a. 2$x$2 + 4$x$ - 5 b. 4$x$2 + 2$x$ + 5 c. 4$x$2 + 2$x$ - 5 d. 2$x$2 + 5

5.
Identify the simplified expression for the perimeter of the triangle using algebra tiles.

 a. 11$x$2 + 4$x$ b. 11$x$ + 4 c. 11$x$ - 4 d. 9$x$ + 5

6.
Express the perimeter of the figure as a polynomial.

 a. 2$y$2 + 2 b. 4$y$4 + 2 c. 6$y$ + 2 d. 6$y$ - 6

7.
Add the two polynomials 5$y$3 - 5$y$2 + 4$y$ - 6 and 6$y$ + 6$y$2 - 7.
 a. 5$y$3 + $y$2 + 10$y$ - 13 b. 5$y$3 - $y$2 + 10$y$ - 13 c. 5$y$3 + $y$2 + 10$y$ + 13 d. 5$y$3 - $y$2 - 10$y$ + 13

8.
Subtract the polynomial 6$y$ - 6$y$2 - 4 from 10$y$ + 6 - 3$y$2.
 a. - 3$y$2 - 4$y$ - 10 b. - 3$y$2 + 4$y$ + 10 c. - 3$y$2 + 4$y$ - 10 d. 3$y$2 + 4$y$ + 10

9.
Subtract the polynomial 16$y$2 from 21$y$2.
 a. 5$y$2 b. - 5$y$2 c. 37$y$2 d. 8$y$2

The volume of a cube is (4$x$3 + 8) m3. A smaller cube with volume ($x$3 + 4) m3 is cut out of the cube. Identify a polynomial for the remaining volume.
 a. (3$x$3 + 12) m3 b. 8 m3 c. (5$x$3 +12) m3 d. (3$x$3 + 4) m3


text:
[This article was first published on R – Statisfaction, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Hi,

Just to play a bit with the gganimate package, and to celebrate National Coupling Day, the above plot shows different couplings of two univariate Normal distributions, Normal(0,1) and Normal(2,1). That is, each point is a pair (x,y) where x follows a Normal(0,1) and y follows a Normal(2,1). Below I’ll recall briefly how each coupling operates, in the Normal case. The code is available at the end of the post.

To create the plots, x-values were drawn from a Normal(0,1) distribution and kept fixed. Only the y-values change from a coupling to the next.

The optimal transport coupling is the simplest here. The y-values are simply defined by y = x + 2, i.e. they are translated by 2, the difference between the means of Normal(0,1) and Normal(2,1). It leads to the smallest expected value for the distance between y and x, over all couplings of the given Normals. The multivariate Normal case is well explained in this blog post by Djalil Chafaï.

The reflection coupling is also simple. Each point is reflected with respect to the midpoint between the means. Here it just amounts to defining y = 2 – x. Reflection couplings can be used to study stochastic processses, for instance multivariate diffusions as in this important 1986 paper by Lindvall and Rogers, and this more recent one by Eberle in 2016.

A variant of the reflection coupling, termed “reflection-maximal” coupling in the above plot, appears in this recent study of Hamiltonian Monte Carlo by Bou-Rabee, Eberle and Zimmer. It’s a maximal coupling with a reflection element to it (see Eq. (15) in that article for a precise definition). Essentially, there is an attempt at accepting x as a draw from a Normal(2,1). If this does not succeed, then y is defined as 2 – x (a reflection). The procedure is a maximal coupling because the probability of the event {x = y} is maximal over all possible couplings.

Finally the coupling referred to as “maximal coupling” in the plot is obtained with the procedure described in this earlier post. It is also a maximal coupling (these are not unique), but the distribution of y given that “y is not x” is independent of x.

That’s it! The code is below.

library(ggplot2)
library(gganimate)
set.seed(1)

# normal means
mu1 <- 0
mu2 <- 2
# std deviation
sigma <- 1
# number of samples
nsamples <- 1000
# reflection-maximal coupling
reflmax_samples <- matrix(nrow = nsamples, ncol = 2)
# draw x components first
reflmax_samples[,1] <- rnorm(nsamples)
# this follows the notation of Bou-Rabee et al, 2018, roughly
z <- mu1 - mu2
normz <- sqrt(sum(z^2))
e <- z / normz
utilde <- runif(nsamples, 0, 1)
accepts <- (log(utilde) < (dnorm(e * reflmax_samples[,1] + normz, 0, 1, log = TRUE) - dnorm(e*reflmax_samples[,1], log = TRUE)))
eta <- reflmax_samples[,1]
eta[accepts] <- reflmax_samples[accepts,1] + z
eta[!accepts]<- reflmax_samples[!accepts,1] - 2 * (e * reflmax_samples[!accepts,1]) * e
reflmax_samples[,2] <- mu2 + eta

df <- data.frame(coupling = rep("reflection-maximal", nsamples), x = reflmax_samples[,1], y = reflmax_samples[,2])

# reflection coupling
refl_samples <- matrix(0, nrow = nsamples, ncol = 2)
refl_samples[,1] <- reflmax_samples[,1]
refl_samples[,2] <- (mu2-mu1)-refl_samples[,1]

df <- rbind(df, data.frame(coupling = rep("reflection", nsamples), x = refl_samples[,1], y = refl_samples[,2]))

# optimal transport coupling
transport_samples <- matrix(0, nrow = nsamples, ncol = 2)
transport_samples[,1] <- reflmax_samples[,1]
transport_samples[,2] <- mu2 - mu1 + transport_samples[,1]

df <- rbind(df, data.frame(coupling = rep("optimal transport", nsamples), x = transport_samples[,1], y = transport_samples[,2]))

# max coupling
max_samples <- matrix(0, nrow = nsamples, ncol = 2)
max_samples[,1] <- reflmax_samples[,1]
dp <- function(x) dnorm(x, mean = mu1, sd = 1, log = TRUE)
dq <- function(x) dnorm(x, mean = mu2, sd = 1, log = TRUE)
rq <- function(n) rnorm(n, mean = mu2, sd = 1)
for (isample in 1:nsamples){
x <- max_samples[isample,1]
if (dp(x) + log(runif(1)) < dq(x)){
max_samples[isample,2] <- x
} else {
reject <- TRUE
y <- NA
while (reject){
y <- rq(1)
reject <- (dq(y) + log(runif(1)) < dp(y))
}
max_samples[isample,2] <- y
}
}
df <- rbind(df, data.frame(coupling = rep("maximal", nsamples), x = max_samples[,1], y = max_samples[,2]))

## Scatter plots and marginals
# ggplot(df, aes(x=x, y=y, group = coupling, colour = factor(coupling))) +
# geom_point()+
# theme_minimal() + viridis::scale_color_viridis(discrete=T)
#
# ggplot(df, aes(x=x, group = coupling, fill = factor(coupling))) + geom_histogram(aes(y = ..density..), position = position_dodge()) +
# theme_minimal() + viridis::scale_fill_viridis(discrete=T)
#
# ggplot(df, aes(x=y, group = coupling, fill = factor(coupling))) + geom_histogram(aes(y = ..density..), position = position_dodge()) +
# theme_minimal() + viridis::scale_fill_viridis(discrete=T)

# gganimate

ggplot(df, aes(x = x, y = y)) + xlim(-4, 4) + ylim(-5, 6) +
geom_point()+ geom_text(data = data.frame(coupling = unique(df\$coupling)), aes(label = coupling, x = -1, y = -4), size = 10) +
theme_minimal() +
transition_states(coupling, 3, 1)

To leave a comment for the author, please follow the link and comment on their blog: R – Statisfaction.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

# Never miss an update! Subscribe to R-bloggers to receive e-mails with the latest R posts.(You will not see this message again.)

Click here to close (This popup will not appear again)


text:
In the verge of coronavirus pandemic, we are providing FREE access to our entire Online Curriculum to ensure Learning Doesn't STOP!

# Ex.10.5 Q1 Practical Geometry Solution- NCERT Maths Class 7

Go back to  'Ex.10.5'

## Question

Construct the right angled $$ΔPQR$$, where $$m∠Q = 90^\circ$$, $$QR = 8 \rm{cm}$$ and $$PR = 10\, \rm{cm}.$$

Video Solution
Practical Geometry
Ex 10.5 | Question 1

## Text Solution

What is known?

Length of two side of a right angled $$ΔPQR$$.

To construct:

A right angled $$ΔPQR$$, where $$∠Q = 90^\circ$$, $$QR = 8 \rm{cm}$$ and $$PR = 10\, \rm{cm}.$$

Reasoning:

To construct a right-angled $$ΔPQR$$, where $$∠Q = 90^\circ$$, $$QR = 8\,\rm{cm}$$ and $$PR = 10 \,\rm{cm}$$, draw a rough sketch and mark the measures. Remember to mark the right angle and follow the steps given below.

Steps:

Steps of construction :

1. Draw $$QR$$ of length $$8\, \rm{cm}.$$
2. At $$Q$$, draw $$QX\,\text{perpendicular}\,QR.$$
3. With $$R$$ as centre, draw an arc of radius $$10\,\rm{ cm}$$ which should intersect $$QX$$ at point $$P$$.
4. Join $$P$$ and $$R$$.

$$ΔPQR$$ is the required triangle.

Learn from the best math teachers and top your exams

• Live one on one classroom and doubt clearing
• Practice worksheets in and after class for conceptual clarity
• Personalized curriculum to keep up with school


text:
Select Page

# Cheenta. passion for mathematics.

Pause for a moment. Let us divide letters by letters!

What if you wanted to divide the base by an exponent? This situation comes up quite often in Elementary Number Theory. Consider the following equation:

$$\displaystyle{ k! + 48 = 48 \times (k+1)^m }$$

Can you show that k divides m? The answer is hidden somewhere in our library articles.

#### What is Cheenta?

Cheenta delivers outstanding programs in Mathematics for Olympiads, I.S.I. & C.M.I. Entrance and College.

Since 2010, we have worked with hundreds of students from India, United States, UK, Australia, Singapore and Middle East

All of our classes are delivered exclusively live and online. Our main center in Calcutta (India) office hosts a reading facility for advanced learners.

#### Who are Teaching?

We have ex-Olympians and outstanding researchers who teach out of love for the subject.

In India: Indian Statistical Institute, Chennai Mathematical Institute, IISER, TIFR, Calcutta University, IIT KGP

Outside India: the University of Wisconsin Milwaukee (USA), University of North Carolina (USA), St. Louis University (USA), IMPA (Brazil), E’Cole (France)

Admission to a Cheenta program is highly selective. The prospective student must first go through a trial class.

Our courses are significantly more intense than regular school or college programs. Apply only if you are thrilled by the beauty of mathematics.

Math Olympiad, I.S.I. Entrance and College Mathematics candidates form the core student body of Cheenta.

## Stories in Real Analysis – Inverse Maps

Inverse maps are very important in Real analysis. They form the backbone of the definition of continuity. We explore one of it’s properties.

## RMO 2018 Tamil Nadu Problem 3 – Nonlinear Diophantine Equation

RMO 2018 Tamil Nadu Problem 3 Sequential Hints and Solution. A number theory problem with a pinch from diophantine equation.

RMO 2018 Tamil Nadu Problem 2 Sequential Hints and Solution. A polynomial problem with seasoning from geometric progression.

## RMO 2018 Tamil Nadu Problem 1 – angle bisector

RMO 2018 Tamil Nadu Problem 1 Sequential Hints and Solution. A beautiful geometry problem that uses properties of cyclic quadrilaterals.

## RMO2018 Tamil Nadu Solutions and Problems

Regional Math Olympiad (Tamil Nadu Region, 2018) Problems, Sequential Hints and Discussion.

## Golden Ratio and Right Triangles – when geometry meets number theory

The golden ratio is arguably the third most interesting number in mathematics. We explore a beautiful problem connecting Number Theory and Geometry.

## Proper Metric Spaces can be modeled by Rays!

‘Proper’ is a heavily overloaded term, both in life and in mathematics. It may mean different stuff in different contexts. Thankfully mathematics is far less complicated that life and we can rigorously define properness.

## Parity and Symbolic Divisibility – an excursion in Number Theory

Parity and divisibility are two interesting tools of elementary number theory. Coupled with an estimation with AM-GM inequality, we have excursion into the queen of mathematical disciplines.

## Compact Set, Proper Spaces and Annulus

Compact set in proper topological (metric) spaces have ‘euclidean’ character. We consider an example that takes advantage of this.

## I.S.I Entrance Solution – locus of a moving point

This is an I.S.I. Entrance Solution Problem: P is a variable point on a circle C and Q is a fixed point on the outside of C. R is a point in PQ dividing it in the ratio p:q, where p> 0 and q > 0 are fixed. Then the locus of R is (A) a circle; (B) an ellipse; ...

An advanced program in Mathematics for brilliant school students. Taught by ex-Olympians and active researchers in Mathematics.

By the way, are you interested in the fourth dimension? Here is a beauty to behold! Tetracube created the beautiful image of the Omnitruncated tesseract.

# Training brilliant minds.

Since 2010.

Cheenta has worked with brilliant maths and science olympiad students from over 6 countries. Our courses are specifically geared toward students with an exceptional interest in Mathematical Sciences.

Outstanding mathematics program for deserving school students.

For children who are starting out in Mathematics and Science.

#### I.S.I. & C.M.I. Entrance

For B.Stat and B.Math entrance at Indian Statistical Institute, B.Sc. Math at C.M.I. & KVPY.

#### College Mathematics

For I.S.I. M.Math, Mathematics Subject GRE, TIFR; Groups Analysis, Topology and more

# I.S.I. & C.M.I. Entrance

B.Stat, B.Math Entrance at I.S.I. and B.Sc. Math Entrance at C.M.I. require special training in Number Theory, Geometry, Combinatorics and Algebra (apart from regular High School topics).

Problems from standard topics such as Calculus, Trigonometry or Coordinate geometry can significantly tricky.

Number Theory, Combinatorics, Algebra, and Geometry at Olympiad standard are both necessary and useful components of this course.

#### Regular High School Topics

Advance problems from Calculus, Trigonometry, Coordinate Geometry and Algebra are bread and butter for handling more complicated ones.

# College Mathematics

An advanced program for College Students as well as adults interested in modern mathematics. This program is useful for I.S.I. M.Math Entrance, Subject GRE, IIT JAM and similar entrances.

We work on Groups, Rings, Fields, Linear Algebra, Analysis, Topology and other advanced topics. As usual problem solving remains the driving force of the program.

The hyperbolic 3 space may come up in this course. Behold this beautiful Hyperideal Honeycomb created by Royce3 (under creative commons).

#### Continuing Education

Many adults, who are pursuing jobs or industry, have taken this program. A curious mind, coupled with a determination to take up challenges is sufficient.

This program is for the true math fanatic, who yearn to understand the anatomy of ‘reason’ a little better. Advanced problem-solving session every week!

# What is Torsion?

Geometry is everywhere. Enjoy this bit.

# Testimonials…

“a wide range of mathematical topics, and every lesson is packed with insights and methods. We are extremely pleased with the difference he has been making. Under his tutelage Sam has secured several gold awards from the UK Mathematics Trust (UKMT)and Scottish Mathematical Council (SMC).” Jayanta Majumdar

Glasgow, UK

“Shuborno has been studying under Ashani from last one year. During this period, we have seen our son grow both intellectually and emotionally. His concepts and approach towards solving a problem has become more mature now. Not that he can solve each and every problem but he loves to think on the tough concepts. For this, all credit goes to Ashani, who is never in a hurry to solve a problem quickly. Rather he tries to slowly build the foundation..” Shubrangshu Das

Bangalore, India

“Our experience with Cheenta has been excellent. Even though my son started in Middle School, they understood his Math level and took personal interest in developing a long-term plan considering his strengths and weakness areas. Through out the semester courses they have nourished him with challenging problems and necessary homework. His guidance has helped my son to perform well at competitions including USAJMO and others. He has grown more confident in his math abilities over the past year and half and is hoping to do well in the future.

I am impressed with their quality and professionalism. We are very thankful to Cheenta and hope to benefit from them in the coming years. I would strongly recommend them to any student who wants to learn Math by doing challenging problems, specially if they are looking for Math than what their school can offer.” Murali Kadaveru

Virginia, USA


text:
Answer
Comment
Share
Q)

# Atomic radius is of the order of $10^{-8} cm$ and nuclear radius is of the order of $10^{-13}$ cm. calculate what fraction of atom is occupied by nucleus?

$(a)\;10^{-14} \times V_{atom}\qquad(b)\;10^{-13} \times V_{atom}\qquad(c)\;10^{-15} \times V_{atom}\qquad(d)\;10^{-11} \times V_{atom}$

## 1 Answer

Comment
A)
Need homework help? Click here.
Volume of nucleus = $\large\frac{4}{3}\pi r^3 = \large\frac{4}{3}\pi(10^{-3})^3 cm^3$
Volume of atom = $\large\frac{4}{3}\pi(10^{-8})^3cm^3$
$\large\frac{V_N}{V_{atom}} = \large\frac{10^{-39}}{10^{-24}}$
$V_{nucleus} = 10^{-15}\times V_{atom}$
Hence answer is (c)


text:
Three sisters have an average (arithmetic mean) age of 25 ye : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 19 Feb 2017, 18:26

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Three sisters have an average (arithmetic mean) age of 25 ye

Author Message
TAGS:

### Hide Tags

Manager
Joined: 12 Dec 2012
Posts: 162
Location: Poland
Followers: 5

Kudos [?]: 178 [0], given: 67

Three sisters have an average (arithmetic mean) age of 25 ye [#permalink]

### Show Tags

14 Jan 2013, 05:16
3
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

68% (01:52) correct 32% (00:51) wrong based on 134 sessions

### HideShow timer Statistics

Three sisters have an average (arithmetic mean) age of 25 years and a median age of 24 years. What is the minimum possible age, in years, of the oldest sister?

(A) 24
(B) 25
(C) 26
(D) 27
(E) 28

[Reveal] Spoiler:
f = age of the first sister, etc.
M = Median = 24
m = mean

$$\frac{f+s+t}{3}=25=m$$

$$M=s=24$$

$$f+s=51$$

My assumption:
The problem says about the oldest sister, so I assumed that:

f≤s<t

In case the younger sisters were twins. The book explains: The youngest sister must be less than or equal to 24 years old. Agreed.

However, the book also assumes that:

s≤t:

Of course, the oldest sister must be at least as old as the middle sister (...) Not agreed. (Further implications concerning M=24 that turn the ≤ into the < possibility are correct.)

My thinking is: If there is one sister that is the oldest, she must not be the same age as the younger sister(s). Hypothetically, she could be 9 months older and still born in the same year, but I think it is impossible from the medical point of view. Or the sisters could be a step sisters, etc. Nevertheless, this situation is purely hypothetical and - even if the point was to mislead the thinker - in my opinion this is a bit too much, because the very natural assumption for expression of an age is it be an integer.

Moreover, if there were a hypothetical sets:

A={24,25,25},
OR
B={25,25,25},

none of the elements in each set were the greatest (oldest), because "the greatest" is an expression inherently relative to some other objects.

Disputably, in the A'={24,25} we could point 25 as "the greatest", because it's the greatest within the set, even though inside the set it is only "the greater" element, because there is only one other element to be relatively smaller (24).

If you have a one brother, you never say "I am his oldest brother" (unless you're joking).
Instead, you will say: "I am his older brother.". Ain't right?

And if you have two siblings, you will say: "I am the oldest one (of us three).", won't you?

[Reveal] Spoiler: OA

_________________

If I answered your question with this post, use the motivating power of kudos!

Last edited by stonecold on 15 Dec 2016, 14:35, edited 1 time in total.
OE Hidden
Manager
Joined: 18 Oct 2011
Posts: 90
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 69 [0], given: 0

Re: Three sisters have an average (arithmetic mean) age of 25 ye [#permalink]

### Show Tags

15 Jan 2013, 08:32
This question is fairly simple. Note that in the question stem they do not say that each sister has a different age..meaning two could have the same age. If we have a median of 24 that means the middle sister is 24. If we have a mean of 25 that means that the total age of all 3 sisters is 75. If you take out the middle sisters age from the total you get 51...the youngest and oldest sisters must combine for 51 years.
The first answer choice that makes sense is 27 years for the oldest sister leaving the middle and youngest to be 24.
Manager
Joined: 12 Dec 2012
Posts: 162
Location: Poland
Followers: 5

Kudos [?]: 178 [0], given: 67

Re: Three sisters have an average (arithmetic mean) age of 25 ye [#permalink]

### Show Tags

15 Jan 2013, 08:59
Dear sambam,
Quote:
This post is about a doubtful assumption, perhaps an error in the book, which however doesn't influence the answer to the original question.

Solving the problem as such is not the purpose of my post.
_________________

If I answered your question with this post, use the motivating power of kudos!

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1926
Followers: 59

Kudos [?]: 418 [0], given: 476

Three sisters have an average (arithmetic mean) age of 25 ye [#permalink]

### Show Tags

15 Dec 2016, 14:38
Nice Question.
Here is my Solution to this one ->

Let the Age of the three sister in ascending order be ->
S1
S2
S3

Mean = 25

$$Using Mean =Sum/#$$

Sum(3)=25*3=75

Hene S1+S2+S3=75

As #=3=Odd => Median = 2nd term = S2
S2=24

Now to minimise the largest term that is S3 we must maximise all other terms.
S1=S2=24

Hence 2*24+S3=75
S3=75-48=27

Hence D

_________________

Give me a hell yeah ...!!!!!

Intern
Joined: 13 Dec 2013
Posts: 36
Location: United States
GPA: 4
WE: Consulting (Consulting)
Followers: 2

Kudos [?]: 10 [0], given: 76

Re: Three sisters have an average (arithmetic mean) age of 25 ye [#permalink]

### Show Tags

20 Dec 2016, 03:40
1
This post was
BOOKMARKED
The median is 24, which means that the age of the middle sister must be 24. So we have x, 24, y, where x is the age of the youngest sister and y is the age of the oldest sister. To find the minimum age of the oldest sister the other values should be maximized. We also know that the sum of all three ages is 75. Setting x as 24 (the highest value it can be if the median is 24) gives y as 27.

POE for A-C:

A) x must be 24 or lower (for 24 to be the mean). If y is 24 the sum of 75 cannot be met.
B) x must be 24 or lower (for 24 to be the mean). If y is 25 the sum of 75 cannot be met.
C) x must be 24 or lower (for 24 to be the mean). If y is 26 the sum of 75 cannot be met.
Re: Three sisters have an average (arithmetic mean) age of 25 ye   [#permalink] 20 Dec 2016, 03:40
Similar topics Replies Last post
Similar
Topics:
If the average (arithmetic mean) of x, 25, y, and 30 is x + y, which 4 27 Dec 2015, 08:09
8 Three straight metal rods have an average (arithmetic mean) 9 27 Feb 2013, 21:23
210 Seven pieces of rope have an average (arithmetic mean) lengt 43 20 Dec 2012, 06:46
37 Three boxes of supplies have an average (arithmetic mean) 11 05 Dec 2010, 13:17
7 The average (arithmetic mean) of the multiples of 6 5 28 May 2010, 12:57
Display posts from previous: Sort by


text:
# Stellar Population Models

Note: This page describes algorithms applied to the DR12 BOSS data and included in DR13 via symlinks. They were not re-applied to the latest e/BOSS spectral pipeline data in DR13.

## Spectro-Photometric Model Fitting

The stellar population models of Maraston (2005) and Maraston et al. (2009) are used to perform a best-fit to the observed ugriz magnitudes of BOSS galaxies with the spectroscopic redshift determined by the BOSS pipeline, using an adaptation of the publicly available Hyper-Z code of Bolzonella, Miralles & Pelló (2000). The fit is carried out on extinction corrected model magnitudes that are scaled to the i-band c-model magnitude, i.e.:

 mag_x = modelmag_x - extinction_x + (cmodelmag_i - modelmag_i),

where x denotes the photometric band (ugriz).

Two sets of template spectra are used (see Maraston et al. 2012 for details):

1. a passively evolving galaxy with a two-component metallicity of same age and no ongoing star formation or reddening, as in Maraston et al. (2009),
2. an ensemble of canonical star formation modes, including exponentially-declining, constant with truncation, and constant, star formation, for various timescales and various metallicities, as in Maraston et al. (2006). In order to minimize the event of low-age, high-dust fake solutions, reddening is not included (Pforr, Maraston & Tonini 2012 [submitted to MNRAS]). Both template sets are available for Salpeter and Kroupa initial mass functions.

The output of the fit for each galaxy includes: age, star formation mode, metallicity, k-corrected absolute magnitudes in ugriz, plus the reduced χ2. Additionally, the best fit model spectrum as well as the probability distribution function (PDF) for the stellar mass are provided. Stellar masses and star formation rates are computed from the best-fit SED as in Maraston et al. (2006). Furthermore the stellar mass at the median PDF and 68% confidence levels are provided. Mass loss due to stellar evolution and the account of mass in stellar remnants is included.

The algorithm assumes a ΛCDM cosmology with H0 = 71.9, Ωm = 0.258, and ΩΛ = 0.742.

## Emission Line Kinematics

An adaptation of the publicly available Gas AND Absorption Line Fitting (GANDALF, Sarzi et al. 2006) and penalised PiXel Fitting (pPXF, Cappellari & Emsellem 2004) codes are used to fit the stellar population synthesis models of Maraston & Strömbäck (2011) and Thomas, Maraston & Johansson (2011) to observed BOSS galaxy spectra. We chose these codes as GANDALF simultaneously fits stellar templates and Gaussian emission-line models.

The stellar population synthesis models used were all at fixed solar metallicity to limit computing time, utilised the MILES stellar library and had age ranges from 6.5 Myr to 11 Gyr. Since we were not using this fit to extract stellar population metallicities and ages, considering only solar metallicity did not impact on our results and age-metallicity degeneracy effects were unimportant. We adopted the MILES resolution calculated in Beifiori et al. (2011).

Outputs from this fitting process that we are providing include the emission-line fluxes (both observed and de-reddened) and equivalent widths, the gas kinematics, the stellar kinematics, an E(B-V) value and derived BPT classifications. Our reddening values can be obtained by plugging the E(B-V) value for each object into the dust attenuation equation of Calzetti et al. (2000).

Outputs from this fitting process that we are providing include the emission-line fluxes (both observed and de-reddened) and equivalent widths, the gas kinematics, the stellar kinematics, two E(B-V) values (explained below), absorption line indices and derived BPT classifications.

A reduced χ2 value is also provided for the fit, as well as Amplitude-over-Noise (AoN) values for each of the emission lines.

## Principal Component Analysis (PCA) Method

Chen et al. (2012) model physical galaxy parameters based on a library of model spectra for which principal components (PCs) have been identified. The method is applied in the following steps.

### Create library of model spectra

The library of model spectra is based on Bruzual & Charlot (2003) stellar population synthesis models. The model is parameterized by the following characteristics.

#### Star formation histories (SFHs)

Figure 1: Three different examples of SFHs.

Each SFH consists of three parts: an underlying continuous model + a series of super-imposed stochastic bursts + a random probability for star formation to stop exponentially (i.e. truncation). Figure 1 shows three examples of SFHs. The top panel is a continuous model, middle panel shows a continuous model with two random bursts, a truncation can be found in the bottom panel.

#### Metallicity

95% of the model galaxies in the library are distributed uniformly in metallicity from 0.2 - 2.5 Z; 5% of the model galaxies are distributed uniformly between 0.02 and 0.2 Z.

#### Dust extinction

Dust extinction is modelled using the two-component model described in Charlot & Fall (2000). The V-band optical depth has a Gaussian distribution over the range 0 < τV < 6. with a peak at 1.2 and 68% of the total probability distribution distributed over the range 0~2. This prior distribution of τV values is motivated by the observed distribution of Balmer decrements in SDSS spectra (Brinchmann et al. 2004). The fraction of the optical depth that affects stellar populations older than 0.01 Gyr is parametrized as μ, which is again modeled as a Gaussian with a peak at μ = 0.3, and a 68 percentile range of 0.1~1.

#### Velocity dispersion

Each of the model spectra is convolved to a velocity that is uniformly distributed over the range of values from 75 to 400 km/s.

### Principal components (PCs) are identified from the model library

Figure 2: From top to bottom: the mean spectrum of the model library followed by the first to the seventh eigenspectra.

The regions around nebular emission lines are masked in the model spectra. We mask 500 km/s around the [OII]3726.03, [OII]3728.82, Hζ3889.05, [NeIII]3869.06, Hδ4101.73, Hγ4340.46, Hβ4861.33, [OIII]4959.91, and [OIII]5007.84 Å lines. Each spectrum in the masked library is normalized to its mean flux between 3700-5500 Å (this is the range we use for analysis). The mean spectrum of the masked library is calculated and subtracted from each of the model spectra.

PCA code is run on the "residual" spectra. Figure 2 presents the mean spectrum and the top seven PCs for the input model library.

### Project BOSS data and models onto PCs

Figure 3: An example of projection. The black is the BOSS spectrum. The red is the PCA fit.

Figure 3 shows an example of projection. The black is the BOSS spectrum. The red is the PCA fit, it is a linear combination of the mean spectrum and the PCs, namely, fit = mean + C1 × PC1 + C2 × PC2 + … + C7 × PC7, where Cα (α = 1–7) are the coefficients of the projection.

### Estimate galaxy physical parameters for BOSS

For an observed galaxy at redshift z, we select only models that have an age smaller than the age of the universe at that redshift. We step through the models one at a time, calculating the χ2 as follows:

where Cα (α = 1–7) represents the projection coefficients. The superscript "m" and "d" refer to model and data. i represents the i-th model. Pα,α′ is the inverse of the covariance matrix of Cα. The covariance matrix of Cα is calculated in the projection process.

## Full spectral fitting

### firefly

In DR14 is introduced a new stellar population model fitting code: firefly described here


text:
Pathfinding has gained prominence in the early 1950's in the context of routing; that is, finding shortest directions between two or more nodes. In 1956, the Dutch software engineer Edsger Wybe Dijkstra created the best-known of these algorithms : Dijkstra.

Dijkstra’s algorithm finds the shortest path from a root node to every other node (until the target is reached). Dijkstra is one of the most useful graph algorithms; furthermore, it can easily be modified to solve many different problems.

Traversal algorithms such as breadth-first-search and depth-first-search explore all possibilities : they iterate over all possible paths until they reach the target. However, it may not be necessary to examine all possible paths; Dijkstra’s algorithm eliminates useless traversal using heuristics to find the optimal paths.

### Some applications

• Widely used in Network routing protocols.
• In digital mapping services such as Google Maps.
• In Biology by finding the network model in spreading of infectious diseases.
• In finding the optimal agenda of flights.
• In path planning for mobile robot transportation...

This algorithm begins with a root (or start) node and a queue of candidate nodes. At each step, we compute minimal distance between the root and each unvisited neighbors. Then, we add them to the queue; the one with the lowest distance is the next one that will be taken from the queue. This process repeats until a path to the destination has been found.

Since the lowest distance nodes are examined first, the first time the destination is found, the path to it will be the shortest path.

Minimizing the distance from the root node is our heuristic here.

Here is the distance map computed for a maze from the top left corner (root). You may notice that each connection between two adjacent nodes has a distance cost of 1.

## Steps

Let's take a root node and note D the distance from a node to the root. Dijkstra's algorithm will assign some initial distance values and improve them step by step.

• 1. Set all node distance D to infinity except for the root (current) node which distance is 0.
• 2. Mark current node as visited and update D for all of its unvisited neighbours with the shortest distance.
Note: we can stop the algorithm here if we have reached the target node.
• 3. Add to the queue the unvisited neighbours and go back to step 2.
Yes, one of the most useful and used algorithms is as simple as that !

As we have seen : by calculating and continually updating the shortest distance, the algorithm compiles the shortest path to the destination. A key part of this approach is maintaining an ordered line of nodes to visit next; to set up that part of the algorithm, we will use a priority queue (a regular queue with the ability to set priorities).

For Dijkstra’s algorithm, it is always recommended to use priority queue (or heap) as the required operations (extract minimum and decrease key) match with specialty this data structure. Here the priority is defined by D (the distance between a node and the root). Higher priorities are given for nodes with lower distance D.

You may see it as a regular attraction queue with some people having access to shortcut heading to different checkpoints. A priority queue should have the following methods:

// Add new element at the end of the queue
void enqueue(const T& data, const int priority);

// Remove element from the beginning of the queue
void dequeue();

// Change the priority of the element in the queue.
void changePriority(const T& item, const int priority);

Now that we know all we need to know, here is the implementation (the visual explanation follows):

## Code

Dijkstra(Maze maze, Node start, Node end) {
priority_queue queue();

// Init all distances with infinity
for (auto&& node : maze.nodes) node.distance = Infinity;

// Distance to the root itself is zero
start.distance = 0;

// Init queue with the root node

// Iterate over the priority queue until it is empty.
while (!queue.isEmpty()) {
curNode = queue.dequeue();  // Fetch next closest node
curNode.discovered = true;  // Mark as discovered

// Iterate over unvisited neighbors
for (auto&& neighbor : curNode.GetUnvisitedNeighbors())
{
// Update minimal distance to neighbor
// Note: distance between to adjacent node is constant and equal 1 in our grid
const minDistance = Math.min(neighbor.distance, curNode.distance + 1);
if (minDistance !== neighbor.distance) {
neighbor.distance = minDistance;  // update mininmal distance
neighbor.parent = curNode;        // update best parent

// Change queue priority of the neighbor since it have became closer.
if (queue.has(neighbor)) queue.setPriority(neighbor, minDistance);
}

// Add neighbor to the queue for further visiting.
if (!queue.has(neighbor)) queue.add(neighbor, neighbor.distance);
}
}

// Done ! At this point we just have to walk back from the end using the parent
// If end does not have a parent, it means that it has not been found.
}

NOTE
Dijkstra’s algorithm does not support negative distances. The algorithm assumes that adding a relationship to a path can never make a path shorter, an invariant that would be violated with negative distances.
Nodes in all the different directions are explored uniformly, appearing more-or-less as a circular wavefront (as the breadth-first-search) as we use a constant cost of 1 for all connections between two adjacent nodes.

Using a priority queue instead of a regular queue changes the way the frontier expands. Contour lines (based on distances) are one way to see this.

See how the frontier expands more slowly through the forests (source : redblobgames).


text:
# Possible to not make light blend colors?

I'm working on animating a logo that was created for me in photoshop which is just some text and two different colors that cut across the text simulating light. In animating the logo I decided to place two lights which I would toggle on during the animation. However, as expected, light blends colors and in this case red and white light make pink. Is it possible to not allow the light to blend or is there a better way to approach this?

Image is what is desired to animate/duplicate

• What do you mean by "toggle on during the animation"? Are lights supposed to be flashing on and off? Are the lights going to be moving around as if it were a searchlight? Could you please make your question easier to interpret. – masterj2001 Aug 8 '17 at 2:04
• My apologizes, at a certain keyframe X I am changing the energy value of the white light, and then later at keyframe Y I am doing the same thing to the red light. The lights are fixed at a position in the lower right corner to obtain the desired cross cutting effect. – Matt R Aug 8 '17 at 2:14
• If you want well defined edges between colors wouldn't it be much easier to just use geometry instead? – Duarte Farrajota Ramos Aug 8 '17 at 2:23
• Would I still be able to animate it shooting from the bottom right out across the text? It'd be quick and subtle, i'm just wondering. I don't really know the best way to approach something like this – Matt R Aug 8 '17 at 2:29

Ok, so this is going to be pretty extensive and difficult to explain through text and images but I'll do my best.

Make sure you're in cycles render

Now lets create our layers, name layer 1 and layer 2 (name choice is up to you). Make the first layer associated with layer 1 and the second layer with layer 2

Add a camera into your scene, press 5 and then 7 to enter top down orthographic view, and then Ctrl+Alt+0 to move the camera to your current perspective

(you can then modify how close the camera is to the text with g and then z, or using the axis arrows).

Move to the second layer and create 3 planes (one will be the red light, white light and colour of the text) Make sure that these three planes are spaced out along the z-axis to ensure that they aren't intersecting. From here, enter edit mode and manipulate the vertices to match the shape you're trying to create for the lights.

You should have something that looks like this:

Select one of the planes that is representing a light, select the object settings and under Cycles Settings deselect diffuse. Do this for both planes representing lights.

Go into the node editor, select one of the planes representing a light and create this node setup:

Once you have done this for both light planes, create a similar node setup for the plane that will represent the text's colour. Should look like this:

(The emission colour will effect the text's colour)

Tick the transparent option, shift select both layers and hit render.

After rendering go into the compositor and create this setup:

This is pretty much the final result, now all you need to do is animate the colour ramps to emulate the lights, crank the white value closer to the black and that will remove your issue of the colours blending.

Hope this helps and resolved your issue, sorry if any of this is hard to understand. If so, just let me know and I'll do my best to reiterate what I was trying to say. I will also attach the .blend file so that you can dissect what I did if you get stuck.

• After more time than I wish learning Blender took, I've almost got this. The last two questions I have are that I'm trying to fade in the text now at the start of the animation. I've got a mix shader that i'm running a Diffuse and Transparent too and animating keying the transparency factor. But that's messing with my background color, and not showing the text (though I've selected it to be rendered; only the "lights" are rendering). Any ideas? – Matt R Aug 24 '17 at 1:14
• If you have a node setup like so: imgur.com/MvNLx5w for the text then you should be all good. Works for me when I render it. Just double check that you have both layers selected. If you upload a version of your .blend file I will happily check it out to find a solution. blend-exchange.giantcowfilms.com – masterj2001 Aug 26 '17 at 0:06


text:
• # question_answer Camel carts are used in which one of the following places as a means of transport? A)  Desert B)  Mountains C)  Sea D)  Cities

Correct Answer: A

Solution :

You need to login to perform this action.
You will be redirected in 3 sec


text:
# How exactly do I calculate and interpret factors in Fama-French model?

Could anyone explain me how to interpret factors and what kind of regressions I should run?

I have already calculated the factor returns as well as 6 Fama-French portfolio returns, the only problem is I do not know how to properly combine all the information and reach useful results.

Do I run regressions on SMB and HML to find whether those factors explain market movements by looking at R squared and then run regressions on 6 portfolios to see how significant the portfolio returns are?

• If any of the answers were helpful accepting it is appreciated - Thank you – vonjd Jan 13 '17 at 16:59

The clearest hands-on explanation I have seen so far is the following:

Bernstein, W.: Rolling Your Own: Three-Factor Analysis

Everything is explained very clearly and step-by-step with Excel.

Concerning your question: The R-squared tells you how much percent are explained by the factors. The intercept is your alpha, the coefficients of the factors tell you in which direction the portfolio is tilted (e.g. HML for a value fund) and the t- and p-values tell you whether the factors are statistically significant.

As @WillGu correctly mentions you should use the data from the FF website.

Hope this helps to get you started.

I believe you have every right to "calculate" the FF factor returns, but you might just use the factors returns on their website. As you mentioned, you can regress on these factors and $R^2$ should tell you how much of the variance in your return series can be explained by FF factors.

I'm not quite sure what goal you are trying to achieve, but one use case would be something like "alpha research". If these factors are represented by available products in the market, you might just subtract their contributions from your returns series and focus on the residuals.

On the other hand, running regression on the 6 portfolios (returns also available on their website among others) shows how much of your return variance can be explained by the 6-portfolio returns. The only usefulness of this kind of analysis IMHO is to see what existing portfolio does your return series mostly look like.

The Fama French SMB and HML portfolios represent the Size premium and the Value premium respectively observed in the equity markets.

Its not clear what your intention is but here's what I would suggest

1. Take the return series of your portfolio, align it with the factor returns of the SMB and HML portfolios which you can download from Kenneth French's website as pointed by @WillGu

2. Run a multiple regression of your portfolio returns vs HML and SMB with an intercept.

3. Observe the coefficients on SMB, HML and also the intercept as well as their t-stats (p-values)

4. Observe the R-squared

5. Here is one interpretation

• If you observe high R-squared and significant coefficients, this would mean a large percentage of your returns are explained by SMB and HML.

• In addition, if you observe a significant and nonzero intercept - it would mean your portfolio returns are also being explained by factors outside of SMB and HML.