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# Research articles for the 2021-07-21

Bank Earnings Management Using Loan Loss Provisions: Comparing the UK, France, South Africa and Egypt
Ozili, Peterson K
SSRN
This paper investigates bank earnings management using loan loss provision (LLP). The paper examines income smoothing which is a type of earnings management. It compares the income smoothing behaviour of banks in the UK, France, South Africa and Egypt. The findings show that bank income smoothing is present in the UK and Egypt, and absent in France and South Africa during the period examined. Banks in Egypt used LLPs to smooth income before the global financial crisis. Meanwhile, bank income smoothing is pronounced in France during and after the financial crisis but is absent in the pre-crisis period. Also, bank income smoothing is reduced in countries that (i) have strict banking supervision, (ii) adopt common law such as the United Kingdom, and (iii) adopt civil law such as France and Egypt. Bank earnings management is also greater in countries that adopt a mixed legal system such as South Africa, and in countries that adopt IFRS accounting standards.

Calibration of Local-Stochastic Volatility Models by Optimal Transport
Ivan Guo,Gregoire Loeper,Shiyi Wang
arXiv

In this paper, we study a semi-martingale optimal transport problem and its application to the calibration of Local-Stochastic Volatility (LSV) models. Rather than considering the classical constraints on marginal distributions at initial and final time, we optimise our cost function given the prices of a finite number of European options. We formulate the problem as a convex optimisation problem, for which we provide a PDE formulation along with its dual counterpart. Then we solve numerically the dual problem, which involves a fully non-linear Hamilton-Jacobi-Bellman equation. The method is tested by calibrating a Heston-like LSV model with simulated data and foreign exchange market data.

Capital Reallocation and Firm-Level Productivity Under Political Uncertainty
Tut, Daniel,Cao, Melanie
SSRN
Does policy uncertainty affect productivity? Policy uncertainty creates delays as firms await new information about prices, costs and other market conditions before committing resources. Such delays can have real consequences on firmsâ€™ productivity and corporate decisions. First, we find that economic policy uncertainty has a negative impact on firm-level productivity. Second, debt magnifies the adverse effects of policy uncertainty on productivity, but access to external financing during periods of significant policy uncertainty shocks has a positive impact on firm-level productivity. Third, Policy uncertainty is positively related to cash holdings but this effect is mostly driven by highly productive firms and by firms with higher levels of irreversible investments since these firms face higher opportunity costs in future states. The three findings are robust to various specifications and provide an affirmative answer to the opening question.

Currency Network Risk
Mykola Babiak,Jozef Barunik
arXiv

This paper identifies new currency risk stemming from a network of idiosyncratic option-based currency volatilities and shows how such network risk is priced in the cross-section of currency returns. A portfolio that buys net-receivers and sells net-transmitters of short-term linkages between currency volatilities generates a significant Sharpe ratio. The network strategy formed on causal connections is uncorrelated with popular benchmarks and generates a significant alpha, while network returns formed on aggregate connections, which are driven by a strong correlation component, are partially subsumed by standard factors. Long-term linkages are priced less, indicating a downward-sloping term structure of network risk.

Customer Liquidity Provision in Corporate Bond Markets: Electronic Trading versus Dealer Intermediation
Mattmann, Brian
SSRN
We investigate electronic trading among customers under normal market conditions and during the Covid-19 crisis using a unique data sample of U.S. corporate bond transactions from UBS Bond Port. We show that electronic customer-to-customer (C-to-C) trading is beneficial in terms of costs for orders up to $1 million. The advantage of electronic C-to-C trading primarily benefits liquidity-consuming customers, as dealers penalize liquidity takers more than the electronic trading channel. Contrary to expectations, at the onset of the Covid-19 crisis the costs for liquidity takers selling bonds electronically inverted, resulting in negative aggressor markups. We argue that this effect is allocated to the trading protocol of a firm and transparent order book. Volumes in electronic C-to-C trading are more driven by orders wherein the liquidity-consuming party is selling; this effect is amplified in stressed markets. Whereas electronic liquidity provision by dealers is primarily concentrated to normal market conditions, electronic C-to-C trading becomes more important in stressed markets. Literature underestimates the effect of inverting markups during the Covid-19 crisis and thus undervalues electronic C-to-C trading as a viable liquidity pool in stressed markets. Deep Learning, Predictability, and Optimal Portfolio Returns Mykola Babiak,Jozef Barunik arXiv We study dynamic portfolio choice of a long-horizon investor who uses deep learning methods to predict equity returns when forming optimal portfolios. Our results show statistically and economically significant benefits from using deep learning to form optimal portfolios through certainty equivalent returns and Sharpe ratios. We demonstrate that a long-short-term-memory recurrent neural network, which excels in learning complex time-series dependencies, generates a superior performance among a variety of networks considered. Return predictability via deep learning generates substantially improved portfolio performance across different subsamples, particularly during recessionary periods. These gains are robust to including transaction costs, short-selling and borrowing constraints. Default Distances Based on the KMV-CEV Model Wen Su arXiv This paper presents a new method to assess default risk based on applying non constant volatility to the KMV model, taking the CEV model as an instance. We find the evidence that the classical KMV model could not distinguish ST companies in China stock market. Aiming at improve the accuracy of the KMV model, we assume the firm's asset value dynamics are given by the CEV process$\frac{dV_A}{V_A} = \mu_A dt + \delta V_A^{\beta-1}dB$and use fixed effects model and equivalent volatility method to estimate parameters. The estimation results show the$\beta>1$for non ST companies while$\beta<1\$ for ST companies and the equivalent volatility method estimate the parameters much more precisely. Compared with the classical KMV model, our CEV-KMV model fits the market better in forecasting the default probability. We also provide an insight that other volatility model can be applied, too.

Dynamic Clearing and Contagion in Financial Networks
Tathagata Banerjee,Alex Bernstein,Zachary Feinstein
arXiv

In this paper we introduce a generalized extension of the Eisenberg-Noe model of financial contagion to allow for time dynamics of the interbank liabilities, including a dynamic examination of default risk. Such a system allows us to distinguish between defaults resulting from either insolvency or illiquidity, and to analyze the resulting effects on the rest of the network. As a special case, we are also able to recover the solution to the Eisenberg-Noe system under certain model choices within the dynamic framework.

Forecasting performance of workforce reskilling programmes
Evan Hurwitz,George Cevora
arXiv

Estimating success rates for programmes aiming to reintegrate theunemployed into the workforce is essential for good stewardship of publicfinances. At the current moment, the methods used for this task arebased on the historical performance of comparable programmes. In lightof Brexit and Covid-19 simultaneously causing a shock to the labourmarket in the UK we developed an estimation method that is basedon fundamental factors involved - workforce demand and supply - asopposed to the historical values which are quickly becoming irrelevant.With an average error of 3.9% of the re-integration success rate, ourmodel outperforms the best benchmark known to us by 53%

Funk Brothers: An Exercise in Obviousness
Tu, S. Sean
SSRN
This article departs from the dogma that Funk Brothers delineates the limits of patentable subject matter and gives several rationales for why Funk Brothers is, in actuality, a case that outlines an obviousness standard. As an initial matter, one only needs to look to the historical background in which Funk Brothers sits to understand this maxim. Funk Brothers was decided before the codification of the 1952 Patent Act and, in fact, simply defines the current obviousness standard later codified in 35 U.S.C. Â§ 103(a). Accordingly, Funk Brothers should not be cited as a case against the patentability of genes under non-patentable subject matter (35 U.S.C. Â§101). Interestingly, the analysis that the Funk Brothers Court uses is, at its core, an obviousness analysis. This article suggests that the breadth of subject matter patentability should be kept broad. Furthermore, this article suggests that the novelty and obviousness standards are better tools that can limit and define the boundaries of patentability for gene patents.

Order Book Queue Hawkes-Markovian Modeling
Philip Protter,Qianfan Wu,Shihao Yang
arXiv

This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classify intraday order book trading events into a range of categories based on their order types and the price changes after their arrivals. To capture the stimulating effects between multiple types of order book events, we use the multivariate Hawkes process to model the self- and mutually-exciting event arrivals. We also integrate a Markovian baseline intensity into the event arrival dynamic, by including the impacts of order book liquidity state and time factor to the baseline intensity. A regression-based non-parametric estimation procedure is adopted to estimate the model parameters in our Hawkes+Markovian model. To eliminate redundant model parameters, LASSO regularization is incorporated in the estimation procedure. Besides, model selection method based on Akaike Information Criteria is applied to evaluate the effect of each part of the proposed model. An implementation example based on real LOB data is provided. Through the example, we study the empirical shapes of Hawkes excitement functions, the effects of liquidity state as well as time factors, the LASSO variable selection, and the explanatory power of Hawkes and Markovian elements to the dynamics of the order book.

Pricing Exchange Option Based on Copulas by MCMC Algorithm
Wen Su
arXiv

This paper focus on pricing exchange option based on copulas by MCMC algorithm. Initially, we introduce the methodologies concerned about risk-netural pricing, copulas and MCMC algorithm. After the basic knowledge, we compare the option prices given by different models, the results show except Gumbel copula, the other model provide similar estimation.

The Adoption of Blockchain-based Decentralized Exchanges
Agostino Capponi,Ruizhe Jia
arXiv

We investigate the market microstructure of Automated Market Makers (AMMs), the most prominent type of blockchain-based decentralized exchanges. We show that the order execution mechanism yields token value loss for liquidity providers if token exchange rates are volatile. AMMs are adopted only if their token pairs are of high personal use for investors, or the token price movements of the pair are highly correlated. A pricing curve with higher curvature reduces the arbitrage problem but also investors' surplus. Pooling multiple tokens exacerbates the arbitrage problem. We provide statistical support for our main model implications using transaction-level data of AMMs.

What Explains Gender Gap in Unpaid Household and Care Work in India?
Athary Janiso,Prakash Kumar Shukla,Bheemeshwar Reddy A
arXiv

Due to the unavailability of nationally representative data on time use, a systematic analysis of the gender gap in unpaid household and care work has not been undertaken in the context of India. The present paper, using the recent Time Use Survey (2019) data, examines the socioeconomic and demographic factors associated with variation in time spent on unpaid household and care work among men and women. It analyses how much of the gender gap in the time allocated to unpaid work can be explained by differences in these factors. The findings show that women spend much higher time compared to men in unpaid household and care work. The decomposition results reveal that differences in socioeconomic and demographic factors between men and women do not explain most of the gender gap in unpaid household work. Our results indicate that unobserved gender norms and practices most crucially govern the allocation of unpaid work within Indian households.


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# Interesting Hat Problem

This is a logic puzzle that I really enjoy, but it doesn't translate well to the "input your answer" format. That aside, I thought people on Brilliant might enjoy it too.

The logic mastermind has taken 100 mathematicians hostage. The mathematicians are told that they will each be given a hat out of 100 possible colors (the mathematicians are told the possible colors in advance). The mathematicians must then simultaneously guess their own hat colors. (Note that they all must guess; no one may abstain.)

The mathematicians are able to see the other 99 hats but not their own. Moreover, they are not allowed to communicate any information to the other mathematicians (e.g. by physical movement or change in tone) on pain of death - they must only guess.

The mathematicians will be set free if EXACTLY ONE mathematician guesses correctly. Unfortunately, they are told that their hat colors may not necessarily be distinct - for example, while there are 100 possible hat colors, they might all be given yellow hats.

The mathematicians are allowed to devise a strategy before they don their hats and guess. Can they succeed and win their freedom? If so, what is their strategy?

###### This problem is not original.

Note by Maggie Miller
1 year, 8 months ago

Sort by:

And there are several other hat problems like this and this and this. That's amazing! Thanks Maggie! Staff · 1 year, 8 months ago

There are 100 caps, that might be distinctively colored or similarly. Since there is no observed pattern of slaying the riddle, nor is there any mention of the colours, its practically impossible to find the right colour of the hat unless guesses are allowed.

Oppositions to my answer are most welcome! :) · 1 year ago

Well they are each guessing - no one certainly knows their own hat color, but they do know that exactly one person will guess correctly. There is a solution :) · 1 year ago

I have a solution for this problem. But I don't see how the mathematicians can do it without communicating. The solution involves assigning numbers, which involves communication. I suppose that means I don't have a solution. · 1 year, 8 months ago

The mathematicians are allowed to devise a strategy before putting on hats, so they may communicate at that time. They can't communicate once the hats are on. · 1 year, 8 months ago

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# Wheatstone Bridge Calculator

Formula for Bridge Voltage: Vb= Vin*(RxRx+Rc RbRb+Ra )

Input Voltage (Vin): v

Resistance (Ra): ohms

Resistance (Rb): ohms

Resistance (Rc): ohms

Resistance (Rx): ohms

Bridge Voltage (Vb) = v

Wheatstone Bridge Calculator is a free online tool that displays the bridge voltage of the circuit. BYJU’S online Wheatstone bridge calculator tool performs the calculation faster, and it displays the bridge voltage in a fraction of seconds.

## How to Use the Wheatstone Bridge Calculator?

The procedure to use the Wheatstone bridge calculator is as follows:

Step 1: Enter the input voltage, resistance value in the input field

Step 2: Now click the button “Calculate Bridge Voltage” to get the result

Step 3: Finally, the bridge voltage will be displayed in the output field

### What is Meant by the Wheatstone Bridge?

In Physics, the Wheatstone bridge is also known as the resistance bridge. The Wheatstone bridge consists of four arms. The two arms consist of known resistance, and the other two arms consist of variable resistance and unknown resistance. The Wheatstone bridge consists of an electromotive force and a galvanometer. It works on the principle of null deflection. The bridge is considered to be in a balanced condition when no current flows through the galvanometer. Generally, this condition is achieved by adjusting the known and the variable resistance. The formula to calculate the bridge voltage is given as:

$$\begin{array}{l}v_{b}= v_{in}\ast (\frac{R_{x}}{R_{x}+R_{c}}-\frac{R_{b}}{R_{b}+R_{a}})\end{array}$$

Where

Vin is the input voltage

Vb is the bridge voltage

Ra, Rb, Rc, Rx are the resistance.


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Tuesday
June 18, 2013

# Homework Help: High School

math
Simran Gill speed walks around the school playground every evening. The playground is 80m long and 45m wide. a.) What is the perimater of the playground? b.) Suppose Simran took a longer walk. Suggest some ways he could do that.
Tuesday, December 18, 2012 at 12:46pm

URGENT LANGUAGE ARTS
Which sentence has a misplaced modifier? A. Covered with mold and dust, Mr. Rudolph examined the old textbooks on the shelf. B. I think that my favorite teacher will be Mrs. Alvarado, who is from Guatemala. C. Slowly walking through the crowded hallway, Darlene clutched her ...
Tuesday, December 18, 2012 at 12:37pm

from "When Greek Meets Greek" 1. What can you conclude from the wording of the following text? “One morning Ramkilawansingh (after this, we calling this man Ram) was making a study of the noticeboards along Westbourne Grove what does advertise rooms to let.”...
Tuesday, December 18, 2012 at 12:12am

Statistics
An economist found that a random sample of 42 high school teachers had an average annual salary of $56,490. A previous study showed that the population standard deviation is$4150. Find the 99% confidence interval for µ, the average annual salary of all high school ...
Monday, December 17, 2012 at 11:16pm

Math
Jean surveyed 25% of all eighth graders and 75% of all 7th graders. John surveyed 50% of all eighth graders and 50% of all 7th graders at the same school. Jean surveyed a total of 152 John surveyed a total of 144 What is the number of eighth graders?
Monday, December 17, 2012 at 9:06pm

Degree
Is a Graduate school the same as a Professional school? Can you receive a masters degree from a Professional school?
Monday, December 17, 2012 at 6:05pm

language arts
I have to do a school essay but don't have a awesome intro please help!!! B.T.W it has to do with candy canes
Monday, December 17, 2012 at 5:50pm

Language Arts Need Help!!
Ok these are questions from my language arts book that I was assigned can you please check them i want to make sure they are correct so I now I'm making progress or not thx :-) Read the passage below, and answer the questions that follow. Let's Play! "How many of ...
Monday, December 17, 2012 at 1:30pm

social science
Read the speech below. It is a fictitious political speech by Peter, a candidate for the upcoming national election. Then answer the following questions: List all of the arguments in the speech List all of the non-arguments in the speech List all of the factual contents in the...
Monday, December 17, 2012 at 12:12am

physics
One strategy in a snowball ﬁght is to throw a snowball at a high angle over level ground. While your opponent is watching this ﬁrst snowball, you throw a second snowball at a low angle and time it to arrive at the same time as the ﬁrst. Assume both ...
Sunday, December 16, 2012 at 10:30pm

Writing
Read the passage below. It is a fictitious political speech by Peter, a candidate for the upcoming national election. Then answer the following questions: 1. List the arguments 2. List the non-arguments 3. List the facts 4. List the non-facts 5. What statements are subjective...
Sunday, December 16, 2012 at 10:08pm

Math
For a history project, Marcus built a replica of the Texas State Capitol building. His model has a scale factor of 1/100. If the height of the Capitol's dome is 310 feet, how high is the dome on Marcus' replica?
Sunday, December 16, 2012 at 6:58pm

Religion
The Gospel of John uses High Christology in its account of Jesus’ life. First, define High Christology. Then, describe 2 ways that John depicts Jesus using High Christology and give examples for each from the gospel.
Sunday, December 16, 2012 at 6:39pm

1.21 Three professors at Northern Kentucky University compared two different approaches to teaching courses in the school of business (M. W. Ford, D. W. Kent, and S. Devoto, “Learning from the Pros: Influence of Web-Based Expert Commentary on Vicarious Learning about ...
Sunday, December 16, 2012 at 6:37pm

Intermediate Algebra
Standing on a platform 60 feet high, a person accidentally fires a gun straight into the air. the formula h=-16t^2+100t+60 describes the bullet's height above the ground, h, in feet,t seconds after the gun is fired. how long will it take for the bullet to hit the ground? ...
Sunday, December 16, 2012 at 3:05pm

an automobile to be transported by ship is raised above the dock by a crane. If the gravitational potential energy of the car is 6.6 x 10^4 and the mass is 960 kg how high has the car been lifted?
Sunday, December 16, 2012 at 2:05pm

maths
A wall 24m long, 0.4m thick and 6m high is constructed with the bricks each of dimensions 25cm X 16cm X 10cm. If the mortar occupies 1/10th of the volume of the wall, then find the number of bricks used in constructing the wall.
Sunday, December 16, 2012 at 1:57pm

math
A random group of seniors was selected from a university and asked about their plans for the following year. The school advising office claims that 60% of the students plan to work, 30% of the students plan to continue in school, and 10% of the students plan to take some time ...
Sunday, December 16, 2012 at 1:45pm

literary
What does my teacher mean by this? So I'm writing an essay on the great gatsby and I told my teacher about it via emai. (I'm doing online school) and this is what he told me... Also, make sure you develop the theme more than merely "mortality." I always tell ...
Sunday, December 16, 2012 at 11:53am

statistics
The accompanying multiple regression outputs estimate the following model: annual cost = 0 + 1(Type of School) + 2(Average Total SAT) where: annual cost = annual cost at a college in thousands of dollars Average Total SAT = average scholastic aptitude ...
Sunday, December 16, 2012 at 2:09am

1.21 Three professors at Northern Kentucky University compared two different approaches to teaching courses in the school of business (M. W. Ford, D. W. Kent, and S. Devoto, “Learning from the Pros: Influence of Web-Based Expert Commentary on Vicarious Learning about ...
Saturday, December 15, 2012 at 9:52pm

math
the distance from jill house to school is 3 3/5 miles. jill walks 1/6 of the way. how far does she walk
Saturday, December 15, 2012 at 5:51pm

Math
One student studied for 8 years in college and her tuition bills are recorded. Years. One semester tuition 1. 4680 2. 4960 3. 5510 4. 6060 5. 6845 6. 7600 7. 8435 8. 9250 Construct the scatter plot for the data with the scales.choose 3 points,find a quadratic equation in ...
Saturday, December 15, 2012 at 5:41pm

1.21 Three professors at Northern Kentucky University compared two different approaches to teaching courses in the school of business (M. W. Ford, D. W. Kent, and S. Devoto, “Learning from the Pros: Influence of Web-Based Expert Commentary on Vicarious Learning about ...
Saturday, December 15, 2012 at 3:34pm

geometry
A rectangular wall is 22.7 feet long and 7.5 feet high. If the door in the wall is 2 feet wide and 6.5 feet high, what is the area of the wall excluding the door?
Saturday, December 15, 2012 at 2:15pm

English
1. She often missed classes. 2. She often skipped classes. (Are bothe the same? Do you use some other expressions instead of 'missed'?) 3. She wore the same old dress to school every day. 4. She wore the same old dress when she goes to school every day. (Does #3 mean #...
Saturday, December 15, 2012 at 5:53am

ricon high school
A 6 kg ball is thrown by a catapult at 30 m/s. what is the ball's momentum?
Saturday, December 15, 2012 at 2:37am

physics
During a baseball game, a batter hits a popup to a ﬁelder 64 m away. The acceleration of gravity is 9.8 m/s 2 . If the ball remains in the air for 6.7 s, how high does it rise? Answer in units of m
Friday, December 14, 2012 at 11:23pm

chimistry
A latex balloon, wall thickness 3.091 x 10-4 m, contains helium at a concentration of 0.82 kg m-3. Under these conditions the total surface area of the balloon is 0.39 m2. The diffusion coefficient of He in latex at room temperature is 4.9 x 10-9 m2s-1. Calculate the rate of ...
Friday, December 14, 2012 at 1:23pm

chimistry
You wish to increase the carbon content of a slab of steel by exposing it to a carburizing atmosphere at elevated temperature. The carbon concentration in the steel before carburization is 100.0 ppm and is initially uniform through the thickness of the steel. The atmosphere of...
Friday, December 14, 2012 at 1:23pm

chemistry
Chemical analysis of a silicon crystal reveals gallium at a level of 3.091*10^-7 atomic percent. Assuming that the concentration of thermally excited charge carriers from the Si matrix is negligible, what is the density of free charge carriers (free carriers/cm3) in this Si ...
Friday, December 14, 2012 at 1:22pm

Math, Algrebra II High school
You have 29 coins, the total value of which is $1.77. The number of quarter is eight less than the number of pennies and the rest are nickels. How many of each coin do you have? Friday, December 14, 2012 at 5:47am maths --plse help me.. A school has a hall which is 22 m long and 15.5 m broad . A carpet is laid inside the leaving all around a margin of 75 cm from the walls . Find the area of the carpet and the area of strip left uncovered . If the width of carpet is 82cm ,find its cost at the rate of Rs60 per m. Friday, December 14, 2012 at 5:26am maths --plse help me.. A school has a hall which is 22 m long and 15.5 m broad . A carpet is laid inside the leaving all around a margin of 75 cm from the walls . Find the area of the carpet and the area of strip left uncovered . If the width of carpet is 82cm ,find its cost at the rate of Rs60 per m. Friday, December 14, 2012 at 3:42am Algebra II math high school To get the necessary funds for a planned expansion, a small company took out three loans totaling$25,000. The company was able to borrow some money at 8%. It borrowed $2000 more than half the amount of the 8% loan at 10% and the rest at 9%. The total annual interest was$2200...
Thursday, December 13, 2012 at 10:18pm

Math Algebra , high school
A biologist has three salt solutions: some 5% solution, some 15% solution, and some 25% solution. She needs to mix some of each to get 50 liters of 20% solution. She wants to us twice as much of the 5% solution as the 15% solution. How much of each solution should she use? How...
Thursday, December 13, 2012 at 10:14pm

physics
How high does a rocket have to go above the Earth’s surface so that its weight is reduced to 33.7 % of its weight at the Earth’s surface? The radius of the Earth is 6380 km and the universal gravitational constant is 6.67 × 10 −11 N · m 2 /kg 2 . ...
Thursday, December 13, 2012 at 9:33pm

art through the ages
Compare Raphael’s School of Athens to Veronese’s Christ in the House of Levi. Explain how each artist reflected the political and social environment of Rome and Venice during the Renaissance period
Thursday, December 13, 2012 at 8:59pm

is this a good story can i get ideas She left that morning, taking all she could with her clothes, money, phone; as she headed toward the straggle subway as she bounded many people screamed at her and told her names but she didn’t care she was so lost in this maroon world...
Thursday, December 13, 2012 at 8:33pm

Physics
An arrow is shot straight upward at 55 m/s. a) find the time until the arrow reaches its peak b)how high was the arrow at its peak c)find the total time the arrow is in the air d)what was the velocity of the arrow after 3.5 seconds e)how high was it at 3.5 seconds
Thursday, December 13, 2012 at 8:10pm

physics
A place kicker must kick a football from a point 32.2 m from a goal. As a result of the kick, the ball must clear the crossbar, which is 3.05 m high. When kicked the ball leaves the ground with a speed of 20.8 m/s at an angle of 53° to the horizontal. (a) By how much does ...
Thursday, December 13, 2012 at 8:09pm

1. If you were writing a persuasive essay about the need to install solar panels on top of big apartment buildings, what counterargument should you address? (1 point) Homeowners can get tax breaks for installing solar panels on their homes. People are getting very interested ...
Thursday, December 13, 2012 at 8:09pm

Physics
An arrow is shot straight upward at 55 m/s. a) find the time until the arrow reaches its peak b)how high was the arrow at its peak c)find the total time the arrow is in the air d)what was the velocity of the arrow after 3.5 seconds e)how high was it at 3.5 seconds
Thursday, December 13, 2012 at 8:09pm

Physics
An arrow is shot straight upward at 55 m/s. a) find the time until the arrow reaches its peak b)how high was the arrow at its peak c)find the total time the arrow is in the air d)what was the velocity of the arrow after 3.5 seconds e)how high was it at 3.5 seconds
Thursday, December 13, 2012 at 8:09pm

Earth Science
Computer models of Earth's climate project increases in the average temperature from 2Â°C to 6Â°C by the end of the century. Have these high temperatures ever occurred before in the past 400 000 years?
Thursday, December 13, 2012 at 7:55pm

Fraction
So I have figured this out but I don't think this is the way I am suppose to write the equation fraction out. 8 1/2 years ago, Steven was 7 years old. How old is he now? Do I write it out like this 8/1 + 1/2 + 7/1 ??? But it comes out too high of a number. I know I am ...
Thursday, December 13, 2012 at 5:47pm

physics
how tall must a water filled manometer be to measure blood pressure as high as 300 mm Hg? what do i use for pressure, density and height?
Wednesday, December 12, 2012 at 11:09pm

biology
The classification of bacterial species does not fit the usual definition of species. This is because bacteria A) cannot exchange genetic material. B) are eukaryotic. C) have a high rate of gene flow. D) reproduce asexually
Wednesday, December 12, 2012 at 9:39pm

People
who is a famous person who didnt go to college or didnt graduate high school and is in bad shape because of it. (aka is poor or cant get a job or turned into a criminal etc)
Wednesday, December 12, 2012 at 4:49pm

Chemistry - solubility, not "Methode Champenoise"
Is CO2 soluble in ethanol? I know that CO2 is nonpolar, so that means it's soluble in nonpolar solvents, but CO2 is soluble in H2O. H2O is polar. Also, if CO2 were obeying Henry's Law, would it be soluble in ethanol at a high pressure?
Tuesday, December 11, 2012 at 11:47pm

geometry
an A-frame house is 45 feet high and 32 feet wide. find the measure of the angle that the roof makes with the floor. Round to the nearest degree.
Tuesday, December 11, 2012 at 9:14pm

geometry
an A-frame house is 45 feet high and 32 feet wide. find the measure of the angle that the roof makes with the floor. Round to the nearest degree.
Tuesday, December 11, 2012 at 8:16pm

Math
Tuesday, December 11, 2012 at 7:45pm

High School English
How did The Masque of the red death show evil? Ive read it over and over and cant seem to find evil no where in this story.
Tuesday, December 11, 2012 at 6:55pm

My teacher for my english class at school marked off for these questions and said I could redo it and turn it in tomorrow. I am for sure I did these right. Here are the questions. Underline the verb in the parentheses that agrees with the subject. 1. In the Northern Hemisphere...
Tuesday, December 11, 2012 at 4:22pm

Introduction to High School
All of the following are characteristics of an effective study environment EXCEPT: A. a relaxing area such as your bedroom B. comfortable and balanced temperature C. ample amounts of natural light D. a deck stocked with supplies
Tuesday, December 11, 2012 at 3:20pm

Physics
Assuming the fluid has a density of 1.00 (g/cm^) at what height h should the bottle be placed so the liquid pressure is 38mm-Hg ? B.At what height h should the bottle be placed so the liquid pressure is 460mm-H_2O ? C.If the blood pressure is 18 {mm-Hg} above atmospheric ...
Tuesday, December 11, 2012 at 9:26am

Chemistry
Here is the phase diagram of water with attention given to phases at high pressure. Name all phases present at the markers 1, 2 and 3. Phases present at 1: Liquid I II III IV V VI VII VIII IX Phases present at 2: Liquid I II III IV V VI VII VIII IX Phases present at 3: Liquid ...
Tuesday, December 11, 2012 at 3:17am

English
I read this story, I need help with some questions please by Katherine Mansfield Miss Brill Although it was so brilliantly fine - the blue sky powdered with gold and great spots of light like white wine splashed over the Jardins Publiques - Miss Brill was glad that she had ...
Monday, December 10, 2012 at 8:11pm

Math
Coach Lewis was training for a marathon. After 15 minutes he had run 5 blocks if he continues at this pace how many blocks will he have run in 1 1/4 hours a.75 b.15 c.25 d.17 c? Mrs Win is preparing party bags for the school dance it takes her 5 min to fill 3 bags with goodies...
Monday, December 10, 2012 at 7:02pm

Math
The rim of the London Eye (a 135m diameter ferris wheel) moves 26 cm/sec, slow enough for passengers to safely get on the wheel from the platform (2 meters above ground level) without stopping the wheel at the bottom of its rotation. What's the height at the bottom of the ...
Monday, December 10, 2012 at 4:53pm

Math
If a cat can jump 5 times the length of its tail. How high can the cap jump, if his tail is 13 inches long? (Algebra)
Monday, December 10, 2012 at 4:01pm

algebra
A linear regression equation of best fit between a student's attendance and the degree of success in school is h = .5x + 68.5. The correlation coefficient, r, for these data would be? 1. <?r<1 2. -1<?r<0 3. r=0 4. r=-1
Monday, December 10, 2012 at 3:59pm

algebra
A linear regression wquation of best best fit between a student's attendance and the degree of success in school is h = .5x + 68.5. The correlation coefficient, r, for these data would be
Monday, December 10, 2012 at 3:56pm

Lang Arts
3. Identify the simple sentence. In 1970, my mother graduated from Point Pleasant Boro High School. The gymnast swung around the bar, and the coach stepped on the mat. The tornado bypassed the town, but the townspeople remained in their shelters. The factory closed its doors, ...
Monday, December 10, 2012 at 3:05pm

psychology 220
# 1.36 (1 pts.) Based on the incidence of Fetal Alcohol Syndrome in various ethnic groups, which of the following individuals would be considered high risk? A) a woman of French Canadian descent B) a woman of Irish descent C) a woman of Italian descent D) a woman of Native ...
Monday, December 10, 2012 at 2:52pm

case management
12. What is an example of a high conflict intensity? A. coach client B. appeal to external ombudsman C. use target’s grievance procedures D. mobilize organized consumers groups
Monday, December 10, 2012 at 12:11pm

Math
Eliza and Jamie are making cupcakes for a bake sale at school. Eliza need 2one third c of flour for her recipe and Jamie needs 1three fourths c for her recipe. They have 4 c of flour. Do they have enough flour for both recipes? Explain.
Monday, December 10, 2012 at 2:20am

physics
A child and sled with a combined mass of 58.9 kg slide down a frictionless hill that is 8.09 m high at an angle of 23◦ from horizontal. The acceleration of gravity is 9.81 m/s2 . If the sled starts from rest, what is its speed at the bottom of the hill? Answer in units ...
Sunday, December 9, 2012 at 11:32pm

Psychology 220
1.65 (1 pts.) David is a junior at the local high school. The school's administration believes his recent emotional outbursts during class may be due to problems in his home life. Who might be best suited to deal with this situation? A) the principal B) a guidance ...
Sunday, December 9, 2012 at 9:31pm

math
Sue was in excellent shape in high school, she could ride her 10-speed bicycle 4.8miles to her grandmother's house in 11 minutes. Her return trip home took 14 minutes. The times are different due to there being a slight downhill slop on part of the trip to her grandmothers...
Sunday, December 9, 2012 at 9:14pm

Statistics of Psychology
Create a numerical and verbal hypothesis statement: People who are cyber bullied have, for the most part, been bullied in more traditional manners as well." Their research showed that the incidence increased over time, with 23 cases (56%) taking place between 2003 and ...
Sunday, December 9, 2012 at 8:37pm

Statistics of Psychology
Create a numerical and verbal hypothesis statement: People who are cyber bullied have, for the most part, been bullied in more traditional manners as well." Their research showed that the incidence increased over time, with 23 cases (56%) taking place between 2003 and ...
Sunday, December 9, 2012 at 8:36pm

Psychology 220
# 1.36 (1 pts.) Based on the incidence of Fetal Alcohol Syndrome in various ethnic groups, which of the following individuals would be considered high risk? A) a woman of French Canadian descent B) a woman of Irish descent C) a woman of Italian descent D) a woman of Native ...
Sunday, December 9, 2012 at 7:31pm

Math
Sue was in excellent shape in high school, she could ride her 10-speed bicycle 4.8miles to her grandmother's house in 11 minutes. Her return trip home took 14 minutes. The times are different due to there being a slight downhill slop on part of the trip to her grandmothers...
Sunday, December 9, 2012 at 6:30pm

Chemistry
What is true for water? A) In a phase diagram the solid-liquid coexistance line has a negative slope. B) In a phase diagram the solid-liquid coexistance line has a positive slope. C) The solid is more dense than the liquid. D) The solid is less dense than the liquid. E) The ...
Sunday, December 9, 2012 at 6:01pm

Social Studies
What was the purpose of the Homstead Act? Did congress achieve this goal? I got what the homstead act was, but i'm confused on the second part. I put that congress did not achieve there goal because only about 20% of the homstead land went directly to small farmers. Also, ...
Sunday, December 9, 2012 at 3:53pm

Physics
A(n) 80.0-kg student eats a 160-Calorie doughnut. To burn-it-off, he decides to climb the steps of a tall building. How high (in m) would he have to climb to expend an equivalent amount of work?
Sunday, December 9, 2012 at 2:54pm

Statistics
A number of grade school students were asked about their perceived math ability and the results are in the table below. Below Average = BA Average = A Above Average = AV BA A AV Girls 61 54 21 Boys 43 61 42 Test at the 0.01 level if there is a difference between girls and boys...
Sunday, December 9, 2012 at 2:43pm

English narrative
Hello and thanks for starting reading this post :) I have written a english narrative that has very very bad grammar and the rest... :D I would be very thankful if you could help me fix that narrative :) Here it is (BTW it is not a real story, I made it up cause I had no ideas...
Sunday, December 9, 2012 at 12:09pm

physics- TEST TMRW PLS HELP!
Why is the following situation impossible? A librarian lifts a book from the ground to a high shelf, doing 20.0 J of work in the lifting process. As he turns his back, the book falls off the shelf back to the ground. The gravitational force from the Earth on the book does 20.0...
Sunday, December 9, 2012 at 8:45am

math
According to the statistics of a famous high school in Canada, all their graduates went to either A or B for university study. Following are the proportions of graduates who went to the two universities. University Proportion A 1-k B k Suppose k = 0.4 (a) What is the standard ...
Sunday, December 9, 2012 at 5:41am

Why is the following situation impossible? A librarian lifts a book from the ground to a high shelf, doing 20.0 J of work in the lifting process. As he turns his back, the book falls off the shelf back to the ground. The gravitational force from the Earth on the book does 20.0...
Saturday, December 8, 2012 at 3:09pm

thermodynamics
if a pump discharges 75 gpm of water whose specific weight is 61.5 lb/ft^3(g=31.95fps^2). find a) the mass flow rate in lb/min, and b) and total time required to fill a vertical cylinder tank 10ft in diameter and 12ft high.
Saturday, December 8, 2012 at 1:01am

algebra
A weather balloon is directly west of two observing stations that are 10 miles apart. The angles of elevation of the balloon from the two stations are 17.6 degrees and 78.2 degrees. How high is the balloon?
Saturday, December 8, 2012 at 1:01am

english
How can the A Plan of Action help you address a current problem or challenge you are having with school?''
Saturday, December 8, 2012 at 12:58am

The Age Of Jefferson To The American Expansion
1. Which of the following utopian communities was founded and established in New York State? A. Shaker Village B. Spiritualist C. Oneida D. New Harmony 2. The first fully developed American factory system emerged in the _______ industry. A. textile B. sugarcane C. distilling D...
Friday, December 7, 2012 at 5:36pm

Choose the option that correctly identifies the words in () in each sentence. 5. (Stretching for 210 miles) , the Thames is in England. (1 point) prepositional phrase gerund phrase participial phrase appositive phrase 6. (Eating flesh with razor-sharp teeth) is how piranhas ...
Friday, December 7, 2012 at 9:44am

Grammar
Identify the parts of speech the this sentence. When they raise me to a high position, then ill get a raise
Friday, December 7, 2012 at 9:39am

Math
Marty is a cheerleader. His school colors are red,white,and blue. Marty's uniform consists of a red sweater and a blue sweater/ He has 3 pairs of uniform pants: one red one white and one blue. Draw a diagram showing all the possible ways Marty can combine his uniform ...
Thursday, December 6, 2012 at 9:17pm

English - ms. sue
ms. sue my sister write out story here it is. On Monday she looked in her mailbox, although she had no reason to expect a letter so soon. But there it was, a small, square car. She held it in her two hands, testing its weight. It was an invitation to an exhibition of drawings ...
Thursday, December 6, 2012 at 8:46pm

Math(Sample Spaces)
Elsa had a rubber disc that was red on one side and blue on the other. She tossed this disc 3 times. Draw a diagram showing all the possible outcomes she could get in 3 tosses of the same rubber disc 1st toss can be red or blue 2nd toss can be red or blue and 3rd toss can be ...
Thursday, December 6, 2012 at 5:56pm

calculus
A ball is thrown vertically upwards from a height of 6 ft with an initial velocity of 60 ft per second. How high will the ball go? Note that the acceleration of the ball is given by a(t)= 32 feet per second per second.
Thursday, December 6, 2012 at 1:49pm

Economics
Which of the following is a characteristic of a traditional economy? A. It encourages innovation and change. B. It is usually based on light industrial production. C. It has a high standard of living. D. It revolves around the family unit.
Thursday, December 6, 2012 at 10:50am

physics
A boy throws a ball at 5.5 m/s at an angle of 25.4° above the horizontal off a cliff which is 70.8 m high. What angle does the velocity of the ball make with the horizontal 0.78 s after the throw? (make the angle positive if the angle is above the horizontal, and negative ...
Thursday, December 6, 2012 at 7:54am

Child day care
12. Which of the following is a factor that's very important to high-quality child care, but not often covered in state licensing regulations? A. The group size B. A fire safety clearance C. The staff-to-child ratio D. An annual visit by a representative of the licensing ...
Thursday, December 6, 2012 at 12:09am

Political science
If the Federal Reserve is printing money, why is the CPI not reporting a threat from inflation? A) because China is selling expensive goods to American consumers B) because the Federal Reserve is keeping interest rates high, C) because we have a huge trade surplus, D) because ...
Wednesday, December 5, 2012 at 11:12pm

Patsy has cheerleading practice on every fourth school day. She wants to be in the school play, but they have practice on every sixth school day. If both started on September 5th, what would be the first date that she has to choose between cheerleading and play practice? LCM 4...
Wednesday, December 5, 2012 at 11:04pm

Political science
The laffer curve is a theory that says? A) if you raise taxes too high, revenue decreases because people won't work B) if you stimulate the economy with low interest rates, the economy speeds up C) if you stimulate the economy with low interest rates, the economy slows ...
Wednesday, December 5, 2012 at 11:00pm

math
Patsy has cheerleading practice on every fourth school day. She wants to be in the school play, but they have practice on every sixth school day. If both started on September 5th, what would be the first date that she has to choose between cheerleading and play practice? I ...
Wednesday, December 5, 2012 at 10:00pm

Math word problem
Patsy has cheerleading practice on every fourth school day. She wants to be in the school play, but they have practice on every sixth school day. If both started on September 5th, what would be the first date that she has to choose between cheerleading and play practice? I ...
Wednesday, December 5, 2012 at 9:33pm

Hi I am writing a paper for school about cancer cells. I can't seem to get a good introductory paragraph going. Can you give me some ideas? Thanks!
Wednesday, December 5, 2012 at 9:15pm

i need to do a reading essay on maya angelou this is what i have intoduction: maya angelou was born april 4, 1928 in st.louis missouri. she is an author, poet, playwright, stage and screen performer, and director. she has a brother named bailey when they were young they were ...
Wednesday, December 5, 2012 at 7:57pm

i need to do a reading essay on maya angelou this is what i have intoduction: maya angelou was born april 4, 1928 in st.louis missouri. she is an author, poet, playwright, stage and screen performer, and director. she has a brother named bailey when they were young they were ...
Wednesday, December 5, 2012 at 7:34pm

I had to give an interview to a parent about Teens and Cell phones. I got ten questions, gave the interview, and reported results. Thanks for any and all feedback. Cell Phones and social networking 1) Do you think that teenagers, and kids, need to be more responsible? 2) ...
Wednesday, December 5, 2012 at 6:14pm

math
The jelly junior high school color is made by mixing red oaint and yellow the ratio is 3 to 5 how monch red paint needed to be mix if u have 20 oz of yellow
Wednesday, December 5, 2012 at 5:30pm

Fats help maintain your cell membranes. (1 point) True False 12. Your body does not use energy when you sleep. (1 point) True False 13. People with anorexia nervosa eat large amounts of food and then purge. (1 point) True False 14. Your body image is the way others see your ...
Wednesday, December 5, 2012 at 3:53pm

Grammar
Identify the abbreviations in this sentence. When they raise me to a high position, then ill get a raise.
Wednesday, December 5, 2012 at 2:46pm

Physics
What power is needed to lift a 358 crate of bricks from the ground to the top of a 25.0 -high building in 1 minute?
Wednesday, December 5, 2012 at 2:26pm

Child Care
Research suggest that every youngster should receive emotional support from at least three... a)legal guardians b)nonparental adults c)peers d)school friends I'm really stuck on this one.
Wednesday, December 5, 2012 at 1:32pm

physics
7. A drop of oil is placed on a glass block. The glass has an index of refraction of 1.55. When light shines from the glass into the droplet, total internal reflection occurs at a critical angle of 59.0(degrees).find the index of refraction of oil.(this method is capable of ...
Wednesday, December 5, 2012 at 1:05pm

Physics
A high diver of mass 68.2 kg jumps off a board 10.4 m above the water. The acceleration of gravity is 9.8 m/s2 . If his downward motion is stopped 3.58 s after he enters the water, what average upward force did the water exert on him? I already calculated that his velocity ...
Wednesday, December 5, 2012 at 11:30am

math
there are 4 students sitting on the stage at the school assembly waiting to receive their prizes.Alan and Julia wanted to sit together. If they did,how many different arrangements of students would there be?
Wednesday, December 5, 2012 at 9:01am

math
â€¢You and three (3) of your friends were in the same advance placement high school chemistry class in high school. All four (4) of you decided to take the same chemistry class together at the local university along with 21 other students. On the first day of ...
Tuesday, December 4, 2012 at 8:14pm

math
On Wednesday, the low temperature was 56derees F and the high temperature was 72.What is the difference between the two temperature?
Tuesday, December 4, 2012 at 7:45pm

chemistry
A magic number is the name given to certain numbers of protons or neutrons that have a high correlation to stability in nuclei. Magic # of protons: 2,8,20,28,50,82 Magic # of neutrons: 2,8,20,38,50,82,126, 184 Using general trends, predict the stability of the following nuclei...
Tuesday, December 4, 2012 at 4:33pm

physic
Question Part Points Submissions Used A soccer player kicks a rock horizontally off a 41.7 m high cliff into a pool of water. If the player hears the sound of the splash 3.11 s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343 m/s.
Monday, December 3, 2012 at 11:25pm

science
Sandy walked to school this morning because it was nice and warm outside.When school let out, a cold front was moving through. What was the weather most likely as she walked home? A)warmer C)the same B)cooler D)it is unpredictable my answer is A),am i right if not please tell ...
Monday, December 3, 2012 at 9:03pm

Math (trigonometry)
MONDAY  December 3, 2012 SCHOOL SUBJECTS Art Business Computers English Foreign Languages Health Home Economics Math Music Physical Education Science Social Studies GRADE LEVELS Preschool Kindergarten Elementary School 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th...
Monday, December 3, 2012 at 8:14pm

physics
wave speed: the violin is a four stringed instrument tuned so that the ratio of the frequencies of adjacent strings is 3:2. (This is the ratio when taken as high frequency to lower frequency.) If the diameter of E string (the highest frequency) on a violin is 0.25 mm, find the...
Monday, December 3, 2012 at 7:59pm

Trig
A population of animals oscillates annually from a low of 1300 on January 1st to a high of 2200 on July 1st, and back to a low of 1300 on the following January. Assume that the population is well-approximated by a sine or a cosine function. a. Find a formula for the population...
Monday, December 3, 2012 at 7:06pm

math
A 16-ft ladder is placed 4-ft from the base of the building. How high on the building will the ladder reach?
Monday, December 3, 2012 at 6:17pm

physics
During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1800 revolutions per minute. The radius of the barrel is 26 cm. a. Determine the speed of the clothes (in m/s) which are located on the wall of the ...
Monday, December 3, 2012 at 5:24pm

math
The ladders shown below are standing against the wall at the same angle. How high up the wall does the longer ladder go? (All measurements are in feet.) ladders 11.25 ft 12.5 ft 14 ft 14 ft 2. The pair of polygons is similar. Find the value of x. polygons 187.5 in. 12 in. 30 ...
Monday, December 3, 2012 at 3:05pm

social studies
Multiple Choice 1. While Earth's orbit around the sun takes roughly 365 days, a single rotation of Earth takes about 8 hours. 24 hours. 1 month. 12 months. 2. During the summer solstice in the United States, the ______ _______ is tilted farthest toward the sun. Northern ...
Monday, December 3, 2012 at 2:51pm

math
if 20%of the people in school use the emergency room at the hospital in one year. find the probabilities for a sample of 8 people
Monday, December 3, 2012 at 12:55pm

Physics
An X-ray scattering from an electron with negligible initial kinetic energy is observed to undergo a change in wavelength by 2.561 pm.Â  i.e.Â  The scattered X-ray photon has a wavelength 2.561 pm larger than the incident X-ray photon. Â  Find ...
Monday, December 3, 2012 at 12:38pm

Physics
An X-ray scattering from an electron with negligible initial kinetic energy is observed to undergo a change in wavelength by 2.561 pm.Â  i.e.Â  The scattered X-ray photon has a wavelength 2.561 pm larger than the incident X-ray photon. Â  Find ...
Monday, December 3, 2012 at 12:36pm

Mr. White (invested $20,000) and Mr. Black (invested$10,000) are in a partnership to run a marketing firm. They share profits and losses in the ratio of 2:1, which is also the ratio of their initial investment in the business. Mr. White manages the office but Mr. Black gets ...
Monday, December 3, 2012 at 11:19am

Chemistry question
Why do ionic compounds have high melting points?
Monday, December 3, 2012 at 10:58am

math
father gives his son three coins totaling 55 cents for school lunch. What coins did the boy receive if one coin is not a nickel?
Monday, December 3, 2012 at 8:54am

Nutrition
How can I write although reading, writing and math are important in school so is health and physical education?
Monday, December 3, 2012 at 6:45am

Pre-Calc
The cable in the center portion of a bridge is supported by five pillars to form a parabola. The center support is 10 ft high, the tallest supports are 210 feet high, and the distance between the two tallest supports is 400 ft. Find the height of the two supports equally ...
Monday, December 3, 2012 at 4:22am

Statics
17. The Student Health Service assumes, based on historical data, that the height of female students is normally distributed with a standard deviation of 3 inches. The school nurse wants to estimate the average height of this year’s entering female students by examining ...
Sunday, December 2, 2012 at 10:42am

LAN network workshop
6. School network LAN A school wants to have their 5 computers labs with Internet connection. Each lab having 21 computers that directly connected to each other and to the Internet. Each lab is aligned vertically at each floor from ground to fifth floor. The main Internet ...
Sunday, December 2, 2012 at 4:24am

English
i need some help with qustions for this story Identities - W.D. Valgardson Normally, he goes clean-shaven into the world, but the promise of a Saturday liquid with sunshine draws him first from his study to the backyard, from there to his front lawn. The smell of burning ...
Saturday, December 1, 2012 at 8:27pm

Chemistry
If you place 10.0 L of propanol (C3H8O) in a sealed room that is 7.5 m long, 3 m wide, and 3 m high, will all the propanol evaporate? If some liquid remains, how much will there be? The vapor pressure of propanol is 10.7 torr at 25 °C, and the density of the liquid at this...
Saturday, December 1, 2012 at 3:11pm

grammar
need help with this one : 2. To enroll in film school being my primary goal, so I am always saving my money and watching for scholarship opportunities.
Saturday, December 1, 2012 at 2:24pm

grammar
revise the following sentences to eliminate faulty sentence structure, making them clear and grammatically need help with the following sentences: An effective Web site is well designed, provides useful information, and links are given to other relevant sites. To enroll in ...
Saturday, December 1, 2012 at 12:39pm

math - linear programming
A woman wishes to invest \$12,000 in three of bonds: municipal bonds paying 7% interest per year, bank investment certificates paying 8%, and high-risk bonds paying 12%. For tax reasons she wants the amount invested in municipal bonds to be at least three times the amount ...
Saturday, December 1, 2012 at 12:07pm

Physics
a tennis ball is thrown vertically upward from the ground and the student gazing out of the window sees it moving upward pass him at 5 m/sec. the window is 10 m above the ground. how high does the ball go above the ground
Saturday, December 1, 2012 at 10:58am

After receiving a grant for music education, a school decides to build a new band room for its expanded music program. Quadrilateral ABCD represents the floor plan of the new band room. What is the area of the room? AE = 32 ft. BE = 12 ft. CE = 26 ft. DE = 26 ft. There is a ...
Saturday, December 1, 2012 at 12:39am

English
1. At school, I enjoy chatting with my close friends. 2. At school, I enjoy cleaning with other classmates. 3. At school, I enjoy playing soccer in the playground. 4. At school, I enjoy eating cookies at the school shop. 5. At school, I enjoy playing basketball in the gym. 6. ...
Friday, November 30, 2012 at 11:04pm

sat essay
Assignment: Should heroes be defined as people who say what they think when we ourselves lack the courage to say it? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from your reading, ...
Friday, November 30, 2012 at 7:11pm

SAT Essay
Assignment: Should heroes be defined as people who say what they think when we ourselves lack the courage to say it? Plan and write an essay in which you develop your point of view on this issue. Support your position with reasoning and examples taken from your reading, ...
Friday, November 30, 2012 at 3:53pm

hvac school
What temp would a fixed volume of gas need to be heated in order to double its pressure if it starts out at 25?
Friday, November 30, 2012 at 2:35pm

Physics
A 17kg child slides down a 2.7m -high playground slide. She starts from rest, and her speed at the bottom is 1.8 m/s. What is the change in the thermal energy of the slide and the seat of her pants?
Friday, November 30, 2012 at 11:16am

physics
1. During storm roof of house is blown off 2.It is dangerous to stand near the railway track when a train is moving with high speed
Friday, November 30, 2012 at 11:07am

calculus
A conical water tank with vertex down has a radius of 12 feet at the top and is 23 feet high. If water flows into the tank at a rate of 20 {\rm ft}^3{\rm /min}, how fast is the depth of the water increasing when the water is 17 feet deep?
Friday, November 30, 2012 at 10:48am

SAT Essay
Mainly directed to Mr. Pursley and Write Teacher but feel free to critique! Thank you so much. Assignment: Do you think that ease does not challenge us and that we need adversity to help us discover who we are? Plan and write an essay in which you develop your point of view on...
Friday, November 30, 2012 at 9:49am

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text:
## The Tamagawa number conjecture for CM elliptic curves.(English)Zbl 1159.11311

The Bloch-Kato conjecture describes the special values of the $$L$$-function of a smooth proper variety $$X$$ over a number field $$K$$ in terms of the regulator maps of the $$K$$-theory of $$X$$ into Deligne cohomology and $$p$$-adic étale cohomology, respectively. The most widely used formulation of this (Tamagawa number) conjecture in Iwasawa theory is due to K. Kato [Iwasawa theory and $$p$$-adic Hodge theory, Kodai Math. J. 16, No. 1, 1–31 (1993; Zbl 0798.11050)] which is also thoroughly recalled in the paper under review. There are only two special cases for which this conjecture is proven so far in the non-critical situation, both being accomplished by S. Bloch and K. Kato in 1990.
In this article, the author provides a proof of the (weak form of) the Bloch-Kato conjecture for elliptic curves with complex multiplication by the ring of integers in a quadratic number field. His powerful approach is based on a method combining several new ingredients in very subtle and effective a manner. First, there is an explicit description of the Deligne regulator map for elliptic CM curves due to C. Deninger [Invent. Math. 96, No. 1, 1–69 (1989; Zbl 0721.14004)] using Eisenstein symbols à la Beilinson. This leads to a proof of the weak form of the Beilinson conjecture for CM elliptic curves. Secondly, A. Huber and the author have established, in an earlier paper [cf. Invent. Math., 135, No. 3, 545–594 (1999; Zbl 0955.11027)] the relation of the $$p$$-adic regulator of the Eisenstein symbol with the specialization of the $$p$$-adic elliptic polylogarithm sheaf, which now leaves the problem of computing these specializations in $$p$$-adic cohomology in order to tackle the Bloch-Kato conjecture for CM elliptic curves. Whereas the absolute Hodge realization of the elliptic polylogarithm was well understood, due to the extensive work of A. Beilinson and M. Levin (1994), a theory of the $$p$$-adic realization giving manageable étale cohomology classes in the elliptic case had to be developed as a further new ingredient. This is done by exhibiting the elliptic polylogarithm as an inverse limit of $$p^n$$-torsion points of certain one-motives, which leads then to an explicit description of the cohomology classes of the elliptic polylogarithm sheaf by classes of certain line bundles. Finally, this is combined with K. Rubin’s “Main Conjecture” in Iwasawa theory for imaginary quadratic number fields [cf. K. Rubin, Invent. Math. 103, No. 1, 25–68 (1991; Zbl 0737.11030)] to obtain a bound on the kernel and the cokernel of the Soulé map [cf. C. Soulé, Duke Math. J. 54, 249–269 (1987; Zbl 0627.14010)] from elliptic units to the étale cohomology.
At the end of the paper, all the various new results a put together and yield a complete proof of the Bloch-Kato conjecture for CM elliptic curves (Main Theorem 1.1.5).

### MSC:

 11G40 $$L$$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11G05 Elliptic curves over global fields 11G55 Polylogarithms and relations with $$K$$-theory 11G10 Abelian varieties of dimension $$> 1$$ 11G15 Complex multiplication and moduli of abelian varieties 14F30 $$p$$-adic cohomology, crystalline cohomology 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
Full Text:


text:
# Bivariate maps with ggplot2 and sf

The above map shows income (in-)equality in Switzerland on the municipality level by visualizing two variables at the same time: the Gini coefficient and average income (in Swiss Francs). It uses a so-called bivariate color scale, blending two different color scales into one. Lastly, it uses the beautiful relief depicting the mountainous Swiss landscape. Here we’re going to show you how to produce such a map exclusively with R.

For this blog post, I worked together with my colleague Angelo Zehr who recently published a nice bivariate thematic map comparing income (in-)equality and average income in Switzerland. We took this opportunity to give a major update of my post on thematic maps with ggplot2 which is more than two years old, but still attracts hundreds of visits each week.

What is different from said post?

• With the sf packacke and its integration into ggplot2 through the geom_sf() function, it is nowadays even easier to quickly create thematic maps.
• This post does not only show how to produce a simple univariate choropleth (another word for a thematic map where the (fill) color is used as the main visual variable) but also how to combine two variables into a bivariate color scale.
• It introduces a suitable legend for bivariate color scales using geom_tile().
• It shows how to add annotations that explain spatial patterns.

## Outline

This tutorial is structured as follows:

• Read in the thematic data and geodata and join them.
• Define a general map theme.
• Create a univariate thematic map showing the average income. This largely draws from the previous post and involves techniques for custom color classes and advanced aesthetics. People who merely want an update regarding sf and how it interacts with ggplot2 can just read this section.
• Create a bivariate thematic map showing average income and income (in-)equality at the same time. In this process, a custom legend is created and added to the plot, and annotations explaining different spatial patterns are added as well.
• Oh, and lakes and cantonal borders (cantons = Swiss provinces) are now added as well.

Let’s go!

## Reproducibility

As always, you can reproduce, reuse and remix everything you find here, just go to this repository and clone it. All the needed input files are in the input folder, and the main file to execute is index.Rmd. Right now, knitting it produces an index.md that I use for my blog post on timogrossenbacher.ch, but you can adapt the script to produce an HTML file, too. The PNGs produced herein are saved to wp-content/uploads/2019/04 so I can display them directly in my blog, but of course you can also adjust this.

CC-BY-SA

### Version information

This report was generated on 2019-11-23 13:01:05. R version: 3.5.3 on x86_64-pc-linux-gnu. For this report, CRAN packages as of 2019-03-01 were used.

## Preparations

### Clear workspace and install necessary packages

What follows from here until the section Data Sources is just the usual routine: Detach all packages, remove all variables in the global environment, etc, and then load the packages from the MRAN server (a snapshot from March 1st, 2019). With this, we ensure reproducibility and cross-device compatibility. We use Timo’s freely available template for this, with some adaptions detailed under Reproducibility.

## [1] "package package:rmarkdown detached"

### Define packages

For this project, we use the usual suspects, i.e. tidyverse packages including ggplot2 for plotting, sf for geodata processing and raster for working with (spatial) raster data, i.e. the relief. Also, the viridis package imports the beautiful Viridis color scale we use for the univariate map. Lastly, cowplot is used to combine the bivariate map and its custom legend.

# from https://mran.revolutionanalytics.com/web/packages/checkpoint/vignettes/using-checkpoint-with-knitr.html
# if you don't need a package, remove it from here (commenting is probably not sufficient)
cat("
library(rstudioapi)
library(tidyverse) # ggplot2, dplyr, tidyr, readr, purrr, tibble
library(magrittr) # pipes
library(lintr) # code linting
library(sf) # spatial data handling
library(raster) # raster handling (needed for relief)
library(viridis) # viridis color scale
library(cowplot) # stack ggplots
library(rmarkdown)",
file = "manifest.R")

### Install packages

If you’re interested in what the following does, we recommend going through the explanations for rddj-template.

# if checkpoint is not yet installed, install it (for people using this
# system for the first time)
if (!require(checkpoint)) {
if (!require(devtools)) {
install.packages("devtools", repos = "http://cran.us.r-project.org")
require(devtools)
}
devtools::install_github("RevolutionAnalytics/checkpoint",
ref = "v0.3.2", # could be adapted later,
# as of now (beginning of July 2017
# this is the current release on CRAN)
repos = "http://cran.us.r-project.org")
require(checkpoint)
}
# nolint start
if (!dir.exists("~/.checkpoint")) {
dir.create("~/.checkpoint")
}
# nolint end
# install packages for the specified CRAN snapshot date
checkpoint(snapshotDate = package_date,
project = path_to_wd,
verbose = T,
scanForPackages = T,
use.knitr = F,
R.version = R_version)
rm(package_date)

Here the packages are actually loaded. From the sessionInfo() output you can see the exact version numbers of packages used herein.

source("manifest.R")
sessionInfo()
## R version 3.5.3 (2019-03-11)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.3 LTS
##
## Matrix products: default
## BLAS: /opt/R/R-3.5.3/lib/R/lib/libRblas.so
## LAPACK: /opt/R/R-3.5.3/lib/R/lib/libRlapack.so
##
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C
##  [3] LC_TIME=de_CH.UTF-8        LC_COLLATE=en_US.UTF-8
##  [5] LC_MONETARY=de_CH.UTF-8    LC_MESSAGES=en_US.UTF-8
##  [7] LC_PAPER=de_CH.UTF-8       LC_NAME=C
## [11] LC_MEASUREMENT=de_CH.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base
##
## other attached packages:
##  [1] rmarkdown_1.11    cowplot_0.9.4     viridis_0.5.1
##  [4] viridisLite_0.3.0 raster_2.8-19     sp_1.3-1
##  [7] sf_0.7-3          lintr_1.0.3       magrittr_1.5
## [10] forcats_0.4.0     stringr_1.4.0     dplyr_0.8.0.1
## [16] tibble_2.0.1      ggplot2_3.1.0     tidyverse_1.2.1
## [19] checkpoint_0.4.0  rstudioapi_0.9.0  knitr_1.21
##
## loaded via a namespace (and not attached):
##  [1] tidyselect_0.2.5 xfun_0.5         haven_2.1.0      lattice_0.20-38
##  [5] colorspace_1.4-0 generics_0.0.2   htmltools_0.3.6  yaml_2.2.0
##  [9] rlang_0.3.1      e1071_1.7-0.1    pillar_1.3.1     glue_1.3.0
## [13] withr_2.1.2      DBI_1.0.0        modelr_0.1.4     readxl_1.3.0
## [17] plyr_1.8.4       munsell_0.5.0    gtable_0.2.0     cellranger_1.1.0
## [21] rvest_0.3.2      codetools_0.2-16 evaluate_0.13    rex_1.1.2
## [25] class_7.3-15     broom_0.5.1      Rcpp_1.0.0       scales_1.0.0
## [29] backports_1.1.3  classInt_0.3-1   jsonlite_1.6     gridExtra_2.3
## [33] hms_0.4.2        digest_0.6.18    stringi_1.3.1    grid_3.5.3
## [37] cli_1.0.1        tools_3.5.3      lazyeval_0.2.1   crayon_1.3.4
## [41] pkgconfig_2.0.2  xml2_1.2.0       lubridate_1.7.4  assertthat_0.2.0
## [45] httr_1.4.0       R6_2.4.0         units_0.6-2      nlme_3.1-137
## [49] compiler_3.5.3

## Data Sources

### Thematic Data

Here the thematic data to be visualized is loaded. It is contained in a CSV consisting of columns:

• municipality (municipality name, not used),
• bfs_id (ID to match with geodata),
• mean (average income in the municipality)
• gini (the Gini index for income (in-)equality)

The data provider in this case is the Swiss Federal Tax Administration (FTA), where the original data (as an Excel) can be downloaded from here. The columns used were mean_reinka and gini_reinka for mean and gini (in the “Gemeinden - Communes” tab), respectively. See the first tabs in the Excel for a short explanation. Find additional explanations on the FTA website (German), especially in this PDF.

We used the year 2015 as it is the youngest in the available time series.

### Geodata

Various geodata from the Swiss Federal Statistical Office (FSO) and the Swiss Federal Office of Topography (swisstopo) depicting Swiss borders as of 2015 are used herein.

• input/gde-1-1-15.*: These geometries do not show the political borders of Swiss municipalities, but the so-called “productive” area, i.e., larger lakes and other “unproductive” areas such as mountains are excluded. This has two advantages: 1) The relatively sparsely populated but very large municipalities in the Alps don’t have too much visual weight and 2) it allows us to use the beautiful raster relief of the Alps as a background. These data are now freely available from the FSO. Click on “Download map (ZIP)”, the polygon files are in /PRO/01_INST/Vegetationsfläche_vf/K4_polgYYYYMMDD_vf; different timestamps are available, the 2015 data used here stem from another data set.
• input/g2*: National (s) as well as cantonal borders (k) and lakes (l). Available here.
• (Hillshaded) relief: This is a freely available GeoTIFF from swisstopo. For the sake of simplicity, it was converted to the “ESRI ASCII” format using gdal_translate -of AAIGrid 02-relief-georef.tif 02-relief-ascii.asc on the CLI. The raster can read that format natively, without the need of explicitly installing the rgdal package – which is not the case for GeoTIFF files.

# read productive area (2324 municipalities)

# read in raster of relief
relief <- raster("input/02-relief-ascii.asc") %>%
# hide relief outside of Switzerland by masking with country borders
as("SpatialPixelsDataFrame") %>%
as.data.frame() %>%
rename(value = X02.relief.ascii)

# clean up
rm(country_geo)

### Join Geodata with Thematic Data

In the following chunk, the municipality geodata is extended (joined) with the thematic data over each municipality’s unique identifier, so we end up with a data frame consisting of the thematic data as well as the geometries. Note that the class of this resulting object is still sf as well as data.frame.

municipality_prod_geo %<>%
left_join(data, by = c("BFS_ID" = "bfs_id"))
class(municipality_prod_geo)
## [1] "sf"         "tbl_df"     "tbl"        "data.frame"

## Define a Map Theme

We first define a unique theme for the map, e.g. remove all axes, add a subtle grid (that you might not be able to see on a bright screen) etc. We mostly copied this from another of Timo’s blog posts.

theme_map <- function(...) {
theme_minimal() +
theme(
text = element_text(family = default_font_family,
color = default_font_color),
# remove all axes
axis.line = element_blank(),
axis.text.x = element_blank(),
axis.text.y = element_blank(),
axis.ticks = element_blank(),
panel.grid.major = element_line(color = "#dbdbd9", size = 0.2),
panel.grid.minor = element_blank(),
# background colors
plot.background = element_rect(fill = default_background_color,
color = NA),
panel.background = element_rect(fill = default_background_color,
color = NA),
legend.background = element_rect(fill = default_background_color,
color = NA),
# borders and margins
plot.margin = unit(c(.5, .5, .2, .5), "cm"),
panel.border = element_blank(),
panel.spacing = unit(c(-.1, 0.2, .2, 0.2), "cm"),
# titles
legend.title = element_text(size = 11),
legend.text = element_text(size = 9, hjust = 0,
color = default_font_color),
plot.title = element_text(size = 15, hjust = 0.5,
color = default_font_color),
plot.subtitle = element_text(size = 10, hjust = 0.5,
color = default_font_color,
margin = margin(b = -0.1,
t = -0.1,
l = 2,
unit = "cm"),
debug = F),
# captions
plot.caption = element_text(size = 7,
hjust = .5,
margin = margin(t = 0.2,
b = 0,
unit = "cm"),
color = "#939184"),
...
)
}

## Create a Univariate Choropleth

First, let’s create a standard (univariate) choropleth map based on the average income alone, i.e. the mean variable.

Without going into much detail, this is basically the same process as in the 2016 blog post, detailed in the respective section, just using sf instead of sp.

1. We first calculate quantiles from the average income to form 6 different classes of average income (quantiles are used so each color class contains approximately the same amount of municipalities). From this, we generate a new variable mean_quantiles which is actually visualized on the map. We also generate custom labels for the classes.

2. We generate and draw the ggplot2 object as follows:

• Specify the main data source.
• Add the relief through a call to geom_raster().
• Add a truncated alpha scale for the relief, as the “fill” aesthetic is already taken (refer to this section for an explanation).
• Use geom_sf() without an additional data argument to specify the main fill aesthetic (the visual variable showing the average income per municipality) and to visualize municipal borders.
• Add the Viridis color scale for that fill aesthetic.
• Use two more geom_sf() calls to add cantonal borders and lakes stemming from the canton_geo and lake_geo datasets, respectively.
• Specify our previously defined map theme.
# define number of classes
no_classes <- 6

# extract quantiles
quantiles <- municipality_prod_geo %>%
pull(mean) %>%
quantile(probs = seq(0, 1, length.out = no_classes + 1)) %>%
as.vector() # to remove names of quantiles, so idx below is numeric

# here we create custom labels
labels <- imap_chr(quantiles, function(., idx){
return(paste0(round(quantiles[idx] / 1000, 0),
"k",
" – ",
round(quantiles[idx + 1] / 1000, 0),
"k"))
})

# we need to remove the last label
# because that would be something like "478k - NA"
labels <- labels[1:length(labels) - 1]

# here we actually create a new
# variable on the dataset with the quantiles
municipality_prod_geo %<>%
mutate(mean_quantiles = cut(mean,
breaks = quantiles,
labels = labels,
include.lowest = T))

ggplot(
# define main data source
data = municipality_prod_geo
) +
# first: draw the relief
geom_raster(
data = relief,
inherit.aes = FALSE,
aes(
x = x,
y = y,
alpha = value
)
) +
# use the "alpha hack" (as the "fill" aesthetic is already taken)
scale_alpha(name = "",
range = c(0.6, 0),
guide = F) + # suppress legend
# use thin white stroke for municipality borders
geom_sf(
mapping = aes(
fill = mean_quantiles
),
color = "white",
size = 0.1
) +
# use the Viridis color scale
scale_fill_viridis(
option = "magma",
name = "Average\nincome in CHF",
alpha = 0.8, # make fill a bit brighter
begin = 0.1, # this option seems to be new (compared to 2016):
# with this we can truncate the
# color scale, so that extreme colors (very dark and very bright) are not
# used, which makes the map a bit more aesthetic
end = 0.9,
discrete = T, # discrete classes, thus guide_legend instead of _colorbar
direction = 1, # dark is lowest, yellow is highest
guide = guide_legend(
keyheight = unit(5, units = "mm"),
title.position = "top",
reverse = T # display highest income on top
)) +
# use thicker white stroke for cantonal borders
geom_sf(
data = canton_geo,
fill = "transparent",
color = "white",
size = 0.5
) +
# draw lakes in light blue
geom_sf(
data = lake_geo,
fill = "#D6F1FF",
color = "transparent"
) +
labs(x = NULL,
y = NULL,
title = "Switzerland's regional income",
subtitle = "Average yearly income in Swiss municipalities, 2015",
caption = default_caption) +
theme_map()

## Create a Bivariate Choropleth

In this last section, we eventually create the bivariate map. For this, we first specify a bivariate color scale, using an external software to calculate the appropriate color values. Then we draw the map with basically the same logic as for the univariate map. We then add custom annotations to the map. Lastly, we come up with a possible design of a legend and add that to the overall plot in the end.

### Create the Bivariate Color Scale

Joshua Stevens has a nice write-up on how to create the color codes for a sequential bivariate color scheme. He also gives some background on readability and accessibility of such maps and thus we refrain from discussing these points here. Our blog post is intended to remain purely technical, also for the sake of conciceness and reading time.

Using the “Sketch” software we combined two scales with fill “blue” (base color #1E8CE3) and “red” (base color #C91024), each with three different opacities (20%, 50%, 80%), and blend mode “multiply”, which resulted in the 3 * 3 = 9 hex values specified manually below. Side note: If somebody comes up with a handy way of “blending” hex values in R, or even knows a package for that, please notify us in the comments. Automation never hurts.

This GIF from Joshua’s blog nicely shows the process of blending the two scales:

To match the 9 different colors with appropriate classes, we calculate 1/3-quantiles for both variables.

# create 3 buckets for gini
quantiles_gini <- data %>%
pull(gini) %>%
quantile(probs = seq(0, 1, length.out = 4))

# create 3 buckets for mean income
quantiles_mean <- data %>%
pull(mean) %>%
quantile(probs = seq(0, 1, length.out = 4))

# create color scale that encodes two variables
# red for gini and blue for mean income
# the special notation with gather is due to readibility reasons
bivariate_color_scale <- tibble(
"3 - 3" = "#3F2949", # high inequality, high income
"2 - 3" = "#435786",
"1 - 3" = "#4885C1", # low inequality, high income
"3 - 2" = "#77324C",
"2 - 2" = "#806A8A", # medium inequality, medium income
"1 - 2" = "#89A1C8",
"3 - 1" = "#AE3A4E", # high inequality, low income
"2 - 1" = "#BC7C8F",
"1 - 1" = "#CABED0" # low inequality, low income
) %>%
gather("group", "fill")

### Join Color Codes to the Data

Here the municipalities are put into the appropriate class corresponding to their average income and income (in-)equality.

# cut into groups defined above and join fill
municipality_prod_geo %<>%
mutate(
gini_quantiles = cut(
gini,
breaks = quantiles_gini,
include.lowest = TRUE
),
mean_quantiles = cut(
mean,
breaks = quantiles_mean,
include.lowest = TRUE
),
# by pasting the factors together as numbers we match the groups defined
# in the tibble bivariate_color_scale
group = paste(
as.numeric(gini_quantiles), "-",
as.numeric(mean_quantiles)
)
) %>%
# we now join the actual hex values per "group"
# so each municipality knows its hex value based on the his gini and avg
# income value
left_join(bivariate_color_scale, by = "group")

### Draw the Map

As said above, this is basically the same approach as in the univariate case, except for the custom legend and annotations.

Adding the annotations is a bit cumbersome because the curvature and nudge_* arguments cannot be specified as data-driven aesthetics for geom_curve() and geom_text(), respectively. However, we need them to be data-driven, as we don’t want to specify the same curvature for all arrows, for example. For this reason we need to save all annotations into a separate data frame. We then call geom_curve() and geom_text() separately for each annotation to specify dynamic curvature and nudge_* arguments.

To find out from where to where an annotation arrow should be drawn, we looked at the Swiss national map and manually extracted the x- and y- coordinates of the start and the end point of the arrow.

annotations <- tibble(
label = c(
"Grey areas mean\nlow income and\nlow inequality",
"Blue areas mean\nhigh income and\nlow inequality",
"Violet areas mean\nhigh income and\nhigh inequality",
"Red areas mean\nlow income and\nhigh inequality"
),
arrow_from = c(
"548921,232972", # grey
"771356,238335", # blue
"781136,125067", # violet
"616348,81869" # red
),
arrow_to = c(
"622435,206784", # grey
"712671,261998", # blue
"786229,149597", # violet
"602334,122674" # red
),
curvature = c(
0.2, # grey
0.1, # blue
-0.1, # violet
-0.2 # red
),
nudge = c(
"-3000,0", # grey
"3000,5000", # blue
"0,-5000", # violet
"3000,0" # red
),
just = c(
"1,0", # grey
"0,1", # blue
"0.5,1", # violet
"0,1" # red
)
) %>%
separate(arrow_from, into = c("x", "y")) %>%
separate(arrow_to, into = c("xend", "yend")) %>%
separate(nudge, into = c("nudge_x", "nudge_y"), sep = "\\,") %>%
separate(just, into = c("hjust", "vjust"), sep = "\\,")

Now that the annotations data frame is ready, we can do the following:

• Specify a basic map ggplot2 object, following the same order as in the univariate case (we use scale_fill_identity() instead of the Viridis color scale).
• We then loop over each row of the annotations data frame and add each annotation (geom_curve() and geom_text() calls) to the map object one by one.
• Note that we need to manually specify the font family for the labels again.
map <- ggplot(
# use the same dataset as before
data = municipality_prod_geo
) +
# first: draw the relief
geom_raster(
data = relief,
aes(
x = x,
y = y,
alpha = value
)
) +
# use the "alpha hack" (as the "fill" aesthetic is already taken)
scale_alpha(name = "",
range = c(0.6, 0),
guide = F) + # suppress legend
# color municipalities according to their gini / income combination
geom_sf(
aes(
fill = fill
),
# use thin white stroke for municipalities
color = "white",
size = 0.1
) +
# as the sf object municipality_prod_geo has a column with name "fill" that
# contains the literal color as hex code for each municipality, we can use
# scale_fill_identity here
scale_fill_identity() +
# use thicker white stroke for cantons
geom_sf(
data = canton_geo,
fill = "transparent",
color = "white",
size = 0.5
) +
# draw lakes in light blue
geom_sf(
data = lake_geo,
fill = "#D6F1FF",
color = "transparent"
) +
labs(x = NULL,
y = NULL,
title = "Switzerland's regional income (in-)equality",
subtitle = paste0("Average yearly income and income",
" (in-)equality in Swiss municipalities, 2015"),
caption = default_caption) +
theme_map()

# add annotations one by one by walking over the annotations data frame
# this is necessary because we cannot define nudge_x, nudge_y and curvature
# in the aes in a data-driven way like as with x and y, for example
annotations %>%
pwalk(function(...) {
# collect all values in the row in a one-rowed data frame
current <- tibble(...)

# convert all columns from x to vjust to numeric
# as pwalk apparently turns everything into a character (why???)
current %<>%
mutate_at(vars(x:vjust), as.numeric)

# update the plot object with global assignment
map <<- map +
# for each annotation, add an arrow
geom_curve(
data = current,
aes(
x = x,
xend = xend,
y = y,
yend = yend
),
# that's the whole point of doing this loop:
curvature = current %>% pull(curvature),
size = 0.2,
arrow = arrow(
length = unit(0.005, "npc")
)
) +
# for each annotation, add a label
geom_text(
data = current,
aes(
x = x,
y = y,
label = label,
hjust = hjust,
vjust = vjust
),
# that's the whole point of doing this loop:
nudge_x = current %>% pull(nudge_x),
nudge_y = current %>% pull(nudge_y),
# other styles
family = default_font_family,
color = default_font_color,
size = 3
)
})

### Draw the Legend

For the legend we use the geom_tile() geometry of ggplot2. Before that, we have to quickly transform the bivariate_color_scale data frame, which contains all the hex values for all combinations of average income and income (in-)equality classes, so it has an x- and y-column that can be mapped to the respective aesthetics.

# separate the groups
bivariate_color_scale %<>%
separate(group, into = c("gini", "mean"), sep = " - ") %>%
mutate(gini = as.integer(gini),
mean = as.integer(mean))

legend <- ggplot() +
geom_tile(
data = bivariate_color_scale,
mapping = aes(
x = gini,
y = mean,
fill = fill)
) +
scale_fill_identity() +
labs(x = "Higher inequality ⟶",
y = "Higher income ⟶") +
theme_map() +
# make font small enough
theme(
axis.title = element_text(size = 6)
) +
coord_fixed()

### Combine Map and Legend

Here we just combine the legend with the map using the cowplot package. It allows us to specify the exact position of plots on the canvas, and scaling the width and height of plots (as we do with the legend). It would have been nice to rotate the legend by 45° but we didn’t find a way how to do this.

The numeric arguments to draw_plot() are basically trial and error.

ggdraw() +
draw_plot(map, 0, 0, 1, 1) +
draw_plot(legend, 0.05, 0.075, 0.2, 0.2)

That’s it! We hoped you liked this tutorial. If you have any questions or remarks, or know a better way of doing things, please let us know in the comment section.

You can also give us a shout on Twitter: We’re grssnbchr and angelozehr.

The code in this RMarkdown is linted with the lintr package, which is based on the tidyverse style guide.

lintr::lint("index.Rmd")
## index.Rmd:255:18: style: Words within variable and function names should be separated by '_' rather than '.'.
##   rename(value = X02.relief.ascii)
##                  ^~~~~~~~~~~~~~~~~~