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# nLab Weil reciprocity law

Weil reciprocity is a theorem of André Weil about the quotient field $K\left(C\right)$ of an algebraic curve $C$ over an algebraically closed field $K$.

The following 2 articles make parallel between some notions of QFT and of number theory and in particular about the analogy between the Weil reciprocity law for function fields and the Takahashi-Ward identities of quantum field theory:

• Leon Takhtajan, Quantum field theories on algebraic curves and A. Weil reciprocity law, arxiv/0812.0169; Quantum field theories on an algebraic curve, pdf, 2000

Created on July 25, 2011 20:11:50 by Zoran Škoda (212.91.117.206)


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# An Overview of Logistic Regression Analysis

Image Source: Statistical Aid
Logistic regression is a statistical technique to find the association between the categorical dependent (response) variable and one or more categorical or continuous independent (explanatory) variable.
We can define the regression model as,

G(probability of event)=Î²0+Î²1x1+Î²2x2+¦+Î²kxk

We determine G using link function as following,

Y={1 ; Î²0+Î²1x1+Ïµ>0

{0 ; else

There are three types of link fuction. They are,

• Logit
• Normit (probit)
• Gombit

## Why we use logistic regression?

We use it when there exists,

• One Categorical response variable
• One or more explanatory variable.
• No linear relationship between dependent and independent variables.

## Assumptions of Logistic Regression

• The dependent variable should be categorical (binary, ordinal, nominal or count occurrences).
• The predictor or independent variable should be continuous or categorical.
• The correlation among the predictors or independent variable (multi-collinearity) should not be severe but there exists linearity of independent variables and log odds.
• The data should be the representative part of population and record the data in the order its collected.
• The model should provide a good fit of the data.

## Logistic regression vs Linear regression

• In the case of Linear Regression, the outcome is continuous while in the case of logistic regression outcome is discrete (not continuous)
• To perform linear regression, we require a linear relationship between the dependent and independent variables. But to perform Logit we do not require a linear relationship between the dependent and independent variables.
• Linear Regression is all about fitting a straight line in the data while Logit  is about fitting a curve to the data.
• Linear Regression is a regression algorithm for Machine Learning while Logit  is a classification Algorithm for machine learning.
• Linear regression assumes Gaussian (or normal) distribution of the dependent variable. Logit assumes the binomial distribution of the dependent variable.

*Logit=logistic regression

## Types

There are four types of logistic regression. They are,

• Binary logistic: When the dependent variable has two categories and the characteristics are at two levels such as yes or no, pass or fail, high or low etc. then the regression is called binary logistic regression.
• Ordinal logistic: When the dependent variable has three categories and the characteristics are at natural ordering of the levels such as survey results (disagree, neutral, agree) then the regression is called ordinal logistic regression.
• Nominal logistic: When the dependent variable has three or more categories but the characteristics are not at natural ordering of the levels such as colors (red, blue, green) then the regression is called nominal logistic.
• Poisson logistic: When the dependent variable has three or more categories but the characteristics are the number of time of an event occurs such as 0, 1, 2, 3, ¦, etc.  then the regression is called Poisson logistic regression.

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# particular solution to nonhomogenous equation

I want to solve the ODE $y''+4y=x^2+3e^x$

I already found the complemenetary homogenous solutions: $y_1=\cos (2x)$ and $y_2=\sin (2x)$ and also found the wronskian: $|W|=2$

Now, according to http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx the variation of parameters method states that the particular solution is:

$$y_p = -\cos (2x)\int \frac{ \sin (2x)(x^2+3e^x)}{2}dx+\sin (2x)\int \frac{ \cos (2x)(x^2+3e^x)}{2}dx$$

This isn't the most pleasant integral I've seen. Far from it, it doesn't seem feasible to calculate it. Is there another method to find the particular solution?

• Those integrals can be computed by parts, with multiple rounds. – user170231 Feb 4 '15 at 21:40

Yes there is another method which is known as the undetermined coefficients. According to it we assume the particular solution to have the form

$$y_p = A+Bx+cx^2 + De^x \longrightarrow (1)$$

where constants $A,B,C,D$ need to be determined by substituting $y_p, y'_p, y''_p$ in the ode.

The method of undetermined coefficients makes things much simpler.

It is not difficult to check that: $$f(x) = \frac{x^2}{4}-\frac{1}{8}+\frac{3}{5}e^x$$ is a solution, so by setting $y(x) = g(x)+f(x)$ we have that $g$ satisfies the homogeneous ODE: $$g''+4g = 0,$$ for which you already know the solutions.

I am a fan of the Laplace transform technique: $$\mathcal{L}\left\{y''+4y=x^2+3e^x \right\} \\ \implies s^2Y(s)-y'(0)-sy(0)+4Y(s)=\frac{2}{s^3}+\frac{3}{s-1} \\ \implies Y(s)(s^2+4) = \frac{2}{s^3}+\frac{3}{s-1}+y'(0)+sy(0) \\ \implies Y(s) = \frac{2}{s^3(s^2+4)}+\frac{3}{(s-1)(s^2+4)}+\frac{y'(0)}{s^2+4}+\frac{sy(0)}{s^2+4}$$ Then use partial fraction decomposition on $\frac{2}{s^3(s^2+4)}$ and $\frac{3}{(s-1)(s^2+4)}$ to get $$\frac{2}{s^3(s^2+4)}=\frac{1}{2s^3}+\frac{s}{8(s^2+4)}-\frac{1}{8s} \\ \frac{3}{(s-1)(s^2+4)}= \frac{3}{5(s-1)}-\frac{3s}{5(s^2+4)}-\frac{3}{5(s^2+4)}$$ Hence $$Y(s) = \frac{1}{2s^3}+\frac{s}{8(s^2+4)}-\frac{1}{8s}+\frac{3}{5(s-1)}-\frac{3s}{5(s^2+4)}-\frac{3}{5(s^2+4)}+\frac{y'(0)}{s^2+4}+\frac{sy(0)}{s^2+4}$$ and undoing the transform should reveal $$y(x) = \frac{x^2}{4}+\frac{1}{8}\cos(2x)-\frac{1}{8}+\frac{3}{5}e^x-\frac{3}{5}\cos(2x)-\frac{3}{10}\sin(2x)+\frac{y'(0)}{2}\sin(2x)+y(0)\cos(2x) \\ = \frac{x^2}{4}-\frac{1}{8}+\cos(2x)\left(y(0)-\frac{19}{40}\right)+\sin(2x)\left(y'(0)-\frac{3}{10} \right)+\frac{3}{5}e^x$$ This is the solution for whatever initial conditions $y(0), \space y'(0)$ you want. While the method is algebra intensive, you don't have to integrate anything.

\begin{align*}\int\frac{\sin2x(x^2+3e^x)}{2}\,dx&=\frac{1}{2}\left(\int x^2\sin2x\,dx+3\int e^x\sin2x\right)\end{align*} Integrating by parts, you can find that \begin{align*}\int x^2\sin2x\,dx&=-\frac{1}{2}x^2\cos2x+\int x\cos2x\,dx\\ &=-\frac{1}{2}x^2\cos2x+\frac{1}{2}x\sin2x-\frac{1}{2}\int\sin2x\,dx\\ &=-\frac{1}{2}x^2\cos2x+\frac{1}{2}x\sin2x+\frac{1}{4}\cos2x+C_1\end{align*} Similarly, \begin{align*} \int e^x\sin2x&=-\frac{1}{2}e^x\cos2x+\frac{1}{2}\int e^x\cos2x\,dx\\ &=-\frac{1}{2}e^x\cos2x+\frac{1}{2}\left(\frac{1}{2}e^x\sin2x-\frac{1}{2}\int e^x\sin2x\,dx\right)\\ &=-\frac{1}{2}e^x\cos2x+\frac{1}{4}e^x\sin2x-\frac{1}{4}\int e^x\sin2x\,dx\\ \frac{5}{4}\int e^x\sin2x\,dx&=-\frac{1}{2}e^x\cos2x+\frac{1}{4}e^x\sin2x\\ \int e^x\sin2x\,dx&=-\frac{2}{5}e^x\cos2x+\frac{1}{5}e^x\sin2x+C_2\end{align*}


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Changeset 3655 for Papers

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• Papers/jar-cerco-2017/framac.tex

 r3654 follows: \begin{enumerate} \begin{itemize} \item each function is independently processed and associated a WCET that may depend on the cost of the other functions. This is done with a mix between
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# How can I have a corrupt meritocratic government without it being perceived as such?

I like to play with superlatives. I want a government that pretends to be rightly-guided by the most sacred morals and ideals, but in reality is filled with fat cats who only care for themselves. However, the people must not know about it; they know about corruption in other countries, and the clear majority of people truly believe that their country is above that. So how far can I go in my government's corruption?

Background

The general era is something we would recognise as the 15th-16th century. There's steel and gunpowder, but no steam power. There's a literary tradition stretching back a thousand years, but few people are literate. There are religious beliefs but they are not part of the state; in its place is a state philosophy that might as well be a religion. People are steadily growing sceptical of said philosophy, but for now the government (while ostensibly encouraging critical thinking) suppresses diverging thought, passing it off as misguided and/or dangerous.

The ideal

The government, ruling over a hundred million people of many different cultures in a nation the size of Kazakhstan, works on the basis of the following philosophy: rule is only by the virtuous, and every virtuous person will end up ruling. There's imperial exams taken by every young man and a few bright women (the society is still quite sexist), and those with the best results will end up with roles in the bureaucracy. There's layers upon layers of bureaucrats that report to one another, and at the very top is a council of 52 supreme officers, along with a supreme emperor whose only political power is appointing and dismissing those officers (and giving them supreme moral guidance). The position of supreme emperor is for life, but not hereditary; when one dies, the successor is whoever got the very best score in next year's imperial exams, from a different province in the country (rotating between all the provinces).

Now a lot hinges upon the fairness of these exams, so one of the lowest positions in the bureaucracy is overseeing them. That means that the turnover rate is high among the examiners, so there's little opportunity for corruption to take root there.

Every political position of meaning is part of the bureaucracy; hereditary power transfer is virtually non-existent. Outside the state, power structures exist in the form of religious institutions, and private commercial enterprises. But the church is not quite an authority; the state philosophy is religiously pluralistic and states that all gods live together in one pantheon, leaving open which one is the head god (if any). And this is long before corporations became the lobbying influence we have today; a few figures like Jakob Fugger exist but most businesses are small and family-owned.

Practise

That's the theory. Everything stated in the previous section is either accurate or popularly perceived as such. So where can I add corruption? The easiest place is among the bureaucrats. There's so many layers and departments, and people from layer n are generally appointed and dismissed by those from layer n+1. They all socialise with one another so they can get an idea of which of potential candidates for a position would be susceptible to take bribes, and then only promote those people; effectively shutting the true idealists out of the administration beyond a certain layer. Impeachment procedures are rare since people in higher stations are assumed to be more virtuous.

But I want to go beyond that. I am looking for the most effective methods by which the highest officials can evade all scrutiny and turn their backs on the doctrine of virtue deciding position. I want ways to maintain the illusion of social mobility, compatible with the state as described, that allow for large-scale embezzlement and self-enrichment by the powerful.

Take this in a society that is not democratic and without mass media, but also not a totalitarian government that can just make people disappear and it lacks means of communication faster than a horseback courier. How corrupt can I make the country, while everyone still believes that it is not corrupt; and in what ways?

Concrete question

What measures can the government officials and powerful people in general take in this country, to disproportionally enrich themselves, without people at large perceiving their country as corrupt, given the society and history as described? Average citizens who are not closely involved with politics should be able to reasonably think that their leaders are really virtuous and not at all enriching themselves.

• Possible real-world inspiration: The Catholic Church. Nov 12, 2020 at 14:25
• @Philipp Could you elaborate? Nov 12, 2020 at 14:27
• It's an organization which maintains the appearance to be based on virtue (it's literally their brand) and being a meritocracy, but they are very good at keeping scandals under cover. And it is an organisation which is even larger than the administrations of many countries. Nov 12, 2020 at 14:28
• "perceived as such" part makes this very opinion-based. Nov 12, 2020 at 17:33
• @KeizerHarm we may be going a little off-topic here, but the downfall of Catholic Church in several countries in the early XVI century could be in part attributed to "Ninety-five Theses" distributed with the use of printing press. Nov 12, 2020 at 19:55

Unclear Rubrics

The way to check if an exam is corrected fairly is using a rubric. This says what the correct answers are, and exactly what you need to write to get full marks. This lets the marker justify their scores and lets unhappy examinees appeal with some degree of rigor. When I am unhappy with my score I point to the rubric and say "I lost marks for X but it wasn't in the rubric!".

The way to corrupt an exam is by having either no rubric, so the marker can just make up reasons someone got full marks after seeing their script. Or you have a rubric that is so vague they you can do the same.

I suggest there be several layers of increasingly vague rubrics. For example for the essay question Rubric #1 is basic spelling and grammar. #2 is basic reasoning skills, and so on until #10 is something like

Moral character conducive to the proliferation of life, liberty and the pursuit of happiness for all citizens of this great country under God.

Extra points for overblown language.

Rubric #1 is employed by level 1 bureaucrats. They chuck out anyone with bad spelling and grammar, and pass the good scripts upstairs to where level 2 bureaucrats apply Rubric #2. The first few levels work well and ensure the bureaucracy is filled with competent people. It also gives the impression the system is fair, since most people only see the first few levels.

Level 10 exams are rare, since you have to pass exams 1-9 to even sit level 10. Every level 10 exam is marked by the emperor. There is so much room for interpretation about what "moral virtue" means that the rigor disappears and the emperor can appoint whoever they want.

There is also an option to skip the first few levels of assessment if a sufficiently virtuous candidate is found. This is the story when the Chancellor's deaf-mute second cousin the in-law gets appointed Minister of Agriculture. After all, you can teach spelling and grammar but you cannot teach being a good person.

From then on we have the usual problem that no one ever sees the Minister on the street and all their public engagements are highly choreographed for maximum virtue signalling. There is no way for the common man to figure out on their own if the Minister is corrupt or not.

There might still be a basic literacy requirement. I don't think this is a problem. It certainly lines up with the real world where corrupt people in power have to be (a) smart enough to get into power and (b) smart enough to not seem corrupt.

• Sounds good, with the vast majority being righteous and perceived as such, with only the "Top-Scoring" cadets having potential to rise up and only them being affected by the corruption. Nov 12, 2020 at 14:18
• Good solution for corrupting exams. Though makes me wonder how many level 10 examiners are out there to review the millions of exams turned in each year - unless you reserve the higher levels for those already in the bureaucracy, and make them take more complicated (and fuzzy) exams before every potential promotion. Nov 12, 2020 at 14:28
• Is “conman man” a slip of the keyboard or a statement on society?? Nov 12, 2020 at 14:46
• @KeizerHarm The idea is you sit a level 1 exam, and it's marked by other level 1 people. If you pass you get to sit level 2 and that's marked by level 2 people. And so on. The number of potential markers goes down, but so does the number of exams to correct. Nov 12, 2020 at 16:07
• @JoeBloggs Typo I'm afraid. Nov 12, 2020 at 16:07

Education. Private tutors etc rigorously prepare the children of high-ranked members to score as highly as possible on the tests. They know what the expected "correct" answers will be and the tests vary little from year to year so practicing on prior papers is very effective. Note they don't learn anything useful. Just how to ace the exams.

Combine this with a bit of "leaning" on people to go easy or hard on the correct candidates. This gives you hereditary power that over time concentrates in a few families no matter how competent or not individual members are.

Daron's answer already covered vague exams. Take a look at this for a real world example of just how corrupt these things can be: https://metro.co.uk/2017/09/20/could-you-pass-this-test-given-to-black-people-registering-to-vote-in-america-in-1964-6941338/

As to the perception thing, that's easy. You keep the corruption to the higher levels and dress everything up. You control the media, the police, the intelligence services.

Anyone accusing you of corruption is a seditious traitor and needs to be "sent away for re-education".

• Sheesh, that article horrifies me. Nov 12, 2020 at 14:54
• @KeizerHarm One reason I shared it is more people need to know about it. That stuff was real and in use only 60 years ago. People are alive today who were involved in overturning it....and in implementing it. Some of the people who wrote and administered those exams are still alive and voting in the USA... Nov 12, 2020 at 14:56
• But it's a good answer, except for the bit "media, police, and intelligence services". This is a pre-industrial era, there's no media (no printing press), police system is unorganised, and intelligence services not nearly as powerful as the modern equivalents. Also I don't think re-education camps are a thing when the state can't be totalitarian enough. Nov 12, 2020 at 15:18
• @KeizerHarm "media" takes many forms. No printing press but you do have bards, storytellers, legends and ballads. You have monuments, statues, paintings, even buildings and place names. You have announcements and town criers. Nov 12, 2020 at 15:48
• On the other hand I agree that informers, police, spies, etc. may not be as organised or centralized, but they do exist and will generally act to protect authority. Nov 12, 2020 at 15:49

### Require collateral to enter or advance in the bureaucracy.

Serving the people isnt just a job for our committed public servants, but a promise and a commitment to the doctrine of trust and loyalty. Everyone who wants to join this wonderful institution needs to offer some asset as collateral in return for their service and loyalty to their branch of the government.

Externally - "every member of the government has given the deed to their house as collateral in case they cheat or steal from us, I wouldnt steal in this case so our government is obviously very virtuous!"

Practically - whistle blowing is disloyalty to your boss, so any jealous employee trying to smear their boss for selfish reasons obviously will lose their collateral. This should be made very clear on orientation. They'll die homeless and hungry if they cast the government in a bad light, and it will only embarrass their boss or bosses boss at most.

Advancing in the bureaucracy requires more collateral, if you have no more wealth, you need to share a family secret, something worth blackmailing you over (eg a signed letter that your brother confessed to cheating on his partner, true or not, or a detailed account of how your father swindled huge wealth from the masses. Anything embarrassing. Make it up if you need to.) and give that as collateral. It's needed for any promotion. It's to ensure your loyal to your government.

Each promotion requires new information more scandalous than the last.

By the time you get to the upper rungs of the corruption, you've signed letters stating your spouse is kidnapping and eating children, you father burnt down churches, and your children were gifts from satan. Your superiors have so much dirt on you they could get your former friends to burn your entire family at the stake. Any allegations of corruption by a whistleblower can be met with enough evidence to brutality destroy the families reputation enough to dismiss or bury the allegations.

So long as the masses are fed and sheltered and entertained - you could take everything else of value for yourselves.

• I like the idea, but wouldn't the confession system break down trust in government as soon as people are ousted for it? Rule is by the virtuous: if any homosexual, cheater or swindler did end up in high ranks, then the system has already failed. Nov 12, 2020 at 15:59
• @KeizerHarm they'd be caught at the lower levels, because the higher you go, the less likely you are to betray the system. That they were caught can easily be spun as the system working to expose cheats. This is basically the technique nxvm and scientology used.
– Ash
Nov 12, 2020 at 16:03
• @KeizerHarm actually on further thought the nxvm blackmails were family first, then personal. That's probably a better fit here anyway for the reason you gave. I've edited.
– Ash
Nov 12, 2020 at 16:08

Corruption is the merit.

You know, that might be the answer - to act boastfully about something we ought to be ashamed of. That's a trick that never seems to fail.

-- Catch-22

Merit is not, despite the ideal of a meritocracy, some natural, physical constant that can be determined empirically. The government, through culture, media, education, religion, and tradition, determines what is meritorious. Philosophers talk about government virtues or they get put on the banned list. Poets who want the aristocracy to support them flatter them. Teachers and preachers uphold the traditional ideals or else the community will turn on them as renegades.

So there's no need for the merit your meritocracy measures to be the merit we, the readers, would expect or want them to measure. Maybe merit is a measure of how much money you can bring in (and never you mind where it comes from), or how much your farms and workshops can produce in a year. Maybe merit is a popularity contest, and your people think of buying votes through bread and circuses to be meritorious (after all, it makes people happy). Perhaps your definition of merit is ideological purity, or loyalty to a ruling party, or to God.

The key is that, in addition to rigorously testing officials, the meritocracy also vigorously pushes its idea of merit onto the population.

• They keyword is that your income measures your "CONTRIBUTION TO SOCIETY". Nov 12, 2020 at 18:16
• That is really creative, I like it. It only becomes a bit difficult when this country feels so elevated above its neighbouring countries precisely because those countries are "totally corrupt" which the empire "most certainly isn't". So the merit of corruption needs to be specific to the empire; when other countries do it it's a sin. Nov 13, 2020 at 8:09
• @KeizerHarm "Corruption" is a pretty broad term. (Are we talking about graft? Nepotism? Favoritism to a particular group? Backroom deals between power brokers?) It wouldn't be hard to draw a distinction between two practices where we would both see as corrupt, but your nation preaches that one is virtuous and the other not. Nov 13, 2020 at 9:18
• @Cadence You're right. My vision was focused on the self-enrichment and the literal corruption of the values of merit = right; but that can be done through many different ways, some of which may still be compatible with the state philosophy. Nov 13, 2020 at 10:07

## How Should Corruption Be Quanitified?

To measure how corrupt a government can get, and compare it to different measurements, I think we need a way to quantify corruption. I think this approach might work : what % of resources (quantified as GDP), allocated to be spent on public good, actually makes it to that work.

So, for some examples : out of every \$1,000 allocated to schools, only \$10 makes it to the teacher's salary - the government is $$1 - ({10 \over 1000})$$ = 99% corrupt.

## With That In Mind, There Are Some Obvious Ways to Scale This

There is a joke about corruption -- a bureaucrat is charged with repairing a road. He gets two bids : the first bidder asks \$100 to do the job. The second bidder asks \$1,100 to do the job. The bureaucrat asks the second bidder why he's so high. The 2nd bidder says : \$500 for you, \$500 for me, and \\$100 to hire the first bidder.

There exists, I believe, a minimum cost to provide public services. But government and contractor peers can charge any amount of premium on top of that. The bigger the ledger of acquisitions becomes, the harder it is to scrutinize any one particular transaction, and the harder it becomes to prove that a single proven case of corruption is systemic, instead of an outlier.

At any given year, the government needs to appear to be delivering the same amount of service. So, for a while you can increase corruption by increasing the amount of resources you allocate from the people (taxes + inflation) : increasing the cost of the government's services, without providing any new service.

You can get creative with how you tax the people : income taxes are most obvious. Less obvious are sales taxes, head taxes, property taxes, tolls, rents, fees, or inflationary spending (printing extra money - the people who can't get themselves a raise to offset the diluted purchasing power of the money are, in a way, the one's paying a tax -- usually the poorest people).

Taxing the people has a peak upper limit where nearly all of society is working all their waking hours to earn, after taxes, just barely enough to keep them healthy enough to work tomorrow.

## Managed Decline

After taxes have peaked, government can then gradually reduce the service being provided. As long as service reduction is in tiny increments, it's not shocking enough to cause people to clearly motivate people to seek a life somewhere else.

You can make small substitutions : cheapen labor costs for the services you provide by outsourcing jobs, side-stepping your own environmental laws by getting your services from countries with no such laws, cutting non-administrative staff, rationing

## Extremes

Between raising taxes and gradually reduced services, a government can easily hit 100% corruption.

First, maybe we need to change our scale, since really corrupt governments are going to be between 99.9% and 100% corrupt. Let's just count the number of nines after 99% for these extreme cases. A 99.9% corrupt government is 1C. A 99.99999% corrupt government is 5C.

Maybe we need a different metric for really corrupt governments : percentage of potential GDP trickling down to the people, where potential GDP (pGDP) includes off-the-books activity like building your own wagon, farming, mending clothes, and so on. How much bigger than GDP is pGDP? You can press all working-age adults into service for about a 60% increase; press traditional home keeping roles into service, for another 100% increase, so pGDP $$\approx$$ 2.6 $$\times$$ GDP

There's a limit. People have minimal requirements : enough food (2,000 calories per day) to keep going, some water, sleep (about 8 hours per day), and housing. Land costs nothing for a government that can seize it, so the real minimum requirement is whatever it costs for 2,000 calories and the lost labor of 8 hours of sleep (33% of a 24 hour day). And government corruption is = $$1 - ({servicesprovided \over pGDP})$$. If a government provides nothing of value, let services provided = 1

## Trying It Out

Let's assign a value of GDP, so that we can look at some numbers. Let's say our corrupt government has a GDP of 1 million Generic Currency Units (GCU).

A totally corrupt government, providing nothing of value, forcing all able-bodied people to work 40-hour weeks (23% of 7 $$\times$$ 24-hour days), and taxing all of that effort through various means is $$1 - ({1 \over {0.23 \times 2.6 \times 1,000,000}}) =$$ 99.999% (3C) corrupt.

A less corrupt government, allowing the young to go to school and the old to retire, and allowing the people to keep their cultural traditions of half the workforce staying at home to take care of the young and old, but still taxing everything out of a 40-hour work week is $$1 - ({1 \over {0.23 \times 1,000,000}}) =$$ still 99.999% (3C) corrupt.

## Limits

A government requiring all able-bodied people to work all waking hours (16 $$\times$$ 7 = 112) (66% of the week) for the government's benefit and receiving nothing in return is $$1 - ({1 \over {0.66 \times 2.6 \times 1,000,000}}) =$$ 99.9999% (4C) corrupt.

Once people start starving to death, or dying because they fell asleep at the grinder, rebellion isn't far away.

I would suggest 4C is as corrupt as any government can become, by any means, before things fall apart. At 4C corruption has become so bad that people are literally being worked to death and getting no benefit or relief from their rulers. I believe this is a hard limit because even if the populous still believes in the government, they are ceasing to exist due to malnutrition and exhaustion.

There’s a television show, ‘Poldark’ that attempts to demonstrate these conditions in 1770s Britain.

## Meritocratic Governments are VERY easy to corrupt

As a general rule, people who want power will gravitate to where power exists unless some force prevents them from doing so. In the case of democracies and monarchies, the most power hungry members of society are prevented from rising up to the top echelons of power by the electoral process or line of succession respectively. However, any government that allows its members to self-select is much less resistant to corruption because instead of using a system designed to filter corruption out, you have a system designed to filter corruption in.

In a meritocracy, the question always boils down to "How do you define Merit". Because this question is answered by the Government, the answer always eventually transitions to "Whoever the government says has Merit."

Because the government decides who is worthy to be a member, existing members will typically select new members based on who will be the smallest threat their own power rather than who can actually do the job best. So if you are a slightly corrupt leader, you will need to bring in new members who are at least as corrupt as you to make sure that they don't whistleblow you. This creates a sort of natural selection scenario where fitness is defined by a thirst for power and lack of ethics. So, the kinds of unethical things the government is willing to will perpetually grow, but never shrinks.

This kind of Corruption can be see in the Roman Praetorian Guard where after just a few generations of letting Praetorians hand pick whoever they deemed the best of the best, they were extorting the government for salaries and bonuses worth over 20 times a normal soldier's pay, they were assassinating their own emperors and manipulating the line of imperial succession, and basically doing whatever the heck they wanted because they all agreed that they could... and this is just what can happen when a small subsection of your government practices hand-picking new members.

## But It Won't Last Long Enough For The General Population to Notice

In the 15th-16th Century, most people had very little idea about what happened outside of their own little town or neighborhood, but as much as there was less technology for spreading information, there was also less technology for spreading misinformation; so, what is "true" in this world is whatever you are told by another human being... and the only way to find the truth between two conflicting people is to have a system for defining who is more trustworthy.

So, if we replace late medieval Feudalism with a Meritocracy without changing any other cultural or technological elements, what you will see are things like the code of chivalry and the divine right of rulership come into play. The code of chivalry says that people of noble birth have an extra duty to be honest in all things; so, in this world, your leaders will be expected to be chivalrous, and the people they select will be expected to be able to follow the code of chivalry. Then the divine right of rulership says that God himself guides the succession of rulers; so, if a person is promoted to be a member of the government, then this is the will of God and is therefore beyond contestation.

With these factors in place, anything a ruler says is true, and anything a commoner says otherwise must be a lie because commoners are not bound by chivalry and they are not chosen by the will of God, and even if a leader does get caught in a lie, you still can not oppose him without risking your immortal soul by contradicting the will of God who gave them rulership.

In short, the government will become perpetually more corrupt, but never so corrupt that a significant number of people will be willing to question or oppose it. Instead what will happen is that the government will eventually select members who are so motivated by power and care so little about ethics that the leadership itself will be the government's undoing. Instead of selecting new members to bring in, someone will eventually rise up who will want to be the nation's undisputed monarch at which point there will be some manner of civil war or extermination of political opponents followed the dismantling of the meritocratic system all together.


text:
Question

Basic MATH QUESTIONS?Q-1. Solve the algebraic expressions: a. (???? 4 + 3???? 3 − ???? + 1) ÷ (???? 2 +

3)

b. (???? 3 − 1)(???? 7 − 2???? 4 − 5???? 2 + 5)

Q-2. Match the factoring formula with the correct geometric factoring models labeled as a and b.

*DIAGRAN ON ATTACHMENT

Q-3. A rectangle has area and width as indicated in the figure. Factor to find the length.

*

Q-4. Factorize the following: a. 8???? 2???? − 60???????? + 28 b. ???? 2 + 6???? + 9 − ???? 2 c. 4(???? 2 + 1) 2 − 2(???? 2 + 1) 3

Q-5. Perform the indicated operations and simplify:

a. 18−2???? 2 ????2−5????+4 × ???? 2−2????−8 ????2−6????+9 ÷ ( ???? 3−6???? 2 ????2−????−12 × ???? 2−2????+1 ????−????3 ) 6

b. 2????+1 4????−2 + ???? ???? 2−4 − ????−2 ???? 2+????−6 + (???? − 2)

Q-6. Management is attempting to identify the most active person in labor’s efforts to unionize. The following diagram shows how influence flows from one employee to another among the four most active employees.

a. Construct matrix A with elements ???????????? = { 1 if ???? influnces ???? directly 0 ????????ℎ????????????????????????

b. Construct matrix B with elements ???????????? = { 1 if ???? influnces ???? through at most one person, with ???? ≠ ???? 0 ????????ℎ????????????????????????

c. The person i is most active in influencing others if the sum of the elements in row i of the matrix A + B is the largest. Who is the most active person? 3 1 4 2 8

*

Q-7. Find determinant of X matrix and the inverse of the X matrix of following simuaneous equations by using Gauss Jordan method: 7???? + 2???? = 47 5???? − 4???? = 1 By using inverse matrix find the solution of above simuaneous equation.

Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner
Math


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# What is the value of sin(arcsin(4))?

In this case arcsin() is the unrestricted sin inverse function. I know that it is either undefined or has the value of 4. It could be undefined because arcsin() has only a doman of -1...1 and 4 is out of the domain. On the other hand, it could be that since they are inverses the intermediary result does not matter and they will cancel to get back 4. Which one is it?

-

If you are working with real numbers, $\arcsin(4)$ doesn't exist.

Note that the formula

$$\sin(\arcsin(x))=x$$ only holds over the domain of $\arcsin(x)$ which is $x \in [-1,1]$.

Things are different when you work with complex numbers though....

-

Complex values aside, this expression cannot be evaluated since the $arcsin$ can only be taken from valus between -1 and 1 (inclusive) so the cancelation property of the inverses cannot be applied here. Cancelation property of inverses can be used for values that are in the respective domains of the functions. Think about $\sqrt(-2)^2=-2$ where I cancelled the squareroot against the square.

-

If you are willing to allow complex numbers, $\arcsin(4)$ does exist: it is $\pi/2 - i \ln(\sqrt{15}+4)$ (using the principal branch of arcsin). If not, as others have said, the expression is undefined.

-


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Volume 358 - 36th International Cosmic Ray Conference (ICRC2019) - NU - Neutrino
Subluminal Magnetic Monopole Search with NOvA
M. Frank,* A. Antoshkin, C. Dukes, R. Ehrlich, E. Song
*corresponding author
Full text: pdf
Pre-published on: 2019 July 22
Published on:
Abstract
Proof of the existence of the magnetic monopole has eluded physicists for centuries. The NOvA far detector (FD), used for neutrino oscillation searches, has the ability to identify magnetic monopoles at subluminal velocities (v < c/100). With a surface area of over $4,000~ \mathrm{m}^{2}$ and a location near the earth's surface, the 14 kt FD provides unique sensitivity to potential low-mass monopoles unable to penetrate underground experiments. We have designed a novel data-driven triggering scheme that continuously searches the FD's live data stream for monopole-like patterns. At the offline level, the largest challenge in reconstructing monopoles is to reduce the 148,000 Hz speed-of-light cosmic ray background. This poster presents the trigger algorithm, the offline reconstruction algorithm, as well as the background rejection methods that will be used for the first NOvA monopole search.
Open Access


text:
Keywords: performance surfaces, optimum points

## Neural Network Training Technique1

In the articles posted before, several architectures of the neural networks had been proposed. And each neural network had its own learning rule, like, perceptron learning algorithm, Hebbian learning algorithm. What we should do when more and more neural networks come to accumulate is becoming complicated. If we can propose some general methods, we can train new architecture easily by simply modifying existing algorithms. Up to now, we can classify all training rules in three categories in a general way:

1. Performance Learning
2. Associative Learning
3. Competitive Learning

Linear associator we discussed in ‘Hebbian Learning’ is a kind of associative learning, which is used to build a connection between two events. Competitive learning is a kind of unsupervised learning in which nodes of the neural network compete for the right to respond to a subset of the input data.2 The main topic we are going to discuss today is Performance Learning which is also a widely used training method in neural network projects. By the way, the categories of learning can be classified from variant views. So, this is not the only kind of classification.

## Performance Learning and Performance Index

Training a network is to find suitable parameters of the model to meet our requirements for some specialized tasks. If we can measure how satisfied the neural network is for the task at a certain time, we can then decide what to do next to modify the parameters. Performance learning is the procedure that modifies the parameter of neural networks by their performance through a certain measurement of the performance of the neural network.

The measurement of the performance we investigate here is called performance index and its appearance is called performance surface. What we should also concern is the conditions for the existence of the minima or maxima. Because the minima or maxima decide the final result of the performance of the neural network for the task. In a word, what we need to do is optimizing the performance index by modifying parameters of the neural network to satisfy a certain task(training set).

Performance learning contains several different laws. And there are two steps involved in the optimization process generally:

1. Define the concept what we called ‘performance’
• a quantitative measure of network performance is called performance index which has the properties when the neural network works well it has a lower value but when neural network works poorly it has a larger value
2. Search parameters space to reduce the performance index

This is the heart of performance learning. After defining a performance or building a performance index, we cloud also analyze the characteristics of the performance index before searching for the minima. Because, if the performance index we had selected did not meet the conditions of the existence of minima, searching for a minimum is just a waste of time. Or we can also set the additional condition to guarantee the existence of a minimum point.

## Taylor Series

When we have a suitable performance index, what we need is a certain algorithm or a framework to deal with the optimization task. To design such a framework, we should study the performance index function firstly. Taylor series is a powerful tool to analyze function.

### Scalar form function

A function $F(x)$ is analytic function which means all derivatives of $F(x)$ exist. Then the Taylor series expansion about some nominal points $x^{\star}$

\begin{aligned} F(x)=F(x^{\star})&+\frac{d}{dx}F(x)|_{x=x^{\star}}(x-x^{\star})\\ &+\frac{1}{2}\frac{d^2}{d^2x}F(x)|_{x=x^{\star}}(x-x^{\star})^2\\ &\vdots \\ &+\frac{1}{n!}\frac{d^n}{d^nx}F(x)|_{x=x^{\star}}(x-x^{\star})^n \end{aligned}\tag{1}

This series with infinity items can exactly equal to the origin analytic function.

If we only want to approximate the function in a small region near $x^{\star}$, only finite items in equation(1) are needed.

For instance, we have a function $F(x)=\cos(x)$ when $x^{\star}=0$, then:

\begin{aligned} F(x)=\cos(x)&=\cos(0)-\sin(0)(x-0)-\frac{1}{2}\cos(0)(x-0)^2+\cdots\\ &=1-\frac{1}{2}x^2+\frac{1}{24}x^4+\cdots \end{aligned}\tag{2}
• $0^{\text{th}}$ order approximation of $F(x)$ near $0$ is $F(x)\approx F_0(x)=1$
• $1^{\text{st}}$ order approximation of $F(x)$ near $0$ is $F(x)\approx F_1(x)=1+0$
• $2^{\text{nd}}$ order approximation of $F(x)$ near $0$ is $F(x)\approx F_2(x)=1+0-\frac{1}{2}x^2$
• $3^{\text{rd}}$ order approximation of $F(x)$ near $0$ is $F(x)\approx F_3(x)=1+0-\frac{1}{2}x^2+0$
• $4^{\text{th}}$ order approximation of $F(x)$ near $0$ is $F(x)\approx F_4(x)=1+0-\frac{1}{2}x^2+0+\frac{1}{24}x^4$

Odd number$^{\text{th}}$ iterm is $0$ because of the value of $\sin(x)$ at $0$ is $0$

And the $0^{\text{th}},1^{\text{st}},2^{\text{nd}},3^{\text{rd}}$ and $4^{\text{th}}$ approximation of $F(x)$ looks like:

and, from the figure above we can observe that $F_0(x)$ can only approximate $F(x)$ at $x^{\star}=0$ point. While in the interval between $-1$ and $+1$, $F(x)$ can be precisely approximated by $F_2(x)$. In a more wider interval like $[-1.6,+1.6]$ to approximate $F(x)$, $4^{\text{th}}$ order Taylor series are needed. Then we can get a conclusion that if we want a certain precise extent in a relatively larger interval we need more items in the Taylor series. And we should pay attention to the interval out of the precise region, such as $F_2(x)$ in the interval $(-\infty,-1]\cup [1,+\infty)$ are going away from $F(x)$ as $x$ moving away from $x^{\star}=0$

### Vector form function

When the performance index is a function of a vector $\boldsymbol{x}$, a vector form the Taylor series should be presented. And in the neural network, parameters are variables of the performance index so vector form Taylor series is the basic tool in performance learning. Function $F(\boldsymbol{x})$ can be decomposed in any precise:

\begin{aligned} F(\boldsymbol{x})=F(\boldsymbol{x}^{\star})& +\frac{\partial}{\partial x_1}F(\boldsymbol{x})|_{\boldsymbol{x}=\boldsymbol{x}^{\star}}(x_1-x_1^{\star})\\ &+\frac{\partial}{\partial x_2}F(\boldsymbol{x})|_{\boldsymbol{x}=\boldsymbol{x}^{\star}}(x_2-x_2^{\star})+\cdots\\ &+\frac{1}{2}\frac{\partial^2}{\partial^2 x_1}F(\boldsymbol{x})|_{\boldsymbol{x}=\boldsymbol{x}^{\star}}(x_1-x_1^{\star})^2\\ &+\frac{1}{2}\frac{\partial^2}{\partial x_1 \partial x_2}F(\boldsymbol{x})|_{\boldsymbol{x}=\boldsymbol{x}^{\star}}(x_1-x_1^{\star})(x_2-x_2^{\star}) +\cdots\\ &\vdots \end{aligned}\tag{3}

if we notate the gradient as :

$$\nabla F(x)=\begin{bmatrix} \frac{\partial F}{\partial x_1}\\ \frac{\partial F}{\partial x_2}\\ \vdots\\ \frac{\partial F}{\partial x_n} \end{bmatrix}\tag{4}$$

then the Taylor series can be written as:

\begin{aligned} F(\boldsymbol{x})=F(\boldsymbol{x}^{\star})&+(\boldsymbol{x}-\boldsymbol{x}^{\star})^T\nabla F(x)|_{\boldsymbol{x}=\boldsymbol{x}^{\star}}\\ &+\frac{1}{2}(\boldsymbol{x}-\boldsymbol{x}^{\star})^T\nabla^2 F(x)|_{\boldsymbol{x}=\boldsymbol{x}^{\star}}(x_1-x_1^{\star})\\ & \vdots \end{aligned}\tag{5}

The coefficients of the second-order item can be written in a matrix form, and it is also called the Hessian matrix:

$$\nabla^2 F(x) = \begin{bmatrix} \frac{\partial^2}{\partial^2 x_1}&\cdots&\frac{\partial^2}{\partial x_1 \partial x_n}\\ \vdots&\ddots&\vdots \\ \frac{\partial^2}{\partial x_n \partial x_1}&\cdots&\frac{\partial^2}{\partial^2 x_n} \end{bmatrix}\tag{6}$$

Hessian matrix has many beautiful properties, such as it is always

• Square matrix
• Symmetric matrix

In the matrix, the elements on the diagonal are $\frac{\partial^2 F}{\partial^2 x_i}$ is the $2^{\text{nd}}$ derivative along the $x_i$-axis and in the gradient vector, $\frac{d F}{d x_i}$ is the first derivative along the $x_i$-axis.

To calculate the $1^{\text{st}}$ or $2^{\text{nd}}$ derivative along arbitrary deriction $\boldsymbol{p}$, we have:

1. $1^{\text{st}}$-order derivative along $\boldsymbol{p}$ : $\frac{\boldsymbol{p}^T\nabla F(\boldsymbol{x})}{||\boldsymbol{p}||}$
2. $2^{\text{nd}}$-order derivative along $\boldsymbol{p}$ : $\frac{\boldsymbol{p}^T\nabla^2 F(\boldsymbol{x})\boldsymbol{p}}{||\boldsymbol{p}||^2}$

For instance, we have a function

$$F(\boldsymbol{x})=x_1^2+2x_2^2\tag{7}$$

to find the derivative at $\boldsymbol{x}^{\star}=\begin{bmatrix}0.5\\0.5\end{bmatrix}$ in the direction $\boldsymbol{p}=\begin{bmatrix}2\\-1\end{bmatrix}$, we get the derivative at $\boldsymbol{x}^{\star}=\begin{bmatrix}0.5\\0.5\end{bmatrix}$:

$$\nabla F|_{\boldsymbol{x}=\boldsymbol{x}^{\star}} = \begin{bmatrix} \frac{\partial F}{\partial x_1}\\ \frac{\partial F}{\partial x_2} \end{bmatrix}\bigg|_{\boldsymbol{x}=\boldsymbol{x}^{\star}}=\begin{bmatrix} 2x_1\\ 4x_2 \end{bmatrix}\bigg|_{\boldsymbol{x}=\boldsymbol{x}^{\star}}=\begin{bmatrix} 1\\ 2 \end{bmatrix}\tag{8}$$

and the direction $\boldsymbol{p}=\begin{bmatrix}2\\-1\end{bmatrix}$, the derivative is

$$\frac{\boldsymbol{p}^T\nabla F(\boldsymbol{x}^{\star})}{||\boldsymbol{p}||}= \frac{\begin{bmatrix}2&-1\end{bmatrix} \begin{bmatrix}1\\2\end{bmatrix}}{\sqrt{2^2+(-1)^2}}=\frac{0}{\sqrt{5}}=0\tag{9}$$

$0$ is a special number in the whole real numbers set. And the derivative is zero also useful in optimization procedure. And to find a zero slop direction we should solve the equation:

$$\frac{\boldsymbol{p}^T\nabla F(\boldsymbol{x}^{\star})}{||\boldsymbol{p}||}=0\tag{10}$$

this means $\boldsymbol{p}$ is not $\boldsymbol{0}$ because $0$ length is insignificant. and $\boldsymbol{p}_{\text{unit}}=\frac{\boldsymbol{p}}{||\boldsymbol{p}||}$ is a unit vector along deriction $\boldsymbol{p}$ so this can be written as:

$$\boldsymbol{p}_{\text{unit}}^T\nabla F(\boldsymbol{x}^{\star})=0\tag{11}$$

which means $\boldsymbol{p}_{\text{unit}}$ is orthogonal to gradient $\nabla F(\boldsymbol{x}^{\star})$

Another special deriction is which one has the greatest slop. Assuming the deriction $\boldsymbol{p}_{\text{unit}}=\frac{\boldsymbol{p}}{||\boldsymbol{p}||}$ is the greatest slope, so:

$$\boldsymbol{p}_{\text{unit}}^T\nabla F(\boldsymbol{x}^{\star})=||\boldsymbol{p}_{\text{unit}}^T|| \cdot ||\nabla F(\boldsymbol{x}^{\star})||\cos(\theta)\tag{12}$$

has the greatest value. We know this can only happen when $\cos(\theta)=1$ which means the direction of the gradient has the greatest slop.

## References

1 Demuth, H.B., Beale, M.H., De Jess, O. and Hagan, M.T., 2014. Neural network design. Martin Hagan.


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# How do you find the antiderivative of f(x)= x^(3/4) + x^(4/3)?

Mar 6, 2018

$\frac{4}{7} {x}^{\frac{7}{4}} + \frac{3}{7} {x}^{\frac{7}{3}} + c$

#### Explanation:

$\text{integrate each term using the "color(blue)"power rule}$

•color(white)(x)int(ax^n)dx=a/(n+1)x^(n+1)

$\Rightarrow \int \left({x}^{\frac{3}{4}} + {x}^{\frac{4}{3}}\right) \mathrm{dx}$

$= \frac{1}{\frac{7}{4}} {x}^{\frac{7}{4}} + \frac{1}{\frac{7}{3}} {x}^{\frac{7}{3}} + c$

$= \frac{4}{7} {x}^{\frac{7}{4}} + \frac{3}{7} {x}^{\frac{7}{3}} + c$

$\text{where c is the constant of integration}$


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# Tag Info

1

Your first formula in your question is generally wrong, that's why you can't prove it. The correct formula is $$\sum_{n=-\infty}^{\infty}x[n]y^*[n]=\frac{1}{2\pi}\int_{-\pi}^{\pi}X(e^{j\omega})Y^*(e^{j\omega})d\omega\tag{1}$$ which is just Parseval's theorem. If $x[n]$ and $y[n]$ are real-valued, $(1)$ can be written as $$\sum_{n=-\infty}^{\infty}x[n]y[n]... 4 Two codewords c_1 and c_2 of length n, with elements in \lbrace +1, -1 \rbrace, and Hamming distance d, have a cross-correlation given by$$(n-d) -d = n-2d. The reason is that there are $n-d$ bits that are equal and their product is $1$, and $d$ bits that are different and their product is $-1$. Note that: The larger the distance $d$, the ...

3

Well, as you can easily verify, these two criteria aren't the same if you define "minimum correlation" to mean that the absolute value of the correlation coefficient is minimized (i.e. 0): In $\mathbb F_2^N$, the vector that's the farthest away from any given vector $v$ is its bit-wise inverse $\overline v$ (using Hamming distance) Using your mapping, the ...

2

Figures that the same day I post a bounty I answer my own question. The answer to this question is dead/speckle like pixels. For a fixed number of dead pixels of a given brightness, the smaller the relative shift between the two images, the fewer dead pixels that are needed to cause the (0,0) pixel to spike. It can take fewer brighter dead pixels to have ...

Top 50 recent answers are included


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## Online Course Discussion Forum

### Question 7 & 8 Physics

Re: Question 7 & 8 Physics

Hi Hayden,

Thanks for your patience.

For Question 7, recall a Bq is just 1 decay per second, so the question is just asking if there are currently on average 1.75 decays per second for the sample. This problem is somewhat similar to example 30-9 in the book (this example solves for the number of decays, we want to instead solve for the time)

For Question 8, Table 30-1 gives the different masses of protons, electrons, and neutrons in various units. Note when measuring the masses we want to give the neutral atoms, so we either use electrons as well or use the mass of hydrogen (as given in that table) for the calculation. Note the actual mass is less because of binding energy, which is why the question is worded as "less than or equal to".

Hope this helps!


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# Transformations with Matrices Worksheet

Transformations with Matrices Worksheet
• Page 1
1.
Which of the transformations is applied on the rectangle 1 to obtain the rectangle 2?

 a. Dilation b. Reflection c. Translation d. Rotation

#### Solution:

Rectangle 1 is turned through an angle of 90o to get rectangle 2 about the point P.

The transformation is rotation.

2.
Describe the transformation for the figures (1) and (2).

 a. Dilation b. Translation c. Reflection d. Rotation

#### Solution:

y-axis is the axis of symmetry for the figures (1) and (2).

The transformation is reflection.

3.
What is the transformation from figure 1 to figure 2?

 a. Translation b. Reflection c. Dilation d. Rotation

#### Solution:

Figure 1 is enlarged by a scale factor of 2. The transformation from figure 1 to figure 2 is dilation.

4.
Write the ordered pairs in matrix form: A (4, 5), B (2,4), C (- 4, 7)
 a. b. c. d.

#### Solution:

A   B   C
 x-coordinatey-coordinate (42- 454   7)

5.
Identify the vertices of quadrilateral PQRS in matrix form.

 a. $\left(\begin{array}{cccc}- 2& 4& 3& 2\\ 1& 1& 3& 1\end{array}\right)$ b. $\left(\begin{array}{cccc}- 2& 4& 3& 1\\ 1& 1& 3& 2\end{array}\right)$ c. $\left(\begin{array}{cccc}- 2& 1& 3& 2\\ 1& 4& 3& 1\end{array}\right)$ d. $\left(\begin{array}{cccc}- 2& 1& 1& 4\\ 3& 3& 2& 1\end{array}\right)$

#### Solution:

The vertices of quadrilateral PQRS are

P (- 2, 1), Q (1, 4), R (3, 3) and S (2, 1)

P   Q   R    S
 x-coordinatey-coordinate (- 21321431)

6.
The matrix represents the vertices of a triangle. Translate 4 units right and 4 units down and choose the vertices of the image as a matrix.
 a. $\left(\begin{array}{ccc}-1& 8& 10\\ -1& 5& 4\end{array}\right)$ b. c. d.

#### Solution:

Vertices of triangle  Translation matrix
(- 5   46   3- 10)     +    (   4   4   4- 4- 4- 4)
[Add 4 to each x co-ordinate. Subtract 4 from each y coordinate.]

= (-1   8   10-1- 5- 4)
[Vertices of the image in matrix form.]

7.
The matrix represents the vertices of a quadrilateral. Translate 2 units right and 2 units up and choose the vertices of the image as a matrix.
 a. b. c. d.

#### Solution:

Vertices of           Translation Matrix
(- 3- 12   3- 2   21- 1)    +   (22222222)

= (- 1145   0431)
[Vertices of the image in matrix form.]

8.
The matrix [T] = $\left(\begin{array}{ccc}- 2& 2& 1\\ 3& 4& 1\end{array}\right)$ represents the triangle shown. Identify the transformation applied to obtain the matrix $\left(\begin{array}{ccc}- 7& -3& -4\\ 8& 9& 6\end{array}\right)$.

 a. translation of 5 units right and 5 units down b. a translation of 5 units left and 5 units down c. a translation of 5 units right and 5 units up d. a translation of 5 units left and 5 units up

#### Solution:

[T] = (- 2 213 41).
[Given.]

(- 7 -3-48 96) - (- 2 213 41) = (-5-5-5555)

Therefore, a translation of 5 units left and 5 units up describes the translation.

9.
Find the coordinates of the image of the quadrilateral ABCD under a translation of 4 units right and 3 units down.

 a. (6, 4), (4, - 6), (8, - 8), (9, - 5) b. (- 6, - 4), (- 4, - 6), (8, - 8), (9, - 5) c. (6, - 4), (4, - 6), (8, - 8), (9, - 5) d. (6, 0), (4, -2), (8, 8), (9, -1)

#### Solution:

Vertices of the quadrilateral ABCD are (2, - 1), (0, - 3), (4, - 5), (5, - 2)

 Vertices of quadrilateral Translation matrix (   2   0   4   5- 1- 3- 5- 2)  + (   4   4   4   4- 3- 3- 3- 3)

[Add 4 to each x-coordinate. Subtract 3 from each y-coordinate.]

= (  6  4  8  9- 4- 6- 8- 5)

Therefore, vertices of the image of the quadrilateral ABCD are (6, - 4), (4, - 6), (8, - 8), (9, - 5).

10.
Identify the matrix that represents the vertices of graph $f$ and graph $g$.

 a. I b. IV c. III d. II

#### Solution:

The vertices of graph f are (- 2, 4), (- 2, 1), (3, 1)

The vertices of graph g are (2, 4), (2, 1), (7, 1)

Therefore, f: (- 2- 23411), g: (227411)


text:
End of Summer - hours only!Up to 80% off on all courses and bundles.-Close
Introduction
Quick Refresher
PARTITION BY ORDER BY with Ranking
PARTITION BY ORDER BY with Window Frames
Using PARTITION BY ORDER BY with Analytical Functions
Summary and Review
19. Summary

## Instruction

Good for you - you've learned how to use PARTITION BY with ORDER BY!

Now you know that you can use PARTITION BY ORDER BY to create rankings and do row-level analytics independently for each partition in a single T-SQL query.

Are you ready for a short quiz?

## Exercise

Click to continue.


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# The fate of the vector potential in the case of the existence of a mag

1. Mar 8, 2013

### sergiokapone

The vector potential in classical electrodynamics can be introduced due to the fact that the magnetic field is the vortex:
$div \vec B = 0 → \vec B = rot \vec A$
In the four-dimensional form (including gauge) Maxwell's equations look particularly beautiful:
$\partial_{\mu}\partial^{\mu} A^{\nu} = j ^{\nu}$
where $A^{\nu}$ - 4-potential.

Given the existence of a monopole, the magnetic field is no longer a vortex. Then, how to change the form of Maxwell's equations in 4-dimensional form (via potentials)? Whether to reject the concept of the vector potential?

2. Mar 8, 2013

3. Mar 8, 2013

### sergiokapone

Thank you. But there representing the equations of Maxwell, expressed in terms of the field, and not in terms of the potentials.


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WORKING DRAFT authorea.com/37198

Abstract

# Abstract

We present ProCS15: A program that computes the isotropic chemical shielding values of backbone and C$$\beta$$ atoms given a protein structure in less than a second. ProCS15 is based on around 2.35 million OPBE/6-31G(d,p)//PM6 calculations on tripeptides and small structural models of hydrogen-bonding. The ProCS15-predicted chemical shielding values are compared to experimentally measured chemical shifts for Ubiquitin and the third IgG-binding domain of Protein G through linear regression and yield RMSD values below 2.2, 0.7, and 4.8 ppm for carbon, hydrogen, and nitrogen atoms respectively. These RMSD values are very similar to corresponding RMSD values computed using OPBE/6-31G(d,p) for the entire structure for each protein. The maximum RMSD values can be reduced by using NMR-derived structural ensembles of Ubiquitin. For example, for the largest ensemble the largest RMSD values are 1.7, 0.5, and 3.5 ppm for carbon, hydrogen, and nitrogen. The corresponding RMSD values predicted by several empirical chemical shift predictors range between 0.7 - 1.1, 0.2 - 0.4, and 1.8 - 2.8 ppm for carbon, hydrogen, and nitrogen atoms, respectively.

# Introduction

Chemical shifts hold valuable structural information that is being used more and more in the determination and refinement of protein structures and dynamics (Mulder 2010, Raman 2010, Lange 2012, Bratholm 2015, Robustelli 2010) with the aid of empirical shift predictors such as CamShift (Kohlhoff 2009), Sparta+ (Shen 2010), ShiftX2 (Han 2011), PPM_One (Li 2015) and shAIC (Nielsen 2012). These methods are typically based on approximate physical models with adjustable parameters that are optimized by minimizing the discrepancy between experimental and predicted chemical shifts computed using protein structures derived from x-ray crystallography. The agreement with experiment is quite remarkable with RMSD values around 1, 0.3, and 2 ppm for carbon, hydrogen, and nitrogen atoms. Chemical shift predictions based on quantum mechanical (QM) calculations (mostly density functional theory, DFT) are becoming increasingly feasible for small proteins (Zhu 2012, Zhu 2013, Exner 2012, Sumowski 2014, Swails 2015) and Vila, Scheraga and co-workers have gone on to develop a DFT-based chemical shift predictor for C$$\alpha$$ and C$$\beta$$ atoms called CheShift-2 (Martin 2013). Generally, these QM-based methods yield chemical shifts that deviate significantly more from experiment than the empirical methods, with RMSD values that generally are at least twice as large. However, many of these studies have also shown that the empirical methods are less sensitive to the details of the protein geometry and that QM-based chemical shift predictors may be more suitable for protein refinement (Parker 2006, Sumowski 2014, Vila 2009, Christensen 2013).

Some of us recently showed (Christensen 2013) that protein refinement using a DFT-based backbone amide proton chemical shift predictor (ProCS) yielded more accurate hydrogen-bond geometries and $$^\text{3h}$$J$$_\text{NC'}$$ coupling constants involving backbone amide groups than corresponding refinement with CamShift. Furthermore, the ProCS predictions based on the structurally refined ensemble yielded amide proton chemical shift predictions that were at least as accurate as CamShift. This suggests that the larger RMSD observed for QM-based chemical shift predictions may, at least in part, be due to relatively small errors in the protein structures used for the predictions, and not a deficiency in the underlying method. However, in order to test whether this is true in general we need to include the effect of more than one type of chemical shift in the structural refinement. In this study we extend ProCS to the prediction of chemical shifts of backbone and C$$\beta$$ atoms in a new method we call ProCS15. We describe the underlying theory, which is significantly different from the previous, amide proton-only, version of ProCS (hence the new name) and test the accuracy relative to full DFT calculations as well as experiment for Ubiquitin and the third IgG-binding domain of Protein G (GB3). We also compare the accuracy to CheShift-2 and other commonly used empirical chemical shift predictors using both single structures and NMR-derived ensembles for Ubiquitin.


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# GSEB Class 12 Economics Important Questions Chapter 1 Graphs in Economics

Gujarat Board GSEB Class 12 Commerce Economics Important Questions Chapter 1 Introduction to Partnership Important Questions and Answers.

## GSEB Class 12 Economics Important Questions Chapter 1 Introduction to Partnership

Question 1.
How economics is useful in todays?
Economics provide an explanation and world? analysis of various economic events occurring in the real world.

Question 2.
Which are the two types of pictures that depict economic information?
Diagrams and graphs

Question 3.
Which type of frequency distribution is presented for data using diagram?
Discrete frequency distribution of data is presented by a diagram.

Question 4.
How is continuous frequency distribution of data presented for easy is understanding?
Continuous frequency distribution of data presented using graphs for ea understanding.

Question 5.
List down two importance of diagrams and graphs in economics.

1. Trends of certain economic parameters over various years can be observed through a single diagram or graphs.
2. Changes occurring in vanous sectors of the economy can also be easily understood with the help of diagrams and graphs.

Question 6.
Which graphs are used to show trends of macroeconomic parameters?
Time-series graphs.

Question 7.
What are the aspects to be considered while drawing a diagram and graphs?

1. Choice of type of diagram or graphs and their presentation,
2. Clarity,
3. Scales and measures,
4. representation of axes,
5. data table and source of data and
6. Method of calculating the data.

Question 8.
Why does a data table and source of data accompany a diagram or graph?
A data table and source of data should accompany a diagram/graph to increase the reliability and authenticity of the graph diagram.

Question 9.
List the types of diagrams used in economic study.

1. Pictograph,
2. Scatter diagram,
3. Line diagram,
4. Circle diagram,
5. Bar diagram, and
6. Pie diagram]

Question 10.
What is time-based line diagram?
Time based line diagram is a diagram in which pictures show the shape or slope of a relationship in economics between two variables. For example, demand curve, supply curve, etc.

Question 11.
Give some examples ¡n which time based line diagram can be used.
Time based line diagram can be used to show size of population in different time periods, rate of inflation in various years, literacy rate in various years, etc.

Question 12.
Which are the three types of bar diagram?

1. Simple bar diagram,
2. Clustered diagram, and
3. Divided bar diagram]

Question 13.
Give the meaning simple bar diagram.
A simple bar diagram represents values of only one variable over a base, say various regions or years etc.

Question 14.
What is clustered bar diagram?
The diagram in which the values of a common variable and over a common base are given for rtore than one section of related parameters is known as clustered bar diagram.

Question 15.
Give an example of clustered bar diagram.
Suppose if the base is time period, the variable is literacy level and its values are expressed for two sections namely, females and males then for one time period, two bars showing literacy level for females and males respectively can be drawn in clustered bar diagram.

Question 16.
What should be done in a bar diagram to create proper visual effect and help comparison?
To create proper visual effect and help comparison, each bar is coloured differently and value which it represents are Indicated on it.

Question 17.
List down two aspects to be considered while drawing a bar diagram.

1. The width of the respective bars does not represent any data and hence all bars should be of equal width and
2. The length of the respective bars should be proportional to the value of the variable which they represent.

Question 18.
In which order should the vertical barsof the data series be placed in bar diagram?
Left to right order

Question 19.
Give the formula for obtaining proportional degree for a section on various items in a pie chart.
[Degree = $$\frac{\text { Component value }}{\text { Total value }}$$ × 360

Question 20.
List down aspeçts to be considered while drawing a pie diagram.

1. Ensure that the degrees of the total sections do not exceed 360 degree and
2. Degrees for sub-divisions a’e calculated in proportion to the value of the variable for that division and the sum total or me degrees of all such sub-divisions most be 360 degree.

Question 21.
Which are the different types of graphs?
Time-series graphs, histogram, frequency polygon, frequency curve, cumulative frequency polygon, and cumulative frequency polygon.

Question 22.
What are time-series graphs?
Time series graphs are those graphs which show the trends in changes of trade cycle or changes in cycle of economic activities with the help of statistical tools. In these graphs changes are taken as variable and time period as base.

Question 23.
What are the uses of digital technology?
Digital technology is used for being connected with friends and relatives, for education, to watch movies, to listen to music, to navigate our way while driving, to order purchase goods, to pay our bills, to buy tickets, etc.

Question 24.
Give examples of digital technology.

1. Computer technology,
2. Internet technology
3. Data CDs, etc.

Question 25.
What are the uses of Excel worksheets?
Excel worksheets are used for entering data (figures/observations), processing data by several mathematical and statistical formula and analyzing it. For example, Excel can give us sum, average, correlation, various types of graphs and charts, etc.

Question 26.
List some statistical programmes used for data processing.
[Excel, SPSS, SHAZAM, E-views, SAS, Gretel, PSPP, etc.]

Question 27.
How can we access or preserve important material using computer technology?
By transferring all the material in e-mail, drop-box, Google drive, d191-locker, etc.

Question 28.
What are the cautions to be considered while using computer technology?
The biggest limitation of computer technology is that if we do not use the right commands ¡n a computer, we may end up losing our material. Also, we might get incorrect graphs and data processing if correct formula or command is not entered.

Question 29.
What are the different uses of internet technology?

1. Educational websites acting as tutorials,
2. Active learning,
4. Internet helps to search required information,
5. It helps to get secondary data, etc.

Question 30.
Explain active learning through internet.
Active learning is said to take place when some institutions or experts create live video lectures for students which the students can access through internet in order to gain learning and knowledge.

Question 31.
Name some of the organizations and agencies who pubhsh important data on their websites used for research.
CSO, NSSO, WHO, UNO, CMIE, ILO, IMF, world bank, etc.

Question 32.
What do you mean by authentic data?
Authentic data means data which is published by recognized research institutes after doing comprehensive research.

Question 33.
Give some example of data CDs.
CD of national income accounts of India, CD of census of India, CD of annual survey of industries in India, CD of NSSO, CD of data pertaining to any ministry in India, etc.

Question 1.
Explain briefly the need of diagrams and graphs in the study of economics.

• Economics provides an explanation and analysis of various economic events occurring in the real world.
• For studying these events a lot of data is collected, ft is then analysed and represented in simpler forms.
• Pictorial representation is a very effective and easy way to represent data analysis.
• Diagrams and graphs are two ways of representing the information pictorially so that general public can understand it easily.
• Data understanding and analysis is out of reach and interest of general public. When such information is provided in an easy manner through diagrams and graphs people tend to take interest in them.
• A layman may call diagram and graph as one but Statistics classifies diagrams and graphs as different types of pictures. Both of these are used for distinct purpose. Similarly, even in economics these two are used to fulfill different purposes.

Question 2.
Define diagram and explain it.
Diagram:

• A pictorial representation of observed data is called a diagram.
• Although one needs to make use of scale and measurement to draw a diagram, one does not need to have a thorough knowledge of statistics to draw it.
• A diagram is drawn for data having discrete(discontinuous) frequency distribution. For example, the data could be
1. No. of children born in a month,
2. Price in rupees,
3. No. of road accidents, etc.
• Diagram is self-explanatory in nature and can be easily created and understood by anyone.
• A diagram is used by advertising companies to attract customers, by government and other organizations to provide information, etc.

Example of discrete, (discontinuous) data:

 Price (In Rs.) Demand (in units Frequency) 1 100 2 80 5 70 7 20 10 10

Types of diagrams:
Most common types of diagrams used in economic study are –

• Pictograph
• Scatter diagram
• Line diagram (based on time periods)
• Circle diagram
• Bar diagram
• Pie diagram

Question 3.
What is a graph? Explain.
Graph:

• A pictorial representation of observed data is called a graph.
• A graph is drawn for statistical information which is not self-explanatory. In other words, the graph can neither be created nor be understood by people who do not have thorough knowledge of statistics.
• A graph is drawn for data having continuous frequency distribution. For example,
1. Classification of people into various groups based on their incomes
2. Division of students on the basis of their marks, etc.

Example of continuous data:

 Income of people per month (in Rs.) Number of people earning the income (Frequency) 10,000 – 20,000 500 20,000 – 30,000 300 50,000 – 1,00,000 100

Generally, continuous data is bigger in size and complex in nature. Hence, statistical tools are used to analyze, classify and simplify it.

• A graph is generally drawn on a graph paper. A graph can extend over one or more of the four quadrants obtained by the intersection of ‘X’ and ‘Y’ axis on a plane. Moreover, it cannot be drawn without taking appropriate measurements.
• Graphs are used more by researchers and in higher education.
• Graphs are not used or published for general public. They are created by researchers for their data analysis and understanding purposes only.

Types of graphs:
Important graphs used in economic study are:

1. Time-series graphs
2. Graphs for continuous frequency distribution
• Histogram
• Frequency polygon
• Frequency curve
• Cumulative frequency polygon
3. Graphs for logarithmic data

Question 4.
State the most common types of diagrams.
Most common types of diagrams used in economic study are:

• Pictograph
• Scatter diagram
• Line diagram (based on time periods)
• Circle diagram
• Bar diagram
• Pie diagram

Question 5.
How does statistics classifies graphs? List them. OR Enlist the various types of graphs used in economic study. (2 marks)
Types of graphs:
Statistics classifies the various types of graphs as follows:

1. Time-series graphs
2. Graphs for continuous frequency distribution
• Histogram .
• Frequency polygon
• Frequency curve
• Cumulative frequency polygon
3. Logarithmic graphs

Question 6.
For which difficult to understand economic principles diagrams and graphs are a boon? (2 marks)
Diagrams and graphs help to understand various difficult principles of economics easily.

Example:

• The concepts of expansion and contraction of demand and supply, price elasticity of demand and supply, etc. can be easily understood by pictures.
• Trends of macroeconomic parameters can be clarified through time-series graphs.
• For example, the short-run and long-run irregular fluctuations in agriculture or the regular fluctuations in some industry are calculated by the method of time series and their trends are presented by way of time-series graphs.

Question 7.
Explain time-based line (curve) diagram along with data and brief analysis. (5 marks)
Time-based line (curve) diagram:

• This diagram is used when we have ‘time related data’. For example, price of a given share in last 30 days, number of vehicles passing through a cross road every hour of a day, growth of population from 1951 to 2001, etc.
• The line-diagram represents the relation between the two economic variables and the slope.
• Line-diagram can be used for showing the demand curve, supply curve, etc.
• The independent variable (usually, time) is measured on ‘X’ axis and the dependent variable is measured on ‘Y’ axis.

Use in economics:
In economics, a time-based line diagram is used to show the size of population in different time periods, rate of inflation in various years, literacy rate in various years, etc.

Example:
Percentage growth rate of India’s population since 1951

 Decade Decadal Growth Rate of Population in % 1951-61 21.64 1961-71 24.80 1971-81 24.66 1981-91 23.87 1991-2001 21.54 2001-2011 17.64

Analysis:
The time-based line diagram tells us that if we look from percentage perspective the.. India’s population growth-rate has shown downward trend except in year 1961-71.

Question 8.
What is a bar diagram? How many types of bar diagram are there?
Bar diagram:
A bar diagram is a chart that uses bars to show comparison between categories of data. The bars can be either horizontal or vertical.

Purpose:

• A bar diagram shows distribution of the value of a variable in various sections. For example, literacy rate in a country in various years or literacy rate among females and males in a particular year.
• A vertical or horizontal bar is drawn for each value of the variable.
• A separate bar is drawn for each section and the height/length of the bar indicates the value for that section.
• Thus, by comparing the height/length of the bars a comparison can be made of the values of each section.

Types:
Bar diagrams are generally of three types:
(A) Simple bar diagram
(B) Clustered bar diagram
(C) Divided bar diagram.

Question 9.
Explain simple bar diagram along with data and brief analysis. (5 marks)
Simple bar diagram:

• A simple bar diagram is a bar diagram which represents values of only one variable over a base.
• Through simple bar diagram, one can represent data of sale in various regions, months or years, etc.
• The difference in the length of bars gives a visual effect of the difference in the value of the variable under study.

Example:
Bi-monthly sale of chocolate boxes in a shop

 Months Sale in units Jan-Feb 35 Mar-Apr 60 May-June 65 July-Aug 40 Sep-Oct 50 Nov-Dec 30

Simple Bar Diagram

Analysis:
Looking at the bar diagram we can say that the sale of mobile phones was highest in the months of March and April and May and June. It was lowest in the month of November-December.

Question 10.
Explain clustered bar diagram along with data and brief analysis. (5 marks)
Clustered bar diagram:
In this type of a diagram, values of a common variable and over a common base are displayed for more than one section of related parameters. Hence we get a cluster of bars for the same variable over various values/sections at the base.

Use in economics:

• Suppose a mobile store owner has two branches. If he wish to compare sales of each branch for a given period of time then he can use clustered bar diagram.
• Another example could be variable ‘year’ as the base and comparing literacy of two sections namely males and females. This will be a two clustered bar diagram and each pair of bar will show literacy rate of male as well as female.
• To separate the bars properly, the clustered bars are given either different colours or designs. Each value point is then represented on the bar.

Example:
The example below shows the bi-monthly sale of chocolate boxes of different sizes in a shop.

Number of chocolates sold

Analysis:

• The diagram shows cluster of sale of three different sizes of chocolates for various months.
• Looking at the November-December period we can see that the sale was highest for small size chocolate boxes followed by medium and large. Whereas the data of March-April tells that large boxes made the highest sale.

Question 11.
Explain divided bar diagram along with data and brief analysis.
Divided bar diagram:

• Divided bar diagram is a bar diagram wherein each bar is divided into several segments to represent a set of quantities according to the different proportions of the total amount.
• In this diagram every single value of the variable has sub divisions. Hence we get divisions in all the bars which represent a common variable and common base values.
• Each division of the bar is colored differently to distinguish between the divisions. Values are put on each division so that it is easily understood.

Example:
The example below shows bi-monthly sale of chocolate boxes by a sales person in rural and urban areas in a region.

Sale of chocolates ¡n rural and urban areas

Divided bar Diagram

Analysis:
The sale in urban area is highest in the months of March-April and November-December. In case of rural sales, it is highest in May-June and November-December.

Question 12.
Explain pie diagram along with data and brief analysis. (5 marks)
Pie-diagram:

• A pie diagram (or a circle chart) is a circular statistical diagram which is divided into slices to illustrate numerical proportion.
• Division of a circle in degrees represents a pie diagram.
• If an entire circle is considered as universal set of an entire data and the different sections of this data are represented by dividing the circle in degrees proportional to the data then a pie diagram is obtained.
• Note that we can draw pie diagram for the similar type of data for which a bar diagrams can be drawn.
• The complete circle represents 360°. Hence, the entire data represents 360° and sections/divisions of the data are represented by dividing the circle in degrees proportional to each data section.

Formula for obtaining proportional degree for a section of data:
Degree = $$\frac{\text { Component value }}{\text { Total value }}$$ × 360

Example:
The data below shows the percentage of pocket money spent by a student on various items.

Percentage of pocket money spent by a student on various items

Source: Hypothetical example

Question 13.
State the points to be considered while drawing a pie diagram.
Aspects to be considered while drawing a pie diagram:

• Ensure that the degrees of the total sections do not exceed 360°.
• Degrees for sub divisions are calculated in proportion to the value of the variable for that division. So, the sum total of the degrees of all such sub divisions must be 360°.
• If relevant data is to be compared across regions or time periods then two pie graphs can be drawn side by side. For a data set with a smaller total value, a circle with smaller dimensions is drawn and for a data set with larger total value, a circle with bigger dimensions is drawn.

Question 14.
What is a time series graph? Explain.
Time series graph:

• The illustration of data points at successive time intervals is known as time series graph.
• For example, in a trade cycle or in cycles of economic activities, short term and long term regular or irregular (erratic) changes are observed. The trends of such changes are obtained with the help of statistical tools.
• Graphs drawn by taking these changes as variables and plotting the values of these variables over time as data points are called time series graphs.

Time series graph of accidents taking place in a city (For information only)

Question 15.
State the role of Excel sheets in economics.
Excel worksheets:

• Economics deals with lots of data. Researchers come across data having thousands of observations on a daily basis. It is almost impossible to handle so much data manually.
• Microsoft Excel is a powerful tool for handling large data related to several economic parameters and then and performing analysis on it.
• For example, if we survey on number of items produced by small scale industries in India, we would get thousands of observations.
• We can feed this data in excel and get various figures such as total production, average production, number of units in a given region, total exports, etc. within seconds.
• Excel also has numerous types of graphs and diagrams which can be created within a click.

Question 16.
What are storage tools? How do they help in preserving data? Also, state the various means to store data.
Other tools:

• Microsoft Excel cannot handle very large amount of data. For this purpose there are various statistical software available which are highly advanced, sophisticated and can handle any size of data.
• SPSS, SHAZAM, E-views, SAS, etc. are few of the such statistical software.
• This software can process data for lakhs of observations that too within seconds or minutes.
• Since these statistical software are very costly, they are mostly bought by research institutes or government organizations.
• There are also certain statistical software like Gretl, PSPP, R, etc. which are available free of cost on the internet but does almost same tasks of analysis as done by the costly software.
• Now-a-days many of these functions of a computer are also available on smart phones and tablets.

Question 17.
State the drawback of Excel and means to overcome it. (2 marks)
Other tools:

• Microsoft Excel cannot handle very large amount of data. For this purpose there are various statistical software available which are highly advanced, sophisticated and can handle any size of data.
• SPSS, SHAZAM, E-views, SAS, etc. are few of the such statistical software.
• These software can process data for lakhs of observations that too within seconds or minutes. Since these statistical software are very costly, they are mostly bought by research institutes or government organizations.
• There are also certain statistical software like Gretl, PSPP, R, etc. which are available free of cost on the internet but does almost same tasks of analysis as done by the costly software.
• Now-a-days many of these functions of a computer are also available on smart phones and tablets.

Question 18.
What care should one take care while using computer technology in economics?

• One should never forget that although computer helps in studying, it is not a study material by itself. Computer helps to make the process of studying easier and faster but it does not replace the process of studying.
• One should be able to make wise use of them during their study. One should have good knowledge of computers as well as the statistical tools that we make use in them.
• Computers do not have brain of their own. We may select any data and on one click we may get the diagram and graph we aim for but, it is our duty to see that we select the correct data, give suitable commands and obtain the desired analysis and pictorial representation.
• We may also end up getting incorrect graphs and data processing if we do not know the correct formulae and commands.
• If we do not use the right commands in a computer, we may even end up losing our material.

Question 19.
What kind of secondary data is available on internet? (2 marks)
Data: Economics uses a lot of secondary data. For instance, we use data on budget of a government, on banking, on agricultural production, on value of exports and imports, on poverty, on employment, on industrial production, etc. These data can be accessed from authentic websites. For example, authentic site for data and banking in India is the official website of Reserve Bank of India, for exports and imports is the website of Ministry of Commerce and Industries of Government of India. Budget related information from Ministry of Finance, Government of India and so on. Some organizations and’agencies functioning at national and international levels also collect publish as well as put data on websites. For example, CSO NSSO, WHO, UNO, CMIE, ILO, IME, World Bank and so on.

Question 20.
What care should one take while using internet as a tool for education?
One should take following care while using internet for education:

• Just like computer, internet is also only a tool. It cannot replace books and teachers or our own thinking and reasoning.
• A lot of bogus material, irrelevant information, misleading information, plagiarized articles are available on internet. We must avoid using such information and material.
• Readers must use their own wisdom to identify if the material given is authentic and reliable or not.
• One must use data or information only from those websites which are authentic and reliable.

Question 21.
What difficulty does one face while using data CD?
The data CDs contain voluminous data that too of various types.
Only a person having thorough knowledge about economics and statistics can’ make use of this data. Which data can be used in which manner, how to mix and match various data sheets, what analysis should be done and what should be concluded from the data available in the CD can be done by experts only.

Multiple Choice Questions

Question 1.
Which of the following type of pictures are used to depict information related to economic changes?
(A) Diagrams
(B) Graphs
(C) Both (A) and (B)
(D) Clip arts
(C) Both (A) and (B)

Question 2.
In which of the following, thorough knowledge of statistics is not required?
(A) Diagram
(B) Graphs
(C) Charts
(D) None of these
(A) Diagram

Question 3.
Graphs are mostly used in
(A) primary education
(B) Higher education
(C) Both (A) and (B)
(D) Only used by researchers
(B) Higher education

Question 4.
How can clarity be made while drawing a diagram or a graph?
(A) Appropriate size and scale should be taken
(B) Different colours or shades should be used
(C) Data table should be present with every diagram or graph
(D) Statistical method used should be stated
(B) Different colours or shades should be used

Question 5.
Which of the following is not a type of diagram?
(A) Pictograph
(B) Circle diagram
(C) Scatter diagram
(D) Histogram
(D) Histogram

Question 6.
Which of the following diagrams can be used to represent rate of inflation in various years?
(A) Bar diagram
(B) Scatter diagram
(C) Time based line diagram
(D) Pie diagram
(C) Time based line diagram

Question 7.
Which of the following is not a type of bar diagram?
(A) Cluster bar diagram
(B) Scatter bar diagram
(C) Simple bar diagram
(D) Divided bar diagram
(B) Scatter bar diagram

Question 8.
Which type of diagram represents values of a common variable and over a common base are given for more than one section of related parameters?
(A) Cluster bar diagram
(B) Pie diagram
(C) Divided bar diagram
(D) Circle diagram
(A) Cluster bar diagram

Question 9.
Which of the following should be proportional to the value of the variable which they represent in a bar diagram?
(A) Width of the bars
(B) Distance between all the bars
(C) Order of the bars
(D) Length of the bars
(D) Length of the bars

Question 10.
In a pie diagram, the entire data represents
(A) 90 degree
(B) 180 degree
(C) 360 degree
(D) 270 degree
(C) 360 degree

Question 11.
Which of the following is not a type of graph?
(A) Frequency polygon
(B) Histogram
(C) Pictograph
(D) Time-series
(C) Pictograph

Question 12.
Which of the following graphs show changes in trade cycles and its trends with the help of statistical tools?
(A) Time series graphs
(B) Histogram
(C) Graphs with logarithmic data
(D) Frequency polygon
(A) Time series graphs

Question 13.
Which of the following is a digital tool?
(A) SAS
(B) R
(C) Data CDs
(D) All of these
(D) All of these

Question 14.
Which of the following computer technologies helps us to find out the correlation between variables?
(A) Presentations
(B) Storage tools
(C) Diagrams and graphs
(D) Excel worksheets
(D) Excel worksheets

Question 15.
What can we use to access our stored information in a computer from any part of the world?
(A) By using notebooks
(B) By using hard disc
(C) By using digi-locker or Google drive
(D) By using pen drive
(C) By using digi-locker or Google drive

Question 16
Which of the following is a statistical programme used for data processing?
(A) SPSS
(B) C++
(C) Excel
(D) Both (A) and (C)
(D) Both (A) and (C)

Question 17.
Which of the following software is pretty expensive?
(A) Gretel
(B) PSPP
(C) SAS
(D) R
(C) SAS

Question 18.
Name the term which means enrolling to sites and listening to lectures on net by experts.
(A) Tutorials
(B) Active learning
(D) Data screening
(B) Active learning

Question 19.
Which agency creates data software which can be purchased only by researchers and corporations?
(A) NSSO
(B) CMIE
(C) NIA
(D) Survey Organization of India


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# How can we calculate AIC from a negative binomial GLMM?

Our problem here described is to calculate AIC from a GLMM negbin. Our data compose by 2 Categorical variables (Yes/Not), 3 Numerical variables and our random factor, all without any NA. We want to create a GLMM model with negative binomial family and this model calculates AIC and BIC as NA, but calculate the rest of the model values. In R:

>model<-glmmPQL(X~Categorical1*Categorical2+Numerical1+Numerical2+Numerical3,random=~1|Random1,family=negative.binomial(theta = 1234, link = "log"),data=Data)

>summary(model)

Linear mixed-effects model fit by maximum likelihood

Data: Data

AIC BIC logLik

NA NA NA

We tried using in R: AIC(model), AIC(logLik(model)), BIC(model), BIC(logLik(model)) & extractAIC(model) with NA as a result (in the case of extractAIC we obtain 9 NA). How can we calculate this AIC?

Thank you,

If you want the marginal AIC (i.e., for the implied marginal model that focuses on the fixed effects alone), you can fit the model with the GLMMadaptive package that provides this in the output of the summary() method. E.g., check this example.