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Danny Kaplan teaches statistics, applied math, and computing at Macalester College in St. Paul, Minnesota. He is active nationally in statistics education reform and the author of "Statistical Modeling: A Fresh Approach." This interview has been edited for clarity and flow.

# In which Danny Kaplan discovers statistics

Danny, you're currently engaged in creating a course for DataCamp, Introduction to Statistical Modeling. Perhaps you could tell us a bit about yourself and how you got involved with DataCamp.

My background has been in science, not in math or statistics. I did physics and biomedical engineering, especially in cardiology. I used to work in a physiology department at McGill Medical School, but I came back to the US because I was interested in teaching, and at a small liberal arts college. It happened that, while I was here for my interview, they asked whether or not I could teach statistics. They said, "We always need someone to teach statistics. Could you teach it?" For no other reason than that, that was a job interview, I said, "Sure, that would be fun." I had no experience. I came to Macalester, and I started teaching statistics. I was about a week ahead of my students. I had never heard of a t-test.

I've always enjoyed writing textbooks and my first one was a book on nonlinear dynamics that I wrote with Leon Glass. Then, when I arrived at McAllister, I was teaching stats, but my main emphasis was on computational science. I didn't know anything about statistical software, and when I arrived here in 1996, they gave me a little cardboard box that had JMP on a floppy disc. I had some acquaintance with S+. I asked for the college to get a license for S+, but they said they wouldn't, that it was too expensive, and that we already had SPSS, whatever they say. I heard about this little project in New Zealand, and I FTPed to Auckland to get R.

It was in a very early state, but I did it because I could see that it was a real programming language. It has developed hugely since then, but I believe I'm the first person in the US to teach a course using R. I've been doing it for 20 years, since the very early days. I like this computationally-driven pedagogy. It's different from the usual textbook pedagogy. Since I'm interested in pedagogy, and I'm interested in computation, I've tried to stay familiar with the developments in those areas. A lot of it is developments in publishing. I look for new ways to reach out to students. One of the great accidents in my life was my introduction to Rstudio. At McAllister, we were the beta site for Rstudio. JJ, the principal, and Joe Chang, they actually came here before they released the software.

R has really increased my sophistication, and all of the things that Rstudio has encouraged, Rmarkdown, Shiny. No one will tell you that. I'm interested in how these things work, and I was interested in working with JJ on a better platform for teaching. JJ said, "Start with DataCamp, and see how that's working out for you."

When was that?

That was pretty recently. That was this last summer. I downloaded your teach development software, and I played around with it, and got some things to work. I wanted to see how easy or difficult it would be to write questions. I became interested in this, especially I wanted a way where I could reach out to students directly. My ideas are a little bit unconventional.

Could you tell me a bit about how you feel about the conventional ways of statistics and how it's being taught?

The first thing to say is that the statistics education community is a great community and they're really interested in doing things in an effective and useful way. If you look at statistics, what's taught in Introductory Statistics, from the perspective of a contemporary researcher, there's nothing in it for you. It's teaching you early principles, which were important historically, but have been supplemented by the ability to compute cheaply. The algebraic focus and the formal probability focus, none of that is actually needed to understand statistics. What you lose, when you do this, is the ability to do statistics of relevant complexity to the kinds of problems that people do. In almost every introductory statistics course, there is at most one explanatory variable. The word "Covariate" does not show up in Introductory Statistics textbook.

The idea of the model is completely foreign. Although sometimes you will see a model in the title, they don't really talk about modelling, they end up talking about these very, very simple kinds of...We could call them models, function estimations that are like the t-test and simple linear regression, they call it. My view is that the key skill, the key attribute that students need to have to succeed is motivation. It doesn't actually matter what their technical background is. Admittedly, there are some students who are so mathphobic. You're not going to be able to do much with them. Figure out the technology or the techniques for making that interesting topic accessible to students. Don't start with simple techniques because you think they're simple. Start with interesting techniques and useful techniques.

That always involves covariation. To be honest, it always involves causation, causality. It's a disaster in Introductory Statistics what they do about causality. They say, "If you can't do an experiment, don't say anything about causation." Almost, always we need to say something about causation, and almost all experiments except bench-top lab experiments, as in efficiency, there's non-compliance. There's what they call pollution. When we call them experiment, it's halfway between an ideal experiment and observation. You need those techniques for doing causal inference in statistics.

I like that a lot because what you're promoting is a more holistic approach to the field statistics as well. It comes down to realizing that statistics is a fundamental part of the scientific method, which ties into experimental design, data collection all the way to data analysis and not thinking of statistics, as it's all an entity in itself but it's part of this unified set of tools and concepts. Your course will be on Statistical Modelling. My question for you is, from the get-go, what is the difference between statistical modelling and statistics?

Modelling is always the process of constructing a representation of something for a specific purpose. In statistics, you don't hear much about what the purpose is. You hear about algorithms. That's how it teach us this thought, "Take the mean of this group standard deviations, combine them in a certain formula way, and then look at P at the back of the book. Either the p-value is less than 0.05 or it's not." It's really the way it's taught and it's not surprising then that people have these ideas about p-values, that this has come to dominate the non-statisticians professional views of statistics.

You need to bring to the table your knowledge about the system that you're studying. Data is not sets of numbers. Data is numbers or whatever but in a context. Always, we're working with data because there are some interests in the context and we know something about the context. In modelling, you can bring that information into play. A prerequisite for bringing it into play is having techniques that let you deal with covariance. So long as you're doing a t-test, there's very little creativity that can be applied. You really can lean much more on domain-specific knowledge, which I think is something people have to see at every level on statistics that it starts with domain-specific knowledge.

# The role of DataCamp in Data Science Education

Now you're in the process of creating a course for DataCamp. What can a DataCamp course offer that a book cannot?

I don't want to count the things, but among the things that it offers are the immediate feedback that you get. In DataCamp, they've got it at a very fine level of granularity, so that as you're answering an exercise, you can get hints, and you can see very soon whether or not you have an answer that approaches the correct thing. They also provide an adjustable level of scaffolding. You can give a problem that says, "Do this," or you can say, "Here's some of the steps in doing this. Fill in the missing step," and elaborations on doing that. That's very helpful for pedagogy, whether it's about the computer or not. Feedback, being able to scaffold, giving people easy problems at first, and then as their familiarity with the technique builds up, you can give them less support, less scaffolding. In my case, I think that being able to use a computer properly is the skill that algebra, and trigonometry, and calculus used to be. All of those are ways of calculating things, and they have some mathematical beauty, undeniably. Most people don't see that beauty, they just see them as a source of aggravation, but with the problems we work with today, the kind of calculation you need to do is not algebraic rebalancing and moving things from one side to the other, inverting things. The computations are things you do on a computer.

Students need to learn about computing. Not all of them will become programmers, just as ninth graders who take Algebra II don't all become mathematicians, but they will at least have an appreciation for what's going on, and they can do much more than they otherwise could if they know something about how computers work. DataCamp is, of course, intimately wed to the computational platform. I know you do things in Python, and you do things in R. I use R, but it provides a way of interacting with students that's about computation. That's hard to read about. It's much more effective if you can read it, and do it, and if you can provide the scaffolding so that people can start simple, and then build up. That's a really promising aspect of these tools that you all are developing.

I find this really interesting, because what we're talking about now is a student, sitting at home, coding, having interactive feedback, and having short videos with instruction interspersed. Can you see this type of platform entering the classroom at any point, and would that be beneficial to the academy, to education at the secondary and tertiary level?

First, you said something about teaching them coding. I don't like the word coding. I think that programs are a way of expressing concepts. It shouldn't be a code, it should be a notation for expressing ideas. R is very good at letting you do that, and with the Mosaic package, which I've put together with two colleagues, Randy Prine and Nick Horton, we really tried to strip out the syntactical complexity in R, and let you get straight into just expressing yourself in a concise way. The priority is much the same. You're able to be very concise. It's easier to read than SQL, at least with me. ggplot is another one of these, and we're starting to see them, micro languages with data scraping, data cleaning, and all sorts of techniques. We really are moving away from the code, into concise languages for expressing computational ideas.

The classroom. Whether it will be useful in the classroom depends, first, on whether people use it. It can be hard for many instructors, college level instructors, to have students working with effectively another instructor while they're in the classrooms. There's a lot of prestige built around the idea of being in front of the classroom, maybe of lecturing. Not everything has to be a lecture, and there's much less lecturing than there was when I was in college, but you're handing things off to someone else. I don't know the extent to which instructors will accept that.

But instructors can create their own DataCamp courses, as well, with relative ease.

Instructors can. I find that it's very few people who create a course, and, in fact, there's a knack to writing exercises. It's not so many people who have that knack. That would be challenging. I mean, it's a big commitment of time to develop a course. One thing that I like about the platform is that you make things in small chunks. Developing a course is about five hours of student contact. That's at least approachable, you're not asking for 40 hours, which is what you spend in a classroom in a semester. That's, at least, approachable.

Classes exist because AV technology is poor. It was a voice. Presentation technology was poor, it was a blackboard. Maybe it was a slide projector. It was hard for students to get around. They had to commute to school, and so we arranged things in these hour long chunks, because of the constraints imposed by transportation and audio technology, and the like. These are now completely different. Is it good for students to get together, and to be part of a discussion? I think so. That's a very strong mode of pedagogy. Is a good for them to work together on a project? That's great, too. It's ridiculous to size things in semester long chunks. To look at the absurdity of how it's organized, who in their right mind would arranged that all exams happen in the same week? What are you trying to do, drive students crazy? That part's always going to be the discussions amongst students, students working together, professor watching what his student is doing. I think there is something in the human psychology of dealing face-to-face with someone, is something as well. The idea that students would come to a room with 500 seats, and each one would sit in front of a laptop, and do their electronic courses, I don't see why to do that. Save the classroom time for other purposes.

I agree. I'm speaking more toward a blended teaching approach, where you have traditional classes with this, perhaps mixed in as a module, and being incorporated, in some sense. Is that something you can see being beneficial?

It would be beneficial. Ultimately, we don't know until we try it. It's a little bit shocking to me, but hardly any colleges have policies on work that you do outside of class. You might take a DataCamp course, or a Coursera course for doing something. Colleges don't have processes by which they can accept that as a token of work. The faculties at many schools have indicated that they're not interested in accepting that as a token of work, but just as going back to your room, reading a textbook is a useful form of studying, so is this kind of interactivity that we're getting. It's the textbooks you'd expect at Hogwarts, that can interact with you. How could that not be better?

# The role of Statistics in Data Science

Moving slightly away from the technology, to the content of what you're doing, and what DataCamp is interested in. DataCamp is interested in educating people with respect to the basic skill sets that Data Scientists need. I'm wondering what your opinion is on the role of statistics, and the role of statistical modeling in data science as a broad discipline.

This requires some care. What is it that makes data science different from what we had before? It's the scale of the data, both the number of cases, and the number of variables. It's the flow of the data, data streaming in. That's often an important component. It's often the kinds of goals, so a lot of data science is applied to problems like detecting fraud. It's not exactly building a model, but it's looking at residuals, rather than building a model, if you want. Let's just call it large data, is what's happening with data science. The standard error of things is 1 over root N, so if N is 100 times bigger, your standard error is 10 times smaller. If data are large enough, then you don't need to worry about statistical significance. It's going to happen. That's not to say I want to ignore it. There are statistical concepts which, if you ignore, it can be a disaster for you, no matter how much data you have. There's ideas like multi co-linearity. There are ideas like interactions. That's a modeling technique, but if you study Hadoop, you're not going to hear about interactions. You're not going to think about that style of modeling. I think statistics has a huge amount to offer. It's necessary for people who are interpreting data.

How would your statistical modeling course fit into an introduction to data science course?

A lot of data science is about data wrangling, and cleaning. These are our foundations to data science, because you can no longer type in the numbers on your graphing calculator, something that's still done in a lot of college and high school courses. Those are fundamental. Why is it called statistical modeling? A statistical model is a particular kind of mathematical model. It's one where the stuff you're building it out of is shaped by the data. It's not dictated by the data. You can bring other things into the modeling process, and I think a sensible person does, but it's shaped by data. The people doing data wrangling and visualization, they have the data. Now, they have to learn how to describe that data in a rich, and often quantitative, way. That's what you need statistical modeling for.

# Statisticians and Data

I'm wondering if there are any other current practitioners of statistics or applications of statistics, or statistical modeling that affect your practice, and if so, who influenced you? Who would they be?

Oh, no. [laughs] I wouldn't be anywhere without this very rich community of people who are doing things in statistics. How many to name, but just to name one, Judea Pearl, for example, who has very insightful things to say about how to do the best job you can in thinking about causation, and in relating causation to data, which don't necessarily come from an experiment, or come from an imperfect experiment. That's incredible stuff. There's all sorts of statistical techniques, modeling techniques that are incredible things. Especially now, you're seeing machine learning techniques, a lot of which are very similar to traditional techniques, but explained algorithmically rather than in algebraic formalism. You've seen with this machine learning techniques come in. If I were starting from scratch now, and I'd something of an opportunity to do this with DataCamp, I'd I start by putting modeling in a machine learning context and conceptual machine learning can adequately simplify ways of constructing these models and interpreting the models. So cross validation to name one.

Even before that just having to hold a test set, jut put it into a training set and a test set?

That's right. This has been around for a long time. For a class I was rereading a great article from Brad Efron in the late '70s. He wrote an article for the SIAM Journal. He was writing about these techniques. The article is called, Thinking the Unthinkable and doing these crazy, crazy large calculations, which in 1978 seemed pretty small compared to what we do now. But he was talking about cross-validation. Let's see what else we've got here, my heroes. Here he is, this is an old book by John Chambers. He's had a huge influence on statistical computing, just as Hadley Wickham has, in making methods accessible to people, and providing a nice language. Box, Hunter and Hunter is another fantastic reference.

# On technology, algorithms, pencils and computation

You mentioned thinking about trigonometry, and calculus, and geometry as ways of calculating things. Now, we can do it algorithmically in a lot of respects. Then you mentioned machine learning being an algorithmic way of approaching things. A lot of machine learning techniques, you can write down the equations and analytically in some sense -- not the solutions, of course. For data science purposes, that isn't strictly necessary. Even trying to understand that for budding data scientists can be a hindrance to their practice in a lot of respects. In essence, this field of machine learning or predictive analytics is very results-oriented in terms of the model with the most descriptive power wins. In fact, whether its basis is firm or not in terms of being able to run an equation might not even matter. In that sense, the future may be algorithmic. Is that something you can speak to?

It has always been about technology. The technology might have been moving stones from little bowls to other little bowls, to counting table, or an abacus. Pencils have been very influential in the mathematical sciences. Arabic numerals were a tremendous thing. It wasn't always so, at least in Europe. Starting about 1600 or so, we developed the modern form of algebraic notation. This is the exclusive way we had to communicate for 200 years. This started to be printed tables even in the late 1600s. That was the exclusive way. It is the prestigious way to communicate.

It has all of the hallmarks of religious ritual. It's got special notation that's obscure to people. It's beautiful notation. I love it. It's obscure to people. There's a kind of priesthood -- people who can make sense of it and people who can't make sense of it. We describe things as having a solution when what we mean is they have a solution using that technology. That's become the Platonic truth for us, is these equations, and this formalism for describing stuff. We have now effective other means of communicating about relationships. Software, of course, is the dominant one for all sorts of things outside of academic math. It's a really good way to communicate ideas. At the same time as you're communicating the idea, you're implementing the calculation. You don't have so much to worry about misinterpretation. You can allow people to reproduce things without having to translate a formula, even the quadratic formula. Depending on the numbers you might want to use the standard one or you might want to use a different one because they're unstable in different areas.

Software is just not as prestigious in the academy, but as a matter of practicality and increasing our capabilities it's...and accessibility. It's fantastic. It's fantastic. Newton did not have the idea of an XY graph and of a Cartesian graph. It was Descartes who came up with that, and that's after Newton. It's really hard to read Newton because he doesn't use this technology which we've assimilated into the way we think. We see things in graphical forms, in that XY graphical form. I think we need to learn to see things, or more people need to learn to see things in terms of software.

And algorithms?

Algorithms are very important. What would software be without...What is an algorithm? An algorithm is a way of describing a computation. One of the things that people have to learn... It's one of the things I think that's valuable when people study a little bit of technical computing you learn that an algorithm is a way of expressing a computation in terms of computations that you already know how to perform. That it all depends on what you can do before you build something up out of that to make a new algorithm. With linear programming, for example, all sorts of optimization techniques, constrained optimization techniques become accessible computationally. What are the algorithms that everyone should learn? If you're going to be a literate person in technology what are the algorithms that everyone should learn? There are actually quite good lists of the top 10 algorithms or the top 20 algorithms.

# The Importance of Statistical Modeling

I've got one last question for you, Danny. An ex-colleague of mine, he's a physicist, and when he meets people at a bar and they ask him, "What do you do?" he says, "Ah, I save the world one equation at a time." My question for you is what do you see all of the skills that you're equipping people with, what do you see their import in how you'd describe saving the world?

I'm not so grandiose as to think I'm saving the world. I'm helping people deal intelligently with the problems that they will actually face. 30 years ago it was assumed that managers couldn't type, and all of the work in voice recognition was based on the idea that managers would do better dictating than typing. Now almost everyone needs to know Excel or something like that. That's the lingua franca in business, right? As data become more plentiful we need to move to a higher level so that expected skills for people who work in regular jobs, in regular desk-type jobs, are going to be about data. Just like you wouldn't go into an office now and say, "No, I've never used Excel or a word processor," I think there will be a time when you really need to know something about how to deal with the data that's streaming in. But I was hoping you would ask me what do I think my job is. Your physicist friend said, "Saving the world."

I would love to ask you one final question, Danny, and that is what do you think your job is?

My job is bringing math education into the 20th century. I don't mean the 21st century. We're far from that. Into the 20th century, that's my job.

# Appendix

Covariance: A measure of how much two variables change together.

Covariate: A variable that may (or may not) be helpful in predicting the outcome (or target variable) in a study.

Cross validation: a model validation technique that allows you to assess how well a statistical model will generalize to a data set, independent from the data set the model was trained.

Statistical hypothesis test: A method of statistical inference, in which a hypothesis is tested against experimental data.

t-test (also known as Student's t-test): A particular case of statistical hypothesis testing in which the test statistic follows a particular distribution, the $t-$distribution.


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Radical is used to represent a Square Root of a number. For Example: 5 is square root of number 25. We will denote a radical by symbol ($\sqrt{}$). This is called radical or radix. Number which is put under radical symbol is called a radicand. When a number is written under the radical sign then it is called as radical form. Solving equations is the process of finding the values of the variables or unknown quantities that are satisfied by the condition defined in the equation. An equation is described as the combination of the variables, constants and operations. In this section will discuss about solution of radical equations and how to solve:
• Radical Equations with Rational Exponents and many more

Radical expressions are algebraic expressions containing the radical sign, commonly known as root sign. Radicals denote the inverse operation of exponentiation and also equivalently represented by using fractional exponents. For being able to solve radical equations, it is imperative that we first get rid of the radical. Just like how a polynomial equation can be linear, quadratic, cubic, etc, a radical equation can also be a square root equation, a cubed root equation, a fourth root equation etc.

Examples:

 Sl No. Equation Explanation 1 $\sqrt{x + 4} - 2$ = 2 Variable $x$ is present in the radicand x + 4 2 $\sqrt{2x + 2}$ = x + 6 Variable $x$ is present in the radicand 2x + 2 as well as outside the radical. 3 $\sqrt{2x + 5} + \sqrt{3x - 2}$ = 4 The equation contains two radicals.
.

## Steps to Solve Radical Equations

In general the steps for solving radical equations can be summarized as follows:

1) First we need to isolate the radical expression. If there are two radical expressions, then we need to have them both on different sides of the equal to sign. Note that it cannot be solve with two radical expressions on same side, but it is less cumbersome the other way.

2) Next we square both the sides. This is the main step in solving radical equations. For example, if we have a = b, then on squaring both the sides it becomes $a^{2}$ = $b^{2}$.
3) As a result of above step, the radical can be removed. Now that we have got rid of the radical, we can solve the equation for the unknown variable like any other linear or quadratic equation.

4) The last and most important step. We need to plug back the answers into the original radical equation and check if all the answers that we got actually work or not. It is possible that some of the answers do not work. Such solutions are called ‘extraneous’ solutions.

Radical functions contain functions involving roots. A radical function contains a radical expression with the independent variable in the radicand. An example of radical function is y = $\sqrt{x}$.

Domain of the function should not have a negative value under the square root sign. Otherwise, it will lead to complex number.

Let us solve 5 = $\sqrt{3x}$ + 12
Isolate the radical by subtracting 12 from both the sides.
5 - 12 = $\sqrt{3x}$ + 12 - 12

-7 = $\sqrt{3x}$

Squaring on both sides, we get
49 = 3x
Simplify,
x = 49/3 = 16.33

Sometimes, it is required to square the radical equation twice to get rid of the square roots. Let us see with the help of an example how to solve these type of equations.

For example, consider the equation $\sqrt{x + 1}$ - $\sqrt{2x - 2}$ = $0$

$\sqrt{x + 1}$ = $\sqrt{2x - 2}$                         (Isolate the radicals)

$(\sqrt{x + 1})^{2}$ = $(\sqrt{2x - 2})^{2}$           (Square the equation)

$x + 1$ = $2x - 2$ $\Rightarrow\ x$ = $3$

And, this solution also verifies in the original equation.

## Examples

Example 1: Solve  $\sqrt{(x + 5)}$ = $3$

Solution: Square both the sides.

$\sqrt{(x + 5)^{2}}$ = $3^{2}$

or x + 5 = 9

Subtracting 5 from both the side

x + 5 - 5 = 9 - 5

$\sqrt{(x + 5)}$ = 3

$\sqrt{(4 + 5)}$ = 3

$\sqrt{9}$ = 3

3 = 3

Yes! It works! So the answer that we found is correct.

Example 2: Solve for x and check for extraneous solutions: $\sqrt{2} - \sqrt{x + 6} = -\sqrt{x}$

Solution: $\sqrt{2} - \sqrt{x + 6} = -\sqrt{x}$

$[\sqrt{2} - \sqrt{x + 6}]^{2} = (-\sqrt{x})^{2}$                 (Square the Equation)

2 - $2\sqrt{2(x + 6)}$ + x + 6 = x                                    (Expand the left side)

$-2\sqrt{2x + 12}$ = -8                                                   (Radical isolated)

$\sqrt{2x + 12}$ = 4
After simplifying, we did not get rid of radical. So repeat the steps to isolate x.

$[\sqrt{2x + 12}]^{2}$ = 42                                               (Square the equation)

2x + 12 = 16
x = 2

Check the solution:
$\sqrt{2} - \sqrt{2 + 6} = -\sqrt{2}$
$\sqrt{2} - \sqrt{8} = -\sqrt{2}$
$\sqrt{2} - 3\sqrt{2} = -\sqrt{2}$
$-\sqrt{2} = -\sqrt{2}$
Thus, x = 2 is the solution.

## Practice Problems

Solve the below problems:
1. $\sqrt{x + 4} - 2$ = 2
2. $\sqrt{2x + 5} + \sqrt{3x - 2}$ = 4

format: plain


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# Why does \titlepage cause an error when using Warsaw theme?

Following a recent update, my beamer document will no longer build. I have traced the problem to the \titlepage line.

Here is my minimal working example:

\documentclass{beamer}

\usepackage[T1]{fontenc}

\usepackage{fontspec}

\usepackage[ngerman]{babel}

\usepackage{csquotes}

\usetheme{Warsaw}

\title{Mixeransteuerung mit Leistungselektronik}
\author{Stephen Bosch}
\institute{Johannes-Schlaumeier-Universität Mömbris}
%\date{\today}

\begin{document}

\begin{frame}
\titlepage
\end{frame}

\end{document}

The error messages are:

(./test_umrichtersteuerung.nav) ! Missing { inserted. - l.25 \end{frame} A left brace was mandatory here, so I've put one in. You might want to delete and/or insert some corrections so that I will find a matching right brace soon. (If you're confused by all this, try typing I}' now.)

! Missing { inserted. - l.25 \end{frame} A left brace was mandatory here, so I've put one in. You might want to delete and/or insert some corrections so that I will find a matching right brace soon. (If you're confused by all this, try typing I}' now.)

Overfull \hbox (299.25987pt too wide) detected at line 25 [] []

! Missing } inserted. } l.25 \end{frame} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing 2' now; then my insertion and my current dilemma will both disappear.

! Missing } inserted. } l.25 \end{frame} I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing 2' now; then my insertion and my current dilemma will both disappear.

Package pgf Warning: Your graphic driver pgfsys-xetex.def does not support fadi ngs. This warning is given only once on input line 25.

(I wanted to attach my log file, but couldn't find a way to do it. Suggestions are welcome.)

So far, I have tested with \usetheme{Warsaw} and with the default (no \usetheme statement). If I use the default, it builds fine.

I am using beamer 3.18, because that is what tlmgr installed after a recent update. That's when my problems started. I can see that the current version of beamer is 3.20, but it does not appear as though that version is available to my texlive 2011, which has been frozen in preparation for the new release.

I tried manually installing it to texmf-local using the instructions I found here, but even after running mktexlsr, latex is still using 3.18.

Here are my options, as I see things:

• find a workaround to the bug with Warsaw
• revert to the previous version of beamer (which was working) using tlmgr restore beamer
• install beamer 3.20 over the version currently in my texlive tree (I'm reluctant to try this on my own because I am afraid of breaking something)
• find a way to get texlive to use my local version over the one in the distribution

Any ideas?

-
It's due to the font encoding not the beamer package. – percusse Jun 20 '12 at 23:19
The error is due to TeX trying to do \hbox to \bmb@boxwidth-4bp{...} which is clearly wrong syntax. – egreg Jun 20 '12 at 23:27
@percusse - that doesn't explain why it worked before the update. – Stephen Bosch Jun 20 '12 at 23:31
Did you also update other packages? – percusse Jun 21 '12 at 0:17
do not load package fontspec and run it with pdflatex then it works – Herbert Jun 21 '12 at 6:20

that must be a problem with xelatex and the line

\setbeamercolor*{titlelike}{parent=palette primary}

in the file beamercolorthemewhale.sty. If you run it with lualatex it works well! However, it makes no sense to load package fontenc when not working with pdflatex. Use

\documentclass{beamer}
\usepackage{fontspec}
\usepackage[ngerman]{babel}
\usepackage{csquotes}
\usetheme{Warsaw}

-
Thanks, Herbert. I am not sure I understand, though. I thought Type 1 fonts are part of the PDF/PS standard, and it shouldn't matter how I am generating the PDF. What happens if I want to use a T1-encoded font, for example for math? – Stephen Bosch Jun 21 '12 at 9:54


text:
# Are these $3$ functions linearly independent or dependent?

Are the functions $f, g, h$ given below linearly independent? If they are not linearly independent, find a nontrivial solutions to the equations below:

$$f(x)=e^{2x}- \cos(9x), \quad g(x)=e^{2x}+ \cos(9x), \quad h(x)= \cos(9x)$$

My take so far is that, I know these functions are not linearly independent (meaning this is surely dependent) by Wronskian (as the Wronskian determinant isn't equal to zero), but I have no idea how to find nontrivial solutions to this question. I think I should have an answer as follows:

$$C_1(e^{2x}-\cos(9x)) + C_2(e^{2x}+\cos(9x)) + C_3\cos(9x) = 0 \qquad \text{ where } Cs \text{ are constant }$$

Could I get some help on finding those constants? I've tried $C_1$ as $-1$, $C_2$ as $1$ and $C_3$ as $0$ but that surely cannot be the answer.

• In Mathematica, Wronskian[{Exp[2 x] - Cos[9 x], Exp[2 x] + Cos[9 x], Cos[9 x]}, x] yields $0$, showing that the three functions are linearly dependent. – David G. Stork Feb 8 '16 at 18:19

Those functions are a red herring. ;-)
You basically have the vectors $$v-w,\quad v+w,\quad w$$ in some vector space. These vectors belong to the subspace spanned by $v$ and $w$, which has dimension at most $2$. So a set of three vectors is necessarily linearly dependent.
How to find a nonzero linear combination is easy: $$a(v-w)+b(v+w)+cw=0$$ gives $$(a+b)v+(-a+b+c)w=0$$ so we can choose $b=-a$ and so $c=2a$. If we take $a=1$, we obtain $b=-1$ and $c=2$.
You can take $C_1 = 1, C_2 = -1$ and $C_3 = -2$.
• I choose $C_1 = 1$ (without any reason). Then I wanted to cancel the two exponential so I had to choose $C_2 = -1$. Then I was left with $-2\cos(9x)$ therefore I had to pick $C_3=-2$. – Onil90 Feb 8 '16 at 18:10
$$\begin{bmatrix} f(x)\\ g(x)\\ h(x) \end{bmatrix}= \begin{bmatrix} 1 & -1\\ 1 & 1 \\ 0 & 1 \\ \end{bmatrix}\cdot \begin{bmatrix} -e^{2x}\\ \cos(9x) \end{bmatrix}$$


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# ALGEBRAIC COMBINATORICS

Inclusion-exclusion on Schubert polynomials
Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 209-226.

We prove that an inclusion-exclusion inspired expression of Schubert polynomials of permutations that avoid the patterns $1432$ and $1423$ is nonnegative. Our theorem implies a partial affirmative answer to a recent conjecture of Yibo Gao about principal specializations of Schubert polynomials. We propose a general framework for finding inclusion-exclusion inspired expression of Schubert polynomials of all permutations.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.200
Classification: 05E05
Keywords: Schubert polynomial, principal specialization, nonnegative linear combination.
Mészáros, Karola 1; Tanjaya, Arthur 2

1 Department of Mathematics Cornell University Ithaca, NY 14853 USA.
2 Department of Mathematics Cornell University Ithaca NY 14853 USA.
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author = {M\'esz\'aros, Karola and Tanjaya, Arthur},
title = {Inclusion-exclusion on {Schubert} polynomials},
journal = {Algebraic Combinatorics},
pages = {209--226},
publisher = {The Combinatorics Consortium},
volume = {5},
number = {2},
year = {2022},
doi = {10.5802/alco.200},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.200/}
}
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JO  - Algebraic Combinatorics
PY  - 2022
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SP  - 209
EP  - 226
VL  - 5
IS  - 2
PB  - The Combinatorics Consortium
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%A Tanjaya, Arthur
%T Inclusion-exclusion on Schubert polynomials
%J Algebraic Combinatorics
%D 2022
%P 209-226
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Mészáros, Karola; Tanjaya, Arthur. Inclusion-exclusion on Schubert polynomials. Algebraic Combinatorics, Volume 5 (2022) no. 2, pp. 209-226. doi : 10.5802/alco.200. https://alco.centre-mersenne.org/articles/10.5802/alco.200/

[1] Bergeron, Nantel; Billey, Sara C. RC-graphs and Schubert polynomials, Experiment. Math., Volume 2 (1993) no. 4, pp. 257-269 | DOI | MR | Zbl

[2] Billey, Sara C.; Holroyd, Alexander E.; Young, Benjamin J. A bijective proof of Macdonald’s reduced word formula, Algebr. Comb., Volume 2 (2019) no. 2, pp. 217-248 | DOI | Numdam | MR | Zbl

[3] Billey, Sara C.; Jockusch, William; Stanley, Richard P. Some combinatorial properties of Schubert polynomials, J. Algebraic Combin., Volume 2 (1993) no. 4, pp. 345-374 | DOI | MR | Zbl

[4] Fan, Neil J.; Guo, Peter L. Upper Bounds of Schubert Polynomials, Sci. China Math. (2021) | DOI

[5] Fink, Alex; Mészáros, Karola; St. Dizier, Avery Schubert polynomials as integer point transforms of generalized permutahedra, Adv. Math., Volume 332 (2018), pp. 465-475 | DOI | MR | Zbl

[6] Fink, Alex; Mészáros, Karola; St. Dizier, Avery Zero-one Schubert polynomials, Math. Z., Volume 297 (2021) no. 3-4, pp. 1023-1042 | DOI | MR | Zbl

[7] Fomin, Sergey; Kirillov, Anatol N. The Yang–Baxter equation, symmetric functions, and Schubert polynomials, Discrete Math., Volume 153 (1996) no. 1-3, pp. 123-143 Proceedings of the 5th Conference on Formal Power Series and Algebraic Combinatorics (Florence, 1993) | DOI | MR | Zbl

[8] Fomin, Sergey; Kirillov, Anatol N. Reduced words and plane partitions, J. Algebraic Combin., Volume 6 (1997) no. 4, pp. 311-319 | DOI | MR | Zbl

[9] Fomin, Sergey; Stanley, Richard P. Schubert polynomials and the nilCoxeter algebra, Adv. Math., Volume 103 (1994) no. 2, pp. 196-207 | DOI | MR | Zbl

[10] Gao, Yibo Principal specializations of Schubert polynomials and pattern containment, European J. Combin., Volume 94 (2021), Paper no. 103291, 12 pages | DOI | MR | Zbl

[11] Huh, June; Matherne, Jacob P.; Mészáros, Karola; St. Dizier, Avery Logarithmic concavity of Schur and related polynomials, Trans. Am. Math. Soc. (2022) (https://doi.org/10.1090/tran/8606)

[12] Knutson, Allen; Miller, Ezra Gröbner geometry of Schubert polynomials, Ann. of Math. (2), Volume 161 (2005) no. 3, pp. 1245-1318 | DOI | MR | Zbl

[13] Kraśkiewicz, Witold; Pragacz, Piotr Foncteurs de Schubert, C. R. Acad. Sci. Paris Sér. I Math., Volume 304 (1987) no. 9, pp. 209-211 | MR | Zbl

[14] Lam, Thomas; Lee, Seung Jin; Shimozono, Mark Back stable Schubert calculus, Compos. Math., Volume 157 (2021) no. 5, pp. 883-962 | DOI | MR | Zbl

[15] Lascoux, Alain; Schützenberger, Marcel-Paul Polynômes de Schubert, C. R. Acad. Sci. Paris Sér. I Math., Volume 294 (1982) no. 13, pp. 447-450 | DOI | MR | Zbl

[16] Lenart, Cristian A unified approach to combinatorial formulas for Schubert polynomials, J. Algebraic Combin., Volume 20 (2004) no. 3, pp. 263-299 | DOI | MR | Zbl

[17] Macdonald, Ian G. Notes on Schubert polynomials, Publ. LaCIM, UQAM, Montréal, 1991

[18] Magyar, Peter Schubert polynomials and Bott–Samelson varieties, Comment. Math. Helv., Volume 73 (1998) no. 4, pp. 603-636 | DOI | MR | Zbl

[19] Manivel, Laurent Symmetric functions, Schubert polynomials and degeneracy loci, SMF/AMS Texts and Monographs, 6, American Mathematical Society, Providence, RI; Société Mathématique de France, Paris, 2001, viii+167 pages (Translated from the 1998 French original by John R. Swallow, Cours Spécialisés [Specialized Courses], 3) | MR | Zbl

[20] Monical, Cara; Tokcan, Neriman; Yong, Alexander Newton polytopes in algebraic combinatorics, Selecta Math. (N.S.), Volume 25 (2019) no. 5, Paper no. 66, 37 pages | DOI | MR | Zbl

[21] Morales, Alejandro H.; Pak, Igor; Panova, Greta Asymptotics of principal evaluations of Schubert polynomials for layered permutations, Proc. Amer. Math. Soc., Volume 147 (2019) no. 4, pp. 1377-1389 | DOI | MR | Zbl

[22] Reiner, Victor; Shimozono, Mark Key polynomials and a flagged Littlewood–Richardson rule, J. Combin. Theory Ser. A, Volume 70 (1995) no. 1, pp. 107-143 | DOI | MR | Zbl

[23] Stanley, Richard P. Some Schubert shenanigans (2017) (https://arxiv.org/abs/1704.00851)

[24] Weigandt, Anna; Yong, Alexander The prism tableau model for Schubert polynomials, J. Combin. Theory Ser. A, Volume 154 (2018), pp. 551-582 | DOI | MR | Zbl

[25] Weigandt, Anna E. Schubert polynomials, 132-patterns, and Stanley’s conjecture, Algebr. Comb., Volume 1 (2018) no. 4, pp. 415-423 | DOI | Numdam | MR | Zbl

Cited by Sources:


text:
## Encyclopedia > Human-computer interaction

Article Content

# Human-computer interaction

Human-computer interaction (HCI) is the study of interactions between people and computers. It is an interdisciplinary field, relating computer science, psychology, cognitive science, human factors engineering[?] (ergonomics), sociology, library and information science, and other fields. One of the goals of the field is to make computers more user-friendly.

Although much of the practical work in HCI revolves around the design of graphical user interfaces, HCI is concerned with a number of topics, including

All Wikipedia text is available under the terms of the GNU Free Documentation License

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 Search over one million articles, find something about almost anything!

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 Quadratic formula ... of b/(2a) to both sides, getting $x^2+\frac{b}{a}x+\frac{b^2}{4a^2}=-\frac{c}{a}+\frac{b^2}{4a^2}.$ The left side is now a perfect square; it ...


text:
# How do you rewrite 1/x^-2 with positive exponents?

Feb 7, 2015

As ${x}^{2}$

A negative exponent means that the thing is "under the dividing bar".

So $\frac{1}{x} ^ - 2$ should be written as $\frac{1}{\frac{1}{x} ^ 2}$

And then use the rule of "dividing by a ratio is multiplying by its inverse"

OR:
We could say that every time we change $x$'s from above the bar to below, or the other way around, we change the sign.

So $\frac{1}{x} = \frac{1}{x} ^ \left(+ 1\right) = {x}^{-} \frac{1}{1} = {x}^{-} 1$ and vice versa.

So $\frac{1}{x} ^ \left(- 2\right) = {x}^{+ 2} / 1 = {x}^{2}$


text:
# Why are P/M and D/H defined oppositely in Electromagnetism

1. May 18, 2015

### I<3NickTesla

The definitions of D and H are:

$D=\epsilon_0 E+P$
$H=B/\mu_0-M$

$P=\epsilon_0 \chi E$
$M=\chi H$

I was wondering, if E and B are the fundamental field relating to all charges/currents, why is the definition of the polarisation the opposite for each of them? So why is H in the definition of M and not B, when B is the actual physical field.

Thanks

2. May 18, 2015

### TSny

You can trace the difference in sign to the relations

$\vec{\nabla} \cdot \vec{P} = -\rho_{bound}$ and $\vec{\nabla} \times \vec{M} = +\vec{J}_{bound}$

where $\vec{P}$ and $\vec{M}$ are electric and magnetic polarization vectors.

3. May 19, 2015

### rude man

I would venture that H is more fundamental than B, in the sense that B is H modified by magnetic material, just as D is E modified by dielectric material.
E.g. you have a solenoid with current thru it: the B field is one thing if the core is air and another if the core is iron. But H does not change. Ampere's law is most simply stated as ∫H ds = I.

But that's just a venture.


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# Dynamic FBA¶

dynamicFBA(model, substrateRxns, initConcentrations, initBiomass, timeStep, nSteps, plotRxns, exclUptakeRxns)[source]

Performs dynamic FBA simulation using the static optimization approach

Usage

[concentrationMatrix, excRxnNames, timeVec, biomassVec] = dynamicFBA(model, substrateRxns, initConcentrations, initBiomass, timeStep, nSteps, plotRxns, exclUptakeRxns)

Inputs

• model – COBRA model structure
• substrateRxns – List of exchange reaction names for substrates initially in the media that may change (e.g. not h2o or co2)
• initConcentrations – Initial concentrations of substrates (in the same structure as substrateRxns)
• initBiomass – Initial biomass (must be non zero)
• timeStep – Time step size
• nSteps – Maximum number of time steps

Optional inputs

• plotRxns – Reactions to be plotted (Default = {‘EX_glc(e)’, ‘EX_ac(e)’, ‘EX_for(e)’})
• exclUptakeRxns – List of uptake reactions whose substrate concentrations do not change (Default = {‘EX_co2(e)’, ‘EX_o2(e)’, ‘EX_h2o(e)’, ‘EX_h(e)’})

Outputs

• concentrationMatrix – Matrix of extracellular metabolite concentrations
• excRxnNames – Names of exchange reactions for the EC metabolites
• timeVec – Vector of time points
• biomassVec – Vector of biomass values

If no initial concentration is given for a substrate that has an open uptake in the model (i.e. model.lb < 0) the concentration is assumed to be high enough to not be limiting. If the uptake rate for a nutrient is calculated to exceed the maximum uptake rate for that nutrient specified in the model and the max uptake rate specified is > 0, the maximum uptake rate specified in the model is used instead of the calculated uptake rate.

Note

The dynamic FBA method implemented in this function is essentially the same as the method described in [Varma, A., and B. O. Palsson. Appl. Environ. Microbiol. 60:3724 (1994)]. This function does not implement the dynamic FBA using dynamic optimization approach described in [Mahadevan, R. et al. Biophys J, 83:1331-1340 (2003)].


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UPnP Media Server for PS3 and others: MediaTomb

I wanted to get XBMC on my brother’s PS3, but since he has a PS3 slim, the “otherOS” feature was not available. However, Sony’s got to allow streaming to it right? Yep, via the UPnP (Universal Plug and Play) protocol.

I used this guide to set up MediaTomb. On Ubuntu, basically,

 <pre class="src src-sh">sudo apt-get install mediatomb mediatomb-daemon

## don’t do sudo mediatomb since I will be utilizing daemon sudo emacs -q -nw /etc/mediatomb/config.xml ## change to yes ## uncomment or add this line ## Next, go to http://server.ip:49155/ and add the location of the media

My PS3 didn’t see mediatomb. After debugging with the help of the author over at #mediatomb over on freenode, I found out that the wireless bridge the PS3 was plugged to did not pass over all udp unicasts. There were communications between the two but the connection was not established because there were missing pieces.

In the process of debug, I used cidero and wireshark and tshark (via apt-get) per the faq. Basically, using cidero with my laptop plugged into the wireless bridge, I could see mediatomb. Using the web browser on the PS3 I could get to the mediatomb web ui. Plugging the PS3 onto the primary router, I see mediatomb. Then I used tshark to capture the connection information when the ps3 is searching for a media server and sent the capture to the author and he couldn’t help me any further since it was the setup’s fault. Haven’t found a way around this wireless bridge yet, although I posted in the DD-WRT forum.


text:
Elementary Statistics (12th Edition)

$H_{0}:\mu=33$. $H_{a}:\mu \ne 33.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{35.9-33}{11.1/\sqrt{82}}=2.366.$ The P-value is the interval of probabilities between which the value of the test-statistic lies in the table with degree of freedom=sample size-1=82-1=81, hence P is between 0.01 and 0.02. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is more than $\alpha=0.01$, because it is between 0.01 and 0.02, hence we fail to reject the null hypothesis. Hence we can say that there is not sufficient evidence to reject that the mean age of OScar winning actresses is 33 years.


text:
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# What are the reactants and end products of cellular respiration?

Krishan T.

Apr 18, 2018

Glucose and oxygen are the reactants and the end products are carbon dioxide and water with the liberation of energy in form of ATP.

#### Explanation:

Cellular respiration occurs in living cells. It provides energy to the cell for carrying out its metabolic activities.

Glucose ( $C 6 H 12 O 6$) is the substrate. It is broken down into $C O 2$ and $H 2 O$ in presence of $O 2$, with the liberation of energy in form of ATP molecules.

Cellular respiration occurs in 2 steps:
Glycolysis and Kreb’s cycle or Citric acid cycle .

Glucolysis occurs in absence of oxygen . Glucose is converted into fructose 1;6 di-phosphate that is converted into 2 molecules of pyruvic acid in a series of steps of glycolysis.

Pyruvic acid is converted into oxalacetate that enters Kreb’s cycle . Kreb’s cycle occurs in presence of oxygen. During Kreb’s cycle, $C O 2$ and $N A D P H 2$ are produced. $N A D P H 2$ is oxidised into $N A D P$ in presence of $O 2$ to generate ATP molecules. This process is termed oxidative phosphorylation .

##### Related questions
• What is the chemical equation for cellular respiration?

• How is glucose changed during glycolysis?

• How is gluconeogenesis related to glycolysis?

• How does aerobic respiration release energy from glucose?

• How do cellular respiration and breathing differ?

• What gets oxidized during glycolysis?

• How is glycolysis related to the citric acid cycle?

• What are the steps of glycolysis?

• What is glycolysis?

• What is the citric acid cycle?

See all questions in Aerobic Respiration

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# Reactants and Products of Cellular Respiration

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What Are The Reactants Of Photosynthesis And Cellular Respiration?

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# What Are The Reactants Of Photosynthesis And Cellular Respiration?

by Daniel Nelson
December 12, 2017
in Technology
0

The reactants of photosynthesis are carbon dioxide and water, meaning during photosynthesis carbon dioxide and water are taken in to create energy. The reactants of cellular respiration are glucose (sugar) and oxygen, these are taken in by animals and humans to produce energy.

The cells found in both plants and animals need to produce energy. Trees produce energy via the process of photosynthesis which takes the raw solar energy from the sun and converts it into carbohydrates, or usable chemical energy.

Meanwhile, the cells found in animals, including the cells in your body, perform the process of cellular respiration which makes ATP (a form of usable energy).

## The Relationship Between Photosynthesis and Cellular Respiration

Apart from both being processes that cells use to create energy, is there any relationship between the two processes? As it turns out, yes there is. To find out what it is, let’s take a look at the chemical equations which happen in both cellular respiration and photosynthesis.

Here’s the equation for photosynthesis: 6CO2 + 6H2O → C6H12O6+ 6O2

The reactants of photosynthesis are:

• Carbon Dioxide (CO2)
• Water (H2)

The products of photosynthesis are:

• Energy (C6H12O6)
• Oxygen (O2)

The reactants of cellular respiration are:

• Glucose (sugar)
• Oxygen (O2)

The products of cellular respiration are:

• Carbon Dioxide (CO2)
• Water (H2)
• ATP (Energy)

This equation means that plants take C02 (carbon dioxide) and water, and with the assistance of solar energy, turn it into glucose and oxygen (O2).

The equation for cellular respiration is as follows: C6H12O6 + 6O2 → 6CO2 + 6H2O

This means that cellular respiration utilizes glucose and oxygen and releases carbon dioxide and water as a result. Essentially, the two equations are the exact opposite of one another. Animal cells combine oxygen and hydrogen to form water as a byproduct, while the glucose they use to create the ATP (energy) they need is transformed back into carbon dioxide. Plants use both this water and carbon dioxide to power photosynthesis, and as a byproduct, they release oxygen and glucose.

The complex and intertwined relationship of photosynthesis and respiration are part of what is known as the “ carbon cycle ”, which is what allows carbon molecules to be recycled and work their way through the entire biosphere. Carbon is released into the atmosphere by respiration from animals in the form of carbon dioxide, while photosynthesis from plants absorbs the carbon dioxide and gets it out of the atmosphere.

 Photosynthesis reactants Photosynthesis products Cellular respiration reactants Cellular respiration products Carbon Dioxide (CO2) Energy (C6H12O6) Glucose (sugar) Carbon Dioxide (CO2) Water (H2) Oxygen (O2) Oxygen (O2) Water (H2) ATP (Energy)

Let’s take a closer look at the reactants involved in the carbon process.

## Reactants of the Carbon Process

C6H12O6 – While the formula can technically apply to a number of different molecules, depending on how the individual atoms within the molecule are connected, most of them are various types of sugars. The most famous formation of C6H12O6 is known as glucose , which can be known by other names including dextrose and even blood sugar. In the cells of animals, the process known as glycolysis converts glucose into pyruvate which generates two molecules of ATP along with it.

O2 – Dioxygen, frequently just referred to as oxygen, is what vertebrates used to breathe. In vertebrates, the oxygen is brought into the lungs and is picked up by the red blood cells. The use of oxygen enables the more efficient conversion of glucose into ATP, although ATP can also be generated without oxygen in anaerobic conditions. Oxygen accounts for almost 21% of all our atmosphere.

CO2 – Carbon dioxide is produced by a variety of different microorganisms during both cellular respiration and fermentation. Carbon dioxide can enter the cells of plants through tiny holes in the leaves of plants called stomata. Once the carbon dioxide is inside the cells of the plant, the chloroplasts in the cell use it to undergo photosynthesis and create carbohydrates. Carbon dioxide is a greenhouse gas when it is in the atmosphere, and it contributes to global climate change.

H2O – Water is found everywhere on earth, and it also exists in the cells of most living things. Plants need water in addition to carbon dioxide and sunlight to produce energy for photosynthesis. Plant cells hold the water in structures called vacuoles.

## The Photosynthetic Process

Photosynthesis requires several different components. The photosynthetic process requires the use of pigments and plastids.

Photosynthetic organisms have organelles referred to as plastids floating around in the cytoplasm of their cells. Plastids are multi-membraned organelles which can contain both pigments and other structures like fats and starches. Chloroplasts are examples of plastids. Like mitochondria in animal cells, they have their own collections of genes within them, and in plants, they are responsible for the conversion of solar energy into carbohydrates.

Pigments are what give plants their color, but they also allow plants to trap sunlight. The different colors of pigments can trap different wavelengths of light. There are three primary groups of pigments and these groups are carotenoids, phycobilins, and chlorophylls.

Carotenoids are typically colored yellow, orange, or red. These colors are responsible for absorbing green/blue light. You can think of cartone, which is colored orange, as an example of a carotenoid. In fact, it is how carrots get their color. Phycobilins are either red or blue, and they can absorb the wavelengths of light outside of blue, red, and orange. Examples of organisms employing phycobilins include red algae and cyanobacteria. Finally, chlorophylls are the most famous example of pigments for plants, and they are colored green. Chlorophylls are able to absorb light in the blue and red wavelengths, and they can be further subdivided into three different classes. Chlorophyll can be found in every photosynthesizing plant, and it exists alongside a variant called bacteriochlorophyll which is capable of grabbing light that exists in the infrared spectrum. Bacteriochlorophyll is only found in bacteria, as the name implies.

## Differences Between Plant and Animal Cells

Plant and animal cells both have designated cell structures which are collectively responsible for the production of energy . Plant have chloroplasts, while animal cells have a structure known as mitochondria which utilize glucose and oxygen to produce carbon dioxide, water, and energy (as well as heat). It is important to note that plant cells have mitochondria as well, but animal cells do not have chloroplasts. However, the mitochondria that are in plants function a little differently from the mitochondria that are found in animal cells. The mitochondria in animal cells are used for both aerobic respiration and energy production, while the mitochondria in plant cells are only used to respire.

Plant and animal cells exist in a complex and delicate balance. The two types of organisms rely on substances output by the other organism, and one type of organism could not exist without the other.

### Daniel Nelson

Daniel obtained his BS in Communications and is pursuing a Master’s degree in the science of Human-Computer Interaction. He hopes to work on projects which bridge the sciences and humanities. His background in education and training is diverse including education in computer science, communication theory, psychology, and philosophy. He aims to create content that educates, persuades, entertains and inspires.

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ISSN: 2639-1538 (online)


text:
Conservation of linear momentum

1. Jul 13, 2008

G.Chandra

Why do we apply law of conservation of linear momentum on a body that explodes in air when an external force, gravittional force- mg, is acting on it? The law says that the linear momentum is conserved in absence of the external forces.

Last edited: Jul 13, 2008
2. Jul 13, 2008

pardesi

hmm that's because the force $$mg$$ into the time for which the explaosion happens $$dt=mgdt$$ is aver small qty so
$$P_{f}-P_{i}=mgdt \approx 0$$

3. Jul 13, 2008

tiny-tim

Welcome to PF!

Hi G.Chandra! Welcome to PF!

Because an explosion, like a collision, is taken to be instantaneous.

So the force from gravity (which takes time!) is zero.

4. Jul 13, 2008

pardesi

Re: Welcome to PF!

hmmmm i don't get this explaination of urs?

5. Jul 13, 2008

G.Chandra

This means that the law will not be applicable if duration of explosion is longer?

6. Jul 13, 2008

pardesi

no see it's an approximatiion!!!
so don't wry about the "law holding" or not
what's assumed is that the momentum change due to gravity is negligible as comapred to the initial momentum
say if teh intial momentum was some 500 untis and the change sone 1 or 2 units then it shud hardly matter u
it's an approximation and works real well

7. Jul 13, 2008

Andy Resnick

That's the magic of representing extended objects as mass-points. The center of mass will follow the undisturbed trajectory (within reason- a mid-air collision is different than a 'simple explosion'), even though all the little pieces will tumble hither and yon.

8. Jul 14, 2008

Redbelly98

Staff Emeritus
Re: Welcome to PF!

A better way to say it might be that the impulse due to gravity,

$$F \Delta t = m \ g \ \Delta t$$

is very small since delta-t is small. Equating impulse with change in momentum, we can also say this does not affect the momentum during a collision or explosion.

9. Jul 14, 2008

pardesi

yeah perfect that's hwy i had questioned "tiny-tim"!!!


text:
Conference Paper

# Optimistic Sorting and Information Theoretic Complexity.

Authors:
To read the full-text of this research, you can request a copy directly from the author.

## Abstract

Entropy considerations provide a natural estimate of the number of comparisons to sort incompletely shuffled data, which subsumes most previous measures of configurational complexity. Simple modifications to insertion sort and merge sort improve their performance on such data. The modified merge sort proves efficient both in theory and in practice.

## No full-text available

... A concurrent line of work in adaptive sorting initiated by Mcilroy concerns itself with the information-theoretic properties of a measure of disorder rather than its strict comparison with other measures [32]. ...
... A Note on Independent Work. McIlroy's paper on information-theoretic properties of sorting algorithms [32] proposes a sequential sorting algorithm called mergesort with exponential search, which performs the same number of comparisons as our adaptive mergesort. However, since his algorithm uses a merge step which takes ( ) time, the overall cost of his algorithm is still ( lg ). ...
... McIlroy's Properties Our work is also influenced by McIlroy's perspective on the desirable properties of an adaptive sorting algorithm. Here we describe the six properties he proposes in his 1993 paper [32]. For a permutation , let ( ) denote the number of comparisons required to sort . ...
Preprint
Full-text available
We study the connections between sorting and the binary search tree model, with an aim towards showing that the fields are connected more deeply than is currently known. The main vehicle of our study is the log-interleave bound, a measure of the information-theoretic complexity of a permutation $\pi$. When viewed through the lens of adaptive sorting -- the study of lists which are nearly sorted according to some measure of disorder -- the log-interleave bound is comparable to the most powerful known measure of disorder. Many of these measures of disorder are themselves virtually identical to well-known upper bounds in the BST model, such as the working set bound or the dynamic finger bound, suggesting a connection between BSTs and sorting. We present three results about the log-interleave bound which solidify the aforementioned connections. The first is a proof that the log-interleave bound is always within a $\lg \lg n$ multiplicative factor of a known lower bound in the BST model, meaning that an online BST algorithm matching the log-interleave bound would perform within the same bounds as the state-of-the-art $\lg \lg n$-competitive BST. The second result is an offline algorithm in the BST model which uses $O(\text{LIB}(\pi))$ accesses to search for any permutation $\pi$. The technique used to design this algorithm also serves as a general way to show whether a sorting algorithm can be transformed into an offline BST algorithm. The final result is a mergesort algorithm which performs work within the log-interleave bound of a permutation $\pi$. This mergesort also happens to be highly parallel, adding to a line of work in parallel BST operations.
... The main drawback of this algorithm is that it has no adaptivity and goes possibly quadratic time on some inputs [19]. Both Splaysort [21] and McIlroy's mergesort [20] seems adaptive with respect to almost all accepted measures of presortedness. However, they are not practical. ...
... Let C(X) denote the number of comparisons needed to sort the sequence X. According to the theory of optimal adaptivity202122, a sorting algorithm is Rem-optimal if ...
... where m = Rem(X). Based on McIlroy's analysis, his mergesort is Rem-optimal [20]. Psort [5], which is a library sort function based on PEsort, has a bit Rem-optimal flavor, while its improved version [6] is close to Rem-optimal. ...
Article
The purpose of the paper is twofold. First, we want to search for a more efficient sample sort. Secondly, by analyzing a variant of Samplesort, we want to settle an open problem: the average case analysis of Proportion Extend Sort (PEsort for short). An efficient variant of Samplesort given in the paper is called full sample sort. This algorithm is simple. It has a shorter object code and is almost as fast as PEsort. Theoretically, we show that full sample sort with a linear sampling size performs at most nlogn+O(n) comparisons and O(nlogn) exchanges on the average, but comparisons in the worst case. This is an improvement on the original Samplesort by Frazer and McKellar, which requires comparisons on the average and O(n2) comparisons in the worst case. On the other hand, we use the same analyzing approach to show that PEsort, with any p>0, performs also at most nlogn+O(n) comparisons on the average. Notice, Cole and Kandathil analyzed only the case p=1 of PEsort. For any p>0, they did not. Namely, their approach is suitable only for a special case such as p = 1, while our approach is suitable for the generalized case.
... Quicksort should not be favored by giving it two places. Thus, we have five different sorting methods as participants in this race: insertion sort, shellsort [Knuth, D.E. 1997], mergesort [McIlroy, P. 1993], heapsort [Williams, J. W. J. 1964], and quicksort [Hoare, C.A.R. 1961]. ...
... This qsort is interesting in that it shuns quicksort in favor of mergesort, due to the popularity of timsort [Peters, T. 2002]. Tim Peters created timsort based on Peter McIlroy's idea of natural mergesort [McIlroy, P. 1993], which consists of two processes: in process 1, sorted subarrays (called runs) are identified from the input; in process 2, two runs are merged into one run, until only one run remains. The two processes can be interleaved. ...
... As the first goal of this article, we will try to identify which techniques are more effective and which are less effective through extensive experiments. From now on, by mergesort, we mean natural mergesort [McIlroy, P. 1993]. ...
Article
Sorting is one of the oldest computing problems and is still very important in the age of big data. Various algorithms and implementation techniques have been proposed. In this study, we focus on comparison based, internal sorting algorithms. We created 12 data types of various sizes for experiments and tested extensively various implementations in a single setting. Using some effective techniques, we discovered that quicksort is adaptive to nearly sorted inputs and is still the best overall sorting algorithm. We also identified which techniques are effective in timsort, one of the most popular and efficient sorting method based on natural mergesort, and created our version of mergesort, which runs faster than timsort on nearly sorted instances. Our implementations of quicksort and mergesort are different from other implementations reported in all textbooks or research articles, faster than any version of the C library qsort functions, not only for randomly generated data, but also for various types of nearly sorted data. This experiment can help the user to choose the best sorting algorithm for the hard sorting job at hand. This work provides a platform for anyone to test their own sorting algorithm against the best in the field.
... There is extensive literature on adaptive sorts: e.g., for theoretical foundations see [14,7,16,15] and for more applied investigations see [5,9,4,21,18]. The present paper will consider only stable, natural merge sorts. ...
... Note that in this case, if ℓ ≥ 2, |Z| < |X| since (B-1) and (B-2) imply that |X| ≥ α|Y | ≥ α(α − 1)|Z| and α 2 − α > 1 since ϕ < α. This is the reason why Algorithm 6 does not check for the condition |X| < |Z| in lines[14][15][16] (unlike what is done on line 7). ...
Preprint
Full-text available
We introduce new stable, natural merge sort algorithms, called 2-merge sort and $\alpha$-merge sort. We prove upper and lower bounds for several merge sort algorithms, including Timsort, Shiver's sort, $\alpha$-stack sorts, and our new 2-merge and $\alpha$-merge sorts. The upper and lower bounds have the forms $c \cdot n \log m$ and $c \cdot n \log n$ for inputs of length $n$ comprising $m$ runs. For Timsort, we prove a lower bound of $(1.5 - o(1)) n \log n$. For 2-merge sort, we prove optimal upper and lower bounds of approximately $(1.089 \pm o(1))n \log m$. We prove similar asymptotically matching upper and lower bounds for $\alpha$-merge sort, when $\varphi < \alpha < 2$, where $\varphi$ is the golden ratio. These merge strategies can be used for any stable merge sort, not just natural merge sorts. The new 2-merge and $\alpha$-merge sorts have better worst-case merge cost upper bounds and are slightly simpler to implement than the widely-used Timsort; they also perform better in experiments.
... As discussed earlier, for the network model described in Section 3, the query-processing load in the network can be estimated by d τ when the average search distance is τ. Hence, using the results in Section 5, we obtain: Theorem 3: The query-processing load for a flooding search in the clustered peer-to-peer network defined in Section 3 is (18) for searches initiated in the high-density cluster, and is ...
... Some other places where the entropy expression shows up are: (i) the average number of steps to find a key (i.e. the average depth to which one has to go to find a key in the search tree) in the optimal binary balanced search tree [17], and (ii) as the lower bound on the minimum number of comparisons needed to sort a set of keys (where multiple items in the set may have the same value) [18] where the entropy is on the frequency of occurrence of different keys in the entire set. To the best of our knowledge, no precise discussion of the relevance of entropy to these problems exists in the literature. ...
Article
Full-text available
This paper derives the optimal search time and the optimal search cost that can be achieved in unstructured peer-to-peer networks when the demand pattern exhibits clustering (i.e. file popularities vary across the set of nodes in the network). Clustering in file popularity patterns is evident from measurements on deployed peer-to-peer file sharing networks. In this paper, we provide mechanisms for modeling clustering in file popularity distributions and the consequent non-uniform distribution of file replicas. We derive relations that show the effect of the number of replicas of a file on the search time and on the search cost for a search for that file for the clustered demands case in such networks for both random walk and flooding search mechanisms. The derived relations are used to obtain the optimal search performance for the case of flooding search mechanisms. The potential performance benefit that clustering in demand patterns affords is captured by our results. Interestingly, the performance gains are shown to be independent of whether the search network topology reflects the clustering in file popularity (the optimal file replica distribution to obtain these performance gains, however, does depend on the search network topology).
... In terms of Rem-adaptivity (its definition will appear below), it has good behavior. In some cases, it can achieve even the adaptive performance of McIlroy's Mergesort with Exponential Search (MSES for short) [13]. Like PEsort, it can be guaranteed theoretically to require O(n log n) comparisons in the worst case, and n log n +O(n) comparisons on the average case. ...
... For small values of log Rem(X), Adp SymPsort achieves the same Rem-adaptivity as Merge Sort with Exponential Search (MSES for short) ? due to McIlroy [13]. For large values of log Rem(X), the situation is a little different. ...
Article
In this paper, we propose a useful replacement for quicksort-style utility functions. The replacement is called Symmetry Partition Sort, which has essentially the same principle as Proportion Extend Sort. The maximal difference between them is that the new algorithm always places already partially sorted inputs (used as a basis for the proportional extension) on both ends when entering the partition routine. This is advantageous to speeding up the partition routine. The library function based on the new algorithm is more attractive than Psort which is a library function introduced in 2004. Its implementation mechanism is simple. The source code is clearer. The speed is faster, with O(n log n) performance guarantee. Both the robustness and adaptivity are better. As a library function, it is competitive.
... There is extensive literature on adaptive sorts: e.g., for theoretical foundations see [21,9,26,23] and for more applied investigations see [6,12,5,31,27]. The present paper will consider only stable, natural merge sorts. ...
... and java.util.Collection.sort() methods is an ideal candidate: it is based on a complex combination of merge sort and insertion sort [15,19]. It had a bug history (see www.bugs.java.com/view_bug.do?bug_id=8011944), but was reported as fixed as of Java 8. We decided to verify the actual implementation with only two minor modifications: we stripped the code of generics and we modified one execution path that is irrelevant to the sorting result (see Sect. 7 for details). ...
Article
Full-text available
TimSort is the main sorting algorithm provided by the Java standard library and many other programming frameworks. Our original goal was functional verification of TimSort with mechanical proofs. However, during our verification attempt we discovered a bug which causes the implementation to crash by an uncaught exception. In this paper, we identify conditions under which the bug occurs, and from this we derive a bug-free version that does not compromise performance. We formally specify the new version and verify termination and the absence of exceptions including the bug. This verification is carried out mechanically with KeY, a state-of-the-art interactive verification tool for Java. We provide a detailed description and analysis of the proofs. The complexity of the proofs required extensions and new capabilities in KeY, including symbolic state merging.
... Standard Java sort algorithm [49] for non-primitive types is used for sorting the array. The sort algorithm, called timsort, is a stable, adaptive, iterative mergesort, which implementation is adapted from Tim Peters's list sort for Python [50], that uses techniques from [51] Writing output Writing buckets data to a single output file in the correct order is the last step. This is the most sequential part of the application. ...
Article
Full-text available
Sorting algorithms are among the most commonly used algorithms in computer science and modern software. Having efficient implementation of sorting is necessary for a wide spectrum of scientific applications. This paper describes the sorting algorithm written using the partitioned global address space (PGAS) model, implemented using the Parallel Computing in Java (PCJ) library. The iterative implementation description is used to outline the possible performance issues and provide means to resolve them. The key idea of the implementation is to have an efficient building block that can be easily integrated into many application codes. This paper also presents the performance comparison of the PCJ implementation with the MapReduce approach, using Apache Hadoop TeraSort implementation. The comparison serves to show that the performance of the implementation is good enough, as the PCJ implementation shows similar efficiency to the Hadoop implementation.
... Some other places where the entropy expression shows up are: (i) the average number of steps to find a key (i.e. the average depth to which one has to go to find a key in the search tree) in the optimal binary balanced search tree [17], and (ii) as the lower bound on the minimum number of comparisons needed to sort a set of keys (where multiple items in the set may have the same value) [18] where the entropy is on the frequency of occurrence of different keys in the entire set. To the best of our knowledge, no precise discussion of the relevance of entropy to these problems exists in the literature. ...
Conference Paper
This paper derives the optimal search time and the optimal search cost that can be achieved in unstructured peer-to-peer networks when the demand pattern exhibits clustering (i.e. file popularities vary from region to region in the network). Previous work in this area had assumed a uniform distribution of file replicas throughout the network with an implicit or explicit assumption of uniform file popularity distribution whereas in reality, there is clear evidence of clustering in file popularity patterns. The potential performance benefit that the clustering in demand patterns affords is captured by our results. Interestingly, the performance gains are shown to be independent of whether the search network topology reflects the clustering in file popularity. We also provide the relation between the query-processing load and the number of replicas of each file for the clustered demands case showing that flooding searches may have lower query-processing load than random walk searches in the clustered demands case.
... In fact, one can efficiently sort all distinct states in C. The standard python implementation is timsort [21]. It was developed by Tim Peters based on McIlroy's techniques in [22]. In the worst case, its space and time complexities are O(N) and O(N log N) respectively. ...
Preprint
Full-text available
We put forward new general criteria to design successor rules that generate binary de Bruijn sequences. Prior fast algorithms based on successor rules in the literature are then shown to be special instances. We implement the criteria to join the cycles generated by a number of simple feedback shift registers (FSRs). These include the pure cycling register (PCR) and the pure summing register (PSR). For PCR, we define a preorder on its cycles, based on their weights. For PSR, we define two orders, namely a necklace order on its cycles and a mixed order on the cycles based on both the weight and the necklace orders. Using the new orders, we propose numerous classes of successor rules that can efficiently generate binary de Bruijn sequences. Producing the next bit takes no more than $O(n)$ memory and between $O(n)$ and $O(n \, \log n)$ time. We implemented computational routines to confirm the claims.
... 5 In fact, among a dozen different Unix libraries we found no qsort that could not easily be driven to quadratic behavior; all were derived from the Seventh Edition or from the 1983 Berkeley function. The Seventh 0038-0644/93/111249–17\$13.50 Received 21 August 1992 © 1993 by John Wiley & Sons, Ltd. Revised 10 May 1993 Edition qsort and several others had yet another problem. ...
Article
SUMMARY We recount the history of a new qsort function for a C library. Our function is clearer, faster and more robust than existing sorts. It chooses partitioning elements by a new sampling scheme; it partitions by a novel solution to Dijkstra's Dutch National Flag problem; and it swaps efficiently. Its behavior was assessed with timing and debugging testbeds, and with a program to certify performance. The design techniques apply in domains beyond sorting.
... This complexity is much bigger than the baseline approach and corresponds to long scheduling time. The complexity of SNO and RNO depends on the sorting algorithm, which can be O(n log n) using TimSort [34], [35]. This complexity is much smaller than that of Adapted A-Star and is slightly bigger than that of Baseline while it corresponds to small total cost as presented in Section V. ...
Article
Full-text available
bfCooperative Intelligent Transport Systems (C-ITS) is a promising technology to make transportation safer and more efficient. Ridesharing for long-distance is becoming a key means of transportation in C-ITS. In this paper, we focus on private long-distance ridesharing, which reduces the total cost of vehicle utilization for long-distance journeys. In this context, we investigate journey scheduling problem with shared vehicles to reduce the total cost of vehicle utilization. Most of the existing works directly schedule journeys to vehicles with long scheduling time and only consider the cost of driving travellers instead of the total cost. In contrast, to reduce the total cost and scheduling time, we propose a comprehensive cost model and a two-phase journey scheduling approach, which includes path generation and path scheduling. On this basis, we propose two path generation methods: a simple near optimal method and a reset near optimal method as well as a greedy based path scheduling method. Finally, we present an experimental evaluation with different path generation and path scheduling methods with synthetic data generated based on real-world data. The results reveal that the proposed scheduling approach significantly outperforms baseline methods in terms of total cost (up to 69.8%) and scheduling time (up to 84.0%) and the scheduling time is reasonable (up to 0.16s). The results also show that our approach has higher efficiency (up to 141.7%) than baseline methods.
... and java.util.Collection.sort() method is an ideal candidate: it is based on a complex combination of merge sort and insertion sort [12, 15] . It had a bug history 5 , but was reported as fixed as of Java version 8. We decided to verify the implementation, stripped of generics, but otherwise completely unchanged and fully executable. ...
Conference Paper
Full-text available
We investigate the correctness of TimSort, which is the main sorting algorithm provided by the Java standard library. The goal is functional verification with mechanical proofs. During our verification attempt we discovered a bug which causes the implementation to crash. We characterize the conditions under which the bug occurs, and from this we derive a bug-free version that does not compromise the performance. We formally specify the new version and mechanically verify the absence of this bug with KeY, a state-of-the-art verification tool for Java.
Chapter
Group signatures are considered as one of the most prominent cryptographic primitives to ensure privacy. In essence, group signatures ensure the authenticity of messages while the author of the message remains anonymous. In this study, we propose a dynamic post-quantum group signature (GS) extending the static G-Merkle group signature (PQCRYPTO 2018). In particular, our dynamic G-Merkle (DGM) allows new users to join the group at any time. Similar to G-Merkle scheme, our DGM only involves symmetric primitives and makes use of a One-Time Signature scheme (OTS). Each member of the group receives a certain amount of OTS key pairs and can ask the Manager $$\mathcal {M}$$ for more if needed. Our DGM also provides an innovative way of signing revocation by employing Symmetric Puncturable Encryption (SPE) recently appeared in (ACM CCS 2018). DGM provides a significantly smaller signature size than other GSs based on symmetric primitives and also reduces the influence of the number of group members on the signature size and on the limitations of the application of G-Merkle.
Thesis
Full-text available
This thesis deals with the design of algorithms in computational geometry whose complexity depends on the output-size, the so-called output-sensitive algorithms. We first describe the main paradigms that allow algorithms to be output-sensitive. Then, we give a near-optimal output-sensitive algorithm to compute the convex hull of general planar objects such that the output-size of the convex hull of any pair of objects is bounded. We extend the results to the case of envelopes and the partial decomposition of convex and maximal layers. Finally, we consider the pierceability problem for families of convex objects which has been proven NP-hard. We first study the case of isothetic boxes and give an output-sensitive heuristic that is precision-sensitive. Then, we consider the combinatorial properties of convex objects from the pierceability point of view. We obtain a collection of algorithms for various class of objects, some of them implying Helly-type theorems.
Article
Full-text available
This thesis deals with the design of algorithms in computational geometry whose complexity depends on the output-size, the so-called output-sensitive algorithms. We first describe the main paradigms that allow algorithms to be output-sensitive. Then, we give a near-optimal output-sensitive algorithm to compute the convex hull of general planar objects such that the output síze of the convex hull of any pair of objects is bounded. We extend the results to the case of envelopes and the partial decomposition of convex and maxima layers. Finally, we consider the problem for familles of convex objects which has been proven NP-hard. We first study the case of isothetic boxes and give an output-sensitive heuristic that is precision sensitive. Then,, We Consider the combinatorial properties of convex objects from the piercability point of view. We obtain a collection of algorithms for various class of objects, some of them implying Helly-type theorems.
Article
Adaptivity in sorting algorithms is sometimes gained at the expense of practicality. We give experimental results showing that Splaysort — sorting by repeated insertion into a Splay tree — is a surprisingly efficient method for in-memory sorting. Splaysort appears to be adaptive with respect to all accepted measures of presortedness, and it outperforms Quicksort for sequences with modest amounts of existing order. Although Splaysort has a linear space overhead, there are many applications for which this is reasonable. In these situations Splaysort is an attractive alternative to traditional comparison-based sorting algorithms such as Heapsort, Mergesort, and Quicksort.
Article
Up to now, the most efficient sort function for a C library was a variant of Hoare's Quicksort (qsort, for short), which was proposed by Bentley and Mcllroy in the early 1990s. Here we call this library function BM qsort. This paper introduces a library function which is based on Chen's Proportion Extend Sort (psort). This work is inspired by the fact that psort is generally faster than qsort, and in the worst case, qsort requires O(n2) comparisons, while psort requires O(n log n). In our library function, many tricks used in BM qsort have been adopted, such as sorting a small array by an insertion sort and the handling of equal elements. Some new tricks are also proposed, however, such as the adaptive partitioning scheme. To assess more effectively the behavior of our function, the test cases are enhanced. The empirical results show that our function is robust and faster than BM qsort. On particular classes of inputs, such as 'already sorted', it is linear time.
Conference Paper
Studies have indicated that sorting comprises about 20% of all computing on mainframes. Perhaps the largest use of sorting in computing (particularly business computing) is the sort required for large database operations (e.g. required by joint operations). In these applications the keys are many words long. Since our sorting algorithm hashes the key (rather than compare entire keys as in comparison sorts such as quicksort), our algorithm is even more advantageous in the case of large key lengths; in that case the cutoff is much lower. In case that the compression ratio is high, which can be determined after building the dictionary, we just adopt the previous sorting algorithm, e.g. quick sort. The same techniques can be extended to other problems (e.g. computational geometry problems) to decrease computation by learning the distribution of the inputs
Article
There is an upsurge in interest in the Markov model and also more general stationary ergodic stochastic distributions in theoretical computer science community recently (e.g. see [Vitter,Krishnan91], [Karlin,Philips,Raghavan92], [Raghavan92] for use of Markov models for on-line algorithms, e.g., cashing and prefetching). Their results used the fact that compressible sources are predictable (and vise versa), and showed that on-line algorithms can improve their performance by prediction. Actual page access sequences are in fact somewhat compressible, so their predictive methods can be of benefit. This paper investigates the interesting idea of decreasing computation by using learning in the opposite way, namely to determine the difficulty of prediction. That is, we will approximately learn the input distribution, and then improve the performance of the computation when the input is not too predictable, rather than the reverse. To our knowledge, this is first case of a computational prob...
Conference Paper
Full-text available
A new sorting algorithm is presented. Its running time is O(n(1+log(F/n)) where F=|{(i,j); iij}| is the total number of inversions in the input sequence xn xn–1 xn–2 ... x2 x1. In other words, presorted sequences are sorted quickly, and completely unsorted sequences are sorted in O(n log n) steps. Note that F2/2 always. Furthermore, the constant of proportionality is fairly small and hence the sorting method is competitive with existing methods.
Article
Encroaching lists are a generalization of monotone sequences in permutations. Since ordered permutations contain fewer encroaching lists than random ones, the number of such listsm provides a measure of presortedness with advantages over others in the literature. Experimental and analytic results are presented to cast light on the properties of encroaching lists. Also, we describe a new sorting algorithm,melsort, with complexityO(nlogm). Thus it is linear for well ordered sets and reduces to mergesort andO(nlogn) in the worst case.


text:
## Algebra 1

The family must drive at least $7.\overline{27}$ hours per day.
Let h be the number of hours driven. Given an average speed of 55 miles per hour, the number of miles driven is 55h. If the goal is to drive at least 400 miles per day, the number of miles driven must be greater than or equal to 400. $55h\geq400\longrightarrow$ divide both sides by 55 $55h\div55\geq400\div55\longrightarrow$ divide $h\geq7.\overline{27}$