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# Delve AP Physics C Quiz 3

The exact copy of the test used in class is available for reference; however, the original had multiple errors that resulted in questions 4, 5, 7, 11, and 26 having no valid listed answers. Below, these questions are corrected so that they have a valid answer.

## Multiple Choice

1. A car has a constant acceleration of $$+10 m/s^2$$. It has zero initial velocity with respect to the road. You are moving along with a constant velocity of $$-5 m/s$$ with respect to the road. How far does the car travel in 3 seconds in the reference frame of the road?
1. $$30 m$$
2. $$45 m$$
3. $$55 m$$
4. $$60 m$$
5. $$65 m$$
2. How far does the same car travel in 3 seconds in your reference frame?
1. $$30 m$$
2. $$45 m$$
3. $$55 m$$
4. $$60 m$$
5. $$65 m$$
3. Which of the following is not a vector quantity?
1. Force
2. Velocity
3. Acceleration
4. Energy
5. Momentum
4. A projectile is launched from the ground at an angle of 45 degrees from the horizontal with an initial velocity $$6 m/s$$. What is the maximum height in meters achieved by the projectile?
1. $$0.81 m$$
2. $$0.92 m$$
3. $$1.17 m$$
4. $$1.33 m$$
5. $$1.59 m$$
5. How far from the launch point of the projectile does it hit the ground, in meters?
1. $$2.95 m$$
2. $$3.67 m$$
3. $$4.37 m$$
4. $$4.87 m$$
5. $$5.32 m$$
6. A particle's position is given by the equation $$x(t)=t^3 + 3t^2 + 2t + 4$$. What is the particle's velocity at $$t = 5 s$$?
1. $$214 m/s$$
2. $$42 m/s$$
3. $$107 m/s$$
4. $$92 m/s$$
5. $$36 m/s$$
7. Suppose this particle (from #6) has a mass of 0.2 kg. Which of the following equations gives the net force on the particle as a function of time?
1. $$1.2t + 1.2$$
2. $$30t + 30$$
3. $$3t^2 + 6t + 2$$
4. $$15t^2 + 30t + 10$$
5. $$0.6t^2 + 1.2t + 0.4$$
8. Two blocks, one of mass $$m$$ and one of mass $$M$$, are attached together by a thin rope on a frictionless surface. The block of mass $$m$$ is pulled away from the other block by a force $$F$$. What is the tension in the rope attaching the blocks?
1. $$F \frac{m}{M + m}$$
2. $$F \frac{M + m}{M}$$
3. $$F \frac{M + m}{m}$$
4. $$F \frac{M}{M + m}$$
5. $$F$$
9. A particle moves in a circle with constant speed. Which of the following must be true?
1. The net force on the particle is zero
2. The only force acting on the particle is a centripetal force
3. The particle's momentum is constant
4. There is a net force on the particle radially inward
5. The particle's acceleration is zero
10. A ball of mass m is dropped from a tall tower on earth and experiences a velocity dependent friction force given by $$F = -bv$$, where b is a constant. What is the terminal speed of the ball?
1. $$mg/b$$
2. $$2mg/b$$
3. $$b/mg$$
4. $$2b/mg$$
5. 0
11. An object is constructed by rigidly fixing together two hoops, each of mass $$m$$ and radius $$R$$. The hoops are joined together at a point on their circumferences to make an "8" shape. What is the moment of inertia of this body about the center of one of the hoops? (Recall that the moment of inertia of a single hoop about its center is given by $$MR^2$$.)
1. $$2mR^2$$
2. $$3mR^2$$
3. $$4mR^2$$
4. $$5mR^2$$
5. $$6mR^2$$
12. At some instant in time, the net torque on an object is nonzero. Which of the following must be true?
1. The net force on the object is nonzero
2. The object's angular momentum is changing
3. The object's linear momentum is changing
4. The object is undergoing uniform circular motion
5. None of the above
13. A body is initially moving away from you at a speed of $$5 m/s$$. Suddenly, the body explodes into two pieces of equal mass. One of the pieces returns toward you at a speed of $$5 m/s$$. Which of the following describes the motion of the other body?
1. Toward you at $$5 m/s$$
2. At rest with respect to you
3. Away from you at $$5 m/s$$
4. Away from you at $$10 m/s$$
5. Away from you at $$15 m/s$$
14. In your reference frame, a cart containing sand is traveling forward with some initial speed. A container at rest with respect to you begins dumping more sand into the cart from above. How will the cart's speed as measured by you change with time?
1. The cart's speed will increase
2. The cart's speed will not change
3. The cart's speed will decrease
4. The cart's speed will initially decrease, then increase
5. The cart's speed will initially increase, then decrease
15. Now suppose the container dumping sand into the cart is moving at constant velocity in your reference frame but initially at rest with respect to the cart. How will the cart's speed as measured by you change with time?
1. The cart's speed will increase
2. The cart's speed will not change
3. The cart's speed will decrease
4. The cart's speed will initially decrease, then increase
5. The cart's speed will initially increase, then decrease
16. Kepler's second law states that the line from a star to the planet orbiting it sweeps out equal areas in equal time intervals. This is equivalent to which of the following principles?
1. Conservation of energy
2. Conservation of linear momentum
3. Conservation of angular momentum
4. Conservation of mass
5. None of the above
17. A particle of mass $$m$$ sits at $$x = 1$$, a particle of mass $$2m$$ sits at $$x = 2$$, and a particle of mass $$3m$$ sits at $$x = 3$$. At what value of $$x$$ does the center of mass of this 3-particle system lie?
1. $$2$$
2. $$7/3$$
3. $$8/3$$
4. $$3$$
5. $$2/3$$
18. A solid cylindrical spool of thread of mass m and radius R, initially at rest, is fixed in place by a rod along its center axis. You pull on the thread with a constant tension T. What is the angular speed of the thread at time t after you start pulling?
1. $$\frac{2T t}{m R}$$
2. $$\frac{T t}{m R}$$
3. $$\frac{T}{m R}$$
4. $$\frac{2 m R}{t T}$$
5. $$\frac{m R t}{2 T}$$
19. A set of cubes may be attached end to end to form a rigid rectangular prism. What is the maximum number of cubes that may be stacked vertically such that the stack will not fall over when placed on a 30 degree incline?
1. 0
2. 1
3. 2
4. 3
5. 4
20. How many of these cubes may be stacked vertically such that the stack will not fall over when placed on a 60 degree incline?
1. 0
2. 1
3. 2
4. 3
5. 4
21. The potential energy of an object as a function of its position $$x$$ is given by $$U(x) = 2x^2$$. What is the force on this object as a function of $$x$$?
1. $$-4x$$
2. $$-2x$$
3. $$0$$
4. $$2x$$
5. $$4x$$
22. Suppose this object has mass $$4 kg$$ is released from rest at $$x = 2$$. What will be the period of oscillation of the object about its equilibrium point?
1. $$6.28 s$$
2. $$4.40 s$$
3. $$3.14 s$$
4. $$2.20 s$$
5. $$1.17 s$$
23. Which of the following is not a conservative force?
1. Air friction
2. Gravity
3. Spring force
4. a, b, and c are all conservative
5. a, b, and c are all non-conservative
24. A block of mass m is attached to a spring with spring constant $$k$$. The spring is stretched to a distance $$A$$ from equilibrium and then released. What is the maximum speed achieved by the block?
1. $$A \sqrt{k /m}$$
2. $$A \sqrt{m / k}$$
3. $$0.5A^2 (k / m)$$
4. $$A^2 (k / m)$$
5. None of the above
25. A satellite of mass $$m$$ orbits a planet of mass $$M$$ in uniform circular motion at a radius $$R$$ from the center of the planet. What is the kinetic energy of the satellite?
1. $$−G M m / R$$
2. $$G M m / R$$
3. $$-G M m / 2 R$$
4. $$G M m / 2 R$$
5. $$−G M m / R^2$$
26. What is the orbital period of the satellite?
1. $$2\pi \sqrt{G M / R^3}$$
2. $$2\pi \sqrt{R^3 / G M}$$
3. $$\pi \sqrt{R^3 / G M}$$
4. $$2\pi \sqrt{R^3 / G (M + m)}$$
5. $$\pi \sqrt{R^3 / G (M + m)}$$
27. A car of mass $$2m$$ traveling with speed $$v$$ collides completely inelastically with another car of mass $$m$$. How much kinetic energy is lost in this collision?
1. $$\frac16 m v^2$$
2. $$\frac13 m v^2$$
3. $$\frac12 m v^2$$
4. $$\frac23 m v^2$$
5. $$\frac56 m v^2$$
28. Which of the following is not a true statement about perfectly elastic collisions?
1. Momentum is conserved
2. Kinetic energy is conserved
3. They are symmetric with respect to time in the center of mass frame
4. In every reference frame, at least one body in the collision reverses direction
5. All of the above are true statements
29. A wheel of moment of inertia $$I$$ and mass $$m$$ rolls without slipping down a 30 degree incline. If the wheel starts from rest, what is the speed of its center of mass after rolling a distance $$d$$ along the incline?
1. $$\sqrt{g d}$$
2. $$\sqrt{2 g d}$$
3. $$\sqrt{m g d R^2 / I}$$
4. $$\sqrt{m g d R^2 /2I}$$
5. $$\sqrt{m g d / (m + \frac{I}{R^2})}$$
30. A planet has mass $$M$$ and radius $$R$$. What is the minimum speed required for a body of mass $$m$$ on the planet's surface to permanently escape?
1. $$\sqrt{G M / R}$$
2. $$\sqrt{2 G M / R}$$
3. $$\sqrt{G M / 2 R}$$
4. $$\sqrt{G M m / R}$$
5. $$\sqrt{2 G M m / R}$$

## Solutions

###### Warning

If you didn't happen to take the test in class, it is suggested that you do the test yourself. Use the standard timings: 45 minutes for the multiple choice section and 45 minutes for the free response.


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# Prepare for University - Pure Mathematics

##### Stage: 5 Challenge Level:

Here we collect 10 essential pure mathematics problems to get you thinking before you embark on your degree. They will be very useful to anyone intending to study mathematics at university: they will give you a good mathematical grounding in some of the pure, and possibly unfamiliar, topics likely to arise in your degree course and refine your problem solving skills. You will also find the applied mathematics preparation useful and may be surprised what constitutes applied mathematics at university!

Remember, these problems are designed to make you think and there is not necessarily a 'right' way to do them. Approach them in a thoughtful way; they are hopefully both interesting and stimulating. What questions do they raise in your mind? Where do these questions lead you? Take them to a level that feels comfortable for you.

Finally, once you have done the problems, study the solutions. These will give you additional insights into the problems and the underlying mathematics.

 Proof sorter Get started by reconstructing this classic proof of the irrationality of $\sqrt{2}$, which will be found in all undergraduate courses of mathematics. Mind your Ps and Qs Refine your understanding of logical implication and the all-important $\Rightarrow$ and $\Leftrightarrow$ symbols. Modular fractions Find out about multiplicative inverses in modular arithmetic. Ford Circles Give yourself an algebraic workout and discover the beauty of the Farey sequence. The clue is in the question Practise constructing a complex proof using the properties of a given system. Squareness Explore some interesting relations and their graphs. Complex partial fractions See how the power of algebra is opened up with the help of complex numbers. What is a group Groups are fundamental: get started with the basics here. Cube net Get started with graph theory and some combinatorics. Transformations for 10 Explore how matrices are used to transform vectors in this critical foundation to the mathematics of linear maps.

The following articles, interspersed with small problems for you to try will be interesting and useful:

An introduction to complex numbers

Introduction to Number Theory

Modular Arithmetic

If you have any feedback, please let us know.

format: plain


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# Synopsis: Unconventional pairs

A crystal lacking inversion symmetry shows signatures of unconventional superconducting pairing.

In superconductors, the appearance of dissipationless current is related to the formation of electron pairs with opposite spin and momentum. The symmetry of these pairs, which is constrained by the symmetries of the underlying crystal structure, defines important aspects of the superconducting state. So what happens to superconductivity when electron pairing occurs in a crystal structure that has no center of inversion?

This interesting question has been investigated in detail theoretically, and it was realized that in such cases the superconducting pairing is unconventional. In conventional (centrosymmetric) superconductors there can only be either spin-singlet or spin-triplet electron pairing, but in the absence of space-inversion symmetry the two can mix by the action of spin-orbit interaction (a relativistic effect), leading to unusual superconducting behavior.

This theoretical prediction has been tested experimentally in two independent articles that appear in Physical Review B. Ernst Bauer and collaborators from the Vienna University of Technology, Austria, with collaborators from China and Japan in one group, and Amar Karki and collaborators from Louisiana State University, US, with collaborators from Iowa State University, US, in the other, successfully grow and characterize ${\text{Mo}}_{3}{\text{Al}}_{2}\text{C}$. This material crystallizes in a noncentrosymmetric structure and undergoes a superconducting transition at ${T}_{c}\sim 9\phantom{\rule{0.333em}{0ex}}\text{K}$. Both groups observe signs of unconventional pairing, hinting at a strong connection between noncentrosymmetry and unconventional superconductivity. – Athanasios Chantis

### Announcements

More Announcements »

## Subject Areas

Superconductivity

## Previous Synopsis

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Quantum Information

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### Synopsis: Superconductivity Model Misses Its Target

Researchers have added dopant atoms to a quantum spin liquid in an effort to make it superconduct, but the material upended theory by remaining an insulator. Read More »

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### Focus: Nobel Prize—Topological Phases of Matter

The 2016 Nobel Prize in Physics was awarded to theoretical physicists whose work established the role of topology in understanding exotic forms of matter. Read More »

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### Focus: Detecting Photons With a Thermometer

A new technique detects as few as 200 microwave photons at a time by the heat they supply to an electrical circuit. Read More »


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# Thread: I can't find the root(s) of this equation (indices)

1. ## I can't find the root(s) of this equation (indices)

Here are my workings solve the equation $\displaystyle 2^{2x-1} =16 +2^{x+1}$ :

2. Dear PythagorasNeophyte,

Your quadratic equation is incorrect. It should be, $\displaystyle y^2-4y-32=0~where~y=2^x$.

3. Your error was in going from

$\displaystyle 2^x2^x2^{-1}=2^4+(2)2^x$ to $\displaystyle 2^x2^x=2^5+(4)2^x$

You inadvertently switched the addition and multiplication symbols on the right-hand side.

You could also try

$\displaystyle 2^{2x-1}-2^{x+1}=2^4$

$\displaystyle 2^{2x}-2^{x+2}=2^5$

$\displaystyle 2^x\left[2^x-4\right]=32$

The only two positive numbers that differ by 4 and whose product is 32 are 8 and 4 so by inspection $\displaystyle 2^x=8$

4. Hello, PythagorasNeophyte!

Sheesh . . . you're at this level of algebra
. . and you're still using $\displaystyle \times$ for multiplication?

$\displaystyle 2^{2x-1} \:=\:16 +2^{x+1}$

We have: .$\displaystyle 2^{2x-1} - 2^{x+1} - 16 \:=\:0$

. . . . . $\displaystyle 2^{2x}\cdot2^{-1} - 2^x\cdot 2 - 16 \:=\:0$

. . . . . . . $\displaystyle \frac{1}{2}\!\cdot\!2^{2x} - 2\cdot2^x - 16 \:=\:0$

Multiply by 2: .$\displaystyle 2^{2x} - 4\cdot2^x - 32 \:=\:0$

Let $\displaystyle y = 2^x\!:\;\;y^2 - 4y - 32 \:=\:0\quad\Rightarrow\quad (y + 4)(y-8) \:=\:0 \quad\Rightarrow\quad y \:=\:-4,\:8$

Back-substitute: .$\displaystyle \begin{Bmatrix} 2^x \:=\:\text{-}4 & \Rightarrow & \text{no real roots} \\ 2^x \:=\:8 & \Rightarrow & \boxed{x \:=\:3} \end{Bmatrix}$

5. If you want a fancy solution

$\displaystyle 2^{2x-1}=2^4+2^{x+1}$

divide both sides by 2 to obtain $\displaystyle 2^x$ on the right

$\displaystyle 2^{2x-2}=2^3+2^x$

$\displaystyle 2^{2x-2}-2^3=2^x$

Divide both sides by $\displaystyle 2^x$

$\displaystyle 2^{x-2}-2^{3-x}=1$

The only powers of 2 whose index moduli and values differ by 1 are $\displaystyle 2^0=1$ and $\displaystyle 2^1=2$

$\displaystyle \Rightarrow\ x=3$


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# Chapter 24 - The Chemistry of Life - 24 Assessment - Page 872: 131

a) $C_3H_6O_2$ b) $C_7H_6O_3$

#### Work Step by Step

a) $C_3H_6O_2$ b) $C_7H_6O_3$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


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# Definition:Tensor Product of Abelian Groups

Jump to navigation Jump to search

## Definition

Let $A$ and $B$ be abelian groups.

### Definition 1: by universal property

Their tensor product is a pair $(A \otimes B, \theta)$ where:

such that, for every pair $(C, \omega)$ where:

there exists a unique group homomorphism $g : A \otimes B \to C$ with $\omega = g \circ \theta$.

### Definition 2: construction

Their tensor product is the pair $(A \otimes B, \theta)$ where:

## Tensor product of family of abelian groups

Let $I$ be an indexing set.

Let $\family {G_i}_{i \mathop \in I}$ be a family of abelian groups.

Let $G = \displaystyle \prod_{i \mathop \in I} G_i$ be their direct product.

### Definition 1: by universal property

Their tensor product is a pair $\left( \displaystyle \bigotimes_{i \in I} G_i, \theta \right)$ where:

such that, for every pair $(C, \omega)$ where:

there exists a unique group homomorphism $g : \displaystyle \bigotimes_{i \in I} G_i \to C$ with $\omega = g \circ \theta$.

$\xymatrix{ G \ar[d]_\theta \ar[r]^\omega & C\\ \displaystyle \bigotimes_{i \in I} G_i \[email protected]{.>}[ru]_g }$

### Definition 2: construction

Their tensor product is the pair:

$\tuple {\displaystyle \bigotimes_{i \mathop \in I} G_i, \theta}$

where:

• $\displaystyle \bigotimes_{i \in I} G_i$ is the quotient of the free abelian group $\Z \sqbrk G$ on $G$, by the subgroup generated by the elements of the form $\tuple {x + y, \family {z_i}_{i \mathop \ne j} } - \tuple {x, \family {z_i}_{i \mathop \ne j} } - \tuple {y, \family {z_i}_{i \mathop \ne j} }$
for $j \in I$, $x, y \in G_j$, $\family {z_i}_{i \mathop \ne j} \in \displaystyle \prod_{i \mathop \ne j} G_i$, where we denote $\tuple {x, \family {z_i}_{i \mathop \ne j} }$ for:
• $\theta : G \to \displaystyle \bigotimes_{i \mathop \in I} G_i$ is the composition of the canonical mapping $G \to \Z \sqbrk G$ with the quotient group epimorphism $\Z \sqbrk G \to \displaystyle \bigotimes_{i \mathop \in I} G_i$:
$G \hookrightarrow \Z \sqbrk G \twoheadrightarrow \displaystyle \bigotimes_{i \mathop \in I} G_i$


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# Climate Escapism and the Quest for Tech to Fix it

This February was quite exciting for all space enthusiasts, as three spacecraft were arriving at Mars: Hope (Emirates Mars Mission) and Tianwen-1 (China’s Mars Mission) entered Martian orbit to investigate the Martian atmosphere. And last week, the NASA rover ‘Perseverance’ landed on Mars on its ‘Mars 2020’ mission to look for signs of ancient microbial life or even bring probes back to earth.

These are pretty exciting times, given that interest and investments in space missions were significantly decreased after the Cold War and that to date we haven’t managed (or didn’t want to?) establish a presence in space beside the ISS; let alone that we have built a moon village in the last decade. So it’s great to see this interest being revitalized by the ongoing Mars missions, and SpaceX plans to start colonizing Mars by the middle of this decade.

At the same time, the climate movement Fridays for Future (FFF) released a satirical tourism ad last week, promoting Mars as a perfect travel destination: no war, no pollution, and no pandemics. An untainted planet and a new world. So, who wouldn’t wanna go there? You just need to get used to living in a space station.

Yet, this is pure nonsense. And that was the whole point of the ad. As FFF pointed out to Euronews, 99 % of humanity won’t ever have the chance to travel to Mars. Thus, from the activist’s viewpoint, governments would make better use of money fighting the climate crisis rather than spending billions of dollars on space exploration.

And that is exactly where the ad fails to get its message through: Promoting the idea of traveling to Mars is probably not the most effective way to raise awareness for the climate crisis. Too much escapism, too little focus on how to tackle the actual problem.

Also, it misses the point, as astrobiological research does not infer escapism, neither does cutting down on space exploration provide a good starting point to mobilize additional forces to take climate action. (As it was pointed out before, the U.S. government allocated about \$700 billion to defense in 2019, but only \$21.5 billion to NASA’s science and human exploration programs. The FFF critique seems misplaced at this point*.)

So I don’t believe that the thinking, either we save Earth or travel to Mars, will get us very far. Space exploration has the potential to trigger the general public’s interest in science and technology. It will lead to advancement, push technology and society forward, and will even foster a technological solution to reduce or better capture carbon emissions.

This is judged by the progress in the last century. The Cold War, and in particular the Sputnik crisis, led to a massive surge in space defense projects and innovations, a greater focus on STEM education, and ultimately, massive investments in the chip industry that gave birth to Silicon Valley.

## The Quest for Tech

Today, more and more people get aware of the climate crisis. But the Sputnik event is missing.

Despite the best efforts by Greta and FFF to activate millions of people around the world, so far, political leaders have failed to take adequate action globally. The last UN climate conference, COP25, set a bad example. And while the data on the ongoing climate change is absolutely clear, it is absolutely unclear how to prevent this change given current politics and our state-of-the-art technologies.

Where is the Sputnik event that drives massive efforts in planting trees and recultivating grounds, sky-rocketing carbon taxes, and tighter regulation (even prohibition!) of carbon-intensive activities?

Reducing emissions immediately is still our best bet to mitigate the effects of global warming, and there are many things one can do on an individual level. Yet, the most effective thing of these is activism to urge decision-makers to take climate action. Or to go for moonshot projects.

In the spirit of ‘Doing Good Better,’ following a high risk – high potential outcome path is also a fairly good option: Start a (social) business like Ecosia. Start a non-profit like ClimateScience. Or research and develop technologies e.g. for carbon capture. These paths may not be for everyone, and they pose the risk of failure. But potentially, they may have a huge (i.e. scalable) impact.

Currently, the situation with technological advancement is similar to the agricultural revolution.

As Yuval Noah Harari nicely pointed out in his book Sapiens, agriculture was a trap. Farmers worked longer hours and had worse living conditions than hunter-gatherers. But, since the population exploded, there was no way of going back as hunting and gathering could not feed such a large population. And actually, in the very long run, this turned out to be much better than hunter-gatherer life: without farming, we would not have arrived at our present standard of living.

Similarly, there is no way of going back to a society without technology. In the last century, technology has been the driver of increased living standards worldwide but also provoked environmental pollution and global warming. Given the inertia of politics, the unwillingness of people in ‘developed countries’ to cut down on their standard of living, and the current state of the climate crisis, developing technology further remains crucial. Even if the illusion of a simple technical solution to fix the climate may prevent leaders from taking effective action.

Recently, Elon Musk has announced to donate \$100 billion toward a competition for the most effective carbon capture technology. Trees and other plants already do this, but can it be done technologically more efficiently? Probably. Let’s see which solutions the award will bring up.

## Climate Escapism

During the 2020 Australian bushfire season, vast land areas got burned, and many people had to move, who were then deemed to be the first climate refugees. This is pretty ironic since Australia is also one of these ‘developed countries’ with serious carbon emissions, especially from the coal industry.

In the light of the FFF Mars tourism ad, another form of flight enters the discussion: escapism. Given the ambitions of SpaceX and others, interplanetary space travel will get feasible this or the upcoming decade, which raises several practical and ethical questions: Should ‘the rich’ be allowed to escape to a space station or even to Mars in case of a global catastrophe on Earth?

It reminds me of the sci-fi trilogy ‘Remembrance of Earth’s Past‘ by Cixin Liu, where humanity faces an upcoming invasion of a superior alien species, the Trisolarans. As traces in the intergalactic medium manifest the evidence that a fleet of Trisolarans is on its way to Earth, this constitutes the Sputnik moment that sparks off crisis and depression worldwide.

But then humanity switches into the hyperdrive mode: New inventions and massive investments lead to the construction of space elevators and starships. Governments around the world join forces and envision the ‘Wallface project’ as a global defense strategy. And a global ban on escapism from Earth is rolled out. There it is again, the discussion on escapism.

What would you do today if you would know that a fleet of Trisolaran battleships was to arrive at Earth – in 300 years. You would never encounter Trisolarans yourself. Neither would your children do. But you would know with certainty that at some point, they will arrive and destroy Earth. (Or at least enslave humankind.)

The climate crisis is similar in the sense that it doesn’t really matter whether a huge portion of humankind will get wiped out in 300 years by aliens or natural disasters. But unlike the case of alien invasion, different countries have different interests concerning the climate crisis. Not only the oil-producing countries. Some countries like Russia might even get more hospitable and less frosty and benefit by a few degrees.

The impact of the changing global climate is creeping up, but it is not clear which catastrophe happens next. The Sputnik event is yet to come.

## TL;DR

We should treat the climate crisis with the same seriousness as an upcoming alien invasion. We need to prepare for it, and rather than disregard space exploration as “escapism,” scientists and activists should work closely together on this issue.

*Disclaimer: The climate crisis is a real issue, and FFF is doing overall an amazing job of bringing this issue to people’s attention, which I absolutely support. I just had the impression that this particular clip was not a particularly good PR move.

## The Planet has a Courier

A weekly newsletter, published every Sunday at 8 PM CET, keeping you updated on the latest stuff on The Planet and beyond. Feel free to subscribe!


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Online Calculators

%
%
%

You need 92.00% on the final exam

to get 85.00% in the class.

## Calculator Use

Find what grade you need on the final exam to reach a target grade for the course.

If you know your current grade and the weight of the final exam, you can calculate the grade you need on the final to reach your target course grade.

This calculator uses the formula:

$$F = \dfrac{G - ((1 - w) \times C)}{w}$$

Where:

• F = Final exam grade
• G = Grade you want for the class
• w = Weight of the final exam, divided by 100 (put weight in decimal form vs. percentage form)

Sometimes you'll get your final exam grade but the instructor hasn't yet posted final class grades. You can use this calculator to find your final class grade once you know your final exam score. Use the formula:

$$G = Fw + ((1 - w) \times C)$$

Where:

• F = Final exam grade
• w = Weight of the final exam, divided by 100 (put weight in decimal form vs. percentage form)

### Example Final Exam Grade Calculation

My grade in Statistics class is 85%. I want to get at least an A- or 90% in the class for the term. What score do I need on the final exam if it is worth 40% of my grade?

Using the Final Exam Grade formula above, I want a 90 in the class and I currently have an 85. The final is worth 40% of the term grade.

First, convert the weight of the final exam from percent to decimal: 40 ÷ 100 = 0.40

$$F = \dfrac{90 - ((1 - 0.4) \times 85)}{0.4}$$
$$F = \dfrac{90 - ((0.6) \times 85)}{0.4}$$
$$F = \dfrac{90 - 51}{0.4}$$
$$F = \dfrac{39}{0.4}$$
$$F = 97.5$$

So if I have an 85 in the class, I want a 90, and the final exam is worth 40%, I need a 97.5 to get a 90 in the class.

### Example Final Course Grade Calculation

Going into finals my grade in Economics was 91%. My final exam score was 88.6% and it was worth 15% of my grade for the course. What is my final grade in the course?

Using the Final Class Grade formula above, F = 88.6, w = 15, and C = 91.

First, convert the weight of the final exam from percent to decimal: 15 ÷ 100 = 0.15

$$G = 88.6 \times 0.15 + ((1 - 0.15) \times 91)$$
$$G = 88.6 \times 0.15 + (0.85 \times 91)$$
$$G = 88.6 \times 0.15 + 77.35$$
$$G = 13.29 + 77.35$$
$$G = 90.64$$

So I went into the final with a class grade of 91. I got 88.6 on the final which was worth 15% of the course grade. My final grade in the class was 90.64.

Cite this content, page or calculator as:

Furey, Edward "Final Grade Calculator" at https://www.calculatorsoup.com/calculators/statistics/final-grade-calculator.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators


text:
# Friday, January 23, 2015¶

## Authentiation¶

A test case in Lino Così failed: Refusing permission to an anonymous request. A late side-effect of #70. This was a bit tricky to solve. The problem was about how to decide whether django.contrib.sessions needs to be installed. This decision cannot be made by get_installed_apps since it depends on user_model, which in turn depends on the result of get_installed_apps.

Added new method SITE.get_auth_method, mainly to make things more clear.

Another thing which I understood: UserProfiles, UserGroups and UserLevels are defined in lino.modlib.users.choicelists even though they used by the core also when lino.modlib.users is not installed. Why don’t I put them somewhere below lino.core? Answer: because they are choicelists, and as such they need to have an app_label. So I generalized the setup_user_profiles trick from Lino Welfare to all Lino applications.

Continued on #47 : added a new field needed to lino_welfare.modlib.uploads.models.Upload. Wrote a new demo fixture lino_welfare.modlib.uploads.fixtures.demo2.
lino_welfare.modlib.uploads.models.Upload is now a lino.mixins.DatePeriod instead of manually adding two date :class:fields for the validity period. Which means that the database :class:fields valid_from and valid_until must get migrated to start_date and end_date.
• In lino.core.layouts I renamed ListLayout to ColumnsLayout.
• And I moved the ad, dd and rt modules into a separate package lino.api. For backwards compatibility, the old names will still work for some time


text:
# How do chlorofluorocarbons destroy ozone?

May 14, 2018

UV radiation in the atmosphere causes an initial bond cleavage that creates free radical centres.....

#### Explanation:

UV induced cleavage of the C-Cl bond in the chlorofluorocarbon molecule forms a free radical centre in the molecule plus a chlorine atom. The chlorine atom reacts with ozone to form oxygen and Cl-O.

Cl + O_3→ClO + O_2

Cl-O also is able to react with ozone, thereby removing another oxygen atom plus a chlorine atom.....

ClO + O.→Cl + O_2

And the oxygen atom can then react with ozone to form more oxygen (molecules).

O_3 + O.→ 2O_2

So not only can CFC's in the atmosphere react with and depelet ozone, but they react so as to cause the formation of other species that also react with and deplete ozone.

As a result, a single CFC molecule can cause the breakdown of thousands of ozone molecules.


text:
# Electrons in a quantum well

1. Dec 23, 2015

### aaaa202

I am making a finite elements simulation of electrons in the bottom of the conduction band of some material. To do so I assume that the electrons move in the bottom of a flat well with their original mass replaced by the effective mass. The idea is to calculate wave functions for electrons living in the bottom of a heterostructure well, as for example in InGaAs, which has a potential profile as shown on the attached picture.
However for the simulation I have some problems with the "discontinuity" of the kinetic energy operator across the InAs-GaAs interface. The kinetic energy is a matrix given by:
2/2m_eff * 1/Δx2 *A
, where A is a matrix defined by:
A(i,i)=-2
A(i+1,i)=1
A(i,i+1)=1
,i.e. the standard form for the second derivative in the finite element method.
However across the interface the effective mass changes from the effective mass for InAs to the effective mass for InAs. How can I write up the matrix for the kinetic energy such that it "stitches" the wave functions from the two segments correctly together?
If I did it analytically I would have some boundary conditions to use, but I need to do this numerically since I am going to develop it further in a way, where a numerical approach is crucial.

#### Attached Files:

• ###### InGaAs.png
File size:
5 KB
Views:
43
2. Dec 26, 2015

### theodoros.mihos

On similar discontinuity with charge densities I use $tanh$ approximation for the conduct area.


text:
# SemanticImport returning different data versus Import [duplicate]

I'm analyzing data for Covid-19 and found an interesting website: "https://covidtracking.com/api/states/daily.csv". My problem: using SemanticImport, it seems stuck on the data that I read yesterday even though the site is returning data for today.

Running on MMA v12.1, OSX 10.14.6.

The code is simple:

Import["https://covidtracking.com/api/states/daily.csv"]
(* versus *)
SemanticImport["https://covidtracking.com/api/states/daily.csv"]

Import returns:

(*
{{"date", "state", "positive", "negative", "pending", "hospitalized",
"death", "total", "dateChecked", "totalTestResults",
"deathIncrease", "hospitalizedIncrease", "negativeIncrease",
"positiveIncrease", "totalTestResultsIncrease"}, {20200326, "AK",
59, 1801, "", 3, 1, 1860, "2020-03-26T20:00:00Z", 1860, 0, 2, 152,
17, 169}, {20200326, "AL", 506, 3593, "", "", 1, 4099,
"2020-03-26T20:00:00Z", 4099, 1, 0, 1064, 223, 1287}, {20200326,
"AR", 335, 1504, 0, 41, 3, 1839, "2020-03-26T20:00:00Z", 1839, 1,
19, 67, 55, 122},...}
*)

indicating that there is data available for today (2020-03-26) whereas SemanticImport returns this:

Why isn't SemanticImport starting the data from 20200326 as shown by Import? I have quit out of my current session (closed Mathematica) and restarted thinking that some sort of caching is occurring but that had no effect on the result.

If I cannot figure out why these are different, I'll just have to use Import rather than using SemanticImport.

I'm using the returned data to evaluate the progress of testing for Covid-19 in graphs such as this:

• This is essentially a duplicate. I posted a similar question 8 days ago. I submitted a report to WRI. It's a confirmed bug. – david Mar 27 '20 at 1:31
• I didn't realize it was a dup - thanks for letting me know. Perhaps the code I posted in the answer will help you until they fix the bug. – Mark R Mar 27 '20 at 1:35
• This is a duplicate of SemanticImport vs Import differ on same CSV file? – Szabolcs Apr 23 '20 at 18:56
• It's a bug that several of us are affected by. Please contact Wolfram about it. That should help prioritize it. – Szabolcs Apr 23 '20 at 18:56

The following code does what SemanticImport isn't doing correctly:

ImportCSVToDataset[url_] := Block[
{
allData = Import[url, "CSV"],


text:
Freè points for All thank you

Question:

freè points for All thank you

Help with an answer. Confused as heck!

Help with an answer. Confused as heck!...

D. Psychological condition 2. What is the collective term used for the condition of people who develop stress reaction that negatively affect their physical and mental behaviour after suffering from a disaster? a. displaced population b emotional aftershock c. food scarcity d. health tisk disaster that causes a group of people forced to leave their

d. Psychological condition 2. What is the collective term used for the condition of people who develop stress reaction that negatively affect their physical and mental behaviour after suffering from a disaster? a. displaced population b emotional aftershock c. food scarcity d. health tisk disaster t...

If ƒ(x ) = x 2 + 1 and g(x ) = 3x + 1, find 2 · ƒ(4). A. 34 B. 18 C. 65

If ƒ(x ) = x 2 + 1 and g(x ) = 3x + 1, find 2 · ƒ(4). A. 34 B. 18 C. 65...

Solve 23 and 24 and 25

solve 23 and 24 and 25...

Someone can figure this out

Someone can figure this out...

How would you feel if you were faced with discrimination and problems from others. 3-5 sentences plzzzz

How would you feel if you were faced with discrimination and problems from others. 3-5 sentences plzzzz...

PLSSS HELP IF YOU TURLY KNOW THISS

PLSSS HELP IF YOU TURLY KNOW THISS...

Which is equivalent to 4(x - 1)? x- 4 4x-1 4x - 3 4x - 4

Which is equivalent to 4(x - 1)? x- 4 4x-1 4x - 3 4x - 4...

A quart of paint covers 80 square feet. how many quarts should you buy to paint the ramp with two coats(Assume you will not paint the bottom of the ramp.)

a quart of paint covers 80 square feet. how many quarts should you buy to paint the ramp with two coats(Assume you will not paint the bottom of the ramp.)...

How do i add and subtract fractions

how do i add and subtract fractions...

To be _____ is to be tolerant of cultural differences and to have knowledge of cultures, history, world market potential, and global economic, social, and political trends.

To be _____ is to be tolerant of cultural differences and to have knowledge of cultures, history, world market potential, and global economic, social, and political trends....

A tall tale is a story that is difficult to believe or greatly exaggerated. Does this story seem realistic, or does it seem more like a tall tale? Explain your reasoning. The Celebrated Jumping Frog of Calaveras County

A tall tale is a story that is difficult to believe or greatly exaggerated. Does this story seem realistic, or does it seem more like a tall tale? Explain your reasoning. The Celebrated Jumping Frog of Calaveras County...

4X -3 equals 17 solve for X

4X -3 equals 17 solve for X...

At Caesar's Palace Casino in Vegas, there were three poker players, Alice, Bernie and Craig. At the beginning of the night the amount of money each had was split in the ratio 7 : 6 : 5, with Alice starting with the most and Craig the least. At the end of the night, Alice was still ahead and Craig still last, but the money was divided according to the ratio 6 : 5 : 4. This meant that one of the players was up by \$12. What were the combined assets of the players at the beginning of the evening, in

At Caesar's Palace Casino in Vegas, there were three poker players, Alice, Bernie and Craig. At the beginning of the night the amount of money each had was split in the ratio 7 : 6 : 5, with Alice starting with the most and Craig the least. At the end of the night, Alice was still ahead and Craig st...

Find the area of a triangle with a base of 25 inches and a hieght of 30 inches

find the area of a triangle with a base of 25 inches and a hieght of 30 inches...

A house painter mixed 5 gal of blue paint with every 9 gal of yellow paint in order make green paint .which ratio blue paint to gallons of yellow will make that same shade of green paint? A. 30:54 B 6 :10 C 10:45 D 27:15

a house painter mixed 5 gal of blue paint with every 9 gal of yellow paint in order make green paint .which ratio blue paint to gallons of yellow will make that same shade of green paint? A. 30:54 B 6 :10 C 10:45 D 27:15...

Recently Tanya has been caught in heavy traffic when traveling to and from work. This situation has caused her to arrive to work late and arrive home at a much later time than normal. When she comes home, she slams the front door and tends to yell more at her children and husband over things that are rather insignificant. This behavior can BEST be explained by the: a) observational learning theory. b) cognitive dissonance theory. c) mere exposure effect. d) frustration-aggression principle.

Recently Tanya has been caught in heavy traffic when traveling to and from work. This situation has caused her to arrive to work late and arrive home at a much later time than normal. When she comes home, she slams the front door and tends to yell more at her children and husband over things that ar...

Losses caused by damage to your car by another person who is at fault in the accident are covered by

Losses caused by damage to your car by another person who is at fault in the accident are covered by...

-- 0.011985--


text:
# the shorstest cycle containing two given points

I am given a edge-weighted (multi)graph $$G$$ and two of its vertices, $$u, v\in V(G)$$. I want to find two edge-disjoint paths that connects $$u$$ and $$v$$ while minimizing the sum of the lengths of the paths.

what is the complexity of this problem ?

(If can reduce Hamiltonian Cycle to it if we ask for vertex-disjoint paths and allow negatives weights)

Anything known about approximation algorithms in general ? in planar graphs ?

(if we can cheat by an edge twice and paying it twice, then finding a shortest path gives a $$2$$-approximation.)

More generally, what if now I ask for $$k$$ edge-disjoints paths between from $$u$$ to $$v$$ ?

rq: this problem looks somehow related to subset TSP

• This is easily reducible to min-cost flow. – Chandra Chekuri Jan 23 at 14:33

The problem of finding the shortest simple cycle through two vertices in a weighted undirected graph can be solved in the same time as Dijkstra's algorithm for a single shortest path, by applying Suurballe's algorithm for finding disjoint $$s$$$$t$$ shortest paths in a directed graph.


text:
You are currently browsing the category archive for the ‘academia’ category.

Last year I wrote a blog post on being wrong. I also wrote a blog post about being wrong three years ago. It’s not fun to admit being wrong, but sometimes it’s necessary. I have to admit to being wrong again.

To place this admission in context I need to start with Mordell’s finite basis theorem, which has been on my mind this past week. The theorem, proved in 1922, states the rational points on an elliptic curve defined over the rational numbers form a finitely generated abelian group. There is quite a bit of math jargon in this statement that makes it seem somewhat esoteric, but it’s actually a beautiful, fundamental, and accessible result at the crossroads of number theory and algebraic geometry.

First, the phrase elliptic curve is just a fancy name for a polynomial equation of the form y² = x³ + ax + b (subject to some technical conditions). “Defined over the rationals” just means that and b are rational numbers. For example a=-36, b=0 or a=0, b=-26 would each produce an elliptic curve. A “rational point on the curve” refers to a solution to the equation whose coordinates are rational numbers. For example, if we’re looking at the case where a=0 and b=-26 then the elliptic curve is y² = x³ – 26 and one rational solution would be the point (35,-207). This solution also happens to be an integer solution; try to find some others! Elliptic curves are pretty and one can easily explore them in WolframAlpha. For example, the curve y² = x³ – 36x looks like this:

WolframAlpha does more than just provide a picture. It finds integer solutions to the equation. In this case just typing the equation for the elliptic curve into the WolframAlpha box produces:

One of the cool things about elliptic curves is that the points on them form the structure of an abelian group. That is to say, there is a way to “add” points on the curves. I’m not going to go through how this works here but there is a very good introduction to this connection between elliptic curves and groups in an exposition by Tanuj Nayak, an undergrad at Carnegie Mellon University.

Interestingly, even just the rational points on an elliptic curve form a group, and Mordell’s theorem says that for an elliptic curve defined over the rational numbers this group is finitely generated. That means that for such an elliptic curve one can describe all rational points on the curve as finite combinations of some finite set of points. In other words, we (humankind) has been interested in studying Diophantine equations since the time of Diophantus (3rd century). Trying to solve arbitrary polynomial equations is very difficult, so we restrict our attention to easier problems (elliptic curves). Working with integers is difficult, so we relax that requirement a bit and work with rational numbers. And here is a theorem that gives us hope, namely the hope that we can find all solutions to such problems because at least the description of the solutions can be finite.

The idea of looking for all solutions to a problem, and not just one solution, is fundamental to mathematics. I recently had the pleasure of attending a lesson for 1st and 2nd graders by Oleg Gleizer, an exceptional mathematician who takes time not only to teach children mathematics, but to develop mathematics (not arithmetic!) curriculum that is accessible to them. The first thing Oleg asks young children is what they see when looking at this picture:

Children are quick to find the answer and reply either “rabbit” or “duck”. But the lesson they learn is that the answer to his question is that there is no single answer! Saying “rabbit” or “duck” is not a complete answer. In mathematics we seek all solutions to a problem. From this point of view, WolframAlpha’s “integer solutions” section is not satisfactory (it omits x=6, y=0), but while in principle one might worry that one would have to search forever, Mordell’s finite basis theorem provides some peace of mind for an important class of questions in number theory. It also guides mathematicians: if interested in a specific elliptic curve, think about how to find the (finite) generators for the associated group. Now the proof of Mordell’s theorem, or its natural generalization, the Mordell-Weil theorem, is not simple and requires some knowledge of algebraic geometry, but the statement of Mordell’s theorem and its meaning can be explained to kids via simple examples.

I don’t recall exactly when I learned Mordell’s theorem but I think it was while preparing for my qualifying exam in graduate school, when I studied Silverman’s book on elliptic curves for the cryptography section on my qualifying exam- yes, this math is even related to some very powerful schemes for cryptography! But I do remember when a few years later a (mathematician) friend mentioned to me “the coolest paper ever”, a paper related to generalizations of Mordell’s theorem, the very theorem that I had studied for my exam. The paper was by two mathematicians, Steven Zucker and David Cox, and it was titled Intersection Number of Sections of Elliptic Surfaces. The paper described an algorithm for determining whether some sections form a basis for the Mordell-Weil group for certain elliptic surfaces. The content was not why my friend thought this paper was cool, and in fact I don’t think he ever read it. The excitement was because of the juxtaposition of author names. Apparently David Cox had realized that if he could coauthor a paper with his colleague Steven Zucker, they could publish a theorem, which when named after the authors, would produce a misogynistic and homophobic slur. Cox sought out Zucker for this purpose, and their mission was a “success”. Another mathematician, Charles Schwartz, wrote a paper in which he built on this “joke”. From his paper:

So now, in the mathematics literature, in an interesting part of number theory, you have the Cox-Zucker machine. Many mathematicians think this is hilarious. I thought this was hilarious. In fact, when I was younger I frequently boasted about this “joke”, and how cool mathematicians are for coming up with clever stuff like this.

I was wrong.

I first started to wonder about the Zucker and Cox stunt when a friend pointed out to me, after I had used the term C-S to demean someone, that I had just spouted a misogynistic and homophobic slur. I started to notice the use of the C-S phrase all around me and it made me increasingly uncomfortable. I stopped using it. I stopped thinking that the Zucker-Cox stunt was funny (while noticing the irony that the sexual innuendo they constructed was much more cited than their math), and I started to think about the implications of this sort of thing for my profession. How would one explain the Zucker-Cox result to kids? How would undergraduates write a term paper about it without sexual innuendo distracting from the math? How would one discuss the result, the actual math, with colleagues? What kind of environment emerges when misogynistic and homophobic language is not only tolerated in a field, but is a source of pride by the men who dominate it?

These questions have been on my mind this past week as I’ve considered the result of the NIPS conference naming deliberation. This conference was named in 1987 by founders who, as far as I understand, did not consider the sexual connotations (they dismissed the fact that the abbreviation is a racial slur since they considered it all but extinct). Regardless of original intentions I write this post to lend my voice to those who are insisting that the conference change its name. I do so for many reasons. I hear from many of my colleagues that they are deeply offended by the name. That is already reason enough. I do so because the phrase NIPS has been weaponized and is being used to demean and degrade women at one of the main annual machine learning conferences. I don’t make this claim lightly. Consider, for example, TITS 2017 (the (un)official sister event to NIPS). I’ve thought about this specific aggression a lot because in mathematics there is a mathematician by the name of Tits who has many important objects named after him (e.g. Tits buildings). So I have worked through the thought experiment of trying to understand why I think it’s wrong to name a conference NIPS but I’m fine talking about the mathematician Tits. I remember when I first learned of Tits buildings I was taken aback for a moment. But I learned to understand the name Tits as French and I pronounce it as such in my mind and with my voice when I use it. There is no problem there, nor is there a problem with many names that clash across cultures and languages. TITS 2017 is something completely different. It is a deliberate use of NIPS and TITS in a way that can and will make many women uncomfortable. As for NIPS itself perhaps there is a “solution” to interpreting the name that doesn’t involve a racial slur or sexual innuendo (Neural Information Processing Systems). Maybe some people see a rabbit. But others see a duck. All the “solutions” matter. The fact is many women are uncomfortable because instead of being respected as scientists, their bodies and looks have become a subtext for the science that is being discussed. This is a longstanding problem at NIPS (see e.g., Lenna). Furthermore, it’s not only women who are uncomfortable. I am uncomfortable with the NIPS name for the reasons I gave above, and I know many other men are as well. I’m not at ease at conferences where racial slurs and sexual innuendo are featured prominently, and if there are men who are (cf. NIPS poll data) then they should be ignored.

I think this is an extremely important issue not only for computer science, but for all of science. It’s about much more than a name of some conference. This is about recognizing centuries of discriminatory and exclusionary practices against women and minorities, and about eliminating such practices when they occur now rather than encouraging them. The NIPS conference must change their name. #protestNIPS

A few years ago I wrote a post arguing that it is time to end ordered authorship. However that time has not yet arrived, and it appears that it is unlikely to arrive anytime soon. In the meantime, if one is writing a paper with 10 authors, a choice for authorship ordering and equal contribution designation must be made from among the almost 2 billion possibilities (1857945600 to be exact). No wonder authorship arguments are commonplace! The purpose of this short post is to explain the number 1857945600.

At first glance the enumeration of authorship orderings seems to be straightforward, namely that in a paper with n authors there are n! ways to order the authors. However this solution fails to account for designation of authors as “equal contributors”. For example, in the four author paper Structural origin of slow diffusion in protein folding, the first two authors contributed equally, and separately from that, so did the last two (as articulated via a designation of “co-corresponding” authorship). Another such example is the paper PRDM/Blimp1 downregulates expression of germinal center genes LMO2 and HGAL. Equal contribution designations can be more complex. In the recent preprint Connect-seq to superimpose molecular on anatomical neural circuit maps the first and second authors contributed equally, as did the third and fourth (though the equal contributions of the first and second authors was distinct from that of the third and fourth). Sometimes there are also more than two authors who contributed equally. In SeqVis: Visualization of compositional heterogeneity in large alignments of nucleotides the first eight authors contributed equally. A study on “equal contribution” designation in biomedical papers found that this type of designation is becoming increasingly common and can be associated with nearly every position in the byline.

To account for “equal contribution” groupings, I make the assumption that a set of authors who contributed equally must be consecutive in the authorship ordering. This assumption is certainly reasonable in the biological sciences given that there are two gradients of “contribution” (one from the front and one from the end of the authorship list), and that contributions for those in the end gradient are fundamentally distinct from those in the front. An authorship designation for a paper with n authors therefore consists of two separate parts: the n! ways to order the authors, and then the $2^{n-1}$ ways of designating groups of equal contribution for consecutive authors. The latter enumeration is simple: designation of equal authorship is in one-to-one correspondence with placement of dividers in the n-1 gaps between the authors in the authorship list. In the extreme case of placement of no dividers the corresponding designation is that all authors contributed equally. Similarly, the placement of dividers between all consecutive pairs of authors corresponds to all contributions being distinct. Thus, the total number of authorship orderings/designations is given by $n! \cdot 2^{n-1}$. These numbers also enumerate the number of ways to lace a shoe. Other examples of objects whose enumeration results in these numbers are given in the Online Encyclopedia of Integer Sequences entry for this sequence (A002866). The first twenty numbers are:

1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280, 1857945600, 40874803200, 980995276800, 25505877196800, 714164561510400, 21424936845312000, 685597979049984000, 23310331287699456000, 839171926357180416000, 31888533201572855808000, 1275541328062914232320000.

In the case of a paper with 60 authors, the number of ways to order authors and designate equal contribution is much larger than the number of atoms in the universe. Good luck with your next consortium project!

Six years ago I received an email from a colleague in the mathematics department at UC Berkeley asking me whether he should participate in a study that involved “collecting DNA from the brightest minds in the fields of theoretical physics and mathematics.”  I later learned that the codename for the study was “Project Einstein“, an initiative of entrepreneur Jonathan Rothberg with the goal of finding the genetic basis for “math genius”. After replying to my colleague I received an inquiry from another professor in the department, and then another and another… All were clearly flattered that they were selected for their “brightest mind”, and curious to understand the genetic secret of their brilliance.

I counseled my colleagues not to participate in this ill-advised genome-wide association study. The phenotype was ill-defined and in any case the study would be underpowered (only 400 “geniuses” were solicited), but I believe many of them sent in their samples. As far as I know their DNA now languishes in one of Jonathan Rothberg’s freezers. No result has ever emerged from “Project Einstein”, and I’d pretty much forgotten about the ego-driven inquiries I had received years ago. Then, last week, I remembered them when reading a series of blog posts and associated commentary on evolutionary biology by some of the most distinguished mathematicians in the world.

1. Sir Timothy Gowers is blogging about evolutionary biology?

It turns out that mathematicians such as Timothy Gowers and Terence Tao are hosting discussions about evolutionary biology (see On the recently removed paper from the New York Journal of Mathematics, Has an uncomfortable truth been suppressed, Additional thoughts on the Ted Hill paper) because some mathematician wrote a paper titled “An Evolutionary Theory for the Variability Hypothesis“, and an ensuing publication kerfuffle has the mathematics community up in arms. I’ll get to that in a moment, but first I want to focus on the scientific discourse in these elite math blogs. If you scroll to the bottom of the blog posts you’ll see hundreds of comments, many written by eminent mathematicians who are engaged in pseudoscientific speculation littered with sexist tropes. The number of inane comments is astonishing. For example, in a comment on Timothy Gowers’ blog, Gabriel Nivasch, a lecturer at Ariel University writes

“It’s also ironic that what causes so much controversy is not humans having descended from apes, which since Darwin people sort-of managed to swallow, but rather the relatively minor issue of differences between the sexes.”

This person’s understanding of the theory of evolution is where the Victorian public was at in England ca. 1871:

In mathematics, just a year later in 1872, Karl Weierstrass published what at the time was considered another monstrosity, one that threw the entire mathematics community into disarray. The result was just as counterintuitive for mathematics as Darwin’s theory of evolution was for biology. Weierstrass had constructed a function that is uniformly continuous on the real line, but not differentiable on any interval:

$f(x) = \sum_{n=0}^{\infty} \left( \frac{1}{2} \right)^ncos({11}^n\pi x)$.

Not only does this construction remain valid today as it was back then, but lots of mathematics has been developed in its wake. What is certain is that if one doesn’t understand the first thing about Weierstrass’ construction, e.g. one doesn’t know what a derivative is, one won’t be able to contribute meaningfully to modern research in analysis. With that in mind consider the level of ignorance of someone who does not even understand the notion of common ancestor in evolutionary biology, and who presumes that biologists have been idle and have learned nothing during the last 150 years. Imagine the hubris of mathematicians spewing incoherent theories about sexual selection when they literally don’t know anything about human genetics or evolutionary biology, and haven’t read any of the relevant scientific literature about the subject they are rambling about. You don’t have to imagine. Just go and read the Tao and Gowers blogs and the hundreds of comments they have accrued over the past few days.

2. Hijacking a journal

To understand what is going on requires an introduction to Igor Rivin, a professor of mathematics at Temple University and, of relevance in this mathematics matter, an editor of  the New York Journal of Mathematics (NYJM) [Update November 21, 2018: Igor Rivin is no longer an editor of NYJM]. Last year Rivin invited the author of a paper on the variability hypothesis to submit his work to NYJM. He solicited two reviews and published it in the journal. For a mathematics paper such a process is standard practice at NYJM,  but in this case the facts point to Igor Rivin hijacking the editorial process to advance a sexist agenda. To wit:

• The paper in question, “An Evolutionary Theory for the Variability Hypothesis” is not a mathematics or biology paper but rather a sexist opinion piece. As such it was not suitable for publication in any mathematics or biology journal, let alone in the NYJM which is a venue for publication of pure mathematics.
• Editor Igor Rivin did not understand the topic and therefore had no business soliciting or handling review of the paper.
• The “reviewers” of the paper were not experts in the relevant mathematics or biology.

To elaborate on these points I begin with a brief history of the variability hypothesis. Its origin is Darwin’s 1875 book on “The Descent of Man and Selection in Relation to Sex” which was ostensibly the beginning of the study of sexual selection. However as explained in Stephanie Shields’ excellent review, while the variability hypothesis started out as a hypothesis about variance in physical and intellectual traits, at the turn of 20th century it morphed to a specific statement about sex differences in intelligence. I will not, in this blog post, attempt to review the entire field of sexual selection nor will I discuss in detail the breadth of work on the variability hypothesis. But there are three important points to glean from the Shields review: 1. The variability hypothesis is about intellectual differences between men and women and in fact this is what “An evolutionary theory for the variability hypothesis” tries really hard to get across. Specifically, that the best mathematicians are males because of biology. 2. There has been dispute for over a century about the extent of differences, should they even exist, and 3. Naïve attempts at modeling sexual selection are seriously flawed and completely unrealistic. For example naïve models that assume the same genetic mechanism produces both high IQ and mental deficits are ignoring ample evidence to the contrary.

Insofar as modeling of sexual selection is concerned, there was already statistical work in the area by Karl Pearson in 1895 (see “Note on regression and inheritance in the case of two parents“). In the paper Pearson explicitly considers the sex-specific variance of traits and the relationship of said variance to heritability. However as with much of population genetics, it was Ronald Fisher, first in the 1930s (Fisher’s principle) and then later in important work from 1958 what is now referred to as Darwin-Fisher theory (see, e.g. Kirkpatrick, Price and Arnold 1990) who significantly advanced the theory of sexual selection. Amazingly, despite including 51 citations in the final arXiv version of “An Evolutionary Theory for the Variability Hypothesis”, there isn’t a single reference to prior work in the area. I believe the author was completely unaware of the 150 years of work by biologists, statisticians, and mathematical biologists in the field.

What is cited in “An Evolutionary Theory for the Variability Hypothesis”? There is an inordinate amount of cherry picking of quotes from papers to bolster the message the author is intent on getting across: that there are sex-differences in variance of intelligence (whatever that means), specifically males are more variable. The arXiv posting has undergone eight revisions, and somewhere among these revisions there is even a brief cameo by Lawrence Summers and a regurgitation of his infamous sexist remarks. One of the thorough papers reviewing evidence for such claims is “The science of sex differences in science and mathematics” by Halpern et al. 2007. The author cherry picks a quote from the abstract of that paper, namely that “the reasons why males are often more variable remain elusive.” and follows it with a question posed by statistician Howard Wainer that implicitly makes a claim: “Why was our genetic structure built to yield greater variation among males than females?” An actual reading of the Halpern et al. paper reveals that the excess of males in the top tail of the distribution of quantitative reasoning has dramatically decreased during the last few decades, an observation that cannot be explained by genetics. Furthermore, females have a greater variability in reading and writing than males. They point out that these findings “run counter to the usual conclusion that males are more variable in all cognitive ability domains”. The author of “An Evolutionary Theory for the Variability Hypothesis” conveniently omits this from a very short section titled “Primary Analyses Inconsistent with the Greater Male Variability Hypothesis.” This is serious amateur time.

One of the commenters on Terence Tao’s blog explained that the mathematical theory in “An Evolutionary Theory for the Variability Hypothesis” is “obviously true”, and explained its premise for the layman:

It’s assumed that women only pick the “best” – according to some quantity X percent of men as partners where X is (much) smaller than 50, let’s assume. On the contrary, men are OK to date women from the best Y percent where Y is above 50 or at least greater than X.

Let’s go with this for a second, but think about how this premise would have to change to be consistent with results for reading and writing (where variance is higher in females). Then we must go with the following premise for everything to work out:

It’s assumed that men only pick the “best” – according to some quantity X percent of women as partners where X is (much) smaller than 50, let’s assume. On the contrary, women are OK to date men from the best Y percent where Y is above 50 or at least greater than X.

Perhaps I should write up this up (citing only studies on reading and writing) and send it to Igor Rivin, editor at the New York Journal of Mathematics as my explanation for my greater variability hypothesis?

Actually, I hope that will not be possible. Igor Rivin should be immediately removed from the editorial board of the New York Journal of Mathematics. I looked up Rivin’s credentials in terms of handling a paper in mathematical biology. Rivin has an impressive publication list, mostly in geometry but also a handful of publications in other areas. He, and separately Mary Rees, are known for showing that the number of simple closed geodesics of length at most L grows polynomially in L (this result was the beginning of some of the impressive results of Maryam Mirzakhani who went much further and subsequently won the Fields Medal for her work). Nowhere among Rivin’s publications, or in many of his talks which are online, or in his extensive online writings (on Twitter, Facebook etc.) is there any evidence that he has a shred of knowledge about evolutionary biology. The fact that he accepted a paper that is completely untethered from the field in which it purports to make an advance is further evidence of his ignorance.

Ignorance is one thing but hijacking a journal for a sexist agenda is another. Last year I encountered a Facebook thread on which Rivin had commented in response to a BuzzFeed article titled A Former Student Says UC Berkeley’s Star Philosophy Professor Groped Her and Watched Porn at Work. It discussed a lawsuit alleging that John Searle had sexually harassed, assaulted and retaliated against a former student and employee. While working for Searle the student was paid $1,000 a month with an additional$3,000 for being his assistant. On the Facebook thread Igor Rivin wrote

Here is an editor of the NYJM suggesting that a student should have effectively known that if she was paid \$36K/year for work as an assistant of a professor (not a high salary for such work), she ought to expect sexual harassment and sexual assault as part of her job. Her LinkedIn profile (which he linked to) showed her to have worked a summer in litigation. So he was essentially saying that this victim prostituted herself with the intent of benefiting financially via suing John Searle. Below is, thankfully, a quick and stern rebuke from a professor of mathematics at Indiana University:

I mention this because it shows that Igor Rivin has a documented history of misogyny. Thus his acceptance of a paper providing a “theory” for “higher general intelligence” in males, a paper in an area he knows nothing about to a journal in pure mathematics is nothing other than hijacking the editorial process of the journal to further a sexist agenda.

How did he actually do it? He solicited a paper that had been rejected elsewhere, and sent it out for review to two reviewers who turned it around in 3 weeks. I mentioned above that the “reviewers” of the paper were not experts in the relevant mathematics or biology. This is clear from an examination of the version of the paper that the NYJM accepted. The 51 references were reduced to 11 (one of them is to the author’s preprint). None of the remaining 10 references cite any relevant prior work in evolutionary biology on sexual selection. The fundamental flaws of the paper remain unaddressed. The entire content of the reviews was presumably something along the lines of “please tone down some of the blatant sexism in the paper by removing 40 gratuitous references”. In defending the three week turnaround Rivin wrote (on Gowers’ blog) “Three weeks: I assume you have read the paper, if so, you will have found that it is quite short and does not require a huge amount of background.” Since when does a mathematician judge the complexity of reviewing a paper by its length? I took a look at Rivin’s publications; many of them are very short. Consider for example “On geometry of convex ideal polyhedra in hyperbolic 3-space”. The paper is 5 pages with 3 references. It was received 15 October 1990 and in revised form 27 January 1992. Also excuse me, but if one thinks that a mathematical biology paper “does not require a huge amount of background” then one simply doesn’t know any mathematical biology.

3. Time for mathematicians to wet their paws

The irony of mathematicians who believe they are in the high end tail of some ill-specified distribution of intelligence demonstrating en masse that they are idiots is not lost on those of us who actually work in mathematics and biology. Gian-Carlo Rota’s ghost can be heard screaming from Vigevano “The lack of real contact between mathematics and biology is either a tragedy, a scandal, or a challenge, it is hard to decide which!!” I’ve spent the past 15 years of my career focusing on Rota’s call to address the challenge of making more contacts between mathematics and biology. The two cultures are sometimes far apart but the potential for both fields, if there is real contact, is tremendous. Not only can mathematics lead to breakthroughs in biology, biology can also lead to new theorems in mathematics. In response to incoherent rambling about genetics on Gowers’ blog, Noah Snyder, a math professor at Indiana University gave sage advice:

I really wish you wouldn’t do this. A bunch of mathematicians speculating about stuff they know nothing about is not a good way to get to the truth. If you really want to do some modeling of evolutionary biology, then find some experts to collaborate or at least spend a year learning some background.

What he is saying is  די קאַץ האָט ליב פֿיש אָבער זי װיל ניט די פֿיס אײַננעצן (the cat likes fish but she doesn’t want to wet her paws). If you’re a mathematician who is interested in questions of evolutionary biology, great! But first you must get your paws wet. If you refuse to do so then you can do real harm. It might be tempting to imagine that mathematics is divorced from reality and has no impact or influence on the world, but nothing could be farther from the truth. Mathematics matters. In the case discussed in this blog post, the underlying subtext is pervasive sexism and misogyny in the mathematics profession, and if this sham paper on the variance hypothesis had gotten the stamp of approval of a journal as respected as NYJM, real harm to women in mathematics and women who in the future may have chosen to study mathematics could have been done. It’s no different than the case of Andrew Wakefield‘s paper in The Lancet implying a link between vaccinations and autism. By the time of the retraction (twelve years after publication of the article, in 2010), the paper had significantly damaged public health, and even today its effects, namely death as a result of reduced vaccination, continue to be felt. It’s not good enough to say:

“Once the rockets are up,
who cares where they come down?
That’s not my department,”
says Wernher von Braun.

I’m thrilled to announce that I will be moving to Caltech next year where I will be professor of computational biology!

Some people have asked me why I’m moving. First and foremost, we (my family) feel it is the right move for us as for a variety of reasons that I won’t get into here. For me personally, Caltech represents a unique, special, and extraordinary opportunity because it is an institution that fosters an environment facilitating research and teaching that, inasmuch as possible, is unencumbered by the minutiae of academia. In particular, Caltech is unintimidated by disciplinary boundaries, and enables a culture that I’ve yearned for my whole career. It doesn’t throw hundreds of millions of dollars at a football team (although the basketball team is doing pretty well). Its priorities are aligned with mine.

I’m leaving behind Berkeley, a university I started working at 17 years ago as a visiting assistant professor. I’ll miss Berkeley. I still remember the January 1999 phone call from Prof. Tsit Yuen Lam, announcing my appointment. I was honored to have been invited to conduct research and to teach at one of the world’s great institutions. Berkeley was, and still is, distinguished by it’s mission of providing world-class affordable public education. I can’t think of any university in the world that has done as well in pursuing this noble goal. Consider, for example, that UC Berkeley has almost as many Pell Grant recipients as all eight Ivy League schools combined. But with time, as I was allowed to drop the prefixes in my title, I found myself increasingly aware of the structure, organization and financing of the university. Two numbers that I learned have stuck in my mind: today, state funding comprises only 13% of the budget (likely even lower next year), less than half of what it was when I arrived. At the same time, tuition has increased by over a factor of three during the same time period. The squeeze has harmed the institution not just because of reductions in resources (though there have been many), but also because of the strain placed on the morale and mission of the university. Over time I started to question whether its world-class education was sustainable, and lamented that its affordability was becoming a myth. Over the past two years I’ve become increasingly aware that the reality of the university is at odds with my values. I’m sad for the University of California and for the citizens who are being harmed by the blows it is taking, and very much wish that the state will protect and nurture its education treasure. But I will be rooting for it from the sidelines.

I can’t wait to start at Caltech, and look forward to the next phase of my career!

My doppelgänger, Charlie Eppes, who developed algebraic statistics for computational biology at “CalSci” (Caltech).

The Journal lmpact Factor (JIF) was first proposed by Eugene Garfield of Institute for Scientific Information (ISI) fame in 1955. It is a journal specific yearly citation measure, defined to be the average number of citations per paper of the papers published in the preceding two years. Obsession with the impact factor in the face of widespread recognition of its shortcomings as a tool for judging the value of science is an unfortunate example of “the tragedy of the commons”.

Leaving aside for a moment the flaws of the JIF, one may wonder whether journals do in fact have any impact? By “impact”one might imagine something along the lines of the simple definition in the Merriam-Webster Dictionary: “to have a strong and often bad effect on (something or someone)” and as an object for the impact one could study the researchers who publish, the scientific community as a whole, or the papers themselves. On the question of impact on papers, common sense suggests that publishing in a high profile journal helps a paper succeed and there is pseudoscience to support that case. However there is little in the way of direct measurement. Twitter to the rescue.

At the end of last year my twitter account was approaching 5,000 followers. Inspired by others, I found myself reflecting on this “milestone” and in anticipation of the event, I started to ponder the scientific utility of amassing such a large numbers of followers. There is, of course, a lot of work being done on natural language processing of twitter feeds, but it struck me that with 5,000 followers I was in a position to use twitter for proactive experimentation rather than just passive mining. Impact factors, followers, and twitter… it was just the right mix for a little experiment…

Starting in August of 2015, I began occasionally tweeting articles about 5 minutes apart, using the exact same text (the article title or brief description) but doing it once with the article linked via the journal website so that the journal name was displayed in the link and once with an a bit.ly link that revealed nothing about the journal source. Twitter analytics allowed me to see, for each tweet, a number of (highly correlated) tweet statistics, and I settled on measuring the number of clicks on the link embedded in the tweet. By switching the order of named/anonymized tweets I figured I could control for a temporal effect in tweet appearance, e.g. it seemed likely that users would click on the most recent links on their feed resulting in more views/clicks etc. for later tweets identical except for link type . Ideally this control would have been performed by A/B testing but that was not a possibility (see Supplementary Materials and Notes). I did my tweeting manually, generally waiting a few weeks between batches of tweets so that nobody would catch on to what I was doing (and thereby ruin the experiment). I was eventually caught forcing me to end the experiment but not before I squeezed in enough tests to achieve a significant p-value for something.

I hypothesized that twitter users will click on articles when, and only when, the titles or topics reflect research of interest to them. Thus, I expected not to find a difference in analytics between tweets made with journal names as opposed to bit.ly links. Strikingly, tweets of articles from Cell, Nature and Science journals (CNS) all resulted in higher clicks on the journal title rather than the anonymized link (p-value 0.0078). The average effect was a ratio of 2.166 between clicks on links with the journal name in comparison to clicks on bit.ly links. I would say that this number is the real journal impact factor of what are now called the “glamour journals” (I’ve reported it to three decimal digits to be consistent with the practice of most journals in advertising their JIFs). To avoid confusion with the standard JIF, I call my measured impact factor the RIF (relative impact factor).

One possible objection to the results reported above is that perhaps the RIF reflects an aversion to clicking on bit.ly links, rather than a preference for clicking on (glamour) journal links. I decided to test that by performing the same test (journal link vs. bit.ly link) with PLoS One articles:

Strikingly, in three out of the four cases tested users displayed an aversion to clicking on PLoS One links. Does this mean that publishing in PLoS One is career suicide? Certainly not (I note that I have published PLoS One papers that I am very proud of, e.g. Disordered Microbial Communities in Asthmatic Airways), but the PLoS One RIF of 0.877 that I measured (average ratio of journal:bit.ly clicks, as explained above) is certainly not very encouraging for those who hope for science to be journal name blind. It also suggests that the RIF of glamour journals does not reflect an aversion to clicking on bit.ly links, but rather an affinity for.. what else to call it but.. glamour.

Academics frequently complain that administrators are at fault for driving researchers to  emphasize JIFs, but at the recent Gaming Metrics meeting I attend UC Davis University Librarian MacKenzie Smith pointed out something which my little experiment confirms: “It’s you!

## Supplementary Material and Notes

The journal Nature Communications is not obviously a “glamour journal”, however I included it in that category because the journal link name began nature.com/… Removing the Nature Communications tweet from the glamour analysis increases the glamour journal RIF to 2.264.

The ideal platform for my experiment is an A/B testing setup, and as my former coauthor Dmitry Ryaboy , head of the experimentation team at twitter explains in a blog post, twitter does perform such testing on users for internal purposes. However I could not perform A/B testing directly from my account, hence the implementation of the design described above.

I tried to tweet the journal/bit.ly tweets exactly 5 minutes apart, but once or twice I got distracted reading nonsense on twitter and was delayed by a bit. Perhaps if I’d been more diligent (and been better at dragging out the experiment) I’d have gotten more and better data. I am comforted by the fact that my sample size was >1.

Twitter analytics provided multiple measures, e.g. number of retweets, impressions, total engagements etc., but I settled on link clicks because that data type gave the best results for the argument I wanted to make. The table with the full dataset is available for download from here (or in pdf). The full list of tweets is here.

So you’re an academic and you’ve written some bioinformatics software. You heard that:

1. Somebody will build on your code.

Nope. Ok, maybe not never but almost certainly not. There are many reasons for this. The primary reason in my view is that most bioinformatics software is of very poor quality (more on why this is the case in #2). Who wants to read junk software, let alone try to edit it or build on it? Most bioinformatics software is also targeted at specific applications. Biologists who use application specific software are typically not interested in developing or improving software because methods development is not their main interest and software development is not their best skill. In the computational biology areas I have worked in during the past 20 years (and I have reviewed/tested/examined/used hundreds or even thousands of programs) I can count the software programs that have been extended or developed by someone other than the author on a single hand. Software that has been built on/extended is typically of the framework kind (e.g. SAMtools being a notable example) but even then development of code by anyone other than the author is rare. For example, for the FSA alignment project we used HMMoC, a convenient compiler for HMMs, but has anyone ever built on the codebase? Doesn’t look like it. You may have been told by your PI that your software will take on a life of its own, like Linux, but the data suggests that is simply not going to happen. No, Gnu is Not Unix and your spliced aligner is not the Linux kernel. Most likely you alone will be the only user of your software, so at least put in some comments, because otherwise the first time you have to fix your own bug you won’t remember what you were doing in the code, and that is just sad.

2. You should have assembled a team to build your software.

3. If you choose the right license more people will use and build on your program.

4. Making your software free for commercial use shows you are not against companies.

5. You should maintain your software indefinitely.

Nope. Someday you will die. Before that you will get a job, or not. Plan for your software to have a limited shelf-life, and act accordingly.

6. Your “stable URL” can exist forever.

Nope. When I started out as a computational biologist in the late 1990s I worked on genome alignment. At the time I was excited about Dynamite: a flexible code generating language for dynamic programming methods used in sequence comparison. This was a framework for specifying bioinformatics related dynamic programming algorithms, such as the Needleman-Wunsch or Smith-Waterman algorithms. The authors wrote that “A stable URL for Dynamite documentation, help and information is http://www.sanger.ac.uk/~birney/dynamite/” Of course the URL is long gone, and by no fault of the authors. The website hosting model of the late 1990s is long extinct. To his credit, Ewan now hosts the Dynamite code on GitHub, following a welcome trend that is likely to extend the life of bioinformatics programs in the future. Will GitHub be around forever? We’ll see. But more importantly, software becomes extinct (or ought to) for reasons other than just 404 errors. For example, returning to sequence alignment, the ClustalW program of 1994 was surpassed in accuracy and speed by many other multiple alignment programs developed in the 2000s. Yet people kept using ClustalW anyway, perhaps because it felt like a “safe bet” with its many citations (eventually in 2011 Clustalw was updated to Clustal Omega). The lag in improving ClustalW resulted in a lot of poor alignments being utilized in genomics studies for a decade (no fault of the authors of ClustalW, but harmful nonetheless). I’ve started the habit of retiring my programs, via announcement on my website and PubMed. Please do the same when the time comes.

7. You should make your software “idiot proof”.

Nope. Your users, hopefully biologists (and not other bioinformatics programmers benchmarking your program to show that they beat it) are not idiots. Listen to them. Back in 2004 Nicolas Bray and I published a webserver for the alignment program MAVID. Users were required to input FASTA files. But can you guess why we had to write a script called checkfasta? (hint: the most popular word processor was and is Microsoft Word). We could have stopped there and laughed at our users, but after much feedback we realized the real issue was that FASTA was not necessarily the appropriate input to begin with. Our users wanted to be able to directly input Genbank accessions for alignment, and eventually Nicolas Bray wrote the perl scripts to allow them to do that (the feature lives on here). The take home message for you is that you should deal with user requests wisely, and your time will be needed not only to fix bugs but to address use cases and requested features you never thought of in the first place. Be prepared to treat your users respectfully, and you and your software will benefit enormously.

8. You used the right programming language for the task.

Nope. First it was perl, now it’s python. First it was MATLAB, now it’s R. First it was  C, then C++.  First it was multithreading now it’s Spark. There is always something new coming, which is yet another reason that almost certainly nobody is going to build on your code. By the time someone gets around to having to do something you may have worked on, there will be better ways. Therefore, the main thing is that your software should be written in a way that makes it easy to find and fix bugs, fast, and efficient (in terms of memory usage). If you can do that in Fortran great. In fact, in some fields not very far from bioinformatics, people do exactly that. My advice: stay away from Fortran (but do adopt some of the best practice advice offered here).

9. You should have read Lior Pachter’s blog post about the myths of bioinformatics software before starting your project.

Nope. Lior Pachter was an author on the Vista paper describing a program for which the source code was available only “upon request”.


text:
# Calculating the Magnetic Component of a Photon

I've been trying to figure this out for some time. I have found some formulae on other sites that claim to allow me to calculate the magnetic component of a photon, but I have seen so many variants of the formulae that I'm skeptical about their reliability.

I am aware that a photon is an electromagnetic wave and it consists of an electric field and a magnetic field that are perpendicular to each other. Considering that they propagate each other, it would be that at certain times, the wave would be entirely electric and at other times, it would be entirely magnetic.

Would it then be possible to calculate the magnetic field strength (B-field) of the electromagnetic wave at the point of maximum amplitude (i.e. when the wave is entirely magnetic)?

• In an electromagnetical wave in vacuum the electric and magnetic components are in phase, not out of phase. Furthermore, as coherent light waves are coherent states of photons you can extract the information (if you are only interested in mean values) from formula for classical light waves. – Sebastian Riese May 31 '15 at 16:36
• "Considering that they propagate each other, it would be that at certain times, the wave would be entirely electric and at other times, it would be entirely magnetic." You are right with your thoughts but not in accordance with the modern teaching. See the links in this answer physics.stackexchange.com/questions/152758/… – HolgerFiedler May 31 '15 at 18:05
• From what I see in the pic, it looks like the two waves are out of phase with each other. Wouldn't this mean that there would be a point where it would have a maximum magnetic field strength? – ashiswin Jun 1 '15 at 2:42

Remember that if the electric and magnetic field components are perpendicular and in phase, then you can always calculate the magnetic induction component as $|\vec{B}| = \frac{1}{v}|\vec{E}|$; where $v$ is the speed of the wave, and is given by $v = \frac{1}{\sqrt{\epsilon\mu}}$, where $\epsilon$ and $\mu$ are the relative permittivity and permeability of the medium.