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# Build Cop and Build Farmer Guide¶

This page covers two rotating developer roles we have on the ROS 2 team, the build cop and the build farmer. These two roles are related, but subtly different.

The build cop is responsible for monitoring our Continuous Integration (CI) server to make sure our “nightly” jobs and “packaging” jobs do not accumulate new regressions. This allows us to build on relatively stable “ci” (or “manual”) jobs when checking to see if a new feature or bug fix introduces any new regressions.

The build farmer, on the other hand, is responsible for ensuring that the machines that run all of our CI jobs are up, running, and up-to-date, so that they are available for other developers to check their pull requests.

These two jobs have so far been the same person for periods of about two weeks, but they are separated here so that they could be different people in the future and to make a distinction between the roles and responsibilities.

This document is meant mostly for ROS 2 team developers, but it might be useful for others too.

## On-boarding¶

If you are becoming the next build cop or build farmer you should:

• Make sure you are subscribed to and have the “deliver every email” option turned on for this mailing list:

• Make sure you are “watching” this GitHub repository:

• Talk with the previous build cop and/or build farmer about on-going issues

• Update the description of the main view on Jenkins to the current date and your name:

## Retirement¶

If you are finishing your stint as either build cop or build farmer you should:

• Unsubscribe or switch to “digest” for this mailing list:

• “Unwatch” this GitHub repository:

• Summarize the on-going issues for the next build cop or build farmer to which you are handing off

## Build Cop¶

This section assumes that you have reviewed the ROS 2 on boarding document.

### Mission¶

The goal of the build cop is to keep the jobs “green” (succeeding without test failures or warnings) on the buildfarm and to report any regression to the appropriate person. This will reduce the overhead of several people looking at, or investigating, the same build failures. This will also allow the other people on the team not to receive nightly email for the failing and/or unstable builds.

Every morning the build cop should go through all the nightly jobs and packaging jobs and act on new failing or unstable jobs. The “ci” jobs, which are started manually by developers, are not the responsibility of the build cop unless all “ci” are failing, which would indicate something was merged to the default branches which is broken. How to classify and deal with new failures is described in the next section.

Additionally, the build cop should strive to keep track of existing issues which are either preexisting or cannot be resolved with a day or so. Issues are tracked on this repository which only the build cop must be “watching” (getting GitHub notifications), though anyone interested can follow it too:

https://github.com/ros2/build_cop/issues

The above repository is also used to track Build Farmer issues. It is meant to be a way for the build cop or build farmer to track long running items for handing off to the next person and so they can “mention” individuals on particular issues without the whole team getting notified of every issue.

#### Types of Failures¶

Each failure can be categorized into one of a few classifications:

• Node failure:

• failures which appear to be due to a machine configuration and not a code change

• pass it on to the build farmer

• Trivial failure:

• Linter failure

• New warnings

• Critical failure:

• Breaking builds on the “default” branch

• Regression (existing tests which were passing are now failing)

• New tests that are failing (never were passing)

• Important failure:

• New feature which is not fully covered by tests

• Increase flakiness (new flaky tests or made existing flaky tests more flaky)

#### New Failure Actions¶

In each case different actions should be taken by the build cop:

• Trivial failure should be fixed by the Build Cop right away:

• Pushed on a branch

• Tested on CI

• Merged to the default branch

• Add a comment to the PR introducing the failure referencing the fixing commit

• Critical failures:

• Failure should be reported on the PR introducing it by tagging the submitter and the reviewer that +1’d it.

• Submitter of the PR has to act on it during the next half day by either:

• Reverting the change and ticketing the problem / comment on the PR the reason it’s been reverted

• Submit a patch to fix the failure

• Important failures:

• Failure should be reported on the PR introducing it by tagging the submitter + the reviewer the +1’d it.

• Submitter has to either:

• Address it the same week

• Add it to the next sprint

#### Tips¶

• You can search for PRs merged between two dates with, e.g.:

• To get the exact list of code that changed, generate a diff between the output of vcs export --exact between two builds.

• This is particularly useful for external repos such as FastRTPS where old commits may get pushed to the master branch overnight, and are difficult to spot in the GitHub UI.

• Times displayed at the top of jenkins jobs are in UTC. You can convert the times with e.g.:

• If linter failures occur overnight it is usually because of a new version of a linter.

• Create a diff of the last pip freeze output of two builds to see which versions changed.

• If it’s a regression in a dependency you can pin the older version temporarily, see this PR for an example.

## Build Farmer¶

This section assumes that you have reviewed the ROS 2 on boarding document.

### Mission¶

The mission of the build farmer is to keep the build farm in a healthy, up-to-date state. Ideally all Jenkins nodes will have the same/latest version of every package. This will require monitoring and patching up any node when things come up.

• Monitor the buildfarm (using the https://groups.google.com/forum/#!forum/ros2-buildfarm mailing list for email notifications)

• Take failing nodes off-line with descriptive message about the issue and investigate the failure ASAP.

• Taking a node off-line:

• click on the node in the left column of Jenkins UI (e.g. osx_slave_mini1)

• click on “Mark this node temporary off-line” button (top right corner)

• Investigate the failure (see section below)

• Report error and fixing attempt using the Build Farmer Reporting Form

• If the same problem and action is taken on multiple nodes, select all the relevant nodes in the form before submitting it

• If fixing attempt failed:

• Keep the node off-line on the farm

• Update the reason for node being off-line

• Put the status and error message in the status sheet of the logbook

• Allocate time in the next few days to dive in the problem

• If you rescue a previously off-line node:

• Update the status sheet of the logbook by:

• Removing the error message in the status column

• Update the date next to it

• Once investigation is finished, clean the machine: close all your windows, stash or remove any local changes

• Rationale

• Anybody logging into the machine need to know that no one is working on it

• If the machine reboots the machine needs to be in an operational state without local changes

• Making sure install instructions are up to date

• Use the existing logbook to put together an FAQ or best practice to rescue nodes

#### How to Investigate a Failing Node¶

If the node failed to build, look at the console output of the failing build:

• Click on the link of the failing job received by email or go to ci.ros2.org and click on the number (e.g. #2345) next to the failing job(red icon).

• Click on Console Output in the left column

• Look for the reason of the failure

• If the failure is not due to a machine configuration, relay to the build cop

If you need to access a machine:

• See this spreadsheet (private) for credentials for all the different Jenkins Nodes:

• For machines hosted at OSRF, you’ll need to be on the OSRF network or have a VPN connection.

• For machines which require ssh keys ask on ros@osrfoundation.org for your public keys to be added.

• The Packet.net nodes (with “packet” in the name):

• Can be managed by logging in at https://packet.net with <brian’s email address>/<the usual company password>

• This will change after we set up a team account to manage servers.

• Can be accessed with Tully’s or Brian’s ssh key.

• This will change after we set up a team account to manage servers.

#### Troubleshooting¶

If a node goes off-line:

• For machines with VNC, you should try that first because many failures can be due to pop-up windows or required updates

• If you don’t have any pop-ups and relaunching the jenkins client doesn’t fix it, then you’ll have to start troubleshooting.

• Looking at configuration difference between the nodes may be useful (java version, pip freeze, etc.)

• For Linux nodes that have gone off-line (e.g. because of a reboot), they can be reconnected through the Jenkins web interface of that node

Other tips:

The environment variables on Windows machines are output at the beginning of Jenkins jobs (search for ==> set). If you are modifying environment variables on Windows nodes, you may need to restart the machine before the changes are reflected in the jobs. This is due to the Jenkins slave session caching the environment variables to some degree.

On the Windows machines, the Jenkins slave program runs as a service as the System account. For this user, the “home” directory seems to be C:\Windows\system32\config\systemprofile. You can “become” the system user to debug stuff by downloading pxexec:

https://technet.microsoft.com/en-us/sysinternals/pxexec

Then you extract the zip, then open a command-prompt as administrator, and then run psexec -i -s cmd.exe.

This is all pieced together from a couple of pages here:

http://blog.thomasvandoren.com/jenkins-windows-slave-with-git.html

and here:


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# How do you find the coordinates of the other endpoint of a segment with the given endpoint T(-3.5,-6) and the midpoint M(1.5,4.5)?

May 20, 2017

See a solution process below:

#### Explanation:

The formula to find the mid-point of a line segment give the two end points is:

$M = \left(\frac{\textcolor{red}{{x}_{1}} + \textcolor{b l u e}{{x}_{2}}}{2} , \frac{\textcolor{red}{{y}_{1}} + \textcolor{b l u e}{{y}_{2}}}{2}\right)$

Where $M$ is the midpoint and the given points are:

$\left(\textcolor{red}{\left({x}_{1} , {y}_{1}\right)}\right)$ and $\left(\textcolor{b l u e}{\left({x}_{2} , {y}_{2}\right)}\right)$

Substituting the information we have gives:

$\left(1.5 , 4.5\right) = \left(\frac{\textcolor{red}{- 3.5} + \textcolor{b l u e}{{x}_{2}}}{2} , \frac{\textcolor{red}{- 6} + \textcolor{b l u e}{{y}_{2}}}{2}\right)$

To find $\textcolor{b l u e}{{x}_{2}}$ we need to solve this equation:

$1.5 = \frac{\textcolor{red}{- 3.5} + \textcolor{b l u e}{{x}_{2}}}{2}$

$\textcolor{g r e e n}{2} \times 1.5 = \textcolor{g r e e n}{2} \times \frac{\textcolor{red}{- 3.5} + \textcolor{b l u e}{{x}_{2}}}{2}$

$3 = \cancel{\textcolor{g r e e n}{2}} \times \frac{\textcolor{red}{- 3.5} + \textcolor{b l u e}{{x}_{2}}}{\textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{2}}}}$

$3 = \textcolor{red}{- 3.5} + \textcolor{b l u e}{{x}_{2}}$

$3.5 + 3 = 3.5 \textcolor{red}{- 3.5} + \textcolor{b l u e}{{x}_{2}}$

$6.5 = 0 + \textcolor{b l u e}{{x}_{2}}$

$6.5 = \textcolor{b l u e}{{x}_{2}}$

$\textcolor{b l u e}{{x}_{2}} = 6.5$

To find $\textcolor{b l u e}{{y}_{2}}$ we need to solve this equation:

$4.5 = \frac{\textcolor{red}{- 6} + \textcolor{b l u e}{{y}_{2}}}{2}$

$\textcolor{g r e e n}{2} \times 4.5 = \textcolor{g r e e n}{2} \times \frac{\textcolor{red}{- 6} + \textcolor{b l u e}{{y}_{2}}}{2}$

$9 = \cancel{\textcolor{g r e e n}{2}} \times \frac{\textcolor{red}{- 6} + \textcolor{b l u e}{{y}_{2}}}{\textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{2}}}}$

$9 = \textcolor{red}{- 6} + \textcolor{b l u e}{{y}_{2}}$

$9 + 6 = 6 \textcolor{red}{- 6} + \textcolor{b l u e}{{y}_{2}}$

$15 = 0 + \textcolor{b l u e}{{y}_{2}}$

$15 = \textcolor{b l u e}{{y}_{2}}$

$\textcolor{b l u e}{{y}_{2}} = 15$

The other end point of the segment is: $\left(\textcolor{b l u e}{6.5} , \textcolor{b l u e}{15}\right)$

format: plain


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Propagation with Holmes-Featherstone Attraction Model is too different than reality

Hi everyone !

I’m trying to estimate the errors caused by my numerical propagator and came up with the following method :
I recover the orbital elements from a TLE at a certain date, say the 1st of March, and propagate to another date, for example the 9th of March. I then compare the results of my propagation with the updated TLE of this same satellite at the exact date of the results.
I also compare the results of my propagator with and without the added ForceModels.
However, my results seem way off. I compute the relative errors on the position with \frac{abs(x_{th} - x_{exp})}{ x_{th}} and for some reason I have more error when propagating with the “realistic” ForceModels than without.

I brute forced an investigation by trying all the combinations of forces I had, and discovered that the HolmesFeatherstoneAttractionModel is the main cause of the problem. When i remove it from the propagator, my results are way closer to the updated TLE (the reference), and i don’t understand why or how…

some pseudo code to illustrate my thoughts :

# define all the characteristics of the spacecraft
satellite_mass = ...

# I know the following part is not a good thing to do, but i don't know how to do it properly
# get the TLE at the initial date, and extract the orbital parameters from it
sat_initial_tle = TLE(line1,line2)
sat_initial_orbit = user_defined_function_that_creates_a_KeplerianOrbit(sat_initial_TLE)
# get the TLE at the final date, the reference
sat_reference_tle = TLE(line1,line2)
sat_reference_orbit = user_defined_function_that_creates_a_KeplerianOrbit(sat_reference_TLE)

# Create all the ForceModels that are added to the numerical propagator
isotropic_drag = IsotropicDrag(cross_section, drag_coef)
list_of_forces.append(DragForce(SimpleExponentialAtmosphere(earth, 0.0004, 42000.0, 7500.0), isotropic_drag))
gravityProvider = GravityFieldFactory.getNormalizedProvider(10, 10)
list_of_forces.append(HolmesFeatherstoneAttractionModel(FramesFactory.getITRF(IERSConventions.IERS_2010, True), gravityProvider))
list_of_forces.append(ThirdBodyAttraction(moon))
list_of_forces.append(ThirdBodyAttraction(sun))

# create a NumericalPropagator like in the examples
integrator = DormandPrince853Integrator(...)
propagator_num = NumericalPropagator(integrator)
for force in list_of_forces:

# propagate
final_state = propagator_num.propagate(start_date.shiftedBy(duration_between_both_TLE))

# investigate the results
pos_z_theory = sat_reference_orbit.getPVCoordinates().getPosition().z
pos_z_experimental = final_state.orbit.getPVCoordinates().getPosition().z
relative_error = abs(pos_z_theory - pos_e_experimental) / pos_z_theory * 100

# sample output
# relative error on x : 0.12 %
#  relative error on z : 1276%

# when doing the exact same calculations but without any ForceModels :
# relative error on x : 0.081 %
#  relative error on z : 496%

# Again the same calculation with all ForceModels except HolmesFeatherStoneAttractionModel
# relative error on x : 0.088 %
#  relative error on z : 401%

So as you can see, those results are quite unsettling… One explanation could be that the satellite performed a maneuver between the two TLE I used, but I tried on many different satellites and despite the amplitude of the values being lower, the weird trend was still present.

Please let me know if i did something wrong, i’m still a beginner. Thank you all for your feedback.

PS : this is the output PVCoordinates with all forces included, the acceleration on the Z axis seems too high

Theo :  {2020-12-09T09:11:13.098, P(-2.724526618536018E7, 1.1576141046260186E7, 9908.796140895838), V(-822.2336477064472, -1936.9220117427658, 3006.0504020394133), A(0.41864020909753735, -0.17787450029587157, -1.5225472418245217E-4)}
Expe :  {2020-12-09T09:11:13.098, P(-2.727990503738411E7, 1.1493375183418749E7, 136348.45491551282), V(-804.3678414387626, -1944.106155548559, 3006.263174630185), A(0.4192015938477335, -0.17661915775838216, -0.002094830244918838)}

I would say that you are mainly observing the errors in the TLE themselves.

TLE are not an accurate model, by far. They are used because for many satellites this is the only available data, but it is very often way off reality.

I remember a presentation by T.S. Kelso where he showed an extreme case with about 60000km error (he confirmed it was really kilometers, so the satellite was on the wrong side of the Earth, and far from it, and there was a logical explanation for that).

1 Like

You’re probably right, i know TLEs are not reliable and the way i convert them into keplerian elements probably does not help, but i did not think it was that bad …
So can you confirm that the method is not wrong ? and if I find more accurate data it should work ?
Also what bothers me is the fact that we see this problem almost only on the Z axis and i can’t explain it.

I’ll go look for more data, thanks for the help !

As propagation errors mainly increase along track, I would suggest to compare position not in the inertial frame in which it is computed, but rather using one satellite as the reference and using its local orbital frame for the axes. So say you have the PVCoordinates pvRef and pvComputed for your two
evaluations at the same time. Then you could compute:

  Rotation toVNC         = LOFType.VNC.rotationToInertial(pvRef);
Vector3D deltaInertial = pvComputed.getPosition().subtract(pvRef.getPosition());
Vector3D deltaVNC      = toVNC.applyTo(deltaInertial);

Then you could plot the errors as the components of the deltaVNC vector as the X component would be along velocity, the Y component would be along orbital momentum and the Z component would be roughly radial.

It also seems to me your simple atmosphere model uses a reference altitude that is very low (42000m), so take care of its validity at orbital altitudes.

1 Like

Is it the case that TLEs, are an ‘accurate’ model only for SGP4 propagation and, even then, are not valid for longer than a week, or two?

TLE and SGP4/SDP4 are bound together. TLE can be propagated only by SGP4/SDP4, and SDGP4/SDP4 can propagate only TLE. One is the data structure, the other one is the algorithm that handles it. It is never accurate.

Sometimes, even one week or two is too much, particularly in LEO (i.e. SGP4) when drag is involved.

1 Like

In my opinion, beyond 24H or 48H, the accuracy of the TLE propagation is very limited.

1 Like


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The sphere in the figure is of radius 15 cm. How do I find the surface area of the shaded part of the sphere in figure 1? Please help!

As you see the inner triangle has sides $20cm$ and $15cm$ and is right angled, so the third side (that from O to the top of the triangle) must be $25cm$ (it's pythagorean). Also as the radius of the circle is $15cm$ you would have that the height of the triangle is $40cm$.
This means that the the width of the triangle $20cm$ up from the base is half of the base (as it's half-way to the top).
Then you use the formula for the area of a trapezoid. It becomes $A = {30+60\over 2}20 cm^2$
The formula you need for the surface area of the shaded portion of the sphere is $A=2\pi rh$. You have $r=15$ and $h=20$, so $A=600\pi\,cm^2$.


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# Conceptual Understanding of Rates of Change

A rate is a comparison between two quantities with different units.
We often judge performances by using rates. For example:

• Average speed of a motor vehicle is $90$ km per hour.
• Average typing rate is $55$ words per minute.
• Average score of a basketball player is $34$ points per game.

Speed is a commonly used rate. It is the rate of change in distance per unit of time. It is a well-known formula:
$$\text{average speed}=\dfrac{\text{distance travelled}}{\text{time taken}}$$
However, if a car has an average speed of $80$ km/h for a trip, it does not mean that the car travels at exactly $80$ km/h for the whole time.
In fact, the speed will probably vary continuously throughout the trip.
So, how can we calculate the car’s speed at any particular time?

A heavy particle falls from a tower, $50$ metres high, and crashes into the ground. How can we predict the damage the spanner causes when it hits the ground? We will begin by attempting to develop a mathematical model for the speed of the particle as it falls.
Speed is a rate – a measure of distance travelled per unit time. Our modelling thus begins with a review of the rate and the concept of a constant rate.

## Constant Rates of Change

When the rate of change of one quantity with respect to another does not alter, the rate is constant.
For example, if petrol is $80$ cents per litre then every litre of petrol purchased at this rate always costs $80$ cents. This means $10$ litres of petrol would cost $8.00$ dollars and $100$ litres of petrol would cost $80.00$ dollars.

## Variable Rates of Change

The particle travels $50$ metres in $3$ seconds and then stops moving. In other words, it falls $50$ metres and then hits the ground. We also notice that the speed of the particle is not constant but is variable.
If a rate is not constant but is changing then it must be a variable rate.
For example, the amount of electricity used per hour by a household is most likely to be a variable rate as the need for electricity will change throughout the day.

## Average Rates of Change

If a rate is variable it is sometimes useful to know the average rate of change over a specific interval. For example, a tree grew from $5$ m this time last year to $6$ m now.
\begin{align} \text{average rate of growth} &= \dfrac{\text{change in height}}{\text{change in time}} \\ &= \dfrac{(6-5) \text{ m}}{1 \text{ year}} \\ &= 0.2 \text{ m/year} \\ \end{align}
This means that the tree grew $0.2$ metres over the past year but not necessarily constantly as that rate during the year.

## Instantaneous Rates of Change

If a rate is variable, it is often useful to know the rate of change at any given time or point, that is, the instantaneous rate.
For example, a police radar gun is designed to give an instantaneous reading of a vehicle’s speed. This enables the police to make an immediate decision as to whether a car is breaking the speed limit or not.
Instantaneous rates can be found from a curved graph by:

• drawing a tangent to the curve a the point in equation,
• calculating the gradient of the tangent over an appropriate interval, that is, between two points whose coordinates are easily identified.

## Derivative in terms of Rates of Change

$$f^{\prime}(x) = \lim_{h\rightarrow 0}\dfrac{f(x+h)-f(x)}{h}$$
The gradient of the tangent at the variable point $(x,f(x))$ is the limiting value of $\dfrac{f(x+h)-f(x)}{h}$ as $h$ approaches $0$.
This formula gives the gradient of the tangent to the curve $y=f(x)$ at the point $(x,f(x))$, for any value of the variable $x$ for which this limit exists. Since there is at most one value of the gradient for each value of $x$, the formula is actually a function.

## Algebraic vs Calculus in terms of Rates of Change

As stated above, average rates of change is often referred as algebraic rates of change. Algebraic acceleration is the average rates of change, while the acceleration is the term which is instantaneous rates of change of speed of velocity which obtained by differentiating velocity.

Assume $x(t)$ is a displacement, then $x^{\prime}(t)$ or $\dfrac{dx}{dt}$ is the instantaneous rate of change in displacement with respect to time, which is velocity.
Example where quantities vary with time, or with respect to some other value.

• temperature changes
• height of the surface of water in a pond
• speed of a car

$\dfrac{dy}{dx}$ gives the rate of change in $y$ with respect to $x$.
We can therefore use the derivative of a function to inform us the rate at which something is happening.

### Example 1

The number of people in a colony is approximated by the formula $P(t)=30000+72t^2-t^4$ where $t$ is the time in years after the year $2000$.

(a)   Find the number of people in the colony in the year $2000$.

\begin{align} \displaystyle P(0) &= 30000 + 72 \times 0^2-0^4 \\ &= 30000 \\ \end{align}

(b)   Find the number of people in the colony at the year $2008$

\begin{align} \displaystyle P(8) &= 30000 + 72 \times 8^2-8^4 \\ &= 30512 \\ \end{align}

(c)   Find the rate at which the number of people in the colony is changing when $t=2$.

\begin{align} \displaystyle P^{\prime}(t) &= 144t^2 – 4t^3 \\ P^{\prime}(2) &= 144 \times 2 – 4 \times 2^3 \\ &= 256 \\ \end{align}

(d)   Describe the significance of the result of part (c).

after two years, the number of people is increasing by 256 people per year

(e)   Find the rate at which the number of people in the colony is changing when $t=8$.

\begin{align} \displaystyle P^{\prime}(8) &= 144 \times 8 – 4 \times 8^3 \\ &= -896 \\ \end{align}

(f)   Describe the significance of the result of part (e).

after eight years, the number of people is decreasing by $-896$ people per year


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# Description of continuum structures in a discrete basis: Three-body resonances and two-nucleon decays

### Submission summary

 As Contributors: Jesus Casal Arxiv Link: https://arxiv.org/abs/1910.09418v1 Date submitted: 2019-10-22 Submitted by: Casal, Jesus Submitted to: SciPost Physics Proceedings Proceedings issue: 24th European Few Body Conference (University of Surrey, U.K.) Discipline: Physics Subject area: Nuclear Physics - Theory Approach: Theoretical

### Abstract

Weakly bound and unbound three-body nuclei are studied by using the pseudostate method within the hyperspherical formalism. After introducing the theoretical framework, the method is applied first to the $\boldsymbol{^9}$Be nucleus, showing a good agreement with the available data for its low-lying dipole response. Then, recent results on the structure and decay of the two-neutron emitters $\boldsymbol{^{26}}$O and $\boldsymbol{^{16}}$Be are presented. In particular, the role of the $\boldsymbol{n}$-$\boldsymbol{n}$ correlation in shaping their properties is discussed.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1910.09418v1 on 22 October 2019

## Reports on this Submission

### Report

The paper is nicely written in a pretty clean and didactic way. It is easy to follow, and when needed, the proper references are cited.

The content is scientifically relevant and sound, investigating a hot topic in nuclear few-body physics, such as the structure and properties of light nuclei in the vicinity of the driplines.

I consider the paper can be published in its present form.

• validity: high
• significance: good
• originality: good
• clarity: top
• formatting: perfect
• grammar: perfect


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k-mer overrepresentation of WGS Illumina reads
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Entering edit mode
3.8 years ago
Anand Rao ▴ 360

I think I have obtained some weird k-mer patterns after Trimmomatic based trimming of adapters and trimming based on Quality Scores. I wonder if you forum members also consider this weird OR if it is not (much of) a problem at all. I'd like to know if you think that I may proceed with the next step of my analysis pipeline - Error Correction for singleton k-mers using ALLPATHS-LG. Additional info below, please read on:

INPUT FILE - http://imgur.com/a/qBKIg

Post-Trimmomatic FastQC report on k-mer overrepresentation - http://imgur.com/a/IMCa8 Trimmomatic Syntax:

java -jar trimmomatic-0.33.jar PE -threads 6 -phred33 -basein EthFoc-11.S285_L007.1.txt -baseout EthFoc-11_S285_L007_trimmomatic5 -trimlog EthFoc-11_trimmomatic5.log ILLUMINACLIP:TruSeq3-PE.fa:2:30:10:1:true LEADING:3 TRAILING:3

After Trimmomatic, there is k-mer over-representation as shown here. Because I thought this might go away if I clip away the first 10nt away, I performed another Trimmomatic run, this time with HEADCROP:10, so this truncates 10nt at 5' end irrespective of other downstream parameters in the syntax. Post-Trimmomatic FastQC report on k-mer overrepresentation - http://imgur.com/a/y7DVe Trimmomatic modified Syntax:

java -jar trimmomatic-0.33.jar PE -threads 6 -phred33 -basein EthFoc-11.S285_L007.1.txt -baseout EthFoc-11_S285_L007_trimmomatic6 -trimlog EthFoc-11_trimmomatic6.log ILLUMINACLIP:TruSeq3-PE.fa:2:30:10:1:true HEADCROP:10 LEADING:3 TRAILING:3 SLIDINGWINDOW:4:24 MINLEN:54

But this does not seem to fix anything, only makes it look worse than before. Am I not interpreting these FastQC results properly?

NEXTflex-96 DNA Barcodes from BiooScientific were used for multiplexing. The instrument used was HiSeq 4000 and the NGS library prep was using Kapa HyperPlus Library Preparation Kit. And my understanding is that the sequencing center had already de-multiplexed these Illlumina files that I am not working with.

Here are couple of links where such a problem is discussed on Biostars. How to remove kmer profiles? - but for RNASeq, so not directly relevant to my WGS samples fastqc: kmer-content failed - k-mer overrepresentation looks quite similar to mine - one source of this is listed to be random priming. Again, mine is not RNASeq sample, but WGS sample. Importantly, I think there is no random priming and no PCR step during Kapa HyperPlus Library Preparation. So I am puzzled WHY k-mers are overrepresented the way they are? In the second post linked above, I did notice how the scale is very different (18), but even in my analyses, first time log2(Obs/Exp) gets worse from ~5 to ~8...

Since I am new to NGS Illumina sequence QC, any & all advice, education, suggestions are welcome.

Adapter Trimming k-mer Trimmomatic FastQC • 1.5k views
0
Entering edit mode

If this is plain genome sequencing/re-sequencing you should not get hung up on k-mer over-representation. As long as you have assured yourself that the data is clean of adapters/extraneous sequence go on to the next step in analysis.


text:
# A10Riemannian Manifold Learning via Shearlet Approximation

## Analyzing Geometry by Applied Harmonic Analysis Methodologies

Applied harmonic analysis provides powerful methodologies to approximate geometric objects, which might be given as a Riemannian manifold itself or as an approximating point cloud. The main tools are specifically designed representation systems such as shearlets. These systems are of a multiscale type, thus an approximation process provides different resolution levels. One might ask: "Which resolution level allows detection of which geometric properties, such as curvature or torsion?" Project A10 aims to analyze such relations between approximations and learning of geometrical properties.

#### Mission-

Many processes in geometry and dynamics can be considered as time dependent systems. For instance, dynamic geometry studies elementary geometric constructions in which the base elements of a construction may be moved and the dependent elements move accordingly and consistently. Such a movement may be considered as a process in time. In physics there are also time-dependent processes. One may think of a planet orbiting around a sun or an arrangement of atoms moving under mutual forces. Both systems - moving geometric constructions and particle/force systems - suffer from the fundamental problem that singular situations, which occur at a specific moment in time, may prevent the system from being continued beyond this moment. For example, the orbit of a planet, directly heading into a sun, is stopped at the moment of the collision. The philosophy in research project B01 expands the concept of an ordinary linear time flow to a concept in two dimensions, where the time is represented by a variable over the complex numbers. Complex numbers are inherently two-dimensional objects, but in many aspects they behave like ordinary numbers. In particular all formulas governing geometric constructions or force/particle systems allow direct generalizations to complex numbers. Now, figuratively speaking, the two-dimensional nature of complex numbers allows us to bypass critical singular situations by so-called complex detours. At first, this seems to be a purely esoteric approach to geometry and physics. However, this approach, which is a central element in the research in B01, creates possibilities for new, more stable and consistent methods in dynamic geometry as well as for physics simulations.

#### Scientific Details+

This project deals with the study of complexified time in ordinary differential equations and other systems that continuously propagate in time. Structural aspects (underlying Riemann surfaces, monodromy, singularities) as well as algorithmic and simulation aspects (complexified integrators, problem of path jumping, discretization, path following, complexity estimates) will be addressed. One of the main aims of the project, is to apply complex detour approaches that have proved fruitful in the context of dynamic geometry to broader contexts including general straight-line and branching programs, numerical integration and the topology of Riemann surfaces. In particular we want to deal with singular situations (or nearly singular situations) by circumventing them in the complex plane rather than applying standard methods like decreasing the stepsize. Applied to numerical integration this kind of complex integrators also allows for a deeper study of the solution structure of a differential equation by providing information on the underlying Riemann surface. In synergy with the project C1 the project also aims for a general algorithmic framework that applies to the treatment of related problems.

One starting point of the project is the experience with complex detour techniques in the context of situations in dynamic geometry. Dynamic geometry deals with geometric configurations (defined by a collection of constraints or a geometric construction) and the modeling of consistent and continuous (i.e. constraint-stable) movements in their configuration space. A typical problem in this context arises if the configuration approaches a singular point of the configuration space, there an intrinsic ambiguity may cause unnatural behavior in the algorithmic simulation of such a configuration. The problem in this context can be completely resolved by embedding the original configuration into a ambient complex space and avoid the singularities by performing complex detours. Besides interesting theoretical insights in the structure of geometric configuration spaces these techniques allow for a satisfactory algorithmic treatment of such problems

One long term aim of the presented research project is to transfer as much as possible from this approach to the situation of ordinary differential equations. In the situation of ODEs one usually assumes a continuous and real propagation of time. Singular or nearly singular situations may make the numerical simulation of an ODE hard or even impossible (like a simulated particle that is moving directly towards the center of an attracting singular force field). Considering the time as a complex variable introduces new freedom that allows for a resolution of the singularity. Singular situations may by this be understood in a broader framework and for nearly singular situations more stable discretization schemes may be found by this approach. Although this approach seems natural and well motivated, there seems to be only few literature on this topic. Several fundamental difficulties arise that at first sight form fundamental obstacles in such a kind of approach. Resolving these difficulties will be a major research goal in this project. Here we list a few corner stones:

• Avoidance of path jumping: Typical numerical integrates for ODEs (like for instance Runge Kutta methods) involve many evaluations of the right side of the ODE y’(t) = f (g(t)). If the function f is allowed to branch then also the simulation method has to be adapted to this potential branching situation, otherwise path jumping of the solution may occur.
• Understanding monodromy: The complex interpretation of a singular situation may introduce new monodromy into the problem. This monodromy must be understood as part of the structure inherent to a specific ODE and the numerical simulation has to be adapted to the existence of this monodromy.
• Analyzing examples; algorithmic complexity: As soon as reliable algorithmic methods in the above sense are available we will investigate specific interesting examples. We also aim for intrinsic algorithmic bounds for these examples. The extraction of crucial examples that can serve as benchmarks for the developed methods is also of relevance.
• Structure preserving discretization: In particular (and in relation with project A1) we aim for the development for structure preserving or symplectic discretization techniques that still work well for ambient complex spaces of an ODE.

#### Publications+

##### Papers
###### Shearlet approximation of functions with discontinuous derivatives

Author: Petersen, Philipp
Note: preprint
Date: Aug 2015

###### Anisotropic multiscale systems on bounded domains

Authors: Grohs, P. and Kutyniok, G. and Ma, J. and Petersen, P.
Note: preprint
Date: 2015

###### Classification of edges using compactly supported shearlets

Authors: Kutyniok, Gitta and Petersen, Philipp
Journal: Applied and Computational Harmonic Analysis
Date: 2015
DOI: 10.1016/j.acha.2015.08.006

###### Linear independence of compactly supported separable shearlet systems

Authors: Ma, Jackie and Petersen, Philipp
Journal: Journal of Mathematical Analysis and Applications, 428:238-257
Date: 2015
DOI: 10.1016/j.jmaa.2015.03.001

###### $\alpha$-Molecules

Authors: Grohs, Philipp and Keiper, Sandra and Kutyniok, Gitta and Schäfer, Martin
Note: preprint
Date: Jul 2014

###### Regularization and Numerical Solution of the Inverse Scattering Problem using Shearlet Frames

Authors: Kutyniok, Gitta and Mehrmann, Volker and Petersen, Philipp
Note: preprint
Date: Jul 2014

###### Dualizable Shearlet Frames and Sparse Approximation

Authors: Kutyniok, Gitta and Lim, Wang-Q
Note: preprint
Date: 2014

###### ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets

Authors: Kutyniok, Gitta and Lim, Wang-Q and Reisenhofer, Rafael
Note: Preprint
Date: Jan 2014

###### Gabor Shearlets

Authors: Bodmann, Bernhard G. and Kutyniok, Gitta and Zhuang, Xiaosheng
Journal: Appl. Comput. Harmon. Anal.
Note: submitted
Date: Mar 2013

#### Jackie Ma   +

Projects: A10
University: TU Berlin
E-Mail: ma[at]math.tu-berlin.de

#### Philipp Petersen   +

Projects: A10
University: TU Berlin
E-Mail: petersen[at]math.tu-berlin.de


text:
# Self-Avoiding Walks and Connective Constants

• Geoffrey R. Grimmett
• Zhongyang Li
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 300)

## Abstract

The connective constant $$\mu (G)$$ of a quasi-transitive graph G is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on G from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph G.

• We present upper and lower bounds for $$\mu$$ in terms of the vertex-degree and girth of a transitive graph.

• We discuss the question of whether $$\mu \ge \phi$$ for transitive cubic graphs (where $$\phi$$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles).

• We present strict inequalities for the connective constants $$\mu (G)$$ of transitive graphs G, as G varies.

• As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator.

• We describe so-called graph height functions within an account of ‘bridges’ for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function.

• A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions.

• Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not.

• The review closes with a brief account of the ‘speed’ of SAW.

## Keywords

Self-avoiding walk Connective constant Regular graph Transitive graph Quasi-transitive graph Cubic graph Golden mean Fisher transformation Cayley graph Bridge constant Locality theorem Graph height function Unimodularity Speed

## Notes

### Acknowledgements

This work was supported in part by the Engineering and Physical Sciences Research Council under grant EP/I03372X/1. GRG acknowledges valuable conversations with Alexander Holroyd concerning Questions 7 and 10, and the hospitality of UC Berkeley during the completion of the work. ZL acknowledges support from the Simons Foundation under grant #351813, and the National Science Foundation under grant DMS-1608896.

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text:
# Mingling stat mech with quantum info in Maryland

I felt like a yoyo.

I was standing in a hallway at the University of Maryland. On one side stood quantum-information theorists. On the other side stood statistical-mechanics scientists.* The groups eyed each other, like Jets and Sharks in West Side Story, except without fighting or dancing.

This March, the groups were generous enough to host me for a visit. I parked first at QuICS, the Joint Center for Quantum Information and Computer Science. Established in October 2014, QuICS had moved into renovated offices the previous month. QuICSland boasts bright colors, sprawling armchairs, and the scent of novelty. So recently had QuICS arrived that the restroom had not acquired toilet paper (as I learned later than I’d have preferred).

Photo credit: QuICS

From QuICS, I yoyo-ed to the chemistry building, where Chris Jarzynski’s group studies fluctuation relations. Fluctuation relations, introduced elsewhere on this blog, describe out-of-equilibrium systems. A system is out of equilibrium if large-scale properties of it change. Many systems operate out of equilibrium—boiling soup, combustion engines, hurricanes, and living creatures, for instance. Physicists want to describe nonequilibrium processes but have trouble: Living creatures are complicated. Hence the buzz about fluctuation relations.

My first Friday in Maryland, I presented a seminar about quantum voting for QuICS. The next Tuesday, I was to present about one-shot information theory for stat-mech enthusiasts. Each week, the stat-mech crowd invites its speaker to lunch. Chris Jarzynski recommended I invite QuICS. Hence the Jets-and-Sharks tableau.

“Have you interacted before?” I asked the hallway.

“No,” said a voice. QuICS hadn’t existed till last fall, and some QuICSers hadn’t had offices till the previous month.**

Silence.

“We’re QuICS,” volunteered Stephen Jordan, a quantum-computation theorist, “the Joint Center for Quantum Information and Computer Science.”

So began the mingling. It continued at lunch, which we shared at three circular tables we’d dragged into a chain. The mingling continued during the seminar, as QuICSers sat with chemists, materials scientists, and control theorists. The mingling continued the next day, when QuICSer Alexey Gorshkov joined my discussion with the Jarzynski group. Back and forth we yoyo-ed, between buildings and topics.

“Mingled,” said Yigit Subasi. Yigit, a postdoc of Chris’s, specialized in quantum physics as a PhD student. I’d asked how he thinks about quantum fluctuation relations. Since Chris and colleagues ignited fluctuation-relation research, theorems have proliferated like vines in a jungle. Everyone and his aunty seems to have invented a fluctuation theorem. I canvassed Marylanders for bushwhacking tips.

Imagine, said Yigit, a system whose state you know. Imagine a gas, whose temperature you’ve measured, at equilibrium in a box. Or imagine a trapped ion. Begin with a state about which you have information.

Imagine performing work on the system “violently.” Compress the gas quickly, so the particles roil. Shine light on the ion. The system will leave equilibrium. “The information,” said Yigit, “gets mingled.”

Imagine halting the compression. Imagine switching off the light. Combine your information about the initial state with assumptions and physical laws.*** Manipulate equations in the right way, and the information might “unmingle.” You might capture properties of the violence in a fluctuation relation.

With Zhiyue Lu and Andrew Maven Smith of Chris Jarzynski’s group (left) and with QuICSers (right)

I’m grateful to have exchanged information in Maryland, to have yoyo-ed between groups. We have work to perform together. I have transformations to undergo.**** Let the unmingling begin.

With gratitude to Alexey Gorshkov and QuICS, and to Chris Jarzynski and the University of Maryland Department of Chemistry, for their hospitality, conversation, and camaraderie.

*Statistical mechanics is the study of systems that contain vast numbers of particles, like the air we breathe and white dwarf stars. I harp on about statistical mechanics often.

**Before QuICS’s birth, a future QuICSer had collaborated with a postdoc of Chris’s on combining quantum information with fluctuation relations.

***Yes, physical laws are assumptions. But they’re glorified assumptions.

****Hopefully nonviolent transformations.

# Paul Dirac and poetry

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite!

– Paul Dirac

Paul Dirac

I tacked Dirac’s quote onto the bulletin board above my desk, the summer before senior year of high school. I’d picked quotes by T.S. Elliot and Einstein, Catullus and Hatshepsut.* In a closet, I’d found amber-, peach-, and scarlet-colored paper. I’d printed the quotes and arranged them, starting senior year with inspiration that looked like a sunrise.

Not that I knew who Paul Dirac was. Nor did I evaluate his opinion. But I’d enrolled in Advanced Placement Physics C and taken the helm of my school’s literary magazine. The confluence of two passions of mine—science and literature—in Dirac’s quote tickled me.

A fiery lecturer began to alleviate my ignorance in college. Dirac, I learned, had co-invented quantum theory. The “Dee-rac Equa-shun,” my lecturer trilled in her Italian accent, describes relativistic quantum systems—tiny particles associated with high speeds. I developed a taste for spin, a quantum phenomenon encoded in Dirac’s equation. Spin serves quantum-information scientists as two-by-fours serve carpenters: Experimentalists have tried to build quantum computers from particles that have spins. Theorists keep the idea of electron spins in a mental car trunk, to tote out when illustrating abstract ideas with examples.

The next year, I learned that Dirac had predicted the existence of antimatter. Three years later, I learned to represent antimatter mathematically. I memorized the Dirac Equation, forgot it, and re-learned it.

One summer in grad school, visiting my parents, I glanced at my bulletin board.

The sun rises beyond a window across the room from the board. Had the light faded the papers’ colors? If so, I couldn’t tell.

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in the case of poetry, it’s the exact opposite!

Do poets try to obscure ideas everyone understands? Some poets express ideas that people intuit but feel unable, lack the attention, or don’t realize one should, articulate. Reading and hearing poetry helps me grasp the ideas. Some poets express ideas in forms that others haven’t imagined.

Did Dirac not represent physics in a form that others hadn’t imagined?

The Dirac Equation

Would you have imagined that form? I didn’t imagine it until learning it. Do scientists not express ideas—about gravity, time, energy, and matter—that people feel unable, lack the attention, or don’t realize we should, articulate?

The U.S. and Canada have designated April as National Poetry Month. A hub for cousins of poets, Quantum Frontiers salutes. Carry a poem in your pocket this month. Or carry a copy of the Dirac Equation. Or tack either on a bulletin board; I doubt whether their colors will fade.

*“Now my heart turns this way and that, as I think what the people will say. Those who see my monuments in years to come, and who shall speak of what I have done.” I expect to build no such monuments. But here’s to trying.

# Putting back the pieces of a broken hologram

It is Monday afternoon and the day seems to be a productive one, if not yet quite memorable. As I revise some notes on my desk, Beni Yoshida walks into my office to remind me that the high-energy physics seminar is about to start. I hesitate, somewhat apprehensive of the near-certain frustration of being lost during the first few minutes of a talk in an unfamiliar field. I normally avoid such a situation, but in my email I find John’s forecast for an accessible talk by Daniel Harlow and a title with three words I can cling onto. “Quantum error correction” has driven my curiosity for the last seven years. The remaining acronyms in the title will become much more familiar in the four months to come.

Most of you are probably familiar with holograms, these shiny flat films representing a 3D object from essentially any desired angle. I find it quite remarkable how all the information of a 3D object can be printed on an essentially 2D film. True, the colors are not represented as faithfully as in a traditional photograph, but it looks as though we have taken a photograph from every possible angle! The speaker’s main message that day seemed even more provocative than the idea of holography itself. Even if the hologram is broken into pieces, and some of these are lost, we may still use the remaining pieces to recover parts of the 3D image or even the full thing given a sufficiently large portion of the hologram. The 3D object is not only recorded in 2D, it is recorded redundantly!

Left to right: Beni Yoshida, Aleksander Kubica, Aidan Chatwin-Davies and Fernando Pastawski discussing holographic codes.

Half way through Daniel’s exposition, Beni and I exchange a knowing glance. We recognize a familiar pattern from our latest project. A pattern which has gained the moniker of “cleaning lemma” within the quantum information community which can be thought of as a quantitative analog of reconstructing the 3D image from pieces of the hologram. Daniel makes connections using a language that we are familiar with. Beni and I discuss what we have understood and how to make it more concrete as we stride back through campus. We scribble diagrams on the whiteboard and string words such as tensor, encoder, MERA and negative curvature into our discussion. An image from the web gives us some intuition on the latter. We are onto something. We have a model. It is simple. It is new. It is exciting.

Poincare projection of a regular pentagon tiling of negatively curved space.

Food has not come our way so we head to my apartment as we enthusiastically continue our discussion. I can only provide two avocados and some leftover pasta but that is not important, we are sharing the joy of insight. We arrange a meeting with Daniel to present our progress. By Wednesday Beni and I introduce the holographic pentagon code at the group meeting. A core for a new project is already there, but we need some help to navigate the high-energy waters. Who better to guide us in such an endeavor than our mentor, John Preskill, who recognized the importance of quantum information in Holography as early as 1999 and has repeatedly proven himself a master of both trades.

“I feel that the idea of holography has a strong whiff of entanglement—for we have seen that in a profoundly entangled state the amount of information stored locally in the microscopic degrees of freedom can be far less than we would naively expect. For example, in the case of the quantum error-correcting codes, the encoded information may occupy a small ‘global’ subspace of a much larger Hilbert space. Similarly, the distinct topological phases of a fractional quantum Hall system look alike locally in the bulk, but have distinguishable edge states at the boundary.”
-J. Preskill, 1999

As Beni puts it, the time for using modern quantum information tools in high-energy physics has come. By this he means quantum error correction and maybe tensor networks. First privately, then more openly, we continue to sharpen and shape our project. Through conferences, Skype calls and emails, we further our discussion and progressively shape ideas. Many speculations mature to conjectures and fall victim to counterexamples. Some stand the test of simulations or are even promoted to theorems by virtue of mathematical proofs.

Beni Yoshida presenting our work at a quantum entanglement conference in Puerto Rico.

I publicly present the project for the first time at a select quantum information conference in Australia. Two months later, after a particularly intense writing, revising and editing process, the article is almost complete. As we finalize the text and relabel the figures, Daniel and Beni unveil our work to quantum entanglement experts in Puerto Rico. The talks are a hit and it is time to let all our peers read about it.

You are invited to do so and Beni will even be serving a reader’s guide in an upcoming post.

# Quantum Frontiers salutes Terry Pratchett.

I blame British novels for my love of physics. Philip Pullman introduced me to elementary particles; Jasper Fforde, to the possibility that multiple worlds exist; Diana Wynne Jones, to questions about space and time.

So began the personal statement in my application to Caltech’s PhD program. I didn’t mention Sir Terry Pratchett, but he belongs in the list. Pratchett wrote over 70 books, blending science fiction with fantasy, humor, and truths about humankind. Pratchett passed away last week, having completed several novels after doctors diagnosed him with early-onset Alzheimer’s. According to the San Francisco Chronicle, Pratchett “parodie[d] everything in sight.” Everything in sight included physics.

Terry Pratchett continues to influence my trajectory through physics: This cover has a cameo in a seminar I’m presenting in Maryland this March.

Pratchett set many novels on the Discworld, a pancake of a land perched atop four elephants, which balance on the shell of a turtle that swims through space. Discworld wizards quantify magic in units called thaums. Units impressed their importance upon me in week one of my first high-school physics class. We define one meter as “the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.” Wizards define one thaum as “the amount of magic needed to create one small white pigeon or three normal-sized billiard balls.”

Wizards study the thaum in a High-Energy Magic Building reminiscent of Caltech’s Lauritsen-Downs Building. To split the thaum, the wizards built a Thaumatic Resonator. Particle physicists in our world have split atoms into constituent particles called mesons and baryons. Discworld wizards discovered that the thaum consists of resons. Mesons and baryons consist of quarks, seemingly elementary particles that we believe cannot be split. Quarks fall into six types, called flavors: up, down, charmed, strange, top (or truth), and bottom (or beauty). Resons, too, consist of quarks. The Discworld’s quarks have the flavors up, down, sideways, sex appeal, and peppermint.

Reading about the Discworld since high school, I’ve wanted to grasp Pratchett’s allusions. I’ve wanted to do more than laugh at them. In Pyramids, Pratchett describes “ideas that would make even a quantum mechanic give in and hand back his toolbox.” Pratchett’s ideas have given me a hankering for that toolbox. Pratchett nudged me toward training as a quantum mechanic.

Pratchett hasn’t only piqued my curiosity about his allusions. He’s piqued my desire to create as he did, to do physics as he wrote. While reading or writing, we build worlds in our imaginations. We visualize settings; we grow acquainted with characters; we sense a plot’s consistency or the consistency of a system of magic. We build worlds in our imaginations also when doing and studying physics and math. The Standard Model is a system that encapsulates the consistency of our knowledge about particles. We tell stories about electrons’ behaviors in magnetic fields. Theorems’ proofs have logical structures like plots’. Pratchett and other authors trained me to build worlds in my imagination. Little wonder I’m training to build worlds as a physicist.

Around the time I graduated from college, Diana Wynne Jones passed away. So did Brian Jacques (another British novelist) and Madeleine L’Engle. L’Engle wasn’t British, but I forgave her because her Time Quartet introduced me to dimensions beyond three. As I completed one stage of intellectual growth, creators who’d led me there left.

Terry Pratchett has joined Jones, Jacques, and L’Engle. I will probably create nothing as valuable as his Discworld, let alone a character in the Standard Model toward which the Discworld steered me.

But, because of Terry Pratchett, I have to try.

# Always look on the bright side…of CPTP maps.

Once upon a time, I worked with a postdoc who shaped my views of mathematical physics, research, and life. Each week, I’d email him a PDF of the calculations and insights I’d accrued. He’d respond along the lines of, “Thanks so much for your notes. They look great! I think they’re mostly correct; there are just a few details that might need fixing.” My postdoc would point out the “details” over espresso, at a café table by a window. “Are you familiar with…?” he’d begin, and pull out of his back pocket some bit of math I’d never heard of. My calculations appeared to crumble like biscotti.

Some of the math involved CPTP maps. “CPTP” stands for a phrase little more enlightening than the acronym: “completely positive trace-preserving”. CPTP maps represent processes undergone by quantum systems. Imagine preparing some system—an electron, a photon, a superconductor, etc.—in a state I’ll call “$\rho$“. Imagine turning on a magnetic field, or coupling one electron to another, or letting the superconductor sit untouched. A CPTP map, labeled as $\mathcal{E}$, represents every such evolution.

“Trace-preserving” means the following: Imagine that, instead of switching on the magnetic field, you measured some property of $\rho$. If your measurement device (your photodetector, spectrometer, etc.) worked perfectly, you’d read out one of several possible numbers. Let $p_i$ denote the probability that you read out the $i^{\rm{th}}$ possible number. Because your device outputs some number, the probabilities sum to one: $\sum_i p_i = 1$.  We say that $\rho$ “has trace one.” But you don’t measure $\rho$; you switch on the magnetic field. $\rho$ undergoes the process $\mathcal{E}$, becoming a quantum state $\mathcal{E(\rho)}$. Imagine that, after the process ended, you measured a property of $\mathcal{E(\rho)}$. If your measurement device worked perfectly, you’d read out one of several possible numbers. Let $q_a$ denote the probability that you read out the $a^{\rm{th}}$ possible number. The probabilities sum to one: $\sum_a q_a =1$. $\mathcal{E(\rho)}$ “has trace one”, so the map $\mathcal{E}$ is “trace preserving”.

Now that we understand trace preservation, we can understand positivity. The probabilities $p_i$ are positive (actually, nonnegative) because they lie between zero and one. Since the $p_i$ characterize a crucial aspect of $\rho$, we call $\rho$ “positive” (though we should call $\rho$ “nonnegative”). $\mathcal{E}$ turns the positive $\rho$ into the positive $\mathcal{E(\rho)}$. Since $\mathcal{E}$ maps positive objects to positive objects, we call $\mathcal{E}$ “positive”. $\mathcal{E}$ also satisfies a stronger condition, so we call such maps “completely positive.”**

So I called my postdoc. “It’s almost right,” he’d repeat, nudging aside his espresso and pulling out a pencil. We’d patch the holes in my calculations. We might rewrite my conclusions, strengthen my assumptions, or prove another lemma. Always, we salvaged cargo. Always, I learned.

I no longer email weekly updates to a postdoc. But I apply what I learned at that café table, about entanglement and monotones and complete positivity. “It’s almost right,” I tell myself when a hole yawns in my calculations and a week’s work appears to fly out the window. “I have to fix a few details.”

Am I certain? No. But I remain positive.

*Experts: “Trace-preserving” means $\rm{Tr}(\rho) =1 \Rightarrow \rm{Tr}(\mathcal{E}(\rho)) = 1$.

**Experts: Suppose that ρ is defined on a Hilbert space  and that  is defined on . “ is positive” means

To understand what “completely positive” means, imagine that our quantum system interacts with an environment. For example, suppose the system consists of photons in a box. If the box leaks, the photons interact with the electromagnetic field outside the box. Suppose the system-and-environment composite begins in a state  defined on a Hilbert space .  acts on the system’s part of state. Let  denote the identity operation that maps every possible environment state to itself. Suppose that  changes the system’s state while  preserves the environment’s state. The system-and-environment composite ends up in the state . This state is positive, so we call  “completely positive”:

# Celebrating Theoretical Physics at Caltech’s Burke Institute

Editor’s Note: Yesterday and today, Caltech is celebrating the inauguration of the Walter Burke Institute for Theoretical Physics. John Preskill made the following remarks at a dinner last night honoring the board of the Sherman Fairchild Foundation.

This is an exciting night for me and all of us at Caltech. Tonight we celebrate physics. Especially theoretical physics. And in particular the Walter Burke Institute for Theoretical Physics.

Some of our dinner guests are theoretical physicists. Why do we do what we do?

I don’t have to convince this crowd that physics has a profound impact on society. You all know that. We’re celebrating this year the 100th anniversary of general relativity, which transformed how we think about space and time. It may be less well known that two years later Einstein laid the foundations of laser science. Einstein was a genius for sure, but I don’t think he envisioned in 1917 that we would use his discoveries to play movies in our houses, or print documents, or repair our vision. Or see an awesome light show at Disneyland.

And where did this phone in my pocket come from? Well, the story of the integrated circuit is fascinating, prominently involving Sherman Fairchild, and other good friends of Caltech like Arnold Beckman and Gordon Moore. But when you dig a little deeper, at the heart of the story are two theorists, Bill Shockley and John Bardeen, with an exceptionally clear understanding of how electrons move through semiconductors. Which led to transistors, and integrated circuits, and this phone. And we all know it doesn’t stop here. When the computers take over the world, you’ll know who to blame.

Incidentally, while Shockley was a Caltech grad (BS class of 1932), John Bardeen, one of the great theoretical physicists of the 20th century, grew up in Wisconsin and studied physics and electrical engineering at the University of Wisconsin at Madison. I suppose that in the 1920s Wisconsin had no pressing need for physicists, but think of the return on the investment the state of Wisconsin made in the education of John Bardeen.1

So, physics is a great investment, of incalculable value to society. But … that’s not why I do it. I suppose few physicists choose to do physics for that reason. So why do we do it? Yes, we like it, we’re good at it, but there is a stronger pull than just that. We honestly think there is no more engaging intellectual adventure than struggling to understand Nature at the deepest level. This requires attitude. Maybe you’ve heard that theoretical physicists have a reputation for arrogance. Okay, it’s true, we are arrogant, we have to be. But it is not that we overestimate our own prowess, our ability to understand the world. In fact, the opposite is often true. Physics works, it’s successful, and this often surprises us; we wind up being shocked again and again by “unreasonable effectiveness of mathematics in the natural sciences.” It’s hard to believe that the equations you write down on a piece of paper can really describe the world. But they do.

And to display my own arrogance, I’ll tell you more about myself. This occasion has given me cause to reflect on my own 30+ years on the Caltech faculty, and what I’ve learned about doing theoretical physics successfully. And I’ll tell you just three principles, which have been important for me, and may be relevant to the future of the Burke Institute. I’m not saying these are universal principles – we’re all different and we all contribute in different ways, but these are principles that have been important for me.

My first principle is: We learn by teaching.

Why do physics at universities, at institutions of higher learning? Well, not all great physics is done at universities. Excellent physics is done at industrial laboratories and at our national laboratories. But the great engine of discovery in the physical sciences is still our universities, and US universities like Caltech in particular. Granted, US preeminence in science is not what it once was — it is a great national asset to be cherished and protected — but world changing discoveries are still flowing from Caltech and other great universities.

Why? Well, when I contemplate my own career, I realize I could never have accomplished what I have as a research scientist if I were not also a teacher. And it’s not just because the students and postdocs have all the great ideas. No, it’s more interesting than that. Most of what I know about physics, most of what I really understand, I learned by teaching it to others. When I first came to Caltech 30 years ago I taught advanced elementary particle physics, and I’m still reaping the return from what I learned those first few years. Later I got interested in black holes, and most of what I know about that I learned by teaching general relativity at Caltech. And when I became interested in quantum computing, a really new subject for me, I learned all about it by teaching it.2

Part of what makes teaching so valuable for the teacher is that we’re forced to simplify, to strip down a field of knowledge to what is really indispensable, a tremendously useful exercise. Feynman liked to say that if you really understand something you should be able to explain it in a lecture for the freshman. Okay, he meant the Caltech freshman. They’re smart, but they don’t know all the sophisticated tools we use in our everyday work. Whether you can explain the core idea without all the peripheral technical machinery is a great test of understanding.

And of course it’s not just the teachers, but also the students and the postdocs who benefit from the teaching. They learn things faster than we do and often we’re just providing some gentle steering; the effect is to amplify greatly what we could do on our own. All the more so when they leave Caltech and go elsewhere to change the world, as they so often do, like those who are returning tonight for this Symposium. We’re proud of you!

My second principle is: The two-trick pony has a leg up.

I’m a firm believer that advances are often made when different ideas collide and a synthesis occurs. I learned this early, when as a student I was fascinated by two topics in physics, elementary particles and cosmology. Nowadays everyone recognizes that particle physics and cosmology are closely related, because when the universe was very young it was also very hot, and particles were colliding at very high energies. But back in the 1970s, the connection was less widely appreciated. By knowing something about cosmology and about particle physics, by being a two-trick pony, I was able to think through what happens as the universe cools, which turned out to be my ticket to becoming a Caltech professor.

It takes a community to produce two-trick ponies. I learned cosmology from one set of colleagues and particle physics from another set of colleagues. I didn’t know either subject as well as the real experts. But I was a two-trick pony, so I had a leg up. I’ve tried to be a two-trick pony ever since.

Another great example of a two-trick pony is my Caltech colleague Alexei Kitaev. Alexei studied condensed matter physics, but he also became intensely interested in computer science, and learned all about that. Back in the 1990s, perhaps no one else in the world combined so deep an understanding of both condensed matter physics and computer science, and that led Alexei to many novel insights. Perhaps most remarkably, he connected ideas about error-correcting code, which protect information from damage, with ideas about novel quantum phases of matter, leading to radical new suggestions about how to operate a quantum computer using exotic particles we call anyons. These ideas had an invigorating impact on experimental physics and may someday have a transformative effect on technology. (We don’t know that yet; it’s still way too early to tell.) Alexei could produce an idea like that because he was a two-trick pony.3

Which brings me to my third principle: Nature is subtle.

Yes, mathematics is unreasonably effective. Yes, we can succeed at formulating laws of Nature with amazing explanatory power. But it’s a struggle. Nature does not give up her secrets so readily. Things are often different than they seem on the surface, and we’re easily fooled. Nature is subtle.4

Perhaps there is no greater illustration of Nature’s subtlety than what we call the holographic principle. This principle says that, in a sense, all the information that is stored in this room, or any room, is really encoded entirely and with perfect accuracy on the boundary of the room, on its walls, ceiling and floor. Things just don’t seem that way, and if we underestimate the subtlety of Nature we’ll conclude that it can’t possibly be true. But unless our current ideas about the quantum theory of gravity are on the wrong track, it really is true. It’s just that the holographic encoding of information on the boundary of the room is extremely complex and we don’t really understand in detail how to decode it. At least not yet.

This holographic principle, arguably the deepest idea about physics to emerge in my lifetime, is still mysterious. How can we make progress toward understanding it well enough to explain it to freshmen? Well, I think we need more two-trick ponies. Except maybe in this case we’ll need ponies who can do three tricks or even more. Explaining how spacetime might emerge from some more fundamental notion is one of the hardest problems we face in physics, and it’s not going to yield easily. We’ll need to combine ideas from gravitational physics, information science, and condensed matter physics to make real progress, and maybe completely new ideas as well. Some of our former Sherman Fairchild Prize Fellows are leading the way at bringing these ideas together, people like Guifre Vidal, who is here tonight, and Patrick Hayden, who very much wanted to be here.5 We’re very proud of what they and others have accomplished.

Bringing ideas together is what the Walter Burke Institute for Theoretical Physics is all about. I’m not talking about only the holographic principle, which is just one example, but all the great challenges of theoretical physics, which will require ingenuity and synthesis of great ideas if we hope to make real progress. We need a community of people coming from different backgrounds, with enough intellectual common ground to produce a new generation of two-trick ponies.

Finally, it seems to me that an occasion as important as the inauguration of the Burke Institute should be celebrated in verse. And so …

Who studies spacetime stress and strain
And excitations on a brane,
Where particles go back in time,
And physicists engage in rhyme?

Whose speedy code blows up a star
(Though it won’t quite blow up so far),
Where anyons, which braid and roam
Annihilate when they get home?

Who makes math and physics blend
Inside black holes where time may end?
Where do they do all this work?
The Institute of Walter Burke!

We’re very grateful to the Burke family and to the Sherman Fairchild Foundation. And we’re confident that your generosity will make great things happen!

1. I was reminded of this when I read about a recent proposal by the current governor of Wisconsin.
2. And by the way, I put my lecture notes online, and thousands of people still download them and read them. So even before MOOCs – massive open online courses – the Internet was greatly expanding the impact of our teaching. Handwritten versions of my old particle theory and relativity notes are also online here
3. Okay, I admit it’s not quite that simple. At that same time I was also very interested in both error correction and in anyons, without imagining any connection between the two. It helps to be a genius. But a genius who is also a two-trick pony can be especially awesome.
4. We made that the tagline of IQIM.
5. Patrick can’t be here for a happy reason, because today he and his wife Mary Race welcomed a new baby girl, Caroline Eleanor Hayden, their first child. The Burke Institute is not the only good thing being inaugurated today.

# Democrat plus Republican over the square-root of two

I wish I could superpose votes on Election Day.

However much I agree with Candidate A about social issues, I dislike his running mate. I lean toward Candidate B’s economic plans and C’s science-funding record, but nobody’s foreign policy impresses me. Must I settle on one candidate? May I not vote

Now you can—at least in theory. Caltech postdoc Ning Bao and I concocted quantum elections in which voters can superpose, entangle, and create probabilistic mixtures of votes.

Previous quantum-voting work has focused on privacy and cryptography. Ning and I channeled quantum game theory. Quantum game theorists ask what happens if players in classical games, such as the Prisoner’s Dilemma, could superpose strategies and share entanglement. Quantization can change the landscape of possible outcomes.

The Prisoner’s Dilemma, for example, concerns two thugs whom the police have arrested and have isolated in separate cells. Each prisoner must decide whether to rat out the other. How much time each serves depends on who, if anyone, confesses. Since neither prisoner knows the other’s decision, each should rat to minimize his or her jail time. But both would serve less time if neither confessed. The prisoners can escape this dilemma using quantum resources.

Introducing superpositions and entanglement into games helps us understand the power of quantum mechanics. Elections involve gameplay; pundits have been feeding off Hilary Clinton’s for months. So superpositions and entanglement merit introduction into elections.

How can you model elections with quantum systems? Though multiple options exist, Ning and I followed two principles: (1) A general quantum process—a preparation procedure, an evolution, and a measurement—should model a quantum election. (2) Quantum elections should remain as true as possible to classical.

Given our quantum voting system, one can violate a quantum analogue of Arrow’s Impossibility Theorem. Arrow’s Theorem, developed by the Nobel-winning economist Kenneth Arrow during the mid-20th century, is a no-go theorem about elections: If a constitution has three innocuous-seeming properties, it’s a dictatorship. Ning and I translated the theorem as faithfully as we knew how into our quantum voting scheme. The result, dubbed the Quantum Arrow Conjecture, rang false.

Superposing (and probabilistically mixing) votes entices me for a reason that science does: I feel ignorant. I read articles and interview political junkies about national defense; but I miss out on evidence and subtleties. I read quantum-physics books and work through papers; but I miss out on known mathematical tools and physical interpretations. Not to mention tools and interpretations that humans haven’t discovered.

Science involves identifying (and diminishing) what humanity doesn’t know. Science frees me to acknowledge my ignorance. I can’t throw all my weight behind Candidate A’s defense policy because I haven’t weighed all the arguments about defense, because I don’t know all the arguments. Believing that I do would violate my job description. How could I not vote for elections that accommodate superpositions?

Though Ning and I identified applications of superpositions and entanglement, more quantum strategies might await discovery. Monogamy of entanglement, discussed elsewhere on this blog, might limit the influence voters exert on each other. Also, we quantized ordinal voting systems (in which each voter ranks candidates, as in “A above C above B”). The quantization of cardinal voting (in which each voter grades the candidates, as in “5 points to A, 3 points to C, 2 points to B”) or another voting scheme might yield more insights.

If you have such insights, drop us a line. Ideally before the presidential smack-down of 2016.