A Pandemic puzzle to placate the pandemonium

Hey folks,

Here’s a fun puzzle to turn fear of a pandemic into an opportunity to generate some interesting mathematical intuition.

Suppose I have an NxN grid and I can infect k squares of the grid. After some time interval, t, all uninfected squares that share two edges with infected squares become infected. All infected squares remain infected. We continue to advance time, in intervals of t, until the infection is no longer spreading. What is the minimum number, k, for which the whole grid gets infected? See below for a pictorial example.

And this would continue until all the squares are infected.

NSF GRFP Awards!

Congrats to all the winners of the NSF GRFP!

From our group, Albert Chen won an award and Ben Lyo and Adam Kline each received an Honorable Mention. Excited for all the great things y’all are gonna do!

What have we been up to?

The past month or so has been quite eventful! I’ll break up the posts over the next few days, but at a social level, some of our lab participated in the Cider Century Bike Ride in Michigan in late September. Other members have attended a workshop in Toronto and other members still recently presented work at Neuroscience 2019 in Chicago! Check out some photos from Toronto and Chicago.

A picture of the Toronto backdrop while these three (Ben Hoshal, Stephanie Palmer, and Albert Chen from left to right) enjoy the Mathematics of Vision Workshop
An occluded picture of a poster about occlusion, as presented by Albert Chen and Jennifer Ding
This was supposed to be a picture of Jen but instead, please enjoy the back of this gentleman’s head. Also, Jen promised not to get mad at me for this.
Bing Liu, Stephanie Palmer, and Neha Lingareddy from left to right in front of Neha’s poster on models of efficient coding.
He’s back! Jared Salisbury presenting his work at Neuro 2019.
Me, letting my hands do more of the talking than my voice. It’s an odd habit but it’s mine.

A new take on an old birthday puzzle

Hi folks,

To celebrate the birthday of Finley (and me), I’ve put together a little math puzzle for you to enjoy.

Congrats! You’re hired. Here at PretendPalmerLab Inc., we expect you are available every day of the calendar year, with February 29th a mandatory day off. We take no vacations except when celebrating the birthdays of our lab members, in which case, we all take the full day off. This is to say, we’re all expected to be at work each day unless one person in the lab has their birthday on that day.

Stephanie’s first project for you is a simple one: determine the maximal number of people she can hire before encountering a loss in productivity. She measures productivity in terms of total number of person days (ie the number of people in the lab times the number of days per year they work) per year.

There’s a first author publication if you complete this so snap to it!

Two Upcoming Workshops!

Hi folks,

I just wanted to take a moment to advertise two upcoming workshops that the Palmer group is extremely excited about.

Mind Bytes Research Computing Expo: Taking place on November 5th of 2019, Mind Bytes is a unique opportunity to explore the use of high-end computational resources to push forth the state-of-the-art in the fields. This year’s theme is “Data Science: The Complexity of Connections”. If you’re interested in presenting, listening, or just getting a chance to be at the University of Chicago, come check it out! https://mindbytes.uchicago.edu/

Mathematics of Vision Workshop: The Fields Institute at the University of Toronto is hosting a workshop on October 17th-18th to explore vision science. The workshop intends to explore broad themes in neuroscience and artificial intelligence, such as the biophysics of vision, information theoretic approaches to understanding encoding schemes, and machine learning in modeling of vision, just to name a few. If interested, check it out! Plus, I hear Toronto’s got a great restaurant scene. http://www.fields.utoronto.ca/activities/19-20/vision

A Farewell to the First Graduate Student

After ~6 years of graduate work and ~2 years of postdoctoral scholar work, Jared Salisbury has officially concluded his time with the Palmer lab. He was the first graduate student to join the Palmer lab and was engaged in a number of projects that laid the foundation for his own scientific career as well as many who will come after him. Jared was involved in projects studying predictive coding in the retina (part of which involved experiments in Paris) and was a part of the establishment of the natural motion database. We wish Jared good luck in his coming endeavors!

Dr. Jared Salisbury all dressed up in his graduation regalia

Junior High students develop neuroprosthetics!

Amy Farkas, a middle school teacher out of Riverview, Michigan, recently collaborated with Backyard Brains to teach her students neuroscience and prepare them to pursue a lofty goal: designing neuroprosthetics for senior citizens with limited mobility. Using designs inspired by The Claw, the students built devices that aid in opening bottles, brushing teeth, and turning book pages just to list a few examples. For more information, see the following link.

Congratulations to Vaughn!

Vaughn Spurrier successfully defended his thesis, entitled ‘Motion Tunings to Drifting Gratings and Water Flow’, today! We wish him luck in his future endeavor. He’ll be starting full time work at Tempus later this month.

Until then, please enjoy these pictures of Vaughn at his defense and his post-thesis party.

Comparison between Vaughn at his Thesis Defense and Vaughn in his days at Temple University
Vaughn using his charisma to entertain a crowd while he struggles to open a champagne bottle
Dr. Stephanie Palmer, Dr. Jason MacLean, and Dr. Vaughn Spurrier enjoying a glass of celebratory champagne

Puzzle 08/06/19

Sorry for the delay!

First, a new puzzle.

Can you construct a 9 digit number using the digits 1-9 such that the first k digits are divisible by k? There is only one such number. For example, if I was trying to do this with a 2 digit number using the digits 1-2, 12 would be a solution, as 1 is divisible by 1, and 12 is divisible by 2.

For an added challenge, try this in different bases.

Second, the solution to last week’s puzzle. If you said the answer was probability 1/2, you’d be correct! A simple approach to the solution is to consider the following:

There are three possible cases – one in which Finley sits in his own seat, another in which Finley sits in the last guest’s seat, and another in which Finley sits in someone else’s seat. In the first two cases, the contribution to the last guest’s ability to sit in their seat is trivial, but in the third case, the problem becomes recursive, as the next guest to sit (who can no longer choose their own seat), is faced with a similar (but slightly different) three cases: the first is where this guest occupies a seat which should have been occupied by one of the preceding guests, another in which they occupy the last guest’s seat, and the last in which they occupy someone else’s seat. One can quickly see this is effectively a question of whether or not Finley’s seat is occupied before the last guest’s seat. The guest who takes one of those two seats is unbiased, so they do so with 1/2 probability. For the full mathematical detail of how one could derive this solution, check out: www.cut-the-knot.org/Probability/LostPass.shtml