Category: Bookmark

🔖 Collaborative Workshop for Women in Mathematical Biology | IPAM

Bookmarked Collaborative Workshop for Women in Mathematical Biology (IPAM)

June 17-21, 2019

This workshop will tackle a variety of biological and medical questions using mathematical models to understand complex system dynamics. Working in collaborative teams of 6, each with a senior research mentor, participants will spend a week making significant progress with a research project and foster innovation in the application of mathematical, statistical, and computational methods in the resolution of problems in the biosciences. By matching senior research mentors with junior mathematicians, the workshop will expand and support the community of scholars in mathematical biosciences. In addition to the modeling goals, an aim of this workshop is to foster research collaboration among women in mathematical biology. Results from the workshop will be published in a peer-reviewed volume, highlighting the contributions of the newly-formed groups. Previous workshops in this series have occurred at IMA, NIMBioS, and MBI.

This workshop will have a special format designed to facilitate effective collaborations.

  • Each senior group leader will present a problem and lead a research group.
  • Group leaders will work with a more junior co-leader, someone with whom they do not have a long-standing collaboration, but who has enough experience to take on a leadership role.
  • Additional team members will be chosen from applicants and invitees. We anticipate a total of five or six people per group.

It is expected that each group will continue to work on their project together after the workshop, and that they will submit results to the Proceedings volume for the workshop.

The benefit of such a structured program with leaders, projects and working groups planned in advance is based on the successful WIN, Women In Numbers, conferences and is intended to provide vertically integrated mentoring: senior women will meet, mentor, and collaborate with the brightest young women in their field on a part of their research agenda of their choosing, and junior women and graduate students will develop their network of colleagues and supporters and encounter important new research areas to work in, thereby fostering a successful research career. This workshop is partially supported by NSF-HRD 1500481 – AWM ADVANCE grant.

ORGANIZING COMMITTEE

Rebecca Segal (Virginia Commonwealth University)
Blerta Shtylla (Pomona College)
Suzanne Sindi (University of California, Merced)

🔖 Sans Forgetica | RMIT

Bookmarked Sans Forgetica (sansforgetica.rmit)
Sans Forgetica is a typeface designed using the principles of cognitive psychology to help you to better remember your study notes. It was created by a multidisciplinary team of designers and behavioural scientists from RMIT University. Sans Forgetica is compatible with both PC and Mac operating systems. Download it for free today, or keep scrolling to learn more about how it was made.

🔖 Sierpinski number | Wikipedia

Bookmarked Sierpiński number (Wikipedia)
In number theory, a Sierpinski or Sierpiński number is an odd natural number k such that {\displaystyle k\times 2^{n}+1} is composite, for all natural numbers n. In 1960, Wacław Sierpiński proved that there are infinitely many odd integers k which have this property. In other words, when k is a Sierpiński number, all members of the following set are composite:
{\displaystyle \left\{\,k\cdot {}2^{n}+1:n\in \mathbb {N} \,\right\}.}

👓 Introducing Trashy.css | CSS Tricks

Read Introducing Trashy.css by Nathan Smith (CSS-Tricks)
It began, as many things do, with a silly conversation. In this case, I was talking with our Front End Technology Competency Director (aka "boss man")
I can’t wait to try this out on some sites. I love that it’s got a browser bookmarklet that will let one test out other sites too.

🔖 Sylvester’s Line Problem | Wolfram MathWorld

Read Sylvester's Line Problem (Wolfram MathWorld)

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through every two of them passes through a third unless they are all on a single line. This problem was proposed by Sylvester (1893), who asked readers to "Prove that it is not possible to arrange any finite number of real points so that a right line through every two of them shall pass through a third, unless they all lie in the same right line."

Woodall (1893) published a four-line "solution," but an editorial comment following his result pointed out two holes in the argument and sketched another line of enquiry, which is characterized as "equally incomplete, but may be worth notice." However, no correct proof was published at the time (Croft et al. 1991, p. 159), but the problem was revived by Erdős (1943) and correctly solved by Grünwald (1944). Coxeter (1948, 1969) transformed the problem into an elementary form, and a very short proof using the notion of Euclidean distance was given by Kelly (Coxeter 1948, 1969; Chvátal 2004). The theorem also follows using projective duality from a result of Melchior (1940) proved by a simple application of Euler's polyhedral formula (Chvátal 2004).

Additional information on the theorem can be found in Borwein and Moser (1990), Erdős and Purdy (1991), Pach and Agarwal (1995), and Chvátal (2003).

In September 2003, X. Chen proved a conjecture of Chvátal that, with a certain definition of a line, the Sylvester-Gallai theorem extends to arbitrary finite metric spaces.

🔖 Sylvester’s Problem, Steinberg’s Solution | Cut the Knot

Bookmarked Sylvester's Problem, Gallai's Solution (cut-the-knot.org)
T. Gallai's proof has been outlined by P. Erdös in his submission of the problem to The American Mathematical Monthly in 1943. Solution Given the set Π of noncollinear points, consider the set of lines Σ that pass through at least two points of Π. Such lines are said to be connecting. Among the connecting lines, those that pass through exactly two points of Π are called ordinary.

🔖 Sylvester’s Problem, Steinberg’s Solution | Cut the Knot

Bookmarked Sylvester's Problem, Steinberg's Solution (cut-the-knot.org)
R. Steinberg's was actually the first published solution to Syvester's problem, Solution Given the set Π of noncollinear points, consider the set of lines Σ that pass through at least two points of Π. Such lines are said to be connecting. Among the connecting lines, those that pass through exactly two points of Π are called ordinary. We consider the configuration in the projective plane.

🔖 Sylvester–Gallai theorem | Wikipedia

Bookmarked Sylvester–Gallai theorem (Wikipedia)

The Sylvester–Gallai theorem in geometry states that, given a finite number of points in the Euclidean plane, either
* all the points lie on a single line; or
* there is a line which contains exactly two of the points.
It is named after James Joseph Sylvester, who posed it as a problem in 1893, and Tibor Gallai, who published one of the first proofs of this theorem in 1944.

A line that contains exactly two of a set of points is known as an ordinary line. According to a strengthening of the theorem, every finite point set (not all on a line) has at least a linear number of ordinary lines. There is an algorithm that finds an ordinary line in a set of n points in time proportional to n log n in the worst case.

🔖 The Erdős Discrepancy Problem (6.09.2017) | Terence Tao | YouTube

Bookmarked The Erdős Discrepancy Problem (6.09.2017) at Instytut Matematyczny Uniwersytetu Wrocławskiego by Terence TaoTerence Tao (YouTube)

The discrepancy of a sequence f(1), f(2), ... of numbers is defined to be the largest value of |f(d) + f(2d) + ... + f(nd)| as n and d range over the natural numbers. In the 1930s, Erdős posed the question of whether any sequence consisting only of +1 and -1 could have bounded discrepancy. In 2010, the collaborative Polymath5 project showed (among other things) that the problem could be effectively reduced to a problem involving completely multiplicative sequences. Finally, using recent breakthroughs in the asymptotics of completely multiplicative sequences by Matomaki and Radziwiłł, as well as a surprising application of the Shannon entropy inequalities, the Erdős discrepancy problem was solved in 2015. In his talk TT will discuss this solution and its connection to the Chowla and Elliott conjectures in number theory.

🔖 Tao’s resolution of the Erdős discrepancy problem | AMS | K. Soundararajan

Bookmarked Tao’s resolution of the Erdős discrepancy problem by K. Soundararajan (Bulletin of the American Mathematical Society, Volume 55, Number 1, January 2018, Pages 81–92)

This article gives a simplified account of some of the ideas behind Tao’s resolution of the Erdős discrepancy problem.
http://dx.doi.org/10.1090/bull/1598 | PDF

🔖 The Erdős discrepancy problem | Polymath1Wiki

Bookmarked The Erdős discrepancy problem (Polymath1Wiki)

🔖 The Entropy Decrement Method and the Erdos Discrepancy Problem | Simons Institute for the Theory of Computing

Bookmarked The Entropy Decrement Method and the Erdos Discrepancy Problem (Simons Institute for the Theory of Computing)

Tuesday, April 11th, 2017 9:30 am – 10:30 am
Structure vs. Randomness
Speaker: Terry Tao, UCLA

We discuss a variant of the density and energy increment arguments that we call an "entropy decrement method", which can be used to locate a scale in which two relevant random variables share very little mutual information, and thus behave somewhat like independent random variables.  We were able to use this method to obtain a new correlation estimate for multiplicative functions, which in turn was used to establish the Erdos discrepancy conjecture that any sequence taking values in {-1,+1} had unbounded sums on homogeneous arithmetic progressions.