# Archive | flotsam

RSS feed for this section## Fact of the day: Condorset domains, tiling permutations and contractibility

$latex \def\Real{\mathbb{R}}\def\Z{\mathcal{Z}}\def\sg{\mathfrak{S}}\def\B{\mathbf{B}}

$

Consider a collection of vectors $latex e_1,\ldots,e_n$ in the upper half-plane, such that $latex e_k=(x_k,1)$ and $latex x_1>x_2\gt \ldots \gt x_n$. Minkowski sum of the segments $latex s_k:=[0,e_k]$ is a zonotope $latex \Z$. *Rhombus* in this context are the Minkowski sums $latex \Z(k,l)=s_k\oplus s_l, 1\leq k\lt l\leq n$ of pairs of the segments. Tilings of $latex \Z$ by $latex n\choose 2$ rhombuses $latex \Z(k,l)$ define also an oriented graph (formed by the edges of the rhombuses, and oriented up in the plane).…

## Topologically constrained models of statistical physics.

\(\def\Real{\mathbb{R}}

\def\Int{\mathbb{Z}}

\def\Comp{\mathbb{C}}

\def\Rat{\mathbb{Q}}

\def\Field{\mathbb{F}}

\def\Fun{\mathbf{Fun}}

\def\e{\mathbf{e}}

\def\f{\mathbf{f}}

\def\bv{\mathbf{v}}

\def\blob{\mathcal{B}}

\)

### The Blob

Consider the following planar “spin model”: the state of the system is a function from \(\Int^2\) into \(\{0,1\}\) (on and off states). We interpret the site \((i,j), i,j\in\Int\) as the *plaque*, i.e. the (closed) square given by the inequalities \(s_{ij}:=i-1/2\leq x\leq i+1/2; j-1/2\leq y\leq j+1/2\).

To any configuration \(\eta\) we associate the corresponding active domain,

\[

A_\eta=\bigcup_{(i,j): \eta(i,j)=1} s_{ij}.

\]

We are interested in the statistical ensembles supported by the finite *contractible* active domains – let’s refer to such domains as ** blobs**.…

## Topology in Motion @ICERM Fall’16

If you are interested in Applied Topology, tend to plan far, far ahead and have some free time on your hands in Fall 2016, check this out, and let us know!

## more on humanitarian disaster

#### Bug in the system

Handling of all – not just Salaita’s – cases by U of I is deficient, with the final approval coming only after the move to campus is done. We all are culpable, registering this issue when hired, then happily forgetting about it, waiting for that ticking bomb to explode, relying on assumptions. Debugging this procedure should be done as soon as possible. It seems the administration acts on it.

#### Role of Trustees

in terms of procedure they were fully within their prerogative not confirming Salaita’s appointment, as

…

the Board of Trustees exercises final authority over the University.

## arrieregarde battles of postmodernism

The epicenter of the battle around Salaita’s offer withdrawal seems to be located at the question, whether or not *political considerations* are admissible when appointing a scholar. I checked what Dr. Salaita himself writes about the matter in a 2008 paper dealing specifically with academic freedom.

A general remark on the paper: most of it consists of unsolicited, unadulterated punditry, bloated with (intentionally, I guess) opaque and (sometimes comically) elevated prose, mainly arguing with a group of Internet writers expressing their views too noisily and/or too effectively, to author’s taste.…

## hyperbolic geometry of Google maps

\(\def\Real{\mathbb{R}}

\def\views{\mathbb{G}}

\def\earth{\mathbb{E}}

\def\hsp{\mathbb{H}}

\)

##### Google Maps and the Space of Views

Let’s consider the *geometry* hidden behind one of the best user interfaces in mobile apps ever, – the smartphone maps, the ones which you can swipe, flick and pinch. We are not talking here about the incredible engine that generates the maps on the fly as your finger waddles over the screen – just about the interface, which in a very intuitive and remarkably efficient way allows you to move between various maps.…

## TDA at HCC

This summer Yura Mileyko and I gave a tutorial on Topological Data Analysis at ISIT 2014. It was intended as a gentle introduction aimed at people who never heard about homologies (outside of, say, biology) – and there were plenty of those in the audience!

The result is idiosyncratic and lopsided – here are the slides……

## big bad machine

Is installed in the department: it has reasonable processor, but most importantly, hundreds Gigs of RAM. If you have some really big bad computing to do, we might be able to accommodate some requests.

…