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Topologically constrained models of statistical physics.


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), …

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hyperbolic geometry of Google maps


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 …

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unimodal category

We say that a continuous function is unimodal if all the upper excursion sets
\(e_f(c):=\{f≥c\}\) are contractible. For a nonnegative function
\(f:\mathbb{R}^d\to\mathbb{R}_+\) with compact support its unimodal category UCat(f) as the least number \(u\) of summands in a decomposition \(f=\sum_{i=1}^u …

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linear search

Linear search problems deals with locating an object hidden on a half line (“long road”) by an absent-minded robot which gather everything it sees (see, e.g. here for more details). A program for the robot is a sequence \(0<x_1<x_2<\ldots\) of …

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