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Shuffling the sheep

\(\def\xx{\mathbf{x}}\def\Real{\mathbb{R}} \)

We consider the problem of flock control: what are the natural constraints on the steering agents in reconfiguring an ensemble of agents?

Our basic setup is following: the agents are modeled as points \(\xx=(x_1,\ldots,x_n), x_k\in X, k=1,\ldots, N\), …

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Protected: Curvilinear Origami

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Fact of the day: Brownian centroids

\(\def\Real{\mathbb{R}}\def\Z{\mathcal{Z}}\def\sg{\mathfrak{S}}\def\B{\mathbf{B}}\def\xx{\mathbf{x}}\def\ex{\mathbb{E}}
\)

Consider \(n\) points in Euclidean space, \(\xx=\{x_1,\ldots, x_n\}, x_k\in \Real^d, n\leq d+1\).

Generically, there is a unique sphere in the affine space spanned by those points, containing all of them. This centroid (which we will denote as \(o(x_1,\ldots,x_n)\)) …

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Fact of the day: dice are chiral

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Fact of the day: Condorset domains, tiling permutations and contractibility

\(\def\Real{\mathbb{R}}\def\Z{\mathcal{Z}}\def\sg{\mathfrak{S}}\def\B{\mathbf{B}}
\)

Consider a collection of vectors \(e_1,\ldots,e_n\) in the upper half-plane, such that \(e_k=(x_k,1)\) and \(x_1>x_2\gt \ldots \gt x_n\). Minkowski sum of the segments \(s_k:=[0,e_k]\) is a zonotope \(\Z\). Rhombus in this context are the Minkowski sums \(\Z(k,l)=s_k\oplus s_l, …

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JACT

coming soon.…

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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), …

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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!

logo_tim

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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 …

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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

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