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Ein ehemaliger Mit-Nutzer des Impact Hub München arbeitet jetzt für die Firmen Treescape und Forest Force. Ich weiß zwar nicht genau, was die machen. Aber ich beglückwünsche ihn trotzdem!
https://www.marcelobohrer.com.br/

On the independence number of sparser random Cayley graphs
Marcelo Campos, Gabriel Dahia, Jo\~ao Pedro Marciano
https://arxiv.org/abs/2406.09361 https://…

On the independence number of sparser random Cayley graphs
The Cayley sum graph $Γ_A$ of a set $A \subseteq \mathbb{Z}_n$ is defined to have vertex set $\mathbb{Z}_n$ and an edge between two distinct vertices $x, y \in \mathbb{Z}_n$ if $x + y \in A$. Green and Morris proved that if the set $A$ is a $p$-random subset of $\mathbb{Z}_n$ with $p = 1/2$, then the independence number of $Γ_A$ is asymptotically equal to $α(G(n, 1/2))$ with high probability. Our main theorem is the first extension of their result to $p = o(1)$: we show that, with high proba…

Inverse design of programmable shape-morphing kirigami structures
Xiaoyuan Ying, Dilum Fernando, Marcelo A. Dias
https://arxiv.org/abs/2406.10566 https://<…

Inverse design of programmable shape-morphing kirigami structures
Shape-morphing structures have the capability to transform from one state to another, making them highly valuable in engineering applications. In this study, it is propose a two-stage shape-morphing framework inspired by kirigami structures to design structures that can deploy from a compacted state to a prescribed state under certain mechanical stimuli -- although the framework may also be extended to accommodate various physical fields, such as magnetic, thermal, and electric fields. The fram…

On the independence number of sparser random Cayley graphs
Marcelo Campos, Gabriel Dahia, Jo\~ao Pedro Marciano
https://arxiv.org/abs/2406.09361 https://…

On the independence number of sparser random Cayley graphs
The Cayley sum graph $Γ_A$ of a set $A \subseteq \mathbb{Z}_n$ is defined to have vertex set $\mathbb{Z}_n$ and an edge between two distinct vertices $x, y \in \mathbb{Z}_n$ if $x + y \in A$. Green and Morris proved that if the set $A$ is a $p$-random subset of $\mathbb{Z}_n$ with $p = 1/2$, then the independence number of $Γ_A$ is asymptotically equal to $α(G(n, 1/2))$ with high probability. Our main theorem is the first extension of their result to $p = o(1)$: we show that, with high proba…

Physical networks become what they learn
Menachem Stern, Marcelo Guzman, Felipe Martins, Andrea J Liu, Vijay Balasubramanian
https://arxiv.org/abs/2406.09689

Physical networks become what they learn
Physical networks can develop diverse responses, or functions, by design, evolution or learning. We focus on electrical networks of nodes connected by resistive edges. Such networks can learn by adapting edge conductances to lower a cost function that penalizes deviations from a desired response. The network must also satisfy Kirchhoff's law, balancing currents at nodes, or, equivalently, minimizing total power dissipation by adjusting node voltages. The adaptation is thus a double optimization…