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Rana Shojaei @ranashj.bsky.social · 14/04/2026

These classes take additional chemical complexity into account and thus require the use of multivariate generating functions. The results illustrate the elegance of counting theory, highlighting it as an important tool that should receive more attention in network science.6/N

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Rana Shojaei @ranashj.bsky.social · 14/04/2026

In this work, we provide a comprehensive introduction to generating functions and an introduction to the mathematics of counting network structures and then use them to derive results for two new classes of molecules.5/N

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Rana Shojaei @ranashj.bsky.social · 14/04/2026

In this theorem, a group of permutation actions that leave the adjacency matrix of the network unchanged is summarized into a group cycle index. Via generating function methods, this index that incorporates the bonding and symmetry info of the network leads to correct number of configurations.4/N

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Rana Shojaei @ranashj.bsky.social · 14/04/2026

But it's not an easy task to count them as the process of counting swiftly becomes impossible due to numerous potential structural symmetries that result in the identical configurations. The problem of counting objects in the presence of symmetry is often addressed using Pólya's counting theory.3/N

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Rana Shojaei @ranashj.bsky.social · 14/04/2026

Counting the number of isomers of a chemical molecule is one of the formative problems of graph theory. However, recent progress has been slow, and the problem has largely been ignored in modern network science. 2/N

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Rana Shojaei @ranashj.bsky.social · 14/04/2026

Today, diversity is widely discussed in both human contexts and environmental studies. However, less attention is given to molecular diversity. 1/N

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Rana Shojaei @ranashj.bsky.social · 28/03/2026

It has been about learning how to prioritize, adapt, review, adjust, and keep going, even when things don't go as planned. It's not easy, but it's part of the process.3/3 #PhDLife #AcademicLife #ResearchJourney #TimeManagement #PhDThesis

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Rana Shojaei @ranashj.bsky.social · 28/03/2026

But I think the whole PhD has really been about preparing for exactly this phase: not just the research itself, but learning how to build your own system to deal with uncertainty, limited time, and pressure, and still move forward.2/3

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Rana Shojaei @ranashj.bsky.social · 28/03/2026

Right now, I find myself navigating three major and demanding challenges at once: - German exam - Next research paper - Writing PhD thesis Trying to move all of these forward simultaneously is incredibly challenging, especially while also maintaining some form of personal life and balance.1/3

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Reposted by Rana Shojaei

BioND Lab @biondlab.bsky.social · 23/11/2024

Hello World 🌎🌍🌏 We are the Biodiversity Theory Group led by @thilogross.bsky.social at the @hifmb.bsky.social. Ever wondered about biodiversity and what we can do to better understand it? We do too - with the help of math, data, and network science. Follow us for news and paper announcements!

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