基于图形竞争的强力强化Pólya骨灰盒
Strongly reinforced Pólya urns with graph-based competition
摘要：
我们介绍了一类强化模型，在每个时间步$t$，首先选择一个随机子集$A_t$的颜色（独立于过去）从$n$颜色的球，然后选择一个颜色$i$从这个子集的概率成比例的颜色$i$在瓮中的球的数量提高到权力$α>1$。我们认为这种模型的平衡的稳定性，并建立在一些例子中的相变的存在，包括当颜色是一个图形的边缘，这是一个玩具模型的形成和加强神经连接的背景。
英文摘要：
We introduce a class of reinforcement models where, at each time step $t$, one first chooses a random subset $A_t$ of colours (independent of the past) from $n$ colours of balls, and then chooses a colour $i$ from this subset with probability proportional to the number of balls of colour $i$ in the urn raised to the power $α>1$. We consider stability of equilibria for such models and establish the existence of phase transitions in a number of examples, including when the colours are the edges of a graph, a context which is a toy model for the formation and reinforcement of neural connections.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
