Liquid Hopfield model: an analytically tractable model for retrieval in heterogeneous liquid mixtures
Biological mixtures, such as, the cellular cytoplasm or the plasma membrane, are composed of a large number of different components. From this heterogeneity ordered mesoscopic structures emerge, such as liquid phases with controlled composition. These structures compete with each other for the same components. Although heterogeneous liquids mixtures have been studied before in the literature, it remains unclear what type of interactions yield the retrieval of multiple ordered mesoscopic structures, and what are the physical limitations for the retrieval of said structures. After giving a brief overview of previous studies on this topic, I will present in this seminar an analytically tractable model for liquids capable of retrieving states with target compositions, which we named the liquid Hopfield model in reference to corresponding work in the theory of associative neural networks. By solving this simple model, we will describe the physical conditions under which stable ordered mesoscopic structures appear in heterogeneous liquid mixtures.
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