Grant: Discovery Grants Program - Individual

Major progress in physics is often associated to the identification of a model that encapsulates a new phenomenon in a simple setting, from which it can later be extended. The humble harmonic oscillator, from its origin in mass-spring systems, is now foundational in condensed matter physics and quantum field theory. New phenomena continue to be discovered, and new models identified, particularly as physics opens its arms to interdisciplinary problems in complex systems. In many complex systems, we are interested in the macroscopic behaviour of a diverse array of interacting units. From the astronomical number of ways of arranging distinct units, this entails a combinatorial explosion, which in many systems is exploited. For example, if we consider all the possible arrangements of words in a sentence, then the vast majority of them are not even syntactically correct, let alone meaningful; if we consider networks of biochemical molecules, most of these do not lead to behaviours carrying the hallmarks of life, such as reproduction. Evidently, in these cases the important microstates form a small subset of phase space, and their selection must reflect imposition of constraints as well as optimization. A model system is needed to understand this phenomenon of extreme tuning. In this proposal I consider two model systems where this phenomenon is present, propose a common theoretical framework with which to investigate them, and link these models to key scientific questions, from how a computer can learn a language to the origin of life. The first model system is language syntax. DNA, proteins, and human text have a hidden structure that must be decoded. Are there universal aspects of the map from sequence to structure? This question can be answered by considering the ensemble of all languages in a given class of syntactic structure, and exploiting the tools of statistical physics to extract the behaviour of typical languages. In earlier work, this approach was used to discover a phase transition at which languages begin to carry information, which has implications for the learning of any language. This proposal will expand the syntactic model to be consistent with state-of-the-art knowledge from linguistics, and will connect these works with efforts in the machine learning community to teach computers to understand human language. This research will thus synthesize knowledge from disparate fields and facilitate cross-fertilization. The second model system is a reaction network. Biological systems involve the coordinated action of many large molecules subject to out-of-equilibrium forcing. While a given reaction network can be treated with classical tools, there is little understanding what distinguishes the class of reaction networks appearing in biological systems in the vast `chemical space' of possibilities. By treating the ensemble of all reaction networks in a wide class, this proposal will elucidate this form of evolution-guided tuning.