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A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
The notions of null-sets and nullity are present in all discourses of mathematics. They are based on the dual-pair of notions of "almost-every" and "almost none". A notion of nullity corresponds to a choice of subsets that one interprets as…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
A central biological question is how natural organisms are so evolvable (capable of quickly adapting to new environments). A key driver of evolvability is the widespread modularity of biological networks--their organization as functional,…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
Machine learning is often viewed as an inherently value-neutral process: statistical tendencies in the training inputs are "simply" used to generalize to new examples. However when models impact social systems such as interactions between…
Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…
We present a universal approach to the investigation of the dynamics in generalized models. In these models the processes that are taken into account are not restricted to specific functional forms. Therefore a single generalized models can…
Natural language is characterized by compositionality: the meaning of a complex expression is constructed from the meanings of its constituent parts. To facilitate the evaluation of the compositional abilities of language processing…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
There may be structural principles pertaining to the general behavior of systems that lead to similarities in a variety of different contexts. Classic examples include the descriptive power of fractals, the importance of surface area to…
We present a differentiable framework capable of learning a wide variety of compositions of simple policies that we call skills. By recursively composing skills with themselves, we can create hierarchies that display complex behavior. Skill…
Many human knowledge systems, such as science, law, and invention, are built on documents and the citations that link them. Citations, while serving multiple purposes, primarily function as a way to explicitly document the use of prior work…
From the complex motions of robots to the oxygen binding of hemoglobin, the function of many mechanical systems depends on large, coordinated movements of their components. Such movements arise from a network of physical interactions in the…
In many scientific contexts, different investigators experiment with or observe different variables with data from a domain in which the distinct variable sets might well be related. This sort of fragmentation sometimes occurs in molecular…
A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…
Generic coarse-grained models are designed such that they are (i) simple and (ii) computationally efficient. They do not aim at representing particular materials, but classes of materials, hence they can offer insight into universal…
Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are…