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Full-Text Articles in Physical Sciences and Mathematics
Fibration Symmetries Uncover The Building Blocks Of Biological Networks, Flaviano Morone, Ian Leifer, Hernán A. Makse
Fibration Symmetries Uncover The Building Blocks Of Biological Networks, Flaviano Morone, Ian Leifer, Hernán A. Makse
Publications and Research
A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these networks as a set of input trees, one for each node, which contains all pathways along which information can be transmitted in the network. In this representation, we find remarkable symmetries in the input trees that deconstruct the network into functional building blocks called fibers. Nodes in a fiber have isomorphic input trees and thus process equivalent dynamics and synchronize their activity. Each …
A Comparison Of Boltzmann And Gibbs Definitions Of Microcanonical Entropy For Small Systems, Randall B. Shirts
A Comparison Of Boltzmann And Gibbs Definitions Of Microcanonical Entropy For Small Systems, Randall B. Shirts
Faculty Publications
Two different definitions of entropy, S= klnW, in the microcanonical ensemble have been competing for over 100 years. The Boltzmann/Planck definition is that W is the number of states accessible to the system at its energy E (also called the surface entropy). The Gibbs/Hertz definition is that W is the number of states of the system up to the energy E (also called the volume entropy). These two definitions agree for large systems but differ by terms of order N-1 for small systems, where N is the number of particles in the system. For three analytical …
Comment On “Contact Conditions For The Charge In The Theory Of The Electrical Double Layer”, Douglas Henderson, L. B. Bhuiyan
Comment On “Contact Conditions For The Charge In The Theory Of The Electrical Double Layer”, Douglas Henderson, L. B. Bhuiyan
Faculty Publications
Exact results in any field, including statistical mechanics, are both aesthetically pleasing and very valuable in assessing theoretical approximations.