Detection of hidden structures for arbitrary scales in complex physical

Recent decades have experienced the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of contending atomic- and largerscale configurations. In order to obtain a more detailed understanding of such systems, we need tools that enable the detection of pertinent structures on all spatial and temporal scales. Towards this end, we suggest a new method that applies to both static and dynamic systems which invokes ideas from network analysis and information theory. Our approach efficiently identifies basic unit cells, topological defects, and candidate natural structures. The method is particularly useful where a clear definition of order is lacking, and the identified features may constitute a natural point of departure for further analysis. C urrently, no universal tools exist for examining complex physical systems in a general and systematic way that fleshes out their pertinent features, from the smallest fundamental unit to the largest scale encompassing the entire system. The challenge posed by these complex materials is acute and stands in stark contrast to simple ordered systems. In crystals, atomic unit cells replicate to span the entire system. Historically, the regular shapes of some large-scale single crystals were suggested to reflect the existence of an underlying repetitive atomic scale unit cell structure long before modern microscopy and the advent of scattering and tunneling techniques. This simplicity enables an understanding of many solids in great detail; but in complex systems, rich new structures may appear on additional intermediate scales. Currently, some of the oldest and most heavily investigated complex materials are glasses. Recent challenges include the high temperature cuprate and pnictide superconductors, heavy fermion compounds, and many other compounds including the manganites, the vanadates, and the ruthenates. These systems exhibit a wide array of behavior including superconductivity and metal to insulator transitions, rich magnetic characteristic and incommensurate orders, colossal magneto-resistance, orbital orders, and novel transport properties. A wealth of experimental and numerical data has accumulated on such systems. The discovery of the salient features in such complex materials and more generally of complex large scale physical systems across all spatial resolutions may afford clues to develop a more accurate understanding of these systems. In disparate arenas, guesswork is often invoked as to which features of the systems are important enough to form the foundation for a detailed analysis. With ever-increasing experimental and computational data, such challenges will only sharpen in the coming years. There is a need for methods that may pinpoint central features on all scales, and this work suggests a path towards the solution of this problem in complex amorphous materials. A companion work 1 provides many details that are not provided in this brief summary. An explanation of our core ideas require a few concepts from the physics of glasses and network analysis. Results