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We suggest an approach to study hierarchy, especially hidden one, of complex networks based on the analysis of their vulnerability. Two quantities are proposed as a measure of network hierarchy. The first one is the system vulnerability V.…
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…
The paper addresses design/building frameworks for some kinds of tree-like and hierarchical structures of systems. The following approaches are examined: (1) expert-based procedures, (2) hierarchical clustering; (3) spanning problems (e.g.,…
One of the most important features of spatial networks such as transportation networks, power grids, Internet, neural networks, is the existence of a cost associated with the length of links. Such a cost has a profound influence on the…
The protein folding problem has attracted an increasing attention from physicists. The problem has a flavor of statistical mechanics, but possesses the most common feature of most biological problems -- the profound effects of evolution. I…
Multiscale phenomena exhibit complex structure-function relationships, and predicting their macroscopic behavior requires deducing differential equations at different scales. The complexity of these equations and the number of essential…
Self-assembly processes are widespread in nature, and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
Current analyses of genomes from numerous species show that the diversity of organism's functional and behavioral characters is not proportional to the number of genes that encode the organism. We investigate the hypothesis that the…
Spatially or chemically isolated functional modules composed of several cellular components and carrying discrete functions are considered fundamental building blocks of cellular organization, but their presence in highly integrated…
Hierarchical (first-order) structured deformations are studied from the variational point of view. The main contributions of the present research are the first steps, at the theoretical level, to establish a variational framework to…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…
Unlike most synthetic materials, biological materials often stiffen as they are deformed. This nonlinear elastic response, critical for the physiological function of some tissues, has been documented since at least the 19th century, but the…
There is evidence that the self-assembly of complex molecular systems often proceeds hierarchically, by first building subunits that later assemble in larger entities, in a process that can repeat multiple times. Yet, our understanding of…
Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate…
Healthy cartilage is a remarkable tissue, able to withstand tens of millions of loading cycles with minimal damage. While much is known about the structural origins of its compressive mechanics, how composition determines its mechanical…
Many fibrous materials are modeled as elastic networks featuring a substantial separation between the stiffness scales that characterize different microscopic deformation modes of the network's constituents. This scale separation has been…
Materials, at their essence, are networks defined by homogeneity: uniform bonds, fixed thicknesses, and discrete length scales. Mechanical metamaterials, while representing structurally more diverse microstructures, remain defined by the…
Knits and crochets are mechanical metamaterials with a long history and can typically be produced from a single yarn. Despite the simplicity of the manufacturing process, they exhibit a wide range of structural configurations with diverse…
Cells actively probe and respond to the stiffness of their surroundings. Since mechanosensory cells in connective tissue are surrounded by a disordered network of biopolymers, their in vivo mechanical environment can be extremely…