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Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high-contrast phases with large structural differences. However, the structural changes are more difficult to quantify for phases with high asymmetry and multiscale organization as well as for the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases. Here, we show that graph theoretical (GT) descriptors can successfully characterize different phases of a water/surfactant system and pathways between them for hierarchically organized phases. GT centrality parameters and node-based fractal dimension can identify complex phases more accurately than traditional analyses and quantify the system behavior preceding the transitions, capturing fluctuation-induced breakup of aggregates and their long-range cooperative interactions. GT parametrization can be generalized for a wide range of chemical systems, facilitatingidentification of complex supramolecular phases and engineering nanostructures at multiple scales.

Phase transitions are typically quantified using order parameters, such as crystal lattice distances, Legendre polynomials, and radial distribution functions (RDF). These parameters can identify even subtle changes in packing distances and symmetries being ideally suited for crystalline materials or high-contrast phases with large structural differences. However, the structural changes are more difficult to quantify when the organizational pattern of constituent molecules becomes less ordered and more complex. This is the case for phases with high asymmetry and multiscale organization as well as for the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases. Here, we show that graph theoretical (GT) descriptors can successfully characterize different phases and pathway between them for hierarchically organized nanoscale systems exemplified by binary surfactant/water systems. We found that the GT centrality parameters and node-based fractal dimension can identify complex phases more accurately than traditional analyses and quantify the system behavior preceding the transitions. The trajectories for GT parameter of closeness centrality reflect (1) fluctuation-induced breakup of micelles and (2) long-range cooperative interactions in the network of surfactant molecules. GT parametrization can be generalized for a wide range of nanoscale colloidal systems, which can facilitate identification of complex phases.

Gels self-assembled from colloidal nanoparticles (NPs) translate the size-dependent properties of nanostructures to materials with macroscale volumes. Large spanning networks of NP chains provide high interconnectivity within the material necessary for a wide range of properties from conductivity to viscoelasticity. However, a great challenge for nanoscale engineering of such gels lies in being able to accurately and quantitatively describe their complex non-crystalline structure that combines order and disorder. The quantitative relationships between the mesoscale structural and material properties of nanostructured gels are currently unknown. Here, it is shown that lead telluride NPs spontaneously self-assemble into a spanning network hydrogel. By applying graph theory (GT), a method for quantifying the complex structure of the NP gels is established using a topological descriptor of average nodal connectivity that is found to correlate with the gel's mechanical and charge transport properties. GT descriptions make possible the design of non-crystalline porous materials from a variety of nanoscale components for photonics, catalysis, adsorption, and thermoelectrics.

Understanding the mechanisms by which neurons create or suppress connections to enable communication in brain-derived neuronal cultures can inform how learning, cognition and creative behavior emerge. While prior studies have shown that neuronal cultures possess self-organizing criticality properties, we further demonstrate that in vitro brain-derived neuronal cultures exhibit a self-optimization phenomenon. More precisely, we analyze the multiscale neural growth data obtained from label-free quantitative microscopic imaging experiments and reconstruct the in vitro neuronal culture networks (microscale) and neuronal culture cluster networks (mesoscale). We investigate the structure and evolution of neuronal culture networks and neuronal culture cluster networks by estimating the importance of each network node and their information flow. By analyzing the degree-, closeness-, and betweenness-centrality, the node-to-node degree distribution (informing on neuronal interconnection phenomena), the clustering coefficient/transitivity (assessing the “small-world” properties), and the multifractal spectrum, we demonstrate that murine neurons exhibit self-optimizing behavior over time with topological characteristics distinct from existing complex network models. The time-evolving interconnection among murine neurons optimizes the network information flow, network robustness, and self-organization degree. These findings have complex implications for modeling neuronal cultures and potentially on how to design biological inspired artificial intelligence.

In contrast to the conventional approach of directly comparing genomic sequences using sequence alignment tools, we propose a computational approach that performs comparisons between sequence generators. These sequence generators are learned via a data-driven approach that empirically computes the state machine generating the genomic sequence of interest. As the state machine based generator of the sequence is independent of the sequence length, it provides us with an efficient method to compute the statistical distance between large sets of genomic sequences. Moreover, our technique provides a fast and efficient method to cluster large datasets of genomic sequences, characterize their temporal and spatial evolution in a continuous manner, get insights into the locality sensitive information about the sequences without any need for alignment. Furthermore, we show that the technique can be used to detect local regions with mutation activity, which can then be applied to aid alignment techniques for the fast discovery of mutations. To demonstrate the efficacy of our technique on real genomic data, we cluster different strains of SARS-CoV-2 viral sequences, characterize their evolution and identify regions of the viral sequence with mutations.

Batteries with conformal shape and multiple functionalities could provide new degrees of freedom in the design of robotic devices. For example, the ability to provide both load bearing and energy storage can increase the payload and extend the operational range for robots. However, realizing these kinds of structural power devices requires the development of materials with suitable mechanical and ion transport properties. Here, we report biomimetic aramid nanofibers-based composites with cartilage-like nanoscale morphology that display an unusual combination of mechanical and ion transport properties. Ion-conducting membranes from these aramid nanofiber composites enable pliable zinc-air batteries with cyclic performance exceeding 100 hours that can also serve as protective covers in various robots including soft and flexible miniaturized robots. The unique properties of the aramid ion conductors are attributed to the percolating network architecture of nanofibers with high connectivity and strong nanoscale filaments designed using a graph theory of composite architecture when the continuous aramid filaments are denoted as edges and intersections are denoted as nodes. The total capacity of these body-integrated structural batteries is 72 times greater compared with a stand-alone Li-ion battery with the same volume. These materials and their graph theory description enable a new generation of robotic devices, body prosthetics, and flexible and soft robotics with nature-inspired distributed energy storage.

Evolution is a process of change where mutations in the viral RNA are selected based on their fitness for replication and survival. Given that current phylogenetic analysis of SARS-CoV-2 identifies new viral clades after they exhibit evolutionary selections, one wonders whether we can identify the viral selection and predict the emergence of new viral clades? Inspired by the Kolmogorov complexity concept, we propose a generative complexity (algorithmic) framework capable to analyze the viral RNA sequences by mapping the multiscale nucleotide dependencies onto a state machine, where states represent subsequences of nucleotides and state-transition probabilities encode the higher order interactions between these states. We apply computational learning and classification techniques to identify the active state-transitions and use those as features in clade classifiers to decipher the transient mutations (still evolving within a clade) and stable mutations (typical to a clade). As opposed to current analysis tools that rely on the edit distance between sequences and require sequence alignment, our method is computationally local, does not require sequence alignment and is robust to random errors (substitution, insertions and deletions). Relying on the GISAID viral sequence database, we demonstrate that our method can predict clade emergence, potentially aiding with the design of medications and vaccines.