The shape of the $V-I$ characteristics leading to a peak in the differential resistance $r_d=dV/dI$ in the vicinity of the order-disorder transition in ${\mathrm{NbSe}}_2$ is investigated. $r_d$ is large when measured by dc current. However, for a small $I_{\mathrm{ac}}$ on a dc bias, $r_d$ decreases rapidly with frequency, even at a few hertz, and displays a large out-of-phase signal. In contrast, the ac response increases with frequency in the absence of dc bias. These surprisingly opposite phenomena and the peak in $r_d$ are shown to result from a dynamic coexistence of two vortex matter phases rather than from the commonly assumed plastic depinning.

Climate changes and environmental stresses have a consequential association with crop plant growth and yield, meaning it is necessary to cultivate crops that have tolerance toward the changing climate and environmental disturbances such as water stress, temperature fluctuation, and salt toxicity. Recent studies have shown that trans-acting regulatory elements, including microRNAs (miRNAs) and transcription factors (TFs), are emerging as promising tools for engineering naive improved crop varieties with tolerance for multiple environmental stresses and enhanced quality as well as yield. However, the interwoven complex regulatory function of TFs and miRNAs at transcriptional and post-transcriptional levels is unexplored inOryza sativa. To this end, we have constructed a multiple abiotic stress responsive TF-miRNA-gene regulatory network forO. sativausing a transcriptome and degradome sequencing data meta-analysis approach. The theoretical network approach has shown the networks to be dense, scale-free, and small-world, which makes the network stable. They are also invariant to scale change where an efficient, quick transmission of biological signals occurs within the network on extrinsic hindrance. The analysis also deciphered the existence of communities (cluster of TF, miRNA, and genes) working together to help plants in acclimatizing to multiple stresses. It highlighted that genes, TFs, and miRNAs shared by multiple stress conditions that work as hubs or bottlenecks for signal propagation, for example, during the interaction between stress-responsive genes (TFs/miRNAs/other genes) and genes involved in floral development pathways under multiple environmental stresses. This study further highlights how the fine-tuning feedback mechanism works for balancing stress tolerance and how timely flowering enable crops to survive in adverse conditions. This study developed the abiotic stress-responsive regulatory network, APRegNet database (http://lms.snu.edu.in/APRegNet), which may help researchers studying the roles of miRNAs and TFs. Furthermore, it advances current understanding of multiple abiotic stress tolerance mechanisms.

This paper studies higher-order interactions in social-ecological networks, which formally represent interactions within the social and ecological units of an ecosystem. Many real-world social ecosystems exhibit not only pairwise interactions but also higher-order interactions among their units. Therefore, the conventional graph-theoretic description of networks falls short of capturing these higher-order interactions due to the inherent limitations of the graph definition. In this work, a mathematical framework for capturing the higher-order interactions of a social-ecological system has been given by incorporating notions from combinatorial algebraic topology. In order to achieve this, two different simplicial complexes, the clique and the neighbourhood complex, have been constructed from a pairwise social-ecological network. As a case study, the Q-analysis and a structural study of the interactions in the rural agricultural system of southern Madagascar have been done at various structural levels denoted byq. The results obtained by calculating all the structural vectors for both simplicial complexes, along with exciting results about the participation of facets of the clique complex at differentq-levels, have been discussed. This work also establishes significant theorems concerning the dimension of the neighbourhood complex and clique complex obtained from the parent pairwise network.

Higher-order interactions, that is, interactions among the units of group size greater than two, are a fundamental structural feature of a variety of complex systems across the scale. Simplicial complexes are combinatorial objects that can capture and model the higher-order interactions present in a given complex system and thus represent the complex system as a higher-order network comprising simplices. In this work, a given simplicial complex is viewed as a finite union of d-exclusive simplicial complexes. Thus, to represent a complex system as a higher-order network given by a simplicial complex that captures all orders of interactions present in the system, a family of symmetric adjacency tensors $A(d)$ of dimension d + 1 and appropriate order has been used. Each adjacency tensor $A(d)$ represents a d-exclusive simplicial complex and for $d≥2$ it represents exclusively higher-order interactions of the system. For characterizing the structure of d-exclusive simplicial complexes, the notion of generalized structural centrality indices namely, generalized betweenness centrality and generalized closeness centrality has been established by developing the concepts of generalized walk and generalized distance in the simplicial complex. Generalized centrality indices quantify the contribution of δ-simplices in any d-exclusive simplicial complex Δ, where $δ<d$ and if $d≥2$⁠, it describes the contribution of δ-faces to the higher-order interactions of Δ. These generalized centrality indices provide local structural descriptions, which lead to mesoscale insights into the simplicial complex that comprises the higher-order network. An important theorem providing a general technique for the characterization of connectedness in d-exclusive simplicial complexes in terms of irreducibility of its adjacency tensor has been established. The concepts developed in this work together with concepts of generalized simplex deletion in d-exclusive simplicial complexes have been illustrated using examples. The effect of deletions on the generalized centralities of the complexes in the examples has been discussed.

The process of attachment of a deformable polystyrene colloidal particle to a planar substrate shows features of slow relaxation and aging, typically observed in many-body disordered and glassy systems. This slow dynamics is attributed to the presence of polymeric tethers constituting a few internal degrees of freedom. The effects of these few degrees of freedom are revealed by a Nyquist analysis of the data that demonstrate the existence of only a few discernible basins of attraction as the system reaches the ground state and thus provides a minimal model of complexity and glassy dynamics.