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We obtain bivariate asymptotics for the number of (unicellular) combinatorial maps (a model of discrete surfaces) as both the size and the genus grow. This work is related to two research topics that have been very active recently:…

The principle of similarity, or homophily, is often used to explain patterns observed in complex networks such as transitivity and the abundance of triangles (3-cycles). However, many phenomena from division of labor to protein-protein…

We review the concept of well-posedness in the context of evolutionary problems from mathematical physics for a particular subclass of problems from elasticity theory. The complexity of physical phenomena appears as encoded in so called…

Controlling the self-assembly of supramolecular structures is vital for living cells, and a central challenge for engineering at the nano- and microscales. Nevertheless, even particles without optimized shapes can robustly form well-defined…

Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…

Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures. We introduce patterning as the dual problem: given a desired form of generalization,…

Neural networks achieve outstanding accuracy in classification and regression tasks. However, understanding their behavior still remains an open challenge that requires questions to be addressed on the robustness, explainability and…

How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links…

By linking conceptual theories with observed data, generative models can support reasoning in complex situations. They have come to play a central role both within and beyond statistics, providing the basis for power analysis in molecular…

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

The analysis of the three-dimensional structure of proteins is an important topic in molecular biochemistry. Structure plays a critical role in defining the function of proteins and is more strongly conserved than amino acid sequence over…

Life systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a…

Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…

Cell fate decisions emerge as a consequence of a complex set of gene regulatory networks. Models of these networks are known to have more parameters than data can determine. Recent work, inspired by Waddington's metaphor of a landscape, has…

Network representation learning has aroused widespread interests in recent years. While most of the existing methods deal with edges as pairwise relationships, only a few studies have been proposed for hyper-networks to capture more…

We present a simple model which allows to investigate equilibrium aspects of molecular recognition between rigid biomolecules on a generic level. Using a two-stage approach, which consists of a design and a testing step, the role of…

This work reports a new methodology aimed at describing characteristics of protein structural shapes, and suggests a framework in which to resolve or classify automatically such structures into known families. This new approach to protein…

The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic…

Industrial chain plays an increasingly important role in the sustainable development of national economy. However, as a typical complex network, data-driven deep learning is still in its infancy in describing and analyzing the resilience of…

With the remarkable success of representation learning for prediction problems, we have witnessed a rapid expansion of the use of machine learning and deep learning for the analysis of digital pathology and biopsy image patches. However,…