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Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for…
As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological…
Mesoscopic quantum systems exhibit complex many-body quantum phenomena, where interactions between spins and charges give rise to collective modes and topological states. Even simple, non-interacting theories display a rich landscape of…
Predicting the phase diagram of interacting quantum many-body systems is a challenging problem in condensed matter physics. Strong interactions and correlation effects may lead to exotic states of matter, such as quantum spin liquids and…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
There are diverse mechanisms driving the evolution of social networks. A key open question dealing with understanding their evolution is: How various preferential linking mechanisms produce networks with different features? In this paper we…
The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and…
This work proposes to model the space environment as a stochastic dynamic network where each node is a group of objects of a given class, or species, and their relationship is represented by stochastic links. A set of stochastic dynamic…
Within the conventional statistical physics framework, we study critical phenomena in a class of configuration network models with hidden variables controlling links between pairs of nodes. We find analytical expressions for the average…
Reaction networks are systems in which the populations of a finite number of species evolve through predefined interactions. Such networks are found as modeling tools in many biological disciplines such as biochemistry, ecology,…
We introduce the concept of network susceptibilities quantifying the response of the collective dy- namics of a network to small parameter changes. We distinguish two types of susceptibilities: vertex susceptibilities and edge…
The work presented in this thesis concerns different aspects of dynamical processes on networks. The first subject considered is the theoretical modeling of exploration processes of complex networks, such as the ``traceroute'' process used…
Temporal dynamics, characterised by time-varying degree heterogeneity and homophily effects, are often exhibited in many real-world networks. As observed in an MIT Social Evolution study, the in-degree and out-degree of the nodes show…
Transformations to create more sustainable social-ecological systems are urgently needed. Structural change is a feature of transformations of social-ecological systems that is of critical importance but is little understood. Here, we…
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying…
A fundamental theory is presented for the mechanical response of polymer networks undergoing large deformation which seamlessly integrates statistical mechanical principles with macroscopic thermodynamic constitutive theory. Our formulation…
In this work we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various…
Recent research on the network modeling of complex systems has led to a convenient representation of numerous natural, social, and engineered systems that are now recognized as networks of interacting parts. Such systems can exhibit a…
From longitudinal biomedical studies to social networks, graphs have emerged as a powerful framework for describing evolving interactions between agents in complex systems. In such studies, after pre-processing, the data can be represented…
We present three different neural network algorithms to calculate thermodynamic properties as well as dynamic correlation functions at finite temperatures for quantum lattice models. The first method is based on purification, which allows…