相关论文: A note on Kazdan-Warner equation on networks
We derive Kazdan-Warner type identities for the boundary problem of prescribing nonconstant interior $Q$ curvature and boundary $T$ curvature on the upper hemisphere $\mathbb{S}^4_+$ by a conformal change of the standard metric. Using the…
Complex network theory has been used to study complex systems. However, many real-life systems involve multiple kinds of objects . They can't be described by simple graphs. In order to provide complete information of these systems, we…
Graphical models have gained a lot of attention recently as a tool for learning and representing dependencies among variables in multivariate data. Often, domain scientists are looking specifically for differences among the dependency…
On compact foliated manifolds, we extend the theorem on the existence and uniqueness of solutions to generalized Kazdan-Warner equations. We provide examples of PDEs that we solve, including the transverse Hitchin equation for a diagonal…
In this paper we discuss properties of the KdV equation under periodic boundary conditions, especially those which are important to study perturbations of the equation. Next we review what is known now about long-time behaviour of solutions…
In adaptive networks fragmentation transitions have been observed in which the network breaks into disconnected components. We present an analytical approach for calculating the transition point in general adaptive network models. Using the…
This work examines the problem of topology inference over discrete-time nonlinear stochastic networked dynamical systems. The goal is to recover the underlying digraph linking the network agents, from observations of their state-evolution.…
The fundamental concept of applying the system methodology to network analysis declares that network architecture should take into account services and applications which this network provides and supports. This work introduces a formal…
We consider a nonlocal differential equation of Kirchhoff type with a convolution coefficient involving variable growth. The novelty of our work lies in allowing a variable exponent in the nonlocal term. By relating the variable growth…
We extend Kolchin's results on linear dependence over projective varieties in the constants, to linear dependence over arbitrary complete differential varieties. We show that in this more general setting, the notion of linear dependence…
Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
We present a simple characterization of equivalent Bayesian network structures based on local transformations. The significance of the characterization is twofold. First, we are able to easily prove several new invariant properties of…
We regard a certain type of Loewner's differential equation from a quantum probability point of view and approximate the underlying quantum process by the adjacency matrices of growing graphs which arise from the comb product of certain…
We study the Dirichlet to Neumann operator of the $\overline{\partial}$-Neumann problem, and the relation between the $\overline{\partial}$-Neumann boundary conditions and the Dirichlet to Neumann operator.
We develop a phenomenological theory of critical phenomena in networks with an arbitrary distribution of connections $P(k)$. The theory shows that the critical behavior depends in a crucial way on the form of $P(k)$ and differs strongly…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
We consider kinetic and associated macroscopic equations on networks. The general approach will be explained in this paper for a linear kinetic BGK model and the corresponding limit for small Knudsen number, which is the wave equation.…
Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and…
We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…