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The first order post Newtonian scheme in multiple systems presented by Damour-Soffel-Xu is extended to the second order one for light propagation without changing the advantage of the scheme on the linear partial differential equations of…
Several organelles in eukaryotic cells, including mitochondria and the endoplasmic reticulum, form interconnected tubule networks extending throughout the cell. These tubular networks host many biochemical pathways that rely on proteins…
In communication networks theory the concepts of networkness and network surplus have recently been defined. Together with transmission and betweenness centrality, they were based on the assumption of equal communication between vertices.…
(a) We propose a ``static'' construction procedure for random networks with given correlations of the degrees of the nearest-neighbor vertices. This is an equilibrium graph, maximally random under the constraint that its degree-degree…
The authors recently introduced so-called Vandermonde nets. These digital nets share properties with the well-known polynomial lattices. For example, both can be constructed via component-by-component search algorithms. A striking…
This paper presents a locally decoupled network parameter learning with local propagation. Three elements are taken into account: (i) sets of nonlinear transforms that describe the representations at all nodes, (ii) a local objective at…
Motivated by results of Henry, Pralat and Zhang (PNAS 108.21 (2011): 8605-8610), we propose a general scheme for evolving spatial networks in order to reduce their total edge lengths. We study the properties of the equilbria of two networks…
A major achievement in the study of complex networks is the observation that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet this universality does not naturally translate to…
Image segmentation is a fundamental task in image analysis and clinical practice. The current state-of-the-art techniques are based on U-shape type encoder-decoder networks with skip connections, called U-Net. Despite the powerful…
For any prime power $q$ and any dimension $s \ge 1$, we present a construction of $(t,s)$-sequences in base $q$ with finite-row generating matrices such that, for fixed $q$, the quality parameter $t$ is asymptotically optimal as a function…
Nonlinear wave formation and propagation on a complex network with excitable node dynamics is of fundamental interest in diverse fields in science and engineering. Here, we propose a new model of the Kuramoto type to study nonlinear wave…
We investigate in this paper propagation phenomena for the heterogeneous reaction-diffusion equation $\partial_t u -\Delta u = f(t,u)$, $x\in R^N$, $t\in\R$, where f=f(t,u) is a KPP monostable nonlinearity which depends in a general way on…
Boolean networks have been used in a variety of settings, as models for general complex systems as well as models of specific systems in diverse fields, such as biology, engineering, and computer science. Traditionally, their properties as…
Polarization sets were introduced by Dencker (1982) as a refinement of wavefront sets to the vector-valued case. He also clarified the propagation of polarization sets when the characteristic variety of the pseudodifferential system under…
With the evolution of social networks, the network structure shows dynamic nature in which nodes and edges appear as well as disappear for various reasons. The role of a node in the network is presented as the number of interactions it has…
Establishing a consistent normal orientation for point clouds is a notoriously difficult problem in geometry processing, requiring attention to both local and global shape characteristics. The normal direction of a point is a function of…
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules.…
We report a learning rule for neural networks that computes how much each neuron should contribute to minimize a giving cost function via the estimation of its target value. By theoretical analysis, we show that this learning rule contains…
The formalism of quantum theory over discrete systems is extended in two significant ways. First, quantum evolutions are generalized to act over entire network configurations, so that nodes may find themselves in a quantum superposition of…
Both the path integral measure in field theory and ensembles of neural networks describe distributions over functions. When the central limit theorem can be applied in the infinite-width (infinite-$N$) limit, the ensemble of networks…