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Modern deep learning treats neural networks primarily as endpoint functions from inputs to outputs. Inspired by the shift from force to geometry in physics, we ask whether a network should instead be understood through the geometry of its…
Effectively compressing and optimizing tensor networks requires reliable methods for fixing the latent degrees of freedom of the tensors, known as the gauge. Here we introduce a new algorithm for gauging tensor networks using belief…
Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can…
The study of meme propagation and the prediction of meme trajectory are emerging areas of interest in the field of complex networks research. In addition to the properties of the meme itself, the structural properties of the underlying…
In this paper we introduce the notion of spread net. Spread nets are (safe) Petri nets equipped with vector clocks on places and with ticking functions on transitions, and are such that vector clocks are consistent with the ticking of…
In this paper, we introduce a novel concept for learning of the parameters in a neural network. Our idea is grounded on modeling a learning problem that addresses a trade-off between (i) satisfying local objectives at each node and (ii)…
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
This paper proposes some simple propagation rules which give rise to new binary constant-weight codes.
Understanding the process by which a contagion disseminates throughout a network is of great importance in many real world applications. The required sophistication of the inference approach depends on the type of information we want to…
We introduce frequency propagation, a learning algorithm for nonlinear physical networks. In a resistive electrical circuit with variable resistors, an activation current is applied at a set of input nodes at one frequency, and an error…
We constructs a new network by superposition of hexahedron , which are scale-free, highly sparse,disassortative ,and maximal planar graphs. The network degree distribution, agglomeration coefficient and degree of correlation are computed…
The Fresnel equation governing the propagation of electromagnetic waves for the most general linear constitutive law is derived. The wave normals are found to lie, in general, on a fourth order surface. When the constitutive coefficients…
We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…
We develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element of a specific Besov space. Subsequently we prove an alternative, albeit equivalent…
One of the most important features observed in real networks is that, as a network's topology evolves so does the network's ability to perform various complex tasks. To explain this, it has also been observed that as a network grows certain…
Neural segmentation has a great impact on the smooth implementation of local anesthesia surgery. At present, the network for the segmentation includes U-NET [1] and SegNet [2]. U-NET network has short training time and less training…
Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…
The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…
We present exact results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific…
The topic of this paper is the presentation of a new network model designed for networks consisting of spatial objects. This model allows the development of more advance representations of systems of networked objects and the study of…