Related papers: On the Virtual Network Embedding polytope
With the widespread use of information technologies, information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, telecommunication networks,…
Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing…
This manuscript develops edge-averaged virtual element (EAVE) methodologies to address convection-diffusion problems effectively in the convection-dominated regime. It introduces a variant of EAVE that ensures monotonicity (producing an…
In the conventional cloud service model, computing resources are allocated for tenants on a pay-per-use basis. However, the performance of applications that communicate inside this network is unpredictable because network resources are not…
Recent years have witnessed the remarkable success of applying Graph machine learning (GML) to node/graph classification and link prediction. However, edge classification task that enjoys numerous real-world applications such as social…
We present the non-conforming Virtual Element Method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component…
Virtual reality (VR) over wireless is emerging as an important use case of 5G networks. Immersive VR experience requires the delivery of huge data at ultra-low latency, thus demanding ultra-high transmission rate. This challenge can be…
The rise of 5G/6G network technologies promises to enable applications like autonomous vehicles and virtual reality, resulting in a significant increase in connected devices and necessarily complicating network management. Even worse, these…
Neural networks with piecewise linear activation functions, such as rectified linear units (ReLU) or maxout, are among the most fundamental models in modern machine learning. We make a step towards proving lower bounds on the size of such…
Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding existing spatial…
Network slicing is a critical feature in 5G and beyond communication systems, enabling the creation of multiple virtual networks (i.e., slices) on a shared physical network infrastructure. This involves efficiently mapping each slice…
As one key enabler of Intelligent Transportation System (ITS), Vehicular Ad Hoc Network (VANET) has received remarkable interest from academia and industry. The emerging vehicular applications and the exponential growing data have naturally…
Recent Vision-and-Language Navigation (VLN) advancements are promising, but their idealized assumptions about robot movement and control fail to reflect physically embodied deployment challenges. To bridge this gap, we introduce VLN-PE, a…
As we move from 5G to 6G, edge computing is one of the concepts that needs revisiting. Its core idea is still intriguing: instead of sending all data and tasks from an end user's device to the cloud, possibly covering thousands of…
For the 2D and 3D Virtual Element Methods (VEM), a new approach to improve the conditioning of local and global matrices in the presence of badly-shaped polytopes is proposed. It defines the local projectors and the local degrees of freedom…
Network embedding, which aims to learn low-dimensional representations of nodes, has been used for various graph related tasks including visualization, link prediction and node classification. Most existing embedding methods rely solely on…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of…
Network virtualization is a way to simultaneously run multiple heterogeneous architectures on a shared substrate. The main issue in the virtualization of networks is the problem of mapping virtual networks to the substrate network. How to…
This short note reports a new derivation of the optimal order of the a priori error estimates for conforming virtual element methods (VEM) on 3D polyhedral meshes based on an error equation. The geometric assumptions, which are necessary…