Related papers: Osculating Spaces of Varieties and Linear Network …
The problem of securing a network coding communication system against an eavesdropper adversary is considered. The network implements linear network coding to deliver n packets from source to each receiver, and the adversary can eavesdrop…
We present a family of networks, expanded deterministic Apollonian networks, which are a generalization of the Apollonian networks and are simultaneously scale-free, small-world, and highly clustered. We introduce a labeling of their…
3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the…
We study a class of linear network coding (LNC) schemes, called circular-shift LNC, whose encoding operations consist of only circular-shifts and bit-wise additions (XOR). Formulated as a special vector linear code over GF($2$), an…
A vector sensor, a type of sensor array with six collocated antennas to measure all electromagnetic field components of incident waves, has been shown to be advantageous in estimating the angle of arrival and polarization of the incident…
Spatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is two-dimensional and until recently and traditionally, the metric that was usually considered was the Euclidean distance. In…
Complex networks are a useful tool to investigate various phenomena in social science, economics, and logistics. Node Vector Distance (NVD) is an emerging set of techniques allowing us to estimate the distance and correlation between…
Network embedding is a general-purpose machine learning technique that encodes network structure in vector spaces with tunable dimension. Choosing an appropriate embedding dimension -- small enough to be efficient and large enough to be…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
Random linear network codes can be designed and implemented in a distributed manner, with low computational complexity. However, these codes are classically implemented over finite fields whose size depends on some global network parameters…
Based on ideas of K\"otter and Kschischang we use constant dimension subspaces as codewords in a network. We show a connection to the theory of q-analogues of a combinatorial designs, which has been studied in Braun, Kerber and Laue as a…
In this paper we have found a necessary and sufficient condition for equivalence of two norms on a linear space using the theory of exponential vector space. Exponential vector space is an ordered algebraic structure which can be considered…
We consider the problem of two transmitters wishing to exchange information through a relay in the middle. The channels between the transmitters and the relay are assumed to be synchronized, average power constrained additive white Gaussian…
Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such…
For discrete memoryless multiple-access channels, we propose a general definition of variable length codes with a measure of the transmission rates at the receiver side. This gives a receiver perspective on the multiple-access channel…
Linear codes with large minimal distances are important error correcting codes in information theory.Orthogonal codes have more applications in the other fields of mathematics. In this paper, we study the binary and ternary orthogonal codes…
Linear codes in the projective space $\mathbb{P}_q(n)$, the set of all subspaces of the vector space $\mathbb{F}_q^n$, were first considered by Braun, Etzion and Vardy. The Grassmannian $\mathbb{G}_q(n,k)$ is the collection of all subspaces…
We introduce and study the notion of orthosymmetric spaces over an Archimedean vector lattice as a generalization of finite-dimentional Euclidean inner spaces. A special attention has been paid to linear operators on these spaces.
The problem of obtaining network coding maps for the physical layer network coded two-way relay channel is considered, using the denoise-and-forward forward protocol. It is known that network coding maps used at the relay node which ensure…
We study the Euclidean Distance degree of algebraic neural network models from the perspective of algebraic geometry. Focusing on shallow networks with two neurons, quadratic activation, and scalar output, we identify the associated…