Eigenvectors of block circulant and alternating circulant matrices

The eigenvectors and eigenvalues of block circulant matrices had been found for real symmetric matrices with symmetric submatrices, and for block circulant matrices with circulant submatrices. The eigenvectors are now found for general block circulant matrices, including the Jordan Canonical Form for defective eigenvectors. That analysis is applied to Stephen J. Watson’s alternating circulant matrices, which reduce to block circulant matrices with square submatrices of order 2

Generalized Low-Density Parity-Check Coding Aided Multilevel Codes

Classic Low-Density Parity-Check (LDPC) codes have recently been used as component codes in Multilevel Coding (MLC) due to their impressive BER performance as well as owing to their flexible coding rates. In this paper, we proposed a Multilevel Coding invoking Generalized Low-Density Parity-Check (GLDPC) component codes, which is capable of outperforming the classic LDPC component codes at a reduced decoding latency, when communicating over AWGN and uncorrelated Rayleigh fading channels

Area contraction for harmonic automorphisms of the disk

A harmonic self-homeomorphism of a disk does not increase the area of any concentric disk.Comment: 7 page

Towards an approximate graph entropy measure for identifying incidents in network event data

A key objective of monitoring networks is to identify potential service threatening outages from events within the network before service is interrupted. Identifying causal events, Root Cause Analysis (RCA), is an active area of research, but current approaches are vulnerable to scaling issues with high event rates. Elimination of noisy events that are not causal is key to ensuring the scalability of RCA. In this paper, we introduce vertex-level measures inspired by Graph Entropy and propose their suitability as a categorization metric to identify nodes that are a priori of more interest as a source of events. We consider a class of measures based on Structural, Chromatic and Von Neumann Entropy. These measures require NP-Hard calculations over the whole graph, an approach which obviously does not scale for large dynamic graphs that characterise modern networks. In this work we identify and justify a local measure of vertex graph entropy, which behaves in a similar fashion to global measures of entropy when summed across the whole graph. We show that such measures are correlated with nodes that generate incidents across a network from a real data set