Further results for the Dunkl Transform and the generalized Ces\`aro operator

In this paper, we consider Dunkl theory on R^d associated to a finite reflection group. This theory generalizes classical Fourier anal- ysis. First, we give for 1 < p <= 2, sufficient conditions for weighted Lp-estimates of the Dunkl transform of a function f using respectively the modulus of continuity of f in the radial case and the convolution for f in the general case. In particular, we obtain as application, the integrability of this transform on Besov-Lipschitz spaces. Second, we provide necessary and sufficient conditions on nonnegative functions phi defined on [0; 1] to ensure the boundedness of the generalized Ces\`aro operator C_phi on Herz spaces and we obtain the corresponding operator norm inequalities.Comment: 19 page

SENATUS: An Approach to Joint Traffic Anomaly Detection and Root Cause Analysis

In this paper, we propose a novel approach, called SENATUS, for joint traffic anomaly detection and root-cause analysis. Inspired from the concept of a senate, the key idea of the proposed approach is divided into three stages: election, voting and decision. At the election stage, a small number of \nop{traffic flow sets (termed as senator flows)}senator flows are chosen\nop{, which are used} to represent approximately the total (usually huge) set of traffic flows. In the voting stage, anomaly detection is applied on the senator flows and the detected anomalies are correlated to identify the most possible anomalous time bins. Finally in the decision stage, a machine learning technique is applied to the senator flows of each anomalous time bin to find the root cause of the anomalies. We evaluate SENATUS using traffic traces collected from the Pan European network, GEANT, and compare against another approach which detects anomalies using lossless compression of traffic histograms. We show the effectiveness of SENATUS in diagnosing anomaly types: network scans and DoS/DDoS attacks