Multiscale Haar Orthonormal Matrices with the Corresponding Riesz Products and a Characterization of Cantor-Type Languages

ABSTRACT. We introduce a class of multiscale orthonormal matrices H (m) of orde

An ecological approach to anomaly detection: the EIA Model.

The presented work proposes a new approach for anomaly detection. This approach is based on changes in a population of evolving agents under stress. If conditions are appropriate, changes in the population (modeled by the bioindicators) are representative of the alterations to the environment. This approach, based on an ecological view, improves functionally traditional approaches to the detection of anomalies. To verify this assertion, experiments based on Network Intrussion Detection Systems are presented. The results are compared with the behaviour of other bioinspired approaches and machine learning techniques

Affine dual frames and Extension Principles

In this work we provide three new characterizations of affine dual frames constructed from refinable functions. The first one is similar to Daubechies et al. (2003) [10, Proposition 5.2] but without any decay assumptions on the generators of a pair of affine systems. The second one reveals the geometric significance of the Mixed Fundamental function and the third one shows that the Mixed Oblique Extension Principle actually characterizes dual framelets. We also extend recent results on the characterization of affine Parseval frames obtained in Stavropoulos (2012) [27, Theorem 2.3]. © 2013 Elsevier Inc

Erratum to “On the design of multi-dimensional compactly supported Parseval framelets with directional characteristics” (Linear Algebra and Its Applications (2019) 582 (1–36), (S0024379519303155), (10.1016/j.laa.2019.07.028))

The correct author listing is the following: N. Karantzasa, N. Atreasb, M. Papadakisa, T. Stavropoulosc [Formula presented] Dept. of Mathematics, University of Houston, USA [Formula presented] Dept. of Mathematics, National and Kapodistrian University of Athens, Greece © 2019 Elsevier Inc