On invariant Rings of Sylow subgroups of finite classical groups

In this thesis we study the invariant rings for the Sylow p-subgroups of the nite classical groups. We have successfully constructed presentations for the invariant rings for the Sylow p-subgroups of the unitary groups GU(3; Fq2) and GU(4; Fq2 ), the symplectic group Sp(4; Fq) and the orthogonal group O+(4; Fq) with q odd. In all cases, we obtained a minimal generating set which is also a SAGBI basis. Moreover, we computed the relations among the generators and showed that the invariant ring for these groups are a complete intersection. This shows that, even though the invariant rings of the Sylow p-subgroups of the general linear group are polynomial, the same is not true for Sylow p-subgroups of general classical groups. We also constructed the generators for the invariant elds for the Sylow p-subgroups of GU(n; Fq2 ), Sp(2n; Fq), O+(2n; Fq), O-(2n + 2; Fq) and O(2n + 1; Fq), for every n and q. This is an important step in order to obtain the generators and relations for the invariant rings of all these groups.

Low cost non-intrusive home energy monitoring

This thesis presents a low cost non-intrusive home energy monitor built on top of Non-Intrusive Load Monitoring (NILM) concepts and techniques. NILM solutions are already considered low cost alternatives to the big majority of existing commercial energy monitors but the goal here is to make its cost even lower by using a mini netbook as a whole in one solution. The mini netbook is installed in the homes main circuit breaker and computes power consumption by reading current and voltage from the built-in sound card. At the same time, feedback to the users is provided using the 11’’ LCD screen as well as other built-in I/O modules. Our meter is also capable of detecting changes in power and tries to find out which appliance lead to that change and it is being used as part of an eco-feedback platform that was build to study the long terms of energy eco-feedback in individuals. In this thesis the steps that were taken to come up with such a system are presented, from the basics of AC power measurements to the implementation of an event detector and classifier that was used to disaggregate the power load. In the last chapter results from some validation tests that have been performed are presented in order to validate the experiment. It is believed that such a system will not only be important as an energy monitor, but also as an open system than can be easily changed to accommodate and test new or existing nonintrusive load monitoring techniques.