Cohomology and Support Varieties for Lie Superalgebras II

In \cite{BKN} the authors initiated a study of the representation theory of classical Lie superalgebras via a cohomological approach. Detecting subalgebras were constructed and a theory of support varieties was developed. The dimension of a detecting subalgebra coincides with the defect of the Lie superalgebra and the dimension of the support variety for a simple supermodule was conjectured to equal the atypicality of the supermodule. In this paper the authors compute the support varieties for Kac supermodules for Type I Lie superalgebras and the simple supermodules for $\mathfrak{gl}(m|n)$. The latter result verifies our earlier conjecture for $\mathfrak{gl}(m|n)$. In our investigation we also delineate several of the major differences between Type I versus Type II classical Lie superalgebras. Finally, the connection between atypicality, defect and superdimension is made more precise by using the theory of support varieties and representations of Clifford superalgebras.Comment: 28 pages, the proof of Proposition 4.5.1 was corrected, several other small errors were fixe

Complexity for Modules Over the Classical Lie Superalgebra gl(m|n)

Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus \mathfrak{g}_{\bar{1}}$ be a classical Lie superalgebra and $\mathcal{F}$ be the category of finite dimensional $\mathfrak{g}$-supermodules which are completely reducible over the reductive Lie algebra $\mathfrak{g}_{\bar{0}}$. In an earlier paper the authors demonstrated that for any module $M$ in $\mathcal{F}$ the rate of growth of the minimal projective resolution (i.e., the complexity of $M$) is bounded by the dimension of $\mathfrak{g}_{\bar{1}}$. In this paper we compute the complexity of the simple modules and the Kac modules for the Lie superalgebra $\mathfrak{gl}(m|n)$. In both cases we show that the complexity is related to the atypicality of the block containing the module.Comment: 32 page

Estimation of denitrification potential with respiration based techniques

Denitrification with its prerequisite process nitrification, is a common practice to remove nitrogen from wastewater in activated sludge systems. Although the key factors detrimental to its performance are well recognised, not all links are implemented for optimal design and operation performance. The relation between detailed wastewater characterisation and denitrification potential (DP) is the most crucial example of information that should be better incorporated in design and optimisation procedures. The lumped parameters COD/N and BOD 5 /N (nowadays used in many design approaches) or empirical values of denitrification rates do not allow to predict precisely the denitrification potential due to a unique character of each activated sludge and wastewater. Advanced activated sludge models require the input of a significant number of parameters. Since the estimation of each parameter is difficult and time consuming, the choice of default values is an option but this can lead to erroneous predictions of reality. Far-simplified models, usually based on on-line measurement of process state variables, describe processes with the simplest kinetics what in turn restricts seriously their implementation.In this thesis a methodology is presented to estimate the DP in relation to wastewater and activated sludge characteristics. Two respiration techniques form the basis for two different approaches: the anoxic nitrate utilisation rate (NUR-) test and the aerobic oxygen utilisation rate (OUR-) test. The approach based on the NUR-test is a direct method for the assessment of the DP. The approach based on the OUR-test is an indirect method because a simplified model is necessary to transform oxygen utilisation rate to nitrate utilisation rate. The NUR-test, except of serving as a tool to estimate directly the DP, enables to acquire simplified denitrification kinetics and a relevant wastewater characterisation, leading consequently to a prediction of the denitrification capacity and nitrate effluent quality. Knowledge about actual activated sludge kinetics and wastewater (or other substrate) characteristics allows to establish relations between sludge loading rate and achievable denitrification rate.The OUR-test was the base to formulate the simplified nitrification-denitrification model, where estimated substrate conversion rates are used without biomass population dynamics. Moreover, the aerobic and anoxic organic biodegradable substrate conversions are modelled with the same relations with the only difference that for anoxic conditions appropriate reduction factors are incorporated in conversion kinetics to reflect a slower activity of activated sludge under denitrifying conditions. A novel methodology based on aerobic and anoxic respiration tests is proposed to estimate the reduction factors. The proposed model approach constitutes an alternative for both complex and far-simplified model approaches. It enables to predict the overall N-removal potential and N-effluent quality of a system, based on an actual detailed wastewater and activated sludge characterisation. Good results from dynamic and static testing of the model implicates its possible implementation in control strategies, like e.g. a feed-back control of the denitrification by a nitrate-rich recycle rate, anoxic volume or the addition of an external carbon source.The effect of a decrease in the biodegradable COD-fraction by pre-treatment (pre-precipitation) on the DP was examined. For an evaluation the developed respiration based methodologies were used to estimate the DP in relation to wastewater and activated sludge characteristics. Implemented optimisation procedures revealed that the original denitrification potential of the wastewater determines the process capacity and efficiency. Optimisation steps by the manipulation of technological parameters in the existing process configuration or control strategies may therefore improve process performance only to small extent.</p

DESIGNING AND EVALUATING A PORTABLE LIDAR-BASED SLAM SYSTEM

Mobile Mapping Technology (MMT) has evolved rapidly over the past few decades, especially in using low-cost sensors. This progress is primarily attributed to the appearance of innovative simultaneous localization and mapping (SLAM) algorithms. This article focuses on evaluating the efficiency of a new LiDAR-based portable SLAM system for mapping in dynamic real-world environments. The work proposed a technical solution based on a Livox Avia LiDAR sensor enhanced by gimbal stabilization. The system, named Portable Livox-based Mapping system (PoLiMap), is compared to other similar solutions by acquiring data from various environments, including urban sceneries, underground tunnels and forested areas, and processing them using a modified FAST-LIO-SLAM algorithm. The research presented in the article contributes to the understanding of the capabilities of PoLiMap systems under various conditions and offers significant insight into its potential applications. Accuracy evaluation results prove that the proposed MMT system can successfully tackle various demanding environments and challenge the results of other more costly state-of-the-art portable mobile laser scanning methods

Neural correlates of explicit and implicit emotion processing in relation to treatment response in pediatric anxiety

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136676/1/jcpp12658_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136676/2/jcpp12658.pd