Minimum norm regularization of descriptor systems by mixed output feedback

We study the regularization problem for linear, constant coefficient descriptor systems Ex' = Ax+Bu, y1 = Cx, y2 = Γx' by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and E+BGΓ has a desired rank, i.e., there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Properties of singular vectors using convective available potential energy as final time norm

We study the feasibility of using the singular vector technique to create initial condition perturbations for short-range ensemble prediction systems (SREPS) focussing on predictability of severe local storms and in particular deep convection. For this a new final time semi-norm based on the convective available potential energy (CAPE) is introduced. We compare singular vectors using the CAPE-norm with SVs using the more common total energy (TE) norm for a 2-week summer period in 2007, which includes a case of mesoscale extreme rainfall in the south west of Finland. The CAPE singular vectors perturb the CAPE field by increasing the specific humidity and temperature of the parcel and increase the lapse rate above the parcel in the lower troposphere consistent with physical considerations. The CAPE-SVs are situated in the lower troposphere. This in contrast to TE-SVs with short optimization times which predominantly remain in the high troposphere. By examining the time evolution of the CAPE singular values we observe that the convective event in the south west of Finland is clearly associated with high CAPE singular values.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

The proportion of failures of the Hasse norm principle

For any number field we calculate the exact proportion of rational numbers which are everywhere locally a norm but not globally a norm from the number field.

Norm diffusion within international organizations: a case study of the World Bank

Constructivists often argue that International Organizations (IOs) diffuse norms throughout the international system. This article asks the question: if IOs promote and diffuse specific norms within world politics, where do these norms come from? In particular, this analysis seeks to formulate how IOs' identities emerge in issue areas where rationalist theories give limited explanation, such as the environment. This article posits that IOs interact with and consume norms from non-state actors such as transnational advocacy networks, a process overlooked by the constructivist analysis of institutions. This is examined through a case study of the World Bank's environmental identity where transnational advocacy networks played an important role in the Bank's shift towards sustainable development, through processes characterized here as direct and indirect socialization. This article demonstrates that the Bank's shift was more than instrumental as a result of this interaction, and that constructivists therefore need to examine the role of IOs as norm consumers as well as norm diffusers.

Theorizing norm diffusion within international organizations

International Organizations (IOs) promote and diffuse norms within world politics. This prompts the question: where do these norms come from? This inquiry analyses how IOs have been perceived within the emerging norms literature where IOs are 'norm diffusers' within the international system, and finds that the way in which IOs themselves internalize norms has not been taken into account. This poses a potentially fruitful new avenue of inquiry into why and when IOs behave as norm diffusers. An interpretation of when and why IOs internalize norms is offered by positing that IO identities are not fixed and that they are 'norm consumers' socialized by state and non-state actors.

Norm-based behaviour modification in BDI agents

While there has been much work on developing frameworks and models of norms and normative systems, consideration of the impact of norms on the practical reasoning of agents has attracted less attention. The problem is that traditional agent architectures and their associated languages provide no mechanism to adapt an agent at runtime to norms constraining their behaviour. This is important because if BDI-type agents are to operate in open environments, they need to adapt to changes in the norms that regulate such environments. In response, in this paper we provide a technique to extend BDI agent languages, by enabling them to enact behaviour modification at runtime in response to newly accepted norms. Our solution consists of creating new plans to comply with obligations and suppressing the execution of existing plans that violate prohibitions. We demonstrate the viability of our approach through an implementation of our solution in the AgentSpeak(L) language.

An unified framework based on p-norm for feature aggregation in content- based image retrieval

Feature aggregation is a critical technique in content- based image retrieval systems that employ multiple visual features to characterize image content. In this paper, the p-norm is introduced to feature aggregation that provides a framework to unify various previous feature aggregation schemes such as linear combination, Euclidean distance, Boolean logic and decision fusion schemes in which previous schemes are instances. Some insights of the mechanism of how various aggregation schemes work are discussed through the effects of model parameters in the unified framework. Experiments show that performances vary over feature aggregation schemes that necessitates an unified framework in order to optimize the retrieval performance according to individual queries and user query concept. Revealing experimental results conducted with IAPR TC-12 ImageCLEF2006 benchmark collection that contains over 20,000 photographic images are presented and discussed.