Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page

Spectrum of the three dimensional fuzzy well

We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schr\"odinger equation for a free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well have been calculated

Supporting the externalisation of thinking in criminal intelligence analysis

At the end of the criminal intelligence analysis process there are relatively well established and understood approaches to explicit externalisation and representation of thought that include theories of argumentation, narrative and hybrid approaches that include both of these. However the focus of this paper is on the little understood area of how to support users in the process of arriving at such representations from an initial starting point where little is given. The work is based on theoretical considerations and some initial studies with end users. In focusing on process we discuss the requirements of fluidity and rigor and how to gain traction in investigations, the processes of thinking involved including abductive, deductive and inductive reasoning, how users may use thematic sorting in early stages of investigation and how tactile reasoning may be used to externalize and facilitate reasoning in a productive way. In the conclusion section we discuss the issues raised in this work and directions for future work

How analysts think: how do criminal intelligence analysts recognise and manage significant information?

The Criminal Intelligence Analyst's role is to create exhibits which are relevant, accurate and unbiased. Exhibits can be used as input to assist decision-making in intelligence-led policing. It may also be used as evidence in a court of law. The aim of this study was to determine how Criminal Intelligence Analysts recognise and manage significant information as a method to determine what is relevant for their attention and for the creation of exhibits. This in turn may provide guidance on how to design and incorporate loose and flexible argumentation schemas into sense-making software. The objective is to be informed on how to design software, which affords Criminal Intelligence Analysts with the ability to effortlessly determine the relevance of information, which subsequently could assist with the process of assessing and defending the quality of exhibits

Addition of H_2O and O_2 to Acetone and Dimethylsulfoxide Ligated Uranyl(V) Dioxocations

Gas-phase complexes of the formula [UO_2(lig)]^+ (lig = acetone (aco) or dimethylsulfoxide (dmso)) were generated by electrospray ionization (ESI) and studied by tandem ion-trap mass spectrometry to determine the general effect of ligand charge donation on the reactivity of UO_2^+ with respect to water and dioxygen. The original hypothesis that addition of O_2 is enhanced by strong σ-donor ligands bound to UO_2^+ is supported by results from competitive collision-induced dissociation (CID) experiments, which show near exclusive loss of H_2O from [UO_2(dmso)(H_2O)(O_2)]^+, whereas both H_2O and O_2 are eliminated from the corresponding [UO_2(aco)(H_2O)(O_2)]^+ species. Ligand-addition reaction rates were investigated by monitoring precursor and product ion intensities as a function of ion storage time in the ion-trap mass spectrometer: these experiments suggest that the association of dioxygen to the UO_2^+ complex is enhanced when the more basic dmso ligand was coordinated to the metal complex. Conversely, addition of H_2O is favored for the analogous complex ion that contains an aco ligand. Experimental rate measurements are supported by density function theory calculations of relative energies, which show stronger bonds between UO_2^+ and O_2 when dmso is the coordinating ligand, whereas bonds to H_2O are stronger for the aco complex

How analysts think: navigating uncertainty – aspirations, considerations and strategies

While there has been considerable research in understanding the process of sense making in criminal intelligence analysis as well as the formulation of arguments in the domain of law, there remain gaps in our understanding of how to move seamlessly from the fluidity of the sense making activities to the rigour of argumentation construction. This matter is complicated further with high uncertainty which accompanies sense making and which propagates through to the rigour that accompanies argumentation. This paper attempts to understand how Criminal Intelligence Analysts navigate uncertainty from fluidity to rigour constructs and outlines some of the considerations and strategies deployed by the Criminal Intelligence Analyst to reach, or increase, certainty at a given point in time during the analysis process. This paper concludes by proposing preliminary suggestions with the aim to narrow the gaps in this journey from fluidity to rigour, at least, marginall