Output Feedback Invariants

The paper is concerned with the problem of determining a complete set of invariants for output feedback. Using tools from geometric invariant theory it is shown that there exists a quasi-projective variety whose points parameterize the output feedback orbits in a unique way. If the McMillan degree $n\geq mp$, the product of number of inputs and number of outputs, then it is shown that in the closure of every feedback orbit there is exactly one nondegenerate system.Comment: 15 page

Relative CC"-Numerical Ranges for Applications in Quantum Control and Quantum Information

Motivated by applications in quantum information and quantum control, a new type of $C$"-numerical range, the relative $C$"-numerical range denoted $W_K(C,A)$, is introduced. It arises upon replacing the unitary group U(N) in the definition of the classical $C$"-numerical range by any of its compact and connected subgroups $K \subset U(N)$. The geometric properties of the relative $C$"-numerical range are analysed in detail. Counterexamples prove its geometry is more intricate than in the classical case: e.g. $W_K(C,A)$ is neither star-shaped nor simply-connected. Yet, a well-known result on the rotational symmetry of the classical $C$"-numerical range extends to $W_K(C,A)$, as shown by a new approach based on Lie theory. Furthermore, we concentrate on the subgroup $SU_{\rm loc}(2^n) := SU(2)\otimes ... \otimes SU(2)$, i.e. the $n$-fold tensor product of SU(2), which is of particular interest in applications. In this case, sufficient conditions are derived for $W_{K}(C,A)$ being a circular disc centered at origin of the complex plane. Finally, the previous results are illustrated in detail for $SU(2) \otimes SU(2)$.Comment: accompanying paper to math-ph/070103

Numerical modelling of methyl iodide in the eastern tropical Atlantic

Methyl iodide (CH3I) is a volatile organic halogen compound that contributes significantly to the transport of iodine from the ocean to the atmosphere, where it plays an important role in tropospheric chemistry. CH3I is naturally produced and occurs in the global ocean. The processes involved in the formation of CH3I, however, are not fully understood. In fact, there is an ongoing debate whether production by phytoplankton or photochemical degradation of organic matter is the main source term. Here, both the biological and photochemical production mechanisms are considered in a biogeochemical module that is coupled to a one-dimensional water column model for the eastern tropical Atlantic. The model is able to reproduce observed subsurface maxima of CH3I concentrations. But, the dominating source process cannot be clearly identified as subsurface maxima can occur due to both direct biological and photochemical production. However, good agreement between the observed and simulated difference between surface and subsurface methyl iodide concentrations is achieved only when direct biological production is taken into account. Production rates for the biological CH3I source that were derived from published laboratory studies are shown to be inappropriate for explaining CH3I concentrations in the eastern tropical Atlantic

The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

The Optimal Control Landscape for the Generation of Unitary Transformations with Constrained Dynamics

The reliable and precise generation of quantum unitary transformations is essential to the realization of a number of fundamental objectives, such as quantum control and quantum information processing. Prior work has explored the optimal control problem of generating such unitary transformations as a surface optimization problem over the quantum control landscape, defined as a metric for realizing a desired unitary transformation as a function of the control variables. It was found that under the assumption of non-dissipative and controllable dynamics, the landscape topology is trap-free, implying that any reasonable optimization heuristic should be able to identify globally optimal solutions. The present work is a control landscape analysis incorporating specific constraints in the Hamiltonian corresponding to certain dynamical symmetries in the underlying physical system. It is found that the presence of such symmetries does not destroy the trap-free topology. These findings expand the class of quantum dynamical systems on which control problems are intrinsically amenable to solution by optimal control.Comment: Submitted to Journal of Mathematical Physic

Eccrine porocarcinoma of the head: An important differential diagnosis in the elderly patient

Background: Eccrine porocarcinoma is a rare malignant tumor of the sweat gland, characterized by a broad spectrum of clinicopathologic presentations. Surprisingly, unlike its benign counterpart eccrine poroma, eccrine porocarcinoma is seldom found in areas with a high density of eccrine sweat glands, like the palms or soles. Instead, eccrine porocarcinoma frequently occurs on the lower extremities, trunk and abdomen, but also on the head, resembling various other skin tumors, as illustrated in the patients described herein. Observations: We report 5 cases of eccrine porocarcinoma of the head. All patients were initially diagnosed as having epidermal or melanocytic skin tumors. Only after histopathologic examination were they classified as eccrine porocarcinoma, showing features of epithelial tumors with abortive ductal differentiation. Characteristic clinical, histopathologic and immunohistochemical findings of eccrine porocarcinomas are illustrated. Conclusion: Eccrine porocarcinomas are potentially fatal adnexal malignancies, in which extensive metastatic dissemination may occur. Porocarcinomas are commonly overlooked, or misinterpreted as squamous or basal cell carcinomas as well as other common malignant and even benign skin tumors. Knowledge of the clinical pattern and histologic findings, therefore, is crucial for an early therapeutic intervention, which can reduce the risk of tumor recurrence and serious complications. Copyright (c) 2008 S. Karger AG, Basel

Leukotriene receptor expression in esophageal squamous cell cancer and non-transformed esophageal epithelium: a matched case control study

Study questionnaire. (DOC 21 kb

Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde

From parliamentary pay to party funding: the acceptability of informal institutions in advanced democracies

While direct state funding of political parties has been a prominent theme in cross-national research over the last decade, we still know little about party strategies to access state resources that are not explicitly earmarked for partisan usage. This paper looks at one widespread but often overlooked informal party practice: the ‘taxing’ of MP salaries, i.e., the regular transfer of fixed salary shares to party coffers. Building on notions of informal institutions developed in work on new democracies, our theoretical approach specifies factors that shape the acceptability of this legally non-enforceable intra-organisational practice. It is tested through a selection model applied to a unique data set covering 124 parties across 19 advanced democracies. Controlling for a range of party- and institutional-level variables, we find that the presence of a taxing rule and the collection of demanding tax shares are more common in leftist parties (high internal acceptability) and in systems in which the penetration of state institutions by political parties is intense (high external acceptability)