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

Using Podcasts to Bring National Estuarine Research Reserves into the Classroom for Grades 6-12

In a typical classroom setting, there are significant challenges to exposing students to concepts related to earth sciences and the environment. These challenges are exacerbated when conveying lessons about geographic areas with limited access, such as oceans and coastlines (Louv, 2010). It is now more important than ever for environmental education to improve and adapt to our changing world. Educators may have the opportunity to bring these subjects to life by using media content such as podcasts to introduce students to new places and the scientists, managers and educators that work in those spaces. In the United States, there exists a system of protected coastal lands designated as National Estuarine Research Reserves (NERRs). Although education and public information sharing are part of the mission of the NERRs, there are few pathways to bring NERRs and the associated research, monitoring and conservation into schools that are distant from NERR sites. To address this educational gap, a teacher survey was conducted, and 43 responses were analyzed to identify best practices for middle school and high school lesson formats and assessment strategies. Based on the feedback from teacher surveys, an introductory podcast series called NERR or Far: The Reserves Are Where You Are was created for grades 6-12 on the NERRs of the Southeast, as well as supplemental resources for teachers, including classroom lesson plans. These podcasts are based on audio recordings of interviews with representatives from 7 NERR sites, including NERR managers, coastal training program coordinators and reserve educators. Podcast content covers coastal ecology, management, anthropology, hazard mitigation and opportunities for public interaction with NERR sites. The podcast series and teacher resources are hosted on a website and made freely available to the general public. This podcast series will increase access to regional conservation information and foster stewardship of the coastal waters of the southeast US

Kinetic measurements to investigate the oxygen-sensing properties of plant cysteine oxidases

Enzymatic O2 sensors transduce the availability of O2 within the cell into a physiological, typically adaptive response. One such O2-sensing enzymatic family is the N-terminal cysteine dioxygenases in plants (plant cysteine oxidases [PCOs]). In vitro kinetic studies have determined the O2-sensing capacity of PCOs. Here we describe the rationale and experimental protocol for an assay with which the O2 sensitivity of Arabidopsis thaliana PCOs (AtPCOs) can be measured. We explain each step from the recombinant protein synthesis of AtPCOs to the steady-state kinetic assays of AtPCOs for primary substrate and O2 from which kinetic parameters can be derived. The same techniques can be applied to other N-terminal cysteine thiol dioxygenases, e.g. 2-aminoethanethiol dioxygenase (ADO), and similar principles can be applied to determine kinetic characteristics of other oxygenase enzymes towards O2

The Effects of Acute Thermoneutral and Hot Water Immersion on Cerebrovascular Reactivity

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A dual drug regimen synergistically blocks human parainfluenza virus infection.

International audienceHuman parainfluenza type-3 virus (hPIV-3) is one of the principal aetiological agents of acute respiratory illness in infants worldwide and also shows high disease severity in the elderly and immunocompromised, but neither therapies nor vaccines are available to treat or prevent infection, respectively. Using a multidisciplinary approach we report herein that the approved drug suramin acts as a non-competitive in vitro inhibitor of the hPIV-3 haemagglutinin-neuraminidase (HN). Furthermore, the drug inhibits viral replication in mammalian epithelial cells with an IC50 of 30 μM, when applied post-adsorption. Significantly, we show in cell-based drug-combination studies using virus infection blockade assays, that suramin acts synergistically with the anti-influenza virus drug zanamivir. Our data suggests that lower concentrations of both drugs can be used to yield high levels of inhibition. Finally, using NMR spectroscopy and in silico docking simulations we confirmed that suramin binds HN simultaneously with zanamivir. This binding event occurs most likely in the vicinity of the protein primary binding site, resulting in an enhancement of the inhibitory potential of the N-acetylneuraminic acid-based inhibitor. This study offers a potentially exciting avenue for the treatment of parainfluenza infection by a combinatorial repurposing approach of well-established approved drugs

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

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

A novel dimeric exoglucanase (GH5_38)

An exoglucanase (Exg-D) from the glycoside hydrolase family 5 subfamily 38 (GH5_38) was heterologously expressed and structurally and biochemically characterised at a molecular level for its application in alkyl glycoside synthesis. The purified Exg-D existed in both dimeric and monomeric forms in solution, which showed highest activity on mixed-linked β-glucan (88.0 and 86.7 U/mg protein, respectively) and lichenin (24.5 and 23.7 U/mg protein, respectively). They displayed a broad optimum pH range from 5.5 to 7 and a temperature optimum from 40 to 60 °C. Kinetic studies demonstrated that Exg-D had a higher affinity towards β-glucan, with a Km of 7.9 mg/mL and a kcat of 117.2 s−1, compared to lichenin which had a Km of 21.5 mg/mL and a kcat of 70.0 s−1. The circular dichroism profile of Exg-D showed that its secondary structure consisted of 11% α-helices, 36% β-strands and 53% coils. Exg-D performed transglycosylation using p-nitrophenyl cellobioside as a glycosyl donor and several primary alcohols as acceptors to produce methyl-, ethyl- and propyl-cellobiosides. These products were identified and quantified via thin-layer chromatography (TLC) and liquid chromatography–mass spectrometry (LC-MS). We concluded that Exg-D is a novel and promising oligomeric glycoside hydrolase for the one-step synthesis of alkyl glycosides with more than one monosaccharide unit

Large deviations for the macroscopic motion of an interface

We study the most probable way an interface moves on a macroscopic scale from an initial to a final position within a fixed time in the context of large deviations for a stochastic microscopic lattice system of Ising spins with Kac interaction evolving in time according to Glauber (non-conservative) dynamics. Such interfaces separate two stable phases of a ferromagnetic system and in the macroscopic scale are represented by sharp transitions. We derive quantitative estimates for the upper and the lower bound of the cost functional that penalizes all possible deviations and obtain explicit error terms which are valid also in the macroscopic scale. Furthermore, using the result of a companion paper about the minimizers of this cost functional for the macroscopic motion of the interface in a fixed time, we prove that the probability of such events can concentrate on nucleations should the transition happen fast enough

Beyond Kinetic Relations

We introduce the concept of kinetic equations representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries, link the instantaneous value of the velocity of a defect with an instantaneous value of the driving force. The new approach generalizes kinetic relations by implying a relation between the velocity and the driving force which is nonlocal in time. To make this relations explicit one needs to integrate the system of kinetic equations. We illustrate the difference between kinetic relation and kinetic equations by working out in full detail a prototypical model of an overdamped defect in a one-dimensional discrete lattice. We show that the minimal nonlocal kinetic description containing now an internal time scale is furnished by a system of two ordinary differential equations coupling the spatial location of defect with another internal parameter that describes configuration of the core region.Comment: Revised version, 33 pages, 9 figure