Ground Beetles of Islands in the Western Basin of Lake Erie and the Adjacent Mainland (Coleoptera: Carabidae, Including Cicindelini)

We report 241 species representing 63 genera of ground beetles from the islands of the western basin of Lake Erie and selected mainland sites from a 1991-93 survey, plus specimens examined in public and private collections, and previously published sources. Most species are generally distributed; however, a restricted population of Sphaeroderus schaumii schaumii we rediscovered is no doubt imperiled. Comparison of wing morphotype frequencies of the Lake Erie island species with mainland populations from studies in Ohio and Michigan support a hypothesis that vagility is of increased import in the islands. Regression and correlation analysis show a positive relationship between species number and island area, no correlation between species number and distance from the mainland and an improved fit for a multiple regression which includes collecting effort

Entanglement frustration for Gaussian states on symmetric graphs

We investigate the entanglement properties of multi-mode Gaussian states, which have some symmetry with respect to the ordering of the modes. We show how the symmetry constraints the entanglement between two modes of the system. In particular, we determine the maximal entanglement of formation that can be achieved in symmetric graphs like chains, 2d and 3d lattices, mean field models and the platonic solids. The maximal entanglement is always attained for the ground state of a particular quadratic Hamiltonian. The latter thus yields the maximal entanglement among all quadratic Hamiltonians having the considered symmetry.Comment: 5 pages, 1 figur

Hierarchical Control and Trajectory Planning

Most of the time on this project was spent on the trajectory planning problem. The construction is equivalent to the classical spline construction in the case that the system matrix is nilpotent. If the dimension of the system is n then the spline of degree 2n-1 is constructed. This gives a new approach to the construction of splines that is more efficient than the usual construction and at the same time allows the construction of a much larger class of splines. All known classes of splines are reconstructed using the approach of linear control theory. As a numerical analysis tool control theory gives a very good tool for constructing splines. However, for the purposes of trajectory planning it is quite another story. Enclosed in this document are four reports done under this grant

Theory of impedance networks: The two-point impedance and LC resonances

We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving the equation L u_a = lambda_a u_a^* with orthonormal vectors u_a, the effective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p} - u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identically equal to zero and u_{a,p} is the p-th component of u_a. For networks consisting of inductances (L) and capacitances (C), the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of lambda_a. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.Comment: 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63) correcte

Interference of Quantum Channels

We show how interferometry can be used to characterise certain aspects of general quantum processes, in particular, the coherence of completely positive maps. We derive a measure of coherent fidelity, maximum interference visibility and the closest unitary operator to a given physical process under this measure.Comment: 4 pages, 5 figures, REVTeX 4, typographical corrections and added acknowledgemen

Reversible Eu²⁺ ↔ Eu³⁺ transitions at Eu‐Si interfaces

Valence switching at Eu‐Si interfaces is demonstrated by resonant photoemission during repeated oxidation‐reduction cycles performed by room‐temperature O2 exposure and mild heating. The Eu2+ ↔ Eu3+ transitions are accompanied by Fermi level switching associated with changes in the stoichiometry of the surface heterostructure. The ability to cycle between two well‐defined magnetic states at a surface may be attractive in technological applications

Prediction and classification for GPCR sequences based on ligand specific features

Functional identification of G-Protein Coupled Receptors (GPCRs) is one of the current focus areas of pharmaceutical research. Although thousands of GPCR sequences are known, many of them are orphan sequences (the activating ligand is unknown). Therefore, classification methods for automated characterization of orphan GPCRs are imperative. In this study, for predicting Level 1 subfamilies of GPCRs, a novel method for obtaining class specific features, based on the existence of activating ligand specific patterns, has been developed and utilized for a majority voting classification. Exploiting the fact that there is a non-promiscuous relationship between the specific binding of GPCRs into their ligands and their functional classification, our method classifies Level 1 subfamilies of GPCRs with a high predictive accuracy between 99% and 87% in a three-fold cross validation test. The method also tells us which motifs are significant for class determination which has important design implications. The presented machine learning approach, bridges the gulf between the excess amount of GPCR sequence data and their poor functional characterization

Singular value decomposition and matrix reorderings in quantum information theory

We review Schmidt and Kraus decompositions in the form of singular value decomposition using operations of reshaping, vectorization and reshuffling. We use the introduced notation to analyse the correspondence between quantum states and operations with the help of Jamiolkowski isomorphism. The presented matrix reorderings allow us to obtain simple formulae for the composition of quantum channels and partial operations used in quantum information theory. To provide examples of the discussed operations we utilize a package for the Mathematica computing system implementing basic functions used in the calculations related to quantum information theory.Comment: 11 pages, no figures, see http://zksi.iitis.pl/wiki/projects:mathematica-qi for related softwar

Quantifying nonclassicality: global impact of local unitary evolutions

We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. We derive the exact relation between the global state change induced by local unitary evolutions and the amount of quantum correlations. We prove that the minimal change coincides with the geometric measure of discord (defined via the Hilbert- Schmidt norm), thus providing the latter with an operational interpretation in terms of the capability of a local unitary dynamics to modify a global state. We establish that two-qubit Werner states are maximally quantum correlated, and are thus the ones that maximize this type of global quantum effect. Finally, we show that similar results hold when replacing the Hilbert-Schmidt norm with the trace norm.Comment: 5 pages, 1 figure. To appear in Physical Review