On Numerical Ranges of Rank-Two Operators

Possible shapes of numerical ranges of rank-two operators are studied. In particular it is proved that for 4-by-4 unitarily irreducible matrices with an eigenvalue of geometric multiplicity two, the numerical ranges have at most one flat portion on the boundary and there are no multiply generated round boundary points.     

Subset currents on free groups

We introduce and study the space ${{\mathcal{S}{\rm Curr} (F_N)}}$ of subset currents on the free group F _N , and, more generally, on a word-hyperbolic group. A subset current on F _N is a positive F _N -invariant locally finite Borel measure on the space ${{\mathfrak{C}_N}}$ of all closed subsets of ?F _N consisting of at least two points. The well-studied space Curr(F _N ) of geodesics currents–positive F _N -invariant locally finite Borel measures defined on pairs of different boundary points–is contained in the space of subset currents as a closed ${{\mathbb{R}}}$ -linear Out(F _N )-invariant subspace. Much of the theory of Curr(F _N ) naturally extends to the ${{\mathcal{S}\;{\rm Curr} (F_N)}}$ context, but new dynamical, geometric and algebraic features also arise there. While geodesic currents generalize conjugacy classes of nontrivial group elements, a subset current is a measure-theoretic generalization of the conjugacy class of a nontrivial finitely generated subgroup in F _N . If a free basis A is fixed in F _N , subset currents may be viewed as F _N -invariant measures on a “branching” analog of the geodesic flow space for F _N , whose elements are infinite subtrees (rather than just geodesic lines) of the Cayley graph of F _N with respect to A. Similarly to the case of geodesics currents, there is a continuous Out(F _N )-invariant “co-volume form” between the Outer space cv _N and the space ${{\mathcal{S}\;{\rm Curr} (F_N)}}$ of subset currents. Given a tree ${{T \in {\rm cv}_N}}$ and the “counting current” ${{\eta_H \in \mathcal{S}\;{\rm Curr} (F_N)}}$ corresponding to a finitely generated nontrivial subgroup H ≤  F _N , the value ${{\langle T, \eta_H \rangle}}$ of this intersection form turns out to be equal to the co-volume of H, that is the volume of the metric graph T _H /H, where ${{T_H \subseteq T}}$ is the unique minimal H-invariant subtree of T. However, unlike in the case of geodesic currents, the co-volume form ${{{\rm cv}_N \times \mathcal{S}\;{\rm Curr}(F_N)\; \to [0,\infty)}}$ does not extend to a continuous map ${{\overline{{\rm cv}}_N \times \mathcal{S}\; {\rm Curr} (F_N) \to [0,\infty)}}$ .     

Polynomially scaling spin dynamics II: further state-space compression using Krylov subspace techniques and zero track elimination

We extend the recently proposed state-space restriction (SSR) technique for quantum spin dynamics simulations [Kuprov et al., J. Magn. Reson. 189 (2007) 241-250] to include on-the-fly detection and elimination of unpopulated dimensions from the system density matrix. Further improvements in spin dynamics simulation speed, frequently by several orders of magnitude, are demonstrated. The proposed zero track elimination (ZTE) procedure is computationally inexpensive, reversible, numerically stable and easy to add to any existing simulation code. We demonstrate that it belongs to the same family of Krylov subspace techniques as the well-known Lanczos basis pruning procedure. The combined SSR+ZTE algorithm is recommended for simulations of NMR, EPR and Spin Chemistry experiments on systems containing between 10 and 10(4) coupled spins.     

Elucidating a normal function of huntingtin by functional and microarray analysis of huntingtin-null mouse embryonic fibroblasts

Background

Multi-sensory integration is necessary for organisms to discriminate different environmental stimuli and thus determine behavior. Caenorhabditis elegans has 12 pairs of amphid sensory neurons, which are involved in generating behaviors such as thermotaxis toward cultivation temperature, and chemotaxis toward chemical stimuli. This arrangement of known sensory neurons and measurable behavioral output makes C. elegans suitable for addressing questions of multi-sensory integration in the nervous system. Previous studies have suggested that C. elegans can process different chemoattractants simultaneously. However, little is known about how these organisms can integrate information from stimuli of different modality, such as thermal and chemical stimuli.

Results

We studied the behavior of a population of C. elegans during simultaneous presentation of thermal and chemical stimuli. First, we examined thermotaxis within the radial temperature gradient produced by a feedback-controlled thermoregulator. Separately, we examined chemotaxis toward sodium chloride or isoamyl alcohol. Then, assays for simultaneous presentations of 15°C (colder temperature than 20°C room temperature) and chemoattractant were performed with 15°C-cultivated wild-type worms. Unlike the sum of behavioral indices for each separate behavior, simultaneous presentation resulted in a biased migration to cold regions in the first 10 min of the assay, and sodium chloride-regions in the last 40 min. However, when sodium chloride was replaced with isoamyl alcohol in the simultaneous presentation, the behavioral index was very similar to the sum of separate single presentation indices. We then recorded tracks of single worms and analyzed their behavior. For behavior toward sodium chloride, frequencies of forward and backward movements in simultaneous presentation were significantly different from those in single presentation. Also, migration toward 15°C in simultaneous presentation was faster than that in 15°C-single presentation.

Conclusion

We conclude that worms preferred temperature to chemoattractant at first, but preferred the chemoattractant sodium chloride thereafter. This preference was not seen for isoamyl alcohol presentation. We attribute this phase-dependent preference to the result of integration of thermosensory and chemosensory signals received by distinct sensory neurons.     

Nickel‐Catalyzed Asymmetric Hydrogenation of N‐Sulfonyl Imines

An efficient nickel‐catalyzed asymmetric hydrogenation of N‐tBu ‐ sulfonyl imines was developed with excellent yields and enantioselectivities using (R,R)‐QuinoxP* as a chiral ligand. The use of a much lower catalyst loading (0.0095 mol %, S/C=10500) represents the highest catalytic activity for the Ni‐catalyzed asymmetric hydrogenations reported so far. Mechanistic studies suggest that a coordination equilibrium exists between the nickel salt and its complex, and that excess nickel salt promotes the formation of the active Ni‐complex, and therefore improved the efficiency of the hydrogenation. The catalytic cycle was also investigated by calculations to determine the origin of the enantioselectivity. An extensive network of numerous weak attractive interactions was found to exist between the catalyst and substrate in the transition state and may also contribute to the high catalytic activity.     

Persistence of structure over fluctuations in biological electron-transfer reactions

In the soft-wet environment of biomolecular electron transfer, it is possible that structural fluctuations could wash out medium-specific electronic effects on electron tunneling rates. We show that beyond a transition distance (2-3 A in water and 6-7 A in proteins), fluctuation contributions to the mean-squared donor-to-acceptor tunneling matrix element are likely to dominate over the average matrix element. Even though fluctuations dominate the tunneling mechanism at larger distances, we find that the protein fold is "remembered" by the electronic coupling, and structure remains a key determinant of electron transfer kinetics.     

Modal group time spreads in weakly range-dependent deep ocean environments

The temporal spread of modal group arrivals in weakly range-dependent deep ocean environments is considered. It is assumed that the range dependence is sufficiently weak that mode coupling is predominantly local in mode number. The phrase "modal group arrival" is taken here to mean the contribution to a transient wave field corresponding to a fixed mode number. There are three contributions to modal group time spreads which combine approximately in quadrature. These are the reciprocal bandwidth (the minimal pulse width), a deterministic dispersive contribution that is proportional to bandwidth and grows like range r, and a scattering-induced contribution that grows approximately like r(32). The latter two contributions are shown to be proportional to the waveguide invariant beta, a property of the background sound speed profile. The results presented, based mostly on asymptotic theory, are shown to agree well with full-wave numerical wave field simulations and available exact mode theoretical results. Simulations are shown that correspond approximately to conditions during the LOAPEX acoustic propagation experiment.     

Modeling tip performance for combined STM-luminescence and aperture-SNOM scanning probe: Spatial resolution and collection efficiency

Finite-element simulations of the performance of the tip intended for use in combined aperture-SNOM and the scanning tunneling microscope (STM)-luminescence microscopy are presented. Tip geometry and the role of the opening in the protective metal coating were addressed. It is shown that the tip shape can affect transmittance for the excitation SNOM mode by nearly two orders of magnitude and the metal coating can enhance collection efficiency for the STM-luminescence mode. Desired tip configuration can be chosen based on the interplay between the improving collection efficiency and the deteriorating spatial resolution with increasing opening size.     

Crystal Structure of Decakis(μ-chloro)-tetrakis(1,2,4-triphenylcyclopentadienyl)-hexakis(tetrahydrofuran)-di-potassium-tetra-neodymium(III) Tetrahydrofuran Trisolvate

Journal of Chemical Crystallography - The crystal structure of decakis(μ-chloro)-tetrakis(1,2,4-triphenylcyclopentadienyl)-hexakis(tetrahydrofuran)-di-potassium-tetra-neodymium(III)...