Converse KAM: Theory and practice

We unify, extend, reinterpret and apply criteria of Birkhoff [1], Herman [9], Mather [2, 3], Aubry et al. [4, 5], and Newman and Percival [6] for the nonexistence of invariant circles for area preserving twist maps. The criteria enable one to establish regions of phase space through which no rotational invariant circles pass. For families of maps the same can be done for regions of the combined space of phase points and parameters. The criteria can be implemented rigorously on a computer, and give a practical method of proving quite strong results. As an example, we present a computer program which proved that the standard map has no rotational invariant circles for any parameter value |k|63/64.     

Short lexitropsin that recognizes the DNA minor groove at 5'-ACTAGT-3': understanding the role of isopropyl-thiazole

Isopropyl-thiazole ((iPr)Th) represents a new addition to the building blocks of nucleic acid minor groove-binding molecules. The DNA decamer duplex d(CGACTAGTCG)(2) is bound by a short lexitropsin of sequence formyl-PyPy(iPr)Th-Dp (where Py represents N-methyl pyrrole, (iPr)Th represents thiazole with an isopropyl group attached, and Dp represents dimethylaminopropyl). NMR data indicate ligand binding in the minor groove of DNA to the sequence 5'-ACT(5)AG(7)T-3' at a 2:1 ratio of ligand to DNA duplex. Ligand binding, assisted by the enhanced hydrophobicity of the (iPr)Th group, occurs in a head-to-tail fashion, the formyl headgroups being located toward the 5'-ends of the DNA sequence. Sequence reading is augmented through hydrogen bond formation between the exocyclic amine protons of G(7) and the (iPr)Th nitrogen, which lies on the minor groove floor. The B(I)/B(II) DNA backbone equilibrium is altered at the T(5) 3'-phosphate position to accommodate a B(II) configuration. The ligands bind in a staggered mode with respect to one another creating a six base pair DNA reading frame. The introduction of a new DNA sequence-reading element into the recognition jigsaw, combined with an extended reading frame for a small lexitropsin with enhanced hydrophobicity, holds great promise in the development of new, potentially commercially viable drug lead candidates for gene targeting.     

Hydrosilylation of a dinuclear tantalum dinitrogen complex: cleavage of N2 and functionalization of both nitrogen atoms

Hydrosilylation of the ditantalum dinitrogen complex ([NPN]Ta)2(mu-H)2(mu-eta1:eta2-N2) proceeds via an addition reaction to produce ([NPN]TaH)(mu-H)2(mu-eta1:eta2-N-NSiH2Bu)(Ta[NPN]), which contains a new N-Si bond and a terminal tantalum hydride; this species has been characterized by NMR spectroscopy and X-ray diffraction. This complex undergoes reductive elimination of H2 followed by N-N bond cleavage to generate a new intermediate with the formula ([NPN]TaH)(mu-N)(mu-NSiH2Bu)(Ta[NPN]); confirmation of N-N bond cleavage is evident from the 15N-labeled isotopomer that displays an absence of 15N-15N scalar coupling in the 15N NMR spectrum. In the presence of additional silane, a second hydrosilylation and reductive elimination results to give ([NPN]Ta)2(mu-NSiH2Bu)2, a species in which each dinitrogen-derived N atom has been converted to a bridging silylimide ligand. This latter complex displays C2h symmetry both in solution and in the solid state.     

The effect of varying echo spacing within a multiecho acquisition: better characterization of long T2 components

A 48-echo pulse sequence with five different echo-spacing combinations was examined to determine how one can most effectively measure the T2 relaxation characteristics of cerebral tissue containing a long T2 component. For each scan, the first 32 echoes had an echo spacing of 10 ms, while the spacing for Echoes 33-48 (DeltaTE2) was 10, 20, 30, 40 or 50 ms. In an in vivo study using 10 normal volunteers, it was found that the resolution of T2 distribution peaks for both myelin water (approximately 20 ms) and intracellular/extracellular (IE) water (approximately 80 ms) improved as DeltaTE2 increased. The geometric mean T2 values of the main peak agreed within the error for all DeltaTE2 values. A phantom study simulated T2 relaxation distributions that are expected in the brains of patients with demyelinating diseases. For phantoms in which the T2 values of the IE and lesion (200-500 ms) water compartments were separated by at least a factor of 3, each compartment in the distribution was better resolved when DeltaTE2=40 or 50 ms. On the basis of these results, we recommend the use of extended DeltaTE2 values for imaging patients with lesions, without the risk of losing valuable short T2 information.     

Label-free detection of neuron-drug interactions using acoustic and Kelvin vibrational fields

Kelvin and acoustic fields of high-frequency have been employed in the non-invasive investigation of immortalized hypothalamic neurons, in order to assess their response to different concentrations of specific drugs, toxins, a stress-reducing hormone and neurotrophic factors. In an analytical systems biology approach, this work constitutes a first study of living neuron cultures by scanning Kelvin nanoprobe (SKN) and thickness shear mode (TSM) acoustic wave techniques. N-38 hypothalamic mouse neurons were immobilized on the gold electrode of 9 MHz TSM acoustic wave devices and gold-coated slides for study by SKN. The neurons were exposed to the neurochemicals betaseron, forskolin, TCAP, and cerebrolysin. Signals were collected with the TSM in real-time mode, and with the SKN in scanning and real-time modes, as the drugs were applied at biologically significant concentrations. With the TSM, for all drugs, some frequency and resistance shifts were in the same direction, contrary to normal functioning for this type of instrument. Possible mechanisms are presented to explain this behaviour. An oscillatory signal with periodicity of approximately 2 min was observed for some neuron-coated surfaces, where the amplitude of these oscillations was altered upon application of certain neurotrophic factors. These two new techniques present novel and non-invasive electrodeless methods for detecting changes at the cellular level caused by a variety of neuroactive compounds, without killing or destroying the neurons.     

When Lanchester met Richardson,the outcome was stalemate: A parable for mathematical models of insurgency

Many authors have used dynamical systems to model asymmetric war. We explore this approach more broadly, first returning to the prototypical models such as Richardson’s arms race, Lanchester’s attrition models and Deitchman’s guerrilla model. We investigate combinations of these and their generalizations, understanding how they relate to assumptions about asymmetric conflict. Our main result is that the typical long-term outcome is neither annihilation nor escalation but a stable fixed point, a stalemate. The state cannot defeat the insurgency by force alone, but must alter the underlying parameters. We show how our models relate to or subsume other recent models. This paper is a self-contained introduction to 2D continuous dynamical models of war, and we intend that, by laying bare their assumptions, it should enable the reader to critically evaluate such models and serve as a reminder of their limitations.