On the Structure of the Semigroup of Entire Étale Mappings

The motivation for this paper comes from new ideas for solving the two-dimensional Jacobian Conjecture. The Jacobian Conjecture is one of the most famous open problems in algebraic geometry. This long-standing conjecture is no doubt one of the central problems in this well developed field of mathematics and hence the importance of investigating it. We can consider a semigroup of local diffeomorphisms on the affine space with a composition of mappings as its binary operation. We put a geometric fractal-like structure on this semigroup after equipping it with a natural metric (this is heavily dependent on the fact that our mappings are local diffeomorphisms). This structure is much more general than the structure of the ind-variety suggested by Kambayashi for étale polynomial mappings in the algebraic context. Hence, it applies to other semigroups such as the semigroup of all the entire functions in one complex variable with a nonvanishing first order derivative. This last semigroup is the theme of the current paper. We hope that the corresponding Hausdorff measure and Hausdorff dimension will enable us to relate the structure of the semigroup with arithmetic machinery such as certain Zeta functions.     

Correlation through bounded recall strategies

Two agents independently choose mixed m-recall strategies that take actions in finite action spaces A ₁ and A ₂. The strategies induce a random play, a ₁, a ₂, . . ., where a _t assumes values in A ₁ × A ₂. An M-recall observer observes the play. The goal of the agents is to make the observer believe that the play is similar to a sequence of i.i.d. random actions whose distribution is ${Q\in\Delta(A_1\times A_2)}$ . For nearly every t, the following event should occur with probability close to one: “the distribution of a _t+M given a _t , . . . , a _t+M-1 is close to Q.” We provide a sufficient and necessary condition on m, M, and Q under which this goal can be achieved (for large m). This work is a step in the direction of establishing a folk theorem for repeated games with bounded recall. It tries to tackle the difficulty in computing the individually rational levels (IRL) in the bounded recall setting. Our result implies, for example, that in some games the IRL in the bounded recall game is bounded away below the IRL in the stage game, even when all the players have the same recall capacity.     

Magnetically-induced solid-state electrochemical detection of DNA hybridization

A magnetic triggering of a solid-state electrical transduction of DNA hybridization is described. Positioning of an external magnet below the thick-film electrode attracts the DNA/particle network and enables the solid-state electrochemical stripping detection of the silver tracer. TEM imaging indicates that the hybridization event results in a three-dimensional aggregate structure in which duplex segments link the metal nanoparticles and magnetic spheres, and that most of this assembly is covered with the silver precipitate. This leads to a direct contact of the metal tag with the surface (in connection to the magnetic collection) and enables the solid-state electrochemical transduction (without prior dissolution and subsequent electrodeposition of the metal), using oxidative dissolution of the silver tracer. No such aggregates (and hence magnetic "collection") are observed in the presence of noncomplementary DNA, that is, without the linking hybrid. The new method couples high sensitivity of silver-amplified assays with effective discrimination against excess of closely related nucleotide sequences (including single-base imperfections). Such direct electrical detection of DNA/metal-particle assemblies can bring new capabilities to the detection of DNA hybridization, and could be applied to other bioaffinity assays.     

Stabilization of solid/liquid suspensions

The stability of colloidal graphite dispersions was investigated. A mixed stabilizer (CELAD) consisting of a non-ionic cellulose derivative and an anionic polymer was used to facilitate the grinding process and to stabilize the aqueous dispersions. Measurements of turbidity, ultramicroscopy and scanning electron microscopy were carried out to determine the size of the particles. Adherent films were obtained by spraying the dispersions onto glass plates. The 20 μm thick films had an electrical resistance within the 20–40 Ω cm range. They proved to be suitable for spray application onto the exernal glass cone of cathode ray tubes.     

Physisorption of hydroxide ions from aqueous solution to a hydrophobic surface

We present results from detailed molecular dynamics simulations revealing a counterintuitive spontaneous physical adsorption of hydroxide ions at a water/hydrophobic interface. The driving force for the migration of the hydroxide ions from the aqueous phase is the preferential orientation of the water molecules in the first two water layers away from the hydrophobic surface. This ordering of the water molecules generates an electrical potential gradient that strongly and favorably interacts with the dipole moment of the hydroxide ion. These findings offer a physical mechanism that explains intriguing experimental reports indicating that the interface between water and a nonionic surface is negatively charged.     

Synthetic glycoprotein mimics inhibit L-selectin-mediated rolling and promote L-selectin shedding

L-selectin is a leukocyte cell-surface protein that facilitates the rolling of leukocytes along the endothelium, a process that leads to leukocyte migration to a site of infection. Preventing L-selectin-mediated rolling minimizes leukocyte adhesion and extravasation; therefore, compounds that inhibit rolling may act as anti-inflammatory agents. To investigate the potential role of multivalent ligands as rolling inhibitors, compounds termed neoglycopolymers were synthesized that possess key structural features of physiological L-selectin ligands. Sulfated neoglycopolymers substituted with sialyl Lewis x derivatives (3',6-disulfo Lewis x or 6-sulfo sialyl Lewis x) or a sulfatide analog (3,6-disulfo galactose) inhibited L-selectin-mediated rolling of lymphoid cells. Functional analysis of the inhibitory ligands indicates that they also induce proteolytic release of L-selectin. Thus, their inhibitory potency may arise from their ability to induce shedding. Our data indicate that screening for compounds that promote L-selectin release can identify ligands that inhibit rolling.     

Hidden neuronal correlations in cultured networks

Utilization of a clustering algorithm on neuronal spatiotemporal correlation matrices recorded during a spontaneous activity of in vitro networks revealed the existence of hidden correlations: the sequence of synchronized bursting events (SBEs) is composed of statistically distinguishable subgroups each with its own distinct pattern of interneuron spatiotemporal correlations. These findings hint that each of the SBE subgroups can serve as a template for coding, storage, and retrieval of a specific information.     

Mirror manifolds in higher dimension

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We isolate certain simplifying features present only in dimension three, and supply alternative methods that do not rely on these special characteristics and hence can be generalized to other dimensions. Although the moduli spaces for Calabi-Yaud-folds are not special Kähler manifolds whend>3, they still have a restricted geometry, and we indicate the new geometrical structures which arise. We formulate and apply procedures which allow for the construction of mirror maps and the calculation of order-by-order instanton corrections to Yukawa couplings. Mathematically, these corrections are expected to correspond to calculating Chern classes of various parameter spaces (Hilbert schemes) for rational curves on Calabi-Yau manifolds. Our mirror-aided calculations agree with those Chern class calculations in the limited number of cases for which the latter can be carried out with current mathematical tools. Finally, we make explicit some striking relations between instanton corrections for various Yukawa couplings, derived from the associativity of the operator product algebra.     

A new action photoelectron spectroscopy for anions

We present a new experimental approach, in which anion photodetachment spectroscopy is recorded with electrons of fixed kinetic energy. This approach circumvents some shortcomings of the zero electron kinetic energy method. Our method is based on a modified magnetic bottle photoelectron spectrometer (MBPES). A tunable laser is used to detach electrons from mass selected anions, drifting collinearly with the 40 cm MBPES drift tube. To avoid Doppler broadening, a low voltage pulse removes the velocity component of anions from the detached electrons. Spectra are recorded by collecting the wavelength dependence of electron-signal at a predetermined TOF window, corresponding to a specific electron-kinetic energy. We call this approach PEACE, denoting photoelectron action spectroscopy at constant kinetic energy. Our best resolution is 0.65 meV for 1.5 meV electrons. We present a PEACE spectrum of HgCl(-) together with the corresponding simulated theoretical spectrum. The method is similar in resolution and data collection rates to the slow electron velocity map imaging technique recently introduced by Neumark and co-workers.     

Novel use of a fiber-optic-based on-line trichloroethylene sensor in a column retardation experiment

A newly developed fiber-optic-based trichloroethylene (TCE) sensor previously described [F.P. Milanovich, S.B. Brown, B.W. Colston, Jr., P.F. Daley and K. Langry, Talanta, 41 (1994) 2189], was used to provide analyses of TCE in laboratory tests of retardation of TCE in ground water. The sensor enabled inexpensive real time analyses of TCE in retardation tests conducted in a sand-filled flow-through column. The simultaneous data analysis of TCE, (18)O and Cl(-) breakthrough curves enabled the calculation of an estimated retardation coefficient which was found to be in good agreement with that predicted by the octanol/water partitioning K(d) method. The fiber-optic sensor was demonstrated to be a fast and reliable method for conducting on-line laboratory analyses of TCE at the parts per billion level in a small volume of contaminated water, thus providing excellent temporal resolution of the data as well as minimizing volatile losses during sample collection and analysis.