On noise reduction methods for chaotic data

Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low-pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener-type filters.     

Complex geometry,unification, and quantum gravity. I. The geometry of elementary particles

The Poincaré group is replaced byU(3, 2), the pseudounitary extension of the de Sitter groupSO(3, 2), as internal and space-time symmetries are combined in a geometric setting which invalidates the no-go theorems. A new model of elementary particles as vertical vectors on the principal fiber bundleU(3, 2) U(3, 2)/U(3, 1)×U(1) is introduced and their interactions via Lie bracket analyzed. The model accounts for the four known superselection rules: spin, electric charge, baryon number, and lepton number.     

An algebraic approach to the planar coloring problem

We point out a general relationship between the planar coloring problem withQ colors and the Temperley-Lieb algebra with parameter . This allows us to give a complete algebraic reformulation of the four color result, and to give algebraic interpretations of various other aspects of planar colorings.Work supported in part by NSF Grant #DMS-882602, the program for Mathematics and Molecular Biology, UC Berkeley, and a visiting fellowship of the Japan Society for the promotion of science at Kyoto University, Kyoto, JapanWork supported in part by DOE Contact #DE-AC02-76ERO3075 and by a Packard Fellowship for Science and Engineering     

Direct observation of eta 2-imine formation through beta-H abstraction between amide ligands. Neutron and X-ray diffraction structure of a dihydride imine ditantalum complex

Reactions of Ta(NMe2)5 with D2SiR'Ph (R' = Me, Ph) were found to give a dideuteride eta 2-imine complex (Me2N)3Ta(mu-D)2(mu-N-eta 2-N,C-CH2NMe)Ta(NMe2)3(1-d2) through C-H activation of an amide ligand via beta-H abstraction, and the structure of 1 was confirmed by single crystal neutron and X-ray diffraction.     

Regioselective hydroborations of methylvinylchlorosilanes

The regioselectivity of the hydroboration of the methylchlorovinylsilanes, Cl_nMe_3?nSiCHCH₂ (n= 0 ? 3), has been investigated using BH₃←THF, 9-BBN, disiamyl- and dicyclohexylborane. Methylation of the adducts with methylmagnesium bromide is complicated by formation of tetraalkylboronates. Alkaline hydrogen peroxide oxidation of the boronates gives reasonable yields of the corresponding α- and β-trimethylsilylethanols forn= 0 and 1. Forn= 2 and 3, conversion of the adducts to the corresponding α- and β- deuteroethylsilanes by treatment with excess sodium methoxide in methanol-0-d provides a more effective means of derivatization. Addition of the alkenes,n= 2 or 3, to excess BH₃←THF givesca. 90% of the α-boro-organo-chlorosilanes. For all of the alkenes, the dialkylboranes giveca. 80% of the β-boron adducts.     

Reactions of 6-diazopenicillanates with allylic sulphides,selenides, and bromides

6-Diazopenicillanates react with allylic sulphides, selenides and bromides, to give 6,6-disubstituted penicillanates $\text{via}$ [2,3]-sigmatropic rearrangements.     

Phase relations and exsolution phenomena in the system NiOTiO2

The phase relations in the system NiOTiO₂ were studied between 1000 and 1600°C using quenched powder specimens, DTA runs, and single crystal diffusion couples. Quenching experiments establish the stable phases TiO₂ (rutile), NiTiO₃ an ilmenite structure type, Ni_2(1+x)Ti_1?xO₄ (x ≥ 0.16), a cation-excess spinel, and Ni_1?2xTi_xO (rocksalt structure type). DTA runs reveal the existence of an additional nonstoichiometric ilmenite phase Ni_1?2xTi_1+xO₃ (x ≤ 0.03) above 1260°C. In quenched (1500, 1450°C) or slowly cooled single crystal diffusion couples, mutual oriented exsolutions occur in the rutile crystal and in the ilmenite diffusion zone. Orientation relations are: {101}_rutile{1120}_ilmenite; ∥010〉_rutile∥00.1〉_ilmenite. The cation-excess spinel decomposes below 1375°C into oriented intergrowth of NiTiO₃ (ilmenite) and NiO: {111}_NiO{0001}_NiTiO3; ∥110〉_NiO∥21.0〉_NiTiO3.     

A COMPARISON OF MAMMALIAN CELL SENSITIVITY TO EITHER 254 nm OR ARTIFICIAL "SOLAR" SIMULATED RADIATION

The sensitivity of six mammalian cell strains to either germicidal (254 nm) or artificial "solar" simulated radiation was tested. The solar simulator used had an output similar, in some respects, to natural sunlight. Cellular capacity for Herpes simplex virus production was used as the assay procedure. The tested cells were a strain of African green monkey kidney cells and five human skin fibroblast cell strains. The latter included a "normal" cell strain, and four photosensitive cell strains; three of which were strains of xeroderma pigmentosum cells, and one strain of Bloom's syndrome cells. When comparing the D¹⁰ values, the different cell strains varied by a factor of six in response to germicidal radiation, but only by a factor of two to artificial "solar" simulated radiation. The relative sensitivity of the cells to either type of radiation also varied from 1.7 to 10.9. Large variations in response occurred even among the xeroderma pigmentosum cell strains. These responses suggest that mammalian cell sensitivity to 254 nm radiation may not be a true indicator of a cell's responses to natural sunlight.     

Semiclassical study of collision-induced predissociation: Comparison of the Landau-Zener model with the method of analytic continuation

Semiclassical calculations are carried out by two methods for the problem of collision-induced predissociation of electronically excited I₂. The first method is that of surface-hopping with the Landau-Zener model. The second method is similar to surface-hopping, except that analytic continuation of the adiabatic potential energy surfaces replaces the Landau-Zener model. Results of the calculations by the two methods compare favorably with each other and with experiment. The possible advantages of the second method are discussed.Camille and Henry Dreyfus Teacher-Scholar, Alfred P. Sloan Research Fellow.