A retrospective trust-region method for unconstrained optimization

We introduce a new trust-region method for unconstrained optimization where the radius update is computed using the model information at the current iterate rather than at the preceding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. Global convergence to first- and second-order critical points is proved under classical assumptions and preliminary numerical experiments on CUTEr problems indicate that the new method is very competitive.     

ROOT INITIATION, AUXIN LEVEL AND BIOSYNTHESIS OF PHENOLIC COMPOUNDS

Abstract— With cuttings excised from balsam hypocotyls an analysis was made of the quantitative relations between IAA- like substances and the presence of naturally occuring phenolic compounds. Results suggest that accumulation of the auxin-induced roots is a result of an enhanced biosynthesis of phenolic compounds which are inhibitors of the IAA- oxidizing enzyme.     

On the physical interpretation and the mathematical structure of the combinatorial hierarchy

The combinatorial hierarchy model for basic particle processes is based on elementary entities; any representation they may have is discrete and two-valued. We call themSchnurs to suggest their most fundamental aspect as concatenating strings. Consider a definite small number of them. Consider an elementary creation act as a result of which two different Schnurs generate a new Schnur which is again different. We speak of this process as a discrimination. By this process and by this process alone can the complexity of the universe be explored. By concatenations of this process we create more complex entities which are themselves Schnurs at a new level of complexity. Everything plays a dual role in which something comes in from the outside to interact, and also serves as a synopsis or concatenation of such a process. We thus incorporate the observation metaphysic at the start, rejecting Bohr's reduction to the haptic language of common sense and classical physics. Since discriminations occur sequentially, our model is consistent with a fixed past-uncertain future philosophy of physics. We demonstrate that this model generates four hierarchical levels of rapidly increasing complexity. Concrete interpretation of the four levels of the hierarchy (with cardinals 3,7,127,2¹²⁷-110³⁸) associates the three levels which map up and down with the three absolute conservation laws (charge, baryon number, lepton number) and the spin dichotomy. The first level represents +, –, and ± unit charge. The second has the quantum numbers of a baryon-antibaryon pair and associated charged meson (e.g.,n¯n,p¯n,p¯p,n¯p, ⁺ , ⁰, ^– ). The third level associates this pair, now including four spin states as well as four charge states, with a neutral lepton-antilepton pair (e¯e orv¯v), each pair in four spin states (total, 64 states)—three charged spinless, three charged spin-1, and a neutral spin-1 mesons (15 states), and a neutral vector boson associated with the leptons; this gives 3+15+3×15=63 possible boson states, so a total correct count of 63+64=127 states. Something likeSU ₂×SU ₃ and other indications of quark quantum numbers can occur as substructures at the fourth (unstable) level. Breaking into the (Bose) hierarchy by structures with the quantum numbers of a fermion, if this is an electron, allows us to understand Parker-Rhodes' calculation ofm _p /m _e =1836.1515 in terms of our interpretation of the hierarchy. A slight extension gives us the usual static approximation to the binding energy of the hydrogen atom, ² m _e c ² . We also show that the cosmological implications of the theory are in accord with current experience. We conclude that we have made a promising beginning in the physical interpretation of a theory which could eventually encompass all branches of physics.Work supported by the Department of Energy under contract number EY-76-C-03-051.     

Decay properties of very-high-spin states in transitional Er nuclei aroundA=154

Theγ ray continuum structures of the transitional Er isotopes withA～154 are studied using the reaction⁷⁴Ge(⁸⁴Kr,xn)^158?xEr atE _lab=340 MeV. The measurements include energy spectra, total energies, multiplicities, angular distributions and lifetimes using the DSAM method. The analysis of data confirms the previously observed two-bump structure of the continuum radiation. A meticulous subtraction of discrete contributions proves the persistence of the low-energy bump even at high spins, i.e.I>40?. The angular-distribution measurements assign predominant dipole structure to the bump atE _γ=0.65 MeV, whereas the bump atE _γ=1.3 MeV is of almost pure quadrupole character at high spins. The lifetime measurements give evidence for a strong enhancement of theB(E2) values of the upper bump,B(E2)/B _sp>130. Spin-selection studies reveal, in the spin rangeI=30?50? an almost constant energy for the 1.3 MeV bump,ΔE<60 keV.     

Apparent diffusion coefficient (ADC) measurements may be more reliable and reproducible than lesion volume on diffusion-weighted images from patients with acute ischaemic stroke-implications for study design

Early ischemic change after stroke can be demonstrated with diffusion-weighted imaging (DWI) and quantified by measuring the apparent diffusion coefficient (ADC) and/or lesion volume. We examined the reliability and reproducibility of lesion volume and ADC measurement on DWI images, and discuss the implications for clinical studies. Using 38 DWI scans from 15 stroke patients, two observers (a physicist and a neuroscience graduate) blind to each other, recorded the lesion volume on DWI sequences, measured the ADC values in this volume and calculated the ratio of ischemic: control ADC (ADCr). One observer repeated his measurements blind to his first, and also examined the effect on lesion volume and ADC of deliberately varying by only one pixel, the outline of the visible boundary of the lesion. The inter and intra-rater reliability were worse for lesion volume than ADC or ADCr measurements: lesion volume, inter-rater coefficient of variation (CoV) 85 +/- 130%, intra-rater CoV 20+/-SD80% (p < 0.05); ADC inter-rater CoV 7.7 +/- SD 19%, intra-rater CoV 0.2 +/- SD 12% (p = NS); and ADCr inter-rater CoV 8 +/- SD27%, intra-rater CoV 0.8 +/- SD73% (p = NS). Altering the position of the outline tracing of the lesion boundary by one pixel altered the measured volumes by 22 +/- SD25% (p < 0.05), but ADC values were altered by only 2.9 +/- SD4.9% and ADCr by 2.7 +/- SD4.8% (p = NS). ADC and ADCr values are more reliable and reproducible than DWI lesion size in acute ischemic stroke because altering where the lesion boundary is measured has a much greater impact on lesion volume than on the ADC or ADCr. This effect is greatest in large lesions.     

A homological foundation for scale problems in physics

First steps towards a discrete theory of observation are developed by using algebraic topological concepts, and are shown to account for finite limits of resolution. The cohomology ring on a basic simplicial complex is claimed as the natural language of physical theory. This is illustrated by specific examples and a complete set of generators for such a ring will be called theEddingtonian of a system.The concept of tensorial covariance is logically replaced by that of an isomorphism between base homologies induced by a bijective simplicial map. This is applied to velocity space to produce an abstract form of the Lorentz-Einstein relativity theory and also to discuss an experimental diffraction arrangement devised by Bohm and Aharonov. The latter is shown to be homologically equivalent to the problem of the red shift, and consequently throws light on the question of galactic recession.     

Early onset of ground state deformation in neutron deficient polonium isotopes

In-source resonant ionization laser spectroscopy of the even-A polonium isotopes (192-210,216,218)Po has been performed using the 6p(3)7s (5)S(2) to 6p(3)7p (5)P(2) (λ=843.38 nm) transition in the polonium atom (Po-I) at the CERN ISOLDE facility. The comparison of the measured isotope shifts in (200-210)Po with a previous data set allows us to test for the first time recent large-scale atomic calculations that are essential to extract the changes in the mean-square charge radius of the atomic nucleus. When going to lighter masses, a surprisingly large and early departure from sphericity is observed, which is only partly reproduced by beyond mean field calculations.     

Photo-oxidation of polymers: Part IV—Influence of the processing conditions on the photo-oxidative stability of polystyrene

Processing of polystyrene at 160°C for different periods in the closed chamber of a Brabender Plastograph results in no appreciable oxidation. Therefore, the photo-oxidative stability of the polymer, as measured from retention of the ultimate tensile strength, is not affected by such treatment. On the other hand, acetophenone groups, the concentration of which increases with processing time, are produced at 160°C in the open chamber of the Plastograph as a consequence of extensive thermal oxidation. A quantitative correlation is found between the rate of change of the ultimate tensile strength of polystyrene and the extent of thermal oxidation. It is also demonstrated that a phenolic antioxidant, although it efficiently inhibits the thermal oxidation, has no specific effect on the photo-oxidation of polystyrene. A hindered amine light stabiliser, however, exhibits a pronounced photo-protective effect. A mixture of these additives combines the benefits of both.