Computing proximal points of nonconvex functions

The proximal point mapping is the basis of many optimization techniques for convex functions. By means of variational analysis, the concept of proximal mapping was recently extended to nonconvex functions that are prox-regular and prox-bounded. In such a setting, the proximal point mapping is locally Lipschitz continuous and its set of fixed points coincide with the critical points of the original function. This suggests that the many uses of proximal points, and their corresponding proximal envelopes (Moreau envelopes), will have a natural extension from convex optimization to nonconvex optimization. For example, the inexact proximal point methods for convex optimization might be redesigned to work for nonconvex functions. In order to begin the practical implementation of proximal points in a nonconvex setting, a first crucial step would be to design efficient methods of approximating nonconvex proximal points. This would provide a solid foundation on which future design and analysis for nonconvex proximal point methods could flourish. In this paper we present a methodology based on the computation of proximal points of piecewise affine models of the nonconvex function. These models can be built with only the knowledge obtained from a black box providing, for each point, the function value and one subgradient. Convergence of the method is proved for the class of nonconvex functions that are prox-bounded and lower- ${\mathcal{C}}^2$ and encouraging preliminary numerical testing is reported.     

Incorporating H chemical shift determination into C-direct detected spectroscopy of intrinsically disordered proteins in solution

Exclusively heteronuclear ¹³C-detected NMR spectroscopy of proteins in solution has seen resurgence in the past several years. For disordered or unfolded proteins, which tend to have poor ¹H-amide chemical shift dispersion, these experiments offer enhanced resolution and the possibility of complete heteronuclear resonance assignment at the cost of leaving the ¹H resonances unassigned. Here we report two novel ¹³C-detected NMR experiments which incorporate a ¹H chemical shift evolution period followed by ¹³C-TOCSY mixing for aliphatic ¹H resonance assignment without reliance on ¹H detection.     

Search for Lorentz and CPT violation effects in Muon spin precession

The spin precession frequency of muons stored in the (g-2) storage ring has been analyzed for evidence of Lorentz and CPT violation. Two Lorentz and CPT violation signatures were searched for a nonzero delta omega a(=omega a mu+ - omega a mu-) and a sidereal variation of omega a mu+/-). No significant effect is found, and the following limits on the standard-model extension parameters are obtained: bZ = -(1.0+/-1.1) x 10(-23) GeV; (m mu dZ0 + HXY)=(1.8+/-6.0) x 10(-23) GeV; and the 95% confidence level limits b perpendicular mu+ <1.4 x 10(-24) GeV and b perpendicular mu- <2.6 x 10(-24) GeV.     

DIFFERENTIAL EFFECTS OF TRYPTOPHAN PHOTOPRODUCTS AND H2O2 ON THE GROWTH OF MOUSE EMBRYONIC FIBROBLASTS*

Abstract. Exposure of dilute solutions of L-tryptophan in balanced salt mixtures to near-ultraviolet light (ca. 320–390nm) yield several photoproducts capable of inhibiting the growth of cultured mouse embryonic fibroblasts. Recent literature suggested a need to test the possibility that the major toxic photoproduct is hydrogen peroxide, and therefore several lines of experimentation were pursued. On the basis of chemical and morphological studies and an analysis of the uptake of ³H-thymidine by these cells and its incorporation into their DNA, it is concluded that sufficient hydrogen peroxide could not be generated without the addition of high concentrations of oxygen to influence the growth or DNA synthesis of mouse embryonic fibroblasts.     

Singularity of orbital measures in SU(n)

We show that the minimalk such that μ^κ ∈L ¹(SU(n)) for all central, continuous measures μ on SU(n) isk=n. We do this by exhibiting an elementg∈SU(n) for which the (n−1)-fold product of its conjugacy class has zero Haar measure. This ensures that if μ _g is the corresponding orbital measure supported on the conjugacy class, then μ _g ^n-1 is singular toL ¹. This research is supported in part by NSERC. The hospitality of the University of Waterloo is gratefully acknowledged.     

On the adsorption kinetics of surface-chemically pure n-dodecanoic acid at the air/water interface

The dynamic surface tension data for n-dodecanoic acid in 0.005 M hydrochloric acid, for as-received as well as for surface-chemically pure solutions, show the presence of a prolonged induction period, clearly indicating that the adsorption of this nonionic surfactant is not simply diffusion-controlled. A kinetic model for the reversible formation of monolayer islands, long known in the field of electrochemistry, is shown to also apply to the adsorption of n-dodecanoic acid at the air/water interface. The rate constant increases linearly with increasing bulk concentration, while the induction time decreases exponentially. The phenomenon of nucleation at the air/water interface is consistent with the direct experimental observation of the formation of solid-like patches as the interfacial region is drastically compressed.     

Simultaneous structural and elemental nano-imaging of human brain tissue

Examining chemical and structural characteristics of micro-features in complex tissue matrices is essential for understanding biological systems. Advances in multimodal chemical and structural imaging using synchrotron radiation have overcome many issues in correlative imaging, enabling the characterization of distinct microfeatures at nanoscale resolution in ex vivo tissues. We present a nanoscale imaging method that pairs X-ray ptychography and X-ray fluorescence microscopy (XFM) to simultaneously examine structural features and quantify elemental content of microfeatures in complex ex vivo tissues. We examined the neuropathological microfeatures Lewy bodies, aggregations of superoxide dismutase 1 (SOD1) and neuromelanin in human post-mortem Parkinson''s disease tissue. Although biometals play essential roles in normal neuronal biochemistry, their dyshomeostasis is implicated in Parkinson''s disease aetiology. Here we show that Lewy bodies and SOD1 aggregates have distinct elemental fingerprints yet are similar in structure, whilst neuromelanin exhibits different elemental composition and a distinct, disordered structure. The unique approach we describe is applicable to the structural and chemical characterization of a wide range of complex biological tissues at previously unprecedented levels of detail.

Structural and chemical characterisation of microfeatures in unadulterated Parkinson''s disease brain tissue using synchrotron nanoscale XFM and ptychography.     

Time-resolved infrared spectroscopy of the lowest triplet state of thymine and thymidine

Vibrational spectra of the lowest energy triplet states of thymine and its 2′-deoxyribonucleoside, thymidine, are reported for the first time. Time-resolved infrared (TRIR) difference spectra were recorded over seven decades of time from 300 fs to 3 μs using femtosecond and nanosecond pump-probe techniques. The carbonyl stretch bands in the triplet state are seen at 1603 and 1700 cm⁻¹ in room-temperature acetonitrile-d₃ solution. These bands and additional ones observed between 1300 and 1450 cm⁻¹ are quenched by dissolved oxygen on a nanosecond time scale. Density-functional calculations accurately predict the difference spectrum between triplet and singlet IR absorption cross sections, confirming the peak assignments and elucidating the nature of the vibrational modes. In the triplet state, the C4O carbonyl exhibits substantial single-bond character, explaining the large (70 cm⁻¹) red shift in this vibration, relative to the singlet ground state. Femtosecond TRIR measurements unambiguously demonstrate that the triplet state is fully formed within the first 10 ps after excitation, ruling out a relaxed ¹nπ^* state as the triplet precursor.