Lens Rigidity for a Particle in a Yang–Mills Field

We consider the motion of a classical colored spinless particle under the influence of an external Yang-Mills potential $A$ on a compact manifold with boundary of dimension $\geq 3$. We show that under suitable convexity assumptions, we can recover the potential $A$, up to gauge transformations, from the lens data of the system, namely, scattering data plus travel times between boundary points

A new rock-based definition for the Cryogenian Period (circa 720 - 635 Ma)

The Cryogenian Period was first established in 1988 along with other Precambrian eon, era and period-level subdivisions that were defined numerically by Global Standard Stratigraphic Ages (GSSAs). As absolute age constraints have improved, some of these time intervals no longer bracket adequately the geological event(s), for which they were named. For example, the age discrepancy between the basal Cryogenian GSSA at 850 Ma and the onset of widespread glaciation ca. 717 Ma has rendered the 850 Ma boundary obsolete. The International Commission on Stratigraphy has now formally approved the removal of the Cryogenian GSSA from its International Chronostratigraphic Chart and supports its replacement with a rock-based Global Stratotype Section and Point (GSSP). The new Cryogenian GSSP will be placed at a globally correlative level that lies stratigraphically beneath the first appearance of widespread glaciation and is assigned in the interim a 'calibrated age' of circa 720 Ma. This new definition for the Tonian/Cryogenian boundary should be used in future publications until a formal Cryogenian GSSP can be ratified. The change marks progress towards establishment of a 'natural' (rock-based) scale for Precambrian time

The geodesic X-ray transform with matrix weights

Consider a compact Riemannian manifold of dimension $\geq 3$ with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and Higgs field is injective modulo the natural obstruction for functions and one-forms. We also show that the connection and the Higgs field are uniquely determined by the scattering relation modulo gauge transformations. The proofs involve a reduction to a local result showing that the geodesic X-ray transform with a matrix weight can be inverted locally near a point of strict convexity at the boundary, and a detailed analysis of layer stripping arguments based on strictly convex exhaustion functions. As a somewhat striking corollary, we show that these integral geometry problems can be solved on strictly convex manifolds of dimension $\geq 3$ having non-negative sectional curvature (similar results were known earlier in negative sectional curvature). We also apply our methods to solve some inverse problems in quantum state tomography and polarization tomography

Invariant distributions and the geodesic ray transform

We establish an equivalence principle between the solenoidal injectivity of the geodesic ray transform acting on symmetric $m$-tensors and the existence of invariant distributions or smooth first integrals with prescribed projection over the set of solenoidal $m$-tensors. We work with compact simple manifolds, but several of our results apply to non-trapping manifolds with strictly convex boundary.This is the final version of the article. It first appeared from Mathematical Science Publishers via https://doi.org/10.2140/apde.2016.9.190

Strategies used as spectroscopy of financial markets reveal new stylized facts

We propose a new set of stylized facts quantifying the structure of financial markets. The key idea is to study the combined structure of both investment strategies and prices in order to open a qualitatively new level of understanding of financial and economic markets. We study the detailed order flow on the Shenzhen Stock Exchange of China for the whole year of 2003. This enormous dataset allows us to compare (i) a closed national market (A-shares) with an international market (B-shares), (ii) individuals and institutions and (iii) real investors to random strategies with respect to timing that share otherwise all other characteristics. We find that more trading results in smaller net return due to trading frictions. We unveiled quantitative power laws with non-trivial exponents, that quantify the deterioration of performance with frequency and with holding period of the strategies used by investors. Random strategies are found to perform much better than real ones, both for winners and losers. Surprising large arbitrage opportunities exist, especially when using zero-intelligence strategies. This is a diagnostic of possible inefficiencies of these financial markets.Comment: 13 pages including 5 figures and 1 tabl

Correlative light and electron microscopy suggests that mutant huntingtin dysregulates the endolysosomal pathway in presymptomatic Huntington’s disease

Huntington’s disease (HD) is a late onset, inherited neurodegenerative disorder for which early pathogenic events remain poorly understood. Here we show that mutant exon 1 HTT proteins are recruited to a subset of cytoplasmic aggregates in the cell bodies of neurons in brain sections from presymptomatic HD, but not wild-type, mice. This occurred in a disease stage and polyglutamine-length dependent manner. We successfully adapted a high-resolution correlative light and electron microscopy methodology, originally developed for mammalian and yeast cells, to allow us to correlate light microscopy and electron microscopy images on the same brain section within an accuracy of 100 nm. Using this approach, we identified these recruitment sites as single membrane bound, vesicle-rich endolysosomal organelles, specifically as (1) multivesicular bodies (MVBs), or amphisomes and (2) autolysosomes or residual bodies. The organelles were often found in close-proximity to phagophore-like structures. Immunogold labeling localized mutant HTT to non-fibrillar, electron lucent structures within the lumen of these organelles. In presymptomatic HD, the recruitment organelles were predominantly MVBs/amphisomes, whereas in late-stage HD, there were more autolysosomes or residual bodies. Electron tomograms indicated the fusion of small vesicles with the vacuole within the lumen, suggesting that MVBs develop into residual bodies. We found that markers of MVB-related exocytosis were depleted in presymptomatic mice and throughout the disease course. This suggests that endolysosomal homeostasis has moved away from exocytosis toward lysosome fusion and degradation, in response to the need to clear the chronically aggregating mutant HTT protein, and that this occurs at an early stage in HD pathogenesis

Removal of phenol using sulphate radicals activated by natural zeolite-supported cobalt catalysts

Two Co oxide catalysts supported on natural zeolites from Indonesia (INZ) and Australia (ANZ) were prepared and used to activate peroxymonosulphate for degradation of aqueous phenol. The two catalysts were characterized by several techniques such as X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectroscopy (EDS) and N2 adsorption. It was found that Co/INZ and Co/ANZ are effective in activation of peroxymonosulphate to produce sulphate radicals for phenol degradation. Co/INZ and Co/ANZ could remove phenol up to 100 and 70 %, respectively, at the conditions of 25 ppm phenol (500 mL), 0.2 g catalyst, 1 g oxone and 25 °C. Several parameters such as amount of catalyst loading, phenol concentration, oxidant concentration and temperature were found to be the key factors influencing phenol degradation. A pseudo first order would fit to phenol degradation kinetics, and the activation energies on Co/INZ and Co/ANZ were obtained as 52.4 and 61.3 kJ/mol,respectively

Testing the theory of immune selection in cancers that break the rules of transplantation

Modification of cancer cells likely to reduce their immunogenicity, including loss or down-regulation of MHC molecules, is now well documented and has become the main support for the concept of immune surveillance. The evidence that these modifications, in fact, result from selection by the immune system is less clear, since the possibility that they may result from reorganized metabolism associated with proliferation or from cell de-differentiation remains. Here, we (a) survey old and new transplantation experiments that test the possibility of selection and (b) survey how transmissible tumours of dogs and Tasmanian devils provide naturally evolved tests of immune surveillance

Atropselective syntheses of (-) and (+) rugulotrosin A utilizing point-to-axial chirality transfer

Chiral, dimeric natural products containing complex structures and interesting biological properties have inspired chemists and biologists for decades. A seven-step total synthesis of the axially chiral, dimeric tetrahydroxanthone natural product rugulotrosin A is described. The synthesis employs a one-pot Suzuki coupling/dimerization to generate the requisite 2,2'-biaryl linkage. Highly selective point-to-axial chirality transfer was achieved using palladium catalysis with achiral phosphine ligands. Single X-ray crystal diffraction data were obtained to confirm both the atropisomeric configuration and absolute stereochemistry of rugulotrosin A. Computational studies are described to rationalize the atropselectivity observed in the key dimerization step. Comparison of the crude fungal extract with synthetic rugulotrosin A and its atropisomer verified that nature generates a single atropisomer of the natural product.P50 GM067041 - NIGMS NIH HHS; R01 GM099920 - NIGMS NIH HHS; GM-067041 - NIGMS NIH HHS; GM-099920 - NIGMS NIH HH