Preserving the measure of compatibility between quantum states

In this paper after defining the abstract concept of compatibility-like functions on quantum states, we prove that every bijective transformation on the set of all states which preserves such a function is implemented by an either unitary or antiunitary operator.Comment: 11 pages, submitted for publicatio

Pairing and duality of algebraic quantum groupoids

Algebraic quantum groupoids have been developed by two of the authors (AVD and SHW) of this note in a series of papers. Regular multiplier Hopf algebroids are obtained also by two authors (TT and AVD). Integral theory and duality for those have been studied by one author here (TT). Finally, again two authors of us (TT and AVD) have investigated the relation between weak multiplier Hopf algebras and multiplier Hopf algebroids. In the paper 'Weak multiplier Hopf algebras III. Integrals and duality' (by AVD and SHW), one of the main results is that the dual of an algebraic quantum groupoid, admits a dual of the same type. In the paper 'On duality of algebraic quantum groupoids' (by TT), a result of the same nature is obtained for regular multiplier Hopf algebroids with a single faithful integral. The duality of regular weak multiplier Hopf algebras with a single integral can be obtained from the duality of regular multiplier Hopf algebroids. That is however not the obvious way to obtain this result. It is more difficult and less natural than the direct way. We will discuss this statement further in the paper. Nevertheless, it is interesting to investigate the relation between the two approaches to duality in greater detail. This is what we do in this paper. We build further on the intimate relation between weak multiplier Hopf algebras and multiplier Hopf algebroids. We now add the presence of integrals. That seems to be done best in a framework of dual pairs. It is in fact more general than the duality of these objects coming with integrals

Pseudo-multiplicative unitaries and pseudo-Kac systems on C*-modules

Multiplikative Unitäre und Kac-Systeme auf Hilbert-Räumen wurden von S. Baaj und G. Skandalis eingeführt, um die Pontrjagin-Dualität und die Takesaki-Takai-Dualität von lokal-kompakten abelschen Gruppen auf Quantengruppen zu verallgemeinern. Zur Ausweitung ihrer Ergebnisse auf lokal-kompakte Gruppoide entwickeln wir eine Theorie von pseudo-multiplikativen Unitären und Pseudo-Kac-Systemen auf C*-Moduln. Dabei führt das interne Tensorprodukt von C*-Bimoduln zu Problemen, die durch die Beschränkung auf zerlegbare C*-Module - Gruppoide entspricht das der Einschränkung auf den r-diskreten Fall - und die Einführung der Kategorie von C*-Familien gelöst werden. Im Ergebnis können wir die Pontrjagin-Dualität zum Teil und die Takesaki-Takai-Dualität vollständig auf zerlegbare lokal-kompakte Quantengruppoide übertragen. Abschließend vergleichen wir die entstehende Theorie für Hausdorff-Gruppoide mit klassischen Begriffen und betrachten Gruppoide, die nicht Hausdorffsch sind

An Atlantic-Pacific ventilation seesaw across the last deglaciation

It has been proposed that the rapid rise of atmospheric CO2across the last deglaciation was driven by the release of carbon from an extremely radiocarbon-depleted abyssal ocean reservoir that was ‘vented’ to the atmosphere primarily via the deep-and intermediate overturning loops in the Southern Ocean. While some radiocarbon observations from the intermediate ocean appear to confirm this hypothesis, others appear to refute it. Here we use radiocarbon measurements in paired benthic-and planktonic foraminifera to reconstruct the benthic–planktonic14C age offset (i.e. ‘ventilation age’) of intermediate waters in the western equatorial Atlantic. Our results show clear increases in local radiocarbon-based ventilation ages during Heinrich-Stadial 1 (HS1) and the Younger Dryas (YD). These are found to coincide with opposite changes of similar magnitude observed in the Pacific, demonstrating a ‘seesaw’ in the ventilation of the intermediate Atlantic and Pacific Oceans that numerical model simulations of North Atlantic overturning collapse indicate was primarily driven by North Pacific overturning. We propose that this Atlantic–Pacific ventilation seesaw would have combined with a previously identified North Atlantic–Southern Ocean ventilation seesaw to enhance ocean–atmosphere CO2exchange during a ‘collapse’ of the North Atlantic deep overturning limb. Whereas previous work has emphasized a more passive role for intermediate waters in deglacial climate change (merely conveying changes originating in the Southern Ocean) we suggest instead that the intermediate water seesaw played a more active role via relatively subtle but globally coordinated changes in ocean dynamics that may have further influenced ocean–atmosphere carbon exchange.We are grateful to Adam Scrivner for technical assistance in the laboratory, as well as the Royal Society and NERC grant NE/L006421/1 for research support. The UVic ESCM numerical ex-periments were performed on a computational cluster from the NCI National Facility systems at the Australian National University through the National Computational Merit Allocation Scheme sup-ported by the Australian Government. A.T. and T.F. acknowledge support from the US NSF grants 1341311, 1400914. L.M. is sup-ported by the Australian Research Council grant DE150100107.This is the final version. It was first published by Elsevier at http://www.sciencedirect.com/science/article/pii/S0012821X15003301

Oxidative cytotoxic agent withaferin A resensitizes temozolomide-resistant glioblastomas via MGMT depletion and induces apoptosis through Akt/mTOR pathway inhibitory modulation

Temozolomide (TMZ) has remained the chemotherapy of choice in patients with glioblastoma multiforme (GBM) primarily due to the lack of more effective drugs. Tumors, however, quickly develop resistance to this line of treatment creating a critical need for alternative approaches and strategies to resensitize the cells. Withaferin A (WA), a steroidal lactone derived from several genera of the Solanaceae plant family has previously demonstrated potent anti-cancer activity in multiple tumor models. Here, we examine the effects of WA against TMZ-resistant GBM cells as a monotherapy and in combination with TMZ. WA prevented GBM cell proliferation by dose-dependent G2/M cell cycle arrest and cell death through both intrinsic and extrinsic apoptotic pathways. This effect correlated with depletion of principle proteins of the Akt/mTOR and MAPK survival and proliferation pathways with diminished phosphorylation of Akt, mTOR, and p70 S6K but compensatory activation of ERK1/2. Depletion of tyrosine kinase cell surface receptors c-Met, EGFR, and Her2 was also observed. WA demonstrated induction of N-acetyl-L-cysteine-repressible oxidative stress as measured directly and through a subsequent heat shock response with HSP32 and HSP70 upregulation and decreased HSF1. Finally, pretreatment of TMZ-resistant GBM cells with WA was associated with O6-methylguanine-DNA methyltransferase (MGMT) depletion which potentiated TMZ-mediated MGMT degradation. Combination treatment with both WA and TMZ resulted in resensitization of MGMT-mediated TMZ-resistance but not resistance through mismatch repair mutations. These studies suggest great clinical potential for the utilization of WA in TMZ-resistant GBM as both a monotherapy and a resensitizer in combination with the standard chemotherapeutic agent TMZ