1+1 dimensional compactifications of string theory

We argue that stable, maximally symmetric compactifications of string theory to 1+1 dimensions are in conflict with holography. In particular, the finite horizon entropies of the Rindler wedge in 1+1 dimensional Minkowski and anti-de Sitter space, and of the de Sitter horizon in any dimension, are inconsistent with the symmetries of these spaces. The argument parallels one made recently by the same authors, in which we demonstrated the incompatibility of the finiteness of the entropy and the symmetries of de Sitter space in any dimension. If the horizon entropy is either infinite or zero, the conflict is resolved.     

The Phase Transition in Statistical Models Defined on Farey Fractions

We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as spin chains, with long-range interactions, while another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle–Perron–Frobenius operator), which is defined using the maps (presentation functions) generating the Farey tree. The spectrum of this operator was completely determined by Prellberg. It follows that these models have a second-order phase transition with a specific heat divergence of the form C [ ln² ]^–1. The spin chain models are also rigorously known to have a discontinuity in the magnetization at the phase transition.     

Down-regulation of Bcl-2 and Akt induced by combination of photoactivated hypericin and genistein in human breast cancer cells

Presented experiment considers combination of genistein and photodynamic therapy with hypericin with a view to achieve higher therapeutic outcome in human breast adenocarcinoma cell lines MCF-7 and MDA-MB-231, both identified in our conditions as photodynamic therapy resistant. Since genistein is known to suppress Bcl-2 expression, we predicted that photodynamic therapy with hypericin might benefit from mutual therapeutic combination. In line with our expectations, combined treatment led to down-regulation of Bcl-2 and up-regulation of Bax in both cell lines as well as to suppression of Akt and Erk1/2 phosphorylation induced by photoactivated hypericin in MCF-7 cells. Although Akt and Erk1/2 phosphorylation was not stimulated by photodynamic therapy with hypericin in MDA-MB-231 cells, it was effectively suppressed in combination. Variations in cell death signaling favoring apoptosis were indeed accompanied by cell cycle arrest in G₂/M-phase, activation of caspase-7, PARP cleavage and increased occurrence of cells with apoptotic morphology of nucleus. All these events corresponded with suppression of proliferation and significantly lowered clonogenic ability of treated cells. In conclusion, our results indicate that pre-treatment with tyrosine kinase inhibitor genistein may significantly improve the effectiveness of photodynamic therapy with hypericin in MCF-7 and MDA-MB-231 breast cancer cells.     

Hypericin-mediated photocytotoxic effect on HT-29 adenocarcinoma cells is reduced by light fractionation with longer dark pause between two unequal light doses

The present study demonstrates the in vitro effect of hypericin-mediated PDT with fractionated light delivery. Cells were photosensitized with unequal light fractions separated by dark intervals (1 or 6 h). We compared the changes in viability, cell number, survival, apoptosis and cell cycle on HT-29 cells irradiated with a single light dose (12 J/cm(2)) to the fractionated light delivery (1 + 11 J/cm(2)) 24 and 48 h after photodynamic treatment. We found that a fractionated light regime with a longer dark period resulted in a decrease of hypericin cytotoxicity. Both cell number and survival were higher after light sensitization with a 6-h dark interval. DNA fragmentation occurred after a single light-dose application, but in contrast no apoptotic DNA formation was detected with a 6-h dark pause. After fractionation the percentage of cells in the G1 phase of the cell cycle was increased, while the proportion of cells in the G2 phase decreased as compared to a single light-dose application, i.e. both percentage of cells in the G1 and G2 phase of the cell cycle were near control levels. We presume that the longer dark interval after the irradiation of cells by first light dose makes them resistant to the effect of the second illumination. These findings confirm that the light application scheme together with other photodynamic protocol components is crucial for the photocytotoxicity of hypericin.     

Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field h. Using ideas from dynamical systems and functional analysis, we show that the free energy f in the vicinity of the second-order phase transition is given, exactly, by $$f\sim\frac{t}{\log t}-\frac{1}{2}\frac{h^2}{t}\quad\mbox{for }h^2\ll t\ll1.$$ Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_{c}})$ is a reduced temperature, so that the deviation from the critical point is scaled by the Lyapunov exponent of the Gauss map, λ _G . It follows that λ _G determines the amplitude of both the specific heat and susceptibility singularities. To our knowledge, there is only one other microscopically defined interacting model for which the free energy near a phase transition is known as a function of two variables. Our results confirm what was found previously with a cluster approximation, and show that a clustering mechanism is in fact responsible for the transition. However, the results disagree in part with a renormalisation group treatment.     

O-(α-Phenylethyl)hydroxylamine as a ‘chiral ammonia equivalent’: synthesis and resolution of 5-oxopyrrolidine- and 6-oxopiperidine-3-carboxylic acids

An approach to the synthesis and resolution of five- and six-membered lactams (i.e., 5-oxopyrrolidine- and 6-oxopiperidine-3-carboxylic acids) is described. The method relies on the one-pot Michael reaction—cyclization of itaconic acid or diethyl homoitaconate and enantiopure O-(α-phenylethyl)hydroxylamine as a ‘chiral ammonia equivalent’. It is shown that this chiral auxiliary can be used for the separation of diastereomeric lactam products and then easily removed by catalytic hydrogenolysis.