Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

On the Consistency of a Fermion-Torsion Effective Theory

We discuss the possibility to construct an effective quantum field theory for an axial vector coupled to a Dirac spinor field. A massive axial vector describes antisymmetric torsion. The consistency conditions include unitarity and renormalizability in the low-energy region. The investigation of the Ward identities and the one- and two-loop divergences indicate serious problems arising in the theory. The final conclusion is that torsion may exist as a string excitation, but there are very severe restrictions for the existence of a propagating torsion field, subject to the quantization procedure, at low energies.Comment: LaTeX, 26 pages, 4 figure

Metabolic traits of cancer stem cells

Cancer stem cells are a subpopulation of cells within a tumour believed to confer resistance to standard cancer therapies. Although many studies have addressed the specific mechanisms of tumour recurrence driven by cancer stem cells, cellular metabolism is an often-neglected attribute. The metabolic features of cancer stem cells are still poorly understood, and they thus constitute a promising field in cancer research. The findings published so far point to a distinct metabolic phenotype in cancer stem cells, which might depend on the cancer type, the model system used or even the experimental design, and several controversies still need to be tackled. This Review describes the metabolic phenotype of cancer stem cells by addressing the main metabolic traits in different tumours, including glycolysis and oxidative, glutamine, fatty acid and amino acid metabolism. In the context of these pathways, we also mention the specific alterations in metabolic enzymes and metabolite levels that have a role in the regulation of cancer stemness. Determining the role of metabolism in supporting resistance to therapy driven by cancer stem cells can raise the opportunity for novel therapeutic targets, which might not only eliminate this resistant population, but, more importantly, eradicate the whole tumour in a relapse-free scenario.Funding was provided by NORTE2020 (NORTE-01-0145-FEDER-000029). J.P. is financed through a grant from Fundação para a Ciência e a Tecnologia (SFRH/BD/105694/2015). I3S-Ipatimup is an Associated Laboratory of the Portuguese Ministry of Science, Technology and Higher Education that is partially supported by Fundação para a Ciência e a Tecnologia

On the cosmological effects of the Weyssenhoff spinning fluid in the Einstein-Cartan framework

The effects of non-Riemannian structures in Cosmology have been studied long ago and are still a relevant subject of investigation. In the seventies, it was discovered that singularity avoidance and early accelerated expansion can be induced by torsion in the Einstein-Cartan theory. In this framework, torsion is not dynamical and is completely expressed by means of the spin sources. Thus, in order to study the effects of torsion in the Einstein-Cartan theory, one has to introduce matter with spin. In principle, this can be done in several ways. In this work we consider the cosmological evolution of the universe in the presence of a constant isotropic and homogeneous axial current and the Weyssenhoff spinning fluid. We analyse possible solutions of this model, with and without the spinning fluid.Comment: Work presented at the 7th Alexander Friedmann International Seminar on Gravitation and Cosmology, Joao Pessoa, Brazil, 29 Jun - 5 Jul 2008. No figures, 5 pages. New version with dynamical equation corrected, new reference and a brief comparison with its experimental bound

Biofilm growth in a biological plate tower, BPT, for VOC air pollution treatment

The growth of microorganisms in biofilters and biotrickling filters always leads to the occurrence of clogging. A good efficiency of removal makes it happen faster. To solve clogging and making that kind of process easy to operate steadily for a long time, a new concept of reactor was designed and tested with air polluted with toluene and Pseudomonas putida. The BPT is a cascade of plates to whose surface the bacteria attaches. Water flows down and air flows upwards. The reactor shows very good hydrodynamic performance and operates continuously without problem. When the thickness of the biofilm reaches the maximum value allowable, the set of plates is simply replaced by a clean one and the biomass is dealt with outside the reactor

Biodegradation of toluene in a trickling filter

A trickling filter packed with PVC 16 mm Raschig rings was used to study the degradation of toluene in a polluted air stream, by means of a bacterial biofilm of Pseudomonas putida ATCC 17484. A polluted stream was simulated by blending air with a controlled amount of toluene. The mixing was accomplished in a special mixing chamber designed for that purpose. Induction of the enzymes of the toluene degradative pathway and adaptation of the inoculum were done in batch cultures with minimum mineral media and phenol. The continuous experiments were monitored by mass spectrometry for the quantification of the various gases and of toluene removal. A 94% toluene removal was achieved with contacting times above one minute and toluene concentrations up to 400 ppm