On complexified analytic Hamiltonian flows and geodesics on the space of Kahler metrics

In the case of a compact real analytic symplectic manifold M we describe an approach to the complexification of Hamiltonian flows [Se, Do1, Th1] and corresponding geodesics on the space of Kahler metrics. In this approach, motivated by recent work on quantization, the complexified Hamiltonian flows act, through the Grobner theory of Lie series, on the sheaf of complex valued real analytic functions, changing the sheaves of holomorphic functions. This defines an action on the space of (equivalent) complex structures on M and also a direct action on M. This description is related to the approach of [BLU] where one has an action on a complexification M_C of M followed by projection to M. Our approach allows for the study of some Hamiltonian functions which are not real analytic. It also leads naturally to the consideration of continuous degenerations of diffeomorphisms and of Kahler structures of M. Hence, one can link continuously (geometric quantization) real, and more general non-Kahler, polarizations with Kahler polarizations. This corresponds to the extension of the geodesics to the boundary of the space of Kahler metrics. Three illustrative examples are considered. We find an explicit formula for the complex time evolution of the Kahler potential under the flow. For integral symplectic forms, this formula corresponds to the complexification of the prequantization of Hamiltonian symplectomorphisms. We verify that certain families of Kahler structures, which have been studied in geometric quantization, are geodesic families.Comment: final versio

Geometric quantization, complex structures and the coherent state transform

It is shown that the heat operator in the Hall coherent state transform for a compact Lie group $K$ is related with a Hermitian connection associated to a natural one-parameter family of complex structures on $T^*K$. The unitary parallel transport of this connection establishes the equivalence of (geometric) quantizations of $T^*K$ for different choices of complex structures within the given family. In particular, these results establish a link between coherent state transforms for Lie groups and results of Hitchin and Axelrod, Della Pietra and Witten.Comment: to appear in Journal of Functional Analysi

On the BKS pairing for Kahler quantizations of the cotangent bundle of a Lie group

A natural one-parameter family of K\"ahler quantizations of the cotangent bundle $T^*K$ of a compact Lie group $K$, taking into account the half-form correction, was studied in \cite{FMMN}. In the present paper, it is shown that the associated Blattner-Kostant-Sternberg (BKS) pairing map is unitary and coincides with the parallel transport of the quantum connection introduced in our previous work, from the point of view of \cite{AdPW}. The BKS pairing map is a composition of (unitary) coherent state transforms of $K$, introduced in \cite{Ha1}. Continuity of the Hermitian structure on the quantum bundle, in the limit when one of the K\"ahler polarizations degenerates to the vertical real polarization, leads to the unitarity of the corresponding BKS pairing map. This is in agreement with the unitarity up to scaling (with respect to a rescaled inner product) of this pairing map, established by Hall.Comment: final version, to appear in Journ. Funct. Ana

Colisiones entre defectos topológicos del modelo ϕ^4 vibracionalmente excitados

Tesis por compendio de publicaciones[ES]Esta tesis doctoral proporciona resultados novedosos en el proceso de scattering entre kinks. La línea maestra que caracteriza las investigaciones en esta memoria corresponde con el estudio del comportamiento de los kinks que son excitados vibracionalmente, o como hemos dicho antes, el comportamiento de los llamados wobblers o wobbling kinks. Lo que se pretende es investigar cómo los modos vibracionales presentes en estas soluciones interaccionan con otros, principalmente los modos traslacionales, lo que lleva a transformar energía vibracional en energía cinética, dando un impulso al kink viajero. Este estudio puede realizarse estudiando la colisión entre un wobbling kink y el correspondiente wobbling antikink como por ejemplo, en el paradigmático modelo ϕ4, y analizar las velocidades finales de los kinks y antikinks resultantes, así como su amplitud de vibración. Otra opción para estudiar la interacción entre estos modos es emplear modelos más complejos como, por ejemplo, modelos de dos o más campos escalares, donde podemos encontrar no sólo un modo vibracional sino varios, tanto en el canal longitudinal como en el ortogonal. Este tratamiento nos proporciona resultados sobre el funcionamiento de la dinámica de estos modos normales de vibración y cómo la excitación de alguno de ellos desencadena la excitación de otros y de los mecanismo de emisión de radiación en forma de ondas planas. Cada uno de los trabajos publicados que componen la presente tesis doctoral se centra en un escenario inicial específico: colisiones entre wobbling kinks, colisiones asimétricas entre kinks y wobblers, e interacción entre los modos normales de kinks en teorías de campos de dos componentes. Los resultados nos permiten entender cómo los parámetros de la configuración inicial influyen sobre el patrón fractal encontrado en el diagrama de velocidades y cómo pueden favorecer o desfavorecer el surgimiento de ventanas de reflexión en el régimen de resonancia

Investigating the role of Sphingosine Kinase 1 pathway in cancer cell-monocyte interactions

Strong evidence suggests that the tumour microenvironment is inflammatory and that activation of the innate immune system plays a role in cancer progression, therefore targeting the multiple interactions of tumour cells with other cell types within the tumour microenvironment may lead to development of new cancer therapies. Sphingosine kinase (SPHK1) is a tumour-associated enzyme whose over-expression has been linked to patient mortality in many types of cancer. Here I investigate whether activation of the SPHK1 pathway, with a known involvement in inflammatory responses, is a signal transduction component of the tumour-monocyte/macrophage cellular interaction and a key element in inflammation-related cancer progression. Using a co-culture model, this study shows that the presence of monocytes increases cancer cell proliferation, an effect abrogated by knockdown of SPHK1 in cancer cells. Both monocytes and cancer cells showed a transient increase in SPHK1 activity and mRNA expression levels together with an increase in MCP-1 and IL-6 secretion. Silencing of SPHK1 in cancer cells abrogated SPHK1 activation in monocytes and pharmacological inhibition of SPHK1 in monocytes cells decreased monocyte induced-SPHK1 expression in cancer cells. Mechanistically, activation of AKT was observed in cancer cells upon co-culture with monocytes, an effect that was abrogated when cancer cells were pre-treated with siRNA for SPHK1. Moreover, the increase of phospho-AKT, ERK1/2 and NF-KB in monocytes by cancer cells was also reduced by RNAi-mediated knockdown of SPHK1 in cancer cells. My data show that STAT1 can bind to SPHK1 promoter or coding region and may be involved in SPHK1 transcriptional regulation in cancer cells upon monocyte stimulation, however its role still remains unclear as it acts as a transcriptional repressor of SPHK1. Monocytes induced cancer cell chemoprotection via a SPHK1-dependent mechanism, and reduced the inhibitory effect of docetaxel on cancer cell proliferation. Accordingly, increased AKT and ERK1/2 phosphorylation in monocytes were also affected by siRNA targeting of SPHK1 in docetaxel treated cancer cells. Altogether I show for the first time that selective inhibition of SPHK1 in tumour cells can affect their interaction with surrounding cells through the modulation of signal transduction pathways (ERK, PI3K, NF-kB) and cytokine exchange (IL-6, MCP-1 and potentially S1P, GM-CSF, GROα, IL-32 and ICAM-1). SPHK1-mediated increase in proliferation and chemoresistance of cancer cells conferred by monocytes renders this enzyme a promising target for future cancer therapies.Open Acces

Team-Based Learning in Chemistry Courses with Laboratory Sessions

[EN] The implementation of Team-Based Learning (TBL, http://www.teambasedlearning.org) in one-semester undergraduate courses of chemistry offered to first year students is reported. TBL is an active learning instructional strategy heavily relying on small group interaction. Teaching lab classes in a TBL context presented a specific challenge, as decisions were required about their role in the global framework and the possibility of incorporating lab activities as “teamwork”. The design of lab sessions as TBL team application activities is here also illustrated, both for a course of General Chemistry and a course of Organic Chemistry. TBL dramatically improved students class attendance and participation. Its implementation has provided a unique opportunity for the pedagogical development of teaching staff. A moderate number of students reported discomfort with TBL: the requirement of individual preparation before classes and the impact of team participation in the final grade is indeed a new ground for most students, often perceived as a troubling deviation from the common social paradigm of the learning process. The role of the instructor as a facilitator of individual and team work, and the clear explanation of the method are thus of utmost relevance.The authors thank Faculdade de Ciências e Tecnologia (Universidade Nova de Lisboa) for financial supportAires-De-Sousa, J.; Cardoso, MM.; Ferreira, L.; Lima, J.; Noronha, J.; Nunes, A.; Ponte, M. (2017). Team-Based Learning in Chemistry Courses with Laboratory Sessions. En Proceedings of the 3rd International Conference on Higher Education Advances. Editorial Universitat Politècnica de València. 1213-1218. https://doi.org/10.4995/HEAD17.2017.5559OCS1213121

Matrix Assisted Formation of Ferrihydrite Nanoparticles in a Siloxane/Poly(Oxyethylene) Nanohybrid

Matrix-assisted formation of ferrihydrite, an iron oxide hydroxide analogue of the protein ferritin-core, in a sol-gel derived organic-inorganic hybrid is reported. The hybrid network (named di-ureasil) is composed of poly(oxyethylene) chains of different average polymer molecular weights grafted to siloxane domains by means of urea cross-linkages and accommodates ferrihydrite nanoparticles. Magnetic measurements, Fourier transform infrared and nuclear magnetic resonance spectroscopy reveal that the controlled modification of the polymer molecular weight allows the fine-tuning of the ability of the hybrid matrix to assist and promote iron coordination at the organic-inorganic interface and subsequent nucleation and growth of the ferrihydrite nanoparticles whose core size (2-4 nm) is tuned by the amount of iron incorporated. The polymer chain length, its arrangement and crystallinity, are key factors on the anchoring and formation of the ferrihydrite particles.Comment: 7 pages, 6 figures. To be published in J. Mater. Che