Hölder's inequality: some recent and unexpected applications

Holder's inequality, since its appearance in 1888, has played a fundamental role in Mathematical Analysis and may be considered a milestone in Mathematics. It may seem strange that, nowadays, it keeps resurfacing and bringing new insights to the mathematical community. In this survey we show how a variant of Holder's inequality (although well-known in PDEs) was essentially overlooked in Functional/Complex Analysis and has had a crucial (and in some sense unexpected) influence in very recent advances in different fields of Mathematics. Some of these recent advances have been appearing since 2012 and include the theory of Dirichlet series, the famous Bohr radius problem, certain classical inequalities (such as Bohnenblust-Hille or Hardy-Littlewood), and Mathematical Physics

MTOR pathway is involved in energy homeostasis regulation as a part of the gut?brain axis

Mammalian, or mechanic, target of rapamycin (mTOR) signaling is a crucial factor in the regulation of the energy balance that functions as an energy sensor in the body. The present review explores how the mTOR/S6k intracellular pathway is involved in modulating the production of different signals such as ghrelin and nesfatin-1 in the gastrointestinal tract to regulate food intake and body weight. The role of gastric mTOR signaling in different physiological processes was studied in depth through different genetic models that allow the modulation of mTOR signaling in the stomach and specifically in gastric X/A type cells. It has been described that mTOR signaling in X/A-like gastric cells has a relevant role in the regulation of glucose and lipid homeostasis due to its interaction with different organs such as liver and adipose tissue. These findings highlight possible therapeutic strategies, with the gut-brain axis being one of the most promising targets in the treatment of obesity

The scientific potential of space-based gravitational wave detectors

The millihertz gravitational wave band can only be accessed with a space-based interferometer, but it is one of the richest in potential sources. Observations in this band have amazing scientific potential. The mergers between massive black holes with mass in the range 10 thousand to 10 million solar masses, which are expected to occur following the mergers of their host galaxies, produce strong millihertz gravitational radiation. Observations of these systems will trace the hierarchical assembly of structure in the Universe in a mass range that is very difficult to probe electromagnetically. Stellar mass compact objects falling into such black holes in the centres of galaxies generate detectable gravitational radiation for several years prior to the final plunge and merger with the central black hole. Measurements of these systems offer an unprecedented opportunity to probe the predictions of general relativity in the strong-field and dynamical regime. Millihertz gravitational waves are also generated by millions of ultra-compact binaries in the Milky Way, providing a new way to probe galactic stellar populations. ESA has recognised this great scientific potential by selecting The Gravitational Universe as its theme for the L3 large satellite mission, scheduled for launch in ~2034. In this article we will review the likely sources for millihertz gravitational wave detectors and describe the wide applications that observations of these sources could have for astrophysics, cosmology and fundamental physics.Comment: 18 pages, 2 figures, contribution to Gravitational Wave Astrophysics, the proceedings of the 2014 Sant Cugat Forum on Astrophysics; v2 includes one additional referenc

Non-Linear Effects in Non-Kerr spacetimes

There is a chance that the spacetime around massive compact objects which are expected to be black holes is not described by the Kerr metric, but by a metric which can be considered as a perturbation of the Kerr metric. These non-Kerr spacetimes are also known as bumpy black hole spacetimes. We expect that, if some kind of a bumpy black hole exists, the spacetime around it should possess some features which will make the divergence from a Kerr spacetime detectable. One of the differences is that these non-Kerr spacetimes do not posses all the symmetries needed to make them integrable. We discuss how we can take advantage of this fact by examining EMRIs into the Manko-Novikov spacetime.Comment: 8 pages, 3 Figures; to appear in the proceedings of the conference "Relativity and Gravitation: 100 Years after Einstein in Prague" (2012

Research Update on Extreme-Mass-Ratio Inspirals

The inspirals of stellar-mass mass compact objects into massive black holes in the centres of galaxies are one of the most important sources of gravitational radiation for space-based detectors like LISA or eLISA. These extreme-mass-ratio inspirals (EMRIs) will enable an ambitious research program with implications for astrophysics, cosmology, and fundamental physics. This article is a summary of the talks delivered at the plenary session on EMRIs at the 10th International LISA Symposium. It contains research updates on the following topics: astrophysics of EMRIs; EMRI science potential; and EMRI modeling.Comment: 17 pages, no figures. Proceedings of the LISA Symposium X, to be published at the Journal of Physic

Influence of rainfall on the discharge, nutrient concentrations and loads of a stream of the "Pampa Ondulada" (Buenos Aires, Argentina)

The basin area of the Durazno Stream covers approx. 360 km2 of a plain with a gentle slope, mainly devoted to cattle farming and agriculture. This study examines the variability of chemical composition of surface water of the stream in relation to stream discharge, estimated from a hydrological deterministic model from rainfall data. Fifteen samplings were carried out, four in high flow condition and the rest in baseline flow. In each sampling, the main physico-chemical variables were determined. Since discharge data from this stream were not available, it was estimated in situ through an instantaneous unitary hydrograph model. Both estimations of stream discharge were similar. The main forms of dissolved inorganic nitrogen were ammonium and nitrate. The four significant components of PCA that explained 84.4 % of total variance were: mineral component, particulate matter content, ammonium and dissolved phosphorus levels, and nitrates' level. The decreased concentrations of major ions and conductivity during high flow condition suggest solutes' dilution by the massive inflow of water originated by rainfalls. The highest concentrations and loads of suspended solids (SS) (86 mg/l and 22638 kg/day) and particulate organic carbon (POC) (3.1 mg/l and 832 kg/day) were observed in the sample obtained during the rising limb of the hydrograph following a drought period, suggesting that basin erosive processes are more important during the first hours of the storm. Three of the samplings that were carried out in high flow conditions showed low mineral and nutrient content that revealed better water quality. In contrast, the sampling with the greatest total runoff (14.1 mm) showed high concentrations of ammonium (1205 μg/l) and dissolved phosphorus (561 μg/l), suggesting that a long stagnant period on soils with low permeability, could favor reduction processes of nitrate to ammonium and mobilization of dissolved phosphorus to overlying water. The nutrients' loads increased in high flow conditions most likely due to runoff from the riverbank soils. The rise of nutrients, SS, POC and total organic carbon (TOC), loads in the same or in higher proportion than the stream discharge, alerts on the risk of contamination of surface water in an agricultural basin.La cuenca del Arroyo Durazno abarca aproximadamente 360 km2 de una llanura con suave pendiente, dedicada principalmente a ganadería y agricultura. Este estudio examina la variabilidad en la composición química del agua superficial del arroyo en relación con el caudal estimado a través de un modelo hidrológico determinístico a partir de los datos de lluvia. Se realizaron quince muestreos: cuatro en condiciones de alto caudal, los restantes en caudal base. En cada muestreo se determinaron las principales variables fisico-químicas. Dado que no existen datos publicados de caudal de este arroyo, se lo estimó in situ, y a partir del modelo de hidrograma unitario. Ambas estimaciones resultaron similares. Las principales formas de nitrógeno inorgánico disuelto fueron amonio y nitrato. Los primeros 4 factores extraídos del PCA que explicaron 84.4 % de la varianza total fueron: componente mineral, contenido de material particulado, niveles de amonio y fósforo disuelto y nivel de nitratos. El decrecimiento de iones mayoritarios y conductividad durante las condiciones de alto caudal sugiere su dilución por la entrada masiva de agua por lluvias. Las mayores concentraciones y cargas de sólidos suspendidos (SS) (86 mg/l y 22638 kg/día) y carbono orgánico particulado (COP) (3.1 mg/l y 832 kg/día) se hallaron en el muestreo realizado durante la rama ascendente del hidrograma posterior a un período de sequía, sugiriendo que los procesos erosivos de la cuenca son más importantes en las primeras horas de la tormenta. Tres de los muestreos realizados en condiciones de alto caudal presentaron bajo contenido mineral y de nutrientes, indicando mejor calidad de agua. En cambio en el muestreo de mayor lámina de escorrentía acumulada (14.1 mm) las concentraciones de amonio (1205μg/l) y fósforo disuelto (561μg/l) fueron elevadas, sugiriendo que un prolongado periodo de estancamiento en un suelo de baja permeabilidad favorecería los procesos de reducción de nitratos a amonio y la movilización de fósforo disuelto al agua de inundación. Las cargas de nutrientes aumentaron en condiciones de alto caudal probablemente debido al aporte por escorrentía de suelos ribereños. El ascenso en las cargas de nutrientes, SS, COP y carbono orgánico total en igual o mayor magnitud que el caudal alerta sobre el riesgo de contaminación de las aguas superficiales en una cuenca agrícola

Time-frequency analysis of extreme-mass-ratio inspiral signals in mock LISA data

Extreme-mass-ratio inspirals (EMRIs) of ~ 1-10 solar-mass compact objects into ~ million solar-mass massive black holes can serve as excellent probes of strong-field general relativity. The Laser Interferometer Space Antenna (LISA) is expected to detect gravitational wave signals from apprxomiately one hundred EMRIs per year, but the data analysis of EMRI signals poses a unique set of challenges due to their long duration and the extensive parameter space of possible signals. One possible approach is to carry out a search for EMRI tracks in the time-frequency domain. We have applied a time-frequency search to the data from the Mock LISA Data Challenge (MLDC) with promising results. Our analysis used the Hierarchical Algorithm for Clusters and Ridges to identify tracks in the time-frequency spectrogram corresponding to EMRI sources. We then estimated the EMRI source parameters from these tracks. In these proceedings, we discuss the results of this analysis of the MLDC round 1.3 data.Comment: Amaldi-7 conference proceedings; requires jpconf style file

The evolution of Balmer jump selected galaxies in the ALHAMBRA survey

We present a new color-selection technique, based on the Bruzual & Charlot models convolved with the bands of the ALHAMBRA survey, and the redshifted position of the Balmer jump to select star-forming galaxies in the redshift range 0.5 < z < 1.5. These galaxies are dubbed Balmer jump Galaxies BJGs. We apply the iSEDfit Bayesian approach to fit each detailed SED and determine star-formation rate (SFR), stellar mass, age and absolute magnitudes. The mass of the haloes where these samples reside are found via a clustering analysis. Five volume-limited BJG sub-samples with different mean redshifts are found to reside in haloes of median masses $\sim 10^{12.5 \pm 0.2} M_\odot$ slightly increasing toward z=0.5. This increment is similar to numerical simulations results which suggests that we are tracing the evolution of an evolving population of haloes as they grow to reach a mass of $\sim 10^{12.7 \pm 0.1} M_\odot$ at z=0.5. The likely progenitors of our samples at z$\sim$3 are Lyman Break Galaxies, which at z$\sim$2 would evolve into star-forming BzK galaxies, and their descendants in the local Universe are elliptical galaxies.Hence, this allows us to follow the putative evolution of the SFR, stellar mass and age of these galaxies. From z$\sim$1.0 to z$\sim$0.5, the stellar mass of the volume limited BJG samples nearly does not change with redshift, suggesting that major mergers play a minor role on the evolution of these galaxies. The SFR evolution accounts for the small variations of stellar mass, suggesting that star formation and possible minor mergers are the main channels of mass assembly.Comment: 14 pages, 10 figures. Submitted to A&A. It includes first referee's comments. Abstract abridged due to arXiv requirement