The numerical index of 22-dimensional Lipschitz-free spaces

We provide the explicit formula for the numerical index of any $2$-dimensional Lipschitz-free space, also giving the construction of operators attaining this value as its numerical radius. As a consequence, the numerical index of $2$-dimensional Lipschitz-free spaces can take any value of the interval $[\frac{1}{2},1]$, and this whole range of numerical indices can be attained by taking $2$-dimensional subspaces of any Lipschitz-free space of the form $\mathcal{F}(A)$, where $A\subset {\mathbb{R}}^n$ with $n\geq 2$ is any set with non-empty interior

Quantum cavitation in liquid helium

Using a functional-integral approach, we have determined the temperature below which cavitation in liquid helium is driven by thermally assisted quantum tunneling. For both helium isotopes, we have obtained the crossover temperature in the whole range of allowed negative p essures. Our results are compatible with recent experimental results on 4He.Comment: Typeset using Revtex, 10 pages and 2 figures, Phys. Rev B (1996

DNA methylation dynamics in a coastal foundation seagrass species under abiotic stressors

DNA methylation (DNAm) has been intensively studied in terrestrial plants in response to environmental changes, but its dynamic changes in a temporal scale remain unexplored in marine plants. The seagrass Posidonia oceanica ranks among the slowest-growing and longest-living plants on Earth, and is particularly vulnerable to sea warming and local anthropogenic pressures. Here, we analysed the dynamics of DNAm changes in plants collected from coastal areas differentially impacted by eutrophication (i.e. oligotrophic, Ol; eutrophic, Eu) and exposed to abiotic stressors (nutrients, temperature increase and their combination). Levels of global DNAm (% 5-mC) and the expression of key genes involved in DNAm were assessed after one, two and five weeks of exposure. Results revealed a clear differentiation between plants, depending on environmental stimuli, time of exposure and plants' origin. % 5-mC levels were higher during the initial stress exposure especially in Ol plants, which upregulated almost all genes involved in DNAm. Contrarily, Eu plants showed lower expression levels, which increased under chronic exposure to stressors, particularly to temperature. These findings show that DNAm is dynamic in P. oceanica during stress exposure and underlined that environmental epigenetic variations could be implicated in the regulation of acclimation and phenotypic differences depending on local conditions

Spread of the invasive alga Caulerpa racemosa var. cylindracea (Caulerpales, Chlorophyta) along the Mediterranean Coast of the Murcia region (SE Spain)

The aim of this paper was to document the appearance and spread of the green alga Caulerpa racemosa along the coast of Murcia in south–eastern Spain. It was found for the first time in the area in 2005 and over the next two years the number of new sightings increased almost exponentially. In the period 2005–2007 the total surface area colonised by the alga in the region was estimated to be at least 265 ha. Benthic assemblages colonised by the alga were rocky bottoms with photophilic algae, dead P. oceanica rhizomes, infralittoral and circalittoral soft bottoms and maerl beds. No penetration of the alga was observed in P. oceanica meadows, except in one locality. Biometric analysis indicated high vegetative development in the established colonies in comparison to those described in other Mediterranean areas. Rapid spreading dynamics observed in the Murcia region is a potential threat for native benthic communities. Key words: Biological invasions, Caulerpa racemosa var. cylindracea, Colonised surface area, Distribution, Mediterranean Sea, Spain.En el presente trabajo se documenta la aparición y dispersión del alga verde Caulerpa racemosa a lo largo de la costa de Murcia, región situada en el sureste español. El alga fue detectada por primera vez en el año 2005 y durante los dos años consecutivos se observó un crecimiento casi exponencial en el número de áreas colonizadas. La superficie total colonizada por el alga en Murcia durante el periodo 2005–2007 ha sido estimada en 265 ha., siendo las comunidades bentónicas afectadas algas fotófilas sobre sustrato rocoso, "mata muerta" de P. oceanica, fondos blandos infralitorales y circalitorales y fondos con comunidades de maërl. La presencia del alga dentro de praderas de P. oceanica solamente fue detectada en una localidad. Los estudios biométricos realizados muestran un elevado desarrollo vegetativo de las poblaciones de C. racemosa en Murcia en comparación con colonias de otras áreas del Mediterráneo, siendo esta rápida dinámica de expansión una amenaza potencial para las comunidades bentonicas nativas. Palabras clave: Invasiones biológicas, Caulerpa racemosa var. cylindracea, Superficie colonizada, Mar Mediterraneo, España.The aim of this paper was to document the appearance and spread of the green alga Caulerpa racemosa along the coast of Murcia in south–eastern Spain. It was found for the first time in the area in 2005 and over the next two years the number of new sightings increased almost exponentially. In the period 2005–2007 the total surface area colonised by the alga in the region was estimated to be at least 265 ha. Benthic assemblages colonised by the alga were rocky bottoms with photophilic algae, dead P. oceanica rhizomes, infralittoral and circalittoral soft bottoms and maerl beds. No penetration of the alga was observed in P. oceanica meadows, except in one locality. Biometric analysis indicated high vegetative development in the established colonies in comparison to those described in other Mediterranean areas. Rapid spreading dynamics observed in the Murcia region is a potential threat for native benthic communities. Key words: Biological invasions, Caulerpa racemosa var. cylindracea, Colonised surface area, Distribution, Mediterranean Sea, Spain

Does Warming Enhance the Effects of Eutrophication in the Seagrass Posidonia oceanica?

Seagrass meadows are disappearing at rates comparable to those reported for mangroves, coral reefs, and tropical rainforests. One of the main causes of their decline is the so-called cultural eutrophication, i.e., the input of abnormal amounts of nutrients derived from human activities. Besides the impact of eutrophication at a local scale, the occurrence of additional stress factors such as global sea warming may create synergisms in detriment of seagrass meadows’ health. In the present study, we aimed to evaluate if plants undergoing chronic cultural eutrophication and plants growing in relatively pristine waters are more (or less) sensitive to heat stress, nutrient load and the combination of both stressors. To address this question, a mesocosm experiment was conducted using Posidonia oceanica collected from two environments with different nutrients load history. Plants were exposed in controlled conditions to high nutrient concentrations, increased temperature and their combination for 5 weeks, to assess the effect of the single stressors and their interaction. Our results revealed that plants experiencing chronic cultural eutrophication (EU) are more sensitive to further exposure to multiple stressors than plants growing in oligotrophic habitats (OL). OL and EU plants showed different morphological traits and physiological performances, which corroborates the role of local pressures in activating different strategies in response to global environmental changes. EU-plants appeared to be weaker during the treatments, showing the greatest percentage of mortality, particularly under increased temperature. Temperature and nutrient treatments showed opposite effects when tested individually and an offset response when combined. The activation of physiological strategies with high energetic expenses to cope with excess of nutrients and other stressors, could affect plants present and future persistence, particularly under eutrophic conditions. Our results represent a step forward in understanding the complex interactions that occur in natural environments. Moreover, unraveling intraspecific strategies and the role of local acclimation/adaptation in response to multiple stressors could be crucial for seagrass conservation strategies under a climate change scenario

Does Warming Enhance the Effects of Eutrophication in the Seagrass Posidonia oceanica?

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The Genetic Component of Seagrass Restoration: What We Know and the Way Forwards

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Local environment modulates whole-transcriptome expression in the seagrass Posidonia oceanica under warming and nutrients excess

The intensification of anomalous events of seawater warming and the co-occurrence with local anthropogenic stressors are threatening coastal marine habitats, including seagrasses, which form extensive underwater meadows. Eutrophication highly affects coastal environments, potentially summing up to the widespread effects of global climate changes. In the present study, we investigated for the first time in seagrasses, the transcriptional response of different plant organs (i.e., leaf and shoot apical meristem, SAM) of the Mediterranean seagrass Posidonia oceanica growing in environments with a different history of nutrient enrichment. To this end, a mesocosm experiment exposing plants to single (nutrient enrichment or temperature increase) and multiple stressors (nutrient enrichment plus temperature increase), was performed. Results revealed a differential transcriptome regulation of plants under single and multiple stressors, showing an organ-specific sensitivity depending on plants' origin. While leaf tissues were more responsive to nutrient stress, SAM revealed a higher sensitivity to temperature treatments, especially in plants already impacted in their native environment. The exposure to stress conditions induced the modulation of different biological processes. Plants living in an oligotrophic environment were more responsive to nutrients compared to plants from a eutrophic environment. Evidences that epigenetic mechanisms were involved in the regulation of transcriptional reprogramming were also observed in both plants’ organs. These results represent a further step in the comprehension of seagrass response to abiotic stressors pointing out the importance of local pressures in a global warming scenario.En prens

Generalized van der Waals Hamiltonian: Periodic orbits and C

Agraïments: The first author was partially supported by grant number PEII09-0220-0222. The third author was partially supported by Fundación Séneca de la Región de Murcia grant number 12001/PI/0