On the topology of some hyperspaces of convex bodies associated to tensor norms

For every tuple $d_1,\dots, d_l\geq 2,$ let $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_l}$ denote the tensor product of $\mathbb{R}^{d_i},$ $i=1,\dots,l.$ Let us denote by $\mathcal{B}(d)$ the hyperspace of centrally symmetric convex bodies in $\mathbb{R}^d,$ $d=d_1\cdots d_l,$ endowed with the Hausdorff distance, and by $\mathcal{B}_\otimes(d_1,\dots,d_l)$ the subset of $\mathcal{B}(d)$ consisting of the convex bodies that are closed unit balls of reasonable crossnorms on $\mathbb{R}^{d_1}\otimes\cdots\otimes\mathbb{R}^{d_l}.$ It is known that $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is a closed, contractible and locally compact subset of $\mathcal{B}(d).$ The hyperspace $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is called the space of tensorial bodies. In this work we determine the homeomorphism type of $\mathcal{B}_\otimes(d_1,\dots,d_l).$ We show that even if $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is not closed with respect to the Minkowski sum, it is an absolute retract homeomorphic to $\mathcal{Q}\times\mathbb{R}^p,$ where $\mathcal{Q}$ is the Hilbert cube and $p=\frac{d_1(d_1+1)+\cdots+d_l(d_l+1)}{2}.$ Among other results, the relation between the Banach-Mazur compactum and the Banach-Mazur type compactum associated to $\mathcal{B}_\otimes(d_1,\dots,d_l)$ is examined.Comment: 28 pages. Among others, in this version we added an illustrative figure for the proof of Lemma 2.6. A gap on the selection of $r$ in the proof of lemma 2.6 was corrected. We provide a new sentence for Proposition 5.2. This new statement improves the resul

HETEROFOR 1.0: A spatially explicit model for exploring the response of structurally complex forests to uncertain future conditions-Part 2: Phenology and water cycle

Climate change affects forest growth in numerous and sometimes opposite ways, and the resulting trend is often difficult to predict for a given site. Integrating and structuring the knowledge gained from the monitoring and experimental studies into process-based models is an interesting approach to predict the response of forest ecosystems to climate change. While the first generation of models operates at stand level, one now needs spatially explicit individual-based approaches in order to account for individual variability, local environment modification and tree adaptive behaviour in mixed and uneven-Aged forests that are supposed to be more resilient under stressful conditions. The local environment of a tree is strongly influenced by the neighbouring trees, which modify the resource level through positive and negative interactions with the target tree. Among other things, drought stress and vegetation period length vary with tree size and crown position within the canopy. In this paper, we describe the phenology and water balance modules integrated in the tree growth model HETEROFOR (HETEROgenous FORest) and evaluate them on six heterogeneous sessile oak and European beech stands with different levels of mixing and development stages and installed on various soil types. More precisely, we assess the ability of the model to reproduce key phenological processes (budburst, leaf development, yellowing and fall) as well as water fluxes. Two two-phase models differing regarding their response function to temperature during the chilling period (optimum and sigmoid functions) and a simplified one-phase model are. used to predict budburst date. The two-phase model with the optimum function is the least biased (overestimation of 2.46 d), while the one-phase model best accounts for the interannual variability (Pearson's r D 0:68). For the leaf development, yellowing and fall, predictions and observations are in accordance. Regarding the water balance module, the predicted throughfall is also in close agreement with the measurements (Pearson's r D 0:856; biasD 1:3 %), and the soil water dynamics across the year are well reproduced for all the study sites (Pearson's r was between 0.893 and 0.950, and bias was between 1:81 and 9:33 %). The model also reproduced well the individual transpiration for sessile oak and European beech, with similar performances at the tree and stand scale (Pearson's r of 0.84 0.85 for sessile oak and 0.88 0.89 for European beech). The good results of the model assessment will allow us to use it reliably in projection studies to evaluate the impact of climate change on tree growth in structurally complex stands and test various management strategies to improve forest resilience. © 2020 Author(s)

Observed water and light limitation across global ecosystems

peer reviewedAbstract. With a changing climate, it is becoming increasingly critical to understand vegetation responses to limiting environmental factors. Here, we investigate the spatial and temporal patterns of light and water limitation on photosynthesis using an observational framework. Our study is unique in characterizing the nonlinear relationships between photosynthesis and water and light, acknowledging approximately two regime behaviours (no limitation and varying degrees of limitation). It is also unique in using an observational framework instead of using model-derived photosynthesis properties. We combine data from three different satellite sensors, i.e., sun-induced chlorophyll fluorescence (SIF) from the TROPOspheric Monitoring Instrument (TROPOMI), surface soil moisture from the Soil Moisture Active Passive (SMAP) microwave radiometer, and vegetation greenness from the Moderate Resolution Imaging Spectroradiometer (MODIS). We find both single-regime and two-regime models describe SIF sensitivity to soil moisture and photosynthetically active radiation (PAR) across the globe. The distribution and strength of soil moisture limitation on SIF are mapped in the water-limited environments, while the distribution and strength of PAR limitations are mapped in the energy-limited environments. A two-regime behaviour is detected in 73 % of the cases for water limitation on photosynthesis, while two-regime detection is much lower at 41 % for light limitation on photosynthesis. SIF sensitivity to PAR strongly increases along moisture gradients, reflecting mesic vegetation's adaptation to making rapid usage of incoming light availability on the weekly timescales. The transition point detected between the two regimes is connected to soil type and mean annual precipitation for the SIF–soil moisture relationship and for the SIF–PAR relationship. These thresholds therefore have an explicit relation to properties of the landscape, although they may also be related to finer details of the vegetation and soil interactions not resolved by the spatial scales here. The simple functions and thresholds are emergent behaviours capturing the interaction of many processes. The observational thresholds and strength of coupling can be used as benchmark information for Earth system models, especially those that characterize gross primary production mechanisms and vegetation dynamics

Long-COVID cognitive impairments and reproductive hormone deficits in men may stem from GnRH neuronal death

BACKGROUND: We have recently demonstrated a causal link between loss of gonadotropin-releasing hormone (GnRH), the master molecule regulating reproduction, and cognitive deficits during pathological aging, including Down syndrome and Alzheimer's disease. Olfactory and cognitive alterations, which persist in some COVID-19 patients, and long-term hypotestosteronaemia in SARS-CoV-2-infected men are also reminiscent of the consequences of deficient GnRH, suggesting that GnRH system neuroinvasion could underlie certain post-COVID symptoms and thus lead to accelerated or exacerbated cognitive decline. METHODS: We explored the hormonal profile of COVID-19 patients and targets of SARS-CoV-2 infection in post-mortem patient brains and human fetal tissue. FINDINGS: We found that persistent hypotestosteronaemia in some men could indeed be of hypothalamic origin, favouring post-COVID cognitive or neurological symptoms, and that changes in testosterone levels and body weight over time were inversely correlated. Infection of olfactory sensory neurons and multifunctional hypothalamic glia called tanycytes highlighted at least two viable neuroinvasion routes. Furthermore, GnRH neurons themselves were dying in all patient brains studied, dramatically reducing GnRH expression. Human fetal olfactory and vomeronasal epithelia, from which GnRH neurons arise, and fetal GnRH neurons also appeared susceptible to infection. INTERPRETATION: Putative GnRH neuron and tanycyte dysfunction following SARS-CoV-2 neuroinvasion could be responsible for serious reproductive, metabolic, and mental health consequences in long-COVID and lead to an increased risk of neurodevelopmental and neurodegenerative pathologies over time in all age groups. FUNDING: European Research Council (ERC) grant agreements No 810331, No 725149, No 804236, the European Union Horizon 2020 research and innovation program No 847941, the Fondation pour la Recherche Médicale (FRM) and the Agence Nationale de la Recherche en Santé (ANRS) No ECTZ200878 Long Covid 2021 ANRS0167 SIGNAL, Agence Nationale de la recherche (ANR) grant agreements No ANR-19-CE16-0021-02, No ANR-11-LABEX-0009, No. ANR-10-LABEX-0046, No. ANR-16-IDEX-0004, Inserm Cross-Cutting Scientific Program HuDeCA, the CHU Lille Bonus H, the UK Medical Research Council (MRC) and National Institute of Health and care Research (NIHR)

Peer influence in network markets: a theoretical and empirical analysis

Network externalities spur the growth of networks and the adoption of network goods in two ways. First, they make it more attractive to join a network the larger its installed base. Second, they create incentives for network members to actively recruit new members. Despite indications that the latter "peer effect" can be more important for network growth than the installed-base effect, it has so far been largely ignored in the literature. We address this gap using game-theoretical models. When all early adopters can band together to exert peer influence-an assumption that fits, e.g., the case of firms supporting a technical standard-we find that the peer effect induces additional growth of the network by a factor. When, in contrast, individuals exert peer influence in small groups of size n, the increase in network size is by an additive constant-which, for small networks, can amount to a large relative increase. The difference between small, local, personal networks and large, global, anonymous networks arises endogenously from our analysis. Fundamentally, the first type of networks is "tie-reinforcing," the other, "tie-creating". We use survey data from users of the Internet services, Skype and eBay, to illustrate the main logic of our theoretical results. As predicted by the model, we find that the peer effect matters strongly for the network of Skype users-which effectively consists of numerous small sub-networks-but not for that of eBay users. Since many network goods give rise to small, local networks

Soil Moisture and Permittivity Estimation

The soil moisture and permittivity estimation is vital for the success of the variable rate approaches in the field of the decision agriculture. In this chapter, the development of a novel permittivity estimation and soil moisture sensing approach is presented. The empirical setup and experimental methodology for the power delay measurements used in model are introduced. Moreover, the performance analysis is explained that includes the model validation and error analysis. The transfer functions are reported as well for soil moisture and permittivity estimation. Furthermore, the potential applications of the developed approach in different disciplines are also examined

Forest carbon sequestration:the impact of forest management

In this chapter, we describe alternative ways in which forests and forestry can help to mítigate climate change, along with the potential impact of these activities. The three carbon storage compartments should be considered inall impact estimates. Carbon content in living biomass is easily estimated via species-specific equations or by applying factors to oven-dry biomass weights (e.g.,lbañez et al.,2002, Herrero et al.,2011,Castaño and Bravo, 2012).Litter carbon content has been analysed in many studies on primary forest productivity, though information regarding the influence of forest management on litter carbon content is less abundant (Blanco et al., 2006). In the last decade,efforts have been made to assess soil carbon in forests, but studies on the effect of forest management on soils show discrepancies (Lindner and Karjalainen,2007).Hoover (2011), for example,found no difference in forest floor carbon stocks among stands subjected to partial or complete harvest treatments in the United States.Instituto Universitario de Gestión Forestal Sostenibl