The critical fugacity for surface adsorption of self-avoiding walks on the honeycomb lattice is 1+21+\sqrt{2}

In 2010, Duminil-Copin and Smirnov proved a long-standing conjecture of Nienhuis, made in 1982, that the growth constant of self-avoiding walks on the hexagonal (a.k.a. honeycomb) lattice is $\mu=\sqrt{2+\sqrt{2}}.$ A key identity used in that proof was later generalised by Smirnov so as to apply to a general O(n) loop model with $n\in [-2,2]$ (the case $n=0$ corresponding to SAWs). We modify this model by restricting to a half-plane and introducing a surface fugacity $y$ associated with boundary sites (also called surface sites), and obtain a generalisation of Smirnov's identity. The critical value of the surface fugacity was conjectured by Batchelor and Yung in 1995 to be $y_{\rm c}=1+2/\sqrt{2-n}.$ This value plays a crucial role in our generalized identity, just as the value of growth constant did in Smirnov's identity. For the case $n=0$, corresponding to \saws\ interacting with a surface, we prove the conjectured value of the critical surface fugacity. A crucial part of the proof involves demonstrating that the generating function of self-avoiding bridges of height $T$, taken at its critical point $1/\mu$, tends to 0 as $T$ increases, as predicted from SLE theory.Comment: Major revision, references updated, 25 pages, 13 figure

Exploring, exploiting and evolving diversity of aquatic ecosystem models: A community perspective

Here, we present a community perspective on how to explore, exploit and evolve the diversity in aquatic ecosystem models. These models play an important role in understanding the functioning of aquatic ecosystems, filling in observation gaps and developing effective strategies for water quality management. In this spirit, numerous models have been developed since the 1970s. We set off to explore model diversity by making an inventory among 42 aquatic ecosystem modellers, by categorizing the resulting set of models and by analysing them for diversity. We then focus on how to exploit model diversity by comparing and combining different aspects of existing models. Finally, we discuss how model diversity came about in the past and could evolve in the future. Throughout our study, we use analogies from biodiversity research to analyse and interpret model diversity. We recommend to make models publicly available through open-source policies, to standardize documentation and technical implementation of models, and to compare models through ensemble modelling and interdisciplinary approaches. We end with our perspective on how the field of aquatic ecosystem modelling might develop in the next 5–10 years. To strive for clarity and to improve readability for non-modellers, we include a glossary

Як уникнути підйому рівня води?

East Africa’s Lake Victoria provides resources and services to millions of people on the lake’s shores and abroad. In particular, the lake’s fisheries are an important source of protein, employment, and international economic connections for the whole region. Nonetheless, stock dynamics are poorly understood and currently unpredictable. Furthermore, fishery dynamics are intricately connected to other supporting services of the lake as well as to lakeshore societies and economies. Much research has been carried out piecemeal on different aspects of Lake Victoria’s system; e.g., societies, biodiversity, fisheries, and eutrophication. However, to disentangle drivers and dynamics of change in this complex system, we need to put these pieces together and analyze the system as a whole. We did so by first building a qualitative model of the lake’s social-ecological system. We then investigated the model system through a qualitative loop analysis, and finally examined effects of changes on the system state and structure. The model and its contextual analysis allowed us to investigate system-wide chain reactions resulting from disturbances. Importantly, we built a tool that can be used to analyze the cascading effects of management options and establish the requirements for their success. We found that high connectedness of the system at the exploitation level, through fisheries having multiple target stocks, can increase the stocks’ vulnerability to exploitation but reduce society’s vulnerability to variability in individual stocks. We describe how there are multiple pathways to any change in the system, which makes it difficult to identify the root cause of changes but also broadens the management toolkit. Also, we illustrate how nutrient enrichment is not a self-regulating process, and that explicit management is necessary to halt or reverse eutrophication. This model is simple and usable to assess system-wide effects of management policies, and can serve as a paving stone for future quantitative analyses of system dynamics at local scales

The future of algal blooms in lakes globally is in our hands

Lakes are fundamental to society and nature, yet they are currently exposed to excessive nutrients and climate change, resulting in algal blooms. In the future, this may change, but how and where still needs more scientific attention. Here, we explore future trends in algal blooms in lakes globally for >3,500 ‘representative lakes’ for the year 2050, considering the attribution of both nutrient and climate factors. We soft-coupled a process-based lake ecosystem model (PCLake+) with a watershed nutrient model (MARINA-Multi) to assess trends in algal blooms in terms of the Trophic State Index for chlorophyll-a (TSI-Chla). Globally between 2010 and 2050, we show a rising trend in algal blooms under fossil-fuelled development (TSI-Chla increase in 91% of lakes) and a declining trend under sustainable development (TSI-Chla decrease in 63% of lakes). These changes are significantly attributed to nutrients. While not always significant, climate change attributions point to being unfavourable for lakes in 2050, exacerbating lake water quality. Our study stresses prioritising responsible nutrient and climate management on policy agendas. This implies that the future of algal blooms in lakes is in our hands

Response of Submerged Macrophyte Communities to External and Internal Restoration Measures in North Temperate Shallow Lakes

Submerged macrophytes play a key role in north temperate shallow lakes by stabilising clear-water conditions. Eutrophication has resulted in macrophyte loss and shifts to turbid conditions in many lakes. Considerable efforts have been devoted to shallow lake restoration in many countries, but long-term success depends on a stable recovery of submerged macrophytes. However, recovery patterns vary widely and remain to be fully understood. We hypothesize that reduced external nutrient loading leads to an intermediate recovery state with clear spring and turbid summer conditions similar to the pattern described for eutrophication. In contrast, lake internal restoration measures can result in transient clear-water conditions both in spring and summer and reversals to turbid conditions. Furthermore, we hypothesize that these contrasting restoration measures result in different macrophyte species composition, with added implications for seasonal dynamics due to differences in plant traits. To test these hypotheses, we analysed data on water quality and submerged macrophytes from 49 north temperate shallow lakes that were in a turbid state and subjected to restoration measures. To study the dynamics of macrophytes during nutrient load reduction, we adapted the ecosystem model PCLake. Our survey and model simulations revealed the existence of an intermediate recovery state upon reduced external nutrient loading, characterised by spring clear-water phases and turbid summers, whereas internal lake restoration measures often resulted in clear-water conditions in spring and summer with returns to turbid conditions after some years. External and internal lake restoration measures resulted in different macrophyte communities. The intermediate recovery state following reduced nutrient loading is characterised by a few macrophyte species (mainly pondweeds) that can resist wave action allowing survival in shallow areas, germinate early in spring, have energy-rich vegetative propagules facilitating rapid initial growth and that can complete their life cycle by early summer. Later in the growing season these plants are, according to our simulations, outcompeted by periphyton, leading to late-summer phytoplankton blooms. Internal lake restoration measures often coincide with a rapid but transient colonisation by hornworts, waterweeds or charophytes. Stable clear-water conditions and a diverse macrophyte flora only occurred decades after external nutrient load reduction or when measures were combined.Additional co-authors: Wolf M. Mooij, Ruurd Noordhuis, Geoff Phillips, Jacqueline Rücker, Hans-Heinrich Schuster, Martin Søndergaard, Sven Teurlincx, Klaus van de Weyer, Ellen van Donk, Arno Waterstraat and Carl D. Saye

New paths for modelling freshwater nature futures

Freshwater ecosystems are exceptionally rich in biodiversity and provide essential benefits to people. Yet they are disproportionately threatened compared to terrestrial and marine systems and remain underrepresented in the scenarios and models used for global environmental assessments. The Nature Futures Framework (NFF) has recently been proposed to advance the contribution of scenarios and models for environmental assessments. This framework places the diverse relationships between people and nature at its core, identifying three value perspectives as points of departure: Nature for Nature, Nature for Society, and Nature as Culture. We explore how the NFF may be implemented for improved assessment of freshwater ecosystems. First, we outline how the NFF and its main value perspectives can be translated to freshwater systems and explore what desirable freshwater futures would look like from each of the above perspectives. Second, we review scenario strategies and current models to examine how freshwater modelling can be linked to the NFF in terms of its aims and outcomes. In doing so, we also identify which aspects of the NFF framework are not yet captured in current freshwater models and suggest possible ways to bridge them. Our analysis provides future directions for a more holistic freshwater model and scenario development and demonstrates how society can benefit from freshwater modelling efforts that are integrated with the value-perspectives of the NFF. Graphical abstract: [Figure not available: see fulltext.]</p

Association Between Hypothalamic Volume and Metabolism, Cognition, and Behavior in Patients With Amyotrophic Lateral Sclerosis

BACKGROUND AND OBJECTIVES: Dysfunction of energy metabolism, cognition, and behavior are important nonmotor symptoms of amyotrophic lateral sclerosis (ALS), negatively affecting survival and quality of life, but poorly understood. Neuroimaging is ideally suited to studying nonmotor neurodegeneration in ALS, but few studies have focused on the hypothalamus, a key region for regulating energy homeostasis, cognition, and behavior. We evaluated, therefore, hypothalamic neurodegeneration in ALS and explored the relationship between hypothalamic volumes and dysregulation of energy metabolism, cognitive and behavioral changes, disease progression, and survival. METHODS: Patients with ALS and population-based controls were included for this cross-sectional and longitudinal MRI study. The hypothalamus was segmented into 5 subregions and their volumes were calculated. Linear (mixed) models, adjusted for age, sex, and total intracranial volume, were used to compare hypothalamic volumes between groups and to analyze associations with metabolism, cognition, behavior, and disease progression. Cox proportional hazard models were used to investigate the relationship of hypothalamic volumes with survival. Permutation-based corrections for multiple hypothesis testing were applied to all analyses to control the family-wise error rate. RESULTS: Data were available for 564 patients with ALS and 356 controls. The volume of the anterior superior subregion of the hypothalamus was smaller in patients with ALS than in controls (β = -0.70 [-1.15 to -0.25], p = 0.013). Weight loss, memory impairments, and behavioral disinhibition were associated with a smaller posterior hypothalamus (β = -4.79 [-8.39 to -2.49], p = 0.001, β = -10.14 [-15.88 to -4.39], p = 0.004, and β = -12.09 [-18.83 to -5.35], p = 0.003, respectively). Furthermore, the volume of this subregion decreased faster over time in patients than in controls (β = -0.25 [0.42 to -0.09], p = 0.013), and a smaller volume of this structure was correlated with shorter survival (hazard ratio = 0.36 [0.21-0.61], p = 0.029). DISCUSSION: We obtained evidence for hypothalamic involvement in ALS, specifically marked by atrophy of the anterior superior subregion. Moreover, we found that atrophy of the posterior hypothalamus was associated with weight loss, memory dysfunction, behavioral disinhibition, and survival, and that this subregion deteriorated faster in patients with ALS than in controls. These findings improve our understanding of nonmotor involvement in ALS and could contribute to the identification of new treatment targets for this devastating disease

A putative genomic island, PGI-1, in Ralstonia solanacearum biovar 2 revealed by subtractive hybridization

Ralstonia solanacearum biovar 2, a key bacterial pathogen of potato, has recently established in temperate climate waters. On the basis of isolates obtained from diseased (potato) plants, its genome has been assumed to be virtually clonal, but information on environmental isolates has been lacking. Based on differences in pulsed-field gel electrophoresis patterns, we compared the genomes of two biovar 2 strains with different life histories. Thus, genomic DNA of the novel environmental strain KZR-5 (The Netherlands) was compared to that of reference potato strain 715 (Bangladesh) by suppressive subtractive hybridization. Various strain-specific sequences were found, all being homologous to those found in the genome of reference potato strain 1609. Approximately 20% of these were related to genes involved in recombinational processes. We found a deletion of a 17.6-Kb region, denoted as a putative genomic island PGI-1, in environmental strain KZR-5. The deleted region was, at both extremes, flanked by a composite of two insertion sequence (IS) elements, identified as ISRso2 and ISRso3. The PGI-1 region contained open reading frames that putatively encoded a (p)ppGpp synthetase, a transporter protein, a transcriptional regulator, a cellobiohydrolase, a site-specific integrase/recombinase, a phage-related protein and seven hypothetical proteins. As yet, no phenotype could be assigned to the loss of PGI-1. The ecological behavior of strain KZR-5 was compared to that of reference strain 715. Strain KZR-5 showed enhanced tolerance to 4°C as compared to the reference strain, but was not affected in its virulence on tomato

A perspective on water quality in connected systems : modelling feedback between upstream and downstream transport and local ecological processes

Highlights • Catchment pollution limits water-related ecosystem services such as food production. • Water flow transports energy, substances and organisms downstream. • Organism behaviour causes bidirectional transport across the catchment. • Humans are modifiers of water and organismal transport. • Coupled transport-ecosystem models are essential for water quality assessment.Food production for a growing world population relies on application of fertilisers and pesticides on agricultural lands. However, these substances threaten surface water quality and thereby endanger valued ecosystem services such as drinking water supply, food production and recreational water use. Such deleterious effects do not merely arise on the local scale, but also on the regional scale through transport of substances as well as energy and biota across the catchment. Here we argue that aquatic ecosystem models can provide a process-based understanding of how these transports by water and organisms as vectors affect – and are affected by – ecosystem state and functioning in networks of connected lakes. Such a catchment scale approach is key to setting critical limits for the release of substances by agricultural practices and other human pressures on aquatic ecosystems. Thereby, water and food production and the trade-offs between them may be managed more sustainably