From Broadstone to Zackenberg

Ecological networks are typically complex constructions of species and their interactions. During the last decade, the study of networks has moved from static to dynamic analyses, and has attained a deeper insight into their internal structure, heterogeneity, and temporal and spatial resolution. Here, we review, discuss and suggest research lines in the study of the spatio-temporal heterogeneity of networks and their hierarchical nature. We use case study data from two well-characterized model systems (the food web in Broadstone Stream in England and the pollination network at Zackenberg in Greenland), which are complemented with additional information from other studies. We focus upon eight topics: temporal dynamic space-for-time substitutions linkage constraints habitat borders network modularity individual-based networks invasions of networks and super networks that integrate different network types. Few studies have explicitly examined temporal change in networks, and we present examples that span from daily to decadal change: a common pattern that we see is a stable core surrounded by a group of dynamic, peripheral species, which, in pollinator networks enter the web via preferential linkage to the most generalist species. To some extent, temporal and spatial scales are interchangeable (i.e. networks exhibit ‘ergodicity’) and we explore how space-for-time substitutions can be used in the study of networks. Network structure is commonly constrained by phenological uncoupling (a temporal phenomenon), abundance, body size and population structure. Some potential links are never observed, that is they are ‘forbidden’ (fully constrained) or ‘missing’ (a sampling effect), and their absence can be just as ecologically significant as their presence. Spatial habitat borders can add heterogeneity to network structure, but their importance has rarely been studied: we explore how habitat generalization can be related to other resource dimensions. Many networks are hierarchically structured, with modules forming the basic building blocks, which can result in self-similarity. Scaling down from networks of species reveals another, finer-grained level of individual-based organization, the ecological consequences of which have yet to be fully explored. The few studies of individual-based ecological networks that are available suggest the potential for large intraspecific variance and, in the case of food webs, strong size-structuring. However, such data are still scarce and more studies are required to link individual-level and species-level networks. Invasions by alien species can be tracked by following the topological ‘career’ of the invader as it establishes itself within a network, with potentially important implications for conservation biology. Finally, by scaling up to a higher level of organization, it is possible to combine different network types (e.g. food webs and mutualistic networks) to form super networks, and this new approach has yet to be integrated into mainstream ecological research. We conclude by listing a set of research topics that we see as emerging candidates for ecological network studies in the near future.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Development of self-esteem and relationship satisfaction in couples: Two longitudinal studies

We examined the effects of self-esteem development on the development of relationship satisfaction in 2 samples of couples. Study 1 used data from both partners of 885 couples assessed 5 times over 12 years, and Study 2 used data from both partners of 6,116 couples assessed 3 times over 15 years. The pattern of results was similar across the 2 studies. First, development of relationship satisfaction could be modeled as a couple-level process. Second, initial level of self-esteem of each partner predicted the initial level of the partners’ common relationship satisfaction, and change in self-esteem of each partner predicted change in the partners’ common relationship satisfaction. Third, these effects did not differ by gender and held when controlling for participants’ age, length of relationship, health, and employment status. Fourth, self-esteem similarity among partners did not influence the development of their relationship satisfaction. The findings suggest that the development of self-esteem in both partners of a couple contributes in a meaningful way to the development of the partners’ common satisfaction with their relationship.

The Self-Expanding Symetis Acurate Does Not Increase Cerebral Microembolic Load When Compared to the Balloon-Expandable Edwards Sapien Prosthesis: A Transcranial Doppler Study in Patients Undergoing Transapical Aortic Valve Implantation

Objectives The aim of this study was to quantify potential differences in count, frequency and pattern of high-intensity transient signals (HITS) during transapical transcatheter aortic valve implantation (TA-TAVI), by comparing the Symetis Acurate TA (SA) with the balloon-expandable Edwards Sapien XT (ES) system. Background Recently, the Symetis Acurate TA revalving system has been introduced for TA-TAVI. The Symetis Acurate TA aortic bioprosthesis is self-expanding and is deployed by a specific two-step implantation technique. Whether this novel method increases the load of intraprocedural emboli, detected by transcranial Doppler ultrasound (TCD) as HITS, or not is not clear. Methods Twenty-two patients (n = 11 in each study arm, median logistic EuroScore 20%, median STS score 7%) displayed continuous TCD signals of good quality throughout the entire TA-TAVI procedure and were included in the final analysis. Data are presented as median with interquartile ranges. Results No significant differences were detected in total procedural or interval-related HITS load (SA: 303 [200; 594], ES: 499 [285; 941]; p = 0.16). With both devices, HITS peaked during prosthesis deployment (PD), whereas significantly fewer HITS occurred during instrumentation (SA: p = 0.002; ES: <0.001) or post-implantation PI (SA: p = 0.007; ES: <0.001). PD-associated HITS amounted to almost half of the total HITS load. One patient suffered new disabling stroke at 30 days. Thirty-day mortality amounted to 13.6% (3 of 22 patients). Conclusions Simplified transapical delivery using the self-expanding SA device does not increase HITS, despite of a two-step deployment technique with more interactions with the native aortic valve, when compared to the balloon-expandable ES valve. The similarity in HITS count, frequency and pattern with the two systems suggests a common mechanism for the release of cerebral microemboli.

From supramolecular sheets to fibers and back: establishing the critical parameters that govern the morphology of pyrene-based self-assembled materials

The precise arraying of functional entities in morphologically well-defined shapes remains one of the key challenges in the processing of organic molecules1. Among various π-conjugated species, pyrene exhibits a set of unique properties, which make it an attractive compound for the utilization in materials science2. In this contribution we report on properties of self-assembled structures prepared from amphiphilic pyrene trimers (Py3) consisting of phosphodiester-linked pyrenes. Depending on the geometry of a pyrene core substitution (1.6-, 1.8-, or 2.7- type, see Scheme), the thermally-controlled self-assembly allows the preparation of supramolecular architectures of different morphologies in a bottom-up approach: two-dimensional (2D) nanosheets3 are formed in case of 1.6- and 2.7-substitution4 whereas one-dimensional (1D) fibers are built from 1.8- substituted isomers. The morphologies of the assemblies are established by AFM and TEM, and the results are further correlated with spectroscopic and scattering data. Two-dimensional assemblies consist of an inner layer of hydrophobic pyrenes, sandwiched between a net of phosphates. Due to the repulsion of the negative charges, the 2D assemblies exist mostly as free-standing sheets. An internal alignment of pyrenes leads to strong exciton coupling with an unprecedented observation (simultaneous development of J- and H-bands from two different electronic transitions). Despite the similarity in spectroscopic properties, the structural parameters of the 2D aggregates drastically depend on the preparation procedure. Under certain conditions extra-large sheets (thickness of 2 nm, aspect ratio area/thickness ~107) in aqueous solution are formed4B. Finally, one-dimensional assemblies are formed as micrometer-long and nanometer-thick fibers. Both, planar and linear structures are intriguing objects for the creation of conductive nanowires that may find interest for applications in supramolecular electronics.

From supramolecular sheets to fibers and back: establishing the critical parameters that govern the morphology of pyrene-based self-assembled materials

The precise arraying of functional entities in morphologically well-defined shapes remains one of the key challenges in the processing of organic molecules1. Among various π-conjugated species, pyrene exhibits a set of unique properties, which make it an attractive compound for the utilization in materials science2. In this contribution we report on properties of self-assembled structures prepared from amphiphilic pyrene trimers (Py3) consisting of phosphodiester-linked pyrenes. Depending on the geometry of a pyrene core substitution (1.6-, 1.8-, or 2.7- type, see Scheme), the thermally-controlled self-assembly allows the preparation of supramolecular architectures of different morphologies in a bottom-up approach: two-dimensional (2D) nanosheets3 are formed in case of 1.6- and 2.7-substitution4 whereas one-dimensional (1D) fibers are built from 1.8- substituted isomers. The morphologies of the assemblies are established by AFM and TEM, and the results are further correlated with spectroscopic and scattering data. Two-dimensional assemblies consist of an inner layer of hydrophobic pyrenes, sandwiched between a net of phosphates. Due to the repulsion of the negative charges, the 2D assemblies exist mostly as free-standing sheets. An internal alignment of pyrenes leads to strong exciton coupling with an unprecedented observation (simultaneous development of J- and H-bands from two different electronic transitions). Despite the similarity in spectroscopic properties, the structural parameters of the 2D aggregates drastically depend on the preparation procedure. Under certain conditions extra-large sheets (thickness of 2 nm, aspect ratio area/thickness ~107) in aqueous solution are formed4B. Finally, one-dimensional assemblies are formed as micrometer-long and nanometer-thick fibers. Both, planar and linear structures are intriguing objects for the creation of conductive nanowires that may find interest for applications in supramolecular electronics.

Non-self-adjoint graphs

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.