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Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once—for example, communication within a group rather than person to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental difference from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.

Higher-order networks can sustain topological signals which are variables associated not only to the nodes, but also to the links, to the triangles and in general to the higher dimensional simplices of simplicial complexes. These topological signals can describe a large variety of real systems including currents in the ocean, synaptic currents between neurons and biological transportation networks. In real scenarios topological signal data might be noisy and an important task is to process these signals by improving their signal to noise ratio. So far topological signals are typically processed independently of each other. For instance, node signals are processed independently of link signals, and algorithms that can enforce a consistent processing of topological signals across different dimensions are largely lacking. Here we propose Dirac signal processing, an adaptive, unsupervised signal processing algorithm that learns to jointly filter topological signals supported on nodes, links and triangles of simplicial complexes in a consistent way. The proposed Dirac signal processing algorithm is formulated in terms of the discrete Dirac operator which can be interpreted as ‘square root’ of a higher-order Hodge Laplacian. We discuss in detail the properties of the Dirac operator including its spectrum and the chirality of its eigenvectors and we adopt this operator to formulate Dirac signal processing that can filter noisy signals defined on nodes, links and triangles of simplicial complexes. We test our algorithms on noisy synthetic data and noisy data of drifters in the ocean and find that the algorithm can learn to efficiently reconstruct the true signals outperforming algorithms based exclusively on the Hodge Laplacian.

In recent years, there has been a surge of interest in community detection algorithms for complex networks. A variety of computational heuristics, some with a long history, have been proposed for the identification of communities or, alternatively, of good graph partitions. In most cases, the algorithms maximize a particular objective function, thereby finding the 'right' split into communities. Although a thorough comparison of algorithms is still lacking, there has been an effort to design benchmarks, i.e., random graph models with known community structure against which algorithms can be evaluated. However, popular community detection methods and benchmarks normally assume an implicit notion of community based on clique-like subgraphs, a form of community structure that is not always characteristic of real networks. Specifically, networks that emerge from geometric constraints can have natural non clique-like substructures with large effective diameters, which can be interpreted as long-range communities. In this work, we show that long-range communities escape detection by popular methods, which are blinded by a restricted 'field-of-view' limit, an intrinsic upper scale on the communities they can detect. The field-of-view limit means that long-range communities tend to be overpartitioned. We show how by adopting a dynamical perspective towards community detection [1], [2], in which the evolution of a Markov process on the graph is used as a zooming lens over the structure of the network at all scales, one can detect both clique- or non clique-like communities without imposing an upper scale to the detection. Consequently, the performance of algorithms on inherently low-diameter, clique-like benchmarks may not always be indicative of equally good results in real networks with local, sparser connectivity. We illustrate our ideas with constructive examples and through the analysis of real-world networks from imaging, protein structures and the power grid, where a multiscale structure of non clique-like communities is revealed.

Bayesian statistics has exploded into biology and its sub-disciplines, such as ecology, over the past decade. The free software program WinBUGS, and its open-source sister OpenBugs, is currently the only flexible and general-purpose program available with which the average ecologist can conduct standard and non-standard Bayesian statistics. Comprehensive and richly commented examples illustrate a wide range of models that are most relevant to the research of a modern population ecologistAll WinBUGS/OpenBUGS analyses are completely integrated in software RIncludes complete documentation of all R and WinBUGS code required to conduct analyses and shows all the necessary steps from having the data in a text file out of Excel to interpreting and processing the output from WinBUGS in R

Neuroenhancement is the use of substances by healthy subjects to enhance mood or cognitive function. The prevalence of neuroenhancement among Swiss university students is unknown. Investigating the prevalence of neuroenhancement among students is important to monitor problematic use and evaluate the necessity of prevention programs. To describe the prevalence of the use of prescription medications and drugs of abuse for neuroenhancement among Swiss university students. In this cross-sectional study, students at the University of Zurich, University of Basel, and Swiss Federal Institute of Technology Zurich were invited via e-mail to participate in an online survey. A total of 28,118 students were contacted, and 6,275 students completed the survey. Across all of the institutions, 13.8% of the respondents indicated that they had used prescription drugs (7.6%) or drugs of abuse including alcohol (7.8%) at least once specifically for neuroenhancement. The most frequently used prescription drugs for neuroenhancement were methylphenidate (4.1%), sedatives (2.7%), and beta-blockers (1.2%). Alcohol was used for this purpose by 5.6% of the participants, followed by cannabis (2.5%), amphetamines (0.4%), and cocaine (0.2%). Arguments for neuroenhancement included increased learning (66.2%), relaxation or sleep improvement (51.2%), reduced nervousness (39.1%), coping with performance pressure (34.9%), increased performance (32.2%), and experimentation (20%). Neuroenhancement was significantly more prevalent among more senior students, students who reported higher levels of stress, and students who had previously used illicit drugs. Although \"soft enhancers\", including coffee, energy drinks, vitamins, and tonics, were used daily in the month prior to an exam, prescription drugs or drugs of abuse were used much less frequently. A significant proportion of Swiss university students across most academic disciplines reported neuroenhancement with prescription drugs and drugs of abuse. However, these substances are rarely used on a daily basis and more sporadically used prior to exams.

Single-cell consensus clustering (SC3) provides user-friendly, robust and accurate cell clustering as well as downstream analysis for single-cell RNA-seq data. Single-cell RNA-seq enables the quantitative characterization of cell types based on global transcriptome profiles. We present single-cell consensus clustering (SC3), a user-friendly tool for unsupervised clustering, which achieves high accuracy and robustness by combining multiple clustering solutions through a consensus approach ( http://bioconductor.org/packages/SC3 ). We demonstrate that SC3 is capable of identifying subclones from the transcriptomes of neoplastic cells collected from patients.

Complex systems made of interacting elements are commonly abstracted as networks, in which nodes are associated with dynamic state variables, whose evolution is driven by interactions mediated by the edges. Markov processes have been the prevailing paradigm to model such a network-based dynamics, for instance in the form of random walks or other types of diffusions. Despite the success of this modelling perspective for numerous applications, it represents an over-simplification of several real-world systems. Importantly, simple Markov models lack memory in their dynamics, an assumption often not realistic in practice. Here, we explore possibilities to enrich the system description by means of second-order Markov models, exploiting empirical pathway information. We focus on the problem of community detection and show that standard network algorithms can be generalized in order to extract novel temporal information about the system under investigation. We also apply our methodology to temporal networks, where we can uncover communities shaped by the temporal correlations in the system. Finally, we discuss relations of the framework of second order Markov processes and the recently proposed formalism of using non-backtracking matrices for community detection.

Local population dynamics are driven by local processes such as temporal variation of productivity, survival, emigration and population stage structure, and by processes originating from outside the local population, such as immigration. Populations may operate as sources that contribute more individuals than have died or as sinks that depend on neighbouring populations. Knowing demographic processes driving the dynamics of a local population and the significance of a local population in a system of multiple populations is crucial for understanding population dynamics and requires detailed demographic analyses. We studied demographic drivers in a red kite Milvus milvus population located in Germany that was monitored for 34 years using integrated population modelling. We specified the model in such a way that the numbers of experienced breeders, local recruits, locally born non‐breeders and immigrants are estimated explicitly, applied a retrospective perturbation analysis to identify the demographic drivers and assessed the source‐sink status of the population. The study population increased on average by 1% per year. The number of breeders was about double than the number of locally born non‐breeders, and the number of experienced breeders exceeded the number of local recruits and immigrants by a factor of six to nine. The retrospective analysis identified productivity, i.e. the number of fledglings per breeding pair, as the main demographic driver, followed by adult survival and immigration. As other studies show close links between food supply and productivity, it is likely that food supply plays a critical role in red kite population dynamics. The study population contributed more individuals than it lost through mortality, but due to emigration of locally born individuals it was not self‐sustainable and depended on immigration. This quantifies the population as a dependent source and shows that red kite populations are linked across large spatial scales.

The cardiac vascular and perivascular niche are of major importance in homeostasis and during disease, but we lack a complete understanding of its cellular heterogeneity and alteration in response to injury as a major driver of heart failure. Using combined genetic fate tracing with confocal imaging and single-cell RNA sequencing of this niche in homeostasis and during heart failure, we unravel cell type specific transcriptomic changes in fibroblast, endothelial, pericyte and vascular smooth muscle cell subtypes. We characterize a specific fibroblast subpopulation that exists during homeostasis, acquires Thbs4 expression and expands after injury driving cardiac fibrosis, and identify the transcription factor TEAD1 as a regulator of fibroblast activation. Endothelial cells display a proliferative response after injury, which is not sustained in later remodeling, together with transcriptional changes related to hypoxia, angiogenesis, and migration. Collectively, our data provides an extensive resource of transcriptomic changes in the vascular niche in hypertrophic cardiac remodeling. The cardiac vascular niche is of major importance in homeostasis and disease, but knowledge of its complexity in response to injury remains limited. Here we combine lineage tracing with single cell RNA sequencing to show alterations in fibroblasts, endothelial and mural cells in hypertrophic remodeling.

The use of prescription or recreational drugs for cognitive enhancement (CE) is prevalent among students. However, the prevalence of CE among Swiss school students is unknown. We therefore performed a cross-sectional online survey including ≥ 16-year-old students from bridge-year schools (10th grade), vocational schools, and upper secondary schools (10th-12th grade) in the Canton of Zurich to investigate the prevalence of and motives for the use of prescription drugs, recreational drugs, and/or freely available soft enhancers for CE. A total of 1,139 students were included. Of these, 54.5% reported the use of prescription drugs (9.2%), recreational drugs including alcohol (6.2%), or soft enhancers (51.3%) explicitly for CE at least once in their lives. The last-year and last-month prevalence for CE considering all substances was 45.5% and 39.5%, respectively. Soft enhancers were the substances that were most commonly used (ever, last-year, and last-month, respectively), including energy drinks (33.3%, 28.4%, and 24.6%), coffee (29.8%, 25.1%, and 21.9%), and tobacco (12.6%, 9.3%, and 8.3%). CE with methylphenidate was less prevalent (4.0%, 2.8%, and 2.0%). However, the use of prescription drugs, alcohol, or illegal drugs for CE was reported by 13.3% of the participants. The most common motives for use were to stay awake and improve concentration. CE was more prevalent among students who reported higher levels of stress or performance pressure and students with psychiatric disorders. In conclusion, half of the school students had used a substance at least once in their lives to improve school performance. Soft enhancers were most commonly used. Prevalence rates were similar to those reported by Swiss university students, indicating that the use of prescription or recreational drugs for CE already occurs before starting higher education. Performance pressure, stress, and psychiatric disorders may be associated with CE.