From the Cover: Fiber networks amplify active stress

Large-scale force generation is essential for biological functions such as cell motility, embryonic development, and muscle contraction. In these processes, forces generated at the molecular level by motor proteins are transmitted by disordered fiber networks, resulting in large-scale active stresses. Although these fiber networks are well characterized macroscopically, this stress generation by microscopic active units is not well understood. Here we theoretically study force transmission in these networks. We find that collective fiber buckling in the vicinity of a local active unit results in a rectification of stress towards strongly amplified isotropic contraction. This stress amplification is reinforced by the networks’ disordered nature, but saturates for high densities of active units. Our predictions are quantitatively consistent with experiments on reconstituted tissues and actomyosin networks and shed light on the role of the network microstructure in shaping active stresses in cells and tissue.Living systems constantly convert biochemical energy into forces and motion. In cells, forces are largely generated internally by molecular motors acting on the cytoskeleton, a scaffold of protein fibers (Fig. 1A). Forces from multiple motors are propagated along this fiber network, driving numerous processes such as mitosis and cell motility (1) and allowing the cell as a whole to exert stresses on its surroundings. At the larger scale of connective tissue, many such stress-exerting cells act on another type of fiber network known as the extracellular matrix (Fig. 1B). This network propagates cellular forces to the scale of the whole tissue, powering processes such as wound healing and morphogenesis. Despite important differences in molecular details and length scales, a common physical principle thus governs stress generation in biological matter: Internal forces from multiple localized “active units”—motors or cells—are propagated by a fiber network to generate large-scale stresses. However, a theoretical framework relating microscopic internal active forces to macroscopic stresses in these networks is lacking. Here we propose such a theory for elastic networks.Open in a separate windowFig. 1.Biological fiber networks (green) transmit forces generated by localized active units (red). (A) Myosin molecular motors exert forces on the actin cytoskeleton. (B) Contractile cells exert forces on the extracellular matrix. (C) The large nonlinear deformations induced by a model active unit in the surrounding fiber network result in stress amplification, as shown in this paper. Fiber color code is shown in D. (D) Each bond in the network comprises two rigid segments hinged together to allow buckling.This generic stress generation problem is confounded by the interplay of network disorder and nonlinear elasticity. Active units generate forces at the scale of the network mesh size, and force transmission to larger scales thus sensitively depends on local network heterogeneities. In the special case of linear elastic networks, the macroscopic active stress is simply given by the density of active force dipoles, irrespective of network characteristics (2). Importantly, however, this relationship is not applicable to most biological systems, because typical active forces are amply sufficient to probe the nonlinear properties of their constitutive fibers, which stiffen under tension and buckle under compression (3). Indeed, recent experiments on reconstituted biopolymer gels have shown that individual active units induce widespread buckling and stiffening (4, 5), and theory suggests that such fiber nonlinearities can enhance the range of force propagation (6, 7).Fiber networks also exhibit complex, nonlinear mechanical properties arising at larger scales, owing to collective deformations favored by the networks’ weak connectivity (3, 8). The role of connectivity in elasticity was famously investigated by Maxwell, who noticed that a spring network in dimension d becomes mechanically unstable for connectivities z < 2d. Interestingly, most biological fiber networks exhibit connectivities well below this threshold and therefore cannot be stabilized solely by the longitudinal stretching rigidity of their fibers. Instead, their macroscopic mechanical properties are typically controlled by the fiber bending rigidity (9). In contrast to stretching-dominated networks with connectivities above the Maxwell threshold, such weakly connected, bending-dominated networks are soft and extremely sensitive to mechanical perturbations (9–11). In these networks, stresses generated by active units propagate along intricate force chains (12, 13) whose effects on force transmission remain unexplored. Collections of such active units generate large stresses, with dramatic effects such as macroscopic network stiffening (14–16) and network remodeling (5, 17).Here we study the theoretical principles underlying stress generation by localized active units embedded in disordered fiber networks (Fig. 1C). We find that arbitrary local force distributions generically induce large isotropic, contractile stress fields at the network level, provided that the active forces are large enough to induce buckling in the network. In this case, the stress generated in a biopolymer network dramatically exceeds the stress level that would be produced in a linear elastic medium (2), implying a striking network-induced amplification of active stress. Our findings elucidate the origins and magnitude of stress amplification observed in experiments on reconstituted tissues (4, 18) and actomyosin networks (14, 17). We thus provide a conceptual framework for stress generation in biological fiber networks.     

From the Cover: Convolutional networks for fast,energy-efficient neuromorphic computing

Deep networks are now able to achieve human-level performance on a broad spectrum of recognition tasks. Independently, neuromorphic computing has now demonstrated unprecedented energy-efficiency through a new chip architecture based on spiking neurons, low precision synapses, and a scalable communication network. Here, we demonstrate that neuromorphic computing, despite its novel architectural primitives, can implement deep convolution networks that (i) approach state-of-the-art classification accuracy across eight standard datasets encompassing vision and speech, (ii) perform inference while preserving the hardware’s underlying energy-efficiency and high throughput, running on the aforementioned datasets at between 1,200 and 2,600 frames/s and using between 25 and 275 mW (effectively >6,000 frames/s per Watt), and (iii) can be specified and trained using backpropagation with the same ease-of-use as contemporary deep learning. This approach allows the algorithmic power of deep learning to be merged with the efficiency of neuromorphic processors, bringing the promise of embedded, intelligent, brain-inspired computing one step closer.The human brain is capable of remarkable acts of perception while consuming very little energy. The dream of brain-inspired computing is to build machines that do the same, requiring high-accuracy algorithms and efficient hardware to run those algorithms. On the algorithm front, building on classic work on backpropagation (1), the neocognitron (2), and convolutional networks (3), deep learning has made great strides in achieving human-level performance on a wide range of recognition tasks (4). On the hardware front, building on foundational work on silicon neural systems (5), neuromorphic computing, using novel architectural primitives, has recently demonstrated hardware capable of running 1 million neurons and 256 million synapses for extremely low power (just 70 mW at real-time operation) (6). Bringing these approaches together holds the promise of a new generation of embedded, real-time systems, but first requires reconciling key differences in the structure and operation between contemporary algorithms and hardware. Here, we introduce and demonstrate an approach we call Eedn, energy-efficient deep neuromorphic networks, which creates convolutional networks whose connections, neurons, and weights have been adapted to run inference tasks on neuromorphic hardware.For structure, typical convolutional networks place no constraints on filter sizes, whereas neuromorphic systems can take advantage of blockwise connectivity that limits filter sizes, thereby saving energy because weights can now be stored in local on-chip memory within dedicated neural cores. Here, we present a convolutional network structure that naturally maps to the efficient connection primitives used in contemporary neuromorphic systems. We enforce this connectivity constraint by partitioning filters into multiple groups and yet maintain network integration by interspersing layers whose filter support region is able to cover incoming features from many groups by using a small topographic size (7).For operation, contemporary convolutional networks typically use high precision ( ≥ 32-bit) neurons and synapses to provide continuous derivatives and support small incremental changes to network state, both formally required for backpropagation-based gradient learning. In comparison, neuromorphic designs can use one-bit spikes to provide event-based computation and communication (consuming energy only when necessary) and can use low-precision synapses to colocate memory with computation (keeping data movement local and avoiding off-chip memory bottlenecks). Here, we demonstrate that by introducing two constraints into the learning rule—binary-valued neurons with approximate derivatives and trinary-valued ({−1,0,1}) synapses—it is possible to adapt backpropagation to create networks directly implementable using energy efficient neuromorphic dynamics. This approach draws inspiration from the spiking neurons and low-precision synapses of the brain (8) and builds on work showing that deep learning can create networks with constrained connectivity (9), low-precision synapses (10, 11), low-precision neurons (12–14), or both low-precision synapses and neurons (15, 16). For input data, we use a first layer to transform multivalued, multichannel input into binary channels using convolution filters that are learned via backpropagation (12, 16) and whose output can be sent on chip in the form of spikes. These binary channels, intuitively akin to independent components (17) learned with supervision, provide a parallel distributed representation to carry out high-fidelity computation without the need for high-precision representation.Critically, we demonstrate that bringing the above innovations together allows us to create networks that approach state-of-the-art accuracy performing inference on eight standard datasets, running on a neuromorphic chip at between 1,200 and 2,600 frames/s (FPS), using between 25 and 275 mW. We further explore how our approach scales by simulating multichip configurations. Ease-of-use is achieved using training tools built from existing, optimized deep learning frameworks (18), with learned parameters mapped to hardware using a high-level deployment language (19). Although we choose the IBM TrueNorth chip (6) for our example deployment platform, the essence of our constructions can apply to other emerging neuromorphic approaches (20–23) and may lead to new architectures that incorporate deep learning and efficient hardware primitives from the ground up.     

From the Cover: Fine-tuning gene networks using simple sequence repeats

The parameters in a complex synthetic gene network must be extensively tuned before the network functions as designed. Here, we introduce a simple and general approach to rapidly tune gene networks in Escherichia coli using hypermutable simple sequence repeats embedded in the spacer region of the ribosome binding site. By varying repeat length, we generated expression libraries that incrementally and predictably sample gene expression levels over a 1,000-fold range. We demonstrate the utility of the approach by creating a bistable switch library that programmatically samples the expression space to balance the two states of the switch, and we illustrate the need for tuning by showing that the switch’s behavior is sensitive to host context. Further, we show that mutation rates of the repeats are controllable in vivo for stability or for targeted mutagenesis—suggesting a new approach to optimizing gene networks via directed evolution. This tuning methodology should accelerate the process of engineering functionally complex gene networks.     

From the Cover: Anatomy of funded research in science

Seeking research funding is an essential part of academic life. Funded projects are primarily collaborative in nature through internal and external partnerships, but what role does funding play in the formulation of these partnerships? Here, by examining over 43,000 scientific projects funded over the past three decades by one of the major government research agencies in the world, we characterize how the funding landscape has changed and its impacts on the underlying collaboration networks across different scales. We observed rising inequality in the distribution of funding and that its effect was most noticeable at the institutional level—the leading universities diversified their collaborations and increasingly became the knowledge brokers in the collaboration network. Furthermore, it emerged that these leading universities formed a rich club (i.e., a cohesive core through their close ties) and this reliance among them seemed to be a determining factor for their research success, with the elites in the core overattracting resources but also rewarding in terms of both research breadth and depth. Our results reveal how collaboration networks organize in response to external driving forces, which can have major ramifications on future research strategy and government policy.Higher education institutions are nationally assessed in a periodic manner across the globe [examples include the Research Excellence Framework (www.ref.ac.uk) in the United Kingdom, Excellenzinitiative (mediathek.dfg.de/thema/die-exzellenzinitiative/) in Germany, and Star Metrics (https://www.starmetrics.nih.gov/) in the United States], and tremendous effort has been put in place in maximizing research output, because assessment outcomes often have a direct financial impact on an institution’s revenue (1). Bibliometrics are commonly used for this kind of performance evaluations (2–7), and the volume of grant income is also generally seen as a good indicator of performance. Although many studies have examined the collaboration patterns originating from publication information (8–14), little is known about the characteristics of project collaborations supported by research funding, which is undoubtedly a type of research output in its own right, but also the origin of other research outputs.The volume of funding is often subject to direct and indirect constraints arising from internal research strategies and different levels of policy set out by the funding bodies and ultimately by the national government. This manifests into different emphases on both the research area and mode of collaboration, and potentially influences the way we form a project team. We have already seen examples of adaptive changes in our collaboration practices. For instance, research in the science and engineering sector is said to be increasingly interorganizational (15). In addition, there are different theories on the factors that may affect the establishment of a collaboration and how well a research team operates (13, 16). Elite universities were recognized as catalysts for facilitating large-scale multipartner research collaborations (15), and multidisciplinary collaborations were found to have higher potential to foster research outcomes (17). As a result, the setup of a project consortium for a grant application might require considerable strategic planning, because who and how we collaborate with can potentially affect the outcome of a bid, and we are yet to fully understand the underlying mechanics and dynamics.To shed light into the relations between funding landscapes and scientific collaborations, we here examine over 43,000 projects funded between 1985 and 2013 by the Engineering and Physical Sciences Research Council (EPSRC), the government body in the United Kingdom that provides funding to universities to undertake research in engineering and physical sciences, including mathematics, chemistry, materials science, energy, information and communications technology, and innovative manufacturing. For each year, we constructed two different types of collaboration networks in which the nodes are investigators and their affiliations, respectively, and an edge represents a funded project partnership between two nodes. We applied a network-based approach to analyze the local and global interlinkage in these networks; the former was performed by calculating the degree of brokerage (18–21) of individual nodes, which gauges the connectivity in the neighborhood of a node. As for the global level, we calculated the rich-club coefficient (22, 23) of the network and characterized the members of such core structure using a recently introduced profiling technique (24). In addition, we explored how these patterns evolved over time with the total funding in each year and how they correlated with research performance. Our results allow us to gain an insight into how changes in the funding landscape shaped the way we form research partnerships, providing a case study that is highly reflective of other countries in the European Union and possibly other developed countries worldwide.     

From the Cover: Global view of the protein universe

To explore protein space from a global perspective, we consider 9,710 SCOP (Structural Classification of Proteins) domains with up to 70% sequence identity and present all similarities among them as networks: In the “domain network,” nodes represent domains, and edges connect domains that share “motifs,” i.e., significantly sized segments of similar sequence and structure. We explore the dependence of the network on the thresholds that define the evolutionary relatedness of the domains. At excessively strict thresholds the network falls apart completely; for very lax thresholds, there are network paths between virtually all domains. Interestingly, at intermediate thresholds the network constitutes two regions that can be described as “continuous” versus “discrete.” The continuous region comprises a large connected component, dominated by domains with alternating alpha and beta elements, and the discrete region includes the rest of the domains in isolated islands, each generally corresponding to a fold. We also construct the “motif network,” in which nodes represent recurring motifs, and edges connect motifs that appear in the same domain. This network also features a large and highly connected component of motifs that originate from domains with alternating alpha/beta elements (and some all-alpha domains), and smaller isolated islands. Indeed, the motif network suggests that nature reuses such motifs extensively. The networks suggest evolutionary paths between domains and give hints about protein evolution and the underlying biophysics. They provide natural means of organizing protein space, and could be useful for the development of strategies for protein search and design.How are proteins related to each other? Which physicochemical considerations affect protein evolution and how? A global view of the protein universe may shed light on these fundamental questions. It could also suggest new strategies for protein search and design (1–3). However, forming a global picture of the protein universe is difficult because we have to piece it together from the many local glimpses that our empirical data and computational tools provide. In other words, a global picture needs to portray the relationships among all proteins, yet we only have evidence of such relationships among several proteins, based on the similarity between their sequences, structures, and functions. The considerable size of the Protein Data Bank (4) also complicates this task.In particular, an intensely debated question is whether protein space is “discrete” or “continuous” (2, 3, 5–10). These terms are loosely defined. Discrete implies that the global picture consists of separate, island-like, structural entities. In the hierarchical protein domains Structural Classification of Proteins (SCOP) (11) these entities are termed “folds,” and in the CATH database (12) they are called “topologies.” Alternatively, “continuous” implies that the space between these entities is generally populated by cross-fold similarities (e.g., refs. 2, 5, 6, 9, 13–15). If such similarities are abundant, then one must account for them when organizing and searching proteins (5, 8, 16). In support of the abundance of such similarities is the remarkable success of structure prediction methods that piece together predictions of protein fragments or larger protein segments (e.g., ref. 17).There are different approaches to forming a global view of the protein universe (18). The most significant efforts are the ones embodied in the hierarchical classifications CATH and SCOP. However, a hierarchy implicitly assumes that there are isolated regions in protein space. An alternative approach is to study the protein universe via maps––where domains are represented by points in two or three dimensions, placed so that the distances between them depend on the dissimilarity between their corresponding domains (e.g., refs. 19–21). By coloring the points according to domain characteristics, one can visually identify global properties of the protein universe (19, 20). However, a map representation in low-dimensional Euclidean space implicitly suggests that similarity among domains is transitive (i.e., that similarity within the pairs AB and BC implies that AC is similar too); we know that this is often not the case (6). Finally, a third approach to study protein space is via similarity and cooccurrence networks. In similarity networks, nodes typically represent protein domains and edges connect similar domains. Several successful studies of protein space capitalize on such networks (22, 23). Cooccurrence networks of protein domains, in which nodes represent domains and edges connect cooccurring domains, were also studied to better understand protein evolution (24–26).Here, we study the global nature of the protein universe using domain and motif networks (Fig. 1). To construct these networks, we identify evolutionary relationships among a representative set of SCOP domains; we relate two domains if they share a significantly sized part (denoted motif) with similar structure and sequence. Our analysis reveals that protein space is both discrete and continuous: SCOP domains of the all-alpha, all-beta, and alpha + beta classes, in which alpha and beta elements do not mix, mostly populate the discrete parts, whereas alpha/beta domains, with alternating alpha and beta segments, mostly populate the continuous ones. We also find that recurring motifs are very abundant; the motifs from the all-alpha and alpha/beta domains are the more abundant, and the more gregarious ones.Open in a separate windowFig. 1.Constructing the domain and motif networks. (A) The aligned protein segments, marked in colors, are the motifs. (B) In the domain network, edges connect domains that share similar motifs (e.g., domain d1wjga_ and d1vlua_ that share the cyan motif). (C) In the motif network, edges connect cooccurring motifs (e.g., the orange and cyan motifs cooccur in the d1vlua_ domain).     

From the Cover: Predicting Social Security numbers from public data

Information about an individual''s place and date of birth can be exploited to predict his or her Social Security number (SSN). Using only publicly available information, we observed a correlation between individuals'' SSNs and their birth data and found that for younger cohorts the correlation allows statistical inference of private SSNs. The inferences are made possible by the public availability of the Social Security Administration''s Death Master File and the widespread accessibility of personal information from multiple sources, such as data brokers or profiles on social networking sites. Our results highlight the unexpected privacy consequences of the complex interactions among multiple data sources in modern information economies and quantify privacy risks associated with information revelation in public forums.     

From the Cover: Model of genetic variation in human social networks

Social networks exhibit strikingly systematic patterns across a wide range of human contexts. Although genetic variation accounts for a significant portion of the variation in many complex social behaviors, the heritability of egocentric social network attributes is unknown. Here, we show that 3 of these attributes (in-degree, transitivity, and centrality) are heritable. We then develop a “mirror network” method to test extant network models and show that none account for observed genetic variation in human social networks. We propose an alternative “Attract and Introduce” model with two simple forms of heterogeneity that generates significant heritability and other important network features. We show that the model is well suited to real social networks in humans. These results suggest that natural selection may have played a role in the evolution of social networks. They also suggest that modeling intrinsic variation in network attributes may be important for understanding the way genes affect human behaviors and the way these behaviors spread from person to person.     

From the Cover: Species interactions and the structure of complex communication networks

A universal challenge faced by animal species is the need to communicate effectively against a backdrop of heterospecific signals. It is often assumed that this need results in signal divergence to minimize interference among community members, yet previous support for this idea is mixed, and few studies have tested the opposing hypothesis that interactions among competing species promote widespread convergence in signaling regimes. Using a null model approach to analyze acoustic signaling in 307 species of Amazonian birds, we show that closely related lineages signal together in time and space and that acoustic signals given in temporal or spatial proximity are more similar in design than expected by chance. These results challenge the view that multispecies choruses are structured by temporal, spatial, or acoustic partitioning and instead suggest that social communication between competing species can fundamentally organize signaling assemblages, leading to the opposite pattern of clustering in signals and signaling behavior.One of the core principles of animal communication is that signals should be detectable and convey an accurate message against a noisy background (1–3). This background can involve direct overlap of sounds, as in the case of masking by simultaneous signals (4, 5), or simply the co-occurrence of different species using confusingly similar signals at the same location (6–8). As most animals communicate within assemblages of related species, the problem of signal interference is widespread and may have far-reaching implications for the evolution of signals and signaling behavior. This concept—variously termed the “noisy neighbors” hypothesis (9) or “cocktail party problem” (10)—has attracted much attention over recent years. However, the extent to which it provides a general explanation for patterns of signaling in animal communities remains contentious (6, 8).The traditional view is that the signaling strategies of animals are shaped by limiting similarity among competitors, much as competition for ecological resources is thought to promote partitioning of niche space (11–13). Partitioning of signal space may occur if species compete for position near overcrowded transmission optima, and, concurrently, if overlap in signal design impairs the detection or discrimination of signals mediating mate choice and resource competition (14). Under these conditions, mechanisms of selection against misdirected aggression (e.g., character displacement) or the production of unfit hybrids (e.g., reinforcement) are predicted to drive phenotypic divergence (9), whereas similar mechanisms may lead to related species signaling at different times or in different locations (13). These pathways theoretically lead to structural, temporal, and spatial partitioning of signals and signalers in animal assemblages, but tests of these patterns have produced mixed results (6, 11, 15).A contrasting possibility is that selection for signal divergence is weak and that co-occurring species instead show the opposite pattern of signal clustering (16). One potential driver of this pattern is that shared habitats can exert convergent selection on signals (17). Another is that signals often have dual function in mate attraction and resource defense (18), potentially mediating competition among closely related species for ecological resources (19). Thus, multispecies choruses may operate to some degree as extended communication networks, not only within species (20) but between species. The effect of such a network would be to increase the likelihood of interspecific communication involving closely related species with similar signals. A pattern of signal clustering caused by communication among similar congeners may be further exaggerated when competitive interactions among species promote signal similarity (16). This process may occur when individuals with convergent agonistic signals have higher fitness because they are better at defending resources against both conspecific and heterospecific competitors, driving convergent evolution (21, 22). Taken together, these alternative views suggest that the most pervasive effect of species interactions on animal communication systems may not be partitioning, as generally proposed, but synchrony and stereotypy among competing species.Progress in resolving these opposing viewpoints has been limited because most studies of signaling assemblages have compiled lists of species co-occurring at particular localities and then compared multiple assemblages across regional scales (6, 15). This approach may be misleading because of spatial biases in phylogenetic relationships and habitat. On the one hand, sympatric species tend to be significantly older than allopatric species, at least within radiations (23, 24), and thus the signals of co-occurring lineages may be more divergent than expected by chance simply because they have had more time to diverge, exaggerating the evidence for partitioning. Conversely, species co-occurring at local scales may be less divergent because they are segregated by habitat across a study site and therefore are unlikely to signal together. Although some studies (7, 11) partially overcome these issues by sampling assemblages from single points in space, none has considered the effects of habitat and the potential role of competitive interactions among related species (16). Moreover, previous studies have generally assessed partitioning in relatively small assemblages (<30 species), reducing both the likelihood of competition over transmission optima and the power of statistical tests.Here, we sample >90 signaling assemblages (Fig. S1) containing a combined total of >300 species (Dataset S1) to assess the role of species interactions in structuring and organizing the dawn chorus of Amazonian rainforest birds. Each assemblage comprised species producing acoustic signals, identified from standardized 120-min sound recordings taken at points distributed across a single study locality. We also restricted analyses to 10-min time blocks and assumed that assemblages of species signaling in these blocks were forced to discriminate among each other (i.e., they were each other’s background noise) and also that they had an increased likelihood of signaling simultaneously (i.e., directly masking each other’s signals). We use the term cosignaling to describe pairs of species signaling during the same 10- or 120-min time block and thus not necessarily signaling simultaneously. We coded all assemblages for habitat and time of day, calculated the acoustic similarity of cosignaling species using spectrographic analyses of voice recordings, and estimated the evolutionary relatedness of cosignaling species using a hierarchical taxonomic framework.Our null hypothesis states that species interactions have no effect on chorus structure and thus that species with similar signals are randomly distributed in space and time (Fig. 1A). The distance between signals in observed choruses should not differ significantly from that expected by chance, accounting for habitat and evolutionary relationships. We envisage two scenarios that may falsify the null. The partitioning hypothesis predicts that signal design is evenly spaced across communities, with a larger distance between co-occurring signals than predicted by chance (Fig. 1B). The network hypothesis predicts that competing species interact using phylogenetically conserved signals and thus that signals are clustered in distribution, with a smaller distance between co-occurring signals than predicted by chance (Fig. 1C). The partitioning and network hypotheses involve different forms of species interaction with opposing effects on chorus structure. Although we do not measure species interactions directly, we follow standard approaches in assuming that such interactions predict patterns in the trait structure of assemblages (25).Open in a separate windowFig. 1.Predictions of three hypotheses proposed to structure multispecies choruses, illustrated using hypothetical seven-species choruses with signal design plotted in multivariate signaling space. The null hypothesis that species interactions have no effect predicts that signal structure is random (A), generating an intermediate mean nearest-neighbor distance d. The partitioning hypothesis predicts an evenly spaced signal structure (B) reflected in larger values for d. The network hypothesis predicts that related species will signal together, causing signals to be clustered around optima (C), and generating small values for d. We test these predictions by assessing whether d, viewed across a sample of communities, is higher or lower than expected by chance. We calculated d in two ways: d₁ (Upper) is the mean nearest neighbor distance [nnd] across all community members; and d₂ (Lower) is the mean nnd across the three pairs of species with most similar signals.Our aims were to (i) quantify acoustic properties of signals transmitted in the dawn chorus; (ii) estimate the degree of signal similarity among cosignaling species; and (iii) compare the observed distribution of signal properties with that expected by chance. We also consider spatial explanations for chorus structure, including the reduced cosignaling of species with similar signals through spatial partitioning. This form of segregation may occur because ecological competition is elevated in tropical bird communities (26), causing parapatric (27) or “checkerboard” distributions (28) among closely related species, thus potentially leading to apparent signal partitioning by competitive exclusion. The network hypothesis predicts the opposite pattern as closely related species should synchronize their signaling activity using shared territorial signals. We test these predictions by comparing 120-min (spatially segregated) and 10-min (nonsegregated) choruses and using taxonomic relatedness to estimate the degree of cosignaling between close relatives.The Amazonian dawn chorus provides one of the world’s most diverse multispecies signaling assemblages and an ideal system for exploring the effects of competition on signaling strategies for three reasons. First, visibility is hampered by dense vegetation, and thus long-distance signaling is forced into one modality (acoustic communication). Second, background noise levels are extremely high as a result of other organisms, including insects, amphibians, and primates, suggesting that selection for partitioning of acoustic signals should be maximized (12). Finally, many tropical species are permanently resident and apparently interspecifically territorial, using acoustic signals to mediate competitive interactions with heterospecifics (18, 26, 29). In combination, these factors imply that large numbers of species compete both for ecological resources and a narrow window of optimal signaling space (7, 30), providing a context in which to test the relative importance of acoustic partitioning and interspecific communication networks.     

From the Cover: Quantifying the benefits of vehicle pooling with shareability networks

Taxi services are a vital part of urban transportation, and a considerable contributor to traffic congestion and air pollution causing substantial adverse effects on human health. Sharing taxi trips is a possible way of reducing the negative impact of taxi services on cities, but this comes at the expense of passenger discomfort quantifiable in terms of a longer travel time. Due to computational challenges, taxi sharing has traditionally been approached on small scales, such as within airport perimeters, or with dynamical ad hoc heuristics. However, a mathematical framework for the systematic understanding of the tradeoff between collective benefits of sharing and individual passenger discomfort is lacking. Here we introduce the notion of shareability network, which allows us to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets. We apply this framework to a dataset of millions of taxi trips taken in New York City, showing that with increasing but still relatively low passenger discomfort, cumulative trip length can be cut by 40% or more. This benefit comes with reductions in service cost, emissions, and with split fares, hinting toward a wide passenger acceptance of such a shared service. Simulation of a realistic online system demonstrates the feasibility of a shareable taxi service in New York City. Shareability as a function of trip density saturates fast, suggesting effectiveness of the taxi sharing system also in cities with much sparser taxi fleets or when willingness to share is low.Vehicular traffic congestion––and the air pollution that results from it––is one of the greatest challenges facing cities all over the world. It comes at great monetary and human cost: in the 83 largest urban areas of the United States alone, the amount of wasted time and fuel caused by congestion has been placed at US$ 60 billion (1). At the same time, the World Health Organization has estimated that over one million deaths per year worldwide can be attributed to outdoor air pollution (2), which is to a large part caused by vehicular traffic (3). Further adverse effects include fatalities through road accidents and economic losses from missed business activities. For these reasons, great hope is placed today in the rapid deployment of digital information and communication technologies that could help make cities “smarter” (4), and, in particular, that could help manage vehicular traffic more efficiently. The use of real-time information allows the monitoring of the urban mobility infrastructure to an unprecedented extent, and opens up new potential for the exploitation of unused capacity. One major example is the public mobility infrastructure: taking advantage of the widespread use of smart phones and their capabilities for running real-time applications, it is possible to design new, smarter transportation systems based on the sharing of cars or minivans, effectively providing services that could replace public transportation with the on-demand qualities of individual mobility or taxis (5). However, although this option has been proposed in the past, municipal authorities, city residents, and other stakeholders may be reluctant to invest in it until its benefits have been quantified (6). This is the goal of the present paper.At the basis of a shared taxi service is the concept of ride sharing or carpooling, a long-standing proposition for decreasing road traffic, which originated during the oil crisis in the 1970s (6). During that time, economic incentives outbalanced the psychological barriers on which successful carpooling programs depend: giving up personalized transportation and accepting strangers in the same vehicle. Surveys indicate that the two most important deterrents to potential carpoolers are the extra time requirements and the loss of privacy (7, 8). However, the lack of correlations between socio-demographic variables and carpooling propensity (8), the design of appropriate economic incentives (9), and recent practical implementations of taxi-sharing systems in New York City (http://bandwagon.io) give ample hope that many social obstacles might be overcome in newly emerging “sharing economies” (10, 11).Besides psychological considerations, it is fundamental to understand the logistic limitations of realistic taxi-sharing systems, which is our focus here. From a theoretical perspective, trip sharing is traditionally seen as an instance of “dynamic pickup and delivery” problems (12, 13), in which a number of goods or customers must be picked up and delivered efficiently at specific locations within well-defined time windows. Such problems are typically solved by means of linear programming, in which a function of the system variables is optimized subject to a set of equations that describe the constraints. Whereas linear programming tasks can be solved with standard approaches of Operations Research or with constraint programming (14), their computational feasibility heavily depends on the number of variables and equations, e.g., the pickup and delivery time windows of each customer, used to describe the problem at hand. Most previous taxi studies have therefore focused on small-scale routing problems, such as within airport perimeters (15, 16). Large urban taxi systems, in contrast, involve thousands of vehicles performing hundreds of thousands of trips per day. A first step toward practical taxi ride-sharing systems is ref. 17, where the authors present the design of a dynamic ride-sharing system inclusive of a taxi dispatching strategy and fare management. Due to computational reasons trip sharing in ref. 17 is decided based on a heuristic approach tailored to the specific taxi dispatching strategy at hand. Our approach, by contrast, is the development of a framework which enables investigation in general terms the fundamental tradeoff between the benefit and the passenger discomfort induced by taxi-sharing systems at the city level, as an example from a wide class of spatial sharing problems.Here we introduce the notion of shareability network to model trip sharing in a simple static way, and apply classical methods from graph theory to solve the taxi trip-sharing problem in a provably efficient way. The differences between static trip sharing as considered herein, and dynamic sharing as considered, e.g., in ref. 17, are discussed in detail in SI Appendix. The starting point of our analysis is a dataset composed of the records of over 150 million taxi trips originating and ending in Manhattan in the year 2011 by all 13,586 registered taxis. For each trip, the record reports the vehicle ID, the Global Positioning System (GPS) coordinates of the pickup and drop-off locations, and corresponding times. Pickup and drop-off locations have been associated with the closest street intersection in the road map of Manhattan (Materials and Methods). We impose a natural network structure on an otherwise unstructured, gigantic search space of the type explored in traditional linear programming. To this end we define two parameters: the shareability parameter k, standing for the maximum number of trips that can be shared, and the quality of service parameter Δ, which stands for the maximum delay a customer tolerates in a shared taxi service trip, mathematically equivalent to the notion of “time window” used in other approaches (13, 17). To ease the analysis, we use the Δ formalism; however, when presented in a real implementation to passengers, it might be psychologically more effective to use the neutral wording “time window” rather than explicitly mentioning the maybe more negatively connoted word “delay.” The choice of defining the quality of service parameter as an absolute time, instead of as a percentage increase of the travel time, is in line with similar realizations in the literature (17), and is motivated by the fact that absolute delay information is likely more valuable than percent estimation of travel time increase for potential customers of a shared taxi service. Further, let Ti=(oi,di,tio,tid),i=1…k be k trips where o_i denotes the origin of the trip, d_i the destination, and tio,tid the starting and ending times, respectively. We say that multiple trips T_i are shareable if there exists a route connecting all of the o_i and d_i in any order where each o_i precedes the corresponding d_i, except for configurations where single trips are concatenated and not overlapped like o₁ → d₁ → o₂ → d₂, such that each customer is picked up and dropped off at the respective origin and destination locations with delay at most Δ, with the delay computed as the time difference to the respective single, individual trip. Imposing a bound of k on shareability implies that the k trips can be combined using a taxi of corresponding capacity (Fig. 1G). Deciding whether two or more trips can be shared necessitates knowledge of the travel time between arbitrary intersections in Manhattan, which we estimated using an ad hoc heuristic (SI Appendix, Fig. S2 and Table S1).Open in a separate windowFig. 1.Shareability networks translate spatiotemporal sharing problems into a graph-theoretic framework that provides efficient solutions. (A) Example of seven trips, T₁,…, T₇, requested and to be shared in Manhattan, New York City. (B) Construction of shareability network for k = 2. Trips that could potentially be shared are connected, given the necessary time constraints to hold which we assume here to be the case. Trips 1 and 4 cannot be shared because the total length of the best shared route would be longer than the sum of the single routes. Likewise, trip 7 is an isolated node because it cannot possibly be shared with other trips. (C) Maximum matching of the shareability network gives the maximum number of trip pairs, i.e., the maximum number of shared trips. (D) Implementation (routing) of the maximum matching solution. (E) Alternatively, maximum weighted matching of the shareability network gives the solution with the minimal total travel time, which in this case leads to a different solution than unweighted maximum matching. Here only two pairs of trips are shared, but the amount of travel time saved, given by the sum of link weights of the matching, 30 + 16, is optimal. (F) Implementation (routing) of the weighted maximum matching solution. (G) k sharing and taxi capacity. Each of the three cases involves a number of trips T_i to be shared, but ordered differently in time t. (Top) This case corresponds to a feasible sharing according to our model with k = 2, and the trips can be accommodated in a taxi with capacity ≥2. (Middle) This case corresponds to a model with k = 3 because three trips are combined, but the three trips can be combined in a taxi with capacity = 2 because two of the trips are nonoverlapping. (Bottom) This case corresponds to k = 3, but here a taxi capacity ≥3 is needed to accommodate the combined trips. Here we are assuming one passenger per trip, in line with the data reported in ref. 18, according to which the average number of passengers per trip is 1.3.For the case k = 2, the shareability network associated with a set ?? of trips is obtained by assigning a node T for each trip in ??, and by placing a link between two nodes T_i and T_j if the two trips can be shared for the given value of Δ (Fig. 1 A and B). The value of Δ has a profound impact on topological properties of the resulting shareability network. Increasing Δ capitalizes on well-known effects of time-aggregated networks such as densification (19, 20), capturing the intuitive notion that the more patient the customers, the more opportunities for trip sharing arise (Fig. 2 A and B). For values of k > 2, the shareability network has a hypergraph structure in which up to k nodes can be connected by a link simultaneously. Because of computational reasons, the shareability parameter k has a substantial impact on the feasibility of solving the problem. A solution is tractable for k = 2, heuristically feasible for k = 3, whereas it becomes computationally intractable for k ≥ 4 (SI Appendix). This constraint implies that taxi-sharing services, and social-sharing applications in general, will likely be able to combine only a limited number of trips. However, as we show below, even the minimum possible number of trip combinations (k = 2) can provide immense benefits to a dense enough community like the city of New York.Open in a separate windowFig. 2.Shareability networks densify with longer time aggregation, increasing sharing opportunities. This exemplary subset of the shareability network corresponds to 100 consecutive trips for values of (A) Δ = 30 s and (B) Δ = 60 s. Open links point to trips outside the considered set of trips. Isolated nodes are represented as self-loops. Node positions are not preserved across the networks. A similar, although visually not insightful, densification effect is observed in shareability networks obtained when k = 3.With the shareability network, classical algorithms for solving maximum matching on graphs (21, 22) can be used to determine the best trip-sharing strategy according to two optimization criteria: (i) maximizing the number of shared trips, or (ii) minimizing the cumulative time needed to accommodate all trips. To find the best solution according to (i) or (ii), it is sufficient to compute a maximum matching or a weighted maximum matching on the shareability network, respectively (Fig. 1 C and E, Materials and Methods). Because a shared trip can be served by a single taxi instead of two, the number of shared trips can be used as a proxy for the reduction in number of circulating taxis. For instance, an 80% rate of shared trips translates into a 40% reduction of the taxi fleet. Other important objectives such as total system cost and emissions are reasonably approximated by criterion (ii).     

From the Cover: A Bayesian model predicts the response of axons to molecular gradients

Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. We first develop a Bayesian “ideal observer” analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model, we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. These experiments demonstrate a degree of sensitivity much higher than previously reported for any chemotacting system. Together, these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be used by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.     

From the Cover: COVID-19 lockdown induces disease-mitigating structural changes in mobility networks

In the wake of the COVID-19 pandemic many countries implemented containment measures to reduce disease transmission. Studies using digital data sources show that the mobility of individuals was effectively reduced in multiple countries. However, it remains unclear whether these reductions caused deeper structural changes in mobility networks and how such changes may affect dynamic processes on the network. Here we use movement data of mobile phone users to show that mobility in Germany has not only been reduced considerably: Lockdown measures caused substantial and long-lasting structural changes in the mobility network. We find that long-distance travel was reduced disproportionately strongly. The trimming of long-range network connectivity leads to a more local, clustered network and a moderation of the “small-world” effect. We demonstrate that these structural changes have a considerable effect on epidemic spreading processes by “flattening” the epidemic curve and delaying the spread to geographically distant regions.

During the first phase of the coronavirus disease 2019 (COVID-19) pandemic, countries around the world implemented a host of containment policies aimed at mitigating the spread of the disease (1–4). Many policies restricted human mobility, intending to reduce close-proximity contacts, the major driver of the disease’s spread (5). In Germany, these policies included border closures, travel bans, and restrictions of public activity (school and business closures), paired with appeals by the government to avoid trips voluntarily whenever possible (6). We refer to these policies as “lockdown” measures for brevity.Based on various digital data sources such as mobile phone data or social media data, several studies show that mobility significantly changed during lockdowns (7). Most studies focused on general mobility trends and confirmed an overall reduction in mobility in various countries (8–12). Other research focused on the relation between mobility and disease transmission: For instance, it has been argued that mobility reduction is likely instrumental in reducing the effective reproduction number in many countries (13–17), in agreement with theoretical models and simulations, which have shown that containment can effectively slow down disease transmission (18–20).However, it remains an open question whether the mobility restrictions promoted deeper structural changes in mobility networks and how these changes impact epidemic spreading mediated by these networks. Recently, Galeazzi et al. (21) found increased geographical fragmentation of the mobility network. A thorough understanding of how structural mobility network changes impact epidemic spreading is needed to correctly assess the consequences of mobility restrictions not only for the current COVID-19 pandemic, but also for similar scenarios in the future.Here, we analyze structural changes in mobility patterns in Germany during the COVID-19 pandemic. We analyze movements recorded from mobile phones of 43.6 million individuals in Germany. Beyond a general reduction in mobility, we find considerable structural changes in the mobility network. Due to the reduction of long-distance travel, the network becomes more local and lattice-like. Most importantly, we find a changed scaling relation between path lengths and geographic distance: During lockdown, the effective distance (and arrival time in spreading processes) to a destination continually grows with geographic distance. This shows a marked reduction of the “small-world” characteristic, where geographic distance is usually of lesser importance in determining path lengths (22, 23). Using simulations of a commuter-based susceptible-infected-removed (SIR) model, we demonstrate that these changes have considerable practical implications as they suppress (or “flatten”) the curve of an epidemic remarkably and delay the disease’s arrival between distant regions.