On randomly changing conformity bias in cultural transmission

Humans and nonhuman animals display conformist as well as anticonformist biases in cultural transmission. Whereas many previous mathematical models have incorporated constant conformity coefficients, empirical research suggests that the extent of (anti)conformity in populations can change over time. We incorporate stochastic time-varying conformity coefficients into a widely used conformity model, which assumes a fixed number n of “role models” sampled by each individual. We also allow the number of role models to vary over time (nt). Under anticonformity, nonconvergence can occur in deterministic and stochastic models with different parameter values. Even if strong anticonformity may occur, if conformity or random copying (i.e., neither conformity nor anticonformity) is expected, there is convergence to one of the three equilibria seen in previous deterministic models of conformity. Moreover, this result is robust to stochastic variation in nt. However, dynamic properties of these equilibria may be different from those in deterministic models. For example, with random conformity coefficients, all equilibria can be stochastically locally stable simultaneously. Finally, we study the effect of randomly changing weak selection. Allowing the level of conformity, the number of role models, and selection to vary stochastically may produce a more realistic representation of the wide range of group-level properties that can emerge under (anti)conformist biases. This promises to make interpretation of the effect of conformity on differences between populations, for example those connected by migration, rather difficult. Future research incorporating finite population sizes and migration would contribute added realism to these models.

Cavalli-Sforza and Feldman (1) studied the finite population dynamics of a trait whose transmission from one generation to the next depended on the mean value of that trait in the population. This “group transmission” constrained the within-group variability but could lead to increasing variance in the average trait value between groups. Other analyses of cultural transmission biases have incorporated characteristics of trait variation, such as the quality, and characteristics of transmitters, including success and prestige (2). Another class of transmission biases is couched in terms of the frequencies of the cultural variants in the population (3). These “frequency-dependent” biases include conformity and anticonformity, which occur when a more common variant is adopted at a rate greater or less than its population frequency, respectively (4).Humans have exhibited conformity in mental rotation (5), line discrimination (6), and numerical discrimination tasks (7). Anticonformity has been exhibited by young children performing numerical discrimination (7). Unbiased frequency-dependent transmission, known as random copying (8), has been suggested to account for choices of dog breeds (9), Neolithic pottery motifs, patent citations, and baby names (10, 11). However, baby name distributions appear more consistent with frequency-dependent (8, 12) and/or other (13, 14) biases.In nonhuman animals, conformity has been observed in nine-spined sticklebacks choosing a feeder (15) and great tits solving a puzzle box (16, 17) (but see ref. 18). Fruit flies displayed both conformist and anticonformist bias with respect to mate choice (19) (but these authors used a different definition of anticonformity from that of ref. 4, which we use, and therefore did not consider these behaviors to be anticonformist).Asch (20, 21) used a different definition of conformity from ref. 4, namely “the overriding of personal knowledge or behavioral dispositions by countervailing options observed in others” (ref. 22, p. 34). Aschian conformity (22) has been observed in chimpanzees (23, 24), capuchin monkeys (25, 26) (but see ref. 27), vervet monkeys (28), and great tits (16). It has also been empirically tested in at least 133 studies of humans and, in the United States, has declined from the 1950s to the 1990s (29).Temporal variation may also occur in forms of conformity other than Aschian. In ref. 12, popular US baby names from 1960 to 2010 show a concave turnover function indicative of negative frequency-dependent bias, but male baby names from earlier decades (1880 to 1930) show a convex turnover indicative of positive frequency-dependent or direct bias. However, most previous mathematical models of conformity have incorporated constant, rather than time-dependent, conformity coefficients.Cavalli-Sforza and Feldman (ref. 3, chap. 3) and Boyd and Richerson (ref. 4, chap. 7) studied models of frequency-dependent transmission of a cultural trait with two variants. Boyd and Richerson (4) incorporated conformist and anticonformist bias through a conformity coefficient denoted by D. In their simplest model, if the frequency of variant A is p and that of variant B is 1−p, then the frequency of variant A in the offspring generation, p′, isp′=p+Dp(1−p)(2p−1),[1]where D>0 entails conformity (A increases if its frequency is p>12), D<0 entails anticonformity, D=0 entails random copying, and −2<D<1. In this model, each offspring samples the cultural variants of n=3 members of the parental generation (hereafter, role models). Sampling n>3 role models requires different constraints and, if n>4, there are multiple conformity coefficients (Eq. 19).Many subsequent models have built upon Boyd and Richerson’s (4) simplest model (Eq. 1). These have incorporated individual learning, information inaccuracy due to environmental change (30–34), group selection (35), and other transmission biases, including payoff bias (36), direct bias, and prestige bias (37). Other models, which include a single conformity coefficient and preserve the essential features of Eq. 1, incorporate individual learning, environmental variability (32, 38), group selection (39), and multiple cultural variants (38).In agent-based statistical physics models, the up and down spins of an electron are analogous to cultural variants A and B (40, 41). Individuals are nodes in a network and choose among a series of actions with specified probabilities, such as independently acquiring a spin, or sampling neighboring individuals and adopting the majority or minority spin in the sample. The number of sampled role models can be greater than three (42, 43). (Anti)conformity may occur if all (42–47), or if at least r (40, 48), sampled individuals have the same variant. In contrast, Boyd and Richerson’s (4) general model (Eq. 19) allows, for example, stronger conformity to a 60% majority of role models and weaker conformity or anticonformity to a 95% majority (in humans, this might result from a perceived difference between “up-and-coming” and “overly popular” variants).In Boyd and Richerson’s (4) general model, individuals sample n role models, which is more realistic than restricting n to 3 (as in Eq. 1); individuals may be able to observe more than three members of the previous generation. With n>4, different levels of (anti)conformity may occur for different samples j of n role models with one variant. In addition to the example above with 60 and 95% majorities, other relationships between the level of conformity and the sample j of n are possible. For example, the strength of conformity might increase as the number of role models with the more common variant increases. In a recent exploration of Boyd and Richerson’s (4) general model, we found dynamics that departed significantly from those of Eq. 1 (49). If conformity and anticonformity occur for different majorities j of n role models (i.e., j>n2), polymorphic equilibria may exist that were not possible with Eq. 1. In addition, strong enough anticonformity can produce nonconvergence: With as few as 5 role models, stable cycles in variant frequencies may arise, and with as few as 10 role models, chaos is possible. Such complex dynamics may occur with or without selection.Here, we extend both Boyd and Richerson’s (4) simplest (Eq. 1) and general (Eq. 19) models to allow the conformity coefficient(s) to vary randomly across generations, by sampling them from probability distributions. Although some agent-based models allow individuals to switch between “conformist” and “non-” or “anticonformist” states over time (40, 42, 47, 50, 51), to our knowledge, random temporal variation in the conformity coefficients themselves has not been modeled previously. In reality, the degree to which groups of individuals conform may change over time, as illustrated by the finding that young children anti-conformed while older children conformed in a discrimination task (7); thus, it seems reasonable to expect that different generations may also exhibit different levels of conformity. Indeed, generational changes have occurred for Aschian conformity (29) and possibly in frequency-dependent copying of baby names (12). Our stochastic model may therefore produce more realistic population dynamics than previous deterministic models, and comparisons between the two can suggest when the latter is a reasonable approximation to the former.We also allow the number of role models, nt, to vary over time. Agent-based conformity models have incorporated temporal (43) and individual (43, 45, 46) variation in the number of sampled individuals, whereas here, all members of generation t sample the same number nt of role models. Causes of variation in nt are not explored here, but there could be several. For instance, different generations of animals may sample different numbers of role models due to variation in population density. In humans, changes in the use of social media platforms or their features may cause temporal changes in the number of observed individuals. For example, when Facebook added the feature “People You May Know,” the rate of new Facebook connections in a New Orleans dataset nearly doubled (52).In the stochastic model without selection, regardless of the fluctuation in the conformity coefficient(s), if there is conformity on average, the population converges to one of the three equilibria present in Boyd and Richerson’s (4) model with conformity (D(j)>0 for n2<j<n in Eq. 19). These are p*=1 (fixation on variant A), p*=0 (fixation on variant B), and p*=12 (equal representation of A and B). However, their stability properties may differ from those in the deterministic case. In Boyd and Richerson’s (4) model with random copying, every initial frequency p0 is an equilibrium. Here, with random copying expected and independent conformity coefficients, there is convergence to p*=0,12, or 1. In this case, and in the case with conformity expected, convergence to p*=0,12, or 1 also holds with stochastic variation in the number of role models, nt. With either stochastic or constant weak selection in Boyd and Richerson’s (4) simplest model (Eq. 1) and random copying expected, there is convergence to a fixation state (p*=0 or 1). Finally, with anticonformity in the deterministic model or anticonformity expected in the stochastic model, nonconvergence can occur.     

COVID-19 pandemic reveals persistent disparities in nitrogen dioxide pollution

The unequal spatial distribution of ambient nitrogen dioxide (NO2), an air pollutant related to traffic, leads to higher exposure for minority and low socioeconomic status communities. We exploit the unprecedented drop in urban activity during the COVID-19 pandemic and use high-resolution, remotely sensed NO2 observations to investigate disparities in NO2 levels across different demographic subgroups in the United States. We show that, prior to the pandemic, satellite-observed NO2 levels in the least White census tracts of the United States were nearly triple the NO2 levels in the most White tracts. During the pandemic, the largest lockdown-related NO2 reductions occurred in urban neighborhoods that have 2.0 times more non-White residents and 2.1 times more Hispanic residents than neighborhoods with the smallest reductions. NO2 reductions were likely driven by the greater density of highways and interstates in these racially and ethnically diverse areas. Although the largest reductions occurred in marginalized areas, the effect of lockdowns on racial, ethnic, and socioeconomic NO2 disparities was mixed and, for many cities, nonsignificant. For example, the least White tracts still experienced ∼1.5 times higher NO2 levels during the lockdowns than the most White tracts experienced prior to the pandemic. Future policies aimed at eliminating pollution disparities will need to look beyond reducing emissions from only passenger traffic and also consider other collocated sources of emissions such as heavy-duty vehicles.

Adverse air quality is an environmental justice issue, as it disproportionately affects marginalized and disenfranchised populations around the world (1–4). Growing evidence suggests that these populations experience more air pollution than is caused by their consumption (5–7). Within the United States, disparities in exposure are persistent, despite successful regulatory measures that have reduced pollution (8, 9). Nitrogen dioxide (NO2) is a short-lived trace gas formed shortly after fossil fuel combustion and regulated by the National Ambient Air Quality Standards under the Clean Air Act. Exposure to NO2 is associated with a range of respiratory diseases and premature mortality (10–12). NO2 is also a precursor to other pollutants such as ozone and particulate matter (13). Major sources of anthropogenic NO2, such as roadways and industrial facilities, are often located within or nearby marginalized and disenfranchised communities (14, 15), and disparities in NO2 exposure across demographic subgroups have been the focus of several recent studies (4, 8, 16–18).In early 2020, governments around the world imposed lockdowns and shelter-in-place orders in response to the spread of COVID-19. The earliest government-mandated lockdowns in the United States began in California on 19 March 2020, and many states followed suit in the following days. Changes in mobility patterns indicate that self-imposed social distancing practices were underway days to weeks before the formal announcement of lockdowns (19). Lockdowns led to sharp reductions in surface-level NO2 (20–23) and tropospheric column NO2 measured from satellite instruments (21, 24–27) over the United States, China, and Europe. According to government-reported inventories, roughly 60% of anthropogenic emissions of nitrogen oxides (NOx≡ NO + NO2) in the United States in 2010 were emitted by on-road vehicles (28), and up to 80% of ambient NO2 in urban areas can be linked to traffic emissions (29, 30). As such, NO2 is often used as a marker for road traffic in urban areas. Multiple lines of evidence such as seismic quieting and reduced mobility via location-based services point to changes in traffic-related emissions as the main driver of reductions in NO2 pollution during lockdowns, due to the large proportion of the population working from home (21, 23, 31, 32).Here we exploit the unprecedented changes in human activity unique to the COVID-19 lockdowns and remotely sensed NO2 columns with extraordinary spatial resolution and coverage to understand inequalities in the distribution of NO2 pollution for different racial, ethnic, and socioeconomic subgroups in the United States. Specifically, we address the following: Which demographic subgroups received the largest NO2 reductions? Did the lockdowns grow or shrink the perennial disparities in NO2 pollution across different demographic subgroups? Although the lockdowns are economically unsustainable, how can they advance environmental justice and equity by informing long-term policies to reduce NO2 disparities and the associated public health damages?     

Moving Dirac nodes by chemical substitution

Dirac fermions play a central role in the study of topological phases, for they can generate a variety of exotic states, such as Weyl semimetals and topological insulators. The control and manipulation of Dirac fermions constitute a fundamental step toward the realization of novel concepts of electronic devices and quantum computation. By means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, here, we show that Dirac states can be effectively tuned by doping a transition metal sulfide, BaNiS2, through Co/Ni substitution. The symmetry and chemical characteristics of this material, combined with the modification of the charge-transfer gap of BaCo1−xNixS2 across its phase diagram, lead to the formation of Dirac lines, whose position in k-space can be displaced along the Γ−M symmetry direction and their form reshaped. Not only does the doping x tailor the location and shape of the Dirac bands, but it also controls the metal-insulator transition in the same compound, making BaCo1−xNixS2 a model system to functionalize Dirac materials by varying the strength of electron correlations.

In the vast domain of topological Dirac and Weyl materials (1–9), the study of various underlying mechanisms (10–15) leading to the formation of nontrivial band structures is key to discovering new topological electronic states (16–23). A highly desirable feature of these materials is the tunability of the topological properties by an external parameter, which will make them suitable in view of technological applications, such as topological field-effect transistors (24). While a thorough control of band topology can be achieved, in principle, in optical lattices (25) and photonic crystals (26) through the wandering, merging, and reshaping of nodal points and lines in k-space (27, 28), in solid-state systems, such a control is much harder to achieve. Proposals have been made by using optical cavities (29), twisted van der Waals heterostructures (30), intercalation (31), chemical deposition (32, 33), impurities (34), and magnetic and electric applied fields (35), both static (36) and time-periodic (17, 37). Here, we prove that it is possible to move and reshape Dirac nodal lines in reciprocal space by chemical substitution. Namely, by means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, we observe a sizable shift of robust massive Dirac nodes toward Γ in BaCo1−xNixS2 as a function of doping x, obtained by replacing Ni with Co. At variance with previous attempts of controlling Dirac states by doping (19, 38), in our work, we report both a reshape and a significant k-displacement of the Dirac nodes.BaCo1−xNixS2 is a prototypical transition metal system with a simple square lattice (39). In BaCo1−xNixS2 , the same doping parameter x that tunes the position of the Dirac nodes also controls the electronic phase diagram, which features a first-order metal-insulator transition (MIT) at a critical substitution level, xcr∼ 0.22 (40, 41), as shown in Fig. 1A. The Co rich side (x=0) is an insulator with columnar antiferromagnetic (AF) order and with local moments in a high-spin (S = 3/2) configuration (42). This phase can be seen as a spin density wave (SDW) made of antiferromagnetically coupled collinear spin chains. Both electron-correlation strength and charge-transfer gap ΔCT increase with decreasing x, as typically found in the late-transition metal series. The MIT at x=0.22 is of interest because it is driven by electron correlations (43) and is associated with a competition between an insulating antiferromagnetic phase and an unconventional paramagnetic semimetal (44), where the Dirac nodes are found at the Fermi level. We show that a distinctive feature of these Dirac states is their dominant d-orbital character and that the underlying band-inversion mechanism is driven by a large d−p hybridization combined with the nonsymmorphic symmetry (NSS) of the crystal (Fig. 1B). It follows that an essential role in controlling the properties of Dirac states is played by electron correlations and by the charge-transfer gap (Fig. 1C), as they have a direct impact on the hybridization strength. This results into an effective tunability of shape, energy, and wave vector of the Dirac lines in the proximity of the Fermi level. Specifically, the present ARPES study unveils Dirac bands moving from M to Γ with decreasing x. The bands are well explained quantitatively by ab initio calculations, in a hybrid density functional approximation suitable for including nonlocal correlations of screened-exchange type, which affect the hybridization between the d and p states. The same functional is able to describe the insulating SDW phase at x=0, driven by local correlations, upon increase of the optimal screened-exchange fraction. These calculations confirm that the Dirac nodes mobility in k-space stems directly from the evolution of the charge-transfer gap, i.e., the relative position between d and p on-site energies. These results clearly suggest that BaCo1−xNixS2 is a model system to tailor Dirac states and, more generally, that two archetypal features of correlated systems, such as the hybrid d−p bands and the charge-transfer gap, constitute a promising playground to engineer Dirac and topological materials using chemical substitution and other macroscopic control parameters.Open in a separate windowFig. 1.Experimental observation of Dirac states in the phase diagram of BaCo1−xNixS2. (A) Phase diagram of BaCo1−xNixS2. The transition lines between the PM, the paramagnetic insulator (PI), and the antiferromagnetic insulator (AFI) are reported. Colored circles indicate the different doping levels x studied in this work. This doping alters the d−p charge-transfer gap (ΔCT). (B) Crystal structure of BaNiS2. Blue, red, and yellow spheres represent the Ni, S, and Ba atoms, respectively. The tetragonal unit cell is indicated by black solid lines. Lattice parameters are a = 4.44 Å and c = 8.93 Å (45). (B, Upper) Projection of the unit cell in the xy plane, containing two Ni atoms. (C) Schematics of the energy levels. The hybridization of d− and p− orbitals creates the Dirac states, and the d−p charge-transfer gap fixes the position of these states in the E−k space. (D) A three-dimensional ARPES map of BaNiS2 (x=1) taken at 70-eV photon energy. The top surface shows the Fermi surface, and the sides of the cube present the band dispersion along high-symmetry directions. The linearly dispersing bands along Γ−M cross each other at the Fermi level, EF, thus creating four Dirac nodes. (E) We observe the oval-shaped section of the linearly dispersing bands on the kx−ky plane for E−EF=−100 meV. The linearly dispersing bands along the major and minor axis of the oval are also shown.     

From hidden order to antiferromagnetism: Electronic structure changes in Fe-doped URu2Si2

In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic and still unsolved example is the transition of the heavy fermion compound URu2Si2 (URS) into the so-called hidden-order (HO) phase when the temperature drops below T0=17.5 K. Here, we show that the interaction between the heavy fermion and the conduction band states near the Fermi level has a key role in the emergence of the HO phase. Using angle-resolved photoemission spectroscopy, we find that while the Fermi surfaces of the HO and of a neighboring antiferromagnetic (AFM) phase of well-defined order parameter have the same topography, they differ in the size of some, but not all, of their electron pockets. Such a nonrigid change of the electronic structure indicates that a change in the interaction strength between states near the Fermi level is a crucial ingredient for the HO to AFM phase transition.

The transition of URu2Si2 from a high-temperature paramagnetic (PM) phase to the hidden-order (HO) phase below T0 is accompanied by anomalies in specific heat (1–3), electrical resistivity (1, 3), thermal expansion (4), and magnetic susceptibility (2, 3) that are all typical of magnetic ordering. However, the small associated antiferromagnetic (AFM) moment (5) is insufficient to explain the large entropy loss and was shown to be of extrinsic origin (6). Inelastic neutron scattering (INS) experiments revealed gapped magnetic excitations below T0 at commensurate and incommensurate wave vectors (7–9), while an instability and partial gapping of the Fermi surface was observed by angle-resolved photoemission spectroscopy (ARPES) (10–16) and scanning tunneling microscopy/spectroscopy (17, 18). More recently, high-resolution, low-temperature ARPES experiments imaged the Fermi surface reconstruction across the HO transition, unveiling the nesting vectors between Fermi sheets associated with the gapped magnetic excitations seen in INS experiments (14, 19) and quantitatively explaining, from the changes in Fermi surface size and quasiparticle mass, the large entropy loss in the HO phase (19). Nonetheless, the nature of the HO parameter is still hotly debated (20–23).The HO phase is furthermore unstable above a temperature-dependent critical pressure of about 0.7 GPa at T=0, at which it undergoes a first-order transition into a large moment AFM phase where the value of the magnetic moment per U atom exhibits a sharp increase, by a factor of 10 to 50 (6, 24–30). When the system crosses the HO → AFM phase boundary, the characteristic magnetic excitations of the HO phase are either suppressed or modified (8, 31), while resistivity and specific heat measurements suggest that the partial gapping of the Fermi surface is enhanced (24, 27).As the AFM phase has a well-defined order parameter, studying the evolution of the electronic structure across the HO/AFM transition would help develop an understanding of the HO state. So far, the experimental determination of the Fermi surface by Shubnikov de Haas (SdH) oscillations only showed minor changes across the HO → AFM phase boundary (32). Here, we take advantage of the HO/AFM transition induced by chemical pressure in URu2Si2, through the partial substitution of Ru with Fe (33–37), to directly probe its electronic structure in the AFM phase using ARPES. As we shall see, our results reveal that changes in the Ru 4d–U 5f hybridization across the HO/AFM phase boundary seem essential for a better understanding of the HO state.     

Ultrasensitive multispecies spectroscopic breath analysis for real-time health monitoring and diagnostics

Breath analysis enables rapid, noninvasive diagnostics, as well as long-term monitoring of human health, through the identification and quantification of exhaled biomarkers. Here, we demonstrate the remarkable capabilities of mid-infrared (mid-IR) cavity-enhanced direct-frequency comb spectroscopy (CE-DFCS) applied to breath analysis. We simultaneously detect and monitor as a function of time four breath biomarkers—CH3OH, CH4, H2O, and HDO—as well as illustrate the feasibility of detecting at least six more (H2CO, C2H6, OCS, C2H4, CS2, and NH3) without modifications to the experimental apparatus. We achieve ultrahigh detection sensitivity at the parts-per-trillion level. This is made possible by the combination of the broadband spectral coverage of a frequency comb, the high spectral resolution afforded by the individual comb teeth, and the sensitivity enhancement resulting from a high-finesse cavity. Exploiting recent advances in frequency comb, optical coating, and photodetector technologies, we can access a large variety of biomarkers with strong carbon–hydrogen-bond spectral signatures in the mid-IR.

Breath analysis is an exceptionally promising and rapidly developing field of research, which examines the molecular composition of exhaled breath (1–6). The hundreds of different gases that are present in exhaled breath include inorganic compounds, as well as volatile organic compounds (VOCs), and can either result from internal metabolic activity (endogenous emissions) or external factors, such as food consumption or environmental exposure (exogenous emissions). Despite its distinctive advantages of being a rapid, noninvasive technique and its long history dating back to Hippocrates, breath analysis has not yet been as widely deployed for routine diagnostics and monitoring as other methods, such as blood-based analysis. This is partly due to the experimental challenges of dealing with extremely small amounts of gas-phase molecules—in the parts-per-million (ppm) to parts-per-billion (ppb) range for most VOCs—and partly due to the relative scarcity of large-scale clinical studies that can reliably correlate specific diseases with biomarkers present in breath. Nevertheless, through close collaborations between instrument developers, breath-analysis experts, and clinicians, the field of breath analysis is fast approaching its goal of enabling real-time, noninvasive early detection and long-term monitoring of temporary and permanent health conditions (1, 3). Several biomarkers present in breath have been associated with specific conditions—for instance, nitrogen monoxide with asthma, acetone with diabetes, and ammonia with renal failure (5)—and breath is increasingly being used to track diseases and infections, both bacterial and viral (7). Recently, three studies have demonstrated the use of breath analysis to discriminate between SARS-CoV-2–infected patients and patients affected by other conditions (including asthma, chronic obstructive pulmonary disease, bacterial pneumonia, and cardiac conditions) (8, 9) or influenza A-infected patients (10). The possibility of real-time testing for highly infectious diseases in a noninvasive manner, without the need for chemical reagents and complex laboratory facilities, is particularly appealing in view of the current global pandemic.Technologies being explored and adopted for breath analysis include mass spectrometry, nanomaterial-based sensors, and laser spectroscopy. To date, the most widely used analytical technique in breath research is gas chromatography combined with mass spectrometry, which allows for the sensitive detection of hundreds of exhaled molecules, albeit with relatively long analysis times (tens of minutes) limited by the elution time of the various species. On the other hand, selected ion-flow-tube mass spectrometry and proton-transfer reaction mass spectrometry allow for real-time breath analysis at the expense of a reduced number of simultaneously detectable molecules (11). Sensor arrays offer an inexpensive and practical alternative for identifying the presence of a class of compounds based on their functional groups, but they generally do not permit identification of the specific molecules present in the samples (9, 12). Laser spectroscopy is intrinsically fast (≪ second timescale), allowing breath-cycle-resolved (i.e., respiratory-phase-resolved) sampling of breath with high precision and absolute accuracy. Achieving high sensitivity requires both signal enhancement and noise reduction: The former is attained by using multipass cells or high-finesse cavities, while the latter is accomplished through intensity or frequency-modulation techniques. Among others, tunable diode laser absorption spectroscopy, cavity ring-down spectroscopy, cavity-enhanced absorption spectroscopy, and photoacoustic spectroscopy have all successfully been employed in breath analysis, but are typically limited in tunability and therefore in the number of detectable analytes (1). Cavity-enhanced direct-frequency comb spectroscopy (CE-DFCS) offers substantially enhanced capabilities for the simultaneous detection of multiple species due to the combination of high spectral resolution, wide spectral coverage, and high sensitivity (13–18). An early study from 2008 demonstrated this by detecting carbon monoxide, carbon dioxide, methane, ammonia, and water in breath samples by CE-DFCS (19). This previous work measured vibrational (mainly first) overtone transitions in the near-infrared (near-IR) region of the spectrum, from 1.5 μm to 1.7 μm.Here, we report a 2-orders-of-magnitude improvement in the detection sensitivity for multiple species relevant to breath analysis by using CE-DFCS in the mid-infrared (mid-IR) molecular fingerprint region (3.4−3.6 μm). We gain access to fundamental vibrational transitions, as well as employ higher-finesse mid-IR cavity mirrors (15, 20), compared to previous work in this spectral region (21). Exploiting recent advances in frequency comb, high-reflectivity optical coating, and photodetector technologies, we can detect a large variety of biomarkers simultaneously, sensitively, and unambiguously, providing exciting prospects to connect breath to a range of biological functions and diseases.     

Thermodynamic controls on rates of iron oxide reduction by extracellular electron shuttles

Anaerobic microbial respiration in suboxic and anoxic environments often involves particulate ferric iron (oxyhydr-)oxides as terminal electron acceptors. To ensure efficient respiration, a widespread strategy among iron-reducing microorganisms is the use of extracellular electron shuttles (EES) that transfer two electrons from the microbial cell to the iron oxide surface. Yet, a fundamental understanding of how EES–oxide redox thermodynamics affect rates of iron oxide reduction remains elusive. Attempts to rationalize these rates for different EES, solution pH, and iron oxides on the basis of the underlying reaction free energy of the two-electron transfer were unsuccessful. Here, we demonstrate that broadly varying reduction rates determined in this work for different iron oxides and EES at varying solution chemistry as well as previously published data can be reconciled when these rates are instead related to the free energy of the less exergonic (or even endergonic) first of the two electron transfers from the fully, two-electron reduced EES to ferric iron oxide. We show how free energy relationships aid in identifying controls on microbial iron oxide reduction by EES, thereby advancing a more fundamental understanding of anaerobic respiration using iron oxides.

The use of iron oxides as terminal electron acceptors in anaerobic microbial respiration is central to biogeochemical element cycling and pollutant transformations in many suboxic and anoxic environments (1–6). To ensure efficient electron transfer to solid-phase ferric iron, Fe(III), at circumneutral pH, metal-reducing microorganisms from diverse phylae use dissolved extracellular electron shuttle (EES), including quinones (7–9), flavins (10–16), and phenazines (17–19), to transfer two electrons per EES molecule from the respiratory chain proteins in the outer membrane of the microbial cell to the iron oxide (17, 20, 21). The oxidized EES can diffuse back to the cell surface for rereduction, thereby completing the catalytic redox cycle involving the EES.The electron transfer from the reduced EES to Fe(III) is considered a key step in overall microbial Fe(III) respiration. Several lines of evidence suggest that the free energy of the electron transfer reaction, ΔrG, controls Fe(III) reduction rates (15, 17, 22, 23). For instance, microbial Fe(III) oxide reduction by dissolved model quinones as EES was accelerated only for quinones with standard two-electron reduction potentials, EH,1,20, that fell into a relatively narrow range of −180±80 mV at pH 7 (24). Furthermore, in abiotic experiments, Fe(III) reduction rates by EES decreased with increasing ΔrG that resulted from increasing either EH,1,20 of the EES (25, 26), the concentration of Fe(II) in the system (27), or solution pH (25, 26, 28). However, substantial efforts to relate Fe(III) reduction rates for different EES species, iron oxides, and pH to the EH,1,20 averaged over both electrons transferred from the EES to the iron oxides were only partially successful (25, 28). Reaction free energies of complex redox processes involving the transfer of multiple electrons can readily be calculated using differences in the reduction potentials averaged over all electrons transferred, and this approach is well established in biogeochemistry and microbial ecology. For kinetic considerations, however, the use of averaged reduction potentials is inappropriate.Herein, we posit that rates of Fe(III) reduction by EES instead relate to the ΔrG of the less exergonic first one-electron transfer from the two-electron reduced EES species to the iron oxide, following the general notion that reaction rates scale with reaction free energies (29). Our hypothesis is based on the fact that, at circumneutral to acidic pH and for many EES, the reduction potential of the first electron transferred to the fully oxidized EES to form the one-electron reduced intermediate semiquinone species, EH,1, is lower than the reduction potential of the second electron transferred to the semiquinone to form the fully two-electron reduced EES species, EH,2 [i.e., EH,1<EH,2 (30–33)]. This difference in one-electron reduction potentials implies that the two-electron reduced EES (i.e., the hydroquinone) is the weaker one-electron reductant for Fe(III) as compared to the semiquinone species. We therefore expect that rates of iron oxide reduction relate to the ΔrG of the first electron transferred from the hydroquinone to Fe(III). The ΔrG of this first electron transfer may even be endergonic provided that the two-electron transfer is exergonic.We verified our hypothesis in abiotic model systems by demonstrating that reduction rates of two geochemically important crystalline iron oxides, goethite and hematite, by two-electron reduced quinone- and flavin-based EES over a wide pH range, and therefore thermodynamic driving force for Fe(III) reduction, correlate with the ΔrG of the first electron transferred from the fully reduced EES to Fe(III). We further show that rates of goethite and hematite reduction by EES reported in the literature are in excellent agreement with our rate data when comparing rates on the basis of the thermodynamics of the less exergonic first of the two electron transfers.     

Emergent dual scaling of riverine biodiversity

A prevailing paradigm suggests that species richness increases with area in a decelerating way. This ubiquitous power law scaling, the species–area relationship, has formed the foundation of many conservation strategies. In spatially complex ecosystems, however, the area may not be the sole dimension to scale biodiversity patterns because the scale-invariant complexity of fractal ecosystem structure may drive ecological dynamics in space. Here, we use theory and analysis of extensive fish community data from two distinct geographic regions to show that riverine biodiversity follows a robust scaling law along the two orthogonal dimensions of ecosystem size and complexity (i.e., the dual scaling law). In river networks, the recurrent merging of various tributaries forms fractal branching systems, where the prevalence of branching (ecosystem complexity) represents a macroscale control of the ecosystem’s habitat heterogeneity. In the meantime, ecosystem size dictates metacommunity size and total habitat diversity, two factors regulating biodiversity in nature. Our theory predicted that, regardless of simulated species’ traits, larger and more branched “complex” networks support greater species richness due to increased space and environmental heterogeneity. The relationships were linear on logarithmic axes, indicating power law scaling by ecosystem size and complexity. In support of this theoretical prediction, the power laws have consistently emerged in riverine fish communities across the study regions (Hokkaido Island in Japan and the midwestern United States) despite hosting different fauna with distinct evolutionary histories. The emergence of dual scaling law may be a pervasive property of branching networks with important implications for biodiversity conservation.

Ecologists have long sought to understand the general drivers of biodiversity. One of the most robust empirical generalizations in ecology is the positive relationship between species richness and area, that is, the species–area relationship (the SAR) (1). In 1921, Arrhenius (2) formulated the SAR as a power law S=cAz, an equation currently known as the Arrhenius SAR (S is the number of species observed in a given geographic area A, c the constant, and z the scaling exponent). Since then, the spatial scaling of species richness has been observed in many taxonomic groups (3). The SAR is ubiquitous because multiple mechanisms produce an apparently similar pattern. Larger ecosystems typically support more diverse metacommunities due to increased habitat diversity (4), larger metacommunity size (5), and/or enhanced colonization dynamics (6). Importantly, the SAR provides the foundation for global conservation efforts (7–9). For example, conservation ecologists have used SAR estimates to design marine and terrestrial protected areas (7, 8), which currently encompass more than 30 million km² globally (10).Many ecosystems, however, possess a complex spatial structure that cannot be represented by area—a dimension referred to as scale-invariant complexity (11, 12). Such complexity is evident in branching ecosystems, including rivers, trees, and mountain ranges, to name just a few (12). Geomorphic or biological processes generate a pronounced self-similarity in complex branching patterns such that the part and the whole look alike (12). Even though the branching structure is independent of spatial scale, it forms a physical template that dictates habitat diversity and dispersal corridors for living organisms (13). Limited but accumulating evidence suggests that classical metapopulation and metacommunity theories cannot predict ecological dynamics driven by branching structure (14–16), and this recognition has led to recent developments of spatial theories devoted to complex branching ecosystems (17). For example, these studies have highlighted key roles of branching structure in driving local biodiversity patterns, such as increased species richness at merging points of branches (18). However, most research has explored the consequences of branching complexity for local community structure (19) or has relied solely on theoretical arguments with limited replications of branching architecture (20). At present, we lack a comprehensive evaluation of how branching complexity scales biodiversity patterns at the metacommunity level. Filling this knowledge gap may provide common ground for achieving successful conservation in spatially complex ecosystems, where accelerated species loss threatens the delivery of ecosystem services (21).Here, we propose a unified framework of ecosystem size and complexity in scaling biodiversity patterns in rivers—a prime example of complex branching ecosystems. Individual streams and rivers flow through different landscapes with distinct geological and climatic backgrounds, serving as a spatial unit of unique in-stream environments (16, 22–27). The recurrent merging of diverse tributaries ultimately forms a fluvial network with fractal branching patterns (12). As such, the complexity of branching structure, which we define here as the probability of branching per unit river distance (24, 28), may represent a macroscale control of the ecosystem’s habitat heterogeneity (habitat diversity per unit area) (13, 23, 24). Meanwhile, ecosystem size (watershed area) should determine the metacommunity size and total habitat diversity (area times heterogeneity), two factors that regulate biodiversity at the metacommunity level (4, 5). Hence, riverine biodiversity may manifest scaling laws along the two orthogonal dimensions of branching networks. We call this the dual scaling hypothesis of biodiversity.The present study combines theory and analysis of extensive community data from two different regions of the globe to show that multiple ecological pathways converge to the emergence of dual diversity scaling. Specifically, watershed-scale species richness (γ diversity) followed power laws with ecosystem size A and branching probability Pb as γ=cAξ1Pbξ2 (ξ1 and ξ2 are the scaling exponents) regardless of ecological contexts. However, contributing factors of increased γ diversity—either enhanced local species richness (α diversity) and/or spatial variation of species composition (β diversity)—depended on constituent species’ characteristics. Our findings suggest that the dual scaling law is a pervasive yet overlooked feature of complex ecosystems with important implications for biodiversity conservation.     

Entropic barrier of topologically immobilized DNA in hydrogels

The single most intrinsic property of nonrigid polymer chains is their ability to adopt enormous numbers of chain conformations, resulting in huge conformational entropy. When such macromolecules move in media with restrictive spatial constraints, their trajectories are subjected to reductions in their conformational entropy. The corresponding free energy landscapes are interrupted by entropic barriers separating consecutive spatial domains which function as entropic traps where macromolecules can adopt their conformations more favorably. Movement of macromolecules by negotiating a sequence of entropic barriers is a common paradigm for polymer dynamics in restrictive media. However, if a single chain is simultaneously trapped by many entropic traps, it has recently been suggested that the macromolecule does not undergo diffusion and is localized into a topologically frustrated dynamical state, in apparent violation of Einstein’s theorem. Using fluorescently labeled λ-DNA as the guest macromolecule embedded inside a similarly charged hydrogel with more than 95% water content, we present direct evidence for this new state of polymer dynamics at intermediate confinements. Furthermore, using a combination of theory and experiments, we measure the entropic barrier for a single macromolecule as several tens of thermal energy, which is responsible for the extraordinarily long extreme metastability. The combined theory–experiment protocol presented here is a determination of single-molecule entropic barriers in polymer dynamics. Furthermore, this method offers a convenient general procedure to quantify the underlying free energy landscapes behind the ubiquitous phenomenon of movement of single charged macromolecules in crowded environments.

Movement of charged macromolecules in aqueous media with crowded spatial constraints is ubiquitous in biology, biotechnology, and separation science (1–7). A familiar scenario is the movement of messenger RNA inside the milieu of a nucleus of a mammalian cell, which is a thick Coulomb soup, toward the nuclear pore complex in the process of initiating protein synthesis. Another well-known example is the gel electrophoresis used to identify and separate polynucleotides of different lengths. Furthermore, hydrogel-based technology is extensively implemented to perform targeted delivery of drugs and genes (2–6). Parallel to these aqueous systems, movement of macromolecules in congested nonaqueous polymer melts containing nanoparticles, and infiltration of polymer melts through restricted media, are of tremendous interest in terms of fundamental understanding and applications (8–15). Although entropic barriers associated with conformational changes of the moving macromolecules are often invoked in the above examples of both aqueous and nonaqueous polymer systems, the quantitative nature of such entropic barriers remains to be established (16–42). Despite the above-mentioned now-standard experimental protocols and substantial applications, an understanding of how macromolecules navigate themselves in crowded environments continues to be a persistent challenge.Adding fuel to the flames, a recent discovery (41, 42) shows that large charged macromolecules such as λ-DNA and sodium poly(styrene sulfonate) can be immobilized in hydrogels which are essentially water at ambient temperatures, as a strong deviation from Einstein’s theorem on diffusion. In this paper, we present a combination of theory and fluorescence-based single-molecule tracking to directly observe the movement of guest macromolecules and quantify the entropic barriers associated with their movement. We provide direct evidence for the emergence of the recently proposed nondiffusive topologically frustrated dynamical state at intermediate confinements and determine the associated entropic barrier responsible for extraordinarily long-lived metastable dynamical states.The difficulty in attaining an adequate understanding of entropically driven movement of large macromolecules in soft background media stems from the interdependence between the conformational fluctuations of the macromolecule subjected to transport and the spatial correlation of spatial constraints in the crowded background medium. As an example, consider a large macromolecule (guest) embedded inside a host hydrogel (Fig. 1A). Let the radius of gyration of the guest molecule of N monomers be Rg and the cross-link density of the hydrogel be such that the average mesh size (correlation length for local monomer concentration of the host) is ξ. If Rg≲ξ, the guest molecule only brushes against the host matrix and diffuses. On the other hand, if Rg≫ξ, a single guest molecule is partitioned among many meshes, resulting in its localization. In each occupied mesh, the partitioned portion of the guest under confinement can adopt numerous conformations with a confinement free energy. As a result, each occupied mesh functions as a free energy trap relative to its neighboring matrix domains that are inaccessible to the guest. Accounting for excluded volume interactions and ignoring correlations, the confinement free energy is proportional to M2/ξ3, where M≪N is the number of monomers inside a trap of volume ξ3 (42). The localization effect occurs within two boundary regions. One region corresponds to weaker confinement, Rg≲ξ, as mentioned above. At the other boundary region of transition into reptation, where the free energy traps cease to exist (M2/ξ3→0), we expect ξ to be so small that its corresponding three-dimensional mesh does not have enough space for the guest, namely, M→0. Let us define a length ℓc, comparable to that of only a small number of monomers, corresponding to this condition (vanishing confinement free energy). Furthermore, in the limit of very strong confinements with no free energy traps, the guest is confined inside an essentially one-dimensional tube of a diameter comparable to the entanglement length ℓe. The precise value of ℓc and its relation to ℓe are presently unknown. For brevity, we use ℓ in Fig. 1 to denote both ℓc and ℓe, and leave the detailed values of ℓc and ℓe and their relation to persistence length for future investigation (see Conclusions and Perspective). The movement of the guest molecule is dictated by the relative value of Rg to ξ, and the relative value of ξ to the length ℓ defined above. Different possible scenarios based on Rg/ξ and ξ/ℓ are portrayed in Fig. 1B.Open in a separate windowFig. 1.(A) Cartoon of a large charged macromolecule of radius of gyration Rg embedded in a hydrogel of mesh size ξ. (B) Sketch of the dependence of the diffusion coefficient D of the guest molecule on degree of confinement (which increases with a decrease in ξ). The four conventional regimes of polymer dynamics, namely, Zimm, Rouse, entropic barrier, and reptation, and their conditions of experimental relevance are denoted by 1, 2, 3, and 5, respectively. The corresponding scaling laws in these regimes connecting D and the degree of polymerization N of the polymer chain are given in Eq. 1. Regime 4 is the newly hypothesized nondiffusive (D≃0, as denoted by the red horizontal line) topologically frustrated state at intermediate confinements. Direct observation of this new dynamical state and measurement of the entropic barrier responsible for polymer localization are presented in Results. (C) Sketch of partitioning of a single chain into multiple deep entropic traps.Based on experiments during the past seven decades and buttressed by theories (43, 44), four regimes (1, 2, 3, and 5) have been widely recognized. These are described, respectively, by the Stokes–Einstein–Zimm, Rouse, entropic barrier, and reptation models. In all these regimes, the guest molecule undergoes diffusion. The dependence of the diffusion coefficient D on the degree of polymerization N of the polymer molecule is given by the scaling laws as (Fig. 1B)[1]where ν is the size exponent defined through Rg≈Nν, and A is a nonuniversal numerical factor denoting the local structure of the host medium (16). The above four regimes of polymer diffusion have been validated by a preponderance of experimental data in the past (17–20, 22–33).Furthermore, in a recent development, room temperature experiments on charged macromolecules (such as λ-DNA and sodium poly(styrene sulfonate)) embedded inside similarly charged hydrogels at intermediate confinements (Rg≫ξ≫ℓ, regime 4 in Fig. 1B) have revealed an apparent breakdown of even the phenomenon of diffusion, and the emergence of a new nondiffusive topologically frustrated dynamical state. When Rg≫ξ≫ℓ (regime 4 in Fig. 1B), each macromolecule is so large in comparison with the mesh size that it is partitioned among many meshes. Since ξ≫ℓ, each mesh is an entropic trap holding a significant portion of the macromolecule and allowing local Rouse–Zimm dynamics for that portion. Furthermore, that portion can move to a neighboring empty mesh only through an entropic barrier as in regime 3 (where a single entropic barrier is operative for the whole molecule). As a consequence, many sets of entropic barriers must be simultaneously negotiated for the center of mass of one molecule to diffuse. The free energy landscape for the situation in regime 4 is cartooned in Fig. 1C. Theoretical analysis (41) of the simultaneous crossing of multiple entropic barriers by a single chain shows that the net effective free energy barrier U arising only from conformational entropy isU≃kBT ln196ξ8ℓ8,[2]where kB is the Boltzmann constant, and T is the absolute temperature. Thus the barrier U can be enormous depending on ξ/ℓ. For example, for ξ/ℓ=50, U≃27kBT. Such large barriers result in extremely long times for a single chain to diffuse a distance comparable to its own size. As a result, the macromolecule is practically locked into an immobile state in regime 4. Therefore, in regime 4, the time evolution of the mean square displacement of the center of mass Rcm(t) of the guest molecule is hypothesized to be nondiffusive according to⟨Rcm(t)−Rcm(0)2⟩≈t0, (Rg≫ξ≫ℓ).[3]This additional dynamical state is included in Fig. 1B, where the red horizontal line denotes the nondiffusive regime 4.Although the above hypothesis of the emergence of a nondiffusive topologically frustrated long-lived metastable state at intermediate confinements is supported by dynamic light scattering experiments (41, 42), direct evidence for this phenomenon and quantification of the collective entropic barrier responsible for this effect are yet to be established. These are the primary goals of the present paper. Using a combination of theory and statistical analysis of thousands of trajectories of fluorescently labeled λ-DNA inside poly(acrylamide-coacrylate) hydrogels with more than 95% water content, we have measured the entropic barrier that results in the new topologically frustrated state, in addition to finding direct evidence for the immobility of λ-DNA at intermediate confinements.     

Repeating caldera collapse events constrain fault friction at the kilometer scale

Fault friction is central to understanding earthquakes, yet laboratory rock mechanics experiments are restricted to, at most, meter scale. Questions thus remain as to the applicability of measured frictional properties to faulting in situ. In particular, the slip-weakening distance dc strongly influences precursory slip during earthquake nucleation, but scales with fault roughness and is challenging to extrapolate to nature. The 2018 eruption of Kīlauea volcano, Hawaii, caused 62 repeatable collapse events in which the summit caldera dropped several meters, accompanied by MW 4.7 to 5.4 very long period (VLP) earthquakes. Collapses were exceptionally well recorded by global positioning system (GPS) and tilt instruments and represent unique natural kilometer-scale friction experiments. We model a piston collapsing into a magma reservoir. Pressure at the piston base and shear stress on its margin, governed by rate and state friction, balance its weight. Downward motion of the piston compresses the underlying magma, driving flow to the eruption. Monte Carlo estimation of unknowns validates laboratory friction parameters at the kilometer scale, including the magnitude of steady-state velocity weakening. The absence of accelerating precollapse deformation constrains dc to be ≤10 mm, potentially much less. These results support the use of laboratory friction laws and parameters for modeling earthquakes. We identify initial conditions and material and magma-system parameters that lead to episodic caldera collapse, revealing that small differences in eruptive vent elevation can lead to major differences in eruption volume and duration. Most historical basaltic caldera collapses were, at least partly, episodic, implying that the conditions for stick–slip derived here are commonly met in nature.

Our knowledge of rock friction comes from laboratory experiments on samples from centimeters to at most meter scale (1, 2). These experiments have led to rate- and state-dependent friction laws (3, 4), which together with continuum fault models explain many features of natural earthquakes (5, 6). Extrapolation of laboratory-derived constitutive parameters to faults in situ, however, has been challenging, particularly for the characteristic slip weakening distance, dc, the displacement scale over which friction degrades from nominally static to dynamic values. In the laboratory dc ranges from several to tens of micrometers, but scales with fault roughness (7). Some seismological estimates are up to five orders of magnitude larger (8), but are sensitive to the decrease in shear strength at earthquake rupture fronts, leading to weakening lengths that scale with dc, but can be much larger (9, 10). Understanding the magnitude of dc in situ is crucial because the amount of potentially observable precursory slip scales with dc (11). Significant insights have been gained from in situ fluid injection experiments into faults that induce aseismic slip and seismicity (12–14), yet constraints on the parts of faults that actually generate earthquakes are rare.Collapse at basaltic shield volcanoes typically occurs in repeated discrete events, generating characteristic deformation transients and very long period (VLP) earthquakes (15–17). Rapid outflow of magma causes the pressure in subcaldera magma reservoirs to decrease, leading to an increase in stress in the overlying crust. Collapse initiates if this stress reaches the crustal strength, forming ring faults bounding down-dropped block(s) (18). Once initiated, collapse transfers the weight of the overlying crust onto the magma reservoir, maintaining pressure necessary for the eruption to continue (19). Thus, caldera collapse is not simply a response to the rapid withdrawal of magma, but is also an essential process in sustaining these eruptions.The 2018 Kīlauea collapses were quasi-periodic and exceptionally well monitored by nearby global positioning system (GPS) and tilt stations, including GPS stations on the down-dropped block(s). These data can be used to infer stress changes on the caldera-bounding ring faults, making them effectively kilometer-scale stick–slip experiments. The highly repeatable nature of the collapses, as well as constraints on the changes in magma pressure prior to the onset of collapse (20), minimizes uncertainty due to otherwise difficult to constrain initial conditions.     

Evidence and theory for lower rates of depression in larger US urban areas

It is commonly assumed that cities are detrimental to mental health. However, the evidence remains inconsistent and at most, makes the case for differences between rural and urban environments as a whole. Here, we propose a model of depression driven by an individual’s accumulated experience mediated by social networks. The connection between observed systematic variations in socioeconomic networks and built environments with city size provides a link between urbanization and mental health. Surprisingly, this model predicts lower depression rates in larger cities. We confirm this prediction for US cities using four independent datasets. These results are consistent with other behaviors associated with denser socioeconomic networks and suggest that larger cities provide a buffer against depression. This approach introduces a systematic framework for conceptualizing and modeling mental health in complex physical and social networks, producing testable predictions for environmental and social determinants of mental health also applicable to other psychopathologies.

Living in cities changes the way we behave and think (1–3). Over a century ago, the social changes associated with massive urbanization in Europe and in the United States focused social scientists on the nexus between cities and mental life (2). Along with the urban public health crises of the time, a central question became whether cities are good or bad for mental health.Subsequently, social psychologists (1) started to document and measure the systematic behavioral adaptations among people living in cities. These adaptations included a more intense use of time [e.g., faster walking (4)], a greater tolerance for diversity (5), and strategies to curb unwanted social interactions—such that people in larger cities act in colder and more callous ways (1). These studies attributed the influences of urban environments on mental health to the intensity of social life in larger cities, mediated by densely built spaces and associated dynamic and diverse socioeconomic interaction networks. They did not, however, ultimately clarify whether urban environments promote better or worse mental health. Consequently, concerns persisted that cities are mentally taxing (6–9) and can induce “stimulus overload,” including stress, mental fatigue (10), and low levels of subjective well-being (SWB) (11).More recent studies have focused less on urban environments as a whole and more on contextual and environmental factors associated with depression. For example, a study of the entire population in Sweden (9) uncovered a positive association between neighborhood population density and depression-related hospitalizations. In addition, individual factors of gender, age, socioeconomic status, and race, which vary at neighborhood levels within cities, have been found to be statistically associated with depression (12–14). Other studies using various measures of mental health and broader definitions of urban environments have found evidence for an association between poorer mental health in cities vs. rural areas (7, 8). However, this evidence and that linking SWB and cities (15–18) have remained mixed and often explicitly inconsistent (19, 20) due to differences in 1) reporting (e.g., surveys vs. medical records); 2) types of measurement (e.g., surveys vs. interviews); 3) definitions of what constitutes urban; and 4) the mental disorders studied (e.g., schizophrenia vs. depression).For these reasons, it is desirable to create a systematic framework that organizes this diverse body of research and interrogates how varying levels of urbanization influence mental health across different sets of indicators. Here, we begin to build this framework for depression in US cities. We show that, surprisingly, the per capita prevalence of depression decreases systematically with city size.Like earlier classic approaches, our strategy frames the effects of city size on mental health through the lens of the individual experience of urban physical and socioeconomic environments. Crucial to our purposes, many characteristics of cities have been recently found to vary predictably with city population size. These systematic variations in urban indicators are explained by denser built environments and their associated increases in the intensity of human interactions and resulting adaptive behaviors (21).More specifically, people in larger cities have, on average, more socioeconomic connections mediating a greater variety of functions. This effect is understood theoretically by the statistical likelihood to interact with more people over space per unit time, leading to potential mental “overload” but also, to greater stimulation and choice along more dimensions of life. This expansion of socioeconomic networks is supported structurally by economies of scale (e.g., road length) in urban built environments and by occupational specialization and associated increases in economic productivity and exchange (3).This effect leads to a number of quantitative predictions about the nature of urban spaces and socioeconomic variables, the most central of which is the variation of the average number of socioeconomic interactions, k (network degree), with city size, N, as k(N)=k0Nδeξ. Here, k0 is a prefactor independent of city size, and ξ is a residual measuring the distance from the population average. The exponent 0<δ≃1/6<1 measures the percentage increase in the number of connections with each percentage increase in city population, which is an elasticity in the language of economics. Because the ξ reflects city size–independent statistical fluctuations, these errors average out across cities, and k obeys a scaling relationship on average over cities, such that k(N)∼Nδ. This expectation that k follows a scaling law with city population is directly observed in cell phone networks (22) and indirectly via the faster spread of infectious diseases such as COVID-19 (23), and by higher per capita economic productivity and rates of innovation (4, 21).This result is important to mental health because depression is associated, at the individual level, with fewer social contacts (24, 25). To translate the general scaling of social interactions with city size into a model for the incidence of depression in urban areas, we will now need to pay particular attention not only to the average number of social connections in a city of size N, k(N), but also, to its variance across individuals in that city and how they influence depression.     

Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement

Our study of cholesteric lyotropic chromonic liquid crystals in cylindrical confinement reveals the topological aspects of cholesteric liquid crystals. The double-twist configurations we observe exhibit discontinuous layering transitions, domain formation, metastability, and chiral point defects as the concentration of chiral dopant is varied. We demonstrate that these distinct layer states can be distinguished by chiral topological invariants. We show that changes in the layer structure give rise to a chiral soliton similar to a toron, comprising a metastable pair of chiral point defects. Through the applicability of the invariants we describe to general systems, our work has broad relevance to the study of chiral materials.

Chiral liquid crystals (LCs) are ubiquitous, useful, and rich systems (1–4). From the first discovery of the liquid crystalline phase to the variety of chiral structures formed by biomolecules (5–9), the twisted structure, breaking both mirror and continuous spatial symmetries, is omnipresent. The unique structure also makes the chiral nematic (cholesteric) LC, an essential material for applications utilizing the tunable, responsive, and periodic modulation of anisotropic properties.The cholesteric is also a popular model system to study the geometry and topology of partially ordered matter. The twisted ground state of the cholesteric is often incompatible with confinement and external fields, exhibiting a large variety of frustrated and metastable director configurations accompanying topological defects. Besides the classic example of cholesterics in a Grandjean−Cano wedge (10, 11), examples include cholesteric droplets (12–16), colloids (17–19), shells (20–22), tori (23, 24), cylinders (25–29), microfabricated structures (30, 31), and films between parallel plates with external fields (32–40). These structures are typically understood using a combination of nematic (achiral) topology (41, 42) and energetic arguments, for example, the highly successful Landau−de Gennes approach (43). However, traditional extensions of the nematic topological approach to cholesterics are known to be conceptually incomplete and difficult to apply in regimes where the system size is comparable to the cholesteric pitch (41, 44).An alternative perspective, chiral topology, can give a deeper understanding of these structures (45–47). In this approach, the key role is played by the twist density, given in terms of the director field n by n⋅∇×n. This choice is not arbitrary; the Frank free energy prefers n⋅∇×n≈−q0=2π/p0 with a helical pitch p0, and, from a geometric perspective, n⋅∇×n≠0 defines a contact structure (48). This allows a number of new integer-valued invariants of chiral textures to be defined (45). A configuration with a single sign of twist is chiral, and two configurations which cannot be connected by a path of chiral configurations are chirally distinct, and hence separated by a chiral energy barrier. Within each chiral class of configuration, additional topological invariants may be defined using methods of contact topology (45–48), such as layer numbers. Changing these chiral topological invariants requires passing through a nonchiral configuration. Cholesterics serve as model systems for the exploration of chirality in ordered media, and the phenomena we describe here—metastability in chiral systems controlled by chiral topological invariants—has applicability to chiral order generally. This, in particular, includes chiral ferromagnets, where, for example, our results on chiral topological invariants apply to highly twisted nontopological Skyrmions (49, 50) (“Skyrmionium”).Our experimental model to explore the chiral topological invariants is the cholesteric phase of lyotropic chromonic LCs (LCLCs). The majority of experimental systems hitherto studied are based on thermotropic LCs with typical elastic and surface-anchoring properties. The aqueous LCLCs exhibiting unusual elastic properties, that is, very small twist modulus K2 and large saddle-splay modulus K24 (51–56), often leading to chiral symmetry breaking of confined achiral LCLCs (53, 54, 56–61), may enable us to access uncharted configurations and defects of topological interests. For instance, in the layer configuration by cholesteric LCLCs doped with chiral molecules, their small K2 provides energetic flexibility to the thickness of the cholesteric layer, that is, the repeating structure where the director n twists by π. The large K24 affords curvature-induced surface interactions in combination with a weak anchoring strength of the lyotropic LCs (62–64).We present a systematic investigation of the director configuration of cholesteric LCLCs confined in cylinders with degenerate planar anchoring, depending on the chiral dopant concentration. We show that the structure of cholesteric configurations is controlled by higher-order chiral topological invariants. We focus on two intriguing phenomena observed in cylindrically confined cholesterics. First, the cylindrical symmetry renders multiple local minima to the energy landscape and induces discontinuous increase of twist angles, that is, a layering transition, upon the dopant concentration increase. Additionally, the director configurations of local minima coexist as metastable domains with point-like defects between them. We demonstrate that a chiral layer number invariant distinguishes these configurations, protects the distinct layer configurations (45), and explains the existence of the topological defect where the invariant changes.     

Glasses denser than the supercooled liquid

When aged below the glass transition temperature, Tg, the density of a glass cannot exceed that of the metastable supercooled liquid (SCL) state, unless crystals are nucleated. The only exception is when another polyamorphic SCL state exists, with a density higher than that of the ordinary SCL. Experimentally, such polyamorphic states and their corresponding liquid–liquid phase transitions have only been observed in network-forming systems or those with polymorphic crystalline states. In otherwise simple liquids, such phase transitions have not been observed, either in aged or vapor-deposited stable glasses, even near the Kauzmann temperature. Here, we report that the density of thin vapor-deposited films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD) can exceed their corresponding SCL density by as much as 3.5% and can even exceed the crystal density under certain deposition conditions. We identify a previously unidentified high-density supercooled liquid (HD-SCL) phase with a liquid–liquid phase transition temperature (TLL) ∼35 K below the nominal glass transition temperature of the ordinary SCL. The HD-SCL state is observed in glasses deposited in the thickness range of 25 to 55 nm, where thin films of the ordinary SCL have exceptionally enhanced surface mobility with large mobility gradients. The enhanced mobility enables vapor-deposited thin films to overcome kinetic barriers for relaxation and access the HD-SCL state. The HD-SCL state is only thermodynamically favored in thin films and transforms rapidly to the ordinary SCL when the vapor deposition is continued to form films with thicknesses more than 60 nm.

Glasses are formed when the structural relaxations in supercooled liquids (SCLs) become too slow, causing the system to fall out of equilibrium at the glass transition temperature (Tg). The resulting out-of-equilibrium glass state has a thermodynamic driving force to evolve toward the SCL state through physical aging (1). At temperatures just below Tg, the extent of equilibration is limited by the corresponding SCL state, while at much lower temperatures, equilibration is limited by the kinetic barriers for relaxation. As such, the degree of thermodynamic stability achieved through physical aging is limited (2).Physical vapor deposition (PVD) is an effective technique to overcome kinetic barriers for relaxation to produce thermodynamically stable glasses (3–10). The accelerated equilibration in these systems is due to their enhanced surface mobility (11–14). During PVD, when the substrate temperature is held below Tg, molecules or atoms can undergo rearrangements and adopt more stable configurations at the free surface and proximate layers underneath (13). After the molecules are buried deeper into the film, their relaxation dynamics significantly slow down, which prevents further equilibration. Through this surface-mediated equilibration process, stable glasses can achieve low-energy states on the potential energy landscape that would otherwise require thousands or millions of years of physical aging (2, 3, 15, 16).As such, the degree of enhanced surface mobility and mobility gradients are critical factors in the formation of stable glasses (3, 11, 17, 18). While the effect of film thickness on the surface mobility and gradients of liquid-quenched (LQ) glasses has been studied in the past (19, 20), there are limited data on the role of film thickness in the stability of vapor-deposited glasses. In vapor-deposited toluene, it has been shown that decreasing the film thickness from 70 to 5 nm can increase the thermodynamic stability but decrease the apparent kinetic stability (5, 6). In contrast, thin films covered with a top layer of another material do not show a significant evidence of reduced kinetic stability (21), indicating the nontrivial role of mobility gradients in thermal and kinetic stability.Stable glasses of most organic molecules, with short-range intramolecular interactions, have properties that are indicative of the same corresponding metastable SCL state as LQ and aged glasses, without any evidence of the existence of generic liquid–liquid phase transitions that can potentially provide a resolution for the Kauzmann entropy crisis (22). The Kauzmann crisis occurs at the Kauzmann temperature (TK), where the extrapolated SCL has the same structural entropy as the crystal, producing thermodynamically impossible states just below this temperature. Recently, Beasley et al. (16) showed that near-equilibrium states of ethylbenzene can be produced using PVD down to 2 K above TK and hypothesized that any phase transition to an “ideal glass” state to avoid the Kauzmann crisis must occur at TK.In some glasses of elemental substances (23, 24) and hydrogen-bonding compounds (25, 26), liquid–liquid phase transitions can occur between polyamorphic states with distinct local packing structures that correspond to polymorphic crystalline phases. For example, at high pressures, high- and low-density supercooled water phases are interconvertible through a first-order phase transition (27, 28). Recent studies have demonstrated that such polyamorphic states can also be accessed through PVD in hydrogen-bonding systems with polymorphic crystal states at depositions above the nominal Tg (29, 30). However, these structure-specific transitions do not provide a general resolution for the Kauzmann crisis.Here, we report the observation of a liquid–liquid phase transition in vapor-deposited thin films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD). TPD is a molecular glass former with only short-range intermolecular interactions. When thin films of TPD are vapor deposited onto substrates held at deposition temperatures (Tdep) below the nominal glass transition temperature of bulk TPD, Tg (bulk), films in the thickness range of 25 nm<h<55 nm achieve a high-density supercooled liquid (HD-SCL) state, which has not been previously observed. The liquid–liquid phase transition temperature (TLL) between the ordinary SCL and HD-SCL states is measured to be TLL≃Tg(bulk)−35 K. The density of thin films deposited below TLL tangentially follows the HD-SCL line, which has a stronger temperature dependence than the ordinary SCL. When vapor deposition is continued to produce thicker films (h>60 nm), the HD-SCL state transforms into the ordinary SCL state, indicating that the HD-SCL is only thermodynamically favored in the thin-film geometry. This transition is qualitatively different from the previously reported liquid–liquid phase transitions, as it is not related to a specific structural motif in TPD crystals, and it can only be observed in thin films, indicating that the energy landscape of thin films is favoring this high-density state.We observe an apparent correlation between enhanced mobility gradients in LQ thin films of TPD and the thickness range where HD-SCL states are produced during PVD. We hypothesize that enhanced mobility gradients are essential in providing access to regions of the energy landscape corresponding to the HD-SCL state, which are otherwise kinetically inaccessible. This hypothesis should be further investigated to better understand the origin of this phenomenon.     

Low-Reynolds-number,biflagellated Quincke swimmers with multiple forms of motion

In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of nonreciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a biflagellated sphere at low Re via Quincke rotation. These Quincke swimmers exhibit three different forms of motion, including a self-oscillatory state due to elastohydrodynamic–electrohydrodynamic interactions. Each form of motion follows a distinct trajectory in space. Our experiments and numerical results demonstrate a method to generate, and potentially control, the locomotion of artificial flagellated swimmers.

In a Newtonian fluid, locomotion of microswimmers requires nonreciprocal body motions (1–3). Bacteria or eukaryotic cells achieve this by beating or rotating their slender hair-like organelles, flagella (4, 5) or cilia (6), powered by molecular motors. Mimicking these organisms, artificial swimmers propelled by rotating helices (7, 8) or whipping filaments (9–12) have been fabricated. They are commonly driven by an external power source such as a magnetic field (7–9, 13, 14), sound (15), light (16, 17), and biological materials (12). However, there are very few electrically powered microswimmers (18–20), although electric fields have been exploited to drive other active systems (21–26) via a phenomenon called Quincke rotation (27).Quincke rotation originates from an electrohydrodynamic instability (28–30). Submerged in a liquid with permittivity εl and conductivity σl, a spherical particle with permittivity εs and electric conductivity σs is polarized under a uniform, steady electric field E→. When the particle is stationary, the induced dipole p→ due to the free charges is parallel or antiparallel to E→ (Fig. 1A): if the particle’s relaxation time τs=εs/σs is shorter than that of the ambient liquid, τl=εl/σl, p→ points in the same direction as E→; when τs>τl, p→ is opposite to E→, which generates an electric torque Γ→Q=p→×E→ that amplifies any angular perturbation. However, due to the resisting viscous torque Γ→μ, the system becomes unstable only when E=|E→| exceeds a threshold Ec. This instability causes the particle to rotate with a constant angular velocity ω:ω=1τEEc2−1,[1]where τ=εs+2εlσs+2σl is the relaxation time of the system (see SI Appendix, SI Text, or refs. 28, 29, 31 for derivation), and the rotational axis can be in any direction perpendicular to E→. During steady-state Quincke rotation, there is a constant angle between p→ and E→ (Fig. 1A), which results in a nonzero Γ→Q.Open in a separate windowFig. 1.Quincke rotation and the experimental setup. (A) Distribution of free charge and the corresponding dipole p→ on a sphere in a uniform, steady electric field E→. The sphere is (Left) stationary, (Middle) stationary, and (Right) rotating with a constant angular velocity ω. (B) A sketch of the biflagellated swimmer. Dashed lines show the roll axis (blue) and pitch axis (green). (C) A schematic illustration of the experimental setup.Recently, a flagellated swimmer in unbounded space driven by Quincke rotation has been proposed theoretically (32, 33). In light of the theory, we built a laboratory prototype, a biflagellated Quincke swimmer composed of a spherical particle and two attached elastic filaments, as shown in Fig. 1B, and systematically studied its behaviors at low Reynolds number (Re<0.3; Materials and Methods). Varying the electric field E→ and the angle between the two filaments, the Quincke swimmers exhibit three distinct forms of motion—two unidirectional rotations, which we call roll and pitch, and a self-oscillatory rotation, due to the balances between the electrical, elastic, and hydrodynamic torques, resulting in distinct trajectories in space. Surprisingly, it was recently reported (34) that spherical bacteria Magnetococcus marinus exhibit a similar pitch motion as our biflagellated artificial swimmers, which is rarely adopted by other microorganisms. Moreover, we found a threshold tail angle that separates the swimmers’ preferred forms of rotation, and within a small range close to this threshold angle, the three forms of motion coexist.     

Nonsteady fracture of transient networks: The case of vitrimer

We have discovered a peculiar form of fracture that occurs in polymer network formed by covalent adaptable bonds. Due to the dynamic feature of the bonds, fracture of this network is rate dependent, and the crack propagates in a highly nonsteady manner. These phenomena cannot be explained by the existing fracture theories, most of which are based on steady-state assumption. To explain these peculiar characteristics, we first revisit the fundamental difference between the transient network and the covalent network in which we highlighted the transient feature of the cracks. We extend the current fracture criterion for crack initiation to a time-evolution scheme that allows one to track the nonsteady propagation of a crack. Through a combined experimental modeling effort, we show that fracture in transient networks is governed by two parameters: the Weissenberg number W0 that defines the history path of crack-driving force and an extension parameter Z that tells how far a crack can grow. We further use our understanding to explain the peculiar experimental observation. To further leverage on this understanding, we show that one can “program” a specimen’s crack extension dynamics by tuning the loading history.

Understanding the conditions that lead to fracture in polymeric materials is an important problem of both industrial and fundamental interests. A common agreement is that fracture of polymer originates from successive chain scission resulting from the application of an excessive stress on the network (1). This consideration leads to the early work of Griffith that predicts the onset of crack propagation based on the competition between two quantities: the crack tip–driving force Gtip that provides the fuel for fracture and the intrinsic fracture toughness G0, which represents the material’s resistance to fracture (2). To propagate a crack, the former needs to reach or exceed the latter. This criterion further leads to deformation-based measurements such as the critical crack opening distance (COD) (3), critical stretch (4), or network damage models based on the chains’ stretch limit (5–7). These models have so far been instrumental in predicting the fracture of covalent polymer networks that are both elastic (2, 8–10) and viscoelastic (11–17). However, materials formed by weaker bonds [(e.g., covalent adaptable bonds (18), ionic interaction (19, 20), or entanglements (21–23)] exhibit a much richer fracture behavior that does not only depend on deformation but also greatly depends on the rate of loading (21, 22, 24). Due to their inherent weakness, these bonds are prone to spontaneous dissociation and reassociation over time under the effects of thermal fluctuations. This leads to a wide spectrum of rate-dependent mechanical response wherein the networks behave like viscous fluid at slow loading rates (relative to the rate of bond exchange), while they exhibit elastic solid-like behavior at fast loading (21). This coupling between deformation and network relaxation makes the prediction of fracture challenging, since the mechanical response becomes both time and rate dependent. In addition, the physical picture of chain scission at its stretch limit is no longer valid as a chain may dissociate in any conformation. This raises questions about the molecular origin of fracture and on its macroscopic manifestation and particularly, the conditions for its nucleation and its speed of propagation. Although some initial efforts were taken to understand the role of loading rate on fracture (22, 25) in transient networks, a systematic study of the physical rules behind crack characteristics, initiation, and propagation is still not established.To address these questions, we have carried out fracture experiments on a vitrimer network formed by disulfide bonds. In the presence of a catalyst, the bond exchange reaction (Fig. 1B) can be triggered by thermal fluctuations at room temperature (26). A full characterization of this network has been performed in our previous study (27). In this paper, we are specifically interested in the stress relaxation experiment, as it unveils the rate of bond exchange reaction (i.e., the bond dynamics). For this, we conducted a series of stress relaxation experiments at different stretch levels, in which the inverse of characteristic relaxation time is interpreted as the average rate of bond exchange at the applied deformation (28). After calibration, we found that bond dissociation is well described by the relation kd=kd0⁡exp(α(λe−1)), where kd0 is the spontaneous rate, and α=58.4 is a sensitivity parameter, as shown by the relaxation results in Fig. 1C and the fitting of relaxation time τR=1/kd in its Inset. This exponential dependency agrees with Eyring’s model (29, 30) based on the transition state theory. To characterize the response of this vitrimer in fracture, we then devised a pure-shear fracture experiment, where a precut sample of width L=35 mm and height H0 (10 mm), which contains a precut of length c0=15 mm, was stretched vertically at constant nominal strain rate λ˙=H˙/H0 (Fig. 2A). In what follows, this variable is normalized by the bond dynamics rate kd0 so that the ratio W0=λ˙/kd0 (denoted as the nominal Weissenberg number) describes the competition between network deformation and reconfiguration.Open in a separate windowFig. 1.(A) Schematic of the transient network, where (B) bond exchange reaction can spontaneously occur at rate kd. (C) Stress relaxation experiment at different strain λe with uniaxial tensile loading at large deformation (λe>1.3).Open in a separate windowFig. 2.(A) A schematic of fracture of the specimen. The crack tip–driving force G measures the elastic energy infused to the crack tip. (B) Measurement of crack extension during the deformation history. (C). Experimental and finite element simulation snapshots of crack profile under different loading rates. (Scale bar, 10 mm.)Our measurements of crack extension (Fig. 2 B and C) reveal three distinct characteristic regimes depending on the magnitude of W0. For a small loading rate (W0=0.095), the induced cut opens continuously and eventually becomes a curved edge. Over the course of the experiment, no observable fracture is recorded. For an intermediate rate (W0=0.19), a peculiar phenomenon occurs where a sharp crack first nucleates from the tip of the cut and quickly propagates with a characteristic trumpet-shaped profile (Fig. 2C). However, the propagation stops at a finite time, after which the crack “dies” and gives rise to a blunted edge. We note that this phenomenon is not observed in covalently crosslinked networks, since a propagating crack usually travels continuously at constant velocity through the specimen (31) under monotonic loading. Finally, for fast loading (W0=0.38), we similarly observe an initial blunting of the cut, quickly followed by crack nucleation. In this case, this newborn crack accelerates and fully ruptures the specimen. We used image processing techniques and measured the crack extension as a function of stretch λ (Fig. 2B), where we see that crack propagation is highly unsteady with varying velocity. The above observations cannot be explained by the current fracture theories for the following reasons. First, the onset of fracture highly depends on loading rate in addition to the level of deformation, therefore, a criterion derived from the elastic theory such as the COD or the critical stretch cannot be used. Second, the life of a propagation crack varies between loading conditions, where it may accelerate, decelerate, or even stop under monotonic loading.To understand these observations, we have recently developed a theoretical framework that allows one to evaluate the energetic fracture criterion and calculate crack velocity based on the stress field and bond dynamics (32). Combining this approach with finite element simulations (details provided in SI Appendix, Supplemental Information S2), we were able to simulate the nonsteady state fracture behavior of the vitrimer and qualitatively match the experimental crack profiles in Fig. 2C. Predominantly, our simulations suggest that crack initiation and propagation are associated with the increase of strain energy density ψ stored in the network, which itself is a function of nominal Weissenberg number W0 and loading history. In addition, the speed of the crack depends on both the magnitude of ψ and the sensitivity of bond dynamics kd upon deformation. In summary, our simulation work has allowed us to identify three kinetic rates that collectively govern fracture in transient networks: the rate of loading, the rate of bond dynamics, and the rate of crack propagation. The way by which these rates compete during fracture is however unclear. This work’s objective is thus to combine theoretical analysis with experiment and extract the physical mechanisms behind these peculiar phenomena.