Hot streaks in artistic, cultural, and scientific careers.

The hot streak-loosely defined as 'winning begets more winnings'-highlights a specific period during which an individual's performance is substantially better than his or her typical performance. Although hot streaks have been widely debated in sports1,2, gambling3-5 and financial markets6,7 over the past several decades, little is known about whether they apply to individual careers. Here, building on rich literature on the lifecycle of creativity8-22, we collected large-scale career histories of individual artists, film directors and scientists, tracing the artworks, films and scientific publications they produced. We find that, across all three domains, hit works within a career show a high degree of temporal regularity, with each career being characterized by bursts of high-impact works occurring in sequence. We demonstrate that these observations can be explained by a simple hot-streak model, allowing us to probe quantitatively the hot streak phenomenon governing individual careers. We find this phenomemon to be remarkably universal across diverse domains: hot streaks are ubiquitous yet usually unique across different careers. The hot streak emerges randomly within an individual's sequence of works, is temporally localized, and is not associated with any detectable change in productivity. We show that, because works produced during hot streaks garner substantially more impact, the uncovered hot streaks fundamentally drive the collective impact of an individual, and ignoring this leads us to systematically overestimate or underestimate the future impact of a career. These results not only deepen our quantitative understanding of patterns that govern individual ingenuity and success, but also may have implications for identifying and nurturing individuals whose work will have lasting impact.

Kramers-Wannier Duality and Random-Bond Ising Model.

We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on a planar graph and the corresponding dual graph, respectively, thereby explicitly demonstrating the Kramers-Wannier duality. The implications of our derived formula for the Random-Bond Ising Model are further elucidated.

Crossing-Symmetric Dispersion Relations without Spurious Singularities.

Recently, there has been renewed interest in a crossing-symmetric dispersion relation from the 1970s due to its implications for both regular quantum field theory and conformal field theory. However, this dispersion relation introduces nonlocal spurious singularities and requires additional locality constraints for their removal, a process that presents considerable technical challenges. In this Letter, we address this issue by deriving a new crossing-symmetric dispersion relation free of spurious singularities. Our formulation offers a compact and nonperturbative representation of the local block expansion, effectively resumming both Witten (in conformal field theory) and Feynman (in quantum field theory) diagrams. Consequently, we explicitly derive all contact terms in relation to the corresponding perturbative expansion. Our results establish a solid foundation for the Polyakov-Mellin bootstrap in conformal field theories and the crossing-symmetry S-matrix bootstrap in quantum field theories.

Emergence of Polarization in Coevolving Networks.

Polarization is a ubiquitous phenomenon in social systems. Empirical studies document substantial evidence for opinion polarization across social media, showing a typical bipolarized pattern devising individuals into two groups with opposite opinions. While coevolving network models have been proposed to understand polarization, existing works cannot generate a stable bipolarized structure. Moreover, a quantitative and comprehensive theoretical framework capturing generic mechanisms governing polarization remains unaddressed. In this Letter, we discover a universal scaling law for opinion distributions, characterized by a set of scaling exponents. These exponents classify social systems into bipolarized and depolarized phases. We find two generic mechanisms governing the polarization dynamics and propose a coevolving framework that counts for opinion dynamics and network evolution simultaneously. Under a few generic assumptions on social interactions, we find a stable bipolarized community structure emerges naturally from the coevolving dynamics. Our theory analytically predicts two-phase transitions across three different polarization phases in line with the empirical observations for the Facebook and blogosphere data sets. Our theory not only accounts for the empirically observed scaling laws but also allows us to predict scaling exponents quantitatively.

Reciprocal Patterns of Peer Speech in Preschoolers with and without Hearing Loss.

Children with hearing loss often attend inclusive preschool classrooms aimed at improving their spoken language skills. Although preschool classrooms are fertile environments for vocal interaction with peers, little is known about the dyadic processes that influence children's speech to one another and foster their language abilities and how these processes may vary in children with hearing loss. We used new objective measurement approaches to identify and quantify children's vocalizations during social contact, as determined by children's proximity and mutual orientation. The contributions of peer vocalizations to children's future vocalizations and language abilities were examined in oral language inclusion classrooms containing children with hearing loss who use hearing aids or cochlear implants and their typically hearing peers. Across over 600 hours of recorded vocal interactions of twenty-nine 2.5-3.5 year olds (16 girls) in three cohorts of children in a classroom, we found that vocalizations from each peer on a given observation predicted a child's vocalizations to that same peer on the subsequent observation. Children who produced more vocalizations to their peers had higher receptive and expressive language abilities, as measured by a standardized end-of-year language assessment. In fact, vocalizations from peers had an indirect association with end-of-year language abilities as mediated by children's vocalizations to peers. These findings did not vary as a function of hearing status. Overall, then, the results demonstrate the importance of dyadic peer vocal interactions for children's language use and abilities.

Scaling identity connects human mobility and social interactions.

Massive datasets that capture human movements and social interactions have catalyzed rapid advances in our quantitative understanding of human behavior during the past years. One important aspect affecting both areas is the critical role space plays. Indeed, growing evidence suggests both our movements and communication patterns are associated with spatial costs that follow reproducible scaling laws, each characterized by its specific critical exponents. Although human mobility and social networks develop concomitantly as two prolific yet largely separated fields, we lack any known relationships between the critical exponents explored by them, despite the fact that they often study the same datasets. Here, by exploiting three different mobile phone datasets that capture simultaneously these two aspects, we discovered a new scaling relationship, mediated by a universal flux distribution, which links the critical exponents characterizing the spatial dependencies in human mobility and social networks. Therefore, the widely studied scaling laws uncovered in these two areas are not independent but connected through a deeper underlying reality.

Cavity method for force transmission in jammed disordered packings of hard particles.

The force distribution of jammed disordered packings has always been considered a central object in the physics of granular materials. However, many of its features are poorly understood. In particular, analytic relations to other key macroscopic properties of jammed matter, such as the contact network and its coordination number, are still lacking. Here we develop a mean-field theory for this problem, based on the consideration of the contact network as a random graph where the force transmission becomes a constraint satisfaction problem. We can thus use the cavity method developed in the past few decades within the statistical physics of spin glasses and hard computer science problems. This method allows us to compute the force distribution P(f) for random packings of hard particles of any shape, with or without friction. We find a new signature of jamming in the small force behavior P(f) ∼ f(θ), whose exponent has attracted recent active interest: we find a finite value for P(f = 0), along with θ = 0. Furthermore, we relate the force distribution to a lower bound of the average coordination number z[combining macron](µ) of jammed packings of frictional spheres with coefficient µ. This bridges the gap between the two known isostatic limits z[combining macron]c (µ = 0) = 2D (in dimension D) and z[combining macron]c(µ → ∞) = D + 1 by extending the naive Maxwell's counting argument to frictional spheres. The theoretical framework describes different types of systems, such as non-spherical objects in arbitrary dimensions, providing a common mean-field scenario to investigate force transmission, contact networks and coordination numbers of jammed disordered packings.

A phase diagram for jammed matter.

The problem of finding the most efficient way to pack spheres has a long history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal. Apart from its mathematical interest, the problem has practical relevance in a wide range of fields, from granular processing to fruit packing. There are currently numerous experiments showing that the loosest way to pack spheres (random loose packing) gives a density of approximately 55 per cent. On the other hand, the most compact way to pack spheres (random close packing) results in a maximum density of approximately 64 per cent. Although these values seem to be robust, there is as yet no physical interpretation for them. Here we present a statistical description of jammed states in which random close packing can be interpreted as the ground state of the ensemble of jammed matter. Our approach demonstrates that random packings of hard spheres in three dimensions cannot exceed a density limit of approximately 63.4 per cent. We construct a phase diagram that provides a unified view of the hard-sphere packing problem and illuminates various data, including the random-loose-packed state.

Objective quantification of homophily in children with and without disabilities in naturalistic contexts.

Homophily, the tendency for individuals to preferentially interact with others similar to themselves is typically documented via self-report and, for children, adult report. Few studies have investigated homophily directly using objective measures of social movement. We quantified homophily in children with developmental disabilities (DD) and typical development (TD) using objective measures of position/orientation in preschool inclusion classrooms, designed to promote interaction between these groups of children. Objective measurements were collected using ultra-wideband radio-frequency tracking to determine social approach and social contact, measures of social movement and interaction. Observations of 77 preschoolers (47 with DD, and 30 TD) were conducted in eight inclusion classrooms on a total of 26 days. We compared DD and TD groups with respect to how children approached and shared time in social contact with peers using mixed-effects models. Children in concordant dyads (DD-DD and TD-TD) both moved toward each other at higher velocities and spent greater time in social contact than discordant dyads (DD-TD), evidencing homophily. DD-DD dyads spent less time in social contact than TD-TD dyads but were comparable to TD-TD dyads in their social approach velocities. Children's preference for similar peers appears to be a pervasive feature of their naturalistic interactions.

Simulating COVID19 transmission from observed movement.

Current models of COVID-19 transmission predict infection from reported or assumed interactions. Here we leverage high-resolution observations of interaction to simulate infectious processes. Ultra-Wide Radio Frequency Identification (RFID) systems were employed to track the real-time physical movements and directional orientation of children and their teachers in 4 preschool classes over a total of 34 observations. An agent-based transmission model combined observed interaction patterns (individual distance and orientation) with CDC-published risk guidelines to estimate the transmission impact of an infected patient zero attending class on the proportion of overall infections, the average transmission rate, and the time lag to the appearance of symptomatic individuals. These metrics highlighted the prophylactic role of decreased classroom density and teacher vaccinations. Reduction of classroom density to half capacity was associated with an 18.2% drop in overall infection proportion while teacher vaccination receipt was associated with a 25.3% drop. Simulation results of classroom transmission dynamics may inform public policy in the face of COVID-19 and similar infectious threats.

Self-similarity of complex networks.

Complex networks have been studied extensively owing to their relevance to many real systems such as the world-wide web, the Internet, energy landscapes and biological and social networks. A large number of real networks are referred to as 'scale-free' because they show a power-law distribution of the number of links per node. However, it is widely believed that complex networks are not invariant or self-similar under a length-scale transformation. This conclusion originates from the 'small-world' property of these networks, which implies that the number of nodes increases exponentially with the 'diameter' of the network, rather than the power-law relation expected for a self-similar structure. Here we analyse a variety of real complex networks and find that, on the contrary, they consist of self-repeating patterns on all length scales. This result is achieved by the application of a renormalization procedure that coarse-grains the system into boxes containing nodes within a given 'size'. We identify a power-law relation between the number of boxes needed to cover the network and the size of the box, defining a finite self-similar exponent. These fundamental properties help to explain the scale-free nature of complex networks and suggest a common self-organization dynamics.

Emergence of urban growth patterns from human mobility behavior.

Cities grow in a bottom-up manner, leading to fractal-like urban morphologies characterized by scaling laws. The correlated percolation model has succeeded in modeling urban geometries by imposing strong spatial correlations; however, the origin of the underlying mechanisms behind spatially correlated urban growth remains largely unknown. Our understanding of human movements has recently been revolutionized thanks to the increasing availability of large-scale human mobility data. This paper introduces a computational urban growth model that captures spatially correlated urban growth with a micro-foundation in human mobility behavior. We compare the proposed model with three empirical datasets, discovering that strong social interactions and long-term memory effects in human movements are two fundamental principles responsible for fractal-like urban morphology, along with the three important laws of urban growth. Our model connects the empirical findings in urban growth patterns and human mobility behavior.

A granular perspective on inclusion: Objectively measured interactions of preschoolers with and without autism.

Children's preschool experiences have consequences for development. However, it is not clear how children's real-time interactions with peers affect their language development; nor is it clear whether these processes differ between children with autism spectrum disorder (ASD) and two other groups of children, those with general developmental delays (DD) and typically developing (TD) children. We used objective measures of movement and vocalizations to quantify children's real-time dyadic vocal interactions and quantify classroom social networks. Participants included 56 preschoolers (22 female; M = 50.14 months) in five inclusive classrooms for children with ASD or DD and their TD peers. Each class was observed monthly on two to five occasions. Overall, children vocalized more to peers who had vocalized more to them in the previous observation. These dyadic vocalization patterns were associated with group differences in social network analyses. Modularity, the cohesiveness of group ties, was lower among children with ASD than it was among TD children or children with DD. Individually, children with ASD exhibited lower total levels of vocalizations with peers (lower degree centrality) than TD children and children with DD. In an exploratory analysis with a subset of the participants, children's degree centrality was strongly associated with their end-of-year assessed language abilities, even when accounting for mean differences between groups. Findings highlight the impact peers and social networks play in real-time language use and in the developing language abilities of children with ASD in inclusion classrooms. LAY SUMMARY: This study objectively measured associations between children's peer vocal interactions and assessed language abilities in inclusion classrooms for children with autism spectrum disorder (ASD) and their peers. All children benefited from peers talking to them, but children with ASD were less central to classroom speech networks than were typically developing children. Children's centrality to social speech networks, regardless of ASD status, was associated with assessed language abilities.

Small-world to fractal transition in complex networks: a renormalization group approach.

We show that renormalization group (RG) theory applied to complex networks is useful to classify network topologies into universality classes in the space of configurations. The RG flow readily identifies a small-world-fractal transition by finding (i) a trivial stable fixed point of a complete graph, (ii) a nontrivial point of a pure fractal topology that is stable or unstable according to the amount of long-range links in the network, and (iii) another stable point of a fractal with shortcuts that exist exactly at the small-world-fractal transition. As a collateral, the RG technique explains the coexistence of the seemingly contradicting fractal and small-world phases and allows us to extract information on the distribution of shortcuts in real-world networks, a problem of importance for information flow in the system.

Effects of microsurgical repair treatment on the clinical efficacy, complications, and flap follow-up scores of patients with exposed steel plates after surgery for foot and ankle fractures.

BACKGROUND: Treatment of exposed steel plates after surgery for foot and ankle fractures is complicated. This study aims to analyze the effects of microsurgical repair treatment on the clinical efficacy, complications, and flap follow-up scores of patients with exposed steel plates following foot and ankle fracture surgery. METHODS: Eighty-two patients with exposure of steel plates after surgical treatment for foot and ankle fractures in our hospital from March 2017 to March 2018 were included in this study. The patients were divided into a study group (43 patients who received microsurgical repair) and a control group (39 patients who received conventional repair surgery). We compared the clinical efficacy, complication rate, flap followup score, recovery of ankle-hindfoot function and ankle function before treatment and at 3 and 6 months after treatment, and patient satisfaction between the two groups. RESULTS: The clinical effectiveness rate in the study group was 95.35%, which was higher than the control group (76.92%) (P<0.05). The flap appearance, texture, and elasticity scores in the study group were higher than those in the control group (P<0.05). After treatment, the American Orthopedic Foot and Ankle Society (AOFAS) score and Baird ankle score increased significantly in both groups, and reached a peak at 6 months after treatment. The peak scores of the study group were considerably higher than those of the control group at each period after treatment (P<0.05). The incidence of complications in the study group (6.98%) was lower than the control group (25.64%) (P<0.05). Patient satisfaction was higher in the study group (97.67%) than the control group (79.49%) (P<0.05). CONCLUSIONS: Microsurgical repair of exposed steel plates after surgery for foot and ankle fractures has a significant clinical effect. It can improve the flap follow-up scores, accelerate healing of the ankle, improve aesthetics, and reduce the incidence of complications. It is therefore worthy of widespread use in clinics.

Emergence of scaling in complex substitutive systems.

Diffusion processes are central to human interactions. One common prediction of the current modelling frameworks is that initial spreading dynamics follow exponential growth. Here we find that, for subjects ranging from mobile handsets to automobiles and from smartphone apps to scientific fields, early growth patterns follow a power law with non-integer exponents. We test the hypothesis that mechanisms specific to substitution dynamics may play a role, by analysing unique data tracing 3.6 million individuals substituting different mobile handsets. We uncover three generic ingredients governing substitutions, allowing us to develop a minimal substitution model, which not only explains the power-law growth, but also collapses diverse growth trajectories of individual constituents into a single curve. These results offer a mechanistic understanding of power-law early growth patterns emerging from various domains and demonstrate that substitution dynamics are governed by robust self-organizing principles that go beyond the particulars of individual systems.

Continuous measurement of dynamic classroom social interactions.

Human observations can only capture a portion of ongoing classroom social activity, and are not ideal for understanding how children's interactions are spatially structured. Here we demonstrate how social interaction can be investigated by modeling automated continuous measurements of children's location and movement using a commercial system based on radio frequency identification. Continuous location data were obtained from 16 five-year-olds observed during three 1-h classroom free play observations. Illustrative coordinate mapping indicated that boys and girls tended to cluster in different physical locations in the classroom, but there was no suggestion of gender differences in children's velocity (i.e., speed of movement). To detect social interaction, we present the radial distribution function, an index of when children were in social contact at greater than chance levels. Rank-order plots indicated that children were in social contact tens to hundreds of times more with some peers than others. We illustrate the use of social ties (higher than average levels of social contact) to visualize the classroom network. Analysis of the network suggests that transitivity is a potential lens through which to examine male, female, and mixed-sex cliques. The illustrative findings suggest the validity of the new measurement approach by re-examining well-established gender segregation findings from a new perspective.

Particle dynamics and effective temperature of jammed granular matter in a slowly sheared three-dimensional Couette cell.

We report experimental measurements of particle dynamics on slowly sheared granular matter in a three-dimensional Couette cell. A closely packed ensemble of transparent spherical beads is confined by an external pressure and filled with fluid to match both the density and refractive index of the beads. This allows us to track tracer particles embedded in the system and obtain three-dimensional trajectories [r(t),theta(t),z(t)] as a function of time. We study the probability distribution function of the vertical and radial displacements, finding Gaussian and exponential distributions, respectively. For slow shear rates, the mean-square fluctuations in all three directions are found to be dependent only on the angular displacement of the Couette cell, Delta theta e, (Delta z 2) approximately Delta theta e, (Delta r2) approximately Delta theta e alpha, Delta theta 2 approximately Delta theta e beta, where alpha and beta are constants. With Delta theta e proportional to the time between measurements, the values of the constants, alpha and beta , are found to be subdiffusive and superdiffusive, respectively. ThFe linear relation between (Delta z 2) and angular displacement implies a diffusive process, from which we can calculate an "effective temperature," T eff, in the vertical direction, through a fluctuation-dissipation relation. It is of interest to determine whether these systems can be described by analogous equilibrium statistical mechanics concepts such as "effective temperature" and "compactivity." By studying the dynamics of tracer particles, we find the effective temperature defined by the Stokes-Einstein relation to be independent of the tracer particle characteristic features, such as density and size, and dependent only on the packing density of the system. For slow shear rate, both the diffusivity and mobility of tracer particles are proportional to the shear rate, giving rise to a constant effective temperature, characteristic of the jammed system. We finally discuss the significance of the existence of T eff for a statistical mechanics formulation of granular matter.

Quantifying the evolution of individual scientific impact.

Despite the frequent use of numerous quantitative indicators to gauge the professional impact of a scientist, little is known about how scientific impact emerges and evolves in time. Here, we quantify the changes in impact and productivity throughout a career in science, finding that impact, as measured by influential publications, is distributed randomly within a scientist's sequence of publications. This random-impact rule allows us to formulate a stochastic model that uncouples the effects of productivity, individual ability, and luck and unveils the existence of universal patterns governing the emergence of scientific success. The model assigns a unique individual parameter Q to each scientist, which is stable during a career, and it accurately predicts the evolution of a scientist's impact, from the h-index to cumulative citations, and independent recognitions, such as prizes.