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Groundwater exists in underground aquifers and is largely hidden and intangible to water users. As such, groundwater models are one of the main vehicles through which groundwater is made legible. They are critical for water supply planning purposes. However, models are imperfect representations of limited data and contain much uncertainty, posing challenges for the water supply planning process. In this paper, we draw on a case from the Greater Chicago area to examine efforts by the authors and the Illinois State Water Survey to engage with local water managers to develop future water supply scenarios. Much of this area has been dependent upon the Cambrian-Ordovician Aquifer System for over 150 years. Over this period, water levels have declined by over 300 m and aquifers are expected to be unviable by 2030. Here we advance the growing field of participatory groundwater modelling (PGM) to identify forms of uncertainty and their influence on understandings of water supply and risk perceptions of depletion. Conceptually, we draw on the idea of models as world builders, where uncertainties are elucidated through knowledge production in the act of model building, while model development is simultaneously influenced by expectations, beliefs, and ambiguity surrounding those using the models. Through planning meetings and focus group discussions between groundwater modelers and water supply stakeholders, we identify four forms of interconnected uncertainty that hinder planning efforts: 1) hydrogeologic uncertainty, 2) modelling uncertainty; 3) water demand uncertainty; and 4) urban planning uncertainty. We describe our PGM efforts to reduce uncertainty and find stakeholder perceptions are as important as model uncertainties in water management decisions. Participatory modelling is effective in reducing and clarifying these four forms of uncertainty, particularly applied to short-term management decisions in a rapidly changing system. We conclude that future participatory modelling efforts need to focus on reducing communication barriers between scientists and local users.

The social worlds of young children primarily revolve around parents and caregivers, who play a key role in guiding children's social and cognitive development. However, a hallmark of adolescence is a shift in orientation toward nonfamilial social targets, an adaptive process that prepares adolescents for their independence. Little is known regarding neurobiological signatures underlying changes in adolescents' social orientation. Using functional brain imaging of human voice processing in children and adolescents (ages 7-16), we demonstrate distinct neural signatures for mother's voice and nonfamilial voices across child and adolescent development in reward and social valuation systems, instantiated in nucleus accumbens and ventromedial prefrontal cortex. While younger children showed greater activity in these brain systems for mother's voice compared with nonfamilial voices, older adolescents showed the opposite effect with increased activity for nonfamilial compared with mother's voice. Findings uncover a critical role for reward and social valuative brain systems in the pronounced changes in adolescents' orientation toward nonfamilial social targets. Our approach provides a template for examining developmental shifts in social reward and motivation in individuals with pronounced social impairments, including adolescents with autism.SIGNIFICANCE STATEMENTChildren's social worlds undergo a transformation during adolescence. While socialization in young children revolves around parents and caregivers, adolescence is characterized by a shift in social orientation toward nonfamilial social partners. Here we show that this shift is reflected in neural activity measured from reward processing regions in response to brief vocal samples. When younger children hear their mother's voice, reward processing regions show greater activity compared with when they hear nonfamilial, unfamiliar voices. Strikingly, older adolescents show the opposite effect, with increased activity for nonfamilial compared with mother's voice. Findings identify the brain basis of adolescents' switch in social orientation toward nonfamilial social partners and provides a template for understanding neurodevelopment in clinical populations with social and communication difficulties.

During social interactions, speakers signal information about their emotional state through their voice, which is known as emotional prosody. Little is known regarding the precise brain systems underlying emotional prosody decoding in children and whether accurate neural decoding of these vocal cues is linked to social skills. Here, we address critical gaps in the developmental literature by investigating neural representations of prosody and their links to behavior in children. Multivariate pattern analysis revealed that representations in the bilateral middle and posterior superior temporal sulcus (STS) divisions of voice-sensitive auditory cortex decode emotional prosody information in children. Crucially, emotional prosody decoding in middle STS was correlated with standardized measures of social communication abilities; more accurate decoding of prosody stimuli in the STS was predictive of greater social communication abilities in children. Moreover, social communication abilities were specifically related to decoding sadness, highlighting the importance of tuning in to negative emotional vocal cues for strengthening social responsiveness and functioning. Findings bridge an important theoretical gap by showing that the ability of the voice-sensitive cortex to detect emotional cues in speech is predictive of a child’s social skills, including the ability to relate and interact with others.

BACKGROUND Sickle cell disease (SCD) is the most common inherited blood disorder affecting millions of people worldwide. Most patients with SCD experience repeated, unpredictable episodes of severe pain. These pain episodes are the leading cause of emergency department visits among patients with SCD and may last for several weeks. Arguably, the most challenging aspect of treating pain episodes in SCD is assessing and interpreting a patient’s pain intensity level. OBJECTIVE This study aims to learn deep feature representations of subjective pain trajectories using objective physiological signals collected from electronic health records. METHODS This study used electronic health record data collected from 496 Duke University Medical Center participants over 5 consecutive years. Each record contained measures for 6 vital signs and the patient’s self-reported pain score, with an ordinal range from 0 (no pain) to 10 (severe and unbearable pain). We also extracted 3 features related to medication: medication type, medication status (given or applied, or missed or removed or due), and total medication dosage (mg/mL). We used variational autoencoders for representation learning and designed machine learning classification algorithms to build pain prediction models. We evaluated our results using an accuracy and confusion matrix and visualized the qualitative data representations. RESULTS We designed a classification model using raw data and deep representational learning to predict subjective pain scores with average accuracies of 82.8%, 70.6%, 49.3%, and 47.4% for 2-point, 4-point, 6-point, and 11-point pain ratings, respectively. We observed that random forest classification models trained on deep represented features outperformed models trained on unrepresented data for all pain rating scales. We observed that at varying Likert scales, our models performed better when provided with medication data along with vital signs data. We visualized the data representations to understand the underlying latent representations, indicating neighboring representations for similar pain scores with a higher resolution of pain ratings. CONCLUSIONS Our results demonstrate that medication information (the type of medication, total medication dosage, and whether the medication was given or missed) can significantly improve subjective pain prediction modeling compared with modeling with only vital signs. This study shows promise in data-driven estimated pain scores that will help clinicians with additional information about the patient’s condition, in addition to the patient’s self-reported pain scores.

Background Sickle cell disease (SCD) is the most common inherited blood disorder affecting millions of people worldwide. Most patients with SCD experience repeated, unpredictable episodes of severe pain. These pain episodes are the leading cause of emergency department visits among patients with SCD and may last for several weeks. Arguably, the most challenging aspect of treating pain episodes in SCD is assessing and interpreting a patient’s pain intensity level. Objective This study aims to learn deep feature representations of subjective pain trajectories using objective physiological signals collected from electronic health records. Methods This study used electronic health record data collected from 496 Duke University Medical Center participants over 5 consecutive years. Each record contained measures for 6 vital signs and the patient’s self-reported pain score, with an ordinal range from 0 (no pain) to 10 (severe and unbearable pain). We also extracted 3 features related to medication: medication type, medication status (given or applied, or missed or removed or due), and total medication dosage (mg/mL). We used variational autoencoders for representation learning and designed machine learning classification algorithms to build pain prediction models. We evaluated our results using an accuracy and confusion matrix and visualized the qualitative data representations. Results We designed a classification model using raw data and deep representational learning to predict subjective pain scores with average accuracies of 82.8%, 70.6%, 49.3%, and 47.4% for 2-point, 4-point, 6-point, and 11-point pain ratings, respectively. We observed that random forest classification models trained on deep represented features outperformed models trained on unrepresented data for all pain rating scales. We observed that at varying Likert scales, our models performed better when provided with medication data along with vital signs data. We visualized the data representations to understand the underlying latent representations, indicating neighboring representations for similar pain scores with a higher resolution of pain ratings. Conclusions Our results demonstrate that medication information (the type of medication, total medication dosage, and whether the medication was given or missed) can significantly improve subjective pain prediction modeling compared with modeling with only vital signs. This study shows promise in data-driven estimated pain scores that will help clinicians with additional information about the patient’s condition, in addition to the patient’s self-reported pain scores.

Firms in the U.S. spend over 200 billion dollars each year advertising their products to consumers, around one percent of the country's gross domestic product. It is of great interest to understand how that aggregate expenditure affects prices, market efficiency, and overall welfare. Here, we present a mathematical model for the dynamics of competition through advertising and find a surprising prediction: when advertising is relatively cheap compared to the maximum benefit advertising offers, rational firms split into two groups, one with significantly less advertising (a "generic" group) and one with significantly more advertising (a "name brand" group). Our model predicts that this segmentation will also be reflected in price distributions; we use large consumer data sets to test this prediction and find good qualitative agreement., 24 pages, 11 figures

Faults can act as flow barriers or conduits to groundwater flow by introducing heterogeneity in permeability. We examine the hydrogeology of the Sandwich Fault Zone, a 137 km long zone of high-angle faults in northern Illinois, using a large-scale historic aquifer test. The fault zone is poorly understood at depth due to the majority of the faults being buried by glacial deposits and its near-vertical orientation which limits geologic sampling across faults. The aquifer test-perhaps one of the largest in terms of overall withdrawal in North American history-was conducted in 1942 at a facility adjacent to the fault zone. More than 34,000 m3 /day was pumped for 37 days from nine multiaquifer wells open to the stratified Cambrian-Ordovician sandstone aquifer system. We modeled the aquifer test using a transient MODFLOW-USG model and simulated pumping wells with the CLN package. We tested numerous fault core/damage zone conceptualizations and calibrated to drawdown values recorded at production and observation wells. Our analysis indicates that the fault zone is a low-permeability feature that inhibits lateral movement of groundwater and that there is at least an order of magnitude decrease in horizontal hydraulic conductivity in the fault core compared to the undeformed sandstone. Large head declines have occurred north of the fault zone (over 300 m since predevelopment conditions) and modifying fault zone parameters significantly affects calibration to regional drawdown on a decadal scale. The flow-barrier behavior of the fault zone has important implications for future groundwater availability in this highly stressed region.

Deep basin aquifers are increasingly used in water‐stressed areas, though their potential for sustainable development is inhibited by overlying aquitards and limited recharge rates. Long open interval wells (LOIWs)—wells uncased through multiple hydrostratigraphic units—are present in many confined aquifer systems and can be an important mechanism for deep basin aquifers to receive flow across aquitards. LOIWs are a major control on flow in the deep Cambrian–Ordovician sandstone aquifers of the upper Midwest, USA, providing a source of artificial leakage from shallow bedrock aquifers and equilibrating head within the sandstone aquifers despite differential pumpage. Conceptualizing and quantifying this anthropogenic flow has long been a challenge for groundwater flow modellers, particularly on a regional scale. Synoptic measurements of active production wells and well completion data for northeast Illinois form the basis for a transient, head‐specified MODFLOW model that determines mass balance contributions to the region and estimates LOIW leakage to the aquifers. Using this insight, transient LOIW leakage was simulated using transiently changing KV zones in a traditional, Q‐specified MODFLOW‐USG model, a novel approach that allows the KV in a cell containing a LOIW to change transiently by use of the time‐variant materials (TVM) package. With this modification, we achieved a consistent calibration through time, averaging 19.9 m root mean squared error. This model indicates that artificial leakage via LOIWs contributed a minimum of 10–13% of total flow to the sandstone aquifers through the entire history of pumping, up to 50% of flow around 1930. Removal from storage exceeds 40% of flow during peak withdrawals, much of this flow sourced from units other than the primary sandstone aquifers via LOIWs. As such, understanding the timing and magnitude of LOIW leakage is essential for predicting future water availability in deep basin aquifers.

The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Using theoretical analysis and numerical simulation, we demonstrate that competition between individuals that is linked to the mean gamete size will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy., Comment: 8 pages, 8 figures

Sickle cell disease (SCD) is a red blood cell disorder complicated by lifelong issues with pain. Management of SCD related pain is particularly challenging due to its subjective nature. Hence, the development of an objective automatic pain assessment method is critical to pain management in SCD. In this work, we developed a continuous pain assessment model using physiological and body movement sensor signals collected from a wearable wrist-worn device. Specifically, we implemented ensemble feature selection methods to select robust and stable features extracted from wearable data for better understanding of pain. Our experiments showed that the stability of feature selection methods could be substantially increased by using the ensemble approach. Since different ensemble feature selection methods prefer varying feature subsets for pain estimation, we further utilized stacked generalization to maximize the information usage contained in the selected features from different methods. Using this approach, our best performing model obtained the root-mean-square error of 1.526 and the Pearson correlation of 0.618 for continuous pain assessment. This indicates that subjective pain scores can be estimated using objective wearable sensor data with high precision.

Since the 1960s, Democrats and Republicans in U.S. Congress have taken increasingly polarized positions, while the public's policy positions have remained centrist and moderate. We explain this apparent contradiction by developing a dynamical model that predicts ideological positions of political parties. Our approach tackles the challenge of incorporating bounded rationality into mathematical models and integrates the empirical finding of satisficing decision making---voters settle for candidates who are "good enough" when deciding for whom to vote. We test the model using data from the U.S. Congress over the past 150 years, and find that our predictions are consistent with the two major political parties' historical trajectory. In particular, the model explains how polarization between the Democrats and Republicans since the 1960s could be a consequence of increasing ideological homogeneity within the parties., 13 pages, 5 figures

Sickle Cell Disease (SCD) is a hereditary disorder of red blood cells in humans. Complications such as pain, stroke, and organ failure occur in SCD as malformed, sickled red blood cells passing through small blood vessels get trapped. Particularly, acute pain is known to be the primary symptom of SCD. The insidious and subjective nature of SCD pain leads to challenges in pain assessment among Medical Practitioners (MPs). Thus, accurate identification of markers of pain in patients with SCD is crucial for pain management. Classifying clinical notes of patients with SCD based on their pain level enables MPs to give appropriate treatment. We propose a binary classification model to predict pain relevance of clinical notes and a multiclass classification model to predict pain level. While our four binary machine learning (ML) classifiers are comparable in their performance, Decision Trees had the best performance for the multiclass classification task achieving 0.70 in F-measure. Our results show the potential clinical text analysis and machine learning offer to pain management in sickle cell patients., The 42nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society

Pain in sickle cell disease (SCD) is often associated with increased morbidity, mortality, and high healthcare costs. The standard method for predicting the absence, presence, and intensity of pain has long been self-report. However, medical providers struggle to manage patients based on subjective pain reports correctly and pain medications often lead to further difficulties in patient communication as they may cause sedation and sleepiness. Recent studies have shown that objective physiological measures can predict subjective self-reported pain scores for inpatient visits using machine learning (ML) techniques. In this study, we evaluate the generalizability of ML techniques to data collected from 50 patients over an extended period across three types of hospital visits (i.e., inpatient, outpatient and outpatient evaluation). We compare five classification algorithms for various pain intensity levels at both intra-individual (within each patient) and inter-individual (between patients) level. While all the tested classifiers perform much better than chance, a Decision Tree (DT) model performs best at predicting pain on an 11-point severity scale (from 0-10) with an accuracy of 0.728 at an inter-individual level and 0.653 at an intra-individual level. The accuracy of DT significantly improves to 0.941 on a 2-point rating scale (i.e., no/mild pain: 0-5, severe pain: 6-10) at an intra-individual level. Our experimental results demonstrate that ML techniques can provide an objective and quantitative evaluation of pain intensity levels for all three types of hospital visits., Comment: Accepted for presentation at the FIRST WORKSHOP ON COMPUTATIONAL & AFFECTIVE INTELLIGENCE IN HEALTHCARE APPLICATIONS (VULNERABLE POPULATIONS) In Conjunction with the International Conference on Pattern Recognition (ICPR) 2021

Background Sickle cell disease (SCD) is an inherited red blood cell disorder affecting millions worldwide, and it results in many potential medical complications throughout the life course. The hallmark of SCD is pain. Many patients experience daily chronic pain as well as intermittent, unpredictable acute vaso-occlusive painful episodes called pain crises. These pain crises often require acute medical care through the day hospital or emergency department. Following presentation, a number of these patients are subsequently admitted with continued efforts of treatment focused on palliative pain control and hydration for management. Mitigating pain crises is challenging for both the patients and their providers, given the perceived unpredictability and subjective nature of pain. Objective The objective of this study was to show the feasibility of using objective, physiologic measurements obtained from a wearable device during an acute pain crisis to predict patient-reported pain scores (in an app and to nursing staff) using machine learning techniques. Methods For this feasibility study, we enrolled 27 adult patients presenting to the day hospital with acute pain. At the beginning of pain treatment, each participant was given a wearable device (Microsoft Band 2) that collected physiologic measurements. Pain scores from our mobile app, Technology Resources to Understand Pain Assessment in Patients with Pain, and those obtained by nursing staff were both used with wearable signals to complete time stamp matching and feature extraction and selection. Following this, we constructed regression and classification machine learning algorithms to build between-subject pain prediction models. Results Patients were monitored for an average of 3.79 (SD 2.23) hours, with an average of 5826 (SD 2667) objective data values per patient. As expected, we found that pain scores and heart rate decreased for most patients during the course of their stay. Using the wearable sensor data and pain scores, we were able to create a regression model to predict subjective pain scores with a root mean square error of 1.430 and correlation between observations and predictions of 0.706. Furthermore, we verified the hypothesis that the regression model outperformed the classification model by comparing the performances of the support vector machines (SVM) and the SVM for regression. Conclusions The Microsoft Band 2 allowed easy collection of objective, physiologic markers during an acute pain crisis in adults with SCD. Features can be extracted from these data signals and matched with pain scores. Machine learning models can then use these features to feasibly predict patient pain scores.

Background: Sickle Cell Disease (SCD) is a chronic blood disorder in which complications result from vaso-occlusion. Pain is the most common symptom reported in patients with SCD and includes both acute unpredictable pain as well as chronic pain. Chronic pain is clinically defined as having more days with pain than without pain over a period of 6 months. Various classifications systems have been developed to better understand pain phenotypes, however, there is variability in data and groupings of patients. Recent work based on patient-reported outcome data has shown that patients may be classified into three subgroups: infrequent acute pain, limited recent pain with moderate long-term pain, and persistent severe pain. An improved understanding of the ways in which pain dynamics manifest over time will allow patients and medical providers to better manage pain. Using previously-published data which collected self-reported data through a mobile app over 6 months (Clifton et al., 2017, J. Comput. Biol.), we aimed to characterize the different ways in which patients experienced pain over time. In this work, we sought to identify classes of patients based only on their self reported pain levels. Methods: Patients within the previously-published study were asked to self-report their pain levels from 0-10 on a daily basis through a mobile app. The study included 39 patients (16 male, 23 female), with a mean age of 33.4. Patients reported their pain an average of 0.4 times per day over an average of 164.6 days. To allow for the possibility that patients' experiences change over time, we windowed the time series of pain dynamics into non-overlapping two-week windows. Within each window, the data were linearly interpolated to regularly-spaced samples. Then, we applied spectral clustering to identify classes of similar pain trajectories within the windowed data. Within the data, we also identified patients with and without chronic pain within the sample based on whether or not they have taken long-acting opioid medications, which are commonly prescribed for those with a diagnosis of chronic pain. With this identification, we compared patients within the identified classes with patients diagnosed with chronic pain. Results: We found that three classes of pain dynamics may be identified from the data considered: class I, class II, and class III (Figure). Class I pain trajectories have mild baseline pain, typically 0, with acute exacerbations of low to medium pain levels. Class II trajectories show moderate mean pain values, and show large variation within each trajectory. Class III trajectories show consistently high pain levels, rarely dropping below 7. All three classes include patients who have been diagnosed with chronic pain, but the proportion of patients with chronic pain differs. Patients with chronic pain represented 32% of samples in class I, 83% of samples in class II, and 86% of samples in class III. Conclusions: Based only on self-reported pain over time, clustering pain experiences into classes yields three distinct classes. These classes do not perfectly align with chronic pain diagnoses, but classes II and III both contain mostly chronic pain patients. Based on this and the unique behaviors of those classes, it may be useful to differentiate chronic pain into persistent chronic pain and intermittent chronic pain. Moreover, the findings of these classes are similar to results found from analyzing patient reported outcomes and show promise for the continued use of mHealth apps to acquire patient reported symptoms. Figure 1 Figure 1. Disclosures Shah: CSL Behring: Consultancy; Emmaus: Consultancy; Novartis: Research Funding, Speakers Bureau; Bluebird Bio: Consultancy; Guidepoint Global: Consultancy; GLG: Consultancy; Alexion: Speakers Bureau; GBT: Consultancy, Research Funding, Speakers Bureau.

A novel structural engineering design approach is described where flexibility can be added to a masonry shear wall system with the use of a series of steel connector plates that transfer seismic story shear forces to individual masonry wall panels. This innovative form of building construction is termed “hybrid masonry” since structural steel frames resist lateral forces with the help of engineered structural masonry panels. The steel connector plates are undersized to have considerable flexibility and a relatively low flexural strength. Acting as fuses, these connectors will not only reduce the overall lateral stiffness of a building system, but also dissipate seismic energy through hysteresis. In so doing, the integrity of the structural system to withstand earthquake motions is enhanced. As well, repair costs will be minimized since masonry damage can be circumvented. Thus, maintenance issues associated with costly seismic repairs can be avoided. Results of computations are given that show how ...

Speech perception relies on a listener's ability to simultaneously resolve multiple temporal features in the speech signal. Little is known regarding neural mechanisms that enable the simultaneous coding of concurrent temporal features in speech. Here we show that two categories of temporal features in speech, the low-frequency speech envelope and periodicity cues, are processed by distinct neural mechanisms within the same population of cortical neurons. We measured population activity in primary auditory cortex of anesthetized guinea pig in response to three variants of a naturally produced sentence. Results show that the envelope of population responses closely tracks the speech envelope, and this cortical activity more closely reflects wider bandwidths of the speech envelope compared to narrow bands. Additionally, neuronal populations represent the fundamental frequency of speech robustly with phase-locked responses. Importantly, these two temporal features of speech are simultaneously observed within neuronal ensembles in auditory cortex in response to clear, conversation, and compressed speech exemplars. Results show that auditory cortical neurons are adept at simultaneously resolving multiple temporal features in extended speech sentences using discrete coding mechanisms.

Speech engages distributed temporo-fronto-parietal brain regions, however a comprehensive understanding of its intrinsic functional network architecture is lacking. Here we investigate the human speech processing network using the largest sample to date, high temporal resolution resting-state fMRI data, network stability analysis, and theoretically informed models. Network consensus analysis revealed three stable functional modules encompassing: (1) superior temporal plane (STP) and Area Spt, (2) superior temporal sulcus (STS) + ventral frontoparietal cortex, and (3) dorsal frontoparietal cortex. The STS + ventral frontoparietal cortex module showed the highest participation coefficient, and a hub-like organization linking STP with frontoparietal cortical nodes. Node-wise analysis revealed key connectivity features underlying this modular architecture, including a leftward asymmetric connectivity profile, and differential connectivity of STS and STP, with frontoparietal cortex. Our findings, replicated across cohorts, reveal a tripartite functional network architecture supporting speech processing and provide a novel template for future studies.

Urban outputs often scale superlinearly with city population. A difficulty in understanding the mechanism of this phenomenon is that different outputs differ considerably in their scaling behaviors. Here, we formulate a physics-based model for the origin of superlinear scaling in urban outputs by treating human interaction as a random process. Our model suggests that the increased likelihood of finding required collaborations in a larger population can explain this superlinear scaling, which our model predicts to be non-power-law. Moreover, the extent of superlinearity should be greater for activities that require more collaborators. We test this model using a novel dataset for seven crime types and find strong support., Comment: 8 pages, 5 figures

OBJECTIVES: Our aim was to conduct a randomized controlled trial to evaluate a pivotal response treatment package (PRT-P) consisting of parent training and clinician-delivered in-home intervention on the communication skills of children with autism spectrum disorder. METHODS: Forty-eight children with autism spectrum disorder and significant language delay between 2 and 5 years old were randomly assigned to PRT-P (n = 24) or the delayed treatment group (n = 24) for 24 weeks. The effect of treatment on child communication skills was assessed via behavioral coding of parent-child interactions, standardized parent-report measures, and blinded clinician ratings. RESULTS: Analysis of child utterances during the structured laboratory observation revealed that, compared with the delayed treatment group, children in PRT-P demonstrated greater improvement in frequency of functional utterances (F1,41 = 6.07; P = .026; d = 0.61). The majority of parents in the PRT-P group (91%) were able to implement pivotal response treatment (PRT) with fidelity within 24 weeks. Children receiving PRT-P also demonstrated greater improvement on the Brief Observation of Social Communication Change, on the Clinical Global Impressions Improvement subscale, and in number of words used on a parent-report questionnaire. CONCLUSIONS: This is the first 24-week randomized controlled trial in which community treatment is compared with the combination of parent training and clinician-delivered PRT. PRT-P was effective for improving child social communication skills and for teaching parents to implement PRT. Additional research will be needed to understand the optimal combination of treatment settings, intensity, and duration, and to identify child and parent characteristics associated with treatment response.

Perhaps because of the elegance of the central limit theorem, it is often assumed that distributions in nature will approach singly-peaked, unimodal shapes reminiscent of the Gaussian normal distribution. However, many systems behave differently, with variables following apparently bimodal or multimodal distributions. Here we argue that multimodality may emerge naturally as a result of repulsive or inhibitory coupling dynamics, and we show rigorously how it emerges for a broad class of coupling functions in variants of the paradigmatic Kuramoto model., 11 pages, 12 figures