Unperturbed Schelling Segregation in Two or Three Dimensions

Schelling’s models of segregation, first described in 1969 (Am Econ Rev 59:488–493, 1969) are among the best known models of self-organising behaviour. Their original purpose was to identify mechanisms of urban racial segregation. But his models form part of a family which arises in statistical mechanics, neural networks, social science, and beyond, where populations of agents interact on networks. Despite extensive study, unperturbed Schelling models have largely resisted rigorous analysis, prior results generally focusing on variants in which noise is introduced into the dynamics, the resulting system being amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory (Young in Individual strategy and social structure: an evolutionary theory of institutions, Princeton University Press, Princeton, 1998). A series of recent papers (Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012); Barmpalias et al. in: 55th annual IEEE symposium on foundations of computer science, Philadelphia, 2014, J Stat Phys 158:806–852, 2015), has seen the first rigorous analyses of 1-dimensional unperturbed Schelling models, in an asymptotic framework largely unknown in statistical mechanics. Here we provide the first such analysis of 2- and 3-dimensional unperturbed models, establishing most of the phase diagram, and answering a challenge from Brandt et al. in: Proceedings of the 44th annual ACM symposium on theory of computing (STOC 2012), 2012)

Minority population in the one-dimensional Schelling model of segregation

Schelling models of segregation attempt to explain how a population of agents or particles of two types may organise itself into large homogeneous clusters. They can be seen as variants of the Ising model. While such models have been extensively studied, unperturbed (or noiseless) versions have largely resisted rigorous analysis, with most results in the literature pertaining models in which noise is introduced, so as to make them amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. We rigorously analyse the one-dimensional version of the model in which one of the two types is in the minority, and establish various forms of threshold behaviour. Our results are in sharp contrast with the case when the distribution of the two types is uniform (i.e. each agent has equal chance of being of each type in the initial configuration), which was studied in Brandt et al. (in: STOC ’12: proceedings of the 44th symposium on theory of computing, pp. 789–804, 2012) and Barmpalias et al. (in: 55th Annual IEEE symposium on foundations of computer science, Oct 18–21, Philadelphia, FOCS’14, 2014)

EEG correlated functional MRI and postoperative outcome in focal epilepsy

Background: The main challenge in assessing patients with epilepsy for resective surgery is localising seizure onset. Frequently, identification of the irritative and seizure onset zones requires invasive EEG. EEG correlated functional MRI (EEG-fMRI) is a novel imaging technique which may provide localising information with regard to these regions. In patients with focal epilepsy, interictal epileptiform discharge (IED) correlated blood oxygen dependent level (BOLD) signal changes were observed in approximately 50% of patients in whom IEDs are recorded. In 70%, these are concordant with expected seizure onset defined by non-invasive electroclinical information. Assessment of clinical validity requires post-surgical outcome studies which have, to date, been limited to case reports of correlation with intracranial EEG. The value of EEG-fMRI was assessed in patients with focal epilepsy who subsequently underwent epilepsy surgery, and IED correlated fMRI signal changes were related to the resection area and clinical outcome. Methods: Simultaneous EEG-fMRI was recorded in 76 patients undergoing presurgical evaluation and the locations of IED correlated preoperative BOLD signal change were compared with the resected area and postoperative outcome. Results: 21 patients had activations with epileptic activity on EEG-fMRI and 10 underwent surgical resection. Seven of 10 patients were seizure free following surgery and the area of maximal BOLD signal change was concordant with resection in six of seven patients. In the remaining three patients, with reduced seizure frequency post-surgically, areas of significant IED correlated BOLD signal change lay outside the resection. 42 of 55 patients who had no IED related activation underwent resection. Conclusion: These results show the potential value of EEG-fMRI in presurgical evaluation

Model theory of finite and pseudofinite groups

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory

Cognitive behavioural therapy for adults with dissociative seizures (CODES): a pragmatic, multicentre, randomised controlled trial.

BACKGROUND: Dissociative seizures are paroxysmal events resembling epilepsy or syncope with characteristic features that allow them to be distinguished from other medical conditions. We aimed to compare the effectiveness of cognitive behavioural therapy (CBT) plus standardised medical care with standardised medical care alone for the reduction of dissociative seizure frequency. METHODS: In this pragmatic, parallel-arm, multicentre randomised controlled trial, we initially recruited participants at 27 neurology or epilepsy services in England, Scotland, and Wales. Adults (≥18 years) who had dissociative seizures in the previous 8 weeks and no epileptic seizures in the previous 12 months were subsequently randomly assigned (1:1) from 17 liaison or neuropsychiatry services following psychiatric assessment, to receive standardised medical care or CBT plus standardised medical care, using a web-based system. Randomisation was stratified by neuropsychiatry or liaison psychiatry recruitment site. The trial manager, chief investigator, all treating clinicians, and patients were aware of treatment allocation, but outcome data collectors and trial statisticians were unaware of treatment allocation. Patients were followed up 6 months and 12 months after randomisation. The primary outcome was monthly dissociative seizure frequency (ie, frequency in the previous 4 weeks) assessed at 12 months. Secondary outcomes assessed at 12 months were: seizure severity (intensity) and bothersomeness; longest period of seizure freedom in the previous 6 months; complete seizure freedom in the previous 3 months; a greater than 50% reduction in seizure frequency relative to baseline; changes in dissociative seizures (rated by others); health-related quality of life; psychosocial functioning; psychiatric symptoms, psychological distress, and somatic symptom burden; and clinical impression of improvement and satisfaction. p values and statistical significance for outcomes were reported without correction for multiple comparisons as per our protocol. Primary and secondary outcomes were assessed in the intention-to-treat population with multiple imputation for missing observations. This trial is registered with the International Standard Randomised Controlled Trial registry, ISRCTN05681227, and ClinicalTrials.gov, NCT02325544. FINDINGS: Between Jan 16, 2015, and May 31, 2017, we randomly assigned 368 patients to receive CBT plus standardised medical care (n=186) or standardised medical care alone (n=182); of whom 313 had primary outcome data at 12 months (156 [84%] of 186 patients in the CBT plus standardised medical care group and 157 [86%] of 182 patients in the standardised medical care group). At 12 months, no significant difference in monthly dissociative seizure frequency was identified between the groups (median 4 seizures [IQR 0-20] in the CBT plus standardised medical care group vs 7 seizures [1-35] in the standardised medical care group; estimated incidence rate ratio [IRR] 0·78 [95% CI 0·56-1·09]; p=0·144). Dissociative seizures were rated as less bothersome in the CBT plus standardised medical care group than the standardised medical care group (estimated mean difference -0·53 [95% CI -0·97 to -0·08]; p=0·020). The CBT plus standardised medical care group had a longer period of dissociative seizure freedom in the previous 6 months (estimated IRR 1·64 [95% CI 1·22 to 2·20]; p=0·001), reported better health-related quality of life on the EuroQoL-5 Dimensions-5 Level Health Today visual analogue scale (estimated mean difference 6·16 [95% CI 1·48 to 10·84]; p=0·010), less impairment in psychosocial functioning on the Work and Social Adjustment Scale (estimated mean difference -4·12 [95% CI -6·35 to -1·89]; p<0·001), less overall psychological distress than the standardised medical care group on the Clinical Outcomes in Routine Evaluation-10 scale (estimated mean difference -1·65 [95% CI -2·96 to -0·35]; p=0·013), and fewer somatic symptoms on the modified Patient Health Questionnaire-15 scale (estimated mean difference -1·67 [95% CI -2·90 to -0·44]; p=0·008). Clinical improvement at 12 months was greater in the CBT plus standardised medical care group than the standardised medical care alone group as reported by patients (estimated mean difference 0·66 [95% CI 0·26 to 1·04]; p=0·001) and by clinicians (estimated mean difference 0·47 [95% CI 0·21 to 0·73]; p<0·001), and the CBT plus standardised medical care group had greater satisfaction with treatment than did the standardised medical care group (estimated mean difference 0·90 [95% CI 0·48 to 1·31]; p<0·001). No significant differences in patient-reported seizure severity (estimated mean difference -0·11 [95% CI -0·50 to 0·29]; p=0·593) or seizure freedom in the last 3 months of the study (estimated odds ratio [OR] 1·77 [95% CI 0·93 to 3·37]; p=0·083) were identified between the groups. Furthermore, no significant differences were identified in the proportion of patients who had a more than 50% reduction in dissociative seizure frequency compared with baseline (OR 1·27 [95% CI 0·80 to 2·02]; p=0·313). Additionally, the 12-item Short Form survey-version 2 scores (estimated mean difference for the Physical Component Summary score 1·78 [95% CI -0·37 to 3·92]; p=0·105; estimated mean difference for the Mental Component Summary score 2·22 [95% CI -0·30 to 4·75]; p=0·084), the Generalised Anxiety Disorder-7 scale score (estimated mean difference -1·09 [95% CI -2·27 to 0·09]; p=0·069), and the Patient Health Questionnaire-9 scale depression score (estimated mean difference -1·10 [95% CI -2·41 to 0·21]; p=0·099) did not differ significantly between groups. Changes in dissociative seizures (rated by others) could not be assessed due to insufficient data. During the 12-month period, the number of adverse events was similar between the groups: 57 (31%) of 186 participants in the CBT plus standardised medical care group reported 97 adverse events and 53 (29%) of 182 participants in the standardised medical care group reported 79 adverse events. INTERPRETATION: CBT plus standardised medical care had no statistically significant advantage compared with standardised medical care alone for the reduction of monthly seizures. However, improvements were observed in a number of clinically relevant secondary outcomes following CBT plus standardised medical care when compared with standardised medical care alone. Thus, adults with dissociative seizures might benefit from the addition of dissociative seizure-specific CBT to specialist care from neurologists and psychiatrists. Future work is needed to identify patients who would benefit most from a dissociative seizure-specific CBT approach. FUNDING: National Institute for Health Research, Health Technology Assessment programme

Tipping Points in 1-dimensional Schelling Models with Switching Agents

Schelling’s spacial proximity model was an early agent-based model, illustrating how ethnic segregation can emerge, unwanted, from the actions of citizens acting according to individual local preferences. Here a 1-dimensional unperturbed variant is studied under switching agent dynamics, interpretable as being open in that agents may enter and exit the model. Following the authors’ work (Barmpalias et al., FOCS, 2014) and that of Brandt et al. (Proceedings of the 44th ACM Symposium on Theory of Computing (STOC 2012), 2012), rigorous asymptotic results are established. The dynamic allows either type to take over almost everywhere. Tipping points are identified between the regions of takeover and staticity. In a generalization of the models considered in [1] and [3], the model’s parameters comprise the initial proportions of the two types, along with independent values of the tolerance for each type. This model comprises a 1-dimensional spin-1 model with spin dependent external field, as well as providing an example of cascading behaviour within a network

Digital morphogenesis via Schelling segregation

Schelling's model of segregation looks to explain the way in which particles or agents of two types may come to arrange themselves spatially into configurations consisting of large homogeneous clusters, i.e. connected regions consisting of only one type. As one of the earliest agent based models studied by economists and perhaps the most famous model of self-organising behaviour, it also has direct links to areas at the interface between computer science and statistical mechanics, such as the Ising model and the study of contagion and cascading phenomena in networks. While the model has been extensively studied it has largely resisted rigorous analysis, prior results from the literature generally pertaining to variants of the model which are tweaked so as to be amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. In Brandt et al (2012 Proc. 44th Annual ACM Symp. on Theory of Computing) provided the first rigorous analysis of the unperturbed model, for a specific set of input parameters. Here we provide a rigorous analysis of the model's behaviour much more generally and establish some surprising forms of threshold behaviour, notably the existence of situations where an increased level of intolerance for neighbouring agents of opposite type leads almost certainly to decreased segregation

Do linden trees kill bees? Reviewing the causes of bee deaths on silver linden (Tilia tomentosa)

For decades, linden trees (basswoods or lime trees), and particularly silver linden (Tilia tomentosa), have been linked to mass bee deaths. This phenomenon is often attributed to the purported occurrence of the carbohydrate mannose, which is toxic to bees, in Tilia nectar. In this review, however, we conclude that from existing literature there is no experimental evidence for toxicity to bees in linden nectar. Bee deaths on Tilia probably result from starvation, owing to insufficient nectar resources late in the tree's flowering period. We recommend ensuring sufficient alternative food sources in cities during late summer to reduce bee deaths on silver linden. Silver linden metabolites such as floral volatiles, pollen chemistry and nectar secondary compounds remain underexplored, particularly their toxic or behavioural effects on bees. Some evidence for the presence of caffeine in linden nectar may mean that linden trees can chemically deceive foraging bees to make sub-optimal foraging decisions, in some cases leading to their starvation

Revealing a brain network endophenotype in families with idiopathic generalised epilepsy

Idiopathic generalised epilepsy (IGE) has a genetic basis. The mechanism of seizure expression is not fully known, but is assumed to involve large-scale brain networks. We hypothesised that abnormal brain network properties would be detected using EEG in patients with IGE, and would be manifest as a familial endophenotype in their unaffected first-degree relatives. We studied 117 participants: 35 patients with IGE, 42 unaffected first-degree relatives, and 40 normal controls, using scalp EEG. Graph theory was used to describe brain network topology in five frequency bands for each subject. Frequency bands were chosen based on a published Spectral Factor Analysis study which demonstrated these bands to be optimally robust and independent. Groups were compared, using Bonferroni correction to account for nonindependent measures and multiple groups. Degree distribution variance was greater in patients and relatives than controls in the 6-9 Hz band (p = 0.0005, p = 0.0009 respectively). Mean degree was greater in patients than healthy controls in the 6-9 Hz band (p = 0.0064). Clustering coefficient was higher in patients and relatives than controls in the 6-9 Hz band (p = 0.0025, p = 0.0013). Characteristic path length did not differ between groups. No differences were found between patients and unaffected relatives. These findings suggest brain network topology differs between patients with IGE and normal controls, and that some of these network measures show similar deviations in patients and in unaffected relatives who do not have epilepsy. This suggests brain network topology may be an inherited endophenotype of IGE, present in unaffected relatives who do not have epilepsy, as well as in affected patients. We propose that abnormal brain network topology may be an endophenotype of IGE, though not in itself sufficient to cause epilepsy