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Opioid-specific brain connectivity dynamics distinguish analgesia from secondary effects: Studies in male mice

The µ-opioid receptor (MOP) is a critical pharmaceutical target that mediates both the therapeutic benefits and adverse effects of opioid drugs. However, the large-scale neural circuit dynamics underlying key opioid effects, such as analgesia and respiratory depression, remain poorly understood, hindering the development of safer analgesics. Here, we present a multimodal experimental framework that integrates functional ultrasound imaging through the intact skull with behavioral and molecular analyses to investigate opioid-induced large-scale functional responses and their physiological relevance in awake, behaving male mice. Administration of major opioids—morphine, fentanyl, methadone, and buprenorphine—elicited robust, dose- and time-dependent reorganization of functional brain connectivity (FC) patterns, with magnitude scaling according to MOP agonist efficacy. This opioid-specific functional fingerprint is marked by decreased FC between the somatosensory cortex and hippocampal/thalamic regions and increased bilateral FC within the somatosensory cortex. Notably, this fingerprint was attenuated following tolerance induction and abolished by pharmacological or genetic MOP inactivation. Through power Doppler spectral analysis and lagged correlation measurements, we show that morphine perturbs temporal FC dynamics and the propagation of brain-wide oscillatory activity, disrupting critical-state dynamics. Importantly, we identify a dissociation between fast, transient processes—such as cerebral blood volume changes, locomotion, and respiratory depression—and slower processes driving FC reorganization, analgesia, and sustained MOP activation. This study provides mechanistic insights into opioid-induced network reorganization, establishes FC alterations as a reliable biomarker of opioid efficacy, and offers a framework for advancing the development of analgesic compounds with improved therapeutic windows and reduced side effects.

The effect of grade retention on secondary school performance: Evidence from a natural experiment

We study the effects of grade retention on secondary school performance using a change in legislation in Colombia. In 2010, the rule that allowed schools to retain a maximum of 5 percent of their students was abolished. We exploit variation in changes in schools’ retention rates across time in a difference-in-differences framework, and find that higher school retention rates improved performance on high-school exit tests scores. While gains in learning did not differ between STEM and non-STEM subjects, increased retention disproportionately benefited non-retained students, students from higher socioeconomic backgrounds, private schools, and schools operating under a full day shift.

When collagen fails: Zinc isotopes unlock Sumerian lifeways in southern Mesopotamia

Reconstructing past lifeways and diets is essential to understanding the emergence of urban societies. However, in what are now arid environments like southern Mesopotamia, poor collagen preservation has long hampered direct isotopic analysis of trophic levels. This limitation has left key gaps in our understanding of subsistence in one of the world’s earliest urban heartlands. Here, we apply zinc isotope analysis to human and faunal dental enamel from the third-millennium BCE site of Abu Tbeirah (Iraq), integrating δ 13 C, δ 18 O, and trace element ratios (Ba/Ca and Sr/Ca). This multiproxy approach reveals an omnivorous diet based on C 3 cereals, terrestrial animal products (likely including pigs), and limited freshwater resources, with no or little evidence of marine fish consumption, despite the site’s proximity to the ancient shoreline. Dietary patterns do not vary by sex, suggesting broad access to similar food sources within this nonelite population. Moreover, zinc and carbon isotopes proved valuable in identifying animal feeding practices. Our results provide direct dietary evidence from southern Mesopotamia, overcoming long-standing preservation challenges. The results allow us to evaluate specific expectations about diet and animal management in a collagen-poor context, also highlighting early-life feeding behaviors. They demonstrate the power of zinc isotopes to reconstruct trophic level in collagen-poor contexts, opening broad avenues for bioarchaeological research in early complex societies.

Human body dynamics simulation and comfort evaluation of interhospital transport patients with different road conditions

Road unevenness has a significant impact on the comfort of patients during interhospital transport. Vibration is easy to cause dizziness, palpitation, tension, restlessness and other symptoms, and even cause secondary injuries to patients. Therefore, it is very important to analyze the vibration characteristics of human body and take care of vibration reduction. In this paper, the finite element technology, dynamic theory and experimental method are used to establish a “human-vehicle-road” coupling dynamic model, and the human dynamic response under different road conditions is simulated and analyzed. The results show that the human comfort is poor on bumpy road and continuous speed bumps; The vibration of different parts of human body is very different, and the head and sacrococcygeal vibration are the most obvious. Therefore, for patients with interhospital transport, vibration reduction nursing should be focused on the head and sacrococcygeal region. And a variable stiffness damping device is proposed, which has the functions of damping and limiting position. The simulation results show that the vibration reduction of head is more than 35%, and that of sacrococcygeal region is more than 30%. Therefore, the device is of great significance for improving the comfort of patients with interhospital transport.

Bacterial reporter–paired scRNA sequencing reveals cross talk between zinc starvation and zinc toxicity in macrophage antibacterial defense

Mechanisms by which macrophages deploy antibacterial zinc toxicity are poorly understood. To gain insight into this antimicrobial pathway, we developed bacterial reporter–paired single-cell RNA sequencing of human monocyte-derived macrophages (HMDM) infected with an Escherichia coli zinc-stress reporter strain. We identified HMDM subpopulations harboring zinc-stressed E. coli and corresponding mammalian genes predicted to be associated with either zinc toxicity or survival of zinc-stressed bacteria. Consistent with the latter, SLC30A4 that encodes zinc exporter ZNT4 was enriched in one subpopulation of HMDM containing zinc-stressed E. coli and its overexpression in human macrophages increased intracellular E. coli survival. At a population level, SLC30A4 expression was rapidly downregulated in human macrophages responding to E. coli and its ectopic expression in macrophages attenuated zinc starvation of intracellular E. coli . This is consistent with a model in which macrophages switch off SLC30A4 to engage zinc starvation, while also deploying zinc toxicity against bacteria adapting to a low-zinc environment. Consistent with this, intramacrophage E. coli rapidly upregulated znuA messenger RNA (mRNA) that is induced during zinc limitation, with zntA mRNA that is induced during zinc stress peaking later. Moreover, E. coli cultured under conditions of zinc limitation displayed greatly enhanced zinc sensitivity. Susceptibility of zinc-sensitive E. coli to killing by macrophages was also attenuated when zinc uptake by E. coli was inactivated, confirming the coordinated actions of zinc starvation and zinc toxicity in macrophage antibacterial responses. Strategies that enhance zinc starvation of intracellular bacteria could be exploited in the design of host-directed therapeutics that amplify macrophage-mediated antibacterial zinc toxicity.

Correction: Blockade of mTOR ameliorates IgA nephropathy by correcting CD89 and CD71 dysfunctions in humanized mice

Ambient ammonia synthesis from air via tandem water microdroplets–driven oxidation and pulsed photoelectrochemical reduction

Artificial N 2 reduction offers a sustainable approach to green NH 3 synthesis, but the practical implementation is challenged by N 2 activation and competing hydrogen evolution. Photoelectrochemical nitrate and nitrite (NO x – , x = 2 and 3) reduction with favorable thermodynamics represents a promising alternative for NH 3 production, provided that NO x – can be supplied from the atmosphere. Here, through leveraging water microdroplet chemistry and dynamic photoelectrode–electrolyte interface engineering, we report a tandem air–NO x – –NH 3 conversion system that integrates catalyst-free N 2 oxidation with pulsed photoelectrochemical NO x − reduction (mNOR-pPNO x R). The system achieves efficient and selective NH 3 production with a yield rate of 24.5 μmol cm −2 h −1 at −0.2 V RHE , which are two to three orders of magnitude higher than conventional photo/electrocatalytic N 2 fixation. This study introduces insights for decentralized, on-demand ammonia production from air and water and broadens horizons of microdroplet chemistry and pulse strategy for sustainable chemical manufacturing.

Development and validation of a health education module for parents of schoolchildren with overweight and obesity in the UAE

Background Childhood overweight and obesity continue to rise globally and in the United Arab Emirates (UAE), underscoring the need for accessible, evidence-based parental education tools. Objective This study aims to develop and validate a health educational module (HEM) tailored for parents of schoolchildren with overweight and obesity in the UAE. Methods The study was conducted in two phases: module development, and content and face validation. The module development involved an extensive review of national and international guidelines and previous research, followed by the design of infographic-based educational messages. Content and Face Validity were performed by six nutrition experts and 16 parents, respectively, using the Content Validity Index (CVI) and Face Validity Index (FVI). Results The final HEM consisted of 25 infographic messages covering dietary intake, physical activity, behavior change, and family engagement. The module achieved excellent content validity (S-CVI/Ave = 0.97) and face validity (S-FVI/Ave = 0.99). Participant feedback resulted in language refinement, improved illustrations, and removal of outdated elements such as the Food Pyramid. Conclusion The validated HEM is culturally relevant, parent-friendly, and scientifically grounded. It offers a structured, high-quality educational tool suitable for use in research, school-based initiatives, and public-health programs aimed at reducing childhood obesity in the UAE.

Direct and indirect benefits of cooperation in collective defense against predation

The evolution and maintenance of public goods cooperation, despite cheating, remains a key interest in social biology. Identifying how ecological factors determine the direct and indirect benefits that maintain cooperation has proven challenging, as these can vary significantly across species and environments. Here, we study this problem using the social pine sawfly Neodiprion sertifer (Hymenoptera) as a model system. During their larval stage, N. sertifer live in groups and collectively secrete a defensive fluid against predators. This behavior comprises a public good as it is costly to exhibit and beneficial to others, and individuals vary in their contribution to group defense. We experimentally manipulated individual contributions to defense to assess how these influence survival under natural insect predation. Our results indicate that defense has a group-level benefit as individuals were more likely to survive in cooperative groups with a higher proportion of defending larvae. Moreover, being able to deploy defensive fluid confers direct survival benefits. Genetic and phenotypic analyses of natural populations further show that kin selection promotes collective defense, as groups of larvae are often composed of full siblings. We also find that the contribution to defense is female-biased and diminishes in larger, more male-biased groups, and to some extent with decreased kinship, indicating that individuals adjust their contributions based on social context. Overall, we find that contribution to the collective defense provides both direct and indirect benefits and that individuals regulate their contributions mainly based on the social environment, resulting in variation within and among natural populations.

Enhancing cropping intensity and system productivity through early-bulking potato genotypes in potato-based cropping systems

Increasing cropping intensity is a key strategy for enhancing food production in regions facing shrinking arable land and rising population pressure. Early-bulking potato genotypes offer opportunities to redesign potato-based cropping systems by creating temporal space for additional crops. This study evaluated the agronomic performance, system productivity, economic returns, and land use efficiency of early-bulking potato genotypes (7 Alu and Sagitta ) within intensified potato-based cropping patterns at the Regional Agricultural Research Station (RARS), Burirhat, Rangpur, Bangladesh during the 2017–2018 cropping year. Thirteen cropping systems, including the conventional potato– boro rice–T. aman rice system, were assessed using a randomized complete block design with three replications. Results showed that incorporation of early-bulking potato genotypes enabled the inclusion of four to five crops per year, substantially increasing system productivity. Potato equivalent yield increased by 43.8–111.5% in the improved patterns compared with the conventional system. The highest land use efficiency (95.61%), whole pattern gross margin (Tk. 538775 ha −1 ), and marginal benefit-cost ratio (8.17) were achieved in the 7 Alu – garden pea – red amaranth – T. aus rice – T. aman rice pattern, while the highest potato equivalent yield (95.37 t ha −1 ) was recorded in the 7 Alu – cardinal – Mungbean – red amaranth – T. aman rice pattern. This study indicates that inclusion of early bulking potato varieties has the potential to serve as effective entry-point crops for intensifying potato-based cropping systems, improving land use efficiency and farm profitability. These findings represent promising outcomes from a single-season trial and highlight the potential of flexible cropping system designs that warrant further multi-year and multi-location validation.

Elevated phthalate exposure and metabolic susceptibility increased breast cancer risk: A 20-y follow-up study in Taiwan

Widely used phthalates, especially di-(2-ethylhexyl) phthalate (DEHP), increase breast cancer risk in experimental animals and humans, but long-term follow-up evidence of its human breast carcinogenicity remains inconclusive. This nested case–control study included 119 invasive breast cancer cases and 245 matched controls from a longitudinal cohort of 11,923 women recruited in 1991–1992 and followed to 2010 in Taiwan. Urine samples at baseline and follow-up visit were tested for 11 metabolites of seven phthalates using LC-ESI-MS/MS. DEHP metabolism susceptibility was evaluated by the percentage of mono-2-ethylhexyl phthalate (MEHP%) in the sum of five DEHP metabolites (∑DEHP). Odds ratios (ORs) with 95% CI from conditional logistic regression were used to examine risk predictors. DEHP was the only phthalate significantly associated with breast cancer risk. Risk increased significantly with elevated urinary levels of ∑DEHP (> 0.381 μmol/g creatinine, OR = 1.71, 95% CI = 1.02 to 2.43), MEHP (> 0.022 μmol/g creatinine, OR = 1.87, 95% CI = 1.07 to 3.25), and MEHP% (> 6.7%, OR = 1.65, 95% CI = 0.96 to 2.82). Elevated ∑DEHP and MEHP% combined with early menarche (≤ 14 years) was associated with further increased risk (OR = 7.52, 95% CI = 2.68 to 21.05). The intraclass correlation coefficient between paired baseline and follow-up samples of 152 women was 0.06 for ∑DEHP and 0.31 for MEHP%. High DEHP exposure, high MEHP%, and early menarche were associated with increased breast cancer risk. MEHP% was a better biomarker for DEHP metabolism.

Hybrid deep learning and optimized variational mode decomposition for point-interval runoff prediction

Runoff prediction is crucial for water resource allocation and hydropower planning. To address low accuracy and uncertainty in runoff forecasting, this study proposes a framework integrating the Information Acquisition Optimizer (IAO), Variational Mode Decomposition (VMD), Convolutional Neural Network-Support Vector Machine (CNN-SVM), and Kernel Density Estimation (KDE) for interval prediction. An IAO-based optimized VMD (IVMD) is employed to decompose non-stationary runoff series and enhance feature extraction, with the resulting components used as inputs to the CNN-SVM model for point prediction. To quantify predictive uncertainty, KDE is applied to model the prediction error distribution, where a B-spline-based least squares cross-validation bandwidth selection method (LSCV-B) is adopted. By combining B-spline basis functions with data-driven cross-validation, LSCV-B overcomes the limited local adaptability of conventional AMISE-based bandwidth selection, enabling more accurate error density estimation and narrower prediction intervals with reliable coverage. Experiments in the Yangtze River Basin show that the IVMD-CNN-SVM framework reduces RMSE and MAPE by approximately 40–50% on the testing dataset compared with VMD-based counterparts, while producing highly reliable and compact 90% interval predictions.

RGS-YOLO: A lightweight solution for surface defect detection in wind turbines

The defects in wind turbines not only affect energy generation efficiency but can also lead to significant damage if not repaired promptly. To address the challenges of low detection efficiency and high costs in the real-world industrial scenario of wind turbine defect detection, we have designed a lightweight detection model. First, this study introduces Receptive-Field Attention Convolution(RFAConv) and develops the Cross Stage Partial with 2 convolutions and feature fusion-Receptive-Field Attention Convolution(C2f-RFAConv) module, integrating it into the backbone network. This approach allows the model to focus on spatial features while accurately capturing local information in each region through its receptive field, significantly enhancing its feature extraction capabilities. Additionally, we incorporate Group Shuffle Convolution(GSConv) in the neck network to ensure that the model remains lightweight while maintaining a high level of accuracy. In the design of the detection head, we leverage the low redundant computation capability of Spatial and Channel reconstruction Convolution(SCConv), along with its ability to promote the learning of representative features, to develop a detection head-SCConv Head-that integrates classification and detection with low computational cost and parameters. All experimental results are reported as the average of no fewer than three independent runs to ensure the stability and reliability of the results. Experimental results show that, compared to the original You Only Look Once version 8 nano(YOLOv8n), our model reduces its size by 1.16 MB and decreases the floating-point operations by 3.5 G while improving the mean Average Precision (mAP) by 3.7%. These results demonstrate the effectiveness of our model in achieving lightweight performance.

Bayesian hierarchical modelling of academic orientation and advising effects on student retention and progression: Multi-cohort evidence

Student retention and academic progression remain central concerns in higher education, particularly within contexts characterised by widening access and structural inequality. This study examines the independent and interactive effects of academic orientation performance and academic advising utilisation on first-year student retention and progression at a South African public university. Using administrative data from 8,300 undergraduate students across three entry cohorts spanning the 2023–2024 academic periods, we employ Bayesian hierarchical multivariate modelling to account for cohort-level variation and the interdependence between retention and progression outcomes. Retention is operationalised as enrolment in the subsequent academic year and is analysed only for cohorts with observable follow-up data (based on confirmed registration records), while academic progression is examined for all cohorts. Results indicate that stronger performance in academic orientation is positively associated with both retention and progression, while engagement with academic advising is associated with improved outcomes, particularly when combined with higher orientation performance. The observed interaction effects suggest complementary engagement between orientation and advising rather than differential treatment effectiveness, and all estimated relationships are interpreted as associative rather than causal. Model comparison results indicate statistically indistinguishable predictive performance between joint and univariate specifications, with the joint model offering additional inferential advantages by capturing correlations between outcomes. Overall, the findings highlight the value of integrated first-year support interventions and demonstrate the utility of Bayesian hierarchical approaches for analysing complex, multi-cohort educational data in Global South higher education contexts.

Divergent BLA engram circuits orchestrate social preference dynamics in bystander male mice with self-experienced stress

Personal experiences are encoded and stored in memory engram cells and are crucial for social preference dynamics in future social contexts, yet the neural circuit mechanisms involved are still poorly understood. Here, we develop a mouse model that combines self-experienced single social defeat stress with vicarious social defeat stress, demonstrating a social preference with defeat stress-experienced cagemate and social avoidance toward an aggressor. Basolateral amygdala engram cells (BLA EC ) exhibit significant activation, and chemogenetic manipulations confirm their sufficiency and necessity for both social preference and social avoidance behaviors. Virus-based cell-type-specific brain mapping suggests BLA EC project to anterior cingulate cortex (ACC) and these projections are also responsible for modulating social preference dynamics. Distinct projections from BLA-ACC circuit, including ventral/dorsal hippocampus and zona incerta, exert the diverse effects on these behaviors in male mice. Our findings reveal regulation of social preference dynamics by divergent circuits originating from BLA EC , which may contribute to the neurobiological mechanism of social psychopathologies.

Beyond direct-acting antiviral therapy: Characterizing mental health conditions and depressive symptoms among patients recently treated for hepatitis C

The uptake of hepatitis C virus (HCV) treatment, including among under-served populations, has improved significantly in the Direct Acting Antiviral (DAA) era. However, it is unclear whether patients undergoing HCV treatment are receiving adequate support to engage in healthcare for other concurrent conditions. We sought to characterize psychiatric disorders and depressive symptomatology among a cohort of patients recently treated for HCV. We conducted a secondary analysis using data from the Preservation of Sustained Virologic Response (Per-SVR) study, a prospective cohort of individuals who achieved sustained virologic response (SVR) following DAA treatment in British Columbia, Canada. After confirming SVR through receipt of an undetectable HCV viral load test within three months post-treatment, participants were enrolled in the study and completed interviewer-administered surveys. Logistic regression was used to characterize depressive symptoms and psychiatric diagnoses. Among 256 participants, 122 (48%) had significant depressive symptoms and 142 (55%) reported ever having been diagnosed with a psychiatric disorder. Less than half (44%) of those with depressive symptoms had ever been diagnosed with depressive disorder. Participants with depressive symptoms were more likely to report experiencing recent healthcare barriers (adjusted odds ratio: 2.27; 95% confidence interval: 1.02, 5.03). We observed a high prevalence of psychiatric comorbidity among a cohort of patients recently treated for HCV, highlighting an opportunity to engage HCV patients in mental health care. The integration of mental health screening and treatment alongside HCV care may improve health outcomes among HCV-affected populations.

Stochastic resilience enables particle foraging in oligotrophic marine environments

Heterotrophic bacteria play a central role in attenuating the sequestration of carbon to the deep ocean by degrading sinking marine particles. The role of certain copiotrophic adaptations such as surface attachment and motility in particle degradation has remained unclear outside of coastal regions, where the sparsity of particles would appear to preclude a foraging lifestyle based on particle hopping. We show here instead that many oligotrophic marine environments are much more amenable to copiotrophic particle foraging than would be inferred from average-based estimates, because the foraging process samples a broad distribution of particle–bacteria interactions, with large variation in encounter times, particle sizes, and associated survival outcomes, and due to the disproportionate benefit of a particle encounter. We develop a generalized branching process model for particle foraging to assess environment viability and population growth rates based on encounters with particles, for different oceanographic particle size spectra. The results indicate that even bathypelagic environments can support particle foraging bacteria without requiring long-term starvation tolerance or multiyear feast–famine cycles, because stochastic encounters generate sufficient short-interval, high-reward events to sustain population growth despite long mean encounter times. More generally, stochasticity can confer resilience to microbial populations in resource-scarce marine environments.

Characteristics of transferrin saturation and anemia-related biomarkers in patients with uterine adenomyosis

Background Ferritin may be elevated as an acute-phase reactant in inflammatory conditions, potentially masking iron deficiency. We aimed to evaluate the frequency of iron deficiency and the diagnostic significance of transferrin saturation (TSAT) in women with uterine adenomyosis. Methods This retrospective study included non-menopausal women aged 30–55 years who had iron metabolism markers measured at first visit. Anemia was defined as hemoglobin (Hb) <11 g/dL. Iron deficiency was defined using three criteria: ferritin-only (serum ferritin <20 ng/mL), TSAT-only (TSAT <20%), and a combined criterion (ferritin <20 ng/mL and/or TSAT <20%). Functional iron deficiency was defined as TSAT <20%, with ferritin ≥20 ng/mL. We compared the frequencies of anemia and iron deficiency across groups and evaluated correlations between Hb and TSAT (Pearson correlation using log-transformed TSAT; Spearman correlation as sensitivity analysis). Results Iron deficiency was more common than anemia in all patient groups. In the adenomyosis group, the frequency of iron deficiency based on the combined criterion (65.5%) was significantly higher than that diagnosed using ferritin alone (31.0%). In the myoma and no uterine structural abnormality groups, iron deficiency frequency was similar regardless of the diagnostic criteria. The correlation between Hb and log(TSAT) was weak in the adenomyosis group (r = 0.2123, p = 0.1771) but strong in the myoma (r = 0.5465, p < 0.0001) and no uterine structural abnormality groups (r = 0.6945, p < 0.0001). Spearman analyses showed the same qualitative pattern (adenomyosis ρ = 0.358, p = 0.020; myoma ρ = 0.576, p < 0.0001; no uterine structural abnormality ρ = 0.484, p = 0.0004). Agreement between ferritin- and TSAT-based classifications was fair (Cohen’s κ = 0.375; PABAK = 0.371), and a multivariable model for TSAT <20% with ferritin ≥20 ng/mL showed modest discrimination (AUC = 0.678). Conclusions Measuring TSAT and ferritin levels enhances the detection of iron deficiency in women with adenomyosis and may help identify functional iron deficiency when ferritin interpretability is limited by inflammation.

Oligomerization of PER2 as a dynamic mode of regulation of the mammalian circadian clock

PER2 is a central transcriptional regulator in the mammalian circadian clock that closes the negative transcription–translation feedback loop by repressing its own transcription. The balance between the synthesis of PER2 and its degradation is a key factor that determines the circadian period. PER2 stability hinges on antagonistic phosphorylation events—phosphorylation at the familial advanced sleep phase site stabilizes PER2 while phosphorylation at the phosphodegron promotes degradation. The molecular mechanism by which phosphorylation elicits structural changes remains unclear, particularly because the phosphodegron is located in an intrinsically disordered region. Here, we show that the region encompassing the structured PER-ARNT-SIM (PAS) domains of PER2 and the downstream phosphodegron region form a large ~30 subunit homo-oligomer that resembles PER2 microbodies observed in mouse fibroblasts. Oligomerization is an emergent property that requires the cooperative interplay between the ordered PAS domains and the neighboring disordered segment. The phosphodegron is sequestered within this oligomer and inaccessible to Casein Kinase 1 (CK1). Intriguingly, Dark-state Exchange Saturation Transfer NMR experiments reveal that the oligomer coexists with dimeric PER2 and phosphorylation of the phosphodegron by CK1 occurs via this sparsely populated dimer. Using phosphomimetic variants, we then demonstrate that phosphorylation at the phosphodegron region destabilizes the oligomer. Our findings reveal the existence of structural polymorphism in PER2 and establish that oligomerization prevents CK1 from phosphorylating the phosphodegron, while phosphorylation of the dimer opposes oligomerization. This mutually antagonistic switch links structural assembly to posttranslational modifications and provides a mechanism by which phosphorylation tunes PER2 turnover and regulates circadian time-period.

Detection of an arbitrary number of communities in a block spin Ising model

We study the problem of community detection in a general version of the block spin Ising model featuring M groups, a model inspired by the Curie-Weiss model of ferromagnetism in statistical mechanics. We solve the general problem of identifying any number of groups with any possible coupling constants. Up to now, the problem was only solved for the specific situation with two groups of identical size and identical interactions, see [1, 2]. Our results can be applied to the most realistic situations, in which there are many groups of different sizes and different interactions. In addition, we give an explicit algorithm that permits the reconstruction of the structure of the model from a sample of observations based on the comparison of empirical correlations of the spin variables, thus unveiling easy applications of the model to real-world voting data and communities in biology.