diffusion models

Topological and Transport Dynamics of the Golden Mean Vogel Array: A Tight-Binding Analysis

Building upon the continuous momentum space observations of metallic mean Vogel arrays, this report investigates the quantum mechanical properties of the Golden Ratio (m=1) substrate. Using a tight-binding Hamiltonian model with exponentially decaying hopping integrals, we analyze the energy spectrum, state localization, defect tolerance, and quantum diffusion dynamics of this deterministic aperiodic lattice.

perovskite_dd: an open 1-D drift-diffusion solver for perovskite solar cells

A self-contained 1-D drift-diffusion solver for ETL/perovskite/HTL solar cells, written in pure NumPy/SciPy. It couples Poisson's equation with the electron, hole and mobile-ion continuity equations and supports photoinduced halide-segregation (band-gap-coupled) modelling, steady-state J-V curves, scan-rate hysteresis and small-signal impedance spectroscopy.

Nanofibrous aerogels with continuous conductivity gradient for ultrabroadband absorption-dominant electromagnetic interference shielding

Electromagnetic interference (EMI) shields are limited by a severe impedance mismatch with free space, leading to strong reflections and secondary radiation. Here, we introduce ultralight all-polymer aerogels featuring a continuous through-thickness conductivity gradient (MCAs), fabricated in a single step via diffusion-driven oxidative polymerization of pyrrole within aramid nanofiber scaffolds. An exponentially decaying conductivity profile enables ultrabroadband, low-reflection performance in 5-mm-thick samples, achieving reflection power coefficient R < 0.1 across 10.2-40.0 GHz, while maintaining shielding effectiveness > 30 dB under low-conductivity face incidence. Waveguide measurements and simulations show that progressive impedance transition and internal field redistribution drive absorption-dominated ohmic loss rather than surface reflection. A gradient-stratified electromagnetic model delineates an optimal design window for key gradient parameter. Beyond EMI protection, this nanofibrous architecture provides mechanical robustness and facile processability, establishing a diffusion–reaction strategy for spatially programmed conductive networks relevant to electromagnetic, electronic, and energy systems. Electromagnetic interference shields can be limited by impedance mismatch with free space, leading to strong reflections and secondary radiation. Here, the authors introduce lightweight all-polymer aerogels with a continuous through-thickness conductivity gradient, fabricated in a single step via diffusion-driven oxidative polymerization of pyrrole within aramid-nanofiber scaffolds.

dicompare schema: Axon diameter mapping (v1.2)

**Axon Diameter Mapping** **Overview:** Multi-shell diffusion-weighted MRI of the human brain that was optimized for axon diameter mapping using the power-law approach of Veraart et al. (2020) **Hardware requirements:** The modeling approach leverages (a) high *b*-values to suppress extra-axonal signal, and (b) strong diffusion-weighted strengths to maximize the sensitivity of diffusion-weighted MRI signal to restricted diffusion within micrometer-thin axons. Therefore, axon diameter mapping is currently limited to MRI scanners that are equipped with ultra-strong diffusion-weighting gradients, i.e. 300mT/m. Examples include Siemens 3T Connectom, Siemens 3T Connectom.X, and GE 3T Magnus. The protocol was optimized and tested on Siemens 3T Connectom. **Code:** Code to analyze the data is provided in https://github.com/NYU-DiffusionMRI/AxonRadiusMapping. **Supporting data:** Rician signal biases impact the accuracy of Axon Diameter Mapping. Therefore it is important to collect supporting data from which a noise map can be derived. **References:** *Model:* Veraart J, Nunes D, Rudrapatna U, Fieremans E, Jones DK, Novikov DS, Shemesh N. Noninvasive quantification of axon radii using diffusion MRI. Elife. 2020 Feb 12;9:e49855. doi: 10.7554/eLife.49855. *Reproducibility and protocol:* Veraart J, Raven EP, Edwards LJ, Weiskopf N, Jones DK. The variability of MR axon radii estimates in the human white matter. Hum Brain Mapp. 2021 May;42(7):2201-2213. doi: 10.1002/hbm.25359. *Interpretation:* Karat BG, Wren-Jarvis J, Raven EP, Khan AR, Jones DK, Palombo M, Veraart J. Revisiting the interpretation of axon diameter mapping using higher-order signal representations. Imaging Neurosci (Camb). 2026 Jan 9;4:IMAG.a.1080. doi: 10.1162/IMAG.a.1080. This is a dicompare validation schema. View, browse, and use it at https://dicompare.neurodesk.org/schema/Axon_diameter_mapping_v1.2.

TECHNOLOGICAL ADOPTION AND WORKER’S INNOVATIVE BEHAVIOUR OF TEACHING HOSPITALS IN RIVERS STATE

Teaching hospitals in Rivers State continue to grapple with weak innovative behaviour among their workforce, a challenge manifested in sluggish idea generation and the frequent failure of promising improvements to reach implementation, even as investments in technology intensify. This study therefore examined the relationship between technological adoption and worker’s innovative behaviour of teaching hospitals in Rivers State, with technological adoption operationalised through technological infrastructure and technological utilisation, and worker’s innovative behaviour proxied by worker’s idea generation and worker’s idea implementation. Anchored in the Diffusion of Innovations Theory and the Technology Acceptance Model, the study adopted a positivist philosophy and a cross-sectional survey design. The accessible population comprised 320 healthcare workers drawn from the University of Port Harcourt Teaching Hospital and the Rivers State University Teaching Hospital, spanning clinical, administrative, technical and support staff. The Krejcie and Morgan table yielded a sample of 175 respondents selected through simple random sampling, and a structured questionnaire served as the instrument for data collection. Of the instruments administered, 155 (88.57%) were retrieved and 145 (82.86%) were adequately completed and usable. The hypotheses were tested at the 0.05 level of significance using Partial Least Squares-Structural Equation Modelling via SmartPLS 4.1.1.9. The results revealed that technological infrastructure had a negligible, negative and non-significant relationship with worker’s idea generation (β = -0.004, p = 0.583), but a weak, positive and significant relationship with worker’s idea implementation (β = 0.278, p = 0.001); technological utilisation exhibited a very strong, positive and significant relationship with worker’s idea generation (β = 0.981, p = 0.000) and a moderate, positive and significant relationship with worker’s idea implementation (β = 0.414, p = 0.004). The study concludes that the actual utilisation of technology, rather than its mere availability, is the dominant driver of innovative behaviour, and recommends that hospital management prioritise the intensive, work-embedded use of existing systems.

dicompare schema: Protocols for DWI analysis (v1.1)

**Overview:** Diffusion-weighted MRI enable the quantification of brain microstructure and structural connectivity in the living human brain using various modeling and analysis approaches. Each of such modeling and analysis approaches have specific requirements in terms of b-values, diffusion-weighting gradients, and others. Here we provide an overview of minimum and/or recommended protocol settings. **Imaging hardware:** The definition of number of b-values, gradient directions, and others generalize across scanners, but settings such as echo time or repetition time might require customization depending on the available hardware. Therefore the ***intended use*** is primarily the evaluation of compatibility of users' data with modeling and analysis approaches. **Modeling approaches:** - Diffusion Tensor Imaging (DTI) - Diffusion Kurtosis Imaging (DKI) - Standard Model Imaging (SMI) - Neurite Orientation Dispersion and Density Imaging (NODDI) - Axon diameter mapping **Supplementary data:** Diffusion-weighted MRI is impacted by imaging artifacts and thermal noise. Subject motion, noise, and numerous imaging artifacts reduce image quality, degrade anatomical reliability, and lower the accuracy, precision, and robustness of modeling. These artifacts can be mitigated through preprocessing if supplementary data is available using [widely adopted pipelines](https://neurodesk.org/edu/examples/diffusion_imaging/qsiprep.html). Supplementary data might include reverse-phase encoded data or structural MRI data. **References:** 1. Basser PJ. Inferring microstructural features and the physiological state of tissues from diffusion-weighted images. NMR Biomed. 1995;8:333–44. 2. Jensen JH, Helpern JA, Ramani A, Lu H, Kaczynski K. Diffusional kurtosis imaging: The quantification of non-gaussian water diffusion by means of magnetic resonance imaging. Magn Reson Med. 2005;53:1432–40. 3. Novikov DS, Veraart J, Jelescu IO, Fieremans E. Rotationally-invariant mapping of scalar and orientational metrics of neuronal microstructure with diffusion MRI. Neuroimage. 2018;174:518–38. 4. Zhang H, Schneider T, Wheeler-Kingshott CA, Alexander DC. NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain. Neuroimage. 2012;61:1000–16. 5. Palombo M, Ianus A, Guerreri M, Nunes D, Alexander DC, Shemesh N, et al. SANDI: A compartment-based model for non-invasive apparent soma and neurite imaging by diffusion MRI. Neuroimage. 2020;215:116835. 6. Veraart J, Raven EP, Edwards LJ, Weiskopf N, Jones DK. The variability of MR axon radii estimates in the human white matter. Hum Brain Mapp. 2021;42:2201–13. 7. Coelho S, Liao Y, Szczepankiewicz F, Veraart J, Chung S, Lui YW, Novikov DS, Fieremans E. Assessment of precision and accuracy of brain white matter microstructure using combined diffusion MRI and relaxometry. Hum Brain Mapp. 2024 Jun 15;45(9):e26725. **Disclaimer:** This list is not exhaustive. Please contact authors to suggest additional models or modeling approaches and we can update accordingly. This is a dicompare validation schema. View, browse, and use it at https://dicompare.neurodesk.org/schema/Protocols_for_DWI_analysis_v1.1.

Tricking Turing: How to Build a Geometric Checkerboard on Living Tissue

The snake’s head fritillary (Fritillaria meleagris) displays one of the rarest pigmentation motifs in the plant kingdom: a high-contrast checkerboard of alternating purple and white domains on its tepals. Standard reaction–diffusion theory does not generically produce this pattern: Turing instabilities in isotropic media select a length scale but impose no preferred orientation or strict alternation between neighbors. We show that a minimal set of three sequential physical mechanisms — a Gray–Scott reaction–diffusion prepattern guided by vascular veins, anisotropic diffusion confined to interveinal corridors, and a threshold-switch Hill-type pigmentation response, each already documented separately in living systems — is sufficient to produce a square, alternating motif. Agreement with biological measurements is quantified with a purpose-built shape metric, the Square Index (SI [%]), capturing how closely a pigment domain approaches a perfect square. The full model raises SI from the classical Turing-spot value (≈ 76%) to ≈ 83%, closing roughly a third of the remaining gap to an ideal square lattice (100%); the pattern’s strict two-dimensional alternation is instead accounted for structurally, by vein-imposed staggering. These results show how tissue geometry and transport anisotropy can steer diffusion-driven instabilities into a noncanonical spatial pattern.

Shared Landscapes, Shared Futures: Visual Landscape Evolution Modelling for Community Stewardship

Abstract. Landscapes are living systems whose long-term trajectories carry profound cultural, spiritual, and resource significance for Indigenous communities worldwide. Yet the tools capable of simulating long-term landscape change, such as numerical landscape evolution models, remain largely inaccessible outside specialist research communities, constraining their potential contribution to community-led stewardship and land management decision-making. This paper introduces LandEvolve, a landscape evolution modelling framework developed entirely within a free and open-source software ecosystem, designed to extend process-based geomorphic simulation into community-accessible settings. Built upon the Landlab platform, it integrates a Python-based graphical user interface developed using the Qt framework and supporting libraries, enabling users to configure and execute simulations such as fluvial incision, hillslope diffusion, and sediment transport without requiring programming expertise or specialist technical knowledge. The tool and its source code will be made publicly available to enable reuse, modification, and community-driven development. As a primary case study, LandEvolve is co-developed with M¯aori Indigenous communities of Aotearoa New Zealand through an iterative participatory process in which Indigenous knowledge directly informs scenario design and model configuration. This engagement is grounded in geoethical principles and data sovereignty frameworks, ensuring that culturally sensitive information remains under community governance and that communities retain meaningful agency throughout the modelling process. Interactive two-dimensional and three-dimensional visualisation capabilities further support accessible, dialogue-based exploration of landscape futures, illustrating how open-source geospatial tools can be repositioned as instruments of intergenerational stewardship that place long-term landscape futures in the hands of the communities who depend on, and hold responsibility for, them.

From mass-loss histories to lightcurves: a generalised framework for interaction-powered transients

Abstract We introduce a fast (~1–50 ms) and generalised public framework for modelling interaction-powered transients. The framework solves the thin-shell equations of motion for ejecta colliding with circumstellar material (CSM), and supports arbitrary CSM density and velocity profiles, including steady winds, eruptions, and complex time-variable mass-loss histories. For optical/UV lightcurves, we implement two luminosity treatments: a fast one-zone mode based on the thin-shell shock power, and a finite-shell transport mode that evolves trapped radiation, photon diffusion, shock emergence, and post-emergence cooling for finite, static CSM shells. In a benchmark comparison, the transport calculation and an optional time-dependent shock-efficiency prescription reproduce the main qualitative and quantitative features of a one-dimensional radiation-hydrodynamical simulation. We use the same shock solution to post-process radio synchrotron and thermal bremsstrahlung X-ray predictions, enabling self-consistent multi-wavelength diagnostics. We show that the assumed CSM velocity structure can significantly affect inferred parameters even when the density profile at explosion is identical, and that aspherical CSM can mimic multiple spherical shells in bolometric lightcurves. We demonstrate the framework through recovery of a synthetic time-variable mass-loss history and applications to six transients: the Type IIn SN 2010jl, the rapidly evolving stripped-envelope SN 2023xgo, the Type Ia-CSM SN 2020aeuh, the hydrogen-poor superluminous SN 2015bn, the eruptive LBV-like transient SN 2009ip, and the long-duration interacting event iPTF14hls. The inferred CSM structures span steady or enhanced winds, thermonuclear interaction, eruptive density enhancements, and highly structured pre-supernova mass loss, illustrating the framework’s utility for inference on upcoming large samples of interacting transients.

The PMADS project: a longitudinal multimodal cohort study to understand risk for perinatal mood and anxiety disorders

Abstract Background Perinatal mood and anxiety disorders (PMADs) are among the most common and consequential complications of pregnancy. The perinatal period is also characterized by profound hormonal fluctuations and large-scale brain plasticity. However, the mechanisms linking these neurobiological changes to psychiatric risk are poorly understood. Prospective, clinically informed studies are needed to identify quantitative biomarkers and clarify pathways linking perinatal neurobiology to PMADs risk. Methods This report describes the design of a prospective, longitudinal cohort study integrating multimodal neuroimaging, biofluid sampling, and deep clinical phenotyping to enable precision characterization of neurobiological trajectories of PMADs risk. Twenty-five individuals at elevated risk for PMADs will be recruited prior to conception and followed across six in-person timepoints spanning the menstrual cycle, pregnancy, and early postpartum, with additional remote follow-ups through the first postpartum year. Data collection includes high-resolution structural MRI, functional brain mapping using multi-echo resting-state fMRI, diffusion MRI, arterial spin labeling, ultra-high field MR-based techniques for measuring glutamate (GluCEST and 1 HMRS), biofluid sampling, and comprehensive clinical, behavioral, and cognitive assessments. Structured clinical interviews assess categorical diagnoses while dimensional symptom measures capture heterogeneity and transdiagnostic features of perinatal psychopathology. Longitudinal analyses will model nonlinear trajectories of brain and symptom change across the perinatal period as well as evaluate whether preconception network features and menstrual cycle-related brain changes are associated with subsequent perinatal symptom emergence. Discussion This cohort study establishes a longitudinal, multimodal framework for investigating neurobiological changes across the transition to pregnancy in individuals at elevated risk for PMADs. By anchoring pregnancy-related brain changes to preconception and menstrual cycle-related variability within the same individuals, this study is designed to evaluate associations between preconception hormone sensitivity, pregnancy-induced neuroplasticity, and PMADs risk. The resulting dataset will provide a deeply phenotyped longitudinal resource for investigating brain-behavior relationships across the perinatal period. Findings are expected to inform future larger-scale studies aimed at advancing mechanistic understanding of PMADs, improving individualized risk stratification, and supporting development of personalized preventive and neuromodulatory interventions.

Eco-Evolutionary Dynamics of Proliferation Heterogeneity: A Phenotype-Structured Model for Tumor Growth and Treatment Response

Abstract Intra-tumor heterogeneity in proliferation rates fundamentally influences cancer progression and treatment resistance. To investigate how continuous phenotypic variation shapes eco-evolutionary dynamics, we develop a phenotype-structured partial differential equation framework that explicitly models proliferation heterogeneity as a dynamic trait. Our model integrates three key biological principles: (1) phenotypic diffusion capturing heritable variation in proliferation rates, (2) global resource competition enforcing density-dependent growth constraints, and (3) an experimentally grounded life-history trade-off linking elevated proliferation to increased mortality. Using adaptive dynamics, we derive the optimum proliferation rate in a growing tumor, showing that the optimal phenotype dynamically shifts toward slower proliferation as tumors approach carrying capacity under control condition. We perform in silico treatment simulations for four different treatment regimes (pan-proliferation, low-, mid-, and high-proliferation targeting) to show how therapeutic selective pressures reshape fitness landscapes. While all treatments slow down tumor growth, they induce divergent evolutionary trajectories. We connect these dynamics with changes in mean proliferation rates during and after treatment. Our work establishes a predictive, evolutionarily grounded framework for understanding how therapy reshapes tumor proliferation landscapes, offering a mechanistic basis for designing strategies that anticipate and counteract adaptive resistance.

The influence of task similarity and primary task complexity on interruption effects: Evidence from behavioral performance and drift diffusion modeling