Spatial Randomness Research Articles

Mach Fronts in Random Media with Fractal and Hurst Effects.

An investigation of transient second sound phenomena due to moving heat sources on planar random media is conducted. The spatial material randomness of the relaxation time is modeled by Cauchy or Dagum random fields allowing for decoupling of fractal and Hurst effects. The Maxwell-Cattaneo model is solved by a second-order central differencing. The resulting stochastic fluctuations of Mach wedges are examined and compared to unperturbed Mach wedges resulting from the heat source traveling in a homogeneous domain. All the examined cases are illustrated by simulation movies linked to this paper.

Statistical analysis of spatial distribution of pores in metal additive manufacturing

Mechanical properties of additively manufactured parts are sensitive to the presence of pores form during the manufacturing process. The impact of pores on the mechanical performance has been investigated extensively with respect to different parameters, such as pore volume fraction, shape, and size. However, statistical investigations focusing on the relationships between the spatial distribution of pores and process parameters; and consequently, the performance of the manufactured parts are scattered and limited. Also, these sparse investigations usually suffer from an ambiguous definition of terminologies. For instance, the required criteria to consider a point pattern as complete spatial randomness (CSR) are generally not clarified. Moreover, no numerical formalism is yet developed to show how much the observed spatial results are statistically significant. To address these shortcomings, the statistical definition of CSR in a point pattern and the procedure to quantitatively determine the deviation of a pattern from CSR were discussed. The explained statistical approach was used to investigate the effect of scanning speed parameter on the spatial distribution of gas pores in laser powder bed fusion manufactured stainless steel parts. Furthermore, and to highlight the impact of the spatial distribution of pores on mechanical properties, fatigue performances of parts with clustered and randomly distributed pores were simulated by finite element analysis. It is shown that by reducing the scanning speed, the spatial distribution of gas pores deviated more from CSR, and correspondingly fatigue performance deteriorated.

Computationally efficient multiscale modeling for probabilistic analysis of CFRP composites with micro-scale spatial randomness

The physics of spatial material randomness in CFRP composites is incorporated in a concurrent multiscale modeling framework. A sampling based non-intrusive approach is adopted to demonstrate natural variability in the material. The key outcome is the computational efficiency achieved by the proposed numerical model. Improvement in computational cost is achieved by the strategic use of parallel computing tools. Multi-directional fiber composite laminates are numerically modeled to predict progressive damage. The accuracy of the framework is demonstrated by comparing with experimental results of unnotched and open-hole quasi-isotropic laminates.

Identifying mismatches between conservation area networks and vulnerable populations using spatial randomization.

Grassland birds are among the most globally threatened bird groups due to substantial degradation of native grassland habitats. However, the current network of grassland conservation areas may not be adequate for halting population declines and biodiversity loss. Here, we evaluate a network of grassland conservation areas within Wisconsin, U.S.A., that includes both large Focal Landscapes and smaller targeted conservation areas (e.g., Grassland Bird Conservation Areas, GBCAs) established within them. To date, this conservation network has lacked baseline information to assess whether the current placement of these conservation areas aligns with population hot spots of grassland‐dependent taxa. To do so, we fitted data from thousands of avian point‐count surveys collected by citizen scientists as part of Wisconsin's Breeding Bird Atlas II with multinomial N‐mixture models to estimate habitat–abundance relationships, develop spatially explicit predictions of abundance, and establish ecological baselines within priority conservation areas for a suite of obligate grassland songbirds. Next, we developed spatial randomization tests to evaluate the placement of this conservation network relative to randomly placed conservation networks. Overall, less than 20% of species statewide populations were found within the current grassland conservation network. Spatial tests demonstrated a high representation of this bird assemblage within the entire conservation network, but with a bias toward birds associated with moderately tallgrasses relative to those associated with shortgrasses or tallgrasses. We also found that GBCAs had higher representation at Focal Landscape rather than statewide scales. Here, we demonstrated how combining citizen science data with hierarchical modeling is a powerful tool for estimating ecological baselines and conducting large‐scale evaluations of an existing conservation network for multiple grassland birds. Our flexible spatial randomization approach offers the potential to be applied to other protected area networks and serves as a complementary tool for conservation planning efforts globally.

Outage performance and optimal design of MIMO-NOMA enhanced small cell networks with imperfect channel-state information

This paper focuses on boosting the performance of small cell networks (SCNs) by integrating multiple-input multiple-output (MIMO) and nonorthogonal multiple access (NOMA) in consideration of imperfect channel-state information (CSI). The estimation error and the spatial randomness of base stations (BSs) are characterized by using Kronecker model and Poisson point process (PPP), respectively. The outage probabilities of MIMO-NOMA enhanced SCNs are first derived in closed-form by taking into account two grouping policies, including random grouping and distance-based grouping. It is revealed that the average outage probabilities are irrelevant to the intensity of BSs in the interference-limited regime, while the outage performance deteriorates if the intensity is sufficiently low. Besides, as the channel uncertainty lessens, the asymptotic analyses manifest that the target rates must be restricted up to a bound to achieve an arbitrarily low outage probability in the absence of the inter-cell interference. Moreover, highly correlated estimation error ameliorates the outage performance under a low quality of CSI, otherwise it behaves oppositely. Afterwards, the goodput is maximized by choosing appropriate precoding matrix, receiver filters and transmission rates. In the end, the numerical results verify our analysis and corroborate the superiority of our proposed algorithm.

Site Selection of Fire Stations in Large Cities Based on Actual Spatiotemporal Demands: A Case Study of Nanjing City

The rapid expansion of cities brings in new challenges for the urban firefighting security, while the increasing fire frequency poses serious threats to the life, property, and safety of individuals living in cities. Firefighting in cities is a challenging task, and the optimal spatial arrangement of fire stations is critical to firefighting security. However, existing researches lack any consideration of the negative effects of the spatial randomness of fire outbreaks and delayed response time due to traffic jams upon the site selection. Based on the set cover location model integrated with the spatiotemporal big data, this paper combines the fire outbreak point with the traffic situation. The presented site selection strategy manages to ensure the arrival of the firefighting task force at random simulated fire outbreak points within the required time, under the constraints of the actual city planning and traffic situation. Taking Nanjing city as an example, this paper collects multi-source big data for the comprehensive analysis, including the full data of the fire outbreak history from June 2014 to June 2018, the traffic jam data based on the Amap, and the investigation data of the firefighting facilities in Nanjing. The regularity behind fire outbreaks is analyzed, the factors related to fire risks are identified, and the risk score is calculated. The previous fire outbreak points are put through the clustering analysis, the spatial distribution probability at points in each cluster is calculated according to the clustering score, and the random fire outbreak points are generated via the Monte Carlo simulation. Meanwhile, the objective emergency response time is set as five minutes. The average vehicle speed for each road in the urban area is calculated, and the actual traffic network model is built to compute the travel time from massive randomly-distributed simulated fire points. The problem is solved by making the travel time for all simulated demand points below five minutes. At last, the site selection result based on our model is adjusted and validated, according to the planned land use. The presented method incorporates the view of the spatiotemporal big data and provides a new idea and technical method for the modification and efficiency improvement of the fire station site selection model, contributing to a service cover ratio increase from 58% to 90%.

Fastest Local Entanglement Scrambler, Multistage Thermalization, and a Non-Hermitian Phantom

We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process and proved that there are large spectral equivalence classes -- different configurations have the same spectrum. Optimal gates and the protocol that generate entanglement with the fastest theoretically possible rate are identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which is a consequence of non-Hermiticity. In particular, non-Hermiticity can cause the rate to be either faster, or, even more interestingly, slower than predicted by the matrix eigenvalue gap. This is caused by an exponential in system size explosion of expansion coefficient sizes resulting in a 'phantom' eigenvalue, and is due to non-orthogonality of non-Hermitian eigenvectors. We numerically demonstrate that the phenomenon occurs also in random circuits with non-optimal generic gates, random U(4) gates, and also without spatial or temporal randomness, suggesting that it could be of wide importance also in other non-Hermitian settings, including correlations.

Fine‐scale tree spatial patterns are shaped by dispersal limitation which correlates with functional traits in a natural temperate forest

AbstractQuestionsStudying the spatial distribution of tree species is fundamental to understanding the ecological processes governing forest dynamics. Habitat filtering and dispersal limitation are two key processes in the emergence of intraspecific aggregation in natural forest communities. The contributions of these ecological processes vary among species, communities, ontogenetic stages (i.e. juveniles and adults) and spatial scales. In this study, we investigated the ecological processes underlying species spatial distributions in two ontogenetic stages and determined how these processes are linked to species functional traits.LocationA naturally established 2.4‐ha temperate forest located on a limestone hill in SW Belgium.MethodsTrees ≥1.3 m were exhaustively censused and mapped, and environmental variables and functional traits were collected. We applied spatial point pattern modelling to explore the processes underlying species distributions. First, point process models simulating complete spatial randomness, habitat filtering and non‐habitat clustering processes were fitted to observed species point patterns. The analyses were conducted for juveniles and adults both separately and together. The most parsimonious model for each species/ontogenetic stage was selected based on three summary statistics. Secondly, we investigated the links between functional traits and the parameters of the spatial models.Results(a) Dispersal limitation plays a central role in the formation of intraspecific aggregation in this forest, alone or in combination with habitat filtering. (b) Distributions of juveniles are less influenced by habitat filtering than distributions of adults. (c) Dispersal differ substantially among species and interspecific differences in clustering characteristics are explained by seed mass, wood density and maximum height.ConclusionsDispersal limitation can be of major importance in shaping temperate forests. Coupling spatial point pattern modelling and functional traits is an efficient way to understand mechanisms of species assemblages at fine spatial scales in temperate forests.

Ripley’s K‐function for Network‐Constrained Flow Data

Many types of spatial flows, including pedestrian flows and vehicle flows, are constrained by and distribute on spatial networks. In the literature, network‐constrained flows are usually modeled as a direct line in planar space using methods designed for flows in planar space. Further, in spatial statistical analysis of flow patterns, distance measures and the hypothesis of spatial randomness of flows also have a significant impact on the determination of flow patterns. In this study, we extend the global and local Ripley’s K functions for planar flows to network space. Both the network and planar K‐functions for flows are applied to detect the patterns of taxi Origin‐Destination flow data on a road network at multiple scales. The effect of distance measures and simulation methods in the network and planar Ripley’s K functions are examined. We found that the planar K function is more sensitive to the changes in scale and tends to detect more clustered flows compared with the network K function at the same scale. Distance measures and simulation methods have a more significant influence on the detection of patterns of network‐constrained flows than the selection of the network or planar Ripley’s K functions. This study suggests that distance measures and hypotheses of spatial randomness have to be chosen carefully before applying flow pattern analytic methods to network‐constrained flows and interpreting the results of flow patterns.

Large- N theory of critical Fermi surfaces

We describe the large $N$ saddle point, and the structure of fluctuations about the saddle point, of a theory containing a sharp, critical Fermi surface in two spatial dimensions. The theory describes the onset of Ising order in a Fermi liquid, and closely related theories apply to other cases with critical Fermi surfaces. We employ random couplings in flavor space between the fermions and the bosonic order parameter, but there is no spatial randomness: consequently, the $G$-$\Sigma$ path integral of the theory is expressed in terms of fields bilocal in spacetime. The critical exponents of the large $N$ saddle-point are the same as in the well-studied non-random RPA theory; in particular, the entropy density vanishes in the limit of zero temperature. We present a full numerical solution of the large $N$ saddle-point equations, and the results agree with the critical behavior obtained analytically. Following analyses of Sachdev-Ye-Kitaev models, we describe scaling operators which descend from fermion bilinears around the Fermi surface. This leads to a systematic consideration of the role of time reparameterization symmetry, and the scaling of the Cooper pairing and $2k_F$ operators which can determine associated instabilities of the critical Fermi surface. We find no violations of scaling from time reparameterizations. We also consider the same model but with spatially random couplings: this provides a systematic large $N$ theory of a marginal Fermi liquid with Planckian transport.

Integrating spatial analysis and questionnaire survey to better understand human-onager conflict in Southern Iran

Southern Iran is a conservation priority area for the endangered Persian onager (Equus hemionus onager), which is threatened by habitat fragmentation and conflict with local communities. To better understand factors that influence onager conservation, we administered a questionnaire in local communities to survey their ecological knowledge, personal experience related to onager, and attitudes toward traditional solutions for reducing crop damage by onager. In addition, we used resistant kernel and factorial least-cost path analyses to identify core areas and corridors for onager movement, and spatial randomization of vehicle collisions and crossing locations to test the predictive ability of resistant kernel and factorial least-cost path predictions of movement. We found that local communities that were knowledgeable about onagers experienced less crop damage from onager compared with those who used traditional methods. Habitat connectivity models revealed that core areas of movement are highly concentrated at the center of protected areas. Some sections of core areas have been cut off by roads where most vehicle collisions with onagers occurred. We propose that effective onager conservation will require integrated landscape-level management to reduce mortality risk, protection of core areas and corridors, development of mitigation strategies to reduce vehicle collisions, and conflict mediation between local communities and onagers.

Towards Optimal Energy Efficiency in Cell-Free Massive MIMO Systems

Motivated by the ever-growing demand for green wireless communications and the advantages of cell-free (CF) massive multiple-input multiple-output (mMIMO) systems, we focus on the design of their downlink (DL) for optimal energy efficiency (EE). To address this fundamental topic, we assume that each access point (AP) is deployed with multiple antennas and serves multiple users on the same time-frequency resource while the APs are Poisson point process (PPP) distributed, which approaches realistically their opportunistic spatial randomness. Relied on tools from stochastic geometry, we derive a lower bound on the DL average achievable spectral efficiency (SE). Next, we consider a realistic power consumption model for CF mMIMO systems. These steps enable the formulation of a tractable optimization problem concerning the DL EE, which results in the analytical determination of the optimal pilot reuse factor, the AP density, and the number of AP antennas and users that maximize the EE. Hence, we provide useful design guidelines for CF mMIMO systems relating to fundamental system variables towards optimal EE. Among the results, we observe that an optimal pilot reuse factor and AP density exist, while larger values result in an increase of the interference, and subsequently, lower EE. Overall, it is shown that the CF mMIMO technology is a promising candidate for next-generation networks achieving simultaneously high SE and EE.

Random transition of failure modes in concrete shear walls with constitutive parameters involving spatial variation

There are two types of probabilistic dependence between the damage constitutive parameters of concrete, i.e., the probabilistic dependence between the parameters at the same position and the spatial dependence of a parameter at different positions. In this paper, a newly proposed multi-variate random field model by synthesizing the spatial correlation function with the multivariate copula function (SCFVCF) is adopted to generate spatially variant constitutive relationship of concrete in concrete shear walls. Then the failure modes and hysteresis performance of an I-type reinforced concrete shear wall with spatially variant concrete constitutive relationship under compressive and cycling horizontal loading are studied. The failure modes of the shear wall are random in nature due to the spatial randomness involved in the constitutive relationship, e.g., the damage position of the shear wall may transfer to the weaker area at the upper elements for some samples. By observation, the failure modes can be classified into four types. Particularly significant is that random transition of failure modes will occur when the spatial correlation length increases, and consequently the probability of occurrence of different failure modes changes against the spatial correlation length. This means that if the two types of dependence between the material constitutive parameters are not reasonably taken into account, the results of failure analysis of reinforced concrete shear walls might be misleading.

Spatial point pattern methodology for the study of pores 3D patterning in two casting aluminium alloys

Two cast aluminium alloys fabricated by different casting processes (gravity die-casting and lost foam casting) and showing different degrees of porosity were characterized with X-ray Computed tomography. Information concerning the pore distribution inside the investigated materials is obtained in terms of pore size and the pore positions in 3D space. Subsequently, a spatial point pattern analysis is undertaken to investigate the pore distributions. Different methods, including a nearest neighbor analysis, Ripley's K-function and Clark-Evans tests developed for 3D applications, are used to analyse the observed patterns. The results show that the Homogeneous Poisson process, which provides the Complete Spatial Randomness (CSR) is suitable to approximate the spatial distribution of the pores present in the investigated alloys. Synthetic microstructures that mimic key macroscale features of the materials in terms of pore size and the 3D spatial distribution of the pores were generated. These microstructures can be used in the probabilistic modelling of fatigue behavior.

Rapidly spreading seizures arise from large-scale functional brain networks in focal epilepsy

It remains unclear whether epileptogenic networks in focal epilepsy develop on physiological networks. This work aimed to explore the association between the rapid spread of ictal fast activity (IFA), a proposed biomarker for epileptogenic networks, and the functional connectivity or networks of healthy subjects. We reviewed 45 patients with focal epilepsy who underwent electrocorticographic (ECoG) recordings to identify the patients showing the rapid spread of IFA. IFA power was quantified as normalized beta-gamma band power. Using published resting-state functional magnetic resonance imaging databases, we estimated resting-state functional connectivity of healthy subjects (RSFC-HS) and resting-state networks of healthy subjects (RSNs-HS) at the locations corresponding to the patients' electrodes. We predicted the IFA power of each electrode based on RSFC-HS between electrode locations (RSFC-HS-based prediction) using a recently developed method, termed activity flow mapping. RSNs-HS were identified using seed-based and atlas-based methods. We compared IFA power with RSFC-HS-based prediction or RSNs-HS using non-parametric correlation coefficients. RSFC and seed-based RSNs of each patient (RSFC-PT and seed-based RSNs-PT) were also estimated using interictal ECoG data and compared with IFA power in the same way as RSFC-HS and seed-based RSNs-HS. Spatial autocorrelation-preserving randomization tests were performed for significance testing. Nine patients met the inclusion criteria. None of the patients had reflex seizures. Six patients showed pathological evidence of a structural etiology. In total, we analyzed 49 seizures (2–13 seizures per patient). We observed significant correlations between IFA power and RSFC-HS-based prediction, seed-based RSNs-HS, or atlas-based RSNs-HS in 28 (57.1%), 21 (42.9%), and 28 (57.1%) seizures, respectively. Thirty-two (65.3%) seizures showed a significant correlation with either seed-based or atlas-based RSNs-HS, but this ratio varied across patients: 27 (93.1%) of 29 seizures in six patients correlated with either of them. Among atlas-based RSNs-HS, correlated RSNs-HS with IFA power included the default mode, control, dorsal attention, somatomotor, and temporal-parietal networks. We could not obtain RSFC-PT and RSNs-PT in one patient due to frequent interictal epileptiform discharges. In the remaining eight patients, most of the seizures showed significant correlations between IFA power and RSFC-PT-based prediction or seed-based RSNs-PT. Our study provides evidence that the rapid spread of IFA in focal epilepsy can arise from physiological RSNs. This finding suggests an overlap between epileptogenic and functional networks, which may explain why functional networks in patients with focal epilepsy frequently disrupt.

Difference-based deep learning framework for stress predictions in heterogeneous media

Stress analysis of heterogeneous media, like composite materials, using Finite Element Analysis (FEA) has become commonplace in design and analysis. However, determining stress distributions in heterogeneous media using FEA can be computationally expensive in situations like optimization and multi-scaling. To address this, we utilize Deep Learning for developing a set of novel Difference-based Neural Network (DiNN) frameworks based on engineering and statistics knowledge to determine stress distribution in heterogeneous media, for the first time, with special focus on discontinuous domains that manifest high stress concentrations. The novelty of our approach is that instead of directly using several FEA model geometries and stresses as inputs for training a Neural Network, as typically done previously, we focus on highlighting the differences in stress distribution between different input samples for improving the accuracy of prediction in heterogeneous media. Our DiNN framework consists of three main modules: 1) a sample processing module that calculates the difference geometry and stress contours of each sample with respect to a reference contour extracted from the training samples, 2) an Encoder-Decoder module that predicts stress difference contours using geometry difference contours as input, and 3) a stress prediction module that combines the stress difference contours with the reference contour to construct the final prediction of stress contours. We evaluate the performance of DiNN frameworks by considering different types of geometric models that are commonly used in the analysis of composite materials, including volume fraction and spatial randomness. Results show that the DiNN structures significantly enhance the accuracy of stress prediction compared to existing structures, especially for composite models with random volume fraction when localized high stress concentrations are present.

The effect of corrosion spatial randomness and model selection on the ultimate strength of stiffened panels

ABSTRACT The main objective of this study is to investigate the effect of non-uniform thickness reduction and model selection on the predicted ultimate strength of stiffened panels under longitudinal compression. Random fields theory is used to describe the two-dimensional variation of thickness over the plates’ surface. Non-Gaussian sample functions are thus generated using the spectral representation method in combination with translation fields, whereas Monte Carlo simulation is employed to compute the response statistics. The paper provides an insightful guide for the implementation of stochastic finite element method (SFEM) into a deterministic FE software such as Abaqus. The evaluation of stiffened panel's ultimate strength variation due to the described inherent uncertainties of thickness and model selection, namely, the CSR load-end shortening curves analytical relations versus SFEM, is implemented. The results revealed that the uniform thickness approach of CSR using the net-50 scantlings provides a reasonable conservatism on the predicted ultimate strength.

Quantifying surface morphology of manufactured activated carbon and the waste coffee grounds using the Getis-Ord-Gi* statistic and Ripley\u2019s K function

Activated carbon can be manufactured from waste coffee grounds via physical and/or chemical activation processes. However, challenges remain to quantify the differences in surface morphology between manufactured activated carbon granules and the waste coffee grounds. This paper presents a novel quantitative method to determine the quality of the physical and chemical activation processes performed in the presence of intensity inhomogeneity and identify surface characteristics of manufactured activated carbon granules and the waste coffee grounds. The spatial density was calculated by the Getis-Ord-Gi* statistic in scanning electron microscopy images. The spatial characteristics were determined by analyzing Ripley’s K function and complete spatial randomness. Results show that the method introduced in this paper is capable of distinguishing between manufactured activated carbon granules and the waste coffee grounds, in terms of surface morphology.

EXPLORATORY SPECTRAL ANALYSIS IN THREE-DIMENSIONAL SPATIAL POINT PATTERNS

A spatial point pattern is a collection of points irregularly located within a bounded area (2D) or space (3D) that have been generated by some form of stochastic mechanism. Examples of point patterns include locations of trees in a forest, of cases of a disease in a region, or of particles in a microscopic section of a composite material. Spatial Point pattern analysis is used mostly to determine the absence (completely spatial randomness) or presence (regularity and clustering) of spatial dependence structure of the locations. Methods based on the space domain are widely used for this purpose, while methods conducted in the frequency domain (spectral analysis) are still unknown to most researchers. Spectral analysis is a powerful tool to investigate spatial point patterns, since it does not assume any structural characteristics of the data (ex. isotropy), and uses only the autocovariance function, and its Fourier transform. There are some methods based on the spectral frameworks for analyzing 2D spatial point patterns. There is no such methods available for the 3D situation and, therefore, the aim of this work is to develop new methods based on spectral framework for the analysis of three-dimensional point patterns. The emphasis is on relating periodogram structure to the type of stochastic process which could have generated a 3D observed pattern. The results show that the methods based on spectral analysis developed in this work are able to identify patterns of three typical three-dimensional point processes, and can be used, concurrently, with analyzes in the space domain for a better characterization of spatial point patterns.

Fine-Scale Heterogeneity of a Cold-Water Coral Reef and Its Influence on the Distribution of Associated Taxa

Benthic fauna form spatial patterns which are the result of both biotic and abiotic processes, which can be quantified with a range of landscape ecology descriptors. Fine- to medium-scale spatial patterns (<1–10 m) have seldom been quantified in deep-sea habitats, but can provide fundamental ecological insights into species’ niches and interactions. Cold-water coral reefs formed by Desmophyllum pertusum (syn. Lophelia pertusa) and Madrepora oculata are traditionally mapped and surveyed with multibeam echosounders and video transects, which limit the ability to achieve the resolution and/or coverage to undertake fine-scale, centimetric quantification of spatial patterns. However, photomosaics constructed from imagery collected with remotely operated vehicles (ROVs) are becoming a prevalent research tool and can reveal novel information at the scale of individual coral colonies. A survey using a downward facing camera mounted on a ROV traversed the Piddington Mound (Belgica Mound Province, NE Atlantic) in a lawnmower pattern in order to create 3D reconstructions of the reef with Structure-from-Motion techniques. Three high resolution orthorectified photomosaics and digital elevation models (DEM) >200 m2 were created and all organisms were geotagged in order to illustrate their point pattern. The pair correlation function was used to establish whether organisms demonstrated a clustered pattern (CP) at various scales. We further applied a point pattern modelling approach to identify four potential point patterns: complete spatial randomness (CSR), an inhomogeneous pattern influenced by environmental drivers, random clustered point pattern indicating biologically driven clustering and an inhomogeneous clustered point pattern driven by a combination of environmental drivers and biological effects. Reef framework presence and structural complexity determined inhabitant distribution with most organisms showing a departure from CSR. These CPs are likely caused by an affinity to local environmental drivers, growth patterns and restricted dispersion reproductive strategies within the habitat across a range of fine to medium scales. These data provide novel and detailed insights into fine-scale habitat heterogeneity, showing that non-random distributions are apparent and detectable at these fine scales in deep-sea habitats.