Measure Of Structural Complexity Research Articles

Life, its definition, origin, evolution, and four-dimensional hierarchical structure

The main unique features of biological systems are reviewed, and four necessary and sufficient attributes of life are formulated, based on the ideas of Ervin Bauer. The possibility of the occurrence of each of these attributes during the origin of life is analyzed. As a result, different scenarios for the origin of life are presented, with their pros and cons. Next, the mainstream of biological evolution is discussed, considering it as a special case of general complexification, and structuredness is defined as a quantitative measure of structural complexity. By introducing the concepts of post-dissipative structure and ratcheting process based on “frozen” patterns, their role in the generation of biological structures underlying biological evolution is demonstrated. Furthermore, it is proposed that all living things can be divided into micro- (unicellular) and macro- (multicellular) creatures, which differ from each other even more radically than the difference between prokaryotes and unicellular eukaryotes. Then the fifth, sufficient, but not necessary attribute of life, hierarchicality, is formulated, which is fully applicable only to macrolife. It is also shown that living organisms are primarily chemodynamic rather than thermodynamic systems, and three basic laws of biochemodynamics are formulated. Finally, fifteen basic features of living beings, grouped into four basic blocks, are summarized.

Quantifying spatiotemporal patterns in classical and quantum systems out of equilibrium.

A rich variety of nonequilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in many-body systems of completely different nature. In this work we provide a solution to this problem by adopting a structural complexity measure to quantify spatiotemporal patterns in the time-dependent digital representation of a system. On the basis of very limited amount of data our approach allows us to distinguish different dynamical regimes and define critical parameters in both classical and quantum systems. By the example of the discrete time crystal realized in nonequilibrium quantum systems we provide a complete low-level characterization of this nontrivial dynamical phase with only processing bitstrings, which can be considered as a valuable alternative to previous studies based on the calculations of qubit correlation functions.

Structural reorganization in beech forests in central Germany as response to drought-induced mortality in the overstory

Prolonged periods of extreme heat and drought are changing forest health and forest structure. Loss of vitality, signs of dieback, and mortality of trees are reported in many regions of the world. There is a need for information on the quantification of drought effects on forest structure in order to detect drought stress at an early stage. Furthermore, forest structure is linked to growth processes that result from single tree and stand dynamics. In this study, we used mobile laser scanning to objectively assess forest structure in European beech (Fagus sylvatica L.) stands differently affected by drought. We used the box-dimension as a holistic measure of structural complexity that jointly describes both distribution and amount of plant material in a forest, and canopy cover as a measure for overall defoliation. We observed large canopy gaps in heavily damaged stands, but the overall structural complexity of the forest stands remained unchanged. However, when dividing the 3D forest stand model from mobile laser scanning into 5 m height layers, we noticed a “structural flip” with reduced structural complexity in the upper parts of the forests and increased structural complexity in the lower strata. This indicates that the forests are responding to drought with increased mortality of mature trees, resulting in increased light availability in the understory and consequently increased growth of the understory trees. The rather indifferent overall structural complexity of the investigated forests was due to the reorganization of structures by shifting the major foliage layer from top-to-bottom and is interpreted as a successful ecosystem-scale response to the drought events. However, it is unclear how these forests will respond to repeated droughts. The “structural flip” should therefore be regarded as an early warning signal pointing to increased ecosystem stress, though the stress level has not yet exceeded the adaptive capacity in the investigated forest.

Informational assessment of large scale self-similarity in nonlinear random field models

Large-scale behavior of a wide class of spatial and spatiotemporal processes is characterized in terms of informational measures. Specifically, subordinated random fields defined by nonlinear transformations on the family of homogeneous and isotropic Lancaster–Sarmanov random fields are studied under long-range dependence (LRD) assumptions. In the spatial case, it is shown that Shannon mutual information between random field components for infinitely increasing distance, which can be properly interpreted as a measure of large scale structural complexity and diversity, has an asymptotic power law decay that depends on the underlying LRD parameter scaled by the subordinating function rank. Sensitivity with respect to distortion induced by the deformation parameter under the generalized form given by divergence-based Rényi mutual information is also analyzed. In the spatiotemporal framework, a spatial infinite-dimensional random field approach is adopted. The study of the large-scale asymptotic behavior is then extended under the proposal of a functional formulation of the Lancaster–Sarmanov random field class, as well as of divergence-based mutual information. Results are illustrated, in the context of geometrical analysis of sample paths, considering some scenarios based on Gaussian and Chi-Square subordinated spatial and spatiotemporal random fields.

Degree-Based Graph Entropy in Structure-Property Modeling.

Graph entropy plays an essential role in interpreting the structural information and complexity measure of a network. Let G be a graph of order n. Suppose dG(vi) is degree of the vertex vi for each i=1,2,…,n. Now, the k-th degree-based graph entropy for G is defined as Id,k(G)=-∑i=1ndG(vi)k∑j=1ndG(vj)klogdG(vi)k∑j=1ndG(vj)k, where k is real number. The first-degree-based entropy is generated for k=1, which has been well nurtured in last few years. As ∑j=1ndG(vj)k yields the well-known graph invariant first Zagreb index, the Id,k for k=2 is worthy of investigation. We call this graph entropy as the second-degree-based entropy. The present work aims to investigate the role of Id,2 in structure property modeling of molecules.

A nonparametric measure of noise in x-ray diagnostic images—mammography

Objective. In x-ray diagnostics, modern image reconstruction or image processing methods may render established methods of image quality assessment inadequate. Task specific quality assessment by using model observers has the disadvantage of being very labour-intensive. Therefore, it appears highly desirable to develop novel image quality parameters that neither rely on the linearity and the shift-invariace of the imaging system nor require the acquisition of hundreds of images as is necessary for the application of model observers, and which can be derived directly from diagnostic images. Approach. A new measure for the noise based on non-maximum-suppression images is defined and its properties are explored using simulated images before it is applied to an exposure series of mammograms of a homogeneous phantom and a 3D-printed breast phantom to demonstrate its usefulness under realistic conditions. Main results. The new noise parameter cannot only be derived from images with a homogeneous background but it can be extracted directly from images containing anatomic structures and is proportional to the standard deviation of the noise. At present, the applicability is restricted to mammography, which satisfies the assumption of short covariance length of the noise. Significance. The new measure of the noise is but a first step of the development of a set of parameters that are required to quantify image quality directly from diagnostic images without relying on the assumption of a linear, shift-invariant system, e.g. by providing measures of sharpness, contrast and structural complexity, in addition to the noise measure. For mammography, a convenient method is now available to quantify noise in processed diagnostic images.

Scale dependency of lidar‐derived forest structural diversity

AbstractLidar‐derived forest structural diversity (FSD) metrics—including measures of forest canopy height, vegetation arrangement, canopy cover (CC), structural complexity and leaf area and density—are increasingly used to describe forest structural characteristics and can be used to infer many ecosystem functions. Despite broad adoption, the importance of spatial resolution (grain and extent) over which these structural metrics are calculated remains largely unconsidered. Often researchers will quantify FSD at the spatial grain size of the process of interest without considering the scale dependency or statistical behaviour of the FSD metric employed.We investigated the appropriate scale of inference for eight lidar‐derived spatial metrics—CC, canopy relief ratio, foliar height diversity, leaf area index, mean and median canopy height, mean outer canopy height, and rugosity (RT)‐‐representing five FSD categories—canopy arrangement, CC, canopy height, leaf area and density, and canopy complexity. Optimal scale was determined using the representative elementary area (REA) concept whereby the REA is the smallest grain size representative of the extent. Structural metrics were calculated at increasing canopy spatial grain (from 5 to 1000 m) from aerial lidar data collected at nine different forested ecosystems including sub‐boreal, broadleaf temperate, needleleaf temperate, dry tropical, woodland and savanna systems, all sites are part of the National Ecological Observatory Network within the conterminous United States. To identify the REA of each FSD metric, we used changepoint analysis via segmented or piecewise regression which identifies significant changepoints for both the magnitude and variance of each metric.We find that using a spatial grain size between 25 and 75 m sufficiently captures the REA of CC, canopy arrangement, canopy leaf area and canopy complexity metrics across multiple forest types and a grain size of 30–150 m captures the REA of canopy height metrics. However, differences were evident among forest types with higher REA necessary to characterize CC in evergreen needleleaf forests, and canopy height in deciduous broadleaved forests.These findings indicate the appropriate range of spatial grain sizes from which inferences can be drawn from this set of FSD metrics, informing the use of lidar‐derived structural metrics for research and management applications.

Simulation of silvicultural treatments based on real 3D forest data from mobile laser scanning point clouds

Forest management has a direct influence on the structure and stability of forests. In this study, we used the 3D data from mobile laser scanning in real forest stands dominated by European beech (Fagus sylvatica L.) to simulate different silvicultural treatments and assess their impact on the structural complexity and short-term economic return. For the structural assessment, we used the box-dimension (Db), a holistic measure of structural complexity in forest. The expected net revenues of the silvicultural treatments were used as a proxy for short-term economic gain. We simulated six different treatments in 19 different real-world forest stands. The results showed that each treatment had a negative impact on the structural complexity of the stands but with varying severity. The treatments with the smallest effect on stand structural complexity showed the highest net revenue, indicating no trade-offs if a forest owner strives for small stand structural changes and high economic return. The approach used here allows quantifying the structural and economic consequences of different treatments in forest stands prior to the actual application in the real world. This holds large potential for decision making according to the forest owner's objective.

New Structural Complexity Metrics for Forests from Single Terrestrial Lidar Scans

We developed new measures of structural complexity using single point terrestrial laser scanning (TLS) point clouds. These metrics are depth, openness, and isovist. Depth is a three-dimensional, radial measure of the visible distance in all directions from plot center. Openness is the percent of scan pulses in the near-omnidirectional view without a return. Isovists are a measurement of the area visible from the scan location, a quantified measurement of the viewshed within the forest canopy. 243 scans were acquired in 27 forested stands in the Pacific Northwest region of the United States, in different ecoregions representing a broad gradient in structural complexity. All stands were designated natural areas with little to no human perturbations. We created “structural signatures” from depth and openness metrics that can be used to qualitatively visualize differences in forest structures and quantitively distinguish the structural composition of a forest at differing height strata. In most cases, the structural signatures of stands were effective at providing statistically significant metrics differentiating forests from various ecoregions and growth patterns. Isovists were less effective at differentiating between forested stands across multiple ecoregions, but they still quantify the ecological important metric of occlusion. These new metrics appear to capture the structural complexity of forests with a high level of precision and low observer bias and have great potential for quantifying structural change to forest ecosystems, quantifying effects of forest management activities, and describing habitat for organisms. Our measures of structure can be used to ground truth data obtained from aerial lidar to develop models estimating forest structure.

Disentangling the seasonal effects of agricultural intensification on birds and bats in Mediterranean olive groves

Assessing the spatio-temporal impact of agricultural intensification on species and communities is key for biodiversity conservation. Here, we investigated the seasonal effects of olive grove intensification at both local (farming practices and grove structural complexity) and landscape scale (land-cover diversity) on birds and bats, at species and community-level. Both groups were surveyed during spring, summer, and autumn in 60 sites representing varying levels of olive grove intensification throughout the Alentejo region (southern Portugal). At the local scale, the number of chemical applications was used as a proxy for the intensification of farming practices and a Structural Index, which accounted for within-grove variability in tree density and features, was used as a measure of grove structural complexity. At landscape scale, we quantified the proportion of the major land-cover types potentially affecting birds and bats. We found that the abundance of ca. 77% of the species analyzed (ca. 84% and 55% of birds and bats respectively) was negatively related to olive grove intensification in at least one season. The Structural Index was the most influential factor at both species and community-levels, especially for birds, with a consistent and strong effect across seasons. Chemical applications had a stronger negative effect on birds, whereas the amount of olive grove cover had a stronger detrimental effect on bats. Birds and bats showed a variable response to predictor variables depending on the season, particularly for the bat community. Our study shows differences in bird and bat responses associated with the spatio-temporal variability of the agricultural intensification components. On the one hand, birds and bats showed a seasonal pattern of association with the different components of olive grove intensification, probably due to their ecological and biological requirements. On the other hand, the responses of both groups also appear to be scale-dependent: while birds seem to respond to in-farm or local intensification more strongly, bats seem to be more influenced by landscape-scale simplification. Overall, we highlight the importance of the structural complexity of olive groves for birds and bats, an aspect that should be considered in the design of agricultural policies aiming to promote biodiversity conservation.

Intra-habitat structural complexity drives the distribution of fish trait groups on coral reefs

Three-dimensional (3D) habitat complexity is a primary driver of organism distribution and community structure across ecosystems. Identifying the specific metrics and spatial scales at which complexity is functionally important for communities is therefore a critical component in forecasting ecosystem function. Here we pair fish species traits with multiple metrics from habitat photogrammetry to evaluate the most important measures and scales of 3D complexity driving ecological functions within one of the most structurally diverse ecosystems on the planet: coral reefs. From May to July 2019, we collected high-resolution (1 cm) large- and small-scale intra-habitat (25 m2) structural complexity data across eight reefscapes (∼2500 m2) and conducted co-located fish functional group surveys in the Florida Keys, FL, USA. We used a hierarchical clustering analysis to group 80 observed fish species by four traits related to habitat use (social level, body size, crypsis, activity period) and feeding guild to generate mechanistic predictions about fish-habitat relationships. Evaluating relationships between the resulting trait-based functional groups (k = 9) and four metrics of intra-habitat complexity (large-scale vertical relief, and small-scale vector ruggedness [VRM], VRM deviation, and profile curvature) revealed that trait groups respond independently to the various measures and scales of reef complexity. While large-scale complexity (relief) is strongly related to the presence of solitary, cryptic, nocturnal carnivores, likely due to prey availability as well as day-time refuge opportunities, herbivore abundance is unaffected by increasing vertical relief, potentially due to predator avoidance. Instead, gregarious (i.e., schooling) herbivores increase with small-scale complexity measured by VRM and VRM deviation across reefscapes, while less gregarious herbivores only respond to small-scale complexity when these same measures occur in low-relief habitat, possibly due to a tradeoff between grazing resource availability and predator visibility. Our results reveal how unique elements of complexity provided by both biotic benthic communities as well as large-scale habitat features like vertical relief are differentially important to fish functional groups. The general relationships we identified using traits provide a framework for predicting fish community responses to changes in specific measures of structural complexity on coral reefs globally. Our work illustrates how preserving 3D habitat complexity by protecting or augmenting (e.g., via restoration) structure-forming organisms can support diverse organismal communities and overall ecosystem productivity.

Neonatal EEG seizure detection using a new signal structural complexity measure based on matching pursuit decomposition with nonstationary dictionary

Background and objectiveIn newborns, it is often difficult to accurately differentiate between seizure and non-seizure based solely on clinical manifestations. This highlights the importance of electroencephalogram (EEG) in the recognition and management of neonatal seizures. This paper proposes an effective algorithm for the detection of neonatal seizure using multichannel EEG. MethodsNeonatal EEG changes morphology as it alternates between seizure and non-seizure states. A new signal complexity measure based on matching pursuit (MP) decomposition is proposed and used to detect transitions between these two states. The new measure, referred to as weighted structural complexity (WSC), was used for the detection of seizures in 30 newborn EEG records. Multiple IIR filters and an MP-based filter were designed and used to remove artifacts from the EEG data. Geometrical correlation between the EEG data channels was applied to reduce the number of false detections caused by remnant artifacts. The seizure detector's performance was assessed using several epoch-based (e.g., accuracy) and event-based (GDR = good detection rate and FD/h = false detections per hour) metrics. ResultsCompared to the neurologist marking, the proposed detector was able to detect EEG seizures with 94% accuracy, 90.9% GDR, and 0.14 FD/h (95% CI: [0.06, 0.34]). ConclusionsThe high performance of the MP-based detector may have significant implications for the accurate diagnosis of neonatal seizures and the appropriate use of anticonvulsants and ongoing clinical assessment and care of the newborn.

Sexual dimorphism in the relationship between brain complexity, volume and general intelligence (g): a cross-cohort study

Changes in brain morphology have been reported during development, ageing and in relation to different pathologies. Brain morphology described by the shape complexity of gyri and sulci can be captured and quantified using fractal dimension (FD). This measure of brain structural complexity, as well as brain volume, are associated with intelligence, but less is known about the sexual dimorphism of these relationships. In this paper, sex differences in the relationship between brain structural complexity and general intelligence (g) in two diverse geographic and cultural populations (UK and Indian) are investigated. 3D T1-weighted magnetic resonance imaging (MRI) data and a battery of cognitive tests were acquired from participants belonging to three different cohorts: Mysore Parthenon Cohort (MPC); Aberdeen Children of the 1950s (ACONF) and UK Biobank. We computed MRI derived structural brain complexity and g estimated from a battery of cognitive tests for each group. Brain complexity and volume were both positively corelated with intelligence, with the correlations being significant in women but not always in men. This relationship is seen across populations of differing ages and geographical locations and improves understanding of neurobiological sex-differences.

Deviation from a state of perfect uniformity: An indicator of structural complexity in projects

AbstractThe complexity of projects arising from interconnectedness between activities is believed to be one of the most significant challenges for managing projects. Although the literature has long appreciated the significance of measuring complexity, research on this topic is weakened by the lack of a method that accounts for a diverse set of structural characteristics of project networks. To evade this pitfall, this paper introduces the concept of perfect uniformity and develops a comprehensive measure of structural complexity in projects. The proposed method is validated by applying it in two real‐life projects. The validation results confirm that project complexity is positively associated with a higher level of deviation from a state of perfect uniformity. This research is among few studies that draw on the concept of emergence and point out the importance of a system‐level approach in project management to analyse the interdependency between multiple interconnected activities.

Structural and information-theoretic complexity measures of brain networks: Evolutionary aspects and implications

The evolutionary lineage of neuronal phenotype is notably complex even within a limited number of species. One of the approaches resides in the realm of complex network theory. The theory reduces the connectomic data into a hallmarked set of few parameters, some of which might be correlated with a suitably chosen phylogenetic marker. In this first-of-its-kind attempt, interspecific variations of two structural complexity measures (i.e., clustering coefficient and centrality) along with two independent information-theoretic measures (i.e., von Neumann entropy and multifractality) are investigated to decipher any hidden evolutionary signature considering four mammalian connectomes (i.e., felis catus, mus musculus, macaca mulatta, and homo sapiens). All network complexity measures partially corroborate with the phylogenetic order. Nevertheless, monotonicity of the measures with the chosen phylogenetic marker of genome size has been majorly violated because of the mus musculus data point. On the other hand, von Neumann entropy was found to exhibit an allometric scaling behavior with the community structure of all connectomes (p<0.0001, and R2>0.95). The respective scaling exponent was noted to be monotonic with the genome size. Singularities of the real connectomes were also investigated upon carrying out a similar analysis in three equivalent synthetic network models.

Disturbance has variable effects on the structural complexity of a temperate forest landscape

The temporal dynamics of forest canopy structure are influenced by disturbances that alter vegetation quantity and distribution. While canopy structural indicators such as leaf area index (LAI), canopy cover, and canopy height have been widely studied in the context of disturbance, the post-disturbance temporal dynamics of structural complexity, which summarizes the heterogeneity of vegetation arrangement, are poorly understood. With the goal of advancing conceptual and empirical understanding of the temporal dynamics of structural complexity following disturbance, we synthesized results from three large-scale disturbance manipulation experiments at the University of Michigan Biological Station (UMBS): the 4-year Forest Resilience Threshold Experiment (FoRTE) manipulating levels of disturbance severity; the decade-long Forest Accelerated Succession Experiment (FASET), in which all early successional tree species were stem-girdled within 39 ha in the same landscape; and forest chronosequences established following clear-cut harvesting. We found that the temporal dynamics of canopy structure following disturbance were dependent upon three factors: (1) the source and severity of disturbance; (2) the spatial and temporal scales of analysis; and (3) the measure of structure assessed. Unlike vegetation area index and canopy cover, which initially decreased in response to disturbance, structural complexity measures such as canopy and top rugosity did not consistently respond to moderate levels of disturbance severity. Over multi-decadal timescales, structural complexity increased to a maximum, regardless of whether fire occurred at the time of stand establishment, but intervening low-to-moderate severity disturbance in regrown century-old forests altered trajectories of canopy rugosity. We conclude that structural complexity indicators display a more nuanced temporal and directional response to disturbance than conventional leaf area and cover indexes. Predicting what disturbance conditions modify trajectories of structural complexity remains critical to disturbance characterization and the inference of ecosystem functioning.

Education Teaching Evaluation Method Aided by Adaptive Genetic Programming and Robust Scheduling

Process mining technology aims to automatically generate process models by analyzing events, thereby assisting the design and redesign of process models. Although many process mining methods have appeared, they all have deficiencies. These methods focus on mining from the behavioral aspects described by the log, while ignoring the structural nature of the process model itself. The complexity of the process describes the simplicity and ease of understanding of the process. Higher process complexity affects the readability of the process. Genetic programming has strong robustness. Its individual representation based on tree structure can describe the special structure of the process. The introduction of process complexity fitness enables it to consider the complexity of the process model itself while mining log behavior, so as to achieve nonlinear mining of complex processes. This paper analyzes the process mining based on genetic programming and proposes process individuals based on tree structure. By realizing the combination of process complexity measurement and process mining technology, noncomplex process mining can be realized. In this paper, the process complexity is combined with the process mining algorithm based on genetic programming, and a measure of process structural complexity is proposed, which is converted into complexity fitness and introduced into the fitness function of genetic programming, to realize the use of genetic programming. The research results show that the improved new adaptive genetic programming robust scheduling algorithm provides a new idea and method for the evaluation of college sports under different sports conditions. This makes the college sports evaluation management system more intelligent and improves the rational allocation of physical education teaching.

From communities to individuals: Using remote sensing to inform and monitor woodland restoration

SummaryThe benefits of using remote sensing technologies for informing and monitoring ecological restoration of forests from the community to the individual are presented. At the community level, we link remotely sensed measures of structural complexity with animal behaviour. At the plot level, we monitor the return of vegetation structure and ecosystem services (e.g. carbon sequestration) using data‐rich three‐dimensional point clouds. At the individual‐level, we use high‐resolution images to accurately classify plants to species and provenance and show genetic‐based variation in canopy structural traits. To facilitate the wider use of remote sensing in restoration, we discuss the challenges that remain to be resolved.

Complexity Parameters for Molecular Solids

Structural complexity measures based on Shannon information entropy are widely used for inorganic crystal structures. However, the application of these parameters for molecular crystals requires essential modification since atoms in inorganic compounds usually possess more degrees of freedom. In this work, a novel scheme for the calculation of complexity parameters (HmolNet, HmolNet,tot) for molecular crystals is proposed as a sum of the complexity of each molecule, the complexity of intermolecular contacts, and the combined complexity of both. This scheme is tested for several molecular crystal structures.

Crystal Chemical Relations in the Shchurovskyite Family: Synthesis and Crystal Structures of K2Cu[Cu3O]2(PO4)4 and K2.35Cu0.825[Cu3O]2(PO4)4

Single crystals of two novel shchurovskyite-related compounds, K2Cu[Cu3O]2(PO4)4 (1) and K2.35Cu0.825[Cu3O]2(PO4)4 (2), were synthesized by crystallization from gaseous phase and structurally characterized using single-crystal X-ray diffraction analysis. The crystal structures of both compounds are based upon similar Cu-based layers, formed by rods of the [O2Cu6] dimers of oxocentered (OCu4) tetrahedra. The topologies of the layers show both similarities and differences from the shchurovskyite-type layers. The layers are connected in different fashions via additional Cu atoms located in the interlayer, in contrast to shchurovskyite, where the layers are linked by Ca2+ cations. The structures of the shchurovskyite family are characterized using information-based structural complexity measures, which demonstrate that the crystal structure of 1 is the simplest one, whereas that of 2 is the most complex in the family.