Complexity Measures Research Articles

Linking small mammal capture probability with understory structural complexity using a mobile laser scanning‐derived metric: A case study

AbstractForest understory complexity is important for many species, from large herbivores such as deer to small mammals such as mice and voles. For species that utilize the forest understory on a very small scale, it is often impractical to conduct correspondingly fine‐grained manual surveys of the understory, and thus few studies consider this small‐scale variation in understory complexity and instead work with average values on a larger scale. We explored the use of a mobile laser scanning derived understory complexity measure—understory roughness—to predict the capture probability of two representative small mammal species, the yellow‐necked mouse (Apodemus flavicollis) and the bank vole (Clethrionomys glareolus). We found a positive relationship between capture probability and understory roughness for both bank voles and yellow‐necked mice. Our results suggest that mobile laser scanning is a promising technology for measuring understory complexity in an ecologically meaningful way.

Computably enumerable equivalence relations via primitive recursive reductions

Abstract The complexity classification of computably enumerable equivalence relations (or ceers, for short) has received much attention in the recent literature. A measure of complexity is typically provided by an appropriate notion of a reduction. Given binary relations $R$ and $S$ on natural numbers, a total function $f$ is a reduction from $R$ to $S$ if for arbitrary $x$ and $y$, the conditions $x~R~y$ and $f(x)~S~f(y)$ are always equivalent. If the function $f$ can be chosen primitive recursive, then we say that $R$ is primitively recursively reducible to $S$, denoted by $R \leq _{pr} S$. We investigate the degree structure $(\textbf {Ceers},\leq _{pr})$ of $\leq _{pr}$-degrees of ceers. We examine when pairs of incomparable degrees have an infimum and a supremum. In particular, we show that $(\textbf {Ceers},\leq _{pr})$ is neither an upper semilattice nor a lower semilattice. We also study first-order definable subclasses of $(\textbf {Ceers},\leq _{pr})$. In particular, we prove that the set of equivalences that have only finitely many classes is definable in $(\textbf {Ceers},\leq _{pr})$. Finally, we show that the structure of $\leq _{pr}$-degrees of computably enumerable preorders has a hereditarily undecidable theory.

Beyond accuracy

The language of Heritage Speakers (HS), or of early bilinguals of a minority language, is often seen as incomplete or less developed than that of Monolingual Speakers (MS). This study investigates whether 7- to 9-year-old English/Polish HS can be distinguished from MS in terms of linguistic skills when complexity and fluency are focal rather than accuracy. Data from 78 participants shows no significant differences between HS and MS in fluency on an overall measure in either of the languages, although HS produce more fillers and repetitions. On complexity measures, the results for English were similar across groups for Mean Length of T-Unit, but there was a statistically significant difference in Polish, with HS achieving higher values. On a more specific measure of syntactic complexity (Subordination Index), HS achieved higher scores in both languages. There were no significant differences for Lexical Diversity. Corresponding measures were positively correlated across languages, suggesting that the L1 does not impede L2 achievement. Overall, we observed substantial overlap between the groups, with the vast majority of HS falling within the MS norms and the MS falling within the HS norms. This emphasises the need to move away from the deficit approach towards HS.

ClustML: A measure of cluster pattern complexity in scatterplots learnt from human-labeled groupings

Visual quality measures (VQMs) are designed to support analysts by automatically detecting and quantifying patterns in visualizations. We propose a new VQM for visual grouping patterns in scatterplots, called ClustML, which is trained on previously collected human subject judgments. Our model encodes scatterplots in the parametric space of a Gaussian Mixture Model and uses a classifier trained on human judgment data to estimate the perceptual complexity of grouping patterns. The numbers of initial mixture components and final combined groups quantify visual cluster patterns in scatterplots. It improves on existing VQMs, first, by better estimating human judgments on two-Gaussian cluster patterns and, second, by giving higher accuracy when ranking general cluster patterns in scatterplots. We use it to analyze kinship data for genome-wide association studies, in which experts rely on the visual analysis of large sets of scatterplots. We make the benchmark datasets and the new VQM available for practical use and further improvements.

Functional balance at rest of hemispheric homologs assessed via normalized compression distance

IntroductionThe formation and functioning of neural networks hinge critically on the balance between structurally homologous areas in the hemispheres. This balance, reflecting their physiological relationship, is fundamental for learning processes. In our study, we explore this functional homology in the resting state, employing a complexity measure that accounts for the temporal patterns in neurodynamics.MethodsWe used Normalized Compression Distance (NCD) to assess the similarity over time, neurodynamics, of the somatosensory areas associated with hand perception (S1). This assessment was conducted using magnetoencephalography (MEG) in conjunction with Functional Source Separation (FSS). Our primary hypothesis posited that neurodynamic similarity would be more pronounced within individual subjects than across different individuals. Additionally, we investigated whether this similarity is influenced by hemisphere or age at a population level.ResultsOur findings validate the hypothesis, indicating that NCD is a robust tool for capturing balanced functional homology between hemispheric regions. Notably, we observed a higher degree of neurodynamic similarity in the population within the left hemisphere compared to the right. Also, we found that intra-subject functional homology displayed greater variability in older individuals than in younger ones.DiscussionOur approach could be instrumental in investigating chronic neurological conditions marked by imbalances in brain activity, such as depression, addiction, fatigue, and epilepsy. It holds potential for aiding in the development of new therapeutic strategies tailored to these complex conditions, though further research is needed to fully realize this potential.

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.

Temporal ECDSA: A timestamp and signature mask enabled ECDSA algorithm for IoT client node authentication

Internet of Things (IoT) networks are vulnerable to various security threats, especially in client authentication. The current authentication methods require significant resources and are vulnerable to specific attacks. The Non-Interactive Zero Knowledge Proof (NIZKP) concept suits IoT device authentication. Elliptic Curve Digital Signature (ECDSA) is a popular algorithm for IoT device authentication based on elliptic curve cryptography (ECC) and NIZKP. However, an intelligent attacker who captures the ECDSA signatures generated by the same random number can recover the private key. This paper proposes a timestamp based approach to prevent signature reuse and fake signature generation in the ECDSA algorithm. The signature proof is generated differently at each occurrence to prevent the generation of valid signatures from leaked private keys. The proposed approach eliminates the expensive modular inversion operations in signature generation and verification phases, enhancing execution efficiency. The analysis results indicate that the proposed Temporal ECDSA algorithm effectively prevents most attacks on client authentication in IoT networks. Various metrics, including computational complexity and security measures, were used to evaluate the effectiveness of the proposed approach, demonstrating that it outperforms most ECDSA variants.

Time-delay identification from chaotic time series via statistical complexity measures based on ordinal pattern transition networks

Time-delay identification from chaotic time series via statistical complexity measures based on ordinal pattern transition networks

Exploring Physiological Differences in Brain Areas Using Statistical Complexity Analysis of BOLD Signals.

The brain is a fundamental organ for the human body to function properly, for which it needs to receive a continuous flow of blood, which explains the existence of control mechanisms that act to maintain this flow as constant as possible in a process known as cerebral autoregulation. One way to obtain information on how the levels of oxygen supplied to the brain vary is through of BOLD (Magnetic Resonance) images, which have the advantage of greater spatial resolution than other forms of measurement, such as transcranial Doppler. However, they do not provide good temporal resolution nor allow for continuous prolonged examination. Thus, it is of great importance to find a method to detect regional differences from short BOLD signals. One of the existing alternatives is complexity measures that can detect changes in the variability and temporal organisation of a signal that could reflect different physiological states. The so-called statistical complexity, created to overcome the shortcomings of entropy alone to explain the concept of complexity, has shown potential with haemodynamic signals. The aim of this study is to determine by using statistical complexity whether it is possible to find differences between physiologically distinct brain areas in healthy individuals. The data set includes BOLD images of 10 people obtained at the University Hospital of Leicester NHS Trust with a 1.5 Tesla magnetic resonance imaging scanner. The data were captured for 180 s at a frequency of 1 Hz. Using various combinations of statistical complexities, no differences were found between hemispheres. However, differences were detected between grey matter and white matter, indicating that these measurements are sensitive to differences in brain tissues.

Complexity of STG signals and linguistic rhythm: a methodological study for EEG data.

The superior temporal and the Heschl's gyri of the human brain play a fundamental role in speech processing. Neurons synchronize their activity to the amplitude envelope of the speech signal to extract acoustic and linguistic features, a process known as neural tracking/entrainment. Electroencephalography has been extensively used in language-related research due to its high temporal resolution and reduced cost, but it does not allow for a precise source localization. Motivated by the lack of a unified methodology for the interpretation of source reconstructed signals, we propose a method based on modularity and signal complexity. The procedure was tested on data from an experiment in which we investigated the impact of native language on tracking to linguistic rhythms in two groups: English natives and Spanish natives. In the experiment, we found no effect of native language but an effect of language rhythm. Here, we compare source projected signals in the auditory areas of both hemispheres for the different conditions using nonparametric permutation tests, modularity, and a dynamical complexity measure. We found increasing values of complexity for decreased regularity in the stimuli, giving us the possibility to conclude that languages with less complex rhythms are easier to track by the auditory cortex.

Catchment-scale hydrology limits the benefits of geomorphic complexity for instream vegetation communities

Improving instream habitat complexity is a common stream restoration approach despite often limited improvements to stream biota with catchment-scale stressors such as altered hydrology thought to be more important. Instream vegetation is a critical component of lowland stream ecosystems, providing multiple ecological benefits. Thus, we asked: How does instream vegetation respond to (1) geomorphic complexity; (2) different flow regime components; and (3) what is the relationship between geomorphic complexity and flow in driving instream vegetation?We surveyed instream vegetation and geomorphology along 23 lowland stream reaches. We investigated associations between six measures of geomorphic complexity, six flow metrics, and amphibious and aquatic vegetation richness, Shannon diversity and cover.Amphibious vegetation was negatively associated with simplified channels and increasing flood frequency. Increasing depth and width variation, and Julian day low flow variability, were positively associated with aquatic vegetation. Considering sites with complex (stable) or simplified (unstable) geomorphology separately, only vegetation at stable sites showed strong relationships to flow regime components, with variables related to flow flashiness negatively associated with both amphibious and aquatic vegetation, and Julian day low flow variability positively associated with aquatic vegetation.We identified channel complexity, variables related to flow flashiness and variation in low flow timing, as key geomorphic and flow drivers of instream vegetation, respectively. Importantly, our results suggest that instream vegetation benefits from improving geomorphic complexity are likely to be limited without also addressing altered flow regimes.

Automated Measures of Syntactic Complexity in Natural Speech Production: Older and Younger Adults as a Case Study.

Multiple methods have been suggested for quantifying syntactic complexity in speech. We compared eight automated syntactic complexity metrics to determine which best captured verified syntactic differences between old and young adults. We used natural speech samples produced in a picture description task by younger (n = 76, ages 18-22 years) and older (n = 36, ages 53-89 years) healthy participants, manually transcribed and segmented into sentences. We manually verified that older participants produced fewer complex structures. We developed a metric of syntactic complexity using automatically extracted syntactic structures as features in a multidimensional metric. We compared our metric to seven other metrics: Yngve score, Frazier score, Frazier-Roark score, developmental level, syntactic frequency, mean dependency distance, and sentence length. We examined the success of each metric in identifying the age group using logistic regression models. We repeated the analysis with automatic transcription and segmentation using an automatic speech recognition (ASR) system. Our multidimensional metric was successful in predicting age group (area under the curve [AUC] = 0.87), and it performed better than the other metrics. High AUCs were also achieved by the Yngve score (0.84) and sentence length (0.84). However, in a fully automated pipeline with ASR, the performance of these two metrics dropped (to 0.73 and 0.46, respectively), while the performance of the multidimensional metric remained relatively high (0.81). Syntactic complexity in spontaneous speech can be quantified by directly assessing syntactic structures and considering them in a multivariable manner. It can be derived automatically, saving considerable time and effort compared to manually analyzing large-scale corpora, while maintaining high face validity and robustness. https://doi.org/10.23641/asha.24964179.

Bionic modeling and dynamics analysis of heterogeneous brain regions connected by memristive synaptic crosstalk

The coupling dynamics between different brain regions has long been a gap in the study of neural dynamics. To overcome this bottleneck, the synaptic crosstalk characterized by coupled memristors is creatively connected to different brain regions characterized by two heterogeneous Hopfield neural networks (HNNs), forming a novel bionic memristive synaptic crosstalk coupled-HNN (MSC-HNN) model for the first time. Rigorous boundedness and stability analyses ensure that coupling dynamics are generated within a bounded region. Utilizing innovative dynamics methods, it is revealed that the plasticity of synaptic crosstalk allows MSC-HNN to exhibit homogeneous dynamics properties globally, and the two internal HNNs preserve heterogeneous bifurcation processes and attractors. Interestingly, when the initial conditions undergo slight variations, the multistability phenomenon is simultaneously represented by the coexisting parameter bifurcation and the local basin of attraction, which enhances the diversity of activities in MSC-HNN. Furthermore, these novel dynamics effects are evaluated and validated through quantitative calculations of complexity measures and spectra. Subsequently, the developed analog and digital circuit implementation paradigms confirm the feasibility and practical value of MSC-HNN.

Alternations (at) that time: NP versus PP time adjuncts in the history of English.

The present paper investigates variation between nominal and prepositional adjuncts of time as in, for example, [on] that day, they left. The main goals are (i)to assess potential changes in the distribution of these variants in the history of English, specifically from Middle English to Late Modern English (1150-1914), and (ii) to test which factors most strongly impact the choice between the two variants, with a focus on the impact of different complexity measures. To address these questions, the paper makes use of data from the Penn-Helsinki Parsed Corpora of Historical English (PPCME2; PPCEME; PPCMBE), explored by means of logistic regression modelling. The results suggest that there is no dramatic, sweeping change in this abstract alternation over time, but that this variation may mainly plays out on lower, noun-specific levels.

Population-Based Trends in Complexity of Hospital Inpatients

Clinical experience suggests that hospital inpatients have become more complex over time, but few studies have evaluated this impression. To assess whether there has been an increase in measures of hospital inpatient complexity over a 15-year period. This cohort study used population-based administrative health data from nonelective hospitalizations from April 1, 2002, to January 31, 2017, to describe trends in the complexity of inpatients in British Columbia, Canada. Hospitalizations were included for individuals 18 years and older and for which the most responsible diagnosis did not correspond to pregnancy, childbirth, the puerperal period, or the perinatal period. Data analysis was performed from July to November 2023. The passage of time (15-year study interval). Measures of complexity included patient characteristics at the time of admission (eg, advanced age, multimorbidity, polypharmacy, recent hospitalization), features of the index hospitalization (eg, admission via the emergency department, multiple acute medical problems, use of intensive care, prolonged length of stay, in-hospital adverse events, in-hospital death), and 30-day outcomes after hospital discharge (eg, unplanned readmission, all-cause mortality). Logistic regression was used to estimate the relative change in each measure of complexity over the entire 15-year study interval. The final study cohort included 3 367 463 nonelective acute care hospital admissions occurring among 1 272 444 unique individuals (median [IQR] age, 66 [48-79] years; 49.1% female and 50.8% male individuals). Relative to the beginning of the study interval, inpatients at the end of the study interval were more likely to have been admitted via the emergency department (odds ratio [OR], 2.74; 95% CI, 2.71-2.77), to have multimorbidity (OR, 1.50; 95% CI, 1.47-1.53) and polypharmacy (OR, 1.82; 95% CI, 1.78-1.85) at presentation, to receive treatment for 5 or more acute medical issues (OR, 2.06; 95% CI, 2.02-2.09), and to experience an in-hospital adverse event (OR, 1.20; 95% CI, 1.19-1.22). The likelihood of an intensive care unit stay and of in-hospital death declined over the study interval (OR, 0.96; 95% CI, 0.95-0.97, and OR, 0.81; 95% CI, 0.80-0.83, respectively), but the risks of unplanned readmission and death in the 30 days after discharge increased (OR, 1.14; 95% CI, 1.12-1.16, and OR, 1.28; 95% CI, 1.25-1.31, respectively). By most measures, hospital inpatients have become more complex over time. Health system planning should account for these trends.

A corpus-based developmental investigation of linguistic complexity in children's writing

Writing proficiency is associated with linguistic complexity. We used measures of linguistic complexity to investigate the development of children's narrative writing using a large corpus of short stories (N>100,000) written by children aged 5–13 in the UK. Linguistic complexity was assessed using both lexical (N = 30) and syntactic (N = 14) measures. Most measures were associated with age, with writing by older children showing greater lexical density, sophistication, and diversity than writing by younger children. Older children also used longer sentences, and longer T-units and clauses, and the density of smaller syntactic units inside larger units was also higher. Principal Component Analysis identified a number of dimensions associated with complexity, with the first two dimensions capturing nearly 50 % of variance. Lexical diversity was mainly represented on the first dimension and syntactic complexity on the second. Across the age range, there was wider variation in syntactic complexity than in lexical diversity, suggesting that syntactic development is subject to more individual differences than the ability to use a diverse set of lexical items. Our findings quantify the nature and content of children's writing through mid-childhood, and we discuss the utility of analysing children's writing using a computational, data-driven approach.

Functionality of Box Intersection Graphs

Functionality is a graph complexity measure that extends a variety of parameters, such as vertex degree, degeneracy, clique-width, or twin-width. In the present paper, we show that functionality is bounded for box intersection graphs in R1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^1$$\\end{document}, i.e. for interval graphs, and unbounded for box intersection graphs in R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^3$$\\end{document}. We also study a parameter known as symmetric difference, which is intermediate between twin-width and functionality, and show that this parameter is unbounded both for interval graphs and for unit box intersection graphs in R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {R}^2$$\\end{document}.

Linguistic complexity measures of short narrative writings for modeling overall Chinese proficiency

This study investigates whether linguistic complexity measures of short narrative writings can model overall proficiency in Chinese as a second language. A sample of native Japanese undergraduate students with intermediate (n = 34) and advanced (n = 43) levels of Chinese proficiency, and a sample of native speakers of Chinese (n = 43) altogether provided 240 short narrative essays in Chinese, with a minimum length of 30 characters and an actual grand mean length of 45 characters. Linguistic complexity measures, as discussed in relevant literature, were identified and coded in the essays. Multivariate analyses of variance tests suggest that learners across proficiency levels performed significantly differently on 11 complexity measures of short narrative writings. Multinomial logistic regression further revealed that six of these measures (lexical diversity, high-difficulty vocabulary, complex noun phrase ratio, average sentence length, error-free T-unit ratio, and the first-person singular pronoun) could collectively distinguish student writers’ general Chinese proficiency levels, with an overall accuracy rate approaching 0.80. The implications of the findings of this study for writing assessments and writing instruction are discussed.

A network analysis of early arthropod evolution and the potential of the primitive

It is often thought that the primitive is simpler, and that the complex is generated from the simple by some process of self-assembly or self-organization, which ultimately consists of the spontaneous and fortuitous collision of elementary units. This idea is included in the Darwinian theory of evolution, to which is added the competitive mechanism of natural selection. To test this view, we studied the early evolution of arthropods. Twelve groups of arthropods belonging to the Burgess Shale, Orsten Lagerstätte, and extant primitive groups were selected, their external morphology abstracted and codified in the language of network theory. The analysis of these networks through different network measures (network parameters, topological descriptors, complexity measures) was used to carry out a Principal Component Analysis (PCA) and a Hierarchical Cluster Analysis (HCA), which allowed us to obtain an evolutionary tree with distinctive/novel features. The analysis of centrality measures revealed that these measures decreased throughout the evolutionary process, and led to the creation of the concept of evolutionary developmental potential. This potential, which measures the capacity of a morphological unit to generate changes in its surroundings, is concomitantly reduced throughout the evolutionary process, and demonstrates that the primitive is not simple but has a potential that unfolds during this process. This means for us the first empirical evolutionary evidence of our theory of evolution as a process of unfolding.

Research on VVC Intra-Frame Bit Allocation Scheme Based on Significance Detection

This research is based on an intra-frame rate control algorithm based on the Versatile Video Coding (VVC) standard, considering that there is the phenomenon of over-allocating the bitrate of the end coding tree units (CTUs) in the bit allocation process, while the front CTUs are not effectively compressed. Fusing a Canny-based edge detection algorithm, a color contrast-based saliency detection algorithm, a Sum of Absolute Transformed Differences (SATD) based CTU coding complexity measure, and a Partial Least Squares (PLS) regression model, this paper proposes a CTU-level bit allocation improvement scheme for intra-mode code rate control of the VVC standard. First, natural images are selected to produce a lightweight dataset. Second, different metrics are utilized to obtain the significance and complexity values of each coding unit, the relatively important coding units in the whole frame are selected, which are adjusted with different weights, and the optimal adjustment multiplicity is supplemented into the dataset. Finally, the PLS regression model was used to obtain regression equations to refine the weights for adjusting the bit allocation. The proposed bit allocation scheme improves the average rate control accuracy by 0.453%, Y-PSNR by 0.05 dB, BD-rate savings by 0.33%, and BD-PSNR by 0.03 dB compared to the VVC standard rate control algorithm.