Correlation Structure Research Articles

Causally Mapping the Cerebellum in Children and Young Adults: from Motor to Cognition

While the cerebellum’s role in orchestrating motor execution and routines is well established, its functional role in supporting cognition is less clear. Previous studies claim that motricity and cognition are mapped in different areas of the cerebellar cortex, with an anterior/posterior dichotomy. However, most of the studies supporting this claim either use correlational methods (neuroimaging) or are lesion studies that did not consider central covariates (such as age, gender, treatment presence, and deep nuclei impairment) known to influence motor and cognitive recoveries in patients. Here, we used voxel-based lesion-symptom mapping (VLSM) on children and young adults having undergone cerebellar tumor resection. This approach allows to control for these covariates and evaluate causal relationships between brain anatomy and behavioral performances to disentangle the anatomic substrate of motor and cognitive functions. VLSM analyses showed that both motor and cognitive impairments were greater in children and young adults with lesions of the posterior cerebellum. These results highlight distinct and overlapping structural correlates of motor and cognitive performance in the cerebellum and are consistent with structural and functional hypotheses of integration of the cerebellum in motor and cognitive functions.

Correlation of Phase Structure, Defect Relaxation, and Microwave Dielectric Properties in Low-Loss Mgn+1TinO3n+1 Ceramic Systems.

Low-loss microwave dielectrics are of significant importance for the miniaturization and integration of microwave devices. In this paper, the ceramics of nominal composition Mgn+1TinO3n+1 (n = 3-6) are synthesized, and the correlations among their phase compositions, defect behaviors, and microwave dielectric properties are systematically investigated. The analyses indicate that the Mgn+1TinO3n+1 ceramics are a biphasic system consisting of hexagonal ilmenite-structured MgTiO3 and cubic spinel-structured Mg2TiO4. The Rietveld refinement results demonstrate that as the n value increases, the content of the MgTiO3 phase gradually increases, while that of the Mg2TiO4 phase decreases. The results of the thermally stimulated depolarization current (TSDC) indicate that the oxygen vacancy-related defects are considered to be the main types of defects in Mgn+1TinO3n+1. As the value of n increases, the increase of the MgTiO3 phases with a more stable crystal structure leads to a gradual decrease in the concentration of oxygen vacancies. The Mgn+1TinO3n+1 ceramics exhibit excellent microwave dielectric properties at n = 6: εr = 17.55, Q × f = 284,600 GHz, and τf = -46.39 ppm/°C. In addition, the relationship between the dielectric constant and the electric field distribution is solved utilizing high-frequency structure simulator (HFSS) software, and the Q × f values are also predicted. The low-frequency dielectric temperature spectra and direct current pulse charge/discharge tests show that the low-loss Mgn+1TinO3n+1 ceramics can be good candidates for microwave capacitors even when operated under high-temperature conditions.

Comprehensive Analysis of the Immune Response to SARS-CoV-2 Epitopes: Unveiling Potential Targets for Vaccine Development

SARS-CoV-2 continues to be a major global health threat. In this study, we performed a comprehensive meta-analysis on the epitopes of SARS-CoV-2, revealing its immunological landscape. Furthermore, using Shannon entropy for sequence conservation analysis and structural network-based methods identified candidate epitopes that are highly conserved and evolutionarily constrained in SARS-CoV-2 and other zoonotic coronaviruses. Finally, the population coverage of T cell epitopes was analyzed. The results highlighted regions within each SARS-CoV-2 protein where the immunological activity of antibodies, CD4+, and CD8+ T cell responses was predominantly concentrated. Sequence-based correlation analysis found that epitopes recognized by B cells and CD4+ T cells showed a positive correlation with high viral variability, and these high variability regions were typically linked to robust immune responses. Conversely, epitopes recognized by CD8+ T cells exhibited a negative correlation with high variability. From a structural network degree perspective, no clear correlation was identified between B cell antibody epitopes and CD4+ T cell reactivity with the degree of residue network connectivity. However, a significant positive correlation was observed between CD8+ T cell reactivity and the degree of residue network connectivity. By integrating sequence Shannon entropy and structural network correlation analysis, we pinpointed highly conserved and evolutionarily constrained SARS-CoV-2 candidate epitopes. Furthermore, we utilized immunoinformatics to assess the conservation of SARS-CoV-2 within coronaviruses and the population coverage of these epitopes. Our analysis uncovered key immune responses linked to preventing viral infection and viral clearance, emphasized areas of interest for broad-spectrum SARS-CoV-2 vaccine development, and offered insights for future research and clinical applications.

A combinatory approach of non-chain ring and henon map for image encryption application

Algebraic structures play a vital role in securing important data. These structures are utilized to construct the non-linear components of block ciphers. Since constructing non-linear components through algebraic structures is crucial for the confusion aspects of encryption schemes, relying solely on these structures can result in limited key spaces. To address this issue, a complex non-chain ring with combination of Henon map based algorithm is presented. This proposed work aims to enhance both security and key space by utilizing complex algebraic structures. In this study, we investigate the use of unit elements from non-chain rings, establishing a mapping from the group of units to Galois fields to enhance the algebraic robustness of the scheme. A substitution box is constructed from Galois field and is applied in image processing. For pixel mixing, the Henon map is employed, and the exclusive OR operation is performed using a key generated from image pixels and the substitution box. The algorithm’s performance is evaluated using standard parameters such as histograms, Structural Similarity Index Measure (SSIM), correlation analysis, and National Institute of Standards and Technology (NIST) tests. For S-box analysis, we apply the strict avalanche criterion (SAC), bit independence criterion (BIC), linear approximation probability (LAP), and differential approximation probability (DAP). This algebraic approach utilizes a robust and state-of-the-art image encryption system that is highly effective against potential attackers.

Applications of Random Matrix Theory in Neuroscience and Neural Network Analysis: Unraveling High-Dimensional Connectivity

Random Matrix Theory (RMT) has emerged as a powerful mathematical framework to study large-scale, high-dimensional data across various scientific fields. In neuroscience, it provides unparalleled tools to elucidate the functional connectivity and dynamic properties underlying neural activity. By modeling connectivity matrices, synaptic weight distributions, and neural correlation structures through random matrices, researchers can dissect large-scale neural systems’ stability, detect phase transitions in neural firing patterns, and explain emergent phenomena such as criticality in brain networks. Similarly, in the realm of artificial neural networks, RMT guides the understanding of weight initialization, spectral properties of the network’s Jacobian matrices, generalization, and optimization landscapes. This article provides a comprehensive introduction to Random Matrix Theory’s fundamental principles, their application in contemporary neuroscience, and their intersection with modern neural network paradigms. We introduce the theoretical underpinnings and methodological steps for applying RMT to neuroscience data, including sequentially numbered didactic equations. We further present an illustrative code snippet to generate and visualize RMT-based graphs, discussing the results and connecting them to cutting-edge research. In a detailed discussion, we explore the benefits, limitations, and future directions of RMT methodologies in neuroscience, including ongoing challenges and emerging frontiers. This work aims to equip researchers with a robust theoretical and methodological framework, encouraging the integration of RMT into the neuroscience toolbox and catalyzing further breakthroughs in understanding complex neural systems.

Refining fine-mapping: Effect sizes and regional heritability.

Recent statistical approaches have shown that the set of all available genetic variants explains considerably more phenotypic variance of complex traits and diseases than the individual variants that are robustly associated with these phenotypes. However, rapidly increasing sample sizes constantly improve detection and prioritization of individual variants driving the associations between genomic regions and phenotypes. Therefore, it is useful to routinely estimate how much phenotypic variance the detected variants explain for each region by taking into account the correlation structure of variants and the uncertainty in their causal status. Here we extend the FINEMAP software to estimate the effect sizes and regional heritability under the probabilistic model that assumes a handful of causal variants per region. Using the UK Biobank (UKB) data to simulate genomic regions, we demonstrate that FINEMAP provides higher precision and enables more detailed decomposition of regional heritability into individual variants than the variance component model implemented in BOLT or the fixed-effect model implemented in HESS, particularly when there are only a few causal variants in the fine-mapped region. Using data from 2,940 plasma proteins from the UKB study, we observed that on average FINEMAP identified 2.5 causal variants at an association signal and captured 36% more regional heritability than the variant with the lowest P-value. We estimate that in genomic regions with notable contribution to the total heritability, FINEMAP captures on average 13% and 40% more heritability than BOLT and HESS respectively. Our analysis shows how FINEMAP, BOLT and HESS relate to each other in cases where inference of a variant-level picture of the regional genetic architecture is possible.

Molecular Dynamics Simulation Study on Heterogeneous Structure, Rheology, and Dynamic Correlation of Concentrated Aqueous Solutions of a Lithium Salt.

Molecular dynamics simulation of an aqueous solution of lithium bis(trifluoromethanesulfonyl)amide, LiTFSA, was performed at various concentrations to relate its liquid structure with frequency-dependent shear viscosity. The structure factor exhibited a low-q peak that represents a heterogeneous structure composed of water and anion domains, and the lithium ion existed in the water domain due to its strong hydration. The frequency-dependent shear viscosity showed bimodal relaxation, and the relative contribution of the slower mode increased with an increase in the salt concentration. The cross-correlation between the shear stress and the two-body density revealed that the slower viscoelastic mode is assigned to the dynamics of the heterogeneous structure, and the assignment was also confirmed by the comparison between the viscoelastic and structural relaxations. The collective translational motions of the cation and the anion showed a strong negative correlation in a concentrated solution, reflecting the heterogeneous domain structure.

Grazing-incidence X-ray diffraction elucidates structural correlations in fluid monolayers of lipids and surfactants.

Biological membranes predominantly consist of fluid lipid phases featuring lateral mobility and a considerable disorder of their hydrocarbon chains. Langmuir monolayers of lipids at the air/water interface are versatile model systems for fundamental physicochemical and biophysical membrane investigations. Grazing-incidence X-ray diffraction (GIXD) is a powerful tool for the structural characterization of such monolayers but has so far been used almost exclusively for lipid phases of crystalline ordering giving rise to sharp diffraction peaks. Here, we use GIXD for the characterization of fluid monolayers of phospholipids and of water-soluble surfactants. We find that these layers feature spatiotemporally localized, structurally correlated hydrocarbon chain regions that involve only a few molecules and have only a small extension vertically. The abundance of these regions increases with increasing lateral packing density due to compression until the transition into an ordered phase occurs.

General Kernel Machine Methods for Multi-Omics Integration and Genome-Wide Association Testing With Related Individuals.

Integrating multi-omics data may help researchers understand the genetic underpinnings of complex traits and diseases. However, the best ways to integrate multi-omics data and use them to address pressing scientific questions remain a challenge. One important and topical problem is how to assess the aggregate effect of multiple genomic data types (e.g. genotypes and gene expression levels) on a phenotype, particularly while accommodating routine issues, such as having related subjects' data in analyses. In this paper, we extend an existing composite kernel machine regression model to integrate two multi-omics data types, while accommodating for general correlation structures amongst outcomes. Due to the kernel machine regression framework, our methods allow for the integration of high-dimensional omics data with small, nonlinear, and interactive effects, and accommodation of general study designs. Here, we focus on scientific questions that aim to assess the association between a functional grouping (such as a gene or a pathway) and a quantitative trait of interest. We use a kernel machine regression to integrate the two multi-omics data types, as they may relate to the trait, and perform a global test of association. We demonstrate the advantage of this approach over single data type association tests via simulation. Finally, we apply this method to a large, multi-ethnic data set to investigate how predicted gene expression and rare genetic variation may be related to two platelet traits.

Exchange-Biased Fe/FeF2 Nanocomposites: Unveiling the Structural Insights into Spin-Dependent Tunnel Transport.

Spin-dependent charge tunneling transport of magnetic nanocomposites under alternating current or direct current has revolutionized the understanding of the quantum-mechanical phenomenon in complex granular solids. The tunnel magnetodielectric (TMD) and tunnel magnetoresistance (TMR) effects are two critical functionalities in this context, where dielectric permittivity and electrical resistance, respectively, change in response to an applied magnetic field due to charge tunneling. However, the structural correlation between TMD and TMR, as well as the mechanisms, remains poorly understood, largely due to the challenges in directly characterizing nanoscale intergranular interactions. In this work, we fabricated a granular nanocomposite consisting of Fe nanogranules dispersed within an antiferromagnetic FeF2 matrix. The exchange bias interaction between Fe and FeF2 revealed a magnetic transition from superparamagnetic to antiferromagnetic and ferromagnetic behavior at low temperature. This study provides new insights into the interplay between spin-dependent tunneling and granular interactions, facilitated by the antiferromagnetic nature of the matrix─an interaction that is not achievable with conventional composites that use nonmagnetic matrices.

Distinct impact modes of polygenic disposition to dyslexia in the adult brain.

Dyslexia is a common and partially heritable condition that affects reading ability. In a study of up to 35,231 adults, we explored the structural brain correlates of genetic disposition to dyslexia. Individual dyslexia-disposing genetic variants showed distinct patterns of association with brain structure. Independent component analysis revealed various brain networks that each had their own genomic profiles related to dyslexia susceptibility. Circuits involved in motor coordination, vision, and language were implicated. Polygenic scores for eight traits genetically correlated with dyslexia, including cognitive, behavioral, and reading-related psychometric measures, showed partial similarities to dyslexia in terms of brain-wide associations. Notably, microstructure of the internal capsule was consistently implicated across all of these genetic dispositions, while lower volume of the motor cortex was more specifically associated with dyslexia genetic disposition alone. These findings reveal genetic and neurobiological features that may contribute to dyslexia and its associations with other traits at the population level.

Structural Attributes Injection Is Better: Exploring General Approach for Radar Image ATR with a Attribute Alignment Adapter

Nowadays, deep learning techniques are extensively applied in the field of automatic target recognition (ATR) for radar images. However, existing data-driven approaches frequently ignore prior knowledge of the target, leading to a lack of interpretability and poor performance of trained models. To address this issue, we first integrate the knowledge of structural attributes into the training process of an ATR model, providing both category and structural information at the dataset level. Specifically, we propose a Structural Attribute Injection (SAI) module that can be flexibly inserted into any framework constructed based on neural networks for radar image recognition. Our proposed method can encode the structural attributes to provide structural information and category correlation of the target and can further apply the proposed SAI module to map the structural attributes to something high-dimensional and align them with samples, effectively assisting in target recognition. It should be noted that our proposed SAI module can be regarded as a prior feature enhancement method, which means that it can be inserted into all downstream target recognition methods on the same dataset with only a single training session. We evaluated the proposed method using two types of radar image datasets under the conditions of few and sufficient samples. The experimental results demonstrate that our application of our proposed SAI module can significantly improve the recognition accuracy of the baseline models, which is equivalent to the existing state-of-the-art (SOTA) ATR approaches and outperforms the SOTA approaches in terms of resource consumption. Specifically, with the SAI module, our approach can achieve substantial accuracy improvements of 3.48%, 18.22%, 1.52%, and 15.03% over traditional networks in four scenarios while requiring 1/5 of the parameter count and just 1/14 of the FLOPs on average.

Tensor-based Feedback Control for Locally Structured High-Dimensional Streaming Data Under Limited Control Capability

Structured high-dimensional streaming data offers abundant information that are crucial for process feedback control. Nevertheless, traditional control models predominantly emphasize the global patterns of spatiotemporal correlation within responses, often neglecting the local correlation structure. This oversight can be problematic in applications where local correlations play a significant role, such as temperature control of composite plates. Additionally, these models typically fail to incorporate local patterns within the spatial influence of control variables, an essential aspect considering the location-sensitive nature of control impact. Moreover, in practice, the suboptimal uniform placement of control variables can significantly impact the effectiveness of control strategies under insufficient control resources. To address these issues, we propose a tensor-based feedback control model for locally structured high-dimensional (LSHD) streaming data under limited control capabilities. For system modeling, we employ kernel distributions to capture the local structure within (i) the response autocorrelation and (ii) the spatial impact of location-sensitive control variables. For online control, we develop a dynamic control strategy to optimize controller placement, enhancing control efficiency despite resource constraints. Finally, we validate the effectiveness of our proposed framework through simulations and a case study.

Economic Tremors From a Perfect Storm: The Ukrainian Crisis and Its Impact on Regional Stock Market Volatility

This study investigates the impact of the Russia-Ukraine war on stock market volatility in neighboring countries, analyzing five stock market indices (BET, BUX, WIG, SAX, and MOEX) over a three-year period encompassing one year before and two years after the conflict’s outbreak. Employing four volatility estimators (Close-to-Close, Parkinson, Garman-Klass, and Rogers-Satchell), this research examines the evolution of market volatility and inter-market correlations. Findings reveal a general increase in volatility across most indices following the war’s commencement, with the MOEX index experiencing the highest turbulence. The concept of a “proximity penalty” is partially supported, as geographical closeness to the conflict zone does not uniformly correspond to increased volatility. Also, findings show an initial strengthening of correlations between markets in the first year of the war, suggesting a “contagion effect.” However, this is followed by a weakening of correlations in the second year, indicating a potential “decoupling effect” as markets begin to respond more to local economic conditions. These results have significant implications for investors, policymakers, and risk managers, highlighting the need for dynamic portfolio management strategies, tailored policy responses, and flexible risk models that can adapt to changing market conditions during prolonged geopolitical crises. This study contributes to the existing literature by extending the temporal scope of analysis beyond the immediate aftermath of the war’s outbreak and providing insights into the “proximity effect” in the context of a major European conflict. The observed patterns of initial volatility spikes followed by varying degrees of persistence and changing correlation structures offer a nuanced picture of how geopolitical events impact financial markets over time, emphasizing the complex interplay between political events and financial market dynamics. JEL classification: G15, F51 Article History: Received: October 14, 2024; Reviewed: November 27, 2024; Accepted: December 2, 2024; Available online: December 17, 2024.

DNA methylation-based predictors of metabolic traits in Scottish and Singaporean cohorts.

Exploring the molecular correlates of metabolic health measures may identify their shared and unique biological processes and pathways. Molecular proxies of these traits may also provide a more objective approach to their measurement. Here, DNA methylation (DNAm) data were used in epigenome-wide association studies (EWASs) and for training epigenetic scores (EpiScores) of six metabolic traits: body mass index (BMI), body fat percentage, waist-hip ratio, and blood-based measures of glucose, high-density lipoprotein cholesterol, and total cholesterol in >17,000 volunteers from the Generation Scotland (GS) cohort. We observed a maximum of 12,033 significant findings (p<3.6×10-8) for BMI in a marginal linear regression EWAS. By contrast, a joint and conditional Bayesian penalized regression approach yielded 27 high-confidence associations with BMI. EpiScores trained in GS performed well in both Scottish and Singaporean test cohorts (Lothian Birth Cohort 1936 [LBC1936] and Health for Life in Singapore [HELIOS]). The EpiScores for BMI and total cholesterol performed best in HELIOS, explaining 20.8% and 7.1% of the variance in the measured traits, respectively. The corresponding results in LBC1936 were 14.4% and 3.2%, respectively. Differences were observed in HELIOS for body fat, where the EpiScore explained ∼9% of the variance in Chinese and Malay -subgroups but ∼3% in the Indian subgroup. The EpiScores also correlated with cognitive function in LBC1936 (standardized βrange: 0.08-0.12, false discovery rate p [pFDR]<0.05). Accounting for the correlation structure across the methylome can vastly affect the number of lead findings in EWASs. The EpiScores of metabolic traits are broadly applicable across populations and can reflect differences in cognition.

On GEE for Mean-Variance-Correlation Models: Variance Estimation and Model Selection.

Generalized estimating equations (GEE) are of great importance in analyzing clustered data without full specification of multivariate distributions. A recent approach by Luo and Pan jointly models the mean, variance, and correlation coefficients of clustered data through three sets of regressions. We note that it represents a specific case of the more general estimating equations proposed by Yan and Fine which further allow the variance to depend on the mean through a variance function. In certain scenarios, the proposed variance estimators for the variance and correlation parameters in Luo and Pan may face challenges due to the subtle dependence induced by the nested structure of the estimating equations. We characterize specific model settings where their variance estimation approach may encounter limitations and illustrate how the variance estimators in Yan and Fine can correctly account for such dependencies. In addition, we introduce a novel model selection criterion that enables the simultaneous selection of the mean-scale-correlation model. The sandwich variance estimator and the proposed model selection criterion are tested by several simulation studies and real data analysis, which validate its effectiveness in variance estimation and model selection. Our work also extends the R package geepack with the flexibility to apply different working covariance matrices for the variance and correlation structures.

Navigating Islamic Da'wah for Polygamous Family Resilience: Family Communication and the Islamic Mindset

This research examines navigating polygamous family dynamics: family communication and mindset in an Islamic context using a mixed methods explanatory model. Quantitative data from respondents to measure the correlation and influence of family communication, family structure, and religious orientation on the resilience of polygamous families. In contrast, qualitative data from informants were used to analyze navigating polygamous family dynamics: family communication and mindset in an Islamic context which includes communication in building family meaning, relationship maintenance, and problem-solving in polygamous families. The results showed that the resilience of polygamous families can be maintained if family communication, family structure, and religious orientation used are in line with or well accepted by all family members. The calculated F value of 51.331&gt; the F table value of 2.73 and the sig value is 0.01 &lt;0.05 then H0 is rejected and Ha is accepted, meaning that the variables of Family Communication (X1), Family structure (X2), and Religious orientation (X3) affect family resilience (Y). Islamic Da'wah, when applied correctly and contextually, can play an important role in strengthening the resilience of polygamous families by improving effective communication and using the right Islamic mindset.

Time-dependent low-rank input–output operator for forced linearized dynamics with unsteady base flows

Understanding the linear growth of disturbances due to external forcing is crucial for flow stability analysis, flow control, and uncertainty quantification. These applications typically require a large number of forward simulations of the forced linearized dynamics, often in a brute-force fashion. When dealing with simple steady-state or periodic base flows, there exist powerful and cost-effective solution operator techniques. Once these solution operators are constructed, they can be used to determine the response to various forcings with negligible computational cost. However, these methods do not apply to problems with arbitrarily time-dependent base flows. This paper develops and investigates reduced-order modelling with time-dependent bases to build low-rank solution operators for forced linearized dynamics with arbitrarily time-dependent base flows. In particular, we use forced optimally time-dependent decomposition (f-OTD), which extracts the time-dependent correlated structures of the flow response to various excitations. Several demonstrations are included to illustrate the utility of the f-OTD low-rank approximation for performing global transient stability analysis. Additionally, we demonstrate the application of f-OTD in computing the post-transient response of linearized Navier–Stokes equations to a large number of impulses, which has applications in flow control.

Marginal semiparametric accelerated failure time cure model for clustered survival data.

The semiparametric accelerated failure time mixture cure model is an appealing alternative to the proportional hazards mixture cure model in analyzing failure time data with long-term survivors. However, this model was only proposed for independent survival data and it has not been extended to clustered or correlated survival data, partly due to the complexity of the estimation method for the model. In this paper, we consider a marginal semiparametric accelerated failure time mixture cure model for clustered right-censored failure time data with a potential cure fraction. We overcome the complexity of the existing semiparametric method by proposing a generalized estimating equations approach based on the expectation-maximization algorithm to estimate the regression parameters in the model. The correlation structures within clusters are modeled by working correlation matrices in the proposed generalized estimating equations. The large sample properties of the regression estimators are established. Numerical studies demonstrate that the proposed estimation method is easy to use and robust to the misspecification of working matrices and that higher efficiency is achieved when the working correlation structure is closer to the true correlation structure. We apply the proposed model and estimation method to a contralateral breast cancer study and reveal new insights when the potential correlation between patients is taken into account.

A FRET assay to quantitate levels of the human β-cardiac myosin interacting heads motif based on its near-atomic resolution structure.

In cardiac muscle, many myosin molecules are in a resting or "OFF" state with their catalytic heads in a folded structure known as the interacting heads motif (IHM). Many mutations in the human β-cardiac myosin gene that cause hypertrophic cardiomyopathy (HCM) are thought to destabilize (decrease the population of) the IHM state. The effects of pathogenic mutations on the IHM structural state are often studied using indirect assays, including a single-ATP turnover assay that detects the super-relaxed (SRX) biochemical state of myosin functionally. Here we develop and use a fluorescence resonance energy transfer (FRET) based sensor for direct quantification of the IHM state in solution. The FRET sensor was able to quantify destabilization of the IHM state in solution, induced by (a) increasing salt concentration, (b) altering proximal S2 tail length, or (c) introducing the HCM mutation P710R, as well as stabilization of the IHM state by introducing a dilated cardiomyopathy-causing mutation (E525K). Our FRET sensor conclusively showed that these perturbations indeed alter the structural IHM state. These results establish that the structural IHM state is one of the structural correlates of the biochemical SRX state in solution.