Correlation Measures Research Articles

Application of Radiomics to the Differential Diagnosis of Temporal Bone Skull Base Lesions: A Pilot Study.

Temporal bone skull base pathologies represent a complex differential because they can be radiographically obscure and difficult to diagnose without biopsy. Radiomics involves the use of mathematical quantification of imaging data beyond simple intensity, size, and location to inform diagnosis and prognosis. We examined the feasibility of using radiomic parameters to help predict temporal bone tumor type. A total of 117 radiomic parameters were analyzed from 5 magnetic resonance imaging sequences (T1 without contrast, T1 with contrast, T2, fluid-attenuated inversion recovery, apparent diffusion coefficient [ADC]) for each tumor. Statistical analysis was used to delineate known primary, metastatic/secondary, and lymphoma lesions using radiomics. The mean tumor volumes for the 14 primary, 12 secondary, and 8 lymphoma lesions were 2.98 ± 2.11, 3.28 ± 2.31, and 12.16 ± 7.1cm3, respectively (P= 0.2). No significant differences in mean intensity values for any sequence helped distinguish tumors (P > 0.05), but 6 radiomic parameters were significantly correlated with diagnostic accuracy. Discriminant analysis using a stepwise algorithm generated a model where radiomic parameters for T1 cluster prominence, ADC dependence nonuniformity, T1 with contrast zone percentage, and ADC informational measure of correlation 2 achieved the best predictive model (P= 0.0001). These significant characteristics were often indirect measures of tumor heterogeneity on different magnetic resonance imaging sequences. These data suggest that quantitative measures of tumor heterogeneity can be discriminatory of pathology and might be integrated into clinical workflow. Although this pilot study requires further validation, these data support the exploration of radiomics in temporal bone radiographic diagnostics.

Novel Correlation Measure for Generalized Orthopair Fuzzy Sets and Its Decision-Making Applications

Novel Correlation Measure for Generalized Orthopair Fuzzy Sets and Its Decision-Making Applications

Squashed entanglement in one-dimensional quantum matter

Squashed entanglement and its universal upper bound, the quantum conditional mutual information, are faithful measures of bipartite quantum correlations defined in terms of multipartitions. As such, they are sensitive to the fine-grain structure of quantum systems. Building on this observation, we introduce the concept of quantum conditional mutual information between the edges of quantum many-body systems. We show that this quantity characterizes unambiguously one-dimensional topological insulators and superconductors, being equal to Bell-state entanglement in the former and to half Bell-state entanglement in the latter, mirroring the different statistics of the edge modes in the two systems. The edge-to-edge quantum conditional mutual information is robust in the presence of disorder or local perturbations, converges exponentially with the system size to a quantized topological invariant, even in the presence of interactions, and vanishes in the trivial phase. We thus conjecture that it coincides with the edge-to-edge squashed entanglement in the entire ground-state phase diagram of symmetry-protected topological systems, and we provide some analytical evidence supporting the claim. By comparing them with the entanglement negativity, we collect further indications that the quantum conditional mutual information and the squashed entanglement provide a very accurate characterization of nonlocal correlation patterns in one-dimensional quantum matter.

Universal Entanglement and Correlation Measure in Two-Dimensional Conformal Field Theories.

We calculate the amount of entanglement shared by two intervals in the ground state of a (1+1)-dimensional conformal field theory (CFT), quantified by an entanglement measure E based on the computable cross norm (CCNR) criterion. Unlike negativity or mutual information, we show that E has a universal expression even for two disjoint intervals, which depends only on the geometry, the central charge c, and the thermal partition function of the CFT. We prove this universal expression in the replica approach, where the Riemann surface for calculating E at each order n is always a torus topologically. By analytic continuation, the result of n=1/2 gives the value of E. Furthermore, the results of other values of n also yield meaningful conclusions: The n=1 result gives a general formula for the two-interval purity, which enables us to calculate the Rényi-2 N-partite information for N≤4 intervals; while the n=∞ result bounds the correlation function of the two intervals. We verify our findings numerically in the spin-1/2 XXZ chain, whose ground state is described by the Luttinger liquid.

A Parallel Hybrid Feature Selection Approach Based on Multi-Correlation and Evolutionary Multitasking

Particle swarm optimization (PSO) has been successfully applied to feature selection (FS) due to its efficiency and ease of implementation. Like most evolutionary algorithms, they still suffer from a high computational burden and poor generalization ability. Multifactorial optimization (MFO), as an effective evolutionary multitasking paradigm, has been widely used for solving complex problems through implicit knowledge transfer between related tasks. Based on MFO, this study proposes a PSO-based FS method to solve high-dimensional classification via information sharing between two related tasks generated from a dataset using two different measures of correlation. To be specific, two subsets of relevant features are generated using symmetric uncertainty measure and Pearson correlation coefficient, then each subset is assigned to one task. To improve runtime, the authors proposed a parallel fitness evaluation of particles under Apache Spark. The results show that the proposed FS method can achieve higher classification accuracy with a smaller feature subset in a reasonable time.

Coherence controlled generation of Gaussian quantum discord in a quantum beat laser

Quantum discord, an appropriate measure of quantum correlation, is analyzed in a two-mode Gaussian state of the cavity field evolved by a system of quantum beat laser. In the laser system, two arbitrary single-mode Gaussian states of the cavity fields and an external classical field couple to the atomic lasing medium. We calculate the time-dependent expression for the quantum discord both analytically and numerically, by following the reduced density matrix equation of the resulting cavity field. In this framework, we investigate the generation and control of Gaussian quantum discord in the two-mode Gaussian state of the cavity field at the output in terms of the purity and non-classicality of the two input cavity modes, the Rabi frequency of the classical driving field, the relative phase of the coupling parameters, and the damping rates of the cavity modes. The behaviour of quantum discord appears oscillatory due to the quantum beats in the output cavity field developed by the classical driving field in the medium as time passes. Moreover, we find that quantum discord switches on and off while adjusting the relative phase of the coupling parameters. Analysis of the analytical results agrees well with our numerical simulations.

Efficacy and tolerance profile of risperidone use in people with autism spectrum disorder in a clinic in Santarém, Pará, Brazil. A retrospective study.

This study aimed to obtain the profile of efficacy and tolerance of risperidone in the treatment of people with autism spectrum disorder. This research was a cross-sectional and retrospective study. The medical records of 100 patients diagnosed with ASD according to the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) were analyzed and measures of central tendency and correlation between variables such as gender, age at diagnosis, symptoms, daily dose, comorbidities, polytherapy, adverse drug effects, and outcome (improvement, worsening, and drug discontinuation) were calculated using Pearson's R test with a level of statistical significance P < 0.05. The male gender was the most affected, corresponding to 80% of the participants. The mean age at diagnosis was 6.88 ± 6.24 and the mean dose was 1.89 ± 1.68 mg/day. The use of risperidone for patients with aggressiveness, hyperactivity, insomnia, or self-harm improved in 76% of patients and adverse effects were reported in 27% of cases. The presence of self-harm implied lower chances of improvement (P = 0.05/r = -0.20). Adverse effects were strong predictors of discontinuation (P = 0.01/r = 0.39), and epileptic patients were more likely to have them (P = 0.02/r = 0.20). Male gender was associated with dosages lower than 2 mg/day (P = 0.05/r = 0.23). Risperidone is a good option in the management of secondary symptoms of ASD, generally requiring low doses and presenting an acceptable profile of adverse effects. The age of diagnosis does not affect the drug's efficiency, but it can make the management of ASD difficult.

Feature clustering-Assisted feature selection with differential evolution

Modern data collection technologies may produce thousands of or even more features in a single dataset. The high dimensionality of data poses a barrier to determining discriminating features due to the curse of dimensionality. Thanks to the global search ability, many population-based feature selection approaches have been proposed. However, very few studies pay attention on that a feature selection task has multiple optimal feature subsets. To search for multiple optimal feature subsets, we propose a feature clustering-assisted feature selection method. The proposed method employs the knowledge of correlation measures to group features. And, this correlation knowledge is embedded into the encoding method and the search process. A niching-based mutation operator is also used to explore the vicinity of a target individual. The aim is to find different feature subsets with very similar or the same classification performance. In addition, a modification operator is proposed aiming to increase the population diversity to improve the feature selection performance. The experiments on 16 datasets show that the proposed algorithm outperforms other popular feature selection methods in terms of classification accuracy and feature subset size.

New Mathematical Techniques in Information Theory

Information theory is the richer for a surge of recent advances in relevant mathematical techniques. The workshop fostered an exchange of ideas on new mathematical tools which are typically outside the classical toolbox of information theorists and that are yet useful in solving classical and modern problems in information theory and related areas. The focus was on mathematical techniques that are of a general nature and that could benefit a wide class of problems. A number of broad mathematical areas were identified that held promise with established early successes, and key contributors were invited to make presentations and initiate discussions with an emphasis on emergent topics. The areas were: information measures, measure concentration, hypercontractivity and correlation measures, Shannon theory and extremal combinatorics, advanced tools for proving converse results in coding theorems, and recent techniques for proving Gaussian optimality entailing new characterizations of Gaussian distributions.

Survey Evaluation of Building Information Modelling (BIM) for Health and Safety in Building Construction Projects in Malaysia

Traditional safety planning methods that rely on manual inspections result in labour-intensive, time-consuming, and inadequate information transmission, which has significant negative social and economic effects on our society, as well as financial and schedule losses for construction projects. Building information modelling (BIM) is useful for analysing workplace safety issues, preventing risks and hazards, and improving safety throughout the project’s life cycle. This study intends to pinpoint health and safety concerns and to understand the role of BIM adoption in enhancing health and safety in Malaysian building construction projects. Following a survey of 302 Malaysian construction industry professionals, statistical data analysis using the relative importance index, reliability, validity, and correlation measures was performed. The results show that implementing BIM can prevent accidents on construction sites by detecting physical spatial clashes, anticipating project dangers, and providing a wealth of parametric data throughout the entire life cycle of structures. A framework was created to improve the application of BIM to enhance health and safety linked with construction projects. The study found that construction industry stakeholders believe that BIM implementation in construction projects can improve health and safety and reduce accident rates in Malaysia.

Evolution of Rényi-2 quantum correlations in a double cavity–magnon system

This work reports on the stationary evolution of three different kinds of quantum correlations between two distant magnon modes. The system at hand consists of two spatially separated cavities, where each cavity has a microwave (MW) cavity and a magnon mode. The two cavities are coupled to each other via the photon-tunneling process, and both are exposed to the output field of a squeezed vacuum MW fields source. By calculating the covariance matrix fully describing the state of the two magnon modes, we give the explicit expressions of the measures of correlations defined via the Rényi-2 entropy, i.e. the Gaussian quantum steering [Formula: see text], Gaussian Rényi-2 entanglement [Formula: see text] and Gaussian Rényi-2 mutual information [Formula: see text]. We find that, the quantum steering is always upper bounded by the entanglement, which is in turn always upper bounded by half of the total correlations. The obtained results are consistent with the hierarchical Rényi-2 quantum correlations established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett. 117, 220502 (2016)], i.e. they fulfill the hierarchical inequality [Formula: see text]. The influences of the squeezing parameter, the environmental temperature, the cavity–magnon coupling and the cavity–cavity coupling on the correlations are studied in detail.

A Collection of New Trigonometric- and Hyperbolic-FGM-Type Copulas

Copula analysis was created to explain the dependence of two or more quantitative variables. Due to the need for in-depth data analysis involving complex variable relationships, there is always a need for new copula models with original features. As a modern example, for the analysis of circular or periodic data types, trigonometric copulas are particularly attractive and recommended. This is, however, an underexploited topic. In this article, we propose a new collection of eight trigonometric and hyperbolic copulas, four based on the sine function and the others on the tangent function, all derived from the construction of the famous Farlie–Gumbel–Morgenstern copula. In addition to their original trigonometric and hyperbolic functionalities, the proposed copulas have the feature of depending on three parameters with complementary roles: one is a dependence parameter; one is a shape parameter; and the last can be viewed as an angle parameter. In our main findings, for each of the eight copulas, we determine a wide range of admissible values for these parameters. Subsequently, the capabilities, features, and functions of the new copulas are thoroughly examined. The shapes of the main functions of some copulas are illustrated graphically. Theoretically, symmetry in general, stochastic dominance, quadrant dependence, tail dependence, Archimedean nature, correlation measures, and inference on the parameters are investigated. Some copula shapes are illustrated with the help of figures. On the other hand, some two-dimensional inequalities are established and may be of separate interest.

Multivariate generalized linear mixed models for underdispersed count data

Researchers are often interested in understanding the relationship between a set of covariates and a set of response variables. To achieve this goal, the use of regression analysis, either linear or generalized linear models, is largely applied. However, such models only allow users to model one response variable at a time. Moreover, it is not possible to directly calculate from the regression model a correlation measure between the response variables. In this article, we employed the Multivariate Generalized Linear Mixed Models framework, which allows the specification of a set of response variables and calculates the correlation between them through a random effect structure that follows a multivariate normal distribution. We used the maximum likelihood estimation framework to estimate all model parameters using Laplace approximation to integrate out the random effects. The derivatives are provided by automatic differentiation. The outer maximization was made using a general-purpose algorithm such as PORT and Broyden–Fletcher–Goldfarb–Shanno algorithm (BFGS). We delimited this problem by studying count response variables with the following distributions: Poisson, negative binomial, Conway-Maxwell-Poisson (COM-Poisson), and double Poisson. While the first distribution can model only equidispersed data, the second models equi and overdispersed, and the third and fourth models all types of dispersion (i.e. including underdispersion). The models were implemented on software R with package TMB, based on C++ templates. Besides the full specification, models with simpler structures in the covariance matrix were considered (fixed and common variance, and ρ set to 0) and fixed dispersion. These models were applied to a dataset from the National Health and Nutrition Examination Survey, where two response variables are underdispersed and one can be considered equidispersed that were measured at 1281 subjects. The double Poisson full model specification overcame the other three competitors considering three goodness-of-fit measures: Akaike Information Criteria (AIC), Bayesian Information Criteria (BIC), and maximized log-likelihood. Consequently, it estimated parameters with smaller standard error and a greater number of significant correlation coefficients. Therefore, the proposed model can deal with multivariate count responses and measures the correlation between them taking into account the effects of the covariates.

On New Three- and Two-Dimensional Ratio-Power Copulas

In recent decades, a great variety of dependence models for data analysis have been elaborated. Among them, those based on copulas have demonstrated a great ability to capture the possible dependence between quantitative measures. The three-dimensional case has received particular interest in several important applications in the last few years. The most commonly used three-dimensional copulas have one or two parameters and are exchangeable; they are often members of the well-known Archimedean family. In this paper, we go beyond this standard framework by proposing a brand-new three-dimensional copula that depends on three parameters, is mainly non-exchangeable, and is constructed from ratio and power functions. It is thus of the ratio-power type. Our findings are purely theoretical. In particular, wide ranges of valid parameter values are determined, the main related functions (density, survival, etc.) are exhibited, and various correlation measures (medial, Spearman rho, etc.) are examined. Subsequently, a unique two-dimensional copula, derived from the three-dimensional one, is discussed and studied. When comparing it to the famous two-dimensional Farlie-Gumbel-Morgenstern copula, some noteworthy advantages are emphasized. As a result, the restrictions imposed by the exchangeable property, which are typical of traditional three-dimensional copulas in the literature, are removed, creating a promising future for cutting-edge methods of dependent modeling.

Multi-Graph Attention Networks with Bilinear Convolution for Diagnosis of Schizophrenia.

The explorations of brain functional connectivity (FC) network using resting-state functional magnetic resonance imaging (rs-fMRI) can provide crucial insights into discriminative analysis of neuropsychiatric disorders such as schizophrenia (SZ). Graph attention network (GAT), which could capture the local stationary on the network topology and aggregate the features of neighboring nodes, has advantages in learning the feature representation of brain regions. However, GAT only can obtain the node-level features that reflect local information, ignoring the spatial information within the connectivity-based features that proved to be important for SZ diagnosis. In addition, existing graph learning techniques usually rely on a single graph topology to represent neighborhood information, and only consider a single correlation measure for connectivity features. Comprehensive analysis of multiple graph topologies and multiple measures of FC can leverage their complementary information that may contribute to identifying patients. In this paper, we propose a multi-graph attention network (MGAT) with bilinear convolution (BC) neural network framework for SZ diagnosis and functional connectivity analysis. Besides multiple correlation measures to construct connectivity networks from different perspectives, we further propose two different graph construction methods to capture both the low- and high-level graph topologies, respectively. Especially, the MGAT module is developed to learn multiple node interaction features on each graph topology, and the BC module is utilized to learn the spatial connectivity features of the brain network for disease prediction. Importantly, the rationality and advantages of our proposed method can be validated by the experiments on SZ identification. Therefore, we speculate that this framework may also be potentially used as a diagnostic tool for other neuropsychiatric disorders.

Prioritization of Thermal Energy Storage Techniques Using TOPSIS Method Based on Correlation Coefficient for Interval-Valued Intuitionistic Fuzzy Hypersoft Set

The correlation between two disparate variables conquers a significant habitation in statistics. The concept of correlation coefficient (CC) is one of the well-known indicators, but it is not used in interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS) information. It is a generalization of interval-valued intuitionistic fuzzy soft sets and a refined extension of intuitionistic fuzzy hypersoft sets. However, using the CC and weighted correlation coefficient (WCC) has not yet been explored for IVIFHSS information. The core objective of this research is to present the correlation coefficient (CC) and weighted correlation coefficient (WCC) for interval-valued intuitionistic fuzzy hypersoft sets (IVIFHSS) and their mandatory properties. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) is developed based on proposed correlation measures. To ensure the symmetry of the developed scheme, we consider mathematical clarifications of correlation contractions. Based on assessments, it conceded vibrant multi-attribute decision-making (MADM) methodology with the most substantial significance. In addition, a statistical illustration is designated to regulate the operative usage of a decision-making configuration in thermal energy storage techniques. The productivity of the advocated algorithm is more reliable than existing replicas to control the favorable configurations of the premeditated study.

A chaotic decomposition for the fractional Lebesgue–Pascal noise space

Abstract This paper is devoted to study the fractional Pascal noise functionals on compound configuration spaces with special emphasis on the chaotic decomposition of the Hilbert spaces of quadratic integrable functionals with respect to the correlation measure corresponding to the fractional Pascal measure in infinite dimensions.

Imaginary components of out-of-time-order correlator and information scrambling for navigating the learning landscape of a quantum machine learning model

We introduce and analytically illustrate that hitherto unexplored imaginary components of out-of-time correlators can provide unprecedented insight into the information scrambling capacity of a graph neural network. Furthermore, we demonstrate that it can be related to conventional measures of correlation like quantum mutual information and rigorously establish the inherent mathematical bounds (both upper and lower bound) jointly shared by such seemingly disparate quantities. To consolidate the geometrical ramifications of such bounds during the dynamical evolution of training we thereafter construct an emergent convex space. This newly designed space offers much surprising information including the saturation of lower bound by the trained network even for physical systems of large sizes, transference, and quantitative mirroring of spin correlation from the simulated physical system across phase boundaries as desirable features within the latent sub-units of the network (even though the latent units are directly oblivious to the simulated physical system) and the ability of the network to distinguish exotic spin connectivity(volume-law vs area law). Such an analysis demystifies the training of quantum machine learning models by unraveling how quantum information is scrambled through such a network introducing correlation surreptitiously among its constituent sub-systems and open a window into the underlying physical mechanism behind the emulative ability of the model.

Preservation and enhancement of quantum correlations under Stark effect

We analyse the dynamics of quantum correlations by obtaining the exact expression of Bures distance entanglement, trace distance discord, and local quantum uncertainty of two two-level atoms. Here, the atoms undergo two-photon transitions mediated through an intermediate virtual state where each atom is separately coupled to a dissipative reservoir at zero temperature in the presence of the Stark shift effect. We have investigated the dynamics of this atomic system for two different initial conditions of the environment. In the first case, we have assumed the environment's state to be in ground state and in the other case, we have assumed the state to be in the first excited state. The second initial condition is significant as it shows the role played by both the Stark shift parameters in contrast to only one of the Stark shift parameters for the first initial condition. Our results demonstrate that quantum correlations can be sustained for an extended period in the presence of Stark shift effect in the case of both Markovian and non-Markovian reservoirs. The effect in the non-Markovian reservoir is more prominent than the Markovian reservoir, even for a very small value of the Stark shift parameter. We observe that among the correlation measures considered, only local quantum uncertainty is accompanied by a sudden change phenomenon, i.e. an abrupt change in the decay rate of a correlation measure. Our findings are significant as preserving quantum correlations is one of the essential aspects in attaining optimum performance in quantum information tasks.

Local Interpretable Explanations of Energy System Designs

Optimization-based design tools for energy systems often require a large set of parameter assumptions, e.g., about technology efficiencies and costs or the temporal availability of variable renewable energies. Understanding the influence of all these parameters on the computed energy system design via direct sensitivity analysis is not easy for human decision-makers, since they may become overloaded by the multitude of possible results. We thus propose transferring an approach from explaining complex neural networks, so-called locally interpretable model-agnostic explanations (LIME), to this related problem. Specifically, we use variations of a small number of interpretable, high-level parameter features and sparse linear regression to obtain the most important local explanations for a selected design quantity. For a small bottom-up optimization model of a grid-connected building with photovoltaics, we derive intuitive explanations for the optimal battery capacity in terms of different cloud characteristics. For a larger application, namely a national model of the German energy transition until 2050, we relate path dependencies of the electrification of the heating and transport sector to the correlation measures between renewables and thermal loads. Compared to direct sensitivity analysis, the derived explanations are more compact and robust and thus more interpretable for human decision-makers.