Intersection Of Intervals Research Articles

ON THE CONCEPTS OF CONVEXITY AND WEAK O-MINIMALITY FOR PARTIALLY ORDERED STRUCTURES

In this paper, we consider a generalization of the concept of weak o-minimality to partially ordered sets. However, the concept of weak o-minimality is based on the concept of a convex set, the direct transfer of which to partial orders, as it will be shown in the work, is not, in our opinion, the most successful, since then in the class of weakly o-minimal partially ordered structures, it is possible to define any mathematical structure. Moreover, as it will be shown, this can be done using such a simple operation as the intersection of intervals. The article is devoted to the search for various generalizations of the concept of “convex set” to partial orders. Since convex sets on a line also have other properties, such as the ability to represent them as a union or intersection of intervals, convex sets are connected, all these properties can be used as the basis for the definition of a “convex set” for partially ordered structures. Thus, the representation of a convex set as a union of nested intervals (half-intervals, segments) gives us the concept of an “internally convex set,” and the intersection of intervals gives us the concept of an “externally convex set”. In the article, we will build examples that show the non-equivalence of the introduced concepts.

«Relevant correlation» and real typology of dependences on the example of indicators of popular psychological tests

Introduction. The analysis of statistical relation between the characteristics under study is most likely the main type of analytical tasks encountered in almost any psychological study. But as our long-term experience, including my colleagues, shows in psychological research if there is no overabundance of closely related in meaning variable, between the studied indicators dominate, first of all, dependences that are far from linear.Materials and Methods. To study statistical relation, the author's method was used in the work, which makes it possible to study, along with linear dependencies, the simplest nonlinear dependencies: with a maximum and with a minimum, far from linear, monotonic and almost monotonic. This allows not only to expand the range of revealed dependencies and get rid of numerous errors in the traditional interpretation of the correlation coefficient, but also to better understand the complex psychological subject of a particular study. To demonstrate the typology of statistical dependencies, psychological data were selected for 120 subjects using 9 popular methods. The results of diagnostics according to these methods represent 114 quantitative indicators.Results. This article is devoted to the analysis of the ratio of linear and simplest nonlinear dependencies, their features and typology, their interpretation at the intersection of different intervals of dependencies measures obtained both in the study of only linear models and in the study of the simplest nonlinear dependencies, when linear dependencies become an integral part of the entire set dependencies of research interest. For example, for 6441 pairs of psychological indicators, only 17 strong linear relationships are observed, either for the MMPI test scales or for the Leary test scales. At the same time, among the “significant”, but at the same time very weak and weak dependences in the model for quarts, 29 strong simplest non-linear dependences were found (type 2 error). And among the dependencies that did not fall into the zone of significance in the model for quarts, 37 strong simplest non-linear dependencies were found (type 1 error).Discussion and Conclusions. Basically, if we restrict ourselves to the simplest non-linear dependencies, the psychologists should be most interested in dependencies with a maximum or minimum that correspond to the essence of the mental as a subject of study.

Circadian epidemiology: Structuring circadian causes of disease and practical implications

ABSTRACT That disruptions of the body’s internal clockwork can lead to negative health consequences, including cancer, is a plausible hypothesis. Yet, despite strong mechanistic and animal support, the International Agency for Research on Cancer (IARC) experts considered epidemiological evidence as limited regarding the carcinogenicity of “shift-work involving circadian disruption” (2007) and “night shift work” (2019). We use directed acyclic graphs (DAGs) to outline a concept of circadian causes that discloses challenges when choosing appropriate exposure variables. On this basis, we propose to move beyond shift-work alone as a direct cause of disease. Instead, quantifying chronodisruption as individual doses can lead to interpretable circadian epidemiology. The hypothesis is that doses of chronodisruption cause disrupted circadian organisation by leading to desynchronization of circadian rhythms. Chronodisruption can be conceptualized as the split physiological nexus of internal and external times. Biological (or internal) night – an individual’s intrinsically favoured sleep time window – could be the backbone of circadian epidemiology. In practice, individual doses that cause disrupted circadian organisation are derived from the intersection of time intervals of being awake and an individual’s biological night. After numerous studies counted work shifts, chronobiology may now advance circadian epidemiology with more specific dose estimation – albeit with greater challenges in measurement (time-dependent individual data) and analysis (time-dependent confounding).

Optimization assisted autoregressive technique with deep convolution neural network-based entropy filter for image demosaicing

ABSTRACT This paper presents an image demosaicing based on an optimization-driven deep learning model, namely the Autoregressive Water Wave Optimization algorithm (Autoregressive-WWO). The proposed method is devised by assimilating the Wave Optimization algorithm (WWO), and the Conditional autoregressive value at risk (CAViaR) model. Here, the input images are subjected to Autoregressive WWO-based local polynomial approximation and intersection of confidence intervals (LPA-ICI) filter, and Deep Convolution neural network (Deep CNN) in a concurrent manner. The filter coefficients are obtained from the proposed Autoregressive WWO-based LPA-ICI filter and the residual image is obtained from Deep CNN. In order to create the demosaiced image, these two outputs are combined using an entropy measure. The proposed method offered superior performance with the highest Peak signal to noise ratio (PSNR) of 40.049dB, the highest Second derivative measure of enhancement (SDME) of 50.168dB, and highest Structural Index Similarity (SSIM) of 0.9056.

THE EMOTIONAL CONCEPT OF “SADNESS” IN THE COLLECTION OF STORIES “THE ROOM FOR SORROW” BY ANDRII LYUBKA

Scholars from diverse fields of the humanities, including sociology, psychology, philosophy, linguistics, and others, have demonstrated a sustained interest in the realm of emotions. This is primarily because emotions are inextricably linked to crucial aspects of human existence such as behaviour, lifestyle, feelings and their expression, comprehension of the surrounding environment, and the human experience of life-altering circumstances. Every individual’s emotional landscape, as well as their linguistic expression, reflects a unique array of emotions. The article provides an overview of theoretical sources and examines the intricacies of the “concept” notion, which is central to the cognitive linguistics metalanguage. Moreover, the article introduces the term “emotional concept”, which constitutes fragments of the emotional landscape of an individual. In light of this, the language employed by select authors is of significant interest, as their works serve as a model of personal reinterpretation, while also reflecting their way of life, internal experiences, and the accuracy of their linguistic personality’s depiction of reality. The research presented in this article formulates and outlines methods for expressing the emotional concept of “sadness”, using the stories of Transcarpathian writer Andriy Lyubka as an exemplar. The emotional state of sadness has long captivated the attention of scholars across diverse fields of study. This is primarily because, alongside joy, it represents one of the two fundamental, polar emotions. The concept of sadness is universal, as it is comprehensible and relatable across all societies. Individuals can find themselves residing at the intersection of various intervals of sadness, which may arise from losses, disappointments, or physical and emotional pain. Given the universal and profound nature of this emotion, an exploration of Andrii Lyubka’s literary works allows for an examination of how the emotional concept of “sadness” is expressed across multiple language levels, including phraseology, stylistics, phonetics, morphology, and non-verbal communication. This research provides numerous examples that illustrate the description, usage, and implementation of the “sadness” concept within both written texts and spoken language. Key words: cognitive linguistics, linguistics of emotions, concept, emotional concept, emotional picture of the world, Andrii Lyubka.

Fine mapping of a QTL and identification of candidate genes associated with cold tolerance during germination in peanut (Arachis hypogaea L.) on chromosome B09 using whole genome re-sequencing.

Low temperatures significantly affect the growth and yield of peanuts. Temperatures lower than 12 °C are generally detrimental for the germination of peanuts. To date, there has been no report on precise information on the quantitative trait loci (QTL) for cold tolerance during the germination in peanuts. In this study, we developed a recombinant inbred line (RIL) population comprising 807 RILs by tolerant and sensitive parents. Phenotypic frequencies of germination rate low-temperature conditions among RIL population showed normally distributed in five environments. Then, we constructed a high density SNP-based genetic linkage map through whole genome re-sequencing (WGRS) technique and identified a major quantitative trait locus (QTL), qRGRB09, on chromosome B09. The cold tolerance-related QTLs were repeatedly detected in all five environments, and the genetic distance was 6.01 cM (46.74 cM - 61.75 cM) after taking a union set. To further confirm that qRGRB09 was located on chromosome B09, we developed Kompetitive Allele Specific PCR (KASP) markers for the corresponding QTL regions. A regional QTL mapping analysis, which was conducted after taking the intersection of QTL intervals of all environments into account, confirmed that qRGRB09 was between the KASP markers, G22096 and G220967 (chrB09:155637831-155854093), and this region was 216.26 kb in size, wherein a total of 15 annotated genes were detected. This study illustrates the relevance of WGRS-based genetic maps for QTL mapping and KASP genotyping that facilitated QTL fine mapping of peanuts. The results of our study also provided useful information on the genetic architecture underlying cold tolerance during germination in peanuts, which in turn may be useful for those engaged in molecular studies as well as crop improvement in the cold-stressed environment.

Interval Coordination of Multiagent Networks With Antagonistic Interactions

This paper studies interval coordination problems for multiagent systems with antagonistic interactions. For strongly connected signed networks, it is shown that when the intersection of intervals imposed by agents is nonempty: (1) the multiagent system achieves bipartite consensus with structurally balanced network; (2) all agents’ states must converge to 0, if the signed network is structurally unbalanced. We establish the consensus conditions for bipartite consensus and zero-value consensus by employing the Gauge Transformation and robust analysis of signed networks. When the signed networks are strongly connected and the intersection of intervals is empty, the system reaches an asymptotically stable and unique equilibrium. Moreover, the equilibrium states are only decided by the network structure and interval constraints, and are not related to initial agents’ states. Associating the equilibrium of dynamics with the solution of a system of nonlinear equations, we obtain the uniqueness, stability and continuity of equilibria. Finally, numerical simulations are presented to illustrate the theoretical results.

Enhancement of video demosaicing techniques using optimization algorithm

SummaryDemosaicing and denoising are the most significant steps in the imaging process for both images and videos. The correlation noise corrupts the image quality, such that an accurate interpretation of the image is avoided. Thus, demosaicing is utilized to restructure the full‐color image from imperfect color samples. In this article, cat shuffled shepherd optimization‐based local polynomial approximation and intersection of confidence intervals (Cat SSO‐based LPA‐ICI) approach is developed for video demosaicing. The LPA‐ICI model is employed for frame demosaicing in which the second‐order polynomial interpolation filter coefficients are produced using the devised optimization algorithm, named cat SSO technique. Similarly, generative adversarial network classifier is also applied for frame demosaicing. In addition, initialization and flow estimation is performed for the demosaicing process. Besides, spatio temporal demosaicing model is utilized in order to get a noise‐free sequence. However, the developed cat SSO technique is newly devised by the incorporation of the shuffled shepherd optimization algorithm and cat swarm optimization technique. The created video demosaicing model outperformed with peak signal‐to‐noise ratio, root mean square error, and second derivative‐like measure of enhancement values of 56.85 dB, 0.46, and 60.62, respectively.

Comparison of Artificial Neural Networks and Logistic Regression Analysis in PISA Science Literacy Success Prediction

The present study aims to determine which analysis technique-Artificial Neural Networks (ANNs) or Logistic Regression (LR) Analysis-is better at predicting the science literacy success of the 15-year Turkish students who participated in PISA research carried out in 2015 by using learning time spent on science, test anxiety, environmental awareness, environmental optimism, epistemological beliefs, inquiry-based science teaching and learning practices, instrumental motivation, and disciplinary climate in science classes as the predictor variables. For this purpose, the data from 5895 students who participated in the PISA 2015 test were analyzed. Models were developed using LR and ANNs, and the results were compared. As a result, although the classification performance of artificial neural network is significantly better compared to LR, it is understood that practical significance is low due to the intersection of AUC confidence intervals.

Multiagent Interval Consensus With Flocking Dynamics

In this article, we investigate the interval consensus for a network of agents with flocking dynamics, i.e., second-order multiagent systems, where each agent imposes an interval constraint on its preferred consensus values, with the aim of driving the agent into a favorable interval. Specifically, we work on two different frameworks of interval constraints, viz., the first one that the node states are constrained in their own constraint intervals and the second one that the node states are constrained in their neighbors’ constraint intervals. For both of the frameworks, we provide a complete solution to the equilibrium seeking problem by resolving a system of nonlinear equations. It is proved that if the underlying graph is strongly connected and the intersection of constraint intervals is empty, then there exists a unique equilibrium point; and if the intersection is nonempty, then there exist multiple equilibrium points, all of which lead to state consensus. We also establish several conditions for the local stability of the unique equilibrium point (corresponding to the case with empty intersection of constraint intervals) or local constraint consensus (corresponding to the case with nonempty intersection of constraint intervals) by invoking Lyapunov’s indirect method. Characterization of the global behavior of such a second-order multiagent system is technically rather challenging at this stage. As a first step toward this end, we show in two special cases that global convergence to the unique equilibrium point or state consensus can be guaranteed by employing Lyapunov stability theory and robust analysis techniques. Finally, some numerical examples are provided to illustrate the theoretical findings.

Dynamic Connectivity Analysis Using Adaptive Window Size

In this paper, we propose a new method to study and evaluate the time-varying brain network dynamics. The proposed RICI-imCPCC method (relative intersection of confidence intervals for the imaginary component of the complex Pearson correlation coefficient) is based on an adaptive window size and the imaginary part of the complex Pearson correlation coefficient. It reduces the weaknesses of the existing method of constant sliding window analysis with narrow and wide windows. These are the low temporal precision and low reliability for short connectivity periods for wide windows, and high susceptibility to noise for narrow windows, all resulting in low estimation accuracy. The proposed method overcomes these shortcomings by dynamically adjusting the window width using the RICI rule, which is based on the statistical properties of the area around the observed sample. In this paper, we compare the RICI-imCPCC with the existing constant sliding window analysis method and describe its advantages. First, the mathematical principles are established. Then, the comparison between the existing and the proposed method using synthetic and real electroencephalography (EEG) data is presented. The results show that the proposed RICI-imCPCC method has improved temporal resolution and estimation accuracy compared to the existing method and is less affected by the noise. The estimation error energy calculated for the RICI-imCPCC method on synthetic signals was lower by a factor of compared to the error of the constant sliding window analysis using narrow window size imCPCC, by a factor of compared to using wide window size imCPCC, by a factor of compared to using narrow window size wPLI, and by a factor of compared to using wide window size wPLI. Analysis of the real signals shows the ability of the proposed method to detect a P300 response and to detect a decrease in dynamic connectivity due to desynchronization and blockage of mu-rhythms.

On the Use of a Modified Intersection of Confidence Intervals (MICIH) Kernel Density Estimation Approach

Density estimation is an important aspect of statistics. Statistical inference often requires the knowledge of observed data density. A common method of density estimation is the kernel density estimation (KDE). It is a nonparametric estimation approach which requires a kernel function and a window size (smoothing parameter H). It aids density estimation and pattern recognition. So, this work focuses on the use of a modified intersection of confidence intervals (MICIH) approach in estimating density. The Nigerian crime rate data reported to the Police as reported by the National Bureau of Statistics was used to demonstrate this new approach. This approach in the multivariate kernel density estimation is based on the data. The main way to improve density estimation is to obtain a reduced mean squared error (MSE), the errors for this approach was evaluated. Some improvements were seen. The aim is to achieve adaptive kernel density estimation. This was achieved under a sufficiently smoothing technique. This adaptive approach was based on the bandwidths selection. The quality of the estimates obtained of the MICIH approach when applied, showed some improvements over the existing methods. The MICIH approach has reduced mean squared error and relative faster rate of convergence compared to some other approaches. The approach of MICIH has reduced points of discontinuities in the graphical densities the datasets. This will help to correct points of discontinuities and display adaptive density. Keywords: approach, bandwidth, estimate, error, kernel density

Particle-Swarm-Optimization-Enhanced Radial-Basis-Function-Kernel-Based Adaptive Filtering Applied to Maritime Data

The real-life signals captured by different measurement systems (such as modern maritime transport characterized by challenging and varying operating conditions) are often subject to various types of noise and other external factors in the data collection and transmission processes. Therefore, the filtering algorithms are required to reduce the noise level in measured signals, thus enabling more efficient extraction of useful information. This paper proposes a locally-adaptive filtering algorithm based on the radial basis function (RBF) kernel smoother with variable width. The kernel width is calculated using the asymmetrical combined-window relative intersection of confidence intervals (RICI) algorithm, whose parameters are adjusted by applying the particle swarm optimization (PSO) based procedure. The proposed RBF-RICI algorithm’s filtering performances are analyzed on several simulated, synthetic noisy signals, showing its efficiency in noise suppression and filtering error reduction. Moreover, compared to the competing filtering algorithms, the proposed algorithm provides better or competitive filtering performance in most considered test cases. Finally, the proposed algorithm is applied to the noisy measured maritime data, proving to be a possible solution for a successful practical application in data filtering in maritime transport and other sectors.

Phase unwrapping based on accumulation of residual maps with local denoising

Phase unwrapping aims to reconstruct the absolute phase from its values mod 2π, which is a key problem in many non-contact optical metrologies and is still a challenging issue in the presence of noise. We present a robust phase unwrapping method with two steps based on local denoising and the accumulation of residual map (ARM). In the first step, based on the local polynomial approximations and intersection of confidence intervals, we adopt a sine–cosine filtering and iteration algorithm to denoise the wrapped phase, which uses the periodicity of the trigonometric function to avoid the influence of phase jumps effectively. In the second step, the denoised wrapped phase is unwrapped by the improved ARMs method, in which we modify the edge regular term to avoid over-fitting and maintain edge information. The algorithm is tested with a set of numerical simulations under various noise levels, and the experimental results confirm its effectiveness and robustness.

Study on signs of defects in the image of the surface of flat-rolled products

Currently, more and more challenges of modern industrial enterprises require an increase in the reliability of the information on the quality of products. This becomes possible when using digital technologies to assess the quality of products. The cited publication discusses the technology for recognizing defects in the surface of sheet products in images obtained from cameras of the strip inspection system during rolling. The authors proposed a classification of the signs of defects in the image and highlighted the most significant of them also suggested using geometric, optical and spectral features for images of flat-rolled products containing defects of different classes. The research results at this stage, obtained during the processing of digital images, showed that to identify a defect and reduce false-positive and false-negative alarms of the automated defect identification system, it is required to conduct a study of interval estimates and make decision-making rules based on intersection and merging of intervals; introduce additional classes that allow the introduction of signs that characterize the irregularity of the shape of defects and the characteristic location; the use of new technologies of soft computing will reveal the hidden patterns of the manifestation of defects in the images of the surface of the steel strip.

Gravitational-Wave Burst Signals Denoising Based on the Adaptive Modification of the Intersection of Confidence Intervals Rule.

Gravitational-wave data (discovered first in 2015 by the Advanced LIGO interferometers and awarded by the Nobel Prize in 2017) are characterized by non-Gaussian and non-stationary noise. The ever-increasing amount of acquired data requires the development of efficient denoising algorithms that will enable the detection of gravitational-wave events embedded in low signal-to-noise-ratio (SNR) environments. In this paper, an algorithm based on the local polynomial approximation (LPA) combined with the relative intersection of confidence intervals (RICI) rule for the filter support selection is proposed to denoise the gravitational-wave burst signals from core collapse supernovae. The LPA-RICI denoising method’s performance is tested on three different burst signals, numerically generated and injected into the real-life noise data collected by the Advanced LIGO detector. The analysis of the experimental results obtained by several case studies (conducted at different signal source distances corresponding to the different SNR values) indicates that the LPA-RICI method efficiently removes the noise and simultaneously preserves the morphology of the gravitational-wave burst signals. The technique offers reliable denoising performance even at the very low SNR values. Moreover, the analysis shows that the LPA-RICI method outperforms the approach combining LPA and the original intersection of confidence intervals (ICI) rule, total-variation (TV) based method, the method based on the neighboring thresholding in the short-time Fourier transform (STFT) domain, and three wavelet-based denoising techniques by increasing the improvement in the SNR by up to 118.94% and the peak SNR by up to 138.52%, as well as by reducing the root mean squared error by up to 64.59%, the mean absolute error by up to 55.60%, and the maximum absolute error by up to 84.79%.

The effects of a place-based tax cut and minimum wage increase on labor market outcomes

Abstract The benefits of place-based policies are still under debate. In this study, we analyze what is probably one of the boldest interventions in the recent history of Mexico and the rest of the world: the Northern Border Free Zone (NBFZ). Launched in January 2019, this program doubles the minimum wage and substantially lowers taxes in 43 municipalities along the border with the United States, aiming to improve living standards for low-wage workers and foster economic activity within the region. Given the unique features of the NBFZ, we estimate its short-run effects on labor outcomes: employment, wages, and formality. Our primary identification strategy follows a synthetic control method employing monthly administrative data at the municipality level for the period 2015–2019. Using administrative data for formal employment, we find that the policy substantially increased labor income in the NBFZ by approximately 9% over the control municipalities. The results for employment are less clear. Formal employment showed 1.6% less growth in the NBFZ than in the control municipalities, but the estimate is imprecise and we cannot reject a null impact of the program on employment. These results are robust to alternative control groups, including metropolitan areas in the United States. We also use the labor force survey to estimate the effects on formality at the individual level and find results closer to a null effect. These two results suggest that the NBFZ did not substantially affect employment, and the intersection of confidence intervals for the two estimates implies a maximum loss of employment of approximately 24,000 jobs.

A novel approach to extracting useful information from noisy TFDs using 2D local entropy measures

The paper proposes a novel approach for extraction of useful information and blind source separation of signal components from noisy data in the time-frequency domain. The method is based on the local Rényi entropy calculated inside adaptive, data-driven 2D regions, the sizes of which are calculated utilizing the improved, relative intersection of confidence intervals (RICI) algorithm. One of the advantages of the proposed technique is that it does not require any prior knowledge on the signal, its components, or noise, but rather the processing is performed on the noisy signal mixtures. Also, it is shown that the method is robust to the selection of time-frequency distributions (TFDs). It has been tested for different signal-to-noise-ratios (SNRs), both for synthetic and real-life data. When compared to fixed TFD thresholding, adaptive TFD thresholding based on RICI rule and the 1D entropy-based approach, the proposed adaptive method significantly increases classification accuracy (by up to 11.53%) and F1 score (by up to 7.91%). Hence, this adaptive, data-driven, entropy-based technique is an efficient tool for extracting useful information from noisy data in the time-frequency domain.

Improved power system state estimator with preprocessing based on the modified intersection of confidence intervals

Abstract The paper proposes a power system state estimator upgraded by the improved relative intersection of confidence intervals (RICI) algorithm combined with the local polynomial approximation (LPA). In the proposed approach, a novel LPA-RICI denoising technique is utilized to preprocess the input measurements. The accuracy of the adaptive, data-driven LPA-RICI based state estimator was tested on the IEEE test systems with 14 and 30 buses, as well as on a model of the real-life Croatian transmission power system. Due to its adaptivity to high transitions in measurement series achieved by varying filter support size, the LPA-RICI based state estimator enhanced the estimation accuracy for all tested power systems, and at the same time reduced the number of iterations required for the estimator to converge when compared to the classical weighted least squares (WLS) based estimator. Namely, improvement when using the proposed preprocessor was obtained in estimation of the input voltage magnitudes, active and reactive power flows and injections for the Croatian transmission power system by up to 29.3% and 19.4% in terms of the reduction of the mean squared error (MSE) and mean absolute error (MAE), respectively. Furthermore, the LPA-RICI based estimator resulted in an overall estimation quality enhancement for the Croatian transmission power system by up to 13.3%, 12.3%, and 3.7%, in terms of the objective function, variance of the estimated states, and average time for the state estimator to converge, respectively.

An active contour model for medical image segmentation using a quaternion framework

This paper presents a new method for segmenting medical images is based on Hamiltonian quaternions and the associative algebra, method of the active contour model and LPA-ICI (local polynomial approximation - the intersection of confidence intervals) anisotropic gradient. Since for segmentation tasks, the image is usually converted to grayscale, this leads to the loss of important information about color, saturation, and other important information associated color. To solve this problem, we use the quaternion framework to represent a color image to consider all three channels simultaneously when segmenting the RGB image. As a method of noise reduction, adaptive filtering based on local polynomial estimates using the ICI rule is used. The presented new approach allows obtaining clearer and more detailed boundaries of objects of interest. The experiments performed on real medical images (Z-line detection) show that our segmentation method of more efficient compared with the current state-of-art methods.