Integral Measure Research Articles

Some New f-Divergence Measures and Their Basic Properties

In this paper we introduce some new f-divergence measures that we call t-asymmetric/symmetric divergence measure and integral divergence measure, establish their joint convexity and provide some inequalities that connect these f-divergences to the classical one intyroduced by Csiszar in 1963. Applications for the dichotomy class of convex functions are provided as well.

Toward person-centred measures of contraceptive demand: a systematic review of the intentions to use contraception and actual use

Background Understanding people’s motivation and need for modern contraception is critical to ensuring access to quality rights-based contraceptive care and supporting reproductive justice. Current population level measures of contraception demand are proving limited; but there is a promising, more person-centred alternative - intention to use (ITU) contraception. ITU captures a person’s self-reported preferences and could better predict contraceptive use. This systematic review examines whether ITU predicts future contraceptive use and may be a better way to estimate desire to use contraception. Methods We searched PubMed, PsycInfo, Web of Science, and the Cochrane Collaboration to identify studies published from 1975-2020 that: (1) examined contraceptive behaviour, (2) included measures of ITU and future contraceptive use, and (3) included at least one quantitative measure of association between ITU and actual use. The inclusion criteria were: 1) examined contraceptive behaviour (excluding condom use only), (2) included disaggregated integral measures of ITU contraceptives and later contraceptive use, (3) included at least one quantitative measure of the association between ITU contraceptives and actual contraceptive use, (4) study population was women of reproductive age, (5) were peer-reviewed, and (6) written in English. Results 10 prospective cohort studies were included. Six indicated significant, increased, unadjusted odds of subsequent contraceptive use after reporting ITU. Of those, three reported adjusted values for contraceptive use across several covariates that were also significant and positive. The range of potential confounding factors indicate that contraceptive behaviour is a complex psychosocial process shaped by individual and contextual factors. Conclusions People’s self-reported ITU contraception have the potential to be a strong predictor of subsequent contraceptive use. Few studies directly examined the relationship between ITU and contraceptive uptake and recruitment was primarily pregnant or postpartum samples. Further high-quality research measuring the relationship between ITU and contraceptive use using standardized measures and variables are needed.

Fractional order for Multi-criteria Control Performance Assessment

This paper presents an alternative way to do control performance assessment (CPA). The task to measure controller quality has to meet contradictory goals. Generally, the tuning of any controller means reaching a compromise between the accuracy and speed. The demanded ratio between them depends on the process requirements, technological limitations and just the engineering skills. Two fundamental indexes, like the overshoot and settling time fit perfectly into the picture. Considered investigations follow this research path, but with the use of modern measures: L-moments, tail index and ARFIMA filter fractional order estimator. The assessment uses two dimensional Index Ratio Diagrams (IRD), which allow to present and compare contradictory measures in a single diagram. They also allow to define new multi-criteria index able to compare different loops. The validation is compared against commonly used integral measures: means square and absolute errors.

Quality of Life in People Living With Chronic Kidney Disease and Renal Replacement Therapy

Chronic kidney disease is a pathology with fatal outcome in the short and medium term, affecting diverse body structures; it is directly associated with a reduced quality of life; given its irreversible nature, it generates a series of complicated conditions in matters of care and treatment, producing a negative impact on the patient’s quality of life, which implies changes in their lifestyle that have repercussions in the familial, work and social spheres. A proper assessment in quality of life makes it possible to estimate the impact that Chronic Kidney Disease represents in the daily life of people and the consequences it implies over their physical, emotional and social wellbeing; thus, it is fundamental to design effective interventions that guarantee integral health care measures according to the needs of each person. Objective: Evaluate the quality of life in people living with Chronic Kidney Disease undergoing Renal Replacement Therapy through hemodialysis in a second- level hospital in Tepic, Nayarit, Mexico in 2022. Methods and Materials: A descriptive, cross-sectional study with a quantitative approach and simple random sampling, the recollection of data were conducted using a scale to evaluate quality of life, with a Chronbach alfa of 0.86, a prior written informed consent was employed. The statistical analysis was conducted using descriptive and inferential statistics, a statistical significance value of p <0.05 and a reliability of 95% were adopted. Results: The global evaluation in quality of life unveiled that 50.3% of the people interviewed considered their quality of life as good, followed by 40.5% who conveyed having a regular quality of life and in a lower frequency of 9.2% the people who expressed having a poor quality of life. Conclusion: After relating quality of life to each of the dimensions that constitute it, it can be inferred that the most affected dimensions were: physical, psychological and emotional well-being.

Some $f$-Divergence Measures Related to Jensen's One

In this paper, we introduce some $f$-divergence measures that are related to the Jensen's divergence introduced by Burbea and Rao in 1982. We establish their joint convexity and provide some inequalities between these measures and a combination of Csisz\'{a}r's $f$-divergence, $f$-midpoint divergence and $f$-integral divergence measures.

Radon-Nikodýmification of arbitrary measure spaces

We study measurable spaces equipped with a σ-ideal of negligible sets. We find conditions under which they admit a localizable locally determined version – a kind of fiber space that locally describes their directions – defined by a universal property in an appropriate category that we introduce. These methods allow to promote each measure space (X, A , µ) to a strictly localizable version (X̂, Â, µ̂), so that the dual of L1 (X, A , µ) is L∞ (X̂, Â, µ̂). Corresponding to this duality is a generalized Radon-Nikodým theorem. We also provide a characterization of the strictly localizable version in special cases that include integral geometric measures, when the negligibles are the purely unrectifiable sets in a given dimension.

Association of resilience with successful ageing and the mediating role of community participation

AbstractBackgroundHigher level of resilience plays a positive role in successful ageing. Participation was reported as a factor related to resilience and successful ageing. As resilience is developed based on interaction between personal characteristics and environment over time, enhancing resilience level of individuals in later life span is difficult. Finding out modifiable factors which mediate the relationship between resilience and successful ageing can be alternative way to promote successful ageing. The aim of this study was to examine the mediating role of community participation.MethodConvenience sampling was applied to recruit community‐dwelling older adults aged 60 or older who could self‐rate the questionnaire independently. Online and on‐site surveys were conducted using the same questionnaire. Total scores of Korean version of the Connor‐Davidson Resilience Scale (CD‐RISC) and Community Integration Measure (CIM) were used respectively to measure resilience and community participation. Sum score of the satisfaction across four areas‐ subjective health; subjective memory; social relationships; socioeconomic status was used to measure successful ageing. Mediation analysis using SAS 9.4 was conducted to examine the mediating role of community participation in relationship between resilience and successful ageing.ResultData from 284 individuals was analyzed (Mean age: 67.99 ± 7.28; Female: 50.70%). Mean scores of CD‐RISC, CIM, and successful ageing were 60.70, 36.65, 13.05 respectively. A total effect of resilience on successful ageing was statistically significant (β = 0.038, 95% CI = 0.027 to 0.049) after controlling for gender, age, education, living status, employment status, disabilities, depression and chronic disease. Community participation mediated the relationship between resilience and successful ageing (β = 0.006, 95% CI = 0.002 to 0.010). Mediating role of community participation explained 16.44% of total effect of resilience on successful ageing.ConclusionAssisting older adults to increase community participation can be considered as a community‐based health care service to promote successful ageing. Further studies to examine causality among resilience, community participation, and successful ageing is necessary to strengthen the evidence of effect of active community participation on successful ageing.

Cerebrorenal connections in patients with chronic cerebral ischemia living in Republic of Sakha (Yakutia)

Purpose of the study. Identification of cerebrorenal relationships in patients with chronic cerebral ischemia (CCI) of elderly and senile age.Material and methods. We studied 522 elderly and senile patients with stage I and II CCI living in the Republic of Sakha (Yakutia). Doppler ultrasound was the main method for studying cerebral hemodynamics in this work. Glomerular filtration rate (GFR), which is the most reliable integral measure of the functional state of the kidneys, was calculated using the CKD-EPI formula, which takes into account race, gender, age, and serum creatinine levels.Results. Between the value of the glomerular filtration rate and almost all ultrasonic indicators included in the analysis (except for the diameter of the right and left vertebral arteries and the linear velocity of blood flow in the vertebral artery on the right), weak and moderate negative correlations were found. A univariate analysis confirmed the existence of relationships between GFR, age, duration of CCI, and blood lipid parameters.Conclusions. The study revealed a statistical relationship between GFR and age, duration of CCI, lipid spectrum parameters, as well as with all 12 ultrasound parameters characterizing cerebral hemodynamics.

A technique for assessing pulmonary perfusion in patients with previously treated COVID-19 pneumonia: clinical controlled non-randomized study

INTRODUCTION: Evaluating pulmonary lung perfusion in patients with previously treated COVID-19 infection may lead to a better understanding of long-term consequences of the disease, as well as may identify the changes determined by their symptoms. Further research is required for optimization of lung perfusion’s design parameters’ methods in order to implement those in clinical practice.OBJECTIVE: To determine the possibilities of an alternative method for evaluation of relative lung perfusion using three-dimensional ultrafast contrast-enhanced MRI on patients with previously treated COVID-19 pneumonia.MATERIALS AND METHODS: We examined 100 patients (28 male and 72 female, aged 22 to 70) who had laboratory-confirmed COVID-19 infection. The research was conducted using the three-dimensional ultrafast dynamic contrast-enhanced MRI based on 3D T1-weighted images. During the postprocessing, we received the values of rPBF (relative pulmonary blood flow), rPBV (relative pulmonary blood volume), and rMTT (relative mean transit time).Statistics. For non-linear dependence modelling we used natural spline transformation for time and interaction effect with a group. Intergroup comparison on integral measures was based on Kruskall-Wallis test (χ2), pair comparisons were based on Conover’s test (Δ). For multiple hypothesis testing correction, we used the false discovery rate (FDR). Comparisons were determined as statistically significant when p<0.05.RESULTS: The differences in obtained values of lung perfusion among patient groups were confirmed both quantitatively (by rMTT, rPBV, rPBF) and qualitatively (by building the curves of contrast agent accumulation). Patients with previously treated COVID-19 demonstrate slower contrast agent transit and increased relative lung blood volume. Their accumulation curves have qualitative differences as well.DISCUSSION: We suggest a new method of evaluation of lung perfusion indicators in patients with previously treated COVID-19. We conducted an intergroup analysis based on the degree of lung damage during the acute phase of COVID-19 (with no infiltrativechanges, with minor lung damage, and major lung damage). The intergroup differences found are more significant for patients with lung damage (both minor and major) than for patients with no infiltrative lung changes during the acute phase of COVID-19.CONCLUSION: This method of evaluation of pulmonary perfusion is able to adequately characterize the functional lung conditions in patients with previously treated COVID-19 pneumonia. The chosen model is the most optimal.

Reliability and validity of the supine-to-stand test in people with stroke.

To investigate the psychometric properties of the supine-to-stand test in people with stroke. Cross-sectional design. Fifty-two people with stroke (mean (standard deviation) age 63.13 (6.09) years; time post-stroke 93.13 (61.36) months) and 49 healthy older adults (61.90 (7.29) months). Subjects with stroke were recruited from the community dwelling in Hong Kong and assessed with the supineto- stand test, Fugl-Meyer Motor Assessment, ankle muscle strength test, Berg Balance Scale, limit of stability test, Timed Up-and-Go Test, Six-Minute Walk Test, Chinese version of Activities-specific Balance Confidence scale, Community Integration Measure (CIM-C), and 12-item Short-Form Health Survey (SF-12) in a university-based rehabilitation laboratory. The supine-to-stand test completion time demonstrated excellent intra-rater, inter-rater and test-retest reliability (intraclass correlation coefficient 0.946-1.000) for the people with stroke. The completion time was significantly negatively correlated with Berg Balance Scale, Six-Minute Walk Test, limit of stability - maximal excursion, and limit of stability - endpoint excursion results (r = -0.391 to -0.507), whereas it was positively correlated with the Timed Up-and-Go test results (r = 0.461). The optimal cut-off supine-to-stand test completion time of 5.25 s is feasible for a clinical measure to distinguish the performance of people with stroke from healthy older adults (area under the curve = 0.852, sensitivity = 81.1%, specificity = 84.0%). The supine-to-stand test is a reliable, sensitive, specific and easy-to-administer clinical test for assessing the supine-to-stand ability of people with stroke.

Lorentzian quantum gravity via Pachner moves: one-loop evaluation

Lorentzian quantum gravity is believed to cure the pathologies encountered in Euclidean quantum gravity, such as the conformal factor problem. We show that this is the case for the Lorentzian Regge path integral expanded around a flat background. We illustrate how a subset of local changes of the triangulation, so-called Pachner moves, allow to isolate the indefinite nature of the gravitational action at the discrete level. The latter can be accounted for by oppositely chosen deformed contours of integration. Moreover, we construct a discretization-invariant local path integral measure for 3D Lorentzian Regge calculus and point out obstructions in defining such a measure in 4D. We see the work presented here as a first step towards establishing the existence of the non-perturbative Lorentzian path integral for Regge calculus and related frameworks such as spin foams.An extensive appendix provides an overview of Lorentzian Regge calculus, using the recently established concept of the complexified Regge action, and derives useful geometric formulae and identities needed in the main text.

Bicrossproduct vs. twist quantum symmetries in noncommutative geometries: the case of ϱ-Minkowski

We discuss the quantum Poincaré symmetries of the ϱ-Minkowski spacetime, a space characterised by an angular form of noncommutativity. We show that it is possible to give them both a bicrossproduct and a Drinfel’d twist structure. We also obtain a new noncommutative ⋆-product, which is cyclic with respect to the standard integral measure.

Micro-canonical and canonical description for generalised entropy

Few parameters dependent generalised entropy includes Tsallis entropy, Rényi entropy, Sharma-Mittal entropy, Barrow entropy, Kaniadakis entropy, etc as particular representatives. Its relation to physical systems is not always clear. In this paper, we propose the microscopic thermodynamic description for an arbitrary generalised entropy in terms of the particle system. It is shown that the change in the volume of the phase space of the particle system in the micro-canonical description or the difference in the integration measure in the phase space in the canonical description may lead to generalised entropy. Our consideration may help us understand the structure of quantum gravity.

The validity and reliability of the Turkish version of the Community Integration Measure in patients with chronic stroke

Objective To translate and cross-culturally adapt The Community Integration Measure into Turkish (CIM-T) and to assess its reliability and validity in patients with chronic stroke. Patients and Methods Fifty participants completed the CIM-T, Community Integration Questionnaire (CIQ) and the London Handicap Scale (LHS). All participants completed the CIM-T questionnaire twice in 7 days. The internal consistency of the CIM-T was assessed using Cronbach’s alpha, while the Intraclass Correlation Coefficient (ICC) was used to evaluate test-retest reliability. The convergent validity of CIM-T was determined with CIQ and LHS by using Pearson’s and Spearman’s correlation coefficient analysis. Results The CIM-T demonstrated high internal consistency (Cronbach’s α = 0.955) and test-retest reliability (ICC= 0.992). The CIM-T showed a good correlation with CIQ (R = 0.727, p < 0.001) and LHS (R = 0.694, p < 0.001). Conclusion The Turkish version of CIM is a valid and reliable instrument for assessing chronic stroke patients. It is a preferable scale for the clinical evaluation of Turkish-speaking patients with chronic stroke.

Path integral quantization of generalized Stueckelberg electrodynamics: A Faddeev-Jackiw approach

We build a setup for path integral quantization through the Faddeev-Jackiw approach, extending it to include Grassmannian degrees of freedom, to be later implemented in a model of generalized electrodynamics that involves fourth-order derivatives in the components of a massive vector field being endowed with gauge freedom, due to an additional scalar field. Namely, the generalized Stueckelberg electrodynamics. In the first instance, we work on the free case to gain some familiarity with the program and, subsequently, we add the interaction with fermionic matter fields to complete our aim. In addition to deriving the correct classical brackets for such a model, we get the full expression for the associated generating functional and its associated integration measure.

Urban agglomeration and spatial formation of urban growth in the Colombo District

An urban agglomeration is one of the biggest drivers of national or global economic development since its cities are interconnected. The world's population was 55% urban in 2020, compared to 52% in developing countries (United Nations, 2020).Land usage statistics for small and medium-sized town centers were analyzed using primary and secondary sources. Semi-structured interviews capture 30 experts' thoughts. Reviewing historical planning papers, maps, census records, and other secondary data. Hybrid data analysis. GIS and qualitative research study urban agglomeration and spatial formation. Space Syntax and its integration measure street-to-street transitions to define urban design. Space syntax illustrates population integration and interaction. The Landscape Expansion Matrix controls dynamic systems.Research shows Colombo urbanized nuclear style before 1970. That impacted neighboring municipalities and suburbs for 50 years. After the 1990 Open Economy, outer-circle suburbia expansion began. The Civil War halted suburbanization (2001). Rapid exurban growth created ribbon-shaped urban districts. Development plans for Megacity Colombo City after the 2009 civil conflict advocated corridors and extensive urbanization.

Generating functions and large-charge expansion of integrated correlators in \U0001d4a9 = 4 supersymmetric Yang-Mills theory

We recently proved that, when integrating out the spacetime dependence with a certain integration measure, four-point correlators leftlangle {mathcal{O}}_2{mathcal{O}}_2{mathcal{O}}_p^{(i)}{mathcal{O}}_p^{(i)}rightrangle in \U0001d4a9 = 4 supersymmetric Yang-Mills theory with SU(N) gauge group are governed by a universal Laplace-difference equation. Here {mathcal{O}}_p^{(i)} is a superconformal primary with charge p and degeneracy i. These physical observables, called integrated correlators, are modular-invariant functions of Yang-Mills coupling τ. The Laplace-difference equation is a recursion relation that relates integrated correlators of operators with different charges. In this paper, we introduce the generating functions for these integrated correlators that sum over the charge. By utilising the Laplace-difference equation, we determine the generating functions for all the integrated correlators, in terms of the initial data of the recursion relation. We show that the transseries of the integrated correlators in the large-p (i.e. large-charge) expansion for a fixed N consists of three parts: 1) is independent of τ, which behaves as a power series in 1/p, plus an additional log(p) term when i = j; 2) is a power series in 1/p, with coefficients given by a sum of the non-holomorphic Eisenstein series; 3) is a sum of exponentially decayed modular functions in the large-p limit, which can be viewed as a generalisation of the non-holomorphic Eisenstein series. When i = j, there is an additional modular function of τ that is independent of p and is fully determined in terms of the integrated correlator with p = 2. The Laplace-difference equation was obtained with a reorganisation of the operators that means the large-charge limit is taken in a particular way here. From these SL(2, ℤ)-invariant results, we also determine the generalised ’t Hooft genus expansion and the associated large-p non-perturbative corrections of the integrated correlators by introducing λ = p {g}_{YM}^2 . The generating functions have subtle differences between even and odd N, which have important consequences in the large-charge expansion and resurgence analysis. We also consider the generating functions of the integrated correlators for some fixed p by summing over N, and we study their large-N behaviour, as well as comment on the similarities and differences between the large-p expansion and the large-N expansion.

Supersymmetric localization: \U0001d4a9 = (2, 2) theories on S2 and AdS2

Application of the supersymmetric localization method to theories on anti-de Sitter spacetime has received recent interest, yet still remains as a challenging problem. In this paper, we focus on (global) Euclidean AdS2, on which we consider an Abelian \U0001d4a9 = (2, 2) theory and implement localization computation to obtain the exact partition function. For comparison, we also revisit the theory on S2 and perform a parallel computation. We refine the notion of equivariant supersymmetry and use appropriate functional integration measure. For AdS2 we choose a supersymmetric boundary condition which is compatible with the principle of variation. To evaluate the 1-loop determinant about the localization saddle, we use index theory and fixed point formula, where we pay attention to the effect of zero modes and their superpartners. The existence of fermionic superpartner of 1-form boundary zero modes is proven. Obtaining the 1-loop determinant requires expansion of the index that presents an ambiguity, which we resolve using boundary condition. The resulting partition function reveals an overall dependence on the size of the background manifold, AdS2 as well as S2, as a sum of two types of contributions: a local one from local conformal anomaly through the index computation and a global one coming from zero modes. This overall size dependence matches with the perturbative 1-loop evaluation using heat kernel method.

Determinism of indicators of child disability due to mental disorders in the conditions of its registered and calculated level

The purpose of the study was to identify the presence of deterministic rates of childhood disability due to mental disorders in the context of its registered (recorded) and calculated levels.&#x0D; Material and methods. We examined associations between registered, counted and uncounted disability and integral measures of children with mental disorders in 0–14, 15–17 and 0–17years groups. In addition, health resource and activity measures, mental disorder morbidity rates, demographic indicators and their association with child disability rates were examined. Period of analysis was from 2010 to 2020. The study is analytic, non-personalized, retrospective, not randomised. &#x0D; Results. In the Arkhangelsk region, in the 0–14 years group the rate of calculated total disability was on average 55.9% higher than the rate of registered disability. The underreporting of total disability was higher than in the 15–17 years group. We found no significant links between demographic, socio-economic, health resource indicators and the level of official childhood disability.&#x0D; Limitations of the study. To avoid errors of extrapolation, caution should be exercised when attempting to scale the results obtained in the study to the population of other regions or the country as a whole, other types of disability, separate age and gender groups, and individual cases of disability. &#x0D; Conclusions. In the Arkhangelsk region there is underreporting of childhood disability caused by mental disorders. The levels of children’s disability due to mental disorders recorded by official statistics have no significant relationship with indicators reflecting the demographic, socio-economic situation, resources and health care activities. The estimated and unrecorded levels of disability are found to be significantly associated with indicators of socioeconomic status, health care resources, and the overall incidence of mental disorders.

Field theories on ρ-deformed Minkowski space-time

We study one-loop perturbative properties of scalar field theories on the ρ-Minkowski space. The corresponding star-product, together with the involution are characterized from a combination of Weyl quantization and defining properties of the convolution algebra of the Euclidean group linked to the coordinate algebra of the ρ-Minkowski space. The natural integration measure linked to the Haar measure of the Euclidean group defines a trace for the star-product. One-loop properties of the 2-point and 4-point functions for families of complex-valued scalar field theories on ρ-Minkowski space are examined. For scalar theories with orientable interaction, the 2-point function is found to receive UV quadratically diverging one-loop corrections in 4 dimensions while no IR singularities generating UV/IR mixing appears. These however occur in the one-loop corrections to the 4-point function. As well, one-loop 2-point functions for theories with non-orientable interaction involve such IR singularities. These results are discussed.