Convex Measures Research Articles

Predicting cardiac infarctions with reinforcement algorithms through wavelet transform applications in healthcare

Cardiovascular pathology must requires various conditions influenced by the myocardial infarction,sorted using a reinforcement algorithm with distinctive notches in the corona arterial impact ratio.The order in a dataset might consist of 306 factors and 17 chronic impute characteristics that arise with a bardic canicular conglomerate factor within the overall sanguiferous conglomerate ratio and denote the factor measure of carnage thrust,triglyceride measure, and bosom gait ratings of conglomerate rehabilitators.When existing system order with a probability variation of 86.04% in the contour ratio convexity measure,a miniature factor of conjecture with an extent notation of 85.82%,and a cabalistic miniature exposed for the heat map.‘In a proposed system by developing the decrepit search with an order measure of an anecdotal concrete factor with carnal movement,one can access the hazard factor of myocardial infarction in the anecdotal concrete factor when raising the abrupt cardiovascular method with the release of 4.96.When improving the measure of carnage thrust with 0.95,outright regime benefaction in the tranquil ratio is 2641 with a ratio variation of 23.6 by improving the triglyceride measure,and destitute factor variation is 623 with a factor variation of 18.4 when correcting the bosom gait ratings measure.

Everyone knows what convexity is, yet no single convexity measure captures its effect on figure/ground perception

Everyone knows what convexity is, yet no single convexity measure captures its effect on figure/ground perception

Poincaré inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures

Poincaré inequalities and integrated curvature-dimension criterion for generalised Cauchy and convex measures

Risk Measures’ Duality on Ordered Linear Spaces

The aim of this paper is to provide a dual representation of convex and coherent risk measures in partially ordered linear spaces with respect to the algebraic dual space. An algebraic robust representation is deduced by weak separation of convex sets by functionals, which are assumed to be only linear; thus, our framework does not require any topological structure of the underlying spaces, and our robust representations are found without any continuity requirement for the risk measures. We also use such extensions to the representation of acceptability indices.

Analysis of spatio-temporal variability of Pacific water distribution in the Sea of Okhotsk based on Lagrangian approach

The aim of this work is characteristic of spatio-temporal variability of Pacific water distribution in the Sea of Okhotsk based on Lagrangian approach and spatial analysis.Materials and methods. The study is based on geostrophic current data product from satellite altimetry. The dataset has resolution of 0,25° × 0,25° × 1 day. This data is used for calculation of approximately 100000 water parcels trajectories during 400 days back in time for every day from 31st of January 1997 to 17th of April 2022. For each date in this interval, those parcels which intersected the conditional Kuril transect were determined, as well as region and date of transect intersection. Those two parameters were used in cluster analysis with DBSCAN method in order to distinguish individual Pacific intrusions. Position, shape, and size of each intrusion were investigated.Results allowed to suggest two types of indexes describing distribution of Pacific-origin water in the Sea of Okhotsk. First, centroid of particles of Pacific origin with residence time between 1 and 6 months is calculated. Variability of centroid position showed northward displacement of Pacific waters in spring-summer and south[1]ward displacement in autumn-winter. Eastward displacement towards Kamchatka coast usually occurs during winters and opposite westward displacement is usual for summers. In 1998, 2003, 2010, 2013, 2017, and 2019 waters of Pacific origin had the most northern location. Second type of indexes is based on location and shape characteristics of Pacific water intrusions. The fractal dimensionality and convexity measure of intrusions are rapidly decreasing after the intrusion reaches its maximum area. Centroids of the most prominent intrusions follow the path along 152–154 °E. Both types of indices showed intensification of Pacific inflow since 2010.Practical value. The time-series of resulted indexes are suggested to be implemented in integrated ecosystem assessments of the eastern Sea of Okhotsk.

Numerical approximation in the application of Risk Parity with Conditional Value at Risk in case of mixed portfolios

Abstract The 2008 financial crisis has required new methods for portfolios diversification. In the same year, Maillard, Roncalli and Teiletche (2008) suggested a method that maximizes the diversification which is called Risk Parity or Equally weighted Risk Contribution strategy. The most common method to use the Risk Parity approach is to use the standard deviation as risk measure. In this paper, we describe a method to apply Risk Parity to the Expected shortfall or also known as Conditional Value at Risk using a numerical approximation from discrete historical observation. The expected shortfall can use the advantage of being a coherent measure, not to forget that it is also a convex measure, which is very useful in the optimization. Another advantage is that the Risk Parity approach doesn’t need the estimation of the expected return as an input. Usually, the models that require the expected returns, such as the Markowitz, model have higher concentration in a smaller number of assets. This will bring a very high turnover and drawdown of the performance. The performance analysis in this paper is applied in mixed portfolios composed by stock, bonds and commodities. They show also how better this model performs in case of the crisis. We also identify not only the strong points but also the week points of these models.

Risk concentration and the mean‐expected shortfall criterion

AbstractExpected shortfall (ES, also known as CVaR) is the most important coherent risk measure in finance, insurance, risk management, and engineering. Recently, Wang and Zitikis (2021) put forward four economic axioms for portfolio risk assessment and provide the first economic axiomatic foundation for the family of . In particular, the axiom of no reward for concentration (NRC) is arguably quite strong, which imposes an additive form of the risk measure on portfolios with a certain dependence structure. We move away from the axiom of NRC by introducing the notion of concentration aversion, which does not impose any specific form of the risk measure. It turns out that risk measures with concentration aversion are functions of ES and the expectation. Together with the other three standard axioms of monotonicity, translation invariance and lower semicontinuity, concentration aversion uniquely characterizes the family of ES. In addition, we establish an axiomatic foundation for the problem of mean‐ES portfolio selection and new explicit formulas for convex and consistent risk measures. Finally, we provide an economic justification for concentration aversion via a few axioms on the attitude of a regulator towards dependence structures.

Kantorovich type topologies on spaces of measures and convergence of barycenters

We study two topologies $ \tau_{KR} $ and $ \tau_K $ on the space of measures on a completely regular space generated by Kantorovich–Rubinshtein and Kantorovich seminorms analogous to their classical norms in the case of a metric space. The Kantorovich–Rubinshtein topology $ \tau_{KR} $ coincides with the weak topology on nonnegative measures and on bounded uniformly tight sets of measures. A sufficient condition is given for the compactness in the Kantorovich topology. We show that for logarithmically concave measures, some $ s $-convex measures and stable measures weak convergence implies convergence in the Kantorovich topology. We also obtain an efficiently verified condition for convergence of the barycenters of Radon measures from a sequence or net weakly converging on a locally convex space. As an application it is shown that for weakly convergent logarithmically concave measures and stable measures convergence of their barycenters holds without additional conditions. The same is true for measures given by polynomial densities of a fixed degree with respect to logarithmically concave measures.

Pricing and Hedging Bond Power Exchange Options in a Stochastic String Term-Structure Model

We study power exchange options written on zero-coupon bonds under a stochastic string term-structure framework. Closed-form expressions for pricing and hedging bond power exchange options are obtained and, as particular cases, the corresponding expressions for call power options and constant underlying elasticity in strikes (CUES) options. Sufficient conditions for the equivalence of the European and the American versions of bond power exchange options are provided and the put-call parity relation for European bond power exchange options is established. Finally, we consider several applications of our results including duration and convexity measures for bond power exchange options, pricing extendable/accelerable maturity zero-coupon bonds, options to price a zero-coupon bond off of a shifted term-structure, and options on interest rates and rate spreads. In particular, we show that standard formulas for interest rate caplets and floorlets in a LIBOR market model can be obtained as special cases of bond power exchange options under a stochastic string term-structure model.

Three-dimensional orthodontic imaging in children across the age spectrum and correlations with obstructive sleep apnea.

To determine baseline facial convexity measurements in children with obstructive sleep apnea (OSA) across the age spectrum. Polysomnogram, stereophotogrammetry, and biometric data were collected from children aged 0-18 years who were being investigated for OSA. Analyses evaluated differences in facial convexity according to OSA severity and other sleep parameters, while adjusting for age, ethnicity, and sex. Ninety-one children, aged 0.05-16.02 years, met the inclusion criteria for this study. Initial analysis showed that the logarithm of age had a significant effect on facial convexity (P = 8.3·10-7) with significant effects of sex (P = 1.3·10-2), while excluding OSA. Ordinal logistic regression taking into consideration age, sex, weight, height, and ethnicity with OSA severity categorized as obstructive apnea-hypopnea index negative, mild, moderate, or severe showed that facial convexity was associated with OSA severity (P = 2.2·10-3); an increasing obtuse angle of convexity increased the tendency to be classified as having severe OSA. Using three-dimensional imaging, we found an added impact of infancy on changes of facial convexity with age. While modeling could describe facial convexity without any OSA-associated sleep parameters, differences in facial convexity were present among groups with different levels of OSA severity adjusted for growth (age, weight, and height), sex, and ethnicity. The method provides a safer and cheaper alternative to other medical imaging techniques in children and holds potential for future use in studies of craniofacial structure. Tyler G, Machaalani R, Waters KA. Three-dimensional orthodontic imaging in children across the age spectrum and correlations with obstructive sleep apnea. J Clin Sleep Med. 2023;19(2):275-282.

Reduction of variables and constraints in fitting antibuoyant fuzzy measures to data using linear programming

The discrete Choquet integral with respect to various types of fuzzy measures serves as an important aggregation function which accounts for mutual dependencies between the inputs. The Choquet integral can be used as an objective (or constraint) in optimisation problems, and the type of fuzzy measure used determines its complexity. This paper examines the class of antibuoyant fuzzy measures, which restrict the supermodular (convex) measures and satisfy the Pigou–Dalton progressive transfers principle. We determine subsets of extreme points of the set of antibuoyant fuzzy measures, whose convex combinations form a basis of three proposed algorithms for random generation of fuzzy measures from that class, and also for fitting fuzzy measures to empirical data or solving best approximation problems. Potential applications of the proposed methods are envisaged in social welfare, ecology, and optimisation.

On the equivalence of statistical distances for isotropic convex measures

On the equivalence of statistical distances for isotropic convex measures

Angulation Toward Coronal Convexity Measure and Catheter Length Indication Improves the Quality of Ventricular Catheter Placement—A Smartphone-Assisted Guidance Technique

Accurate placement of a ventricular catheter (VC) is crucial to reduce the risk of shunt failure. In the randomized, prospective, multicenter GAVCA (guided application of ventricular catheters) trial, which evaluated the quality of VC placement, the subgroup of patients with detailed length-marked VCs (dVCs) reflected a difference in the primary endpoint of optimal VC placement compared with the subgroup of patients with simplified length-marked VCs (sVCs). The objective of the present analysis was to compare the dVC and sVC groups and the smartphone-assisted guidance technique (GA) with the standard freehand technique (FH) for VC placement. We performed a further analysis of the GAVCA trial in 2 steps. First, we compared the dVCs, which provided a detailed distance from the tip to the base (3-13 cm) in 0.5-cm intervals, with the sVCs with a length indication at 5 and 10 cm from the tip to base. Second, we compared the GA technique with the FH in the dVC group. The data from 137 patients (104 dVC patients vs. 33 sVC patients) were eligible for the present analysis. Optimal VC placement was achieved in 72.1% of the dVC group and 39.4% of the sVC group (odds ratio, 3.9; 95% confidence interval, 1.7-9.3; P ≤ 0.001). In addition, we performed a subgroup analysis of the 104 dVC patients concerning the accuracy of catheter placement using 2 different techniques (GA, n= 54; and FH, n= 50). Optimal catheter placement was achieved in 81.5% of the GA group and 62.0% of the FH group (odds ratio, 2.7; 95% confidence interval, 1.1-6.8; P= 0.03). VC placement using the GA technique was successful in all patients at the primary puncture. In contrast, for 8.7% of the patients in the FH group, multiple attempts were necessary (P= 0.03). The results from the present analysis suggest that the combination of a GA technique and the use of a dVC will improve the rate of accurate VC placement. Compared with the FH technique, patient safety was increased by the reduction of unsuccessful VC placement attempts using the GA technique and dVCs.

Bond Power Exchange Options

We study power exchange options written on zero-coupon bonds under a stochastic string frame- work. We obtain closed-form expressions for pricing and hedging bond power exchange options and, as particular cases, the corresponding expressions for call power options and constant underlying elasticity in strikes (CUES) options. Suffi cient conditions for the equivalence of the European and the American versions of bond power exchange options are provided and the put- call parity relation for this kind of option is also stated. Finally, we consider several applications of our results including duration and convexity measures for bond power exchange options, pric- ing extendable/accelerable maturity zero-coupon bonds, options to price a zero-coupon bond off of a shifted term-structure, and options on interest rates and rate spreads.

An Improved Hand Gesture Recognition Algorithm based on image contours to Identify the American Sign Language

It is an open era of research to provide the assistance communication to hearing and visually impaired people. For the same, this paper proposed a recognition and classification of hand gesture to identify the correct denotation with maximum accurateness for standard American Sign Language. The proposal intelligently used the information based on image contours to identify the character’s representation of hand gesture. The proposal optimizes the performance overhead through identifications of 17 characters and 6 symbols based on image contours and convexity measurement of Standard American Sign Language without using complex algorithms and specialized hardware devices. Accuracy measurement done through simulation, which shows how our proposal provide more accuracy with minimum complexity in comparison to other state-of-art works.

Optimal Scenario-Dependent Multivariate Shortfall Risk Measure and its Application in Capital Allocation

In this paper, we consider a multivariate shortfall risk measure with scenario-dependent allocation weights and examine its properties such as convexity and quasi-convexity. For fixed allocation weights, we show that the resulting risk measure is a convex systemic risk measure in which case the property of translation invariance is dependent on the allocation weights. However, if the allocation weights are chosen optimally on a feasible set, then the resulting risk measure is a quasi-convex systemic risk measure. To evaluate the systemic risk of a financial system with the proposed risk measure computationally, we reformulate it as a two-stage stochastic program which is a finite convex program when the underlying uncertainty is discretely distributed. In the case when the uncertainty is continuously distributed, we propose a polynomial decision rule to tackle the semi-infinite two-stage stochastic program which restricts the scenario-dependent allocation weights to be a class of polynomials of the underlying uncertainty parameters and subsequently reformulate the evaluation problem as a tractable optimization problem. Some convergence results are established for the approximation scheme. Moreover, we apply the proposed risk measure to capital allocation problem and introduce scenario-dependent allocation strategy and deterministic allocation strategy. Finally, we carry out some preliminary tests on the proposed computational schemes for a continuous system, a discrete system and a capital allocation example for a life insurance company.

Optimization of Quasi-convex Function over Product Measure Sets

We consider a generalization of the Bauer maximum principle. We work with tensorial products of convex measures set that are not necessarily compact but generated by their extreme points. We show t...

Temporal Trends in Cervical Spine Curvature of South Korean Adults Assessed by Deep Learning System Segmentation, 2006-2018

The loss of the physiologic cervical lordotic curve is a common degenerative disorder known to be associated with abnormal spinal alignment. However, the changing trends among sex and age groups has not yet been well established. To analyze the temporal trends in cervical curvature across sex and age groups using an automated deep learning system (DLS). A retrospective cross-sectional study was conducted using lateral cervical radiographs of 13 691 individuals from January 1, 2006, to December 31, 2018. The degree of anterior vertical curvature was approximated by a DLS approach and convexity measurement method. This population-based study used the Yonsei University College of Medicine Severance Hospital, Seoul, South Korea, cohort database to identify 13 691 consecutive adults (≥18 years of age) who underwent standing lateral radiography in inpatient and outpatient settings. The prevalence of kyphotic and straight cervical curve as well as the trends of degree of cervical curvature in 2006 to 2018 among sex and age groups were determined. The DLS performance was validated with quantitative metrics and compared with interobserver and intraobserver variations. Automatic cervical spine segmentation was identified from lateral radiographs of 13 691 individuals (mean [SD] age, 49.9 [15.3] years; 8051 women [58.8%]). From 2006 to 2018, the decrease in the lordotic curve was significant across both sexes and age groups younger than 70 years, with the decrease more pronounced in women and successively younger generations (female, -0.05; 95% CI, -0.06 to -0.04; 18-29 years of age, -0.06; 95% CI, -0.08 to -0.04; 30-39 years of age, -0.06; 95% CI, -0.08 to -0.04; and 40-49 years of age, -0.05; 95% CI, -0.06 to -0.03; all P < .001). The prevalence of straight and kyphotic curvature had a significant increasing trend for both sexes and young generations, in which individuals 18 to 29 years of age generally had the highest prevalence rates during the study cycle (in 2018, kyphosis, 16.7%; 95% CI, 10.8%-22.5%; straight, 45.5%; 95% CI, 37.7%-53.3%). Similar trends were observed with longitudinal analysis of repeated measures of individuals, with more pronounced decreases in lordotic curvature observed among women and young adults. This study suggests a significant, increasing loss of normal cervical lordotic curvature for both sexes and young adults that is greater in progressively younger cohorts and women. Further research is necessary to evaluate associations between neck pain and loss of cervical curvature and address the need for active promotion and practical interventions aimed at neck posture correction.

A Measure of Q-convexity for Shape Analysis

In this paper, we study three basic novel measures of convexity for shape analysis. The convexity considered here is the so-called Q-convexity, that is, convexity by quadrants. The measures are based on the geometrical properties of Q-convex shapes and have the following features: (1) their values range from 0 to 1; (2) their values equal 1 if and only if the binary image is Q-convex; and (3) they are invariant by translation, reflection, and rotation by 90 degrees. We design a new algorithm for the computation of the measures whose time complexity is linear in the size of the binary image representation. We investigate the properties of our measures by solving object ranking problems and give an illustrative example of how these convexity descriptors can be utilized in classification problems.

Concentration of information content for convex measures

We establish sharp exponential deviation estimates of the information content as well as a sharp bound on the varentropy for the class of convex measures on Euclidean spaces. This generalizes a similar development for log-concave measures in the recent work of Fradelizi, Madiman and Wang (2016). In particular, our results imply that convex measures in high dimensions are concentrated in an annulus between two convex sets (as in the log-concave case) despite their possibly having much heavier tails. Various tools and consequences are developed, including a sharp comparison result for R\'enyi entropies, inequalities of Kahane-Khinchine type for convex measures that extend those of Koldobsky, Pajor and Yaskin (2008) for log-concave measures, and an extension of Berwald's inequality (1947).