Characteristic Function Research Articles

Gender Stratification, Racial Disparities, and Student Debt Trajectories in the United States

In the United States, post-secondary educational outcomes are stratified by gender, with women attending college and completing their degrees at higher rates. At the same time, student loan debt has become an ubiquitous part of the college process for many pursuing higher education, increasing the financial risks associated with the pursuit of higher education while lessening the financial rewards. Using data from the National Longitudinal Survey of Youth 1997 (NLSY97) of young adults who ever attended a post-secondary institution and growth curve models, we estimate gender disparities in student debt trajectories throughout young adulthood. Building on work on the racialization of the student debt landscape (Houle & Addo 2022), we also investigate the intersection of race and gender, and include both within race gender analyses and within gender racial analyses. Gender differences in student debt at baseline, or at the age of first college enrollment, are large and the gender debt gap grows at 1.2% per year. We document evidence of a curvilinear relationship in student debt in young adulthood, with student debt accumulating at the beginning of the college enrollment period and the rate of increase declining over time as adults age. Women, who start the period with larger amounts of student debt, experience faster growth in their debt accumulation followed by lower declines relative to young adult men. These patterns are magnified among Black young adults, with the gender debt disparity between Black women and Black men growing 3.4% annually. We find no association between gender and student debt trajectories among Latinx and White young adults. Within-gender models highlight the prevalence of the student debt crisis among Black women and Black men. Additional analyses suggest gender differences in debt trajectories are a function of postsecondary and young adult socioeconomic characteristics, reflecting broader societal inequalities that stem from structural elements related to post-secondary schooling and economic status. These patterns may inhibit wealth-building among women and Black adults in the United States.

Prime and Möbius correlations for very short intervals in $\fq[x

abstract: We investigate function field analogs of the distribution of primes, and prime $k$-tuples, in ``very short intervals'' of the form $I(f):=\{f(x) + a : a \in\fp\}$ for $f(x)\in\fp[x]$ and $p$ prime, as well as cancellation in sums of function field analogs of the M\"{o}bius $\mu$ function and its correlations (similar to sums appearing in Chowla's conjecture). For generic $f$, i.e., for $f$ a Morse polynomial, the error terms are roughly of size $O(\sqrt{p})$ (with typical main terms of order $p$). For non-generic $f$ we prove that independence still holds for ``generic'' set of shifts. We can also exhibit examples for which there is no cancellation at all in M\"{o}bius/Chowla type sums (in fact, it turns out that (square root) cancellation in M\"{o}bius sums is {\em equivalent} to (square root) cancellation in Chowla type sums), as well as intervals where the heuristic ``primes are independent'' fails badly. The results are deduced from a general theorem on correlations of arithmetic class functions; these include characteristic functions on primes, the M\"{o}bius $\mu$ function, and divisor functions (e.g., function field analogs of the Titchmarsh divisor problem can be treated). We also prove analogous, but slightly weaker, results in the more delicate fixed characteristic setting, i.e., for $f(x)\in\fq[x]$ and intervals of the form $f(x)+a$ for $a\in\fq$, where $p$ is fixed and $q=p^{l}$ grows.

Determination and economic design of repetitive group sampling plan under two parameter Lindley distribution

ABSTRACT A designing procedure of repetitive group sampling plan for assuring mean life under a two-parameter Lindley distribution is proposed, and the optimization model is developed for finding the optimal plan parameters such that the demands of both supplier and buyer are satisfied simultaneously. A real-time data set of ball bearings is used to explain the application of the proposed plan. A comparison between the proposed plan and the single sampling plan is done to reveal the better performance of the proposed plan based on operating characteristic function and average sample number. Applying the proposed plan to provide lifetime assurance reduces the inspection effort and related costs. We discuss the design of the proposed plan with an economic aspect. In addition, the sensitivity of the optimal sampling plans concerning the failure probability and cost parameters is analyzed. Finally, it is evident from the study that the proposed plan will be preferable to a single sampling plan for providing quality assurance with a minimum cost of the inspection.

#2898 Exposure response model describing hematologic changes with chronic treatment of CKD anemia with vadadustat

Abstract Background and Aims Vadadustat (VADA) is an oral hypoxia-inducible factor (HIF) prolyl hydroxylase inhibitor, a class of drugs that stabilize HIF and stimulate endogenous erythropoietin production, increasing iron mobilization and red blood cell production. VADA is approved in 36 countries globally and is indicated in the European Union for the treatment of symptomatic anaemia associated with chronic kidney disease (CKD) in adults on chronic maintenance dialysis and is an alternative to treatment with erythropoiesis-stimulating agents (ESAs). The aim of this work was to develop a predictive, semi-mechanistic model to understand the effects of VADA and erythropoiesis-stimulating agents (ESAs) on hemoglobin response and to evaluate the impact of intrinsic and extrinsic patient characteristics on that response for non-dialysis dependent (NDD) and dialysis-dependent (DD) patient populations. Method A predictive semi-mechanistic pharmacokinetic/pharmacodynamic (PK/PD) model for VADA and ESA treatment was developed using nonlinear mixed effects methods. The model describes changes in reticulocyte count (RETICs), mature erythrocytes (RBCs) and hemoglobin (Hb) as a function of drug exposure and subject-specific characteristics. The dataset was based on data from 7 Phase 1 to Phase 3 studies (Table 1; N = 894 for VADA; N = 560 for ESA modeling) in healthy volunteers and subjects with NDD- or DD-CKD who were either ESA-naïve or ESA experienced but not receiving treatment at screening. Prior population PK modeling of VADA provided estimated drug exposures for VADA-treated subjects, while dose normalized to standard units (IU/kg/wk) was used as the exposure metric for subjects on ESA. Each of these exposure metrics could vary with time, as the dose was adjusted according to observed Hb response. This work evaluated alternative model structures, as well as covariate effects affecting Hb individual response. Results A predictive semi-mechanistic pharmacokinetic/pharmacodynamic (PK/PD) model for VADA and ESA treatment was developed using nonlinear mixed effects methods. The model describes changes in reticulocyte count (RETICs), mature erythrocytes (RBCs) and hemoglobin (Hb) as a function of drug exposure and subject-specific characteristics. The dataset was based on data from 7 Phase 1 to Phase 3 studies (Table 1; N = 894 for VADA; N = 560 for ESA modeling) in healthy volunteers and subjects with NDD- or DD-CKD who were either ESA-naïve or ESA experienced but not receiving treatment at screening. Prior population PK modeling of VADA provided estimated drug exposures for VADA-treated subjects, while dose normalized to standard units (IU/kg/wk) was used as the exposure metric for subjects on ESA. Each of these exposure metrics could vary with time, as the dose was adjusted according to observed Hb response. This work evaluated alternative model structures, as well as covariate effects affecting Hb individual response. A similar model structure was found to describe early changes in RETICs and longer-term changes in Hb for both VADA and ESAs. In each case, the magnitude of response increases with increased drug exposure up to a maximum value (Emax), and the Emax values were similar between VADA and ESAs. Subject intrinsic predictors of response included eGFR, subject age, BMI, and serum albumin, while extrinsic factors affecting response included geographic region, limits on acceptable Hb values (which also differ by geographic region) and the presence of previous ESA treatment. Interestingly, Hb responses were also correlated with changes in serum hepcidin, a key regulator of iron homeostasis, following both VADA and ESA treatment. Differences between the response to VADA and ESA were also described, including differences in temporal changes in RETICs and Hb. Conclusion This model showed an exposure-response relationship between VADA or ESA treatment and changes in RETICs and Hb for ESA naïve or ESA-experienced CKD subjects. The model will be used to inform dosage recommendations for VADA based on patient characteristics.

A new generalized beta function associated with statistical distribution and fractional kinetic equation

Several authors have extensively investigated beta function, hypergeometric function and confluent hypergeometric function, their extensions and generalizations due to their several application in many areas of engineering, probability theory and science. The main purpose of this paper is to present a new generalization of extended beta function, hypergeometric function and confluent hypergeometric function with the help of m-parameter Mittag-Leffler function, as well as examine some important properties like integral representations, differential formula and summation formulas. We also examine generalized Caputo fractional derivative operator with the help of m-parameter Mittag-Leffler function with associated properties using the generalized beta function. We define a new beta distribution involving the new generalized beta function. The mean, variance, coefficient of variance, moment generating function and characteristic function and cumulative distribution are derived. Further, we derive the solution of fractional Kinetic equation involving generalized hypergeometric function.

Use of the Adaptive Cross Approximation for the Efficient Computation of the Reduced Matrix with the Characteristic Basis Function Method

A technique for the reduction in the CPU-time in the analysis of electromagnetic problems using the Characteristic Basis Function Method (CBFM) is presented here, allowing for analysis of electrically large cases where an iterative solution process cannot be avoided. This technique is based on the use of the Adaptive Cross Approximation (ACA) for the fast computation of the coupling matrix between CBFs belonging to adjacent blocks, as well as the Multilevel Fast Multipole Method (MLFMM) for the computation of matrix−vector products in the solution of the full system. This combination allows for a noticeable reduction in the computational resources during the analysis of electrically large and complex scenarios while maintaining a very good degree of accuracy. A number of test cases serve to validate the presented approach in terms of accuracy, memory and CPU-time compared with conventional techniques.

Field Data Analysis of Pavement Marking Retroreflectivity and Its Relationship with Paint and Glass Bead Characteristics

Pavement marking retroreflectivity, a critical factor for safe driving, depends on the characteristics of both the paint and the embedded glass beads. However, traditional methods for predicting pavement marking service life often overlook these materials properties. This study investigates the influence of paint and glass bead characteristics on pavement marking retroreflectivity performance and addresses the characterization of glass bead size distribution by the coefficient of uniformity and curvature. Three field test sites on a Brazilian highway with various paint and glass bead combinations were evaluated. A statistical model, GAMLSS (Generalized Additive Model for Location, Scale, and Shape), was adjusted to evaluate the performance of the markings’ retroreflectivity as a function of paint and glass bead characteristics. The model revealed that well-graded glass beads increased retroreflectivity by around 10%, while paints with a higher volume of solids improved service life around 65%. Therefore, the results show that acrylic water-based paints with higher volumes of solids and well-graded glass beads with better shape characteristics should be preferred to improve pavement markings’ retroreflectivity and service life. The statistical model identified the key characteristics with the greatest impact on pavement marking retroreflectivity, offering valuable insights for real-world applications, which will assist pavement marking practitioners and road authorities in selecting appropriate materials to achieve enhanced durability.

Evaluation of University’s Place in the Adult Education Ecosystem

The authors of the present paper conducted a comprehensive analysis of university place in the ecosystem of adult education, based on its characteristic functions, priorities of activity and emerging tensions. The participation of universities in the professional training of adults is analyzed. The research focus is projected on the assessment of the situation at the institutional (a university as a social institution) and organizational level (a university as a specific institution of higher education). A discussion of the prospects for transforming the place of higher institution in the ecosystem of adult education is presented. The study was conducted using a semiformalized interview method (n=36) with representatives of the commercial and public sector occupying key positions (heads and top management of universities, corporate universities, educational consulting organizations, providers of non-formal education services, etc.). Main results. Several points of university positioning in the structure of adult education ecosystem are identified: 1) the university is the core of the educational ecosystem and holds this status; 2) the university occupies the central place of the educational ecosystem, but can lose this status by certain actions or inaction; 3) the university is not the core of the educational ecosystem and should not be; 4) the university is not the core of the educational ecosystem, but could become it. According to most experts, universities occupy a central place in the ecosystem of adult education and have a high potential to retain leadership positions, provided that the educational material is relevant and meets the demands of the labor market. At the same time, it is important to consider that some participants of the educational ecosystem (online platforms, corporate universities and others) are rapidly increasing their influence and implementing large-scale educational programs for the population. Universities, having a high level of public trust and being mainly responsible for fundamental professional education, are interested in accumulating the advantages of other participants of the educational ecosystem. It is optimal to present the university as a central hub of educational practices for the population, accumulating the advantages of other actors of the adult education ecosystem. The article is addressed to administrative and managerial staff of universities, representatives of executive authorities and the real sector of the economy, scientific and pedagogical staff and graduate students seeking to study lifelong learning of adults.

Constrained optimal grouping of cloud application components

Cloud applications are built from a set of components often deployed as containers, which can be deployed individually on separate Virtual Machines (VMs) or grouped on a smaller set of VMs. Additionally, the application owner may have inhibition constraints regarding the co-location of components. Finding the best way to deploy an application means finding the best groups of components and the best VMs, and it is not trivial because of the complexity coming from the number of possible options. The problem can be mapped onto may known combinatorial problems as binpacking and knapsack formulations. However, these approaches often assume homogeneus resources and fail to incorporate the inhibition constraints. The main contribution of this paper are firstly a novel formulation of the grouping problem as constrained Coalition Structure Generation (CSG) problem, including the specification of the value function which fulfills the criteria of a Characteristic Function Game (CFG). The CSG problem aims to determine stable and disjoint groups of players collaborating to optimize the joint outcome of the game, and a CFG is a common representation of a CSG, where each group is assigned a value and where the value of the game is the sum of the groups’ contributions. Secondly, the Integer-Partition (IP) CSG algorithm has been modified and extended to handle constraints. The proposed approach is evaluated with the extended IP algorithm, and a novel exhaustive search algorithm establishing the optimum grouping for comparison. The evaluation shows that our approach with the modified algorithm evaluates on average significantly less combinations than the CSG state-of-the-art algorithm. The proposed approach is promising for optimized constrained Cloud application management as the modified IP algorithm can optimally solve constrained grouping problems of attainable sizes.

Forward Starting Option Pricing under Double Fractional Stochastic Volatilities and Jumps

This paper aims to provide an effective method for pricing forward starting options under the double fractional stochastic volatilities mixed-exponential jump-diffusion model. The value of a forward starting option is expressed in terms of the expectation of the forward characteristic function of log return. To obtain the forward characteristic function, we approximate the pricing model with a semimartingale by introducing two small perturbed parameters. Then, we rewrite the forward characteristic function as a conditional expectation of the proportion characteristic function which is expressed in terms of the solution to a classic PDE. With the affine structure of the approximate model, we obtain the solution to the PDE. Based on the derived forward characteristic function and the Fourier transform technique, we develop a pricing algorithm for forward starting options. For comparison, we also develop a simulation scheme for evaluating forward starting options. The numerical results demonstrate that the proposed pricing algorithm is effective. Exhaustive comparative experiments on eight models show that the effects of fractional Brownian motion, mixed-exponential jump, and the second volatility component on forward starting option prices are significant, and especially, the second fractional volatility is necessary to price accurately forward starting options under the framework of fractional Brownian motion.

Optimization of phosphorus wet acid extraction from sewage sludge ashes: Detailed process insight via multi-variate statistical techniques

To tackle the issue of phosphorus (P) supply, Sewage Sludge Ash (SSA) is a promising secondary source. The goal of this research is the optimization of the wet P extraction process in the view of providing valuable insights for the process scale-up. While most of the studies relied on the “one-variable-changed-at-a-time” approach, this work applied a statistical optimization model based on the Design of Experiments technique for investigating the influence of most relevant operating conditions of extraction process on Phosphorus Extraction Efficiency (PEE) with two types of SSA characterized by different levels of alkalinity. Experimental results highlighted the importance of ash characteristics, making some SSA not suitable for cost-effective phosphorus recovery due to the high acid dosage required in extraction process. Type of acid and contact time become significant factors only for Ca-rich ashes, especially when using H2SO4 as extracting agent. Optimal operating conditions (CH2SO4 = 1.3 N, L/S = 20, t = 2 h and CHCl = 2.0 N, L/S = 10, t = 2 h for Ash#1 and CH2SO4/HCl = 0.8 N, L/S = 10 for Ash#2) resulting in high PEE (80–94%) were identified for extraction performed with H2SO4 and HCl as a function of ash characteristics.

A clustering-based partially stratified sampling for high-dimensional structural reliability assessment

Assessing structural reliability problem with high-dimensional random inputs is still challenging due to the “curse of dimensionality”. In this paper, this challenge is addressed by extending the Generalized Distribution Reconstruction Method via Characteristic Function Inversion (GDRM-CFI). Specifically, a clustering-based partially stratified sampling method is proposed for selecting high-dimensional points to numerically evaluate the characteristic function (CF) curve of complex high-dimensional problems. An improved number-theoretical method (i-NTM) is used to establish a uniform, efficient point set, ensuring determinism and reducing variability. Subsequently, a partial stratification approach partitions the high-dimensional space into orthogonal two-dimensional subspaces. The fundamental point set is projected into each subspace, and the k-means clustering algorithm identifies centroids within each, acting as representative points. The complete set of representative points from all subspaces formulates the high-dimensional point set. Numerical examples are investigated, which demonstrate the proposed method is effective for high-dimensional structural reliability assessment.

Global joint position regulation of a class of torque-driven robot manipulators within actuators prescribed safe operating torque–speed area

This paper addresses the joint position regulation of a class of n degrees of freedom torque-driven robot manipulators under a novel practical motivated control objective: Simultaneous Regulation & Prescribed Safe Operating Area (SR&PSOA). More specifically, torque–speed characteristic safe limit functions associated to each actuator are taking into account to ensure that besides of global joint positioning, the requested torque control inputs to robot actuators remain inside user prescribed safe operating torque–speed areas, so avoiding thermal and physical actuator damages. A static smooth nonlinear controller is proposed to achieve global position regulation under prescribed speed-depending bound torque input. Numerical simulations and experimental results are included to illustrate the effectiveness of the proposed controller.

Concealing Organic Neuromorphic Devices with Neuronal-Inspired Supported Lipid Bilayers.

Neurohybrid systems have gained large attention for their potential as in vitro and in vivo platform to interrogate and modulate the activity of cells and tissue within nervous system. In this scenario organic neuromorphic devices have been engineered as bioelectronic platforms to resemble characteristic neuronal functions. However, aiming to a functional communication with neuronal cells, material synthesis, and surface engineering can yet be exploited for optimizing bio-recognition processes at the neuromorphic-neuronal hybrid interface. In this work, artificial neuronal-inspired lipid bilayers have been assembled on an electrochemical neuromorphic organic device (ENODe) to resemble post-synaptic structural and functional features of living synapses. Here, synaptic conditioning has been achieved by introducing two neurotransmitter-mediated biochemical signals, to induce an irreversible change in the device conductance thus achieving Pavlovian associative learning. This new class of in vitro devices can be further exploited for assembling hybrid neuronal networks and potentially for in vivo integration within living neuronal tissues.

Estimation and comparison of Weibull-Normal distribution with some other probability models using Bayesian method of estimation

In statistical applications the Normal distribution is adjudged to be the best. Recent studies Terna (2017) using classical method indicated that Weibull-Normal distribution outperformed the Normal distribution. In this study we used the non-classical Bayesian method of estimation to estimate and compare the Weibull-Normal distribution with some other distributions including Normal and Gamma-Normal distributions. This study derived explicit expressions for basic statistical properties such as moments, moment generating function, the characteristic function, reliability analysis and the distribution of order statistics. It looks at estimation of confidence intervals for the parameters of the Weibull-Normal distribution and estimated the parameters of the new distribution using a non-classical approach for the purpose of theoretical comparisons. The two other distributions whose parameters were also estimated by using Bayesian estimation are the normal distribution and gamma distribution as well as the combination Gamma-Normal distribution. Based on the analyses and interpretations of the results obtained it was found that the parameters and other general properties of Normal distribution gives a better fit than other distributions. R-software was used; the models were written as an R code in R program using the rjags library, the distribution parameters were obtained from a Gibbs sampling of a Bayesian Fit for data set I and data set II. The criteria used in R for comparisons were the negative log-likelihood, AIC (Akaike information criterion), CAIC (Consistent Akaike Information Criterion) and BIC (Bayesian information Criterion).

Optimal semiclassical regularity of projection operators and strong Weyl law

Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of quantum mechanics, projection operators can be seen as the analogue of characteristic functions of subsets of the phase space, which are discontinuous functions. We prove that projection operators indeed converge to characteristic functions of the phase space and that in terms of quantum Sobolev spaces, they exhibit the same maximal regularity as characteristic functions. This can be interpreted as a semiclassical asymptotic on the size of commutators in Schatten norms. Our study answers a question raised in Chong et al. [J. Eur. Math. Soc. (unpublished) (2024)] about the possibility of having projection operators as initial data. It also gives a strong convergence result in Sobolev spaces for the Weyl law in phase space.

The distribution of the product of independent variance-gamma random variables

Let X and Y be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product XY is derived. Some basic distributional properties are also derived, including formulas for the cumulative distribution function and the characteristic function, as well as asymptotic approximations for the density, tail probabilities and the quantile function. As special cases, we deduce some key distributional properties for the product of two independent asymmetric Laplace random variables as well as the product of four jointly correlated zero mean normal random variables with a particular block diagonal covariance matrix. As a by-product of our analysis, we deduce some new reduction formulas for the Meijer G-function.

Characters of [formula omitted] and vertex operators

In this paper, we present a vertex operator approach to construct and compute all complex irreducible characters of the general linear group GLn(Fq). Green's theory of GLn(Fq) is recovered and enhanced under the realization of the Grothendieck ring of representations RG=⨁n≥0R(GLn(Fq)) as two isomorphic Fock spaces associated to two infinite-dimensional F-equivariant Heisenberg Lie algebras hˆF‾ˆq and hˆF‾q, where F is the Frobenius automorphism of the algebraically closed field F‾q. Under this picture, the irreducible characters are realized by the Bernstein vertex operators for Schur functions, the characteristic functions of the conjugacy classes are realized by the vertex operators for the Hall-Littlewood functions, and the character table is completely given by matrix coefficients of vertex operators of these two types. One of the features of the current approach is a simpler identification of the Fock space RG as the Hall algebra of symmetric functions via vertex operator calculus, and another is that we are able to compute in general the character table, where Green's degree formula is demonstrated as an example.

Goodness–of–fit tests based on the min–characteristic function

Tests of fit for classes of distributions that include the Weibull, the Pareto and the Fréchet families are proposed. The new tests employ the novel tool of the min–characteristic function and are based on an L2–type weighted distance between this function and its empirical counterpart applied on suitably standardized data. If data–standardization is performed using the MLE of the distributional parameters then the method reduces to testing for the standard member of the family, with parameter values known and set equal to one. Asymptotic properties of the tests are investigated. A Monte Carlo study is presented that includes the new procedure as well as competitors for the purpose of specification testing with three extreme value distributions. The new tests are also applied on a few real–data sets.

A Cost-Effective Skip-Lot Sampling Scheme Using Loss-Based Capability Index for Product Acceptance Determination

Acceptance sampling plans are essential for quality control and assurance, empowering businesses to make well-informed decisions regarding lot disposition. Among these plans, the skip-lot sampling plan (SkSP) stands out as a cost-effective strategy for suppliers with consistently excellent product quality. In this article, we present an enhanced version of the SkSP, termed Cpm-based SkSP-RGSP, which incorporates a repetitive group sampling plan (RGSP) using the Taguchi capability index Cpm as its reference plan. We develop an optimization model to ensure that the proposed plan meets a two-point condition in its operating characteristic function and effectively minimizes the average sample number (ASN). Through investigations of two critical performance measures, ASN and discriminatory power, we demonstrate the superiority of our plan over conventional sampling approaches. Detailed plan parameters, including required sample size and lot sentencing criteria, are provided to assist examiners in practical implementation. Additionally, we showcase the plan's applicability and practicality through a case study. This research contributes to the field of quality control by offering an efficient and cost-effective sampling scheme for lot disposition.