Discrete Variables Research Articles

Indigenous health in specialized care: perspective of healthcare professionals in a reference hospital in Mato Grosso do Sul State, Brazil

This cross-sectional study aims to identify the perspective of healthcare professionals and residents regarding the challenges faced in providing care to Indigenous users in a reference hospital in Mato Grosso do Sul, a Brazilian state with the second-largest Indigenous population in the country. The study used a semi-structured online questionnaire emailed to each worker between June and August 2020. The discrete variables were summarized as mean and standard deviation and median and interquartile range (5% significance level). Two hundred thirty healthcare professionals and 29 residents participated in the study. Among the findings, only 14.7% of participants knew the ethnicities served, and 60.2% had never witnessed traditional practices in the hospital, indicating low articulation between biomedical and Indigenous forms of care. When comparing responses from residents and professionals, residents were noted to have a more positive view of approaching the Indigenous context, suggesting that they consider it essential to improve this articulation. When comparing professional categories, some differences of opinion among the medical category stand out concerning assistance. In addition, professionals and residents demonstrated some level of difficulty in caring for the Indigenous population. The results highlight the centrality of the biomedical model, the professionals' lack of knowledge about the context of the communities served, and the devaluation of their practices. The findings contribute to discussions about healthcare policies at different levels of care and management and the qualification of hospital care for Indigenous people.

Analysis of control characteristics of intelligent digital pump combined with discrete variables

Analysis of control characteristics of intelligent digital pump combined with discrete variables

Comparison of Postoperative Analgesic Effect of Dexmedetomidine and Morphine as an Adjuvant to Intrathecal Bupivacaine in Infraumbilical Surgeries: A Randomised Clinical Trial

Introduction: Regional anaesthesia is the standard technique for lower limb infraumbilical procedures. To provide a better analgesic profile, adjuvants are added to local anaesthetics to enhance their action. Opioids have been used as an adjuvant for a long-time. With evolving pharmacology, various drugs satisfy the criteria of being an adjuvant. One such drug is Dexmedetomidine, a novel alpha-2 agonist. Aim: To compare the duration of analgesia of intrathecal Morphine and Dexmedetomidine as an adjuvant to bupivacaine in a subarachnoid block for lower limb infraumbilical surgeries. Materials and Methods: In this randomised clinical, doubleblinded study conducted in a multispecialty hospital over the period of June 2020 to February 2021, 70 patients were randomly divided into two groups: Group M received Morphine 125 µg, and Group D received dexmedetomidine 5 µg as an adjuvant to 15 mg of 0.5% hyperbaric bupivacaine. The primary outcome was to compare the duration of postoperative analgesia. The secondary results assessed the block characteristics, haemodynamic parameters, rescue analgesic consumption, sedation score, and side-effects like bradycardia, hypotension, nausea, vomiting, pruritus, and respiratory depression. Data was spread in an Excel sheet and descriptive analysis done. Normally distributed continuous variables were compared using a Student’s t-test, and discrete variables were compared using a Chi-square test. A p-value of <0.05 was considered significant. Results: Both groups were similar with respect to age, sex, body mass index, American Society of Anaesthesiologists grading, and duration of surgery. The duration of analgesia was 956.97±120.043 minutes in group M and 392.83±50.354 minutes in group D (p-value <0.001). The total consumption of paracetamol was 1984.71±499.111 mg in group M and 3543.86±406.17 mg in group D. The onset and regression were significantly faster in group D. There was significant hypotension and bradycardia up to the 40th minute and an increase in heart rate, respiratory rate, and mean arterial pressure between 5-7 hours in group D. The sedation score was more in group D for the initial two hours. Postoperatively, the incidence of nausea, vomiting, and pruritus was more in group M. Conclusion: It can be concluded that 125 µg of intrathecal morphine is a better adjuvant to spinal bupivacaine, providing excellent postoperative analgesia compared to 5 µg of intrathecal dexmedetomidine. However, dexmedetomidine had more incidence of hypotension, bradycardia, and sedation when compared to morphine intrathecally.

Effect of Unexpected Prolonged Fasting on Patients Undergoing Elective Surgery under Spinal Anaesthesia: An Observational Study

Introduction: Preoperative fasting is a standard practice aimed at minimising the risk of pulmonary aspiration during surgery. However, patients often experience prolonged fasting periods beyond the recommended duration due to unanticipated delays in the operating theatre, communication failures between teams, inadequate preoperative planning and other factors. Aim: To investigate the effects of unexpectedly prolonged fasting on intraoperative and postoperative parameters in patients undergoing elective surgery under spinal anaesthesia. Materials and Methods: This prospective observational study was conducted from October 2023 to June 2024 at the Department of Anaesthesiology, Dr. D.Y. Patil Medical College, Hospital and Research Centre, Pimpri, Pune, Maharashtra, India. The study included 70 patients undergoing elective surgery under spinal anaesthesia. Patients were divided into two groups: Group A (AM group, n=35), scheduled for surgery between 8:00 AM and 12:00 PM and Group B (PM group, n=35), scheduled for surgery after 12:00 PM or with delayed surgeries. Intraoperative parameters, including Mean Arterial Pressure (MAP), Heart Rate (HR), oxygen saturation (SpO2 ) and random blood glucose levels, were recorded at specific time points. Postoperative outcomes, such as nausea, vomiting and random blood glucose levels, were also assessed. Continuous and discrete variables were summarised as mean±SD and median, while categorical variables were presented as frequencies and percentages. Associations between categorical variables were tested using Pearson’s Chi-square or Fisher’s-exact test, with p-values<0.05 considered statistically significant. Results: The PM group exhibited higher preoperative random blood glucose levels (102.3±18.7 mg/dL) compared to the AM group (89.2±12.5 mg/dL). Postoperative nausea and vomiting were observed in 5 (14.3%) patients in the AM group and 11 (31.4%) patients in the PM group. Both groups showed a gradual decrease in MAP and HR from the preoperative period to 30 minutes after spinal anaesthesia administration, with slightly higher values noted in the PM group. No significant differences in SpO2 were observed between the groups. Conclusion: Unexpected prolonged fasting before elective surgery under spinal anaesthesia may contribute to higher preoperative blood glucose levels and an increased risk of postoperative nausea and vomiting. These findings underscore the importance of adhering to preoperative fasting guidelines and exploring potential strategies to minimise prolonged fasting periods, such as carbohydrate loading or allowing clear fluids closer to surgery

Quantifying the effects of expectation variability on economic dynamics

The article applies the famous Dornbusch "overshooting" model to investigate the impact of different types of expectations on economic model stability. We tested the well-known Dornbusch model with discrete variables. Initially, we established a foundational model, employing simulations to illustrate the impact of each parameter within the model on the overall solution, starting from an initial value. Subsequently, we explored the influence of different expectation types on the stability of the steady state vector, considering simple, static, adaptive, and rational expectations (Muth-type rational expectation and perfect foresight). It was observed that static expectations and perfect foresight did not contribute to stability. In the case of simple, adaptive, and rational expectations, the stability conditions (parameter combinations) are the same as the stability conditions for the steady state vector of the baseline model. This condition is restricted to four parameters: two related to the interest rate, one to the foreign-domestic price level and one to the adjustment speed. We also run a simulation to show how the inclusion of each type of expectation leads to a change in the global solution of the model for a given initial value.

Multi-objective optimization of geosynthetic reinforced soil structures

Optimization models for reinforced earth structures such as foundation pads, bridge abutments, and embankments based on the Eurocode standard are presented. The developed optimization models, which take into account construction costs and environmental footprint, are used to determine an optimal design for each earth structure. The optimization model uses discrete variables, making the results more suitable for actual construction practice and fully exploiting the geotechnical and structural capacity of earth structures with geosynthetic reinforcement. The multi-objective optimization was performed to find a set of solutions that represent the best trade-off between construction cost and environmental footprint. The results show that the correct selection of geosynthetics leads to a significant reduction in costs and environmental impact. The general observation that emerges from the multi-objective optimization is that when designing the earth structures using geosynthetic reinforcements, due to the discrete set of variables, there are not so many optimal solutions that the designer can choose from. The entire optimization process is illustrated with the help of a numerical example. This study can help engineers to select earth structure and geosynthetic reinforcements that are economical and sustainable.

Foot orientation and trajectory variability in locomotion: Effects of real-world terrain.

Capturing human locomotion in nearly any environment or context is becoming increasingly feasible with wearable sensors, giving access to commonly encountered walking conditions. While important in expanding our understanding of locomotor biomechanics, these more variable environments present challenges to identify changes in data due to person-level factors among the varying environment-level factors. Our study examined foot-specific biomechanics while walking on terrain commonly encountered with the goal of understanding the extent to which these variables change due to terrain. We recruited healthy adults to walk at self-selected speeds on stairs, flat ground, and both shallow and steep sloped terrain. A pair of inertial measurement units were embedded in both shoes to capture foot biomechanics while walking. Foot orientation was calculated using a strapdown procedure and foot trajectory was determined by double integrating the linear acceleration. Stance time, swing time, cadence, sagittal and frontal orientations, stride length and width were extracted as discrete variables. These data were compared within-participant and across terrain conditions. The physical constraints of the stairs resulted in shorter stride lengths, less time spent in swing, toe-first foot contact, and higher variability during stair ascent specifically (p<0.05). Stride lengths increased when ascending compared to descending slopes, and the sagittal foot angle at initial contact was greatest in the steep slope descent condition (p<0.05). No differences were found between conditions for horizontal foot angle in midstance (p≥0.067). Our results show that walking on slopes creates differential changes in foot biomechanics depending on whether one is descending or ascending, and stairs require different biomechanics and gait timing than slopes or flat ground. This may be an important factor to consider when making comparisons of real-world walking bouts, as greater proportions of one terrain feature in a data set could create bias in the outcomes. Classifying terrain in unsupervised walking datasets would be helpful to avoid comparing metrics from different walking terrain scenarios.

Association between bullying at school and tooth loss among 15-19-year-olds from southern Brazil.

This study aimed to investigate the association between bullying at school and tooth loss in southern Brazilian adolescents. This population-based cross-sectional study included a representative sample of 15-19-year-old students attending high schools in Santa Maria, southern Brazil. Data on sociodemographic and behavioral variables were collected through questionnaires. Contextual data on bullying at school was provided by educational institutions (bullying episodes in the previous year: 'no,' 'sometimes,' or 'often'). Tooth loss was clinically assessed by the M component of the DMFT index, modeled as a discrete variable. Multilevel Poisson regression was used, and rate ratios (RR) and 95% confidence intervals (CI) were estimated. The prevalence of tooth loss was 9.2% (95%CI = 7.5-10.8). Adolescents who attended the schools where bullying events often occurred had 0.39 (95%CI = 0.33-0.45) missing teeth, on average, in contrast to an average of 0.14 (95%CI = 0.08-0.19) among those whose schools did not experience bullying in the previous year. After adjusting for important cofactors, the contextual variable of bullying at school remained significantly associated with the study outcome. Adolescents who attended schools where bullying frequently occurred were 2.49-fold more likely to have an additional missing tooth than those whose school did not experience bullying in the previous year (RR = 2.49, 95%CI = 1.37-4.51, p = 0.003). In conclusion, the frequent bullying episodes at school were associated with more permanent teeth lost due to caries in this population. Hence, improving the school environment may improve the oral health of adolescents.

Modelling of Poor Household in East Kalimantan Using Zero Inflated Ordered Probit (ZIOP) Approach

Discrete ordinal response variables often exhibit an “excess” of zeros, which can be attributed to two different data conditions. Conventional ordinal probit models are limited in their ability to explain these excess zeros. The Zero Inflated Ordered Probit (ZIOP) model, which combines binary probit and ordinal probit regression, can be used to address this limitation. This study reviews the empirical analysis of the factors that contribute to poor household levels in East Kalimantan. The goodness-of-fit of the ZIOP and ordinal probit models was assessed using the Vuong test.

Optimization of Lift-Plus-Cruise Vertical Take-Off and Landing Aircraft with Electrified Propulsion

Conventional aircraft sizing methods face challenges in analyzing all-electric or hybrid-electric novel aircraft configurations, such as those for urban air mobility applications. The vast design space containing both continuous and discrete design variables and competing design objectives necessitates searching for not necessarily a unique optimal design but rather an array of Pareto-optimal designs. This paper uses the Parametric Energy-Based Aircraft Configuration Evaluator, an aircraft sizing framework for novel aircraft and propulsion system architectures, to pursue multi-objective optimization of a lift-plus-cruise urban air mobility aircraft with all-electric, hybrid-electric, and turbo-electric propulsion system architectures using Nondominated Sorting Genetic Algorithm II. The optimization cases considered include multiple objective functions, such as maximum takeoff mass, mission time, energy and propulsion mass fraction, and energy used per unit distance per unit payload. Optimization was performed for trip distances of 80, 120, and 150 km and battery specific energy levels of 350 and 400 Wh/kg. Except when mission time was an objective function, Pareto-optimal designs occurred near the lower bound of the velocity range. Raising that bound had an impact on the architectural composition of the final generation. All-electric architectures appeared exclusively for lower trip distances, hybrid-electric designs appeared for longer trip distances, and turbo-electric designs only appeared for combinations of longer trip distances, a higher minimum cruise speed, and a lower battery specific energy level. The sizing results were sensitive to assumptions regarding the overload capacity of lift propulsor motors in postfailure conditions.

Klasterizacija zasnovana na arhetipskoj analizi

Archetypal analysis is a dimensionality reduction technique, which is based on finding a small number of representative elements, called archetypes. The observations are then approximated by convex combinations of the archetypes. The coefficients of the convex combinations can be therefore interpreted as probabilities of discrete random variables. The values of the variables identify the classes, represented by the archetypes, to which the observation belongs. Based on this interpretation, we propose to use the Hellinger distance between probability distributions to measure the distance between the observations in the dataset and to use it as an input to clustering. We apply this procedure to monthly data of zero-coupon yield curves in 2003-2022. We identify the archetypal yield curves and cluster the observed curves into six clusters. Since the observations are measured in time, the resulting clustering also gives a segmentation of the time period under consideration.

Analysis on Probability Mass Function and Probability Density Function

Probability Mass Function (PMF) and Probability Density Function (PDF) are fundamental concepts in probability theory and statistics that play a crucial role in describing the probability distribution of random variables. This abstract provides a comprehensive overview of these concepts, highlighting their definitions, characteristics, and applications. The Probability Mass Function is a concept primarily associated with discrete random variables. It defines the probability of a specific outcome occurring. The PMF assigns probabilities to individual values in the sample space, providing a clear picture of the likelihood of each possible outcome. Commonly denoted as P(X=x), where X is the random variable and x is a specific value, the PMF must satisfy two essential properties: non-negativity and the sum of probabilities over all possible outcomes equals one. On the other hand, the Probability Density Function is a concept applied to continuous random variables. Unlike the PMF, which deals with specific values, the PDF deals with ranges of values. The PDF represents the probability that a continuous random variable falls within a given interval. Denoted as f(x), it is essential to note that the probability of any specific point is zero, and instead, probabilities are defined for intervals. The area under the PDF curve over a given interval corresponds to the probability of the random variable falling within that interval. Understanding the differences and similarities between PMF and PDF is crucial for statistical analysis. While PMF is discrete and deals with specific values, PDF is continuous and provides probabilities for intervals. Both functions are integral to the calculation of various statistical measures, including expected values, variance, and standard deviation. This abstract concludes with a discussion of practical applications in diverse fields, such as finance, engineering, and natural sciences, where a deep understanding of PMF and PDF is essential for making informed decisions and drawing meaningful conclusions from data. The integration of these concepts into statistical models and analyses enhances the accuracy and reliability of predictions, making PMF and PDF indispensable tools in the field of probability and statistics

Bias‐Aware Inference in Fuzzy Regression Discontinuity Designs

We propose new confidence sets (CSs) for the regression discontinuity parameter in fuzzy designs. Our CSs are based on local linear regression, and are bias‐aware, in the sense that they take possible bias explicitly into account. Their construction shares similarities with that of Anderson–Rubin CSs in exactly identified instrumental variable models, and thereby avoids issues with “delta method” approximations that underlie most commonly used existing inference methods for fuzzy regression discontinuity analysis. Our CSs are asymptotically equivalent to existing procedures in canonical settings with strong identification and a continuous running variable. However, they are also valid under a wide range of other empirically relevant conditions, such as setups with discrete running variables, donut designs, and weak identification.

Impact of unit prices on the optimal costs of reinforced concrete beams: A comparative study

Numerous studies have been conducted on optimizing reinforced concrete (RC) structures. However, the existing literature focused on reducing the overall costs of the structural members based on materials' local prices, neglecting that these prices could vary from region to region. Thus, this article investigates the impact of materials' unit prices on the optimal costs of RC beams, considering the prices of three countries: Egypt, the UK, and Brazil. The evolutionary algorithm provided by MS Excel Solver was employed to obtain the optimum designs based on three target functions: total cost, steel weight, and concrete weight. Unlike earlier studies, we provided a sufficient number of discrete design variables that significantly influence the total cost and weights of concrete and steel; these variables include the concrete class, cross-sectional dimensions, and details of reinforcing bars at all the critical sections of the beams. Two benchmark examples were presented to illustrate the robustness of the proposed optimization model in dealing with different span lengths and continuity conditions. The results showed that the optimal designs could significantly vary based on the materials’ unit prices. In Egypt, minimizing the steel weight could save up to 50% of the total cost, compared to reducing the beam concrete dimensions. The optimal steel-to-concrete and span-to-depth ratios were as low as 0.7% and 9, respectively. On the other hand, in the UK and Brazil, cost-effective designs could be achieved by minimizing the concrete dimensions, with higher reinforcement ratio (up to 1.3%) and span-to-depth ratio (up to 11.5). The study outcomes could assist designers in the building sector estimate economical concrete quantities based on the materials’ unit prices during the conceptual stage, enabling more informed decisions.

Localized Phase for the Erdős–Rényi Graph

We analyse the eigenvectors of the adjacency matrix of the Erdős–Rényi graph G(N,d/N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {G}}(N,d/N)$$\\end{document} for logN≪d≲logN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{\\log N} \\ll d \\lesssim \\log N$$\\end{document}. We show the existence of a localized phase, where each eigenvector is exponentially localized around a single vertex of the graph. This complements the completely delocalized phase previously established in Alt et al. (Commun Math Phys 388(1):507–579, 2021). For large enough d, we establish a mobility edge by showing that the localized phase extends up to the boundary of the delocalized phase. We derive explicit asymptotics for the localization length up to the mobility edge and characterize its divergence near the phase boundary. The proof is based on a rigorous verification of Mott’s criterion for localization, comparing the tunnelling amplitude between localization centres with the eigenvalue spacing. The first main ingredient is a new family of global approximate eigenvectors, for which sharp enough estimates on the tunnelling amplitude can be established. The second main ingredient is a lower bound on the spacing of approximate eigenvalues. It follows from an anticoncentration result for these discrete random variables, obtained by a recursive application of a self-improving anticoncentration estimate due to Kesten.

A Versatile Surrogate Model of the Power Distribution Grid Described by a Large Number of Parameters

This paper aims to present a general-purpose Surrogate Model for the probabilistic analysis of power distribution grids with a large number of input parameters. The distinctive feature of the novel technique is the employment of the partial derivatives of output variables versus input parameters to tame the “curse of dimensionality” problem exhibited by prior surrogate model calculation techniques. The second important feature of the proposed Surrogate Model method is that it does not require any a priori assumption about the nature or statistical distribution of the input parameters. In fact, it can be applied whenever design parameters are deterministic variables as well as when they are uncertain and represented by continuous and/or discrete random variables. Relevant applications presented in the paper refer to the probabilistic analysis of the distribution grid in the presence of a large number of photovoltaic sources and electric vehicle charging stations.

Particle filtering on hybrid dynamical systems for sensor fault detection

Sensor faults may be modelled as discrete random variables jointly distributed with process states and measurements, resulting in a hybrid (continuous and discrete) dynamical system. State estimation of such systems is challenging due to the combinatorial explosions following propagation of the discrete states. For this reason, a new algorithm is proposed which leverages the structure of the particle filter to incorporate discrete states representing sensor health. The discrete states characterize either normal or faulty conditions, with unique faults (e.g., stuck, out-of-range, etc.) as individual states. These become additional states to estimate which are subsequently used for fault detection and diagnosis. The method is evaluated using a simulated continuous stirred tank reactor benchmark and diagnoses sensor faults with an average sensitivity > 90% for two fault types and > 70% for three fault types.

On the efficacy of conditioned and progressive Latin hypercube sampling in supervised machine learning

In this paper, Latin Hypercube Sampling (LHS) method is compared as per its effectiveness in supervised machine learning procedures. Employing LHS saves computer's processing time and in conjunction with Latin hypercube design properties and space filling ability, is considered as one of the most advanced mechanisms in terms of sampling. Although more data usually deliver better results, when using LHS techniques, same quality outputs can be produced with less data and, as a result, storage cost and training time are reduced. Conditioned Latin Hypercube Sampling (cLHS) is one of those techniques, successfully performing in supervised machine learning tasks. Unfortunately, the minimum sufficient training dataset size cannot be known in advance. In this case, progressive sampling is recommended since it begins with a small sample and progressively increases its size until model accuracy no longer improves. Combining Latin hypercube sampling and the idea of sequentially incrementing sampling, we test Progressive Latin Hypercube Sampling (PLHS) while monitoring the performance of the sampling-based training as the sample size grows. PLHS and cLHS algorithms are applied in datasets with discrete variables securing that each sample is provided with the Latin hypercube design properties and preserves the principal ability of LHS for space filling, as illustrated in respective sample projecting diagrams. The performance of the above LHS methods in supervised machine learning is evaluated by the degree of training of the model, which is certified through the accuracy of the produced confusion matrices in test files. The results from the use of the above Latin Hypercube Sampling techniques compared against benchmark sampling method empirically prove that machine learning training process becomes less costfull, while remaining reliable.

BOLT-SSI: A Statistical Approach to Screening Interaction Effects for Ultra-High Dimensional Data

Detecting interaction effects among predictors on the response variable is a crucial step in various applications. In this paper, we first propose a simple method for sure screening interactions (SSI). Although its computation complexity is $O(p^2n)$, SSI works well for problems of moderate dimensionality (e.g., $p=10^3\sim10^4$), without the heredity assumption. To ultra-high dimensional problems (e.g., $p = 10^6$), motivated by discretization associated Boolean representation and operations and the contingency table for discrete variables, we propose a fast algorithm, named BOLT-SSI. The statistical theory has been established for SSI and BOLT-SSI, guaranteeing their sure screening property. The performance of SSI and BOLT-SSI are evaluated by comprehensive simulation and real case studies. Numerical results demonstrate that SSI and BOLT-SSI can often outperform their competitors in terms of computational efficiency and statistical accuracy. The proposed method can be applied for fully detecting interactions with more than 300,000 predictors. Based on this study, we believe that there is a great need to rethink the relationship between statistical accuracy and computational efficiency. We have shown that the computational performance of a statistical method can often be greatly improved by exploring the advantages of computational architecture with a tolerable loss of statistical accuracy.

Efficient computation of counterfactual bounds

We assume to be given structural equations over discrete variables inducing a directed acyclic graph, namely, a structural causal model, together with data about its internal nodes. The question we want to answer is how can we compute bounds for partially identifiable counterfactual queries from such an input. We start by giving a map from structural casual models to credal networks. This allows us to compute exact counterfactual bounds via algorithms for credal nets on a subclass of structural causal models. Exact computation is going to be inefficient in general given that, as we show, causal inference is NP-hard even on polytrees. We target then approximate bounds via a causal EM scheme. We evaluate their accuracy by providing credible intervals on the quality of the approximation; we show through a synthetic benchmark that the EM scheme delivers accurate results in a fair number of runs. In the course of the discussion, we also point out what seems to be a neglected limitation to the trending idea that counterfactual bounds can be computed without knowledge of the structural equations. We also present a real case study on palliative care to show how our algorithms can readily be used for practical purposes.