Discrete Variables Research Articles

Application of a novel metaheuristic algorithm inspired by connected banking system in truss size and layout optimum design problems and optimization problems

Optimum design of truss structures can be a challenging and difficult field of study specially if an optimum design problem is comprised of continuous and discrete decision variables such as in truss size and layout optimization problems. Usually metaheuristic approaches are selected to solve these kind of problems and there are many different metaheuristic methods that have been used in dealing with truss optimization problems, which provide optimum solutions for those problems. However, among these various proposed metaheuristics, it is very seldom to face and find a method that is based on technologies such as computer networks. This paper aims to utilize a metaheuristic algorithm which is based on some principals of connected banking systems, which is called the Connected Banking System Optimizer(CBSO) algorithm. The performance of the CBSO is tested against three benchmark truss size/layout optimum design problems namely 15, 18 and 25 bar truss structures. Besides the truss size/layout problems, CEC-BC-2017 test functions with ten dimensions and also three other constrained optimum design problems are also investigated to examine the performance of the CBSO in dealing with these standard unconstrained and constrained test functions. The results of the CBSO optimum designs are presented and compared with some of the available studies in the literature. Statistical analyses are done to have a fair evaluation of the CBSO algorithm’s efficiency and its ability in dealing with the benchmark truss size/layout optimization problems. The CBSO outperforms its rivals and presents lighter weight truss structures. There is no need for configuration of extra parameters in the CBSO algorithm when solving the examined benchmark truss structures, which makes it a robust parameter-free optimization algorithm.

Probabilistic Answer Set Programming with Discrete and Continuous Random Variables

Abstract Probabilistic Answer Set Programming under the credal semantics extends Answer Set Programming with probabilistic facts that represent uncertain information. The probabilistic facts are discrete with Bernoulli distributions. However, several real-world scenarios require a combination of both discrete and continuous random variables. In this paper, we extend the PASP framework to support continuous random variables and propose Hybrid Probabilistic Answer Set Programming. Moreover, we discuss, implement, and assess the performance of two exact algorithms based on projected answer set enumeration and knowledge compilation and two approximate algorithms based on sampling. Empirical results, also in line with known theoretical results, show that exact inference is feasible only for small instances, but knowledge compilation has a huge positive impact on performance. Sampling allows handling larger instances but sometimes requires an increasing amount of memory.

Estimating average treatment effects with only discrete covariates

AbstractWe propose a kernel smoothing method to estimate average treatment effects (ATE) when covariates are all discrete variables. This approach is based on Ouyang et al. (2009), who developed a Econometric Theory, 2009;25: 1–42 who developed least squares cross‐validation (CV) kernel smoothing method dealing with discrete covariates. This method automatically smoothes the irrelevant variables out of the regression model with a high probability, and avoids the problem of loss of efficiency related to the traditional nonparametric frequency‐based method. We derive the asymptotic distribution of our proposed ATE estimator. Monte Carlo simulations and empirical applications showcase the usefulness of the proposed method.

Likert Scale Variables in Personal Finance Research: The Neutral Category Problem

Personal finance research often utilizes Likert-type items and Likert scales as dependent variables, frequently employing standard probit and ordered probit models. If inappropriately modeled, the “neutral” category of discrete dependent variables can bias estimates of the remaining categories. Through the utilization of hierarchical models, this paper demonstrates a methodology that accounts for the econometric issues of the neutral category. We then analyze the technique through an empirical exercise relevant to personal finance research using data from the National Financial Capability Study. We demonstrate that ignoring the “neutral” category bias can lead to incorrect inferences, hindering the progression of personal finance research. Our findings underscore the importance of refining statistical modeling techniques when dealing with Likert-type data. By accounting for the neutral category, we can enhance the reliability of personal finance research outcomes, fostering improved decision-relevant insights.

Probabilistic aspects of Jacobi theta functions

In this note we deduce well-known modular identities for Jacobi theta functions using the spectral representations associated with the real valued Brownian motion taking values on $[-1,+1]$. We consider two cases: (i) reflection at $-1$ and $+1$, (ii) killing at $-1$ and $+1$. It is seen that these two representations give, in a sense, most compact forms of the modular theta-function identities. We study also discrete Gaussian distributions generated by theta functions, and derive, in particular, addition formulas for discrete Gaussian variables.

Incidence of Shoulder Prosthetic Joint Infection Throughout the COVID-19 Pandemic

Introduction1-2% of patients who undergo anatomic and reverse total shoulder arthroplasty are diagnosed with a prosthetic joint infection which requires revision surgery, prolonged recovery and rehabilitation, and antibiotic treatment. During the COVID-19 pandemic, anecdotal evidence suggested an increased rate of PJI among all patient populations. However, there have been no studies characterizing PJI incidence following shoulder arthroplasty during the COVID-19 pandemic. In the present study, we sought to evaluate the incidence of shoulder PJI during the COVID-19 pandemic. Materials & MethodsPatients undergoing revision shoulder arthroplasty for PJI at an academic medical center between 2017-2021 were identified: patients before COVID-19 (2017-2019) and patients during COVID-19 (2020-2021). Patient demographics, laboratory data, history of COVID-19 infection and vaccination, antibiotic treatment, and final surgical treatment were collected. Patient-reported outcome measures (PROMs) (ASES, SANE, SAS, PROMIS (Physical Function, Pain Intensity, Upper Extremity, Global 10), and VR/SF12) were collected. PJI incidence was calculated from a retrospective chart review which identified patients with PJI as defined by the International Consensus meeting (ICM) on Musculoskeletal Infection in 2018 and who underwent revision surgery and antibiotic treatment. Incidence rate analysis and independent t-tests were conducted to compare mean baseline PROMs. Descriptive analysis of the collected data included means and standard deviations for continuous variables and frequencies and percentages for discrete variables. Statistical significance was set at a p-value < 0.05. Results46 patients were identified with 20 patients undergoing a revision surgery for a PJI during the pre-COVID-19 time interval and 26 during the COVID-19 time interval. 20% underwent single stage revision (4 pre-COVID-19 and 5 during COVID-19), 50% underwent two stage revision (10 pre-COVID-19 and 13 during COVID-19), and 30% underwent a DAIR procedure (6 pre-COVID-19 and 8 during COVID-19). There was a significant increase in shoulder PJI infections between the pre-COVID-19 time interval and during COVID-19, with PJI incidence rates of 1.1% and 2.1%, respectively (p = .028). There was no significant difference in any outcome scores, microbes on aspiration, inflammatory markers, or duration of treatment between the two time intervals. ConclusionWhile this study does not show clear evidence to an underlying mechanism explaining the increased PJI incidence observed during the COVID-19 pandemic, this study does show a significant increase in the rate of shoulder PJI status post shoulder arthroplasty during COVID-19. Further investigation into how the vaccine and COVID-19 infection may affect the body’s immune system may provide insight into this increase.

Degenerate Moments and Expectation of Monomials

The aim of this paper is twofold. Firstly, we obtain expressions of the degenerate moments of a discrete nonnegative integer valued random variable. Secondly, we get an expression for the expectation of any monomial in discrete nonnegative integer-valued random variables.

Discrete Joint Random Variables in Fréchet-Weibull Distribution: A Comprehensive Mathematical Framework with Simulations, Goodness-of-Fit Analysis, and Informed Decision-Making

This paper introduces a novel four-parameter discrete bivariate distribution, termed the bivariate discretized Fréchet–Weibull distribution (BDFWD), with marginals derived from the discretized Fréchet–Weibull distribution. Several statistical and reliability properties are thoroughly examined, including the joint cumulative distribution function, joint probability mass function, joint survival function, bivariate hazard rate function, and bivariate reversed hazard rate function, all presented in straightforward forms. Additionally, properties such as moments and their related concepts, the stress–strength model, total positivity of order 2, positive quadrant dependence, and the median are examined. The BDFWD is capable of modeling asymmetric dispersion data across various forms of hazard rate shapes and kurtosis. Following the introduction of the mathematical and statistical frameworks of the BDFWD, the maximum likelihood estimation approach is employed to estimate the model parameters. A simulation study is also conducted to investigate the behavior of the generated estimators. To demonstrate the capability and flexibility of the BDFWD, three distinct datasets are analyzed from various fields, including football score records, recurrence times to infection for kidney dialysis patients, and student marks from two internal examination statistical papers. The study confirms that the BDFWD outperforms competitive distributions in terms of efficiency across various discrete data applications.

Synergy as the Failure of Distributivity

The concept of emergence, or synergy in its simplest form, is widely used but lacks a rigorous definition. Our work connects information and set theory to uncover the mathematical nature of synergy as the failure of distributivity. For the trivial case of discrete random variables, we explore whether and how it is possible to get more information out of lesser parts. The approach is inspired by the role of set theory as the fundamental description of part–whole relations. If taken unaltered, synergistic behavior is forbidden by the set-theoretic axioms. However, random variables are not a perfect analogy of sets: we formalize the distinction, highlighting a single broken axiom—union/intersection distributivity. Nevertheless, it remains possible to describe information using Venn-type diagrams. The proposed multivariate theory resolves the persistent self-contradiction of partial information decomposition and reinstates it as a primary route toward a rigorous definition of emergence. Our results suggest that non-distributive variants of set theory may be used to describe emergent physical systems.

Enhanced Safety and Efficacy of O-Arm Navigation Over C-Arm Guidance in Percutaneous Kyphoplasty for Patients With Osteoporotic Vertebral Compression Fractures and Spinal Deformity: A Comparative Study.

Although percutaneous kyphoplasty (PKP) under C-arm guidance is an effective treatment for osteoporotic vertebral compression fractures (OVCF), obtaining high-definition images in patients with OVCF and spinal deformities can be challenging or insufficient using traditional C-arm guidance, prompting our institution to adopt the O-arm navigation system-which offers comprehensive 3D imaging and precise navigation-and this study compares its safety and efficacy with conventional C-arm-assisted PKP. This was a retrospective study. From February 2019 to February 2022, we enrolled 28 patients with OVCF (44 vertebrae) with spinal deformity treated with O-arm navigation-assisted PKP and 30 patients with OVCF (42 vertebrae) with spinal deformity treated with C-arm-guided PKP. We recorded puncture times, single-segment operation time, number of cases with bone cement leakage, and length of stay. The visual analog scales (VASs), Oswestry disability indexes (ODIs), recovery of Cobbs angle, and vertebral height were used to assess treatment effect before the operation, on the first day postoperation, the first month postoperation, and at the final follow-up. The chi-squared test was utilized for comparing discrete variables, an independent samples t-test was used for continuous variables, and Pearson's chi-squared test and Fisher's exact test were applied for categorical data. Demographic features were comparable between the groups. The O-arm navigation group showed a significant reduction in puncture adjustment per vertebrae, single-segment operation time, and the rate of trocar needle malposition compared to the C-arm guidance group. The rate of cement leakage was decreased in the O-arm-guided PKP group, and other complications did not differ between the two groups. Intragroup comparisons revealed significant improvements in VAS scores and ODI on the first day, first month, and final follow-up after the operation (p < 0.05). The VAS score was significantly lower in the O-arm navigation-assisted PKP group than in the C-arm-guided PKP group on the first day postoperatively (p = 0.049). However, no significant differences in VAS scores were observed between the groups at the first month postoperatively or at the final follow-up. In each follow-up period, there was no significant difference in ODI, Cobb angle, and the percent of anterior vertebral height (AVH %) between the groups. O-arm navigation-assisted PKP demonstrates better clinical safety and efficacy than C-arm-guided PKP, marking it as a minimally invasive, safe, and effective procedure for treating patients with OVCF with spinal deformity.

Boolean Delay Equations: a dynamical approach to modeling complex systems

Boolean delay equations (BDEs) are equations with discrete variables evolving in continuous time. They serve as exploratory tools in the study of nonlinear and complex systems. In this review paper, we outline their formulation and illustrate their properties by application to a solid-earth problem and a climate one. The first problem is the seismotectonic description and prediction of earthquakes and of their clustering. The second one is that of the coupled atmosphere-ocean phenomenon of the El Niño-Southern Oscillation (ENSO). Both involve irregular behavior that is hard to predict, although some form of cyclicity is present in both, especially in ENSO. The paper concludes with broad perspectives on the further use of BDEs in the geosciences and elsewhere.

Maximal point-polyserial correlation for non-normal random distributions.

We consider the problem of determining the maximum value of the point-polyserial correlation between a random variable with an assigned continuous distribution and an ordinal random variable with categories, which are assigned the first natural values , and arbitrary probabilities . For different parametric distributions, we derive a closed-form formula for the maximal point-polyserial correlation as a function of the and of the distribution's parameters; we devise an algorithm for obtaining its maximum value numerically for any given . These maximum values and the features of the corresponding -point discrete random variables are discussed with respect to the underlying continuous distribution. Furthermore, we prove that if we do not assign the values of the ordinal random variable a priori but instead include them in the optimization problem, this latter approach is equivalent to the optimal quantization problem. In some circumstances, it leads to a significant increase in the maximum value of the point-polyserial correlation. An application to real data exemplifies the main findings. A comparison between the discretization leading to the maximum point-polyserial correlation and those obtained from optimal quantization and moment matching is sketched.

A 3D multiobjective multi-item eco-routing problem for refrigerated fresh products delivery using NSGA-II with hybrid chromosome

In a developing countries, say India, about 40 percent fresh foods are wasted during transportation and $14 billion of post harvest products are lost due to inefficiency of cold supply chain such as using non-refrigerated vehicle during last mile transport. Hence, temperature control through refrigerated transportation is very essential. But, the by-product of this process i.e., carbon emission (CE) due to transportation and refrigeration is detrimental for the world. Only logistic transportation contributes about 25 percent of global CE. Due to the world wide infrastructural development, there are several available routes for the road transportation among different cities. For the maintenance of these routes, there are some toll plazas for collection of money. Some routes also cross the rail lines. For maximum profit, a supplier distributes the products at the earliest as the retailers fix the product’s price with respect to its freshness. Again, this process generates more CE. With these realities, a 3D multiobjective multi-item eco-routing problems for refrigerated fresh products (3DMOMIERPsfRFPs) are developed, where a refrigerated vehicle starts from a depot (refrigerated) and comes back after distributing the fresh products to retailers as per their demands. The optimal routing plan, vehicle’s velocity and preservation rate are determined so that total profit and CE are respectively maximized and minimized simultaneously. For solution, an NSGA-II with different modified operators (NSGA-IIwDOs) is developed with hybrid chromosomes having discrete and continuous variables together, probabilistic selection, problem-specific crossover and generation-dependent mutation. Some performance metrics are presented through NSGA-IIwDOs on the standard TSPLIB problems. Results of 3DMOMIERPsfRFPs without and with specific delivery time slots, road-dependent vehicle velocity and time constraints are evaluated. Pareto front for multiobjective are depicted. As a particular case, results of a previous investigation are obtained. Some of the managerial decisions are observed.

Approach for multi-valued integer programming in multi-material topology optimization: Random discrete steepest descent (RDSD) algorithm

The present study models the multi-material topology optimization problems as the multi-valued integer programming (MVIP) or named as combinatorial optimization. By extending classical convex analysis and convex programming to discrete point-set functions, the discrete convex analysis and discrete steepest descent (DSD) algorithm are introduced. To overcome combinatorial complexity of the DSD algorithm, we employ the sequential approximate integer programming (SAIP) to explicitly and linearly approximate the implicit objective and constraint functions. Considering the multiple potential changed directions for multi-valued design variables, the random discrete steepest descent (RDSD) algorithm is proposed, where a random strategy is implemented to select a definitive direction of change. To analytically calculate multi-material discrete variable sensitivities, topological derivatives with material contrast is applied. In all, the MVIP is finally transferred as the linear 0–1 programming that can be efficiently solved by the canonical relaxation algorithm (CRA). Explicit nonlinear examples demonstrate that the RDSD algorithm owns nearly three orders of magnitude improvement compared with the commercial software (GUROBI). The proposed approach, without using any continuous variable relaxation and interpolation penalization schemes, successfully solves the minimum compliance problem, strength-related problem, and frequency-related optimization problems. Given the algorithm efficiency, mathematical generality and merits over other algorithms, the proposed RDSD algorithm is meaningful for other structural and topology optimization problems involving multi-valued discrete design variables.

Plan of Care Visits: Implementation During Hospitalization and Association With 30-Day Readmissions in a Large, Integrated Health Care System.

Plan of Care of Visits (POCV), including the patient, nurse, and hospital provider were implemented across an integrated health system to improve provider-patient communication during hospitalization and patient outcomes. To assess POCV adoption after implementation, patient characteristics assosites were classified as teachsites were classified as teachsites were classified as teachsites were classified as ciated with POCV completion, and association of POCV with 30-day readmissions. This retrospective cohort study utilized electronic medical record (EMR) data of 237,430 adult patients discharged to home from 11 hospitals from January 2020 to December 2022. POCV completion was a discrete EMR variable. POCV adoption was estimated monthly by hospital as proportion of patients with at least 1 POCV during hospitalization, with variation among hospitals measured using the Variance Partition Coefficient (VPC). Multivariable logistic regressions assessed factors associated with POCV completion and POCV association with 30-day readmission. POCV adoption increased from 69% to 94% (2020-2022) and varied by 50% across hospitals (VPC 0.50, 95% CI: 0.29-0.70). Odds of a discharge-day POCV were lower among older patients (≥65 vs. 18-34y, OR 0.81, CI: 0.79-0.83), and higher among female (OR 1.06; CI: 1.04-1.07), Asian (vs. White, OR 1.13; CI: 1.06-1.21), Hispanic (OR 1.09; CI: 1.05-1.13), and surgical patients (vs. medical, OR 1.33; CI: 1.30-1.35). Patients completing discharge-day POCV had lower 30-day readmission odds (2022 OR 0.76, CI: 0.73-0.79). Patients with POCV on ≥75% of hospital days had similar readmission odds trends. POCV implementation was successful, and POCV completion was associated with fewer 30-day readmissions. Future work should focus on increasing POCV adoption while reducing hospital variation.

The Calibrated Safety Constraints Optimal Power Flow for the Operation of Wind-Integrated Power Systems

As the penetration of renewable energy sources (RESs), particularly wind power, continues to rise, the uncertainty in power systems increases. This challenges traditional optimal power flow (OPF) methods. This paper proposes a Calibrated Safety Constraints Optimal Power Flow (CSCOPF) model that uses the Improved Acceleration Coefficient-Based Bee Swarm algorithm (IACBS) in combination with the equivalent current injection (ECI) model. The proposed method addresses key challenges in wind-integrated power systems by ensuring preventive safety scheduling and enabling effective power incident safety analysis (PISA). This improves system reliability and stability. This method incorporates mixed-integer programming, with continuous and discrete variables representing power outputs and control mechanisms. Detailed numerical simulations were conducted on the IEEE 30-bus test system, and the feasibility of the proposed method was further validated on the IEEE 118-bus test system. The results show that the IACBS algorithm outperforms the existing methods in both computational efficiency and robustness. It achieves lower generation costs and faster convergence times. Additionally, the CSCOPF model effectively prevents power grid disruptions during critical incidents, ensuring that wind farms remain operational within predefined safety limits, even in fault scenarios. These findings suggest that the CSCOPF model provides a reliable solution for optimizing power flow in renewable energy-integrated systems, significantly contributing to grid stability and operational safety.

Optimization of vehicle conceptual design problems using an enhanced hunger games search algorithm

Abstract Electric vehicles have become a standard means of transportation in the last 10 years. This paper aims to formalize design optimization problems for electric vehicle components. It presents a tool conceptual design technique with a hunger games search optimizer that incorporates dynamic adversary-based learning and diversity leader (referred to as HGS-DOL-DIL) to overcome the local optimum trap and low convergence rate limitations of the Hunger Games search algorithm to improve the convergence rate. The performance of the proposed algorithms is studied on six widely used engineering design problems, complex constraints, and discrete variables. For the HGS-DOL-DIL practical feasibility analysis, a case study of shape optimization of an electric car suspension arm from the industry is carried out. Overall, the inclusion of the OL strategy has proven its superiority in solving real-world problems, especially in solving real-world problems such as shape optimization of an electric vehicle automobile suspension arm, showing that the algorithm improves the search space improves the solution quality, and reflects its potential to find global optimum solutions in a well-balanced exploration and exploitation phase.

Vine Copula-Based Classifiers with Applications

AbstractThe vine pair-copula construction can be used to fit flexible non-Gaussian multivariate distributions to a mix of continuous and discrete variables. With multiple classes, fitting univariate distributions and a vine to each class lead to posterior probabilities over classes that can be used for discriminant analysis. This is more flexible than methods with the Gaussian and/or independence assumptions, such as quadratic discriminant analysis and naive Bayes. Some variable selection methods are studied to accompany the vine copula-based classifier because unimportant variables can make discrimination worse. Simple numerical performance metrics cannot give a full picture of how well a classifier is doing. We introduce categorical prediction intervals and other summary measures to assess the difficulty of discriminating classes. Through extensive experiments on real data, we demonstrate the superior performance of our approaches compared to traditional discriminant analysis methods and random forests when features have different dependent structures for different classes.

Mixed‐Integer Optimal Control via Reinforcement Learning: A Case Study on Hybrid Electric Vehicle Energy Management

ABSTRACTMany optimal control problems require the simultaneous output of discrete and continuous control variables. These problems are typically formulated as mixed‐integer optimal control (MIOC) problems, which are challenging to solve due to the complexity of the solution space. Numerical methods such as branch‐and‐bound are computationally expensive and undesirable for real‐time control. This article proposes a novel hybrid‐action reinforcement learning (HARL) algorithm, twin delayed deep deterministic actor‐Q (TD3AQ), for MIOC problems. TD3AQ leverages actor‐critic and Q‐learning methods to manage discrete and continuous action spaces simultaneously. The proposed algorithm is evaluated on a plug‐in hybrid electric vehicle (PHEV) energy management problem, where real‐time control of the discrete variables, clutch engagement/disengagement and gear shift, and continuous variable, engine torque, is essential to maximize fuel economy while satisfying driving constraints. Simulation results show that TD3AQ achieves near‐optimal control, with only a 4.69% difference from dynamic programming (DP), and outperforms baseline reinforcement learning algorithms for hybrid action spaces. The sub‐millisecond execution time indicates potential applicability in other time‐critical scenarios, such as autonomous driving or robotic control.

Roboticized AI-assisted microfluidic photocatalytic synthesis and screening up to 10,000 reactions per day

The current throughput of conventional organic chemical synthesis is usually a few experiments for each operator per day. We develop a robotic system for ultra-high-throughput chemical synthesis, online characterization, and large-scale condition screening of photocatalytic reactions, based on the liquid-core waveguide, microfluidic liquid-handling, and artificial intelligence techniques. The system is capable of performing automated reactant mixture preparation, changing, introduction, ultra-fast photocatalytic reactions in seconds, online spectroscopic detection of the reaction product, and screening of different reaction conditions. We apply the system in large-scale screening of 12,000 reaction conditions of a photocatalytic [2 + 2] cycloaddition reaction including multiple continuous and discrete variables, reaching an ultra-high throughput up to 10,000 reaction conditions per day. Based on the data, AI-assisted cross-substrate/photocatalyst prediction is conducted.