Interval Analysis Research Articles

Importance and Uncertainty of λ-Estimation for Box–Cox Transformations to Compute and Verify Reference Intervals in Laboratory Medicine

Reference intervals play an important role in medicine, for instance, for the interpretation of blood test results. They are defined as the central 95% values of a healthy population and are often stratified by sex and age. In recent years, so-called indirect methods for the computation and validation of reference intervals have gained importance. Indirect methods use all values from a laboratory, including the pathological cases, and try to identify the healthy sub-population in the mixture of values. This is only possible under certain model assumptions, i.e., that the majority of the values represent non-pathological values and that the non-pathological values follow a normal distribution after a suitable transformation, commonly a Box–Cox transformation, rendering the parameter λ of the Box–Cox transformation as a nuisance parameter for the estimation of the reference interval. Although indirect methods put high effort on the estimation of λ, they come to very different estimates for λ, even though the estimated reference intervals are quite coherent. Our theoretical considerations and Monte-Carlo simulations show that overestimating λ can lead to intolerable deviations of the reference interval estimates, whereas λ=0 produces usually acceptable estimates. For λ close to 1, its estimate has limited influence on the estimate for the reference interval, and with reasonable sample sizes, the uncertainty for the λ-estimate remains quite high.

Evaluation of clinical and imaging features for differentiating rhabdomyosarcoma from neuroblastoma in pediatric soft tissue.

In this study, we developed a nomogram predictive model based on clinical, CT, and MRI parameters to differentiate soft tissue rhabdomyosarcoma (RMS) from neuroblastoma (NB) in children preoperatively. A total of 103 children with RMS (n=37) and NB (n=66) were enrolled in the study from December 2012 to July 2023. The clinical and imaging data (assessed by two experienced radiologists) were analyzed using univariate analysis, and significant factors were further analyzed by multivariable logistic regression using the forward LR method to develop the clinical model, radiological model, and integrated nomogram model, respectively. The diagnostic performances, goodness of fit, and clinical utility of the integrated nomogram model were assessed using the area under the curve (AUC) of the receiver operator characteristics curve (ROC) with a 95% confidence interval (95% CI), calibration curve, and decision curve analysis (DCA) curves, respectively. Diagnostic efficacy between the model and radiologists' interpretations was examined. The median age at diagnosis in the RMS group was significantly older than the NB group (36.0 months vs. 14.5 months; P=0.003); the fever rates in RMS patients were significantly lower than in patients with NB (0.0% vs.16.7%; P=0.022), and the incidence of palpable mass was higher in patients with RMS compared with the NB patients (89.2% vs. 34.8%; P<0.001). Compare NB on image features: RMS occurred more frequently in the head and neck and displayed homogeneous density on non-enhanced CT than NB (48.6% vs. 9.1%; 35.3% vs. 13.8%, respectively; all P<0.05), and the occurrence of characteristics such as calcification, encasing vessels, and intraspinal tumor extension was significantly less frequent in RMS children compared to children with NB (18.9% vs. 84.8%; 13.5% vs. 34.8%; 2.7% vs. 50.0%, respectively; all P <0.05). Two, three, and four features were identified as independent parameters by multivariate logistic regression analysis to develop the clinical, radiological, and integrated nomogram models, respectively. The AUC value (0.962), calibration curve, and DCA showed that the integrated nomogram model may provide better diagnostic performance, good agreement, and greater clinical net benefits than the clinical model, radiological model, and radiologists' subjective diagnosis. The clinical and imaging features-based nomogram has potential for helping radiologists distinguish between pediatric soft tissue RMS and NB patients preoperatively, and reduce unnecessary interventions.

Implications of an Altered Gut Microbiome in Rat Experimental Vascularized Composite Transplantation.

Vascularized composite allotransplantation is a reconstructive option after severe injury but is fraught with complications, including transplant rejection due to major histocompatibility complex mismatch in the context of allogeneic transplant, which in turn is due to altered immuno-inflammation secondary to transplant. The immunosuppressant tacrolimus can prevent rejection. Because tacrolimus is metabolized predominantly by the gut, this immunosuppressant alters the gut microbiome in multiple ways, thereby possibly affecting immunoinflammation. We performed either allogeneic or syngeneic transplant with or without tacrolimus in rats. We quantified protein-level inflammatory mediators in the skin, muscle, and plasma and assessed the diversity of the gut microbiome through 16S RNA analysis at several timepoints over 31 days posttransplant. Statistical analysis highlighted a complex interaction between major histocompatibility complex and tacrolimus therapy on the relative diversity of the microbiome. Time-interval principal component analysis indicated numerous significant differences in the tissue characteristics of inflammation and gut microbiome that varied over time and across experimental conditions. Classification and regression tree analysis suggested that both inflammatory mediators in specific tissues and changes in the gut microbiome are useful in characterizing the temporal dynamics of posttransplant inflammation. Dynamic network analysis highlighted unique changes in Methanosphaera that were correlated with Peptococcusin allogeneic transplants with and without tacrolimus versus Prevotella in syngeneic transplant with tacrolimus, suggesting that alterations in Methanosphaera might be a biomarker of vascularized composite allotransplant rejection. Our results suggest a complex interaction among major histocompatibility complex, local and systemic immuno-inflammation, and tacrolimus therapy and highlight the potential for novel insights into vascularized composite allotransplant from computational approaches.

Bioframe: operations on genomic intervals in Pandas dataframes.

Genomic intervals are one of the most prevalent data structures in computational genome biology, and used to represent features ranging from genes, to DNA binding sites, to disease variants. Operations on genomic intervals provide a language for asking questions about relationships between features. While there are excellent interval arithmetic tools for the command line, they are not smoothly integrated into Python, one of the most popular general-purpose computational and visualization environments. Bioframe is a library to enable flexible and performant operations on genomic interval dataframes in Python. Bioframe extends the Python data science stack to use cases for computational genome biology by building directly on top of two of the most commonly-used Python libraries, NumPy and Pandas. The bioframe API enables flexible name and column orders, and decouples operations from data formats to avoid unnecessary conversions, a common scourge for bioinformaticians. Bioframe achieves these goals while maintaining high performance and a rich set of features. Bioframe is open-source under MIT license, cross-platform, and can be installed from the Python Package Index. The source code is maintained by Open2C on GitHub at https://github.com/open2c/bioframe.

Neurological and immunological adverse events after pneumococcal conjugate vaccine in children using national immunization programme registry data.

Despite the general consensus on the safety of pneumococcal conjugate vaccine (PCV), safety concerns unveiled during post-licensure surveillance need to be addressed. We investigated whether there is a transient increased risk following a three-dose series of pneumococcal conjugate vaccine (PCV) administered at 2, 4 and 6 months of age. This was a population-based cohort study using the Korea immunization registry data linked to nationwide administrative claims data. Self-controlled risk interval analysis was conducted for PCV recipients who had an outcome of interest within pre-defined risk and control intervals between 2018 and 2022. The outcomes were anaphylaxis, asthma, encephalopathy, febrile seizure, Kawasaki disease and thrombocytopenia. We used conditional Poisson regression model to estimate the incidence rate ratios (IRRs) and 95% confidence intervals (CIs) comparing the outcomes in the risk and control intervals. Of 1 114 096 PCV recipients, 8661 had outcomes either in the risk or control intervals. Their mean age at Dose 1 was 10.0 weeks, 58.3% were boys, and 85.3% received 13-valent PCV. PCV was not associated with an increased risk of any outcomes except for febrile seizure. There were 408 (56.0%) cases of febrile seizure in the risk interval, corresponding to an IRR of 1.27 (95% CI 1.10-1.47). It is reassuring to note that there was no increased risk of the potential safety concerns following PCV administration. Despite the transient increased risk of febrile seizure, absolute numbers of cases were small. Febrile seizure is generally self-limiting with a good prognosis, and should not discourage parents or caregivers from vaccinating their children.

A study on the epidemiology of brucellosis in bovine population of peri-urban and rural areas of district Multan, southern Punjab, Pakistan

BackgroundBrucellosis is a zoonotic disease caused by a bacterial pathogen belonging to the genus Brucella. It is one of the most frequent bacterial zoonoses globally but unfortunately, it is still considered as a neglected disease in the developing world. Keeping in view, this study was conducted to determine the prevalence and risk determinants of brucellosis in large ruminants of peri-urban and rural areas of district Multan-Pakistan. For this purpose, blood samples (n = 490) were collected from the cattle (n = 245) and buffalo (n = 245) population of the study area and subjected to preliminary screening of brucellosis using local and imported RBPT reagents. All the samples were further analyzed using commercially available multi-specie indirect ELISA kit followed by their confirmation by PCR using genus and species-specific primers. Data obtained from lab analysis and questionnaires were subjected to statistical analysis for Pearson Chi-square, Odds Ratio and Confidence intervals (95%).ResultsThe results showed that the maximum seropositivity was recorded with local RBPT reagent (VRI, Pakistan; 12.45%; 95%CI = 9.72–15.65%) followed by RBPT-IDEXX (12.24%; 95%CI = 9.52–15.45%) and RBPT-ID.vet (11.84%; 95%CI = 9.18–14.95%) however statistical difference was non-significant (P = 0.956). The ELISA results showed an overall seroprevalence rate of 11.22% (95%CI = 8.59–14.33%) with comparatively higher rate in cattle (12.65%; 95%CI = 8.82–17.44%) as compared to buffaloes (9.80%; 95%CI = 6.49–14.15%). The PCR analysis confirmed the presence of genus Brucella in all seropositive samples whereas frequency of B. abortus and B. melitensis in seropositive samples was 80% and 20%, respectively. The co-existence of both species was also observed in 5.45% samples. The statistical analysis showed a significant association of bovine brucellosis with herd size, breed, reproductive disorders, mode of insemination, educational status and farmers’ awareness about brucellosis (P < 0.05). Conversely, locality, age, weight, gender, pregnancy status, parity and puberty status had no associations with brucellosis (P > 0.05).ConclusionIn conclusion, brucellosis is prevalent in large ruminants of district Multan, Pakistan. It is suggested to devise and implement stringent policies for the effective control and prevention of brucellosis in the region. Further, the current situation also warrants the need to strengthen interdisciplinary coordination among veterinarians and physicians in one health perspective to ensure and strengthen the human and animal health care systems in the region.

Uncertainty analysis and updated user guidance for interspecies correlation estimation models and low toxicity compounds.

Interspecies correlation estimation (ICE) models are log-linear relationships of acute sensitivity between two species that estimate the sensitivity of an untested species from the known sensitivity of a surrogate. As ICE model use increases globally, additional user guidance is required to ensure consistent use across chemicals and applications. The present study expands ICE uncertainty analyses and user guidance with a focus on low toxicity compounds whose acute values (i.e., reported as mg/L) can be greater than those used to develop a model. In these cases, surrogate values may be outside the ICE model domain and require additional extrapolations to predict acute toxicity. We use the extensive, standardized acute toxicity database underlying ICE models to broadly summarize inter-test variability of acute toxicity data as a measure by which model prediction accuracy can be evaluated. Using the data and models found on the USEPA Web-ICE (www3.epa.gov/webice), we created a set of "truncated" models from data corresponding to the lower 75th percentile of surrogate toxicity. We predicted toxicity for chemicals in the upper 25th percentile as both μg/L beyond the model domain and converted to mg/L (i.e., "scaled" value) and compared these predictions with those from cross-validation of whole ICE models and to the measured value. For ICE models with slopes in the range 0.66-1.33, prediction accuracy of scaled values did not differ from the accuracy of the models when data were entered as μg/L within or beyond the model domain. An uncertainty analysis of ICE confidence intervals was conducted and an interval range of two orders of magnitude was determined to minimize type I and II errors when accepting or rejecting ICE predictions. We updated the ICE user guidance based on these analyses to advance the state of the science for ICE model application and interpretation. Integr Environ Assess Manag 2024;20:1554-1565. Published 2023. This article is a U.S. Government work and is in the public domain in the USA.

Solving systems of homogeneous linear algebraic equations in pricing problems of an alternative financial model

Subject. This article focuses on the problems of solving systems of homogeneous linear algebraic equations in the pricing problems of an alternative financial model. Objectives. The article aims to develop a non-trivial approach to solving the problem of pricing from the scratch in the construction of a national alternative financial model, which boils down to solving large homogeneous systems of linear algebraic equations, complicated by the fuzzy setting of initial parameters (initial data) within the framework of creating a State model of a socially oriented economy, guaranteed to ensure economic, military and other types of integrated security of the Russian Federation. Methods. For the study, we used tensorial notations involving the use of elements of linear algebra, including operations with matrices and vectors, the apparatus of the fuzzy set theory (interval arithmetic), as well as methods and principles of scientific research and complex logical analysis and modeling of pricing and technological processes. Results. The article shows that an effective non-zero (different from zero, i.e. classical, trivial) solution of systems of homogeneous algebraic equations in pricing problems of an alternative financial model from the scratch is possible if the initial parameters are specified by fuzzy sets, which significantly simplifies the procedure of the computational process and the volume of arithmetic operations. Conclusions. The results obtained can be used in structures involved in the creation and testing of financial and economic models both at the federal and the Russian Federation constituent entity levels, as well as in governmental and non-governmental organizations dealing with the issues of pricing, planning and logistics support for business entities not only in the Russian Federation, but also in other countries experiencing problems in the field of financing.

Fractional Mercer's Hermite–Hadamard type inequalities in the frame of interval analysis and its applications to matrix

Fractional Mercer's Hermite–Hadamard type inequalities in the frame of interval analysis and its applications to matrix

Tridiagonal Interval Matrix: Exploring New Perspectives and Application

Tridiagonal interval matrices are relevant in diverse applications, especially in dealing with parameter estimation, optimization and circuit analysis uncertainties. This research paper aims to improve the computational efficiency of obtaining the inverse of a general tridiagonal interval matrix. This matrix is pivotal in electric circuit analysis. We achieve this by employing interval arithmetic operations in the LU decomposition process, enabling effective handling of circuit parameter uncertainties. This approach generates an inverse interval matrix that addresses uncertainties in circuit analyses.

The impact of consumers’ preferences for domestic food on dietary sustainability

A sustainable dietary transition requires knowledge of the drivers and barriers of dietary choices. We investigate the role of preferences for domestic food, as well as environmental and health concerns, as drivers for the consumption of red and white meat, fish, ready-made plant-based food products and self-identification as some type of meat reducer (flexitarian, vegetarian, or vegan). A survey of 1102 consumers was conducted in Norway with questions about food attitudes, beliefs and preferences regarding health, the environment and domestic food as well as dietary habits and demographics. The results from interval and logistic regression analyses show that stronger preferences for domestic food are associated with higher consumption of red meat and a lower likelihood of eating plant-based food and identifying as a meat reducer. Health concerns are associated with higher consumption of white meat and fish, and environmental concern is associated with lower consumption of white meat and a higher likelihood of eating plant-based food. The results also confirm previous research results that disbelief regarding the negative health and environmental impacts of meat correlate with higher meat consumption and a lower likelihood of eating plant-based food. In addition, we find that people who believe that Norway is a country primarily suited for livestock production have higher consumption of meat and a lower likelihood of eating plant-based food. We conclude that to make certain consumers transition away from meat, it is important to provide domestically produced, plant-based alternatives and to implement policy measures that will generate positive storylines of improved farmer livelihoods.

An analysis of Pompe newborn screening data: a new prevalence at birth, insight and discussion.

Primary: Establish a new figure for prevalence at birth for Pompe disease by collecting and analyzing the largest relevant dataset to date and using that result to project population prevalence at birth in a novel way. Secondary: Compare these results to previous analyses to offer a framework for evaluating 'frequency' data that can be applied to other rare, genetic diseases, along with methods to assess quality of estimates.

Monotonicity and the Precision of Program Analysis

It is widely known that the precision of a program analyzer is closely related to intensional program properties, namely, properties concerning how the program is written. This explains, for instance, the interest in code obfuscation techniques, namely, tools explicitly designed to degrade the results of program analysis by operating syntactic program transformations. Less is known about a possible relation between what the program extensionally computes, namely, its input-output relation, and the precision of a program analyzer. In this paper we explore this potential connection in an effort to isolate program fragments that can be precisely analyzed by abstract interpretation, namely, programs for which there exists a complete abstract interpretation. In the field of static inference of numeric invariants, this happens for programs, or parts of programs, that manifest a monotone (either non-decreasing or non-increasing) behavior. We first formalize the notion of program monotonicity with respect to a given input and a set of numerical variables of interest. A sound proof system is then introduced with judgments specifying whether a program is monotone relatively to a set of variables and a set of inputs. The interest in monotonicity is justified because we prove that the family of monotone programs admits a complete abstract interpretation over a specific class of non-trivial numerical abstractions and inputs. This class includes all non-relational abstract domains that refine interval analysis (i.e., at least as precise as the intervals abstraction) and that satisfy a topological convexity hypothesis.

Another computer-assisted proof of unimodality of solutions for Proudman–Johnson equation

This paper presents a computer-assisted proof of the existence and unimodality of steady-state solutions for the Proudman–Johnson equation which is representative of two-dimensional fluid flow. The proposed approach is based on an infinite-dimensional fixed-point theorem with interval arithmetic, and is another proof by Miyaji and Okamoto (Jpn J Ind Appl Math 36:287–298, 2019). Verification results show the validity of both proofs.

Reconstruction of self-oscillating systems with delay time modulation

The aim of our research is to study the possibility of reconstruction from time series the self-oscillating systems with variable time delay, demonstrating regimes of turbulent and laminar chaos. Methods. The object of study is self-oscillating systems described by delay-differential equations, in which the delay time is modulated by an external periodic signal. The possibility of estimating the parameters of systems with delay time modulation from their time series is considered using the known method for reconstructing systems with constant delay time, which is based on statistical analysis of time intervals between all possible pairs of extrema in time series. A new method for estimating the parameters of systems with variable delay time is proposed, based on statistical analysis of time intervals between two successive extrema in time series. Results. It is shown that in some cases the known methods for reconstructing systems with constant delay time are also effective for reconstructing systems with varying delay time. With their help, one can estimate the mean delay time and recove the nonlinear function of the system. The proposed method, aimed at application to time-delay systems with delay time modulation, allows one to estimate the frequency and amplitude of delay time modulation. Conclusion. The obtained results are of interest to various scientific disciplines that study systems with variable delay times based on their time series.

Predictive biomarker discovery in cancer using a unique AI model based on set theory

The current study applies a new artificial intelligence (AI) method, ALiX, which is based on interval arithmetic, to analyze and interpret biological data for a clinical problem: identification of biomarkers for cancer diagnosis. The key unique and important feature of this study is that ALiX provides an explanation to our clinical hypothesis in the form of a list of ranked protein biomarkers that identifies which biomarkers are the most significant drivers of the predicted outcome, a capability that is not currently available in other AI methods. Based on the significant drivers, this study identifies a machine learning model and solution for stratifying cancer patients into subtypes that will predict response to treatment.

Multi-objective cooperative optimization of communication base station and active distribution grid under dual carbon targets

To achieve “carbon peaking” and “carbon neutralization”, access to large-scale 5G communication base stations brings new challenges to the optimal operation of new power systems, but also provides new opportunities for the low-carbon development of distribution networks. This paper develops a method to consider the multi-objective cooperative optimization operation of 5G communication base stations and Active Distribution Network (ADN) and constructs a description model for the operational flexibility of 5G communication base stations. Based on this, a multi-objective cooperative optimization 5G communication base station operating model and active distribution network considering the system operation economy and minimum carbon emissions as the optimization objectives are established. In the above model, by encouraging 5G communication base stations to engage in Demand Response (DR), the Renewable Energy Sources (RES), and 5G communication base stations in ADN are concurrently scheduled, and the uncertainty of RES and communication load is described by using interval optimization method. Finally, the problem is solved by combining the equivalent transformation based on interval analysis and the non-dominated sorting genetic algorithm. The analysis results of the example show that participation in grid-side dispatching through the flexible response capability of 5G communication base stations can enhance the power system’s renewable energy consumption and usage efficiency, resulting in significant low-carbon benefits.

A Survey On Non – linear Optimization And Global Optimization Methods

bjective functions and constraints are not linear. Non-linear optimization involves finding the best solution in the presence of non-linear relationships among the variables. These problems arise in various fields such as engineering design, economics, machine learning, and operational research. The primary challenge in non-linear optimization is the potential existence of multiple local optima, which can make it difficult to identify the global optimum. Global optimization methods are designed to overcome this challenge by searching for the global optimum, which is the best possible solution among all local optima. These methods can be broadly categorized into deterministic and stochastic approaches. Deterministic methods, such as branch and bound, interval analysis, and cutting-plane methods, systematically explore the search space and provide guarantees of finding the global optimum or bounds on the global optimum. These methods are often rigorous but can be computationally expensive, especially for high-dimensional problems. On the other hand, stochastic methods, such as genetic algorithms, simulated annealing, and particle swarm optimization, use probabilistic rules to explore the search space. These methods are inspired by natural processes and heuristics, offering flexibility and often being more efficient for large-scale problems. While they do not guarantee finding the global optimum, they are widely used due to their ability to escape local optima and explore the search space effectively. Hybrid methods that combine deterministic and stochastic approaches have also gained popularity. These methods leverage the strengths of both approaches, enhancing the robustness and efficiency of the optimization process. For example, a hybrid algorithm might use a stochastic method to explore the search space broadly and then apply a deterministic method to refine the search around promising areas. Recent advancements in computational power and algorithmic development have significantly improved the efficiency and applicability of non-linear and global optimization methods. Techniques such as machine learning-based optimization and parallel computing have enabled the handling of more complex and larger-scale optimization problems. Moreover, these advancements have facilitated the integration of optimization methods into real-time and adaptive systems, further broadening their applications.

A Survey On Non – linear Optimization And Global Optimization Methods

Non-linear optimization and global optimization methods are crucial in solving complex real-world problems where the objective functions and constraints are not linear. Non-linear optimization involves finding the best solution in the presence of non-linear relationships among the variables. These problems arise in various fields such as engineering design, economics, machine learning, and operational research. The primary challenge in non-linear optimization is the potential existence of multiple local optima, which can make it difficult to identify the global optimum. Global optimization methods are designed to overcome this challenge by searching for the global optimum, which is the best possible solution among all local optima. These methods can be broadly categorized into deterministic and stochastic approaches. Deterministic methods, such as branch and bound, interval analysis, and cutting-plane methods, systematically explore the search space and provide guarantees of finding the global optimum or bounds on the global optimum. These methods are often rigorous but can be computationally expensive, especially for high-dimensional problems. On the other hand, stochastic methods, such as genetic algorithms, simulated annealing, and particle swarm optimization, use probabilistic rules to explore the search space. These methods are inspired by natural processes and heuristics, offering flexibility and often being more efficient for large-scale problems. While they do not guarantee finding the global optimum, they are widely used due to their ability to escape local optima and explore the search space effectively. Hybrid methods that combine deterministic and stochastic approaches have also gained popularity. These methods leverage the strengths of both approaches, enhancing the robustness and efficiency of the optimization process. For example, a hybrid algorithm might use a stochastic method to explore the search space broadly and then apply a deterministic method to refine the search around promising areas. Recent advancements in computational power and algorithmic development have significantly improved the efficiency and applicability of non-linear and global optimization methods. Techniques such as machine learning-based optimization and parallel computing have enabled the handling of more complex and larger-scale optimization problems. Moreover, these advancements have facilitated the integration of optimization methods into real-time and adaptive systems, further broadening their applications.

Immrax: A Parallelizable and Differentiable Toolbox for Interval Analysis and Mixed Monotone Reachability in JAX

We present an implementation of interval analysis and mixed monotone interval reachability analysis as function transforms in Python, fully composable with the computational framework JAX. The resulting toolbox inherits several key features from JAX, including computational efficiency through Just-In-Time Compilation, GPU acceleration for quick parallelized computations, and Automatic Differentiability We demonstrate the toolbox’s performance on several case studies, including a reachability problem on a vehicle model controlled by a neural network, and a robust closed-loop optimal control problem for a swinging pendulum.