Set Of Intervals Research Articles

Anoxia Tolerance in Four Forensically Important Calliphorid Species

Forensically important blow flies, Diptera: Calliphoridae, are among the first organisms to colonize carrion. After eggs hatch, the larvae of most blow fly species feed in an aggregation or “mass”. While in this mass larvae may experience periods of hypoxia/anoxia, but the tolerance of blow fly larvae to anoxic conditions is poorly studied. We tested the anoxia tolerance of four species of calliphorids (Calliphora vicina, Cochliomyia macellaria, Lucilia sericata, and Phormia regina), by examining actively feeding third-stage larvae across five temperatures. Experiments were conducted by exposing larvae to pure nitrogen environments and determining mortality at set time intervals. All species show significant linear relationships between survival time and temperature under anoxic conditions. Of species tested, C. macellaria had the greatest tolerance to anoxia (LT50 of 9 h at 20 °C). In contrast, C. vicina was the least tolerant (LT50 of 2.2 h at 40 °C). With all species, survivorship decreased with increasing temperature. Unlike many other insects tested in severe hypoxia, the larvae of the calliphorids tested, which included members of three subfamilies, were not tolerant of anoxic conditions. From these findings, it seems likely that hypoxia is a significant limitation for maggots in a maggot mass, particularly when the mass temperature is high (>40 °C). Forensically, these data provide a limit on potential maggot survival on bodies that have been submerged or otherwise experience severe hypoxia before discovery.

Predictors of alcohol consumption among adolescents and young adults in Lusaka, Zambia.

Alcohol consumption among young people in schools and communities presents a major problem of public health concern. We determined the predictors of alcohol consumption among adolescents and young adults in Lusaka, Zambia. A cross-sectional study design was adopted. A total of 196 participants took part in the quantitative study. For the qualitative part, there were 13 participants. The study used multistage and purposive sampling methods. A semi-structured questionnaire and in-depth interviews were used. Quantitative data were analysed using STATA version 14. Ordered logistic regression analysis was used to assess the actual predictors, with confidence interval set at 95% and p-value at 0.05. Qualitative data were analysed thematically. The older age category (20-24) had a greater prevalence of alcohol consumption (63.3%) than the younger age category (36.7%). Age, being employed, unconducive learning environment, limited recreation and sports activities, and adult alcohol drinking culture decreased the odds of consuming alcohol. Limited parental care support increased the odds of alcohol consumption [AOR= 4.21; 95% CI: 1.32-13.45, p=0.015]. Futile alcohol regulatory measures were cited to be contributing to alcohol consumption. Alcohol consumption was highly prevalent among young adults aged 20-24 years. There is need for continuous sensitization on substance abuse and its adverse effects in schools and communities at large. The strengthening, reviewing and amendment of the alcohol regulatory measures and policies should be considered.

Combinatorics of Intervals in the Plane I: Trapezoids

We study arrangements of intervals in \(\mathbb {R}^2\) for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic structure, which we characterise. This leads to some unexpected examples of sets of intervals forming many trapezoids, where an important role is played by degree 2 curves.

Generalized-Hukuhara subdifferential analysis and its application in nonconvex composite interval optimization problems

In this article, we study calculus for gH-subdifferential of convex interval-valued functions (IVFs) and apply it in a nonconvex composite model of an interval optimization problem (IOP). Towards this, we define convexity, convex hull, closedness, and boundedness of a set of interval vectors. In identifying the closedness of the convex hull of a set of interval vectors and the union of closed sets, we analyze the convergence of the sequence of interval vectors. We prove a relation on the gH-directional derivative of the maximum of finitely many comparable IVFs. With the help of existing calculus on the gH-subdifferential of an IVF, we derive a Fritz-John-type and a KKT-type efficiency condition for weak efficient solutions of IOPs. In the sequel, we analyze the supremum and infimum of a set of intervals. Further, we report a characterization of the weak efficient solutions of nonconvex composite IOPs by applying the proposed concepts. The whole analysis is supported by illustrative examples.

Multiple Criteria Decision Analysis Based on Ill-Known Pairwise Comparison Data

The analytic hierarchy process (AHP) provides a systematic approach to the evaluation of alternatives based on pairwise comparison matrices (PCMs) under multiple criteria. As human evaluation is not always accurate and precise, each component of a PCM showing relative importance has been expressed by an interval or a fuzzy number. In this paper, we treat a PCM whose components are represented by twofold intervals. The twofold intervals are composed of inner and outer intervals showing the range of surely acceptable values and the complement of the range of surely unacceptable values for relative importance, respectively. One may apply a fuzzy AHP approach by building a trapezoidal fuzzy number from the inner and outer intervals. However, this approach does not always fit the given information. Because the twofold interval information ambiguously specifies the range of acceptable values for the relative importance. Then we appropriately translate this information into a set of intervals including the inner interval and included in the outer interval, assuming that the decision-maker evaluates the priority weights implicitly as intervals. We investigate the decision analysis based on the twofold interval PCM. Three conflict resolution methods are proposed for treating the inconsistency in the twofold interval PCM. Parametric methods for visualizing possible alternative orderings are proposed. Numerical examples are given to demonstrate the differences between the proposed approach and the previous approaches.

A novel and efficient exact technique for integrated staffing, assignment, routing, and scheduling of home care services under uncertainty

We model and solve integrated multi-period staffing, assignment, routing, and scheduling of caregivers for home care services and obtain insights for the case under uncertainty. The goal is to construct a weekly schedule that adheres to related operational considerations and determines optimal staffing of caregivers by minimizing caregivers’ fixed- and overtime costs. For tractability, we incorporate a priori-generated visit pattern—an existing practical approach that deals effectively with hard assignment decisions. First, we propose a novel mixed-integer program (MIP) for the nominal (deterministic) problem. We then incorporate uncertainty in service and travel times and develop a robust counterpart by hybridizing interval and polyhedral uncertainty sets. Second, we show that there is a special mathematical structure within the model that allows us to develop a novel logic-based Benders branching-decomposition algorithm that systematically delays the resolution of difficult routing/ scheduling problems and efficiently solves both the nominal and robust MIP models, i.e., our solution approach for the deterministic case allowed us to solve the robust model. Using a benchmark and newly generated instances from the literature, we show that CPLEX can solve our nominal model with average optimality gap of 56%. On the other hand, our new exact technique can solve our nominal model to an average optimality gap of 5%. Third, we provide practical insights into (i) the price of robustness and (ii) the impacts of nurse flexibility and overtime. The average total cost does not increase beyond 18% than the nominal solution and the cost-savings of nurse flexibility is about 19% on average and higher than overtime’s. We also demonstrate that nurse flexibility impact is high and comparable in both cases, deterministic and stochastic.

The Clinical Characteristics and Epidemiology of Extramedullary Multiple Myeloma over the Past Two Decades

Background Extramedullary multiple myeloma (EMM) represents a rare and aggressive manifestation of multiple myeloma (MM) in which plasma cells survive outside of the bone marrow microenvironment, arising from a non-medullary site. EMM affects approximately 30% of MM patients and can be present at diagnosis or develop at any timepoint during the disease course [1,2]. Prior studies have demonstrated a higher incidence of high-risk cytogenetics in patients with EMM including gain 1q, translocation (4;14), translocation (14;16) and deletion 17p [3]. There is a paucity of data on clinical characteristics and overall epidemiology of EMM. The purpose of this study is to evaluate the clinical characteristics of patients with EMM over the past 2 decades, and to identify epidemiologic characteristics that may impact overall prognosis. Methods A population-based retrospective cohort study of patients with EMM was conducted using the publicly available Surveillance, Epidemiology, and End Results (SEER) database. In addition, 18 registries in the November 2020 submission database were also utilized (http://www.seer.cancer.gov). All patient-specific information within the databases have been de-identified, and therefore IRB approval was not needed to conduct this study. A total of 858 patients diagnosed with EMM, between 2000 and 2017, were ultimately enrolled in our study. We analyzed demographics, clinical characteristics, and overall mortality (OM) as well as cancer-specific mortality (CSM) of EMM. Variables with a p-value < 0.1 in the univariate Cox regression were incorporated into the multivariate Cox model to determine the independent prognostic factors, with a hazard ratio (HR) of greater than 1 representing adverse prognostic factors. All tests were two-sided, with a confidence interval set as 95% and p value <0.05 deemed statistically significant. All statistical tests were performed by using Software STATA 16.1. Results From a sample of 858 patients with EMM, male gender (63.25%), age range 60-79 years (51.05%) and non-Hispanic whites (66.78%) were the most represented. Central Nervous System (which includes leptomeningeal, intracranial and intraparenchymal involvement) and vertebral column was the most affected site (33.10%). Multivariate cox proportional hazard regression analyses only revealed higher overall mortality (OM) in age group over 80 years (HR = 9.792, 95% CI 4.403-21.774, p=0) and widowed individuals (HR = 1.609, 95% CI 1.101-2.35, p = 0.014). Multivariate cox proportional hazard regression analyses of cancer specific mortality (CSM) also revealed higher mortality of the same groups. Eyes, mouth, and ENT involvement had the lowest CSM in the multivariate analysis. Conclusions EMM is a relatively rare entity that presents in a minority of patients diagnosed with MM [1]. To our knowledge, there is scarcity of data on the clinical characteristics and epidemiology of patients with EMM. This study found that non-Hispanic whites were the most affected population, which contrasts with the overall epidemiology of Multiple Myeloma without extramedullary disease in which the black population is the most affected [4]. Patients were primarily in the 60-79-year age range, and the most commonly affected sites were CNS/vertebral column (33%), bones/soft tissues of the trunk (12.6%) and pelvis/sacrum (11.3%), and eyes/mouth/ears/nose/throat (11.7%). We found that age was the single most important prognostic factor, with older patients having worse outcomes (Table 2). Marital status and tumor location were also found to be independent prognostic factors, with widowed patients having higher mortality rates and patients with EMM affecting eyes/mouth/ears/nose/throat faring better than those with other sites affected (Table 2). We hope that the results of this study will enhance our overall understanding of the clinical presentation of this rare and aggressive manifestation of MM. In better understanding EMM, we hope to inspire larger prospective studies on the management of this subset of patients, which is particularly important in the era of novel agents including immunomodulatory agents, proteasome inhibitors, monoclonal antibodies, and, more recently, the advent of chimeric antigen receptor T-cell therapy (CAR-T) and bispecific agents.

Hematological and biochemical reference intervals of wild-caught and inhouse adult Indian rhesus macaques (Macaca mulatta)

BackgroundNonhuman primates are used for research purposes such as studying diseases and drug discovery and development programs. Various clinical pathology parameters are used as biomarkers of disease conditions in biomedical research. Detailed reports of these parameters are not available for Indian-origin rhesus macaques. To meet the increasing need for information, we conducted this study on 121 adult Indian rhesus macaques (57 wild-sourced and 64 inhouse animals, aged 3–7 years). A total of 18 hematology and 18 biochemistry parameters were evaluated and reported in this study. Data from these parameters were statistically evaluated for significance amongst inhouse and wild-born animals and for differences amongst sexes. The reference range was calculated according to C28-A3 guidelines for reporting reference intervals of clinical laboratory parameters.ResultsSource of the animals and sex appeared to have statistically significant effects on reference values and range. Wild-born animals reported higher WBC, platelets, neutrophils, RBC, hemoglobin, HCT, MCV, and total protein values in comparison to inhouse monkeys. Sex-based differences were observed for parameters such as RBCs, hemoglobin, HCT, creatinine, calcium, phosphorus, albumin, and total protein amongst others.ConclusionsThrough this study, we have established a comprehensive data set of reference values and intervals for certain hematological and biochemical parameters which will help researchers in planning, conducting, and interpreting various aspects of biomedical research employing Indian-origin rhesus monkeys.

The characteristics of the tight gas reservoir with strong heterogeneity and its 3D recovery technology in Yan’an gas field, China

The Yan’an gas field is located in the southeastern part of the Ordos Basin of China. After years of research, we have clarified the characteristics of the upper Paleozoic tight sandstone reservoirs: four main sets of intervals, including the Carboniferous Benxi Formation, the Shan second and Shan first members of the Permian Shanxi Formation, and the He eighth member of the Permian Lower Shihezi Formation, are multilayer complex superposed tight sandstone reservoirs that developed under the control of multiple differential sedimentary systems. Compared with the northern gas field, the upper Paleozoic reservoir is characterized by the small-scale effective sand body and poor physical property in the Yan’an gas field; the heterogeneity of the upper Paleozoic tight reservoir varies greatly: the heterogeneity of the He eighth and the Shan first members was increasing from the north to the south of the research area, owing to the intersection of the north and south provenance. The Shan second member indicates an obviously opposite trend: the heterogeneity of the Benxi Formation weakened from the center to both sides; the Yan’an gas field developed four main superposed composite sand bodies types, including the vertical superposed, lateral migration, cut superposed, and isolated types. Due to the existence of the interlayers rich in mudstone and soft debris near the architectural boundary, the reservoir sand body has strong structural heterogeneity under the interaction of differential diagenesis and densification. Aiming at the strong heterogeneity and multilayer complex superposition characteristics of the Yan’an gas field, we have made clear the constraints and matching relationships between control factors and well-pattern elements on the basis of deep analysis. We have formed the hybrid well pattern for 3D recovery technology that unlocked multilayer complex superposed tight sandstone gas reservoirs with strong heterogeneity in the southeastern portion of the Ordos Basin.

A fuzzy-interval nonlinear programming for boosters under uncertainty

Abstract In this paper, an integration of a fuzzy-interval credibility-constrained (FIC) model expressed by fuzzy interval sets (FIS) and interval nonlinear programming (INP), termed an FIC-INP model, was proposed and applied to two cases. After formulating the FIC-INP model, upper and lower disinfection booster costs can be obtained for two cases under various combinations of credibility levels of upper and lower limits. The results indicated that the upper and lower booster costs increased with the credibility levels of the lower limits. The upper as well as the lower booster costs increased with the booster numbers. For credibility levels of lower limit constraints ranging from 0.6 to 0.9, the upper and lower booster costs increased under enlarging/widening trapezoidal distributions, and the intervals of booster costs increased with interval uncertainty. For a lower limit constraint credibility level of 0.5, the upper and lower booster costs decreased under shrinking/narrowing trapezoidal distributions, and the booster cost intervals increased under larger interval trapezoidal distributions. The degrees of effect of the interval uncertainty are higher than the fuzzy uncertainty. The results obtained can provide more information for managers to make booster schemes under fuzzy and interval uncertainties.

Dynamic Geometric Set Cover and Hitting Set

We investigate dynamic versions of geometric set cover and hitting set where points and ranges may be inserted or deleted, and we want to efficiently maintain an (approximately) optimal solution for the current problem instance. While their static versions have been extensively studied in the past, surprisingly little is known about dynamic geometric set cover and hitting set. For instance, even for the most basic case of one-dimensional interval set cover and hitting set, no nontrivial results were known. The main contribution of our article are two frameworks that lead to efficient data structures for dynamically maintaining set covers and hitting sets in ℝ 1 and ℝ 2 . The first framework uses bootstrapping and gives a (1 + ε)-approximate data structure for dynamic interval set cover in ℝ 1 with O ( n α / ε) amortized update time for any constant α &gt; 0; in ℝ 2 , this method gives O (1)-approximate data structures for unit-square set cover and hitting set with O ( n 1/2+α ) amortized update time. The second framework uses local modification and leads to a (1 + ε)-approximate data structure for dynamic interval hitting set in ℝ 1 with Õ(1/ε) amortized update time; in ℝ 2 , it gives O (1)-approximate data structures for unit-square set cover and hitting set in the partially dynamic settings with Õ(1) amortized update time.

Bilateral Knee Joint Cooling on Anaerobic Capacity and Wheel Cadence during Sprint Cycling Intervals.

We compared the effect of bilateral knee joint cooling with or without a pre-cooling warm-up on sprint cycling performance to a non-cooling control condition. Seventeen healthy young males (25 ± 2 years, 174 ± 6 cm, 70 ± 9 kg) performed three conditions in a counterbalanced order (condition 1: warming + cooling + cycling; condition 2: cooling + cycling; condition 3: cycling). For warming, a single set of cycling intervals (a 10 s sprint with maximal effort followed by a 180 s active recovery; resistive load 4% and 1% body mass for sprint and recovery, respectively) was performed. For cycling, five sets of cycling intervals were performed. For cooling, 20 min of bilateral focal knee joint cooling was applied. Peak and average values of anaerobic capacity and wheel cadence during each set across conditions were statistically compared. There was no condition effect over set (condition × set) in anaerobic capacity (F8,224 < 1.49, p > 0.16) and wheel cadence (F8,224 < 1.48, p > 0.17). Regardless of set (condition effect: F2,224 > 8.64, p < 0.0002), conditions 1 and 2 produced higher values of anaerobic capacity (p ≤ 0.05). Similarly (condition effect: F2,224 > 4.62, p < 0.02), condition 1 showed higher wheel cadence (p < 0.02) than condition 3. A bilateral joint cooling for 20 min with or without pre-cooling warm-up may improve overall sprint cycling capacity during five sets of cycling intervals when compared to the non-cooling condition.

Seeded binary segmentation: a general methodology for fast and optimal changepoint detection

Summary We propose seeded binary segmentation for large-scale changepoint detection problems. We construct a deterministic set of background intervals, called seeded intervals, in which single changepoint candidates are searched for. The final selection of changepoints based on these candidates can be done in various ways, adapted to the problem at hand. The method is thus easy to adapt to many changepoint problems, ranging from univariate to high dimensional. Compared to recently popular random background intervals, seeded intervals lead to reproducibility and much faster computations. For the univariate Gaussian change in mean set-up, the methodology is shown to be asymptotically minimax optimal when paired with appropriate selection criteria. We demonstrate near-linear runtimes and competitive finite sample estimation performance. Furthermore, we illustrate the versatility of our method in high-dimensional settings.

On the Δ-interval and the Δ-convexity numbers of graphs and graph products

Given a graph G and a set S ⊆ V ( G ) , the Δ -interval of S , [ S ] Δ , is the set formed by the vertices of S and every w ∈ V ( G ) forming a triangle with two vertices of S . If [ S ] Δ = S , then S is Δ -convex of G ; if [ S ] Δ = V ( G ) , then S is a Δ -interval set of G . The Δ -interval number of G is the minimum cardinality of a Δ -interval set and the Δ -convexity number of G is the maximum cardinality of a proper Δ -convex subset of V ( G ) . In this work, we show that the problem of computing the Δ -convexity number is W[1]-hard and NP-hard to approximate within a factor O ( n 1 − ɛ ) for any constant ɛ > 0 even for graphs with diameter 2 and that the problem of computing the Δ -interval number is NP-complete for general graphs. For the positive side, we present characterizations that lead to polynomial-time algorithms for computing the Δ -convexity number of chordal graphs and for computing the Δ -interval number of block graphs. We also present results on the Δ -hull, Δ -interval and Δ -convexity numbers concerning the three standard graph products, namely, the Cartesian, the strong and the lexicographic products, in function of these and well-studied parameters of the operands.

Nonparametric Probabilistic Forecasting for Wind Power Generation Using Quadratic Spline Quantile Function and Autoregressive Recurrent Neural Network

Compared with commonly-used point forecasting, probabilistic forecasting provides quantitative information on the uncertainty associated with wind power output. However, most studies focus on modelling only a fixed set of quantiles or intervals, which cannot provide the entire information of wind power distribution. In this paper, we propose a non-parametric and flexible method for probabilistic wind power forecasting. First, the distribution of wind power output is specified by spline quantile function, which avoids assuming a parametric form and also provides flexible shape for wind power density. Then, autoregressive recurrent neural network is used to build the non-linear mapping from input features to the parameters of quadratic spline quantile function. A novel loss function based on continuous ranked probability score (CRPS) is designed to train the forecasting model. We also derive the closed-form solution of the integral required in computing the CRPS-based loss function in order to improve the computational efficiency in training. The effectiveness of our proposed method has been validated with public real-world data from Global Energy Forecasting Competition 2014. Compared with some advanced benchmarks, our proposed approach outperforms them at least six percent in terms of CRPS, indicating that it can provide probabilistic wind power forecasting with high quality.

S1198 Treatment and Hepatocellular Carcinoma Screening Patterns Among Black Patients With Chronic Hepatitis B

Introduction: Significant racial disparities exist in Hepatitis B virus (HBV) infection across the nation, from screening variability to treatment patterns and clinical outcomes. The Black community bears a disproportionately large disease burden. In this study, we sought to compare the disease courses between Black patients seen at a private tertiary referral center vs. those evaluated at a high-volume county safety net hospital. Methods: Using informatics, we identified adult patients with chronic HBV based on ICD-10 codes, who had ≥1 clinic visit between January 1, 2010 and December 31, 2020 at University of Miami Hospital (UM) and Jackson Memorial Hospital (JM). We conducted retrospective chart review to gather demographic and clinical data. We used descriptive statistics, Kruskal-Wallis, and Pearson’s chi squared tests to evaluate for differences between Black patients at each hospital with the significance interval set to p < 0.05. Analyses were conducted using STATA 17.0. Results: Of 649 Black patients detected by informatics, 364 had confirmed HBV with 306 seen at UM and 58 at JM. Compared to JM, UM patients were significantly older, English speakers, and privately insured (p < 0.001) (Table). Most common birth countries included Haiti and the USA, among others (Figure). 78.8% of UM patients were evaluated by Hepatology, compared to 41.1% at JM. More JM patients had active hepatitis, and 15.5% had a high viral load (HBV DNA PCR >20,000) compared to 3.3% at UM. Patients seen at UM were more likely to be treated, 52.9%, vs. 24.6% at JM and placed on newer regimens (ie Tenofovir [TAF] and Entecavir). UM patients were significantly more likely to undergo HbeAg and HbeAb testing, compared to their JM counterparts. Black patients at JM were significantly more likely to have alcoholic liver disease, ascites, and orthotopic liver transplantation. Although more UM patients underwent surveillance for hepatocellular carcinoma (HCC), there was ultimately no significant difference in patients being diagnosed with HCC between hospitals. Conclusion: These findings suggest that significant differences in demographics, referral patterns, laboratory evaluation, and management exist between Black patients at UM vs. JM, despite both hospitals being affiliated with the same academic institution. Our analysis on JM patients is ongoing and will be crucial to inform future interventions aimed at standardizing and providing evidence-based HBV care across medical centers.Figure 1.: Geographic distribution of Black patients’ most common birth countries. Green UM, Orange JM. Table 1. - Comparison of demographics, screening, and management patterns between Black patients at JM vs. those at UM Variable Blacks @ JM (n = 58) Blacks @ UM (n = 306) p-value Median Age, years (IQR) 54 (45-63) 59 (47-66) 0.0001 Male Gender, % 68.3 63.7 0.24 US Born, % 50.9 32.7 0.012 Department seen by, %Hepatology 41.4 78.8 < 0.001 General Internal MedGastroenterology 62.11.7 8.814.1 < 0.0010.008 HbeAg / HbeAb checked, % 52.6 78.5 < 0.001 Active hepatitis, % 19 2.9 < 0.001 High viral load ( >20,000), % 15.5 3.3 < 0.001 Currently on Treatment, % 24.6 52.9 < 0.001 Tenofovir TDF TAF EntecavirAdefovirLamivudine 13.813.713.113.40.68.6 31.412.11.75.201.6 0.0070.740.00140.0780.540.003 Alcoholic Liver Disease, % 14 1.8 < 0.001 Ascites, % 22.8 7.3 < 0.001 OLT, % 26.3 1.8 < 0.001 HCC Screening, %FibroscanAFPSurveillance imaging (< 6 months) 17.542.1158.9 3178.377.9 0.04< 0.0010.003 Diagnosed with HCC 5.1 5.9 0.71 AFP = alpha-fetoprotein; OLT = orthotopic liver transplantation; HCC = hepatocellular carcinoma.

Interval Valued Intuitionistic Fuzzy β-Filters on β-Algebras

This study establishes the concept of interval valued intuitionistic fuzzy (InVInF) β-filters on β-algebras and a few of its related properties are investigated. Some compelling results of interval valued fuzzy β-filters have been examined. Further, the notions of products and strong β-filters are also introduced. In addition that, the level set and homomorphism of interval valued intuitionistic fuzzy β-filters are too discussed. Furthermore, we enacted that the intersection between two interval valued intuitionistic fuzzy β−filters is again an interval valued intuitionistic fuzzy β-filter.

Mathematical Approach to Discrete Representation of Time Ranges of Species: Set and Operations of Half-open Intervals

種の生存期間の離散的表現に向けた数学的アプローチとして，半開区間（左閉右開区間）の集合演算を考察する．はじめに半開区間Tに含まれる半開区間の和集合，共通集合，補集合を求める公式を示す．Tを空集合，単一の半開区間，複数の半開区間の和集合からなる無限集合としたとき，Tは演算に関して閉じている．SO を生存期間がTであるタクソンΣに分類される種の集合としたとき，SO の元（種）の生存期間はTの元であり，その演算によって新しいTの元が矛盾なく生み出される．タクソンΣの生存期間TはSO の元（種）の出現時刻と絶滅時刻を端点とする小区間に直和分割でき，種の生存期間はいくつかの小区間の和集合として表現できる．集合Tの場合と同様に，空集合，単一の小区間，複数の小区間の和集合からなる有限集合TM は集合演算に関して閉じている．最終的に，種の生存期間に関する集合演算は小区間を単位にした離散的処理として矛盾なく実行できると結論した．

Optimal and fast confidence intervals for hypergeometric successes

We present an efficient method of calculating exact confidence intervals for the hypergeometric parameter representing the number of “successes,” or “special items,” in the population. The method inverts minimum-width acceptance intervals after shifting them to make their endpoints nondecreasing while preserving their level. The resulting set of confidence intervals achieves minimum possible average size, and even in comparison with confidence sets not required to be intervals it attains the minimum possible cardinality most of the time, and always within 1. The method compares favorably with existing methods not only in the size of the intervals but also in the time required to compute them. The available R package hyperMCI implements the proposed method.

Anti-hesitant Fuzzy Subalgebras, Ideals and Deductive Systems of Hilbert Algebras

The Hilbert algebra, one of several algebraic structures, was first described by Diego in 1966 [7] and has since been extensively studied by other mathematicians. Torra [18] was the first to suggest the idea of hesitant fuzzy sets (HFSs) in 2010, which is a generalization of the fuzzy sets defined by Zadeh [20] in 1965 as a function from a reference set to a power set of the unit interval. The significance of the ideas of hesitant fuzzy subalgebras, ideals, and filters in the study of the different logical algebras aroused our interest in applying these concepts to Hilbert algebras. In this paper, the concepts of HFSs to subalgebras (SAs), ideals (IDs), and deductive systems (DSs) of Hilbert algebras are introduced in terms of anti-types. We call them anti-hesitant fuzzy subalgebras (AHFSAs), anti-hesitant fuzzy ideals (AHFIDs), and anti-hesitant fuzzy deductive systems (AHFDSs). The relationships between AHFSAs, AHFIDs, and AHFDSs and their lower and strong level subsets are provided. As a result of the study, we found their generalization as follows: every AHFID of a Hilbert algebra Ω is an AHFSA and an AHFDS of Ω. We also study and find the conditions for the complement of an HFS to be an AHFSA, an AHFID, and an AHFDS. In addition, the relationships between the complements of AHFSAs, AHFIDs, and AHFDSs and their upper and strong level subsets are also provided.