Balanced Incomplete Block Research Articles

Experimental investigation of the polyhedral structure of BIBDs

We examine the polyhedral structure of Balanced Incomplete Block Designs (BIBDs) in an effort to improve runtimes for finding optimal solutions via constraint or integer program. For example, an optimal BIBD is one that minimizes the range of blocksums. This range, which we refer to as diffsum, has applications in drug trials and Redundant Arrays of Independent Disks (RAID). The polytope we explore is the convex hull of all lexicographically-ordered BIBD solutions satisfying a given set of parameters, ( v , b , r , k , λ ) , with solutions represented as a vector in R kb . The dimension-reducing equations and the facets for some of the smaller polytopes were found by using the Double-Description Method on a algebraic program modelling these solutions. Because of the presence of the lexicographic ordering, none of these polytopes are full dimensional. After describing some of these smaller BIBD polytopes, we generalize some dimension-reducing equations, and evaluate the efficiency of these equations to optimization models.

Completely reducible super‐simple (v,4,4) $(v,4,4)$‐BIBDs and related constant weight codes

AbstractA design is said to be super‐simple if the intersection of any two blocks has at most two elements. A design with index is said to be completely reducible, if its blocks can be partitioned into nonempty collections , such that each together with the point set forms a design with index unity. In this paper, it is proved that there exists a completely reducible super‐simple (CRSS) balanced incomplete block design (‐BIBD for short) if and only if and or . A ‐ary constant weight code (CWC) of length with weight and distance is denoted as a code. The maximum size of a code is denoted as , and the codes achieving this size are called optimal. CRSS designs with index are closely related to ‐ary CWCs. By using the results of CRSS ‐BIBDs, s are determined for all .

Nestings of BIBDs with block size four

AbstractIn a nesting of a balanced incomplete block design (or BIBD), we wish to add a point (the nested point) to every block of a ‐BIBD in such a way that we end up with a partial ‐BIBD. In the case where the partial ‐BIBD is in fact a ‐BIBD, we have a perfect nesting. We show that a nesting is perfect if and only if . Perfect nestings were previously known to exist in the case of Steiner triple systems (i.e., ‐BIBDs) when , as well as for some symmetric BIBDs. Here we study nestings of ‐BIBDs, which are not perfect nestings. We prove that there is a nested ‐BIBD if and only if , . This is accomplished by a variety of direct and recursive constructions.

PBIB-Designs Arising From BI-Connected Dominating Sets of Cubic Graphs of Order at Most 12

A $(v, b, \gamma_{bc}, r, \lambda_{i})$-design over regular graph $G = (V, E)$ of degree $k$ is an ordered pair $D = (V, B)$, where $|V| = v$ and $B$ is the set of bi-connected dominating sets of $G$ called blocks such that two vertices $\alpha$ and $\beta$ which are $i^{th}$ associates occur together in $ \lambda_{i}$ blocks, the numbers $\lambda_{i}$ being independent of the choice of the pair $\alpha$ and $\beta$. In this paper, we obtain Partially Balanced Incomplete Block (PBIB)-designs arising from bi-connected dominating sets in cubic graphs. Also, we give a complete list of PBIB-designs with respect to the bi-connected dominating sets for cubic graphs of order at most $12$. The discussion of non-existence of some designs corresponding to bi-connected dominating sets from certain graphs concludes the article.

On the Selection of Optimal Balanced Incomplete Block Design using Different Types of Designs

The choice of selecting the best among the types of balanced incomplete block designs (BIBDs) have brought about some controversies in combinatorial design. Prominent methods of constructing BIBD have been proposed by different authors, but none has been juxtaposed the designs with respect to type. In this paper, we proposed the adoption of the concept of optimality criteria such as: A-, D-, E- , and T – optimality criterion to select the best design based on their optimality values using a (15, 15, 7, 7, 3) simulated balanced incomplete block design. A dual design, residue design and derived design were selected as the major three types of BIBDs for investigation. The findings revealed that dual design is the best balanced incomplete block design based on its high optimal value. We discovered that residue and derived design obtained from the simulated balanced incomplete block design by method of block selection and intersection becomes a standard balanced incomplete block design.

The Impact of Pedestrian Interactions at Intersections on the Three Levels of Drivers’ Situation Awareness

Evaluating drivers’ situation awareness (SA) is important in the implementation of alert prioritization. This study investigates the relationship between driving performance measures (speed, acceleration and brake usage, steering wheel and lane deviation), pedestrian interaction (location, direction and motion), and driver SA. To achieve this, a controlled study was conducted with 56 participants using a Balanced Incomplete Block Design, where each participant drove 18 out of 48 possible intersections in a driving simulator environment. The Situational Awareness Global Assessment Technique (SAGAT) method was used to assess drivers’ SA. Mixed effects logit models were developed to examine the different SA Levels (perception, comprehension, projection). The driving performance measures were aggregated across three time windows (1, 3, and 5 s). The findings show significant contributions from both driving performance measures and pedestrian interactions in predicting driver SA. More specifically, a one-second time window was useful for predicting pedestrian direction and a three-second time window was best for predicting pedestrian location and intention to cross. The results indicate the importance of considering different time windows for predicting various levels of driver SA responses. These findings offer insights into factors to be considered in driver SA predictive models.

The vehicle of administration, feed or water, and prandial state influence the oral bioavailability of amoxicillin in piglets.

Feed and water components may interact with drugs and affect their dissolution and bioavailability. The impact of the vehicle of administration (feed and water) and the prandial condition of weaner piglets on amoxicillin´s oral bioavailability was evaluated. First, amoxicillin's in vitro dissolution and stability in purified, soft, and hard water, as well as release kinetics from feed in simulated gastric and intestinal media were assessed. Then, pharmacokinetic parameters and bioavailability were determined in fasted and fed pigs using soft water, hard water, or feed as vehicles of administration following a balanced incomplete block design. Amoxicillin showed similar dissolution profiles in soft and hard water, distinct from the dissolution profile obtained with purified water. Complete dissolution was only achieved in purified water, and merely reached 50% in soft or hard water. Once dissolved, antibiotic concentrations decreased by around 20% after 24h in all solutions. Korsmeyer-Peppas model best described amoxicillin release from feed in simulated gastric and intestinal media. Feed considerably reduced antibiotic dissolution in both simulated media. In vivo, amoxicillin exhibited significantly higher bioavailability when delivered via water to fasted than to fed animals, while in-feed administration yielded the lowest values. All treatments showed a similar rate of drug absorption. In conclusion, we demonstrated that water and feed components, as well as feed present in gastrointestinal tract of piglets decrease amoxicillin´s oral bioavailability. Therefore, the use of oral amoxicillin as a broad-spectrum antibiotic to treat systemic infections in pigs should be thoroughly revised.

Second type second order slope rotatable designs utilizing symmetrical unequal block arrangements with two unequal block sizes

Kim and Ko developed second order slope rotatable designs (SOSRD) of second type utilizing central composite designs (CCD), in which two numbers are used to represent the positions of star points. In this paper, we suggest second type SOSRD utilizing symmetrical unequal block arrangements (SUBA) with two unequal block sizes. In some cases, the suggested method may develop designs containing fewer design points than second type SOSRD obtained utilizing CCD, pairwise balanced designs (PBD) and balanced incomplete block designs (BIBD). The first order partial derivative's for estimated second order response variance for factors 6≤v≤15 is also obtained.

Mutual incidence matrix of two balanced incomplete block designs

AbstractWe propose to consider a mutual incidence matrix of two balanced incomplete block designs built on the same finite set. In the simplest case, this matrix reduces to the standard incidence matrix of one block design. We find all eigenvalues of the matrices and and their eigenspaces.

On Construction of Doubly Nested Partially Balanced Incomplete Block Designs

On Construction of Doubly Nested Partially Balanced Incomplete Block Designs

Biomechanical evaluation of a central collinear entry reconstruction nail for femoral neck fracture prophylaxis

IntroductionReconstruction nails are commonly used to treat proximal femur fractures, with cephalic screw placement for femoral neck “prophylaxis” becoming standard practice. These implants are traditionally introduced through piriformis fossa (PF) or greater trochanter (GT) entry portals. A third “central collinear” (CC) portal has been proposed that allows entry along the femoral anatomic axis and central placement of cephalic screws. The present study aimed to quantify and compare the CC portal femoral neck strength with the two traditional (PF and GT) entry portals. Materials and MethodsEighteen cadaveric femur specimens (nine matched pairs) were divided into three groups using a balanced incomplete block design to control for variations in age and sex: (1) GT, (2) CC, and (3) PF entry points. Specimens and implants were cut to a standard length and instrumented with straight or valgus bend nails of appropriate laterality and two cephalic screws. Specimens were mounted on a custom jig replicating load distribution along the mechanical axis. A 100 N compressive preload was applied to the femoral head, followed by loading to failure at a rate of 10 mm/s until fracture, indicated by 30 % drop in axial force. Results: The three entry points did not differ in load-to-failureGT (6378.7 ± 1494.9 N), P (6912.4 ± 4924.1 N) and CC (7044.2 ± 2911.4 N) (P = 0.948) or maximum displacement, stiffness, and toughness. Most PF specimens failed at the basicervical neck, whereas most GT specimens failed at the subcapital neck; these differences were not significant. CC specimens failed evenly split between subcapital and basicervical. ConclusionThere were no significant difference in femoral neck load-to-failure after placement of a reconstruction nail through a CC entry portal when compared to both GT and PF entry. Clinically, this suggests the CC entry portal is a viable option when clinical considerations warrant its use.

Prioritization of ethical concerns regarding HIV molecular epidemiology by public health practitioners and researchers

BackgroundHIV molecular epidemiology (HIV ME) can support the early detection of emerging clusters of new HIV infections by combining HIV sequence data routinely obtained during the clinical treatment of people living with HIV with behavioral, geographic, and sociodemographic information. While information about emerging clusters promises to facilitate HIV prevention and treatment efforts, the use of this data also raises several ethical concerns. We sought to assess how those working on the frontlines of HIV ME, specifically public health practitioners (PHPs) and researchers, prioritized these issues.MethodsEthical issues were identified through literature review, qualitative in-depth interviews, and stakeholder engagement. PHPs and researchers using HIV ME prioritized the issues using best–worst scaling (BWS). A balanced incomplete block design was used to generate 11 choice tasks each consisting of a sub-set of 5 ethical concerns. In each task, respondents were asked to assess the most and least concerning issue. Data were analyzed using conditional logit, with a Swait-Louviere test of poolability. Latent class analysis was then used to explore preference heterogeneity.ResultsIn total, 57 respondents completed the BWS experiment May–June 2023 with the Swait-Louviere test indicating that researchers and PHPs could be pooled (p = 0.512). Latent class analysis identified two classes, those highlighting “Harms” (n = 29) (prioritizing concerns about potential risk of legal prosecution, individual harm, and group stigma) and those highlighting “Utility” (n = 28) (prioritizing concerns about limited evidence, resource allocation, non-disclosure of data use for HIV ME, and the potential to infer the directionality of HIV transmission). There were no differences in the characteristics of members across classes.ConclusionsThe ethical issues of HIV ME vary in importance among stakeholders, reflecting different perspectives on the potential impact and usefulness of the data. Knowing these differences exist can directly inform the focus of future deliberations about the policies and practices of HIV ME in the United States.

Assessing patient information needs for new antidiabetic medications to inform shared decision-making: A best-worst scaling experiment in China.

Shared decision-making (SDM) is a patient-centred approach to improve the quality of care. An essential requirement for the SDM process is to be fully aware of patient information needs. Our study aimed to assess patient information needs for new antidiabetic medications using the best-worst scaling (BWS) experiment. BWS tasks were developed according to a literature review and the focus group discussion. We used a balanced incomplete block design and blocking techniques to generate choice sets. The final BWS contains 11 attributes, with 6-choice scenarios in each block. The one-to-one, face-to-face BWS survey was conducted among type 2 diabetic patients in Jiangsu Province. Results were analyzed using count-based analysis and modelling approaches. We also conducted a subgroup analysis to observe preference heterogeneity. Data from 539 patients were available for analysis. The most desired information domain was the comparative effectiveness of new antidiabetic medications. It consists of the incidence of macrovascular complications, the length of extended life years, changes in health-related quality of life, the incidence of microvascular complications, and the control of glycated haemoglobin. Of all the attributes, the incidence of macrovascular complications was the primary concern. Patients' glycemic control and whether they had diabetes complications exerted a significant influence on their information needs. Information on health benefits is of critical significance for diabetic patients. Patients have different information needs as their disease progresses. Personalized patient decision aids that integrate patient information needs and provide evidence of new antidiabetic medications are worthy of being established. Before data collection, a pilot survey was carried out among diabetic patients to provide feedback on the acceptability and intelligibility of the attributes.

The pharmacokinetics of single-dose oral atorvastatin and its metabolites support therapeutic use in cockatiels (Nymphicus hollandicus).

To evaluate the plasma concentrations and determine the pharmacokinetic parameters of atorvastatin and its primary active metabolites (para- and orthohydroxyatorvastatin) after administration of a single oral dose in cockatiels (Nymphicus hollandicus). 14 adult cockatiels (7 male, 7 female) around 2 years of age. A compounded oral suspension of atorvastatin 10 mg/mL made with an oral suspending agent and an oral sweetener was administered via oral gavage at 20 mg/kg to each bird. Blood samples were collected at 7 different time points from 0.5 to 24 hours postadministration in a balanced incomplete block design with 3 blood samples per bird and 6 replicates per time point. Plasma concentrations of atorvastatin, parahydroxyatorvastatin, and orthohydroxyatorvastatin were determined by liquid chromatography-tandem mass spectrometry. Pharmacokinetic analysis was performed using noncompartmental analysis. The estimated time to maximum concentration (tmax) for atorvastatin, parahydroxyatorvastatin, and orthohydroxyatorvastatin was 3 hours for each. The estimated maximum plasma concentration (Cmax) for atorvastatin, parahydroxyatorvastatin, and orthohydroxyatorvastatin was 152.6, 172.4, and 68.8 ng/mL, respectively. The terminal half-lives were 4, 6.8, and 4.6 hours, respectively. These results support the therapeutic use of atorvastatin at the dose evaluated in this species based on human pharmacokinetic data. A starting dose of 20 mg/kg PO every 12 to 24 hours could be used to treat lipid disorders in cockatiels pending more data on multidose use and hypolipidemic efficacy.

Evaluating the Douglas-Cohen IRT Goodness of Fit Measure With BIB Sampling of Items.

Methods to detect item response theory (IRT) item-level misfit are typically derived assuming fixed test forms. However, IRT is also employed with more complicated test designs, such as the balanced incomplete block (BIB) design used in large-scale educational assessments. This study investigates two modifications of Douglas and Cohen's 2001 nonparametric method of assessing item misfit, based on A) using block total score and B) pooling booklet level scores for analyzing BIB data. Block-level scores showed extreme inflation of Type I error for short blocks containing 5 or 10 items. The pooled booklet method yielded Type I error rates close to nominal in most conditions and had power to detect misfitting items. The study also found that the Douglas and Cohen procedure is only slightly affected by the presence of other misfitting items in the block. The pooled booklet method is recommended for practical applications of Douglas and Cohen's method with BIB data.

The existence of 23 ${2}^{3}$‐decomposable super‐simple (v,4,6) $(v,4,6)$‐BIBDs

AbstractA design is said to be super‐simple if the intersection of any two blocks has at most two elements. A design with index is said to be ‐decomposable, if its blocks can be partitioned into nonempty collections , , such that each with the point set forms a design with index . In this paper, it is proved that there exists a ‐decomposable super‐simple ‐BIBD (balanced incomplete block design) if and only if and .

Partially balanced nested block designs based on 2-associate-class association schemes for test-control comparisons

In this article, nested partially balanced treatment incomplete block (NPBTIB) designs are introduced for making test treatments-control treatment comparisons. Several methods of constructing such designs are presented. These methods of constructions utilize group divisible treatment (GDTD) designs, nested balanced incomplete block (NBIB) designs, and nested partially balanced incomplete block (NPBIB) designs. A catalogue of efficient NPBTIB designs with 2-associate classes for the number of treatments v ≤ 16 , replications of test treatments r ≤ 15 , and replications of control treatment r 0 ≤ 30 is also included.

Relative Efficiencies of Optimal Designs in Four Dimensions Constructed Using Balanced Incomplete Block Designs

Relative Efficiencies of Optimal Designs in Four Dimensions Constructed Using Balanced Incomplete Block Designs

Symmetric Balanced Incomplete Block Designs (Sbibd) And Construction of Hadamard Rhotrices

Balanced Incomplete Block Designs (BIBD) are the designs obtained from the arrangement of symbols in blocks following established rules and satisfying relevant necessary conditions. BIBDs have broad applications in many fields.The entries in a Hadamard matrix H are all +1’s or -1’s, satisfying the property HHT = n In [2]. Rhotrix is a new concept in mathematics having applications in cryptography. In this paper, using SBIB designs the Hadamard Rhotrices are constructed. AMS Subject classification: 05B05, 05B20, 62K10.

On magic total labelings in combinatorial designs

Let H be a graph and ẞ be an H-decomposition of G. The H-magic total labeling of a graph G is an assignment of integers set [1, |V(G)∪E(G)|] to V(G)∪E(G) such that: any vertex and any edge of G receive distinct integers, and the sum of all vertices receive integers and all edges receive integers on B is a constant for any B ∈ ẞ. In this paper we study the H-super magic problems of balanced incomplete block designs and resolvable balanced incomplete block designs.