Balanced Incomplete Block Research Articles

Assigning readers to cases in imaging studies using balanced incomplete block designs.

In many imaging studies, each case is reviewed by human readers and characterized according to one or more features. Often, the inter-reader agreement of the feature indications is of interest in addition to their diagnostic accuracy or association with clinical outcomes. Complete designs in which all participating readers review all cases maximize efficiency and guarantee estimability of agreement metrics for all pairs of readers but often involve a heavy reading burden. Assigning readers to cases using balanced incomplete block designs substantially reduces reading burden by having each reader review only a subset of cases, while still maintaining estimability of inter-reader agreement for all pairs of readers. Methodology for data analysis and power and sample size calculations under balanced incomplete block designs is presented and applied to simulation studies and an actual example. Simulation studies results suggest that such designs may reduce reading burdens by >40% while in most scenarios incurring a <20% increase in the standard errors and a <8% and <20% reduction in power to detect between-modality differences in diagnostic accuracy and statistics, respectively.

A Construction Technique for Group Divisible (v-1,k,0,1) Partially Balanced Incomplete Block Designs (PBIBDs)

Group Divisible PBIBDs are important combinatorial structures with diverse applications. In this paper, we provided a construction technique for Group Divisible (v-1,k,0,1) PBIBDs. This was achieved by using techniques described in literature to construct Nim addition tables of order 2n, 2≤n≤5 and (k2,b,r,k,1)Resolvable BIBDs respectively. A “block cutting” procedure was thereafter used to generate corresponding Group Divisible (v-1,k,0,1) PBIBDs from the (k2,b,r,k,1)Resolvable BIBDs. These procedures were streamlined and implemented in MATLAB. The generated designs are regular with parameters(15,15,4,4,5,3,0,1);(63,63,8,8,9,7,0,1);(255,255,16,16,17,15,0,1) and (1023,1023,32,32,33,31,0,1). The MATLAB codes written are useful for generating the blocks of the designs which can be easily adapted and utilized in other relevant studies. Also, we have been able to establish a link between the game of Nim and Group Divisible (v-1,k,0,1) PBIBDs.

A method of constructing optimal sliced uniform designs under discrete discrepancy

Sliced uniform designs are useful for generating experimental data with batch structures. In this paper, we employ the discrete discrepancy as the measure of uniformity to construct sliced uniform designs. The construction method is based on an important class of combinatorial configurations, namely, resolvable balanced incomplete block designs; hence, the construction method does not require any computer search. Through resolvable balanced incomplete block designs, under the discrete discrepancy, several infinite classes of new sliced uniform designs are obtained. The obtained design is optimal in the sense that not only the design as a whole but also each of its slices attain the lower bound of the discrete discrepancy. The design parameters are explicitly given, from which experimenters may choose an optimal sliced uniform design with the most suitable run size for their experiment.

Statistical Methods to Support Difficult Diagnoses.

Far too often, one meets patients who went for years or even decades from doctor to doctor without obtaining a valid diagnosis. This brings pain to millions of patients and their families, not to speak of the enormous costs. Often patients cannot tell precisely enough which factors (or combinations thereof) trigger their problems. If conventional methods fail, we propose the use of statistics and algebra to provide doctors much more useful inputs from patients. We use statistical regression for triggering factors of medical problems, and in particular, “balanced incomplete block designs” for factors detection. These methods can supply doctors with much more valuable inputs and can also find combinations of multiple factors through very few tests. In order to show that these methods do work, we briefly describe a case in which these methods helped to solve a 60-year-old problem in a patient and provide some more examples where these methods might be particularly useful. As a conclusion, while regression is used in clinical medicine, it seems to be widely unknown in diagnosing. Statistics and algebra can save the health systems much money, as well as the patients a lot of pain.

On the construction of trend resistant PBIB designs

In agricultural, animal, fisheries and industrial experimentation under block design setup, systematic trend may affect the response under consideration. Although remote, these effects may still have high influence on response and hence should be incorporated in the model for proper model specification. Completely trend resistant block designs, also known as trend free block designs, are an important class of designs where the analysis can be done in usual manner as in case of normal block designs since trend effects and treatment effects are orthogonal. Literature is available on different aspects of trend resistant incomplete block designs mainly focusing on balanced incomplete block designs. This article deals with the construction of completely trend resistant Partially Balanced Incomplete Block (TR-PBIB) designs. Two methods of constructing such designs have been discussed. The information matrices for the class of designs developed have been derived and SAS code for the generation of the developed designs has also been provided.

A survey of resolvable solutions of partially balanced designs

Kageyama (1972) presented a survey of resolvable solutions of balanced incomplete block designs. Clatworthy (1973) produced tables of two associate classes partially balanced designs in the practical range of r, k ≤ 10 and presented resolvable solutions whenever possible. Here, the minimum α (≤1) – resolvable solutions of partially balanced designs not found in Clatworthy (1973) and Saurabh and Sinha (2020) are presented. This paper is in sequel to the paper by Saurabh and Sinha (2020).

A SIMPLE GENERALIZED CONSTRUCTION OF RESOLVABLE BALANCED INCOMPLETE BLOCK DESIGNS WITH PRIME BLOCK SIZES

This paper presents a Simple Generalized Construction of Resolvable Balanced Incomplete Block Designs whose parameter combination is of the form $v=k^2, ~r=k+1, ~\lambda=k^0=1$, where $k$ is prime. The design construction was achieved by using the cyclic subgroup of the symmetric group $S_k$ whose generator is one of the permutations of the $2$-permutation generating set of the Dihedral group $D_k$ and $2$-permutation generating set of the presentation of $S_k$. The method is efficient, sufficient and also mitigate against the tediousness encountered in other methods of construction when $v$ is large.

On traceable results of linear error correcting codes and resolvable BIBDS

In this paper we relate how Equidistant Constant Weight Codes and Different Combinatorial Structures like Resolvable Balanced Incomplete Block Designs (RBIBD) , Nested Balanced Incomplete Block Designs (NBIBD) and Linear Codes are related with each other and then show how these Combinatorial Structures can be used as 2-Traceable (TA) Code.

ON THE EMBEDDING OF GROUPS AND DESIGNS IN A DIFFERENCE BLOCK DESIGN

A difference BIBD is a balanced incomplete block design on a group which isconstructed by transferring a regular perfect difference system by a subgroup of its point set. There is an obvious bijection between these BIBDs and some copies of their point sets as two sets. In this paper, we investigate the algebraic structure of these block designs by definning a group-isomorphism between them and their point sets. It has done by defning some relations between the independent-graphs of difference BIBDs and some Cayley graphs of their point sets. It is shown that some Cayley graphs are embedded in the independent-graph of difference BIBDs as a spanning sub-graphs. Due to find these relations, we find out a configuration ordering on these BIBDs, also we achieve some results about the classification of these BIBDs. All in this paper are on difference BIBDs with even numbers of the points.

The influence of yeasts and copper sulphate addition on aroma of Viennese Rheinriesling wines

The influence of two yeast strains and the addition of copper sulphate on the aroma of Riesling wines was monitored. Two commercially available yeast strains, Zymaflore VL3 and X-Pure, were applied. General composition, volatile thiols, norisoprenoids, free terpenes, aroma fermentation, sulphur compounds and copper content were determined, and the sensory attributes were assessed by 22 tasters in a balanced incomplete block design (BIBD). The VL3 yeast produced a higher concentration of thiols than the X-Pure yeast. Wines treated with copper sulphate showed a higher concentration of 3MH than the wines produced without copper sulphate addition for both yeast strains. Yeast strain and copper sulphate addition both influenced the amount of β-damascenone in Riesling wines significantly, but they showed no significant influence on the level of terpenes. Five out of eight rated sensory attributes showed significant differences. Yeast strain and copper sulphate addition were decisive factors for the sensory profile of experimental wines.

Combinatorial Construction of Second Order Rotatable Designs

In this paper, we constructed a new series for the construction of Second Order Rotatable Design using Partially Balanced Incomplete Block Designs (PBIBD).

Finite Euclidean Geometry Approach for Constructing Balanced Incomplete Block Design (BIBD)

&#x0D; &#x0D; &#x0D; &#x0D; In block design, construction of Balanced Incomplete Block Design (BIBD) remained an unsolved problem in combinatorial design; also various construction techniques have been introduced to build the elements of BIBDs for specific parameters; no general method has been proposed to find a suitable structure for BIBDs. This paper aim at employing Finite Euclidean Geometry FEG (N,s) of N – dimensional space to construct balanced incomplete block design (BIBD). Also geometrical construction of FEG (2,2) BIBDs has been made. The results show that this technique proved a better method for constructing BIBD than other methods in terms of estimation of parameters to build the design structure.&#x0D; &#x0D; &#x0D; &#x0D;

Nested block design as key pre-distribution in wireless sensor networks

An accumulation of wireless sensor nodes is combined together to form the Wireless Sensor Networks. The sensor nodes are distributed haphazardly without any decided method into a natural setting, which is generally inhospitable and it is difficult to provide key-chains to each node for security as they are haphazardly distributed. In this paper, we use Nested Block Design (NBD) as Key Pre-distribution Scheme (KPS) and found out that NBD support large networks with fewer keys in each node than Symmetric Balanced Incomplete Block Designs (SBIBD) and Transversal Design (TD[Formula: see text]), provide higher resiliency than SBIBDs and better connectivity than TD[Formula: see text], tradeoff between local connectivity and resiliency ([Formula: see text]) is lower than SBIBD but more than TD[Formula: see text] and key-node ratio ([Formula: see text]) is same for [Formula: see text] but lower than SBIBD.

Corrigendum: Super‐simple resolvable balanced incomplete block designs with block size 4 and index 2

AbstractIn this note, we present a corrected proof of Lemma 5.8 which was wrong due to the incorrectness of Construction 2.3, from our paper.

Optimal Bibd Extended Design Based Neighbour Discovery in Asynchronous Wsn

For asynchronous Wireless Sensor Networks (WSNs), this research suggests an ideal Balanced Incomplete Block Design (BIBD) extended design based neighbour finding technique. The algorithm takes use of the characteristics of BIBD extended designs to build a series of transmission plans that guarantee effective neighbour detection with little energy consumption and delay. Simulations are used to test the proposed algorithm, and the results show that it significantly outperforms previous approaches in terms of energy usage, latency, and scalability.&#x0D; The value of this study is in the innovative neighbour finding algorithm that it proposes, which overcomes the drawbacks of existing approaches and provides a scalable and energy-efficient solution for large-scale WSNs. The suggested technique may be used in a variety of settings, including environmental monitoring, industrial automation, and healthcare, where accurate and timely data gathering and processing depend on efficient neighbour detection.&#x0D; The suggested algorithm is implemented step by step in the technique section along with the relevant equations and tables. The simulation results for sample input data are shown in the results section along with pertinent tables and graphs. The results are outlined in the conclusion section, which also emphasises the importance of the suggested method.&#x0D; Overall, the suggested technique provides a viable option for rapid neighbour detection in WSNs, potentially having repercussions for a broad variety of applications.

A Rate Scalable Construction of Non-Homogeneous Quantum LDPC Codes of CSS Type Based on Balanced Incomplete Block Design

Balanced incomplete block design (BIBD) offers an important way to construct non-homogeneous quantum low-density-parity-check (LDPC) codes of Calderbank-Shor-Steane (CSS) type. However, the rates of the quantum codes based on this method are limited to be 1-2/m approximately, where m, the number of base blocks chosen from the associated BIBD, is even. We overcome this limitation by providing a rate scalable way to construct non-homogeneous quantum LDPC codes of CSS type. With our method, the rates of the resultant quantum codes are 1-2/m', where m'=m/e and e ∈ {1, 2}. Note that here m' can be odd. Thus, we double the rate range of the codes yielded from the existing strategies. Moreover, one can switch codes between the two rates flexibly adapting to various application scenarios.

Construction of three associate PBIB designs using K - maps

A new series of s (s ≥ 3) associate class Partially Balanced Incomplete Block (PBIB) designs have been constructed by applying hamming distance on Karnaugh maps. In this series, every character is expressed in binary set and calculate the weight, then hamming distance for each literal of k – map. We considersꞌ different factors (s≥3) simultaneously and each factor has two levels, it means each factor is introduced in primal as well as dual form.

Evaluating Measure of Modified Rotatability for Second Degree Polynomial Design Using Balanced Incomplete Block Designs

Box and Hunter (1957) introduced the concept of rotatability. It is an important design criterion for response surface methodology (RSM). In this paper, evaluating measure of modified rotatability for second degree polynomial design using balanced incomplete block designs (3 ≤ V ≤ 11 : v-number of factors) which enables us to assess the degree of modified rotatability for a given response surface designs at different values of rotatability is recommended.

Lower bounds for the spectral norm of digraphs

Let D be a digraph with n vertices and σ1(D)≥σ2(D)≥⋯≥σn(D) the singular values of the adjacency matrix A of D. The spectral norm of D is σ1(D) and the trace norm of D is ‖D‖⁎=∑i=1nσi(D). In this paper we find lower bounds for the spectral norm of a digraph in terms of the structure of the digraph. Moreover, we introduce the concept of almost regular digraphs (extension of the well known almost regular graphs), and show that the lower bounds are attained precisely in almost regular digraphs. When we apply this theory to graphs, we recover well known lower bounds for the spectral radius of graphs. Also, we give a new upper bound for the trace norm of a digraph. Moreover, we determine the digraphs for which this bound is sharp: sink-source complete bipartite digraphs or symmetric balanced incomplete block designs (BIBD).

The Impossibility of Certain Symmetrical Balanced Incomplete Block Designs

The Impossibility of Certain Symmetrical Balanced Incomplete Block Designs