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A design is said to be super‐simple if the intersection of any two blocks has at most two elements. A design with index tλ $t\lambda $ is said to be λt ${\lambda }^{t}$‐decomposable, if its blocks can be partitioned into nonempty collections Bi ${{\rm{ {\mathcal B} }}}_{i}$, 1≤i≤t $1\le i\le t$, such that each Bi ${{\rm{ {\mathcal B} }}}_{i}$ with the point set forms a design with index λ $\lambda $. In this paper, it is proved that there exists a 23 ${2}^{3}$‐decomposable super‐simple (v,4,6) $(v,4,6)$‐BIBD (balanced incomplete block design) if and only if v≥16 $v\ge 16$ and v≡1(mod3) $v\equiv 1(\,\mathrm{mod}\,\,3)$. [ABSTRACT FROM AUTHOR]

The exclusion basis system is a combinatorial formulation of group key management that provides long-term and flexible protection for wireless sensor networks while allowing for reasonable adjustment of the number of keys per node and the number of re-key messages. In this paper, we extend the work of Karst and Wicker to near-resolvable design, symmetric balanced incomplete block designs, and balanced incomplete block designs with the repetition count of a distinct pair of elements equal to one, and it is observed that near-resolvable design provides minimal re-keying compared to symmetric balanced incomplete block designs and balanced incomplete block designs. Also, near-resolvable design and exclusion basis system have the same re-keying size when the number of keys is n - 1 . [ABSTRACT FROM AUTHOR]

A design is said to be super‐simple if the intersection of any two of its blocks has at most two elements. A design with index tλ $t\lambda $ is said to be λ $\lambda $‐decomposable, if its blocks can be partitioned into nonempty collections ℬi ${{\rm{ {\mathcal B} }}}_{i}$, 1≤i≤t $1\le i\le t$, such that each ℬi ${{\rm{ {\mathcal B} }}}_{i}$ with the point set forms a design with index λ $\lambda $. In this paper, it is proved that for λ∈{2,4} $\lambda \in \{2,4\}$, there exists a λ $\lambda $‐decomposable super‐simple (4,2λ) $(4,2\lambda)$‐GDD of type gu ${g}^{u}$ if and only if u≥4 $u\ge 4$, g(u−2)≥2λ $g(u-2)\ge 2\lambda $ and g(u−1)≡0(mod3) $g(u-1)\equiv \,0\,(\mathrm{mod}\,3)$, except for (g,u,λ)=(3,5,2) $(g,u,\lambda)=(3,5,2)$, and except possibly for (g,u,λ)∈{(2,7,2),(6,5,4)} $(g,u,\lambda)\in \{(2,7,2),(6,5,4)\}$. [ABSTRACT FROM AUTHOR]

This paper is to give a novel Jackknife Empirical Likelihood for both smooth and unsmooth statistical functionals. Specifically, we consider the estimation of unknown statistical functionals under the framework of general delete-d jackknife and a usage of the subsampling method which can reduce the computational burden. Moreover, the corresponding statistical inference issues and asymptotic properties of the proposed method are also investigated. Several related application examples are carefully conducted to check the superiority of our new proposed method. Finally, the finite sample simulation studies are also included. [ABSTRACT FROM AUTHOR]

Decomposable designs are important combinatorial designs, and have applications in constant weight codes, perfect threshold schemes and graph decompositions. Let λ $\lambda $ be an even positive integer. A λ2 $\frac{\lambda }{2}$‐decomposable super‐simple (v,k,λ) $(v,k,\lambda)$‐balanced incomplete block design (BIBD) is a super‐simple (v,k,λ) $(v,k,\lambda)$‐BIBD, (V,ℬ) $(V,{\rm{ {\mathcal B} }})$, where ℬ=ℬ1∪ℬ2 ${\rm{ {\mathcal B} }}={{\rm{ {\mathcal B} }}}_{1}\cup {{\rm{ {\mathcal B} }}}_{2}$, and each (V,ℬi) $(V,{{\rm{ {\mathcal B} }}}_{i})$ is a (v,k,λ2) $(v,k,\frac{\lambda }{2})$‐BIBDs for i=1,2 $i=1,2$. In this paper, for λ∈{4,6} $\lambda \in \{4,6\}$, it is proved that the necessary conditions for the existence of a λ2 $\frac{\lambda }{2}$‐decomposable super‐simple (v,4,λ) $(v,4,\lambda)$‐BIBD are also sufficient. [ABSTRACT FROM AUTHOR]

U-statistics are widely used in fields such as economics, machine learning, and statistics. However, while they enjoy desirable statistical properties, they have an obvious drawback in that the computation becomes impractical as the data size n increases. Specifically, the number of combinations, say m, that a U-statistic of order d has to evaluate is O(nd). Many efforts have been made to approximate the original U-statistic using a small subset of combinations since Blom (1976), who referred to such an approximation as an incomplete U-statistic. To the best of our knowledge, all existing methods require m to grow at least faster than n, albeit more slowly than nd, in order for the corresponding incomplete U-statistic to be asymptotically efficient in terms of the mean squared error. In this paper, we introduce a new type of incomplete U-statistic that can be asymptotically efficient, even when m grows more slowly than n. In some cases, m is only required to grow faster than √n. Our theoretical and empirical results both show significant improvements in the statistical efficiency of the new incomplete U-statistic. [ABSTRACT FROM AUTHOR]

In this article, we present a gauge R & R study that is different from the standard setup in several ways. A balanced incomplete block design (BIBD) was used to collect the data because the measurement is destructive. Besides addressing reproducibility, differences in repeatability (i.e., tester variances) were also of interest. Here we use Bayesian methods to analyze the study data to address whether the three tester means and variances are similar. We also consider what happens if the BIBD structure of the data and possibly different tester variances are ignored in analyzing the study data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We introduce here a quick and easy new technique for comparing efficiencies of Partially Balanced Incomplete Block Designs (PBIBDs) with the same values of the parameters v, b, r and k. We demonstrate the use of the newly proposed technique by first constructing some PBIBDs based on some association scheme and then comparing some of the newly constructed PBIBDs with designs already existing in literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to highlight the importance of planar near-rings (PNR) in the construction of balanced incomplete block designs (BIBD), then to give a new precise formula to blocks of this type of BIBD which enables us to generate useful matrices based on the incidence matrix. Moreover, we will improve the efficiency factor and determine the condition to produce a symmetric BIBD from a BIBD. [ABSTRACT FROM AUTHOR]

Incomplete block designs play an important role in both theory and practical for using Mutually Orthogonal Latin Squares (MOLS) and also many incomplete designs are available in the construction for design of experiments, the main drawback hails from their existence for all sets of parameters. Hence, the aspect of their construction becomes very important. In the realm of construction, no unique methodology exists. Different methods of construction of these designs exist in literature. In this paper, the construction of Balanced Incomplete Block Designs (BIBD) through two factorization and coloring graphs using MOLS has been discussed. Application of this method has been established through illustrations. [ABSTRACT FROM AUTHOR]

The number of blocks of all the known series of Incomplete Block Neighbour (IBN) designs are mostly multiple of number of treatments. In this paper, introducing two invariant elements in the initial blocks, the solution of some series of new IBN designs, whose number of blocks is not a multiple of number of treatments are presented. [ABSTRACT FROM AUTHOR]

In this paper, we observe simple yet subtle interconnections among design theory, coding theory and cryptography. Maximum distance separable (MDS) matrices have applications not only in coding theory but are also of great importance in the design of block ciphers and hash functions. It is nontrivial to find MDS matrices which could be used in lightweight cryptography. In the SAC 2004 paper [12], Junod and Vaudenay considered bi-regular matrices which are useful objects to build MDS matrices. Bi-regular matrices are those matrices all of whose entries are nonzero and all of whose 2×2{2\times 2} submatrices are nonsingular. Therefore MDS matrices are bi-regular matrices, but the converse is not true. They proposed the constructions of efficient MDS matrices by studying the two major aspects of a d×d{d\times d} bi-regular matrix M, namely v1⁢(M){v_{1}(M)}, i.e. the number of occurrences of 1 in M, and c1⁢(M){c_{1}(M)}, i.e. the number of distinct elements in M other than 1. They calculated the maximum number of ones that can occur in a d×d{d\times d} bi-regular matrices, i.e. v1d,d{v_{1}^{d,d}} for d up to 8, but with their approach, finding v1d,d{v_{1}^{d,d}} for d≥9{d\geq 9} seems difficult.

The affine linear group of degree one, AGL (1 , F q) , over the finite field F q , acts sharply two-transitively on F q . Given S < AGL (1 , F q) and an integer k, 1 ≤ k ≤ q , does there exist a k-element subset B ⊂ F q whose set-wise stabilizer is S? Our main result is the derivation of two formulas which provide an answer to this question. This result allows us to determine all possible parameters of binary constant weight codes that are constructed from the action of AGL (1 , F q) on F q to meet the Johnson bound. Consequently, for many parameters, we are able to determine the values of the function A 2 (n , d , w) , which is the maximum number of codewords in a binary constant weight code of length n, weight w and minimum distance ≥ d . [ABSTRACT FROM AUTHOR]

In this paper, an empirical study on second order rotatable designs under intra-class correlated structure of errors using a pair of balanced incomplete block designs (BIBD) is suggested. Further, the variance function of the estimated response for different values of intra-class correlated coefficient (ρ) and distance from centre (d) for v factors is suggested. [ABSTRACT FROM AUTHOR]

Reptarenaviruses cause Boid Inclusion Body Disease (BIBD), and co-infections by several reptarenaviruses are common in affected snakes. Reptarenaviruses have only been found in captive snakes, and their reservoir hosts remain unknown. In affected animals, reptarenaviruses appear to replicate in most cell types, but their complete host range, as well as tissue and cell tropism are unknown. As with other enveloped viruses, the glycoproteins (GPs) present on the virion’s surface mediate reptarenavirus cell entry, and therefore, the GPs play a critical role in the virus cell and tissue tropism. Herein, we employed single cycle replication, GP deficient, recombinant vesicular stomatitis virus (VSV) expressing the enhanced green fluorescent protein (scrVSV∆G-eGFP) pseudotyped with different reptarenavirus GPs to study the virus cell tropism. We found that scrVSV∆G-eGFPs pseudotyped with reptarenavirus GPs readily entered mammalian cell lines, and some mammalian cell lines exhibited higher, compared to snake cell lines, susceptibility to reptarenavirus GP-mediated infection. Mammarenavirus GPs used as controls also mediated efficient entry into several snake cell lines. Our results confirm an important role of the virus surface GP in reptarenavirus cell tropism and that mamma-and reptarenaviruses exhibit high cross-species transmission potential.

In this paper, an empirical study of second order rotatable designs under tri-diagonal correlated structure of errors using balanced incomplete block designs is suggested. Further the variance function of the estimated response for tridiagonal correlated coefficient (ρ) and distance from centre (d) is studied. It is shown that this method sometimes leads to designs with less number of design points in some cases. [ABSTRACT FROM AUTHOR]

In this paper, a measure of rotatability for second order response surface designs using symmetrical unequal block arrangements with two unequal block sizes when r > 3λ is suggested, which enables us to assess the degree of rotatability for second order response surface designs. This method leads to measure of rotatability for second order response surface designs with lesser number of design points than the measure of rotatability for second order response surface designs using incomplete block designs, in some cases. [ABSTRACT FROM AUTHOR]

Disk failures are very common in modern storage systems due to the large number of inexpensive disks. As a result, it takes a long time to recover a failed disk due to its large capacity and limited I/O. To speed up the recovery process and maintain a high system reliability, we propose a hierarchical code architecture with erasure codes, OI-RAID, which consists of two layers of codes, outer layer code and inner layer code. Specifically, the outer layer code is deployed with disk grouping technique based on Balanced Incomplete Block Design (BIBD) or complete graph with skewed data layout to provide efficient parallel I/O of all disks for fast failure recovery, and the inner layer code is deployed within each group of disks to provide high reliability. As an example, we deploy RAID5 in both layers to achieve fault tolerance of at least three disk failures, which meets the requirement of data availability in practical systems, as well as much higher speed up ratio for disk failure recovery than existing approaches. Besides, OI-RAID also keeps the optimal data update complexity and incurs low storage overhead in practice. [ABSTRACT FROM AUTHOR]

Pneumonia is a common complication of boid inclusion body disease (BIBD) in snakes. The tracheal mucociliary apparatus of eight boas ( Boa constrictor) and two pythons ( Python regius, Morelia viridis) was examined to assess whether absent or reduced mucociliary clearance could be a predisposing factor. Nine of the examined snakes were positive for BIBD by detection of inclusion bodies and three had lung pathologies other than the formation of inclusion bodies. A considerable individual variation of ciliary beat frequency (CBF, 3.0 ± 0.75 Hz to 7.8 ± 1.27 Hz), transport speed (23.1 ± 12.56 μm/sec to 189.2 ± 41.17 μm/sec), and transport direction (−12.5° ± 11.43° to 36.1° ± 7.53°) was found. CBFs of the BIBD-affected snakes with or without lung pathologies were markedly lower than ranges published for birds or mammals, but the net transport speeds and directions lay well within. The present investigation does therefore not reveal any signs of an inadequate mucociliary clearance in BIBD-affected snakes. [ABSTRACT FROM AUTHOR]

We introduce some sequences of binary constant weight codes which are constructed from the affine constructions of balanced incomplete block designs. They give the values for the function of constant weight codes, and they are optimal since those values reach the Johnson Bound. We focus on the values obtained by this method. [ABSTRACT FROM AUTHOR]

Three methods of constructions of efficient block designs for symmetric parallel line assays have been proposed. These methods are based on balanced incomplete block design (BIBD). Through these designs, all contrasts of interest can be estimated free from block effect and with high efficiency. Any BIB design for which v, the number treatments is strictly greater than twice of block size can be converted into a design that can be used for conducting a symmetric parallel line assay. All methods of construction are demonstrated with some examples. [ABSTRACT FROM AUTHOR]

This paper presents two packings derived from balanced incomplete block designs to construct quasi-cyclic spatially coupled LDPC convolutional codes (SC-LDPC-CCs). The construction gives time-invariant codes, since the sub-blocks corresponding to each time instant of the parity-check matrix are identical. Moreover, it provides flexible design rates and constraint lengths. Simulation results show that the proposed packing-based SC-LDPC-CCs outperform the existing time-invariant codes and perform closely to the time-varying protograph-based codes. [ABSTRACT FROM AUTHOR]

polygons, are useful in survey sampling in terms of balanced sampling plans excluding contiguous units (BSECs) and balanced sampling plans excluding adjacent units (BSAs) when neighboring units in a population provide similar information. In this paper, themethod of cyclic shifts is used and cyclic polygonal designs (CPDs) are constructed with block size k  3 and   1, 2, 3, 4, 6,12 for joint distance   3 and v{21, 22, ,100}treatments.

A design is said to be super-simple if the intersection of any two blocks has at most two elements. A design with index λ is said to be { λ 1 s 1 , λ 2 s 2 , ... , λ r s r } - decomposable , with ∑ i = 1 r s i λ i = λ , if its blocks can be partitioned into nonempty collections B i j , 1 ≤ i ≤ r , 1 ≤ j ≤ s i , such that each B i j with the point set forms a design with index λ i , 1 ≤ λ i < λ. In this paper, it is proved that there exists a 42-decomposable super-simple (v , 4 , 8) -BIBD (balanced incomplete block design) if and only if v ≡ 1 (mod 3) and v ≥ 19. [ABSTRACT FROM AUTHOR]

This paper proposes a group-based collusion-secure code design technique for protecting copyrights on digital contents. Designing collusion-secure codes were difficult and there were problems in creating these codes in large numbers, as these codes should enable detecting collusion attacks when occurring in content with inserted forensic marks. In addition, there was a problem in applying these codes to actual services in that unique user-specific codes could not be issued. This paper proposes group anti-collusion codes (ACCs) made by introducing the concept of groups to existing balanced incomplete block design (BIBD) matrices. This would solve the problem of complexity in code design and increase the number of collusion-secure codes. For the group ACCs, problems in securing the uniqueness and verification of codes were overcome using set operations. Using the group ACCs, code complexity can be reduced when compared to existing collusion-secure codes, and code quantities can be increased when compared to code lengths. [ABSTRACT FROM AUTHOR]

Choreoathetoid involuntary movements are rarely reported in patients with frontotemporal lobar degeneration (FTLD), suggesting their exclusion as a supportive feature in clinical diagnostic criteria for FTLD. Here, we identified three cases of the behavioral variant of frontotemporal dementia (bvFTD) that display chorea with fused in sarcoma (FUS)-positive inclusions (FTLD-FUS) and the basophilic inclusion body disease (BIBD) subtype. We determined the behavioral and cognitive features in this group that were distinct from other FTLD-FUS cases. We also reviewed the clinical records of 72 FTLD cases, and clarified additional clinical features that are predictive of the BIBD pathology. Symptom onset in the three patients with chorea was at 44.0 years of age (±12.0 years), and occurred in the absence of a family history of dementia. The cases were consistent with a clinical form of FTD known as bvFTD, as well as reduced neurological muscle tone in addition to chorea. The three patients showed no or mild parkinsonism, which by contrast, increased substantially in the other FTLD cases until a later stage of disease. The three patients exhibited severe caudate atrophy, which has previously been reported as a histological feature distinguishing FTLD-FUS from FTLD-tau or FTLD-TAR DNA-binding protein 43. Thus, our findings suggest that the clinical feature of choreoathetosis in bvFTD might be associated with FTLD-FUS, and in particular, with the BIBD subtype. [ABSTRACT FROM AUTHOR]

Balanced block designs and in particular balanced incomplete block designs (BIBDs) have been in widespread use in agricultural, ecological, pharmaceutical, and industrial research for many years. However, this “balance” characteristic is only true for BIBDs with uncorrelated observations. With correlated observations within each block, the order of the observations matters and this order impacts variance and hence any notion of “balance”. Thus, there is need of research into construction of these useful designs when any one of a number of different correlation structures might exist within each block of units. In this paper, based on Balanced Incomplete Block Designs (BIBDs), we construct weak universal optimal block designs for the nearest neighbor correlation structure with common block sizes, for the hub correlation structure with any block size, and for circulant correlation with odd block size. We also approximate weak universal optimal block designs for the block-structured correlation. [ABSTRACT FROM AUTHOR]

Bannai–Bannai–Bannai studied intensively the tight relative 2-designs on two shells in H ( n , 2 ) and gained many important results. Their results indicate the relationship among relative t -designs in binary Hamming association schemes, combinatorial t -designs and Hadamard matrices. In this note we study the further relationship between tight relative 2-designs on two shells in H ( n , 2 ) and them. We first prove that the existence of a special tight relative 2-design of H ( n , 2 ) on two shells is equivalent to that of a Hadamard matrix of size m + 1 , where m ≡ − 1 ( mod 4 ) and n = 2 m ; we also show how tight relative 2-designs of H ( n , 2 ) on two shells and BIBD or λ -linked designs are related. Next, for each integer n , where 30 < n ≤ 50 , we determine whether there exists such a tight relative 2-design or not using the above results. Finally, we give a possible list of parameters for the existence of tight relative 2-designs on two shells in H ( n , 2 ) with non-constant weight. [ABSTRACT FROM AUTHOR]

By means of a search design one is able to search for and estimate a small set of non-zero elements from the set of higher order factorial interactions in addition to estimating the lower order factorial effects. One may be interested in estimating the general mean and main effects, in addition to searching for and estimating a non-negligible effect in the set of 2- and 3-factor interactions, assuming 4- and higher-order interactions are all zero. Such a search design is called a 'main effect plus one plan' and is denoted by MEP.1. Construction of such a plan, for 2 m factorial experiments, has been considered and developed by several authors and leads to MEP.1 plans for an odd number m of factors. These designs are generally determined by two arrays, one specifying a main effect plan and the other specifying a follow-up. In this paper we develop the construction of search designs for an even number of factors m, m≠6. The new series of MEP.1 plans is a set of single array designs with a well structured form. Such a structure allows for flexibility in arriving at an appropriate design with optimum properties for search and estimation. [ABSTRACT FROM AUTHOR]

Abstract: We investigated the pathological features of frontotemporal lobar degeneration (FTLD) with fused in sarcoma protein (FUS) accumulation (FTLD-FUS) in the Japanese population. Only one out of nine FTLD-FUS cases showed pathology that corresponds to atypical FTLD with ubiquitin-positive inclusions (aFTLD-U). Five were basophilic inclusion body disease (BIBD) and two were neuronal intermediate filament inclusion disease. The last case was unclassifiable and was associated with dystrophic neurites (DNs) as the predominant FUS pathology. The results of this study indicate an ethnic difference from western countries. In Japan, BIBD is the most common subtype of FTLD-FUS and aFTLD-U is rare, a finding which contrasts with aFTLD-U being the most common form in western countries. Immunohistochemical analyses of these FTLD-FUS cases reveal that FUS abnormally accumulated in neuronal cytoplasmic inclusions (NCIs) and DNs has an immunohistochemical profile distinct from that of normal, nuclear FUS. NCIs and DNs are more readily stained than the nuclei by antibodies to the middle portion of FUS. Antibodies to the carboxyl terminal portion, on the other hand, stain the nuclei more readily than NCIs and DNs. Such an immunohistochemical profile of NCIs and DNs was similar to that of cytoplasmic granular FUS staining which we previously reported to be associated with dendrites and synapses. Redistribution of FUS from the nucleus to the cytoplasm could be associated with the formation of abnormal FUS aggregates in FTLD-FUS. [Copyright &y& Elsevier]

Abstract: Super-simple designs are useful in constructing codes and designs such as superimposed codes and perfect hash families. In this article, we investigate the existence of a super-simple balanced incomplete block design and show that such a design exists if and only if and except possibly when . [Copyright &y& Elsevier]

A pseudo ( v, k, λ)-design is a pair $(X, \mathcal{B})$, where X is a v-set, and $\mathcal{B}=\{B_{1},\ldots,B_{v-1}\}$ is a collection of k-subsets (blocks) of X such that any two distinct B, B intersect in λ elements, and 0≤ λ< k≤ v−1. We use the notion of pseudo designs to characterize graphs of order n whose (adjacency) spectrum contains zero and ± θ with multiplicity ( n−3)/2 where $0<\theta\le\sqrt{2}$. Meanwhile, partial results confirming a conjecture of O. Marrero on a characterization of pseudo ( v, k, λ)-designs are obtained. [ABSTRACT FROM AUTHOR]

A twofold pentagon system of order v is a decomposition of the complete undirected 2-multigraph 2 K into pentagons. A twofold Steiner pentagon system of order v [TSPS( v)] is a twofold pentagon system such that every pair of distinct vertices is joined by a path of length two in exactly two pentagons of the system. A TSPS( v) is said to be super-simple if its underlying ( v, 5, 4)-BIBD is super-simple; that is, if any two blocks of the BIBD intersect in at most two points. In this paper, it is shown that the necessary conditions for the existence of a super-simple TSPS( v); namely, v ≥ 15 and v ≡ 0 or 1 ( mod 5) are sufficient. For these specified orders, the main result of this paper also guarantees the existence of a very special and interesting class of twofold and fourfold Steiner pentagon systems of order v with the additional property that, for any two vertices, the two or four paths of length two joining them are distinct. [ABSTRACT FROM AUTHOR]

Abstract: Let be a subgraph of a graph . An -design of order and index is embedded into a -design of order and index if , and there is an injective mapping such that is a subgraph of for every . The mapping is called the embedding of into . We determine, for every admissible value of and , the minimum value of (except values of ) such that every can be embedded into an . This result implies that we determine also the minimum value of w such that there exists an which embeds an , where is the graph with two parallel edges and without isolated vertices. [Copyright &y& Elsevier]

Abstract: We show the necessary conditions are sufficient for the existence of group divisible designs (or PBIBDs) with block size with three groups of size for any and any two indices with . [Copyright &y& Elsevier]

A balanced incomplete block design (BIBD) is instrumental in design of experiments. This is usually constructed by algebraic methods such as finite algebra or difference sets. However, in algebraic approaches, no unified method exists, and each BIBD has been constructed in some ad hoc ways. On the other hand, computer-based methods apply the same algorithm to all BIBDs; hence, these are unified approaches. Although various meta-heuristic algorithms have been tried, the success of these methods has been rather limited. This article presents an alternative approach to this problem that formulates the problem as a nonlinear mixed integer programming problem. We develop a branch-and-bound algorithm to solve this, and a tabu search algorithm to overcome some weakness in the former algorithm. We compare the performance of these algorithms against some previously developed algorithms, and demonstrate that our algorithms are competitive to these methods. [ABSTRACT FROM AUTHOR]

Wang and Yin have established the existence of a directed BIBD with block size 7 and index 1 (a DBIBD( v, 7, 1)) for all v ≡ 1, 7 (mod 21) except for v = 22 and possibly for 68 other cases. In this paper, we reduce the number of possible exceptions to 4, namely v = 274, 358, 400, 526. Correspondingly, for all such v, our results establish the existence of a T(2, 7, v)-code or equivalently a perfect 5-deletion-correcting code with words of length 7 over an alphabet of size v, where all the coordinates must be different. In the process, we also reduce the possible exceptions for ( v, 7, 2)-BIBDs to 2 cases, v = 274 and 358 (in addition to the non-existent (22, 7, 2)-BIBD). [ABSTRACT FROM AUTHOR]

For secure communications in wireless sensor network in adversarial conditions, one way is providing keys to sensor nodes before deployment. Two sensor nodes can communicate provided they have at least one key in common or there is a path between the two nodes where each pair of neighboring nodes on this path has at least one key in common. However node compromise poses severe security threats in sensor networks. Here we have considered dual BIBD design for the distribution of the keys such that any pair of sensors has exactly one key in common. In this scenario we study the probability of disconnection when a number of nodes, not more than the replication number of the keys are compromised and the resulting status of the network in terms of its resiliency properties. [ABSTRACT FROM AUTHOR]