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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 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]

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.

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]

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.

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]

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]

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]

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]

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]

Abstract: In this paper we study -GDDs of type possessing both the pan-decomposable property introduced by Granville, Moisiadis, Rees, On complementary decompositions of the complete graph, Graphs and Combinatorics 5 (1989) 57–61 and the pan-orientable property introduced by Grüttmüller, Hartmann, Pan-orientable block designs, Australas. J. Combin. 40 (2008) 57–68. We show that the necessary condition for a -GDD satisfying both of these properties, namely (1) , (mod ), and (2) are not both even if is odd are sufficient. When , our designs are super-simple. We also determine the spectrum of -GDDs which are super-simple and possess some of the decomposable/orientable conditions, but are not pan-decomposable or pan-orientable. In particular, we show that the necessary conditions for a super-simple directable -GDD of type are sufficient. [Copyright &y& Elsevier]

Abstract: Let be a subgraph of . 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 subgraph of for every . For every pair of positive integers , , (except when and or and ) we determine the minimum value of such that there exists a balanced incomplete block design of order , index and block-size 4 which embeds a -design of order and index ( denotes the path of length 3). [Copyright &y& Elsevier]

Abstract: In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple -BIBDs have been determined for and 6. When , the necessary conditions of such a design are that and . In this paper, we show that there exists a super-simple -BIBD for each and . [Copyright &y& Elsevier]

Abstract: We give some constructions of new infinite families of group divisible designs, GDD, including one which uses the existence of Bhaskar Rao designs. We show the necessary conditions are sufficient for . For there is one missing critical design. If , then the necessary conditions are sufficient for . For each of , and 20 we indicate a small minimal set of critical designs which, if they exist, would allow construction of all possible designs for that n. The indices of each of these designs are also among those critical indices for every n in the same congruence class mod12. [Copyright &y& Elsevier]

Abstract: Under the right conditions it is possible for the ordered blocks of a path design to be considered as unordered blocks and thereby create a . We call this a tight embedding. We show here that, for any triple system , there is always such an embedding and that the problem is equivalent to the existence of a , i.e., a -Bhaskar Rao Design. That is, we also prove the incidence matrix of any triple system can always be signed to create a and, moreover, the signing determines a natural partition of the blocks of the triple system making it a nested design. [Copyright &y& Elsevier]

Abstract: A Steiner pentagon system of order is said to be super-simple if its underlying -BIBD is super-simple; that is, any two blocks of the BIBD intersect in at most two points. In this paper, it is shown that the necessary condition for the existence of a super-simple ; namely, and or is sufficient, except for , and possibly for . In the process, we also improve an earlier result for the spectrum of super-simple -BIBDs, removing all the possible exceptions. We also give some new examples of Steiner pentagon packing and covering designs (SPPDs and SPCDs). [Copyright &y& Elsevier]

This paper presents. new methods for constructing efficiently encodable quasi-cyclic LDPC codes based on special balanced incomplete block designs (BIBD's). Codes constructed perform well over both the AWGN and binary erasure channels with iterative decoding. [ABSTRACT FROM AUTHOR]

We show the necessary conditions are sufficient for the existence of GDD(n,2,4; λ1, λ2) with two groups and block size four in which every block intersects each group exactly twice (even GDD''s) or in which every block intersects each group in one or three points (odd GDD''s). We give a construction for near 3-resolvable triple systems TS(n,3,6) for every n⩾4, and these are used to provide constructions for several families of GDDs. [Copyright &y& Elsevier]

We solve the existence problem for generalized Bhaskar Rao designs of block size 3 for an infinite family of non-abelian groups, the dihedral groups Dn, of order 2n. In our main result we show that for n&ges;1 and v&ges;3 the following set of conditions is necessary and sufficient for the existence of a GBRD(v,3,λ;Dn):

This paper introduces three new types of combinatorial designs, which we call external difference families (EDF), external BIBDs (EBIBD) and splitting BIBDs. An EDF is a special type of EBIBD, so existence of an EDF implies existence of an EBIBD. We construct optimal splitting A-codes by using EDF. Then we give a new bound on the number of shares required in robust secret sharing schemes (i.e., schemes secure against cheaters). EDF can be used to construct robust secret sharing schemes that are optimal with respect to the new bound. We also prove a weak converse, showing that if there exists an optimal secret sharing scheme, then there exists an EBIBD. Finally, we derive a Fisher-type inequality for splitting BIBDs. We also prove a weak equivalence between splitting BIBDs and splitting A-codes. Further, it is shown that an EDF implies a splitting BIBD. [Copyright &y& Elsevier]

The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that λ(v−1)≡0 mod (k−1), λv(v−1)≡0 mod k(k−1). In this paper we study k=9 with λ=3, 6 and 12. We show that these conditions on v are sufficient, with the possible exceptions of v=177, 345, 385 when λ=3, and v=213 when λ=6. We give constructions of TD3(10,n)s with 13 possible exceptions, namely n∈{5,6,14,20,35,45,55,56,60,78,84,85,102}; we also reduce the number of unknown TDs with block sizes 8 and 9. [Copyright &y& Elsevier]

New constructions of Bhaskar Rao designs (BRDs) and new families of c-BRDs are given using the relationship of BRDs to other combinatorial structures. For example, we use different families and their properties in various ways to obtain natural signings of BIBDs in order to construct c-BRDs. We investigate the extreme possibilities for c relative to λ, and k relative to v, and prove the non-existence of an infinite series of designs. We also give a symmetricized version of Ehlich''s Hadamard construction. [Copyright &y& Elsevier]

A Bhaskar Rao design, i.e., a BRD(v,k,λ), is formed by signing the v by b incidence matrix of a BIBD(v,k,λ) so that the inner product of any two distinct rows is 0. It is proved in the literature that such designs exist for k=4 with 28 possible exceptions. In this paper, we show that a BRD is equivalent to a special kind of group divisible design (GDD). By using the knowledge of GDDs, we resolve the open cases of BRD(v,4,λ) and complete the spectrum problem on their existence. [Copyright &y& Elsevier]

An enclosing of BIBD(v,3,λ) into BIBD(v+s,3,λ+1) is point-wise minimal if s is the smallest positive integer for which an enclosing is possible. We show that the necessary conditions are sufficient for a minimal point-enclosing of any BIBD(v,3,λ) into BIBD(v+s,3,λ+1) for 1&les;λ&les;6. Some other general results on enclosings are presented. [Copyright &y& Elsevier]

In this article we resolve some of the open problems left in two other articles. A c-Bhaskar Rao design, i.e., a c-BRD(v,k,λ), is formed by signing the v by b incidence matrix of a BIBD(v,k,λ) so that the inner product of any two distinct rows is c. We complete Greig, Hurd, McCranie and Sarvate''s work on the spectrum of c-BRD(v,4,λ) when c ≠ 0. In the classic (i.e., c = 0) case, we establish the existence of 0-BRD(3t+1,4,2) for all 3t+1&ges;433, with at most 30 smaller exceptions, all with t odd. Morgan, Preece and Rees have given a list of nested BIBDs with v&les;16 and r&les;30; they have one open case. By reformulating this problem, and constructing a (−1)-BRD(16,10,9), we provide a solution for this open case. [Copyright &y& Elsevier]

The smallest BIBD, as for the number of points and blocks, whose existence is still undecided is 2-(22, 8, 4). Possible subconfigurations of such a design, namely 2-(10, 4, 4) designs, are here ruled out. The result is obtained by classifying all 2-(10, 4, 4) designs and trying to find 2-(22, 8, 4) designs by solving instances of the maximum clique problem. [ABSTRACT FROM AUTHOR]

We consider 2-(9, 3, λ) designs, which are known to exist for all λ ≥ 1, andenumerate such designs for λ = 5 and their resolutions for 3 ≤ λ ≤ 5, the smallestopen cases. The number of nonisomorphic such structures obtained is 5 862 121 434, 426, 149 041, and 203 047732, respectively. The designs are obtained by an orderly algorithm, and the resolutions by two approaches:either by starting from the enumerated designs and applying a clique-finding algorithm on two levels or by anorderly algorithm. [ABSTRACT FROM AUTHOR]

The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: In this paper we study k=9 with λ=2,4 or 8. For λ=8, we show these conditions on v are sufficient, and for λ=2, 4 respectively there are 8 and 3 possible exceptions the largest of which are v=1845 and 783. We also give some examples of group divisible designs derived from balanced ternary designs. [ABSTRACT FROM AUTHOR]

The object of this paper is the construction of balanced incomplete block designs with k=7. This paper continues the work begun by Hanani, who solved the construction problem for designs with a block size of 7, and with λ=6, 7, 21 and 42. The construction problem is solved here for designs with λ > 2 except for v=253, λ= 4,5 ; also for λ= 2, the number of unconstructed designs is reduced to 9 (1 nonexistent, 8 unknown). [ABSTRACT FROM AUTHOR]

The necessary condition for the existence of a resolvable balanced incomplete block design on v points, with λ = 1 and k = 8, is that v ≡ 8 mod 56. With the exception of 66 values of v, this condition is shown to be sufficient. The largest exceptional value of v is 24480. [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. [ABSTRACT FROM AUTHOR]