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[Display omitted] • Rational block design (composition, sequence and length) has established a new diblock copolymer (BP 20) that realizes efficient cytosolic protein delivery both in vitro and in vivo. • When mixed with proteins, BP 20 forms stable nanoparticles and mediates efficient cytosolic delivery of a wide range of proteins including enzymes, toxic proteins and CRISPR/Cas9 ribonucleoproteins (RNP), to various cell lines. • BP 20 modified with folic acid (FA) enables tumor-targeted delivery of Saporin in vivo , which significantly suppresses the tumor growth. Polymer-mediated cytosolic protein delivery demonstrates a promising strategy for the development of protein therapeutics. Here, we propose a new designed diblock copolymer which realizes efficient cytosolic protein delivery both in vitro and in vivo. The polymer contains one protein-binding block composed of phenylboronic acid (PBA) and N-(3-dimethylaminopropyl) (DMAP) pendant units for protein binding and endosomal escape, respectively, followed by the response to ATP enriched in the cytosol which triggers the protein release. The other block is PEG designed to improve particle size control and circulation in vivo. By optimizing the block composition, sequence and length of the copolymer, the optimal one (BP 20) was identified with the binding block containing 20 units of both PBA and DMAP, randomly distributed along the chain. When mixed with proteins, the BP 20 forms stable nanoparticles and mediates efficient cytosolic delivery of a wide range of proteins including enzymes, toxic proteins and CRISPR/Cas9 ribonucleoproteins (RNP), to various cell lines. The PEG block, especially when further modified with folic acid (FA), enables tumor-targeted delivery of Saporin in vivo , which significantly suppresses the tumor growth. Our results shall inspire the design of novel polymeric vehicles with robust capability for cytosolic protein delivery, which holds great potential for both biological research and therapeutic applications. [ABSTRACT FROM AUTHOR]

In this note we answer positively a question of Chris Godsil and Karen Meagher on the existence of a 2-design whose block graph has a non-canonical maximum clique without a design structure. [ABSTRACT FROM AUTHOR]

A μ-way (v,k,t) trade T of volume m consists of μ pairwise disjoint collections Ti,...,Tμ, each of m blocks of size k such that for every t-subset of a v-set V, the number of blocks containing this t-subset is the same in each Ti for 1 ≤ i ≤ μ. If any t-subset of the v-set V occurs at most once in each Ti for 1 ≤ i ≤ μ, then T is called a μ-way (v, k, t) Steiner trade. In 2016, it was proved that there exists a 3-way (v, k, 2) Steiner trade of volume m when 12(k - 1) ≤ m for each k. Here we improve the lower bound to 8(k - 1) for even k, by using a recursive construction. [ABSTRACT FROM AUTHOR]

The usual procedure for indentifying the block design to be connected is rank of C matrix (information matrix) should be (v - 1), if this violates then design becomes disconnected. Several authors obtained robustness criteria against the loss of one block or more than one blocks based on connected property. Because connectedness is one of the important criteria to find the robustness of the residual design. Tsai and Liao (2013) discussed the minimum break down criteria and connectedness criteria of block design to obtain the robust design against the lost of whole block. In this investigation, we have developed other criteria, which is alternate method of Tsai and Liao (2013) to find connectedness of the block design based on block information matrix, Fd of the block design of size two. Further, we have also observed as numbers of blocks are being deleted, the overall A-efficiency of the residual design decreases. [ABSTRACT FROM AUTHOR]

General Efficiency Balance (GEB) is an important property of designs. Variance balance and efficiency balance are special cases of GEB. Here, GEB block designs for comparing treatments belonging to two disjoint sets in the presence of systematic trend have been discussed. Methods of constructing Trend Resistant General Efficiency Balanced Bipartite Block Designs (TR-GEBBPB) designs have been presented. The block designs so obtained are trend resistant, GEB and are more efficient for estimating the contrasts pertaining to two treatments from two different sets.

In this paper we construct distance-regular graphs admitting a vertex transitive action of the five sporadic simple groups discovered by E. Mathieu, the Mathieu groups M 11 , M 12 , M 22 , M 23 and M 24 . From the binary code spanned by an adjacency matrix of the strongly regular graph with parameters (176,70,18,34) we obtain block designs having the full automorphism groups isomorphic to the Higman-Sims finite simple group. Moreover, from that code we obtain eight 2-designs having the full automorphism group isomorphic to M 22 , whose existence cannot be explained neither by the Assmus-Mattson theorem nor by a transitivity argument. Further, we discuss a possibility of permutation decoding of the codes spanned by adjacency matrices of the graphs constructed and find small PD-sets for some of the codes. [ABSTRACT FROM AUTHOR]

Let v, k, t be positive integers and let $ G(v,k,t) $ G (v , k , t) be the uniform subset graph, defined by all k-subsets of a v-set as its vertices with edges connecting all k-subsets intersecting exactly at t elements. In this paper, we give non-trivial dominating sets for $ G(v,k,2) $ G (v , k , 2) -graphs and their complements for k = 3, 4, 5, 6. The given domination numbers of some of these graphs are sharper than the known bounds. [ABSTRACT FROM AUTHOR]

Often, comparative experiments involve a single treatment factor and two blocking factors, for example, augmented row–column, two‐phase, and incomplete row–column experiments. These experiments are widely used in agriculture. Finding good designs for these experiments is a major challenge when the number of treatments is large and the blocking structure is complex. In this paper, we first propose a new search algorithm that is combined with efficient update formulae, so that optimal designs with two blocking factors can be found within a reasonable time. Second, we compare augmented row–column designs generated with our new method to those obtained from CycDesigN, DiGGer, and the OPTEX procedure of SAS in terms of computing times as well as the quality of solutions. Third, we illustrate our proposed approach with four applications. We show an example where our efficient update formulae work while existing update formulae cannot be applied, and we use our search framework to generate augmented row–column, two‐phase, and incomplete row–column designs. We end the paper with a conclusion along with suggestions for potential applications. [ABSTRACT FROM AUTHOR]

Empirical likelihood enables a nonparametric, likelihood-driven style of inference without restrictive assumptions routinely made in parametric models. We develop a framework for applying empirical likelihood to the analysis of experimental designs, addressing issues that arise from blocking and multiple hypothesis testing. In addition to popular designs such as balanced incomplete block designs, our approach allows for highly unbalanced, incomplete block designs. We derive an asymptotic multivariate chi-square distribution for a set of empirical likelihood test statistics and propose two single-step multiple testing procedures: asymptotic Monte Carlo and nonparametric bootstrap. Both procedures asymptotically control the generalised family-wise error rate and efficiently construct simultaneous confidence intervals for comparisons of interest without explicitly considering the underlying covariance structure. A simulation study demonstrates that the performance of the procedures is robust to violations of standard assumptions of linear mixed models. We also present an application to experiments on a pesticide. [ABSTRACT FROM AUTHOR]

We prove that for n \in \mathbb N and an absolute constant C, if p \geq C\log ^2 n / n and L_{i,j} \subseteq [n] is a random subset of [n] where each k\in [n] is included in L_{i,j} independently with probability p for each i, j\in [n], then asymptotically almost surely there is an order-n Latin square in which the entry in the ith row and jth column lies in L_{i,j}. The problem of determining the threshold probability for the existence of an order-n Latin square was raised independently by Johansson [ Triangle factors in random graphs , 2006], by Luria and Simkin [Random Structures Algorithms 55 (2019), pp. 926–949], and by Casselgren and Häggkvist [Graphs Combin. 32 (2016), pp. 533–542]; our result provides an upper bound which is tight up to a factor of \log n and strengthens the bound recently obtained by Sah, Sawhney, and Simkin [ Threshold for Steiner triple systems , arXiv: 2204.03964 , 2022]. We also prove analogous results for Steiner triple systems and 1-factorizations of complete graphs, and moreover, we show that each of these thresholds is at most the threshold for the existence of a 1-factorization of a nearly complete regular bipartite graph. [ABSTRACT FROM AUTHOR]

Introduction: Functional Magnetic Resonance Imaging (fMRI) block-design experiments typically include active ON-blocks with presentation of cognitive tasks which are contrasted with OFF- blocks with no tasks presented. OFF-blocks in between ON-blocks can however, also be seen as a proxy for intermittent periods of resting, inducing temporary resting-states. We still do not know if brain activity during such intermittent periods reflects the same kind of resting-state activity as that obtained during a continuous period, as is typically the case in studies of the classic Default Mode Network (DMN). The purpose of the current study was therefore to investigate both similarities and differences in brain activity between intermittent and continuous resting conditions. Methods: There were 47 healthy participants in the 3T fMRI experiment. Data for the intermittent resting-state condition were acquired from resting-periods in between active task-processing periods in a standard ON-OFF block design, with three different cognitive tasks presented during ON-blocks. Data for the continuous resting-state condition were acquired during a 5 min resting period after the task-design had been presented. Results and discussion: The results showed that activity was overall similar in the two conditions, but with some differences. These differences were within the DMN network, and for the interaction of DMN with other brain networks. DMN maps showed weak overlap between conditions in the medial prefrontal cortex (MPFC), and in particular for the intermittent compared to the continuous restingstate condition. Moreover, DMN showed strong connectivity with the salience network (SN) in the intermittent resting-state condition, particularly in the anterior insula and the supramarginal gyrus. The observed differences may reflect a "carryover" effect from task-processing to the next resting-state period, not present in the continuous resting-state condition, causing interference from the ON-blocks. Further research is needed to fully understand the extent of differences between intermittent and continuous resting-state conditions. [ABSTRACT FROM AUTHOR]

Resolving sets were originally designed to locate vertices of a graph one at a time. For the purpose of locating multiple vertices of the graph simultaneously, {ℓ}-resolving sets were recently introduced. In this paper, we present new results regarding the {ℓ}-resolving sets of a graph. In addition to proving general results, we consider {2}-resolving sets in rook’s graphs and connect them to block designs. We also introduce the concept of ℓ-solid-resolving sets, which is a natural generalisation of solid-resolving sets. We prove some general bounds and characterisations for ℓ-solid-resolving sets and show how ℓ-solid- and {ℓ}-resolving sets are connected to each other. In the last part of the paper, we focus on the infinite graph family of flower snarks. We consider the ℓ-solid- and {ℓ}-metric dimensions of flower snarks. In two proofs regarding flower snarks, we use a new computer-aided reduction-like approach.

IntroductionFunctional Magnetic Resonance Imaging (fMRI) block-design experiments typically include active ON-blocks with presentation of cognitive tasks which are contrasted with OFF- blocks with no tasks presented. OFF-blocks in between ON-blocks can however, also be seen as a proxy for intermittent periods of resting, inducing temporary resting-states. We still do not know if brain activity during such intermittent periods reflects the same kind of resting-state activity as that obtained during a continuous period, as is typically the case in studies of the classic Default Mode Network (DMN). The purpose of the current study was therefore to investigate both similarities and differences in brain activity between intermittent and continuous resting conditions.MethodsThere were 47 healthy participants in the 3T fMRI experiment. Data for the intermittent resting-state condition were acquired from resting-periods in between active task-processing periods in a standard ON-OFF block design, with three different cognitive tasks presented during ON-blocks. Data for the continuous resting-state condition were acquired during a 5 min resting period after the task-design had been presented.Results and discussionThe results showed that activity was overall similar in the two conditions, but with some differences. These differences were within the DMN network, and for the interaction of DMN with other brain networks. DMN maps showed weak overlap between conditions in the medial prefrontal cortex (MPFC), and in particular for the intermittent compared to the continuous resting-state condition. Moreover, DMN showed strong connectivity with the salience network (SN) in the intermittent resting-state condition, particularly in the anterior insula and the supramarginal gyrus. The observed differences may reflect a “carry-over” effect from task-processing to the next resting-state period, not present in the continuous resting-state condition, causing interference from the ON-blocks. Further research is needed to fully understand the extent of differences between intermittent and continuous resting-state conditions.

In this paper we settle the question of whether a finite-dimensional vector space V over F p , with p an odd prime, and the family of all the k-sets of elements of V summing up to a given element x, form a 1- (v , k , λ 1) or a 2- (v , k , λ 2) block design, and, in either case, we find a closed form for λ i and characterize the automorphism group. The question is discussed also in the case where the elements of the k-sets are required to be all nonzero, as the two cases happen to be intrinsically inseparable. The "twin case" p = 2 , which has strict connections with coding theory, was completely discussed in a recent paper by G. Falcone and the present author. [ABSTRACT FROM AUTHOR]

Summary: A host‐switch graph was originally proposed as a graph that represents a network topology of a computer systems with 1‐port host computers and Δ‐port switches. It has been studied from both theoretical and practical aspects in terms of the diameter, the average shortest path length, and the performance of real applications. In recent high‐performance computing systems, however, a host computer is connected to multiple switches by using InfiniBand, NVSwitch, or Omni‐Path, and consequently they provide high bandwidths. Since a host‐switch graph cannot represent such systems, this article extends a host‐switch graph so that it can represent such systems. As a result, a host‐switch graph can include multi‐ported hosts. Furthermore, we propose to use multi‐port hosts for reducing the diameter. We show that the diameter minimization is equivalent to solving the degree diameter problem for bipartite graphs of diameter three. Our experimental results show that we can drastically reduce the diameter as well as increasing the bandwidth and improves performance of MPI applications by up to 162% as compared with networks with single‐ported hosts. [ABSTRACT FROM AUTHOR]

In agricultural experiments, if outliers are present in a data set, inference of experiment may be reversed. The purpose of this article is to develop a method for detection of subset of outlier vectors in block designs for incomplete multiresponse experiments in presence of masking. We defined an influence matrix comprising of Cook-statistics in its diagonal and product of two Cook-statistics in its off-diagonal positions. We then obtained eigenvectors corresponding to large eigenvalues of this matrix which can be used for identification of influential subsets. The proposed procedure has been illustrated with a real life data set. [ABSTRACT FROM AUTHOR]

Introduction. In the middle of the 20th century, technological progress made it possible to enlarge the building elements of buildings as much as possible, which led to the development of new industrial construction systems and increased production rates. However, to date, the issue has not been completely resolved and remains relevant. Modular construction is not sufficiently widely spread today, but many design experts predict its widespread introduction in the near future. The factor that decelerates the development of modular construction is the lack of theoretical foundations in the field of modular design, as well as significant differences from traditional design approach.Materials and methods. The purpose of this work is to develop the theoretical fundamentals of modular design based on the study of regulatory documents, Russian and foreign sources of research works, as well as the implemented projects. The task is to determine the fundamental features of modular elements of maximum readiness: principles of modular design, parameters of a modular element, advantages and disadvantages of a modular system, features of the design processes.Results. The theoretical basis of modular design includes basic concepts, principles and features; the conceptual design process is described using the case of development of an information model; parameters of modular elements of maximum readiness are presented, and the influence of modular items on the life cycle of a construction facility is analyzed.Conclusions. The presented system of principles of design based on modular elements of maximum readiness and parameters of modular elements allow us to systematize the established theoretical aspects of modularity, which make it possible to make modular buildings. The author formulates a new approach to design, which affects the entire life cycle and serves as the basis for new areas of engineering activities and scientific research.

The conventional approach to investigating functional connectivity in the block-designed study usually concatenates task blocks or employs residuals of task activation. While providing many insights into brain functions, the block design adds more manipulation in functional network analysis that may reduce the purity of the blood oxygenation level-dependent signal. Recent studies utilized one single long run for task trials of the same condition, the so-called continuous design, to investigate functional connectivity based on task functional magnetic resonance imaging. Continuous brain activities associated with the single-task condition can be directly utilized for task-related functional connectivity assessment, which has been examined for working memory, sensory, motor, and semantic task experiments in previous research. But it remains unclear how the block and continuous design influence the assessment of task-related functional connectivity networks. This study aimed to disentangle the separable effects of block/continuous design and working memory load on task-related functional connectivity networks, by using repeated-measures analysis of variance. Across 50 young healthy adults, behavioral results of accuracy and reaction time showed a significant main effect of design as well as interaction between design and load. Imaging results revealed that the cingulo-opercular, fronto-parietal, and default model networks were associated with not only task activation, but significant main effects of design and load as well as their interaction on intra- and inter-network functional connectivity and global network topology. Moreover, a significant behavior-brain association was identified for the continuous design. This work has extended the evidence that continuous design can be used to study task-related functional connectivity and subtle brain-behavioral relationships. [ABSTRACT FROM AUTHOR]

Presence of one or more outliers in the observations affect inference procedure in statistical analysis. Designs robust against presence of a single outlier can be found in the literature for both regression and block design set-ups. In this paper, an attempt has been made to find a robust design in a block design set-up for the estimation of a full set of orthonormal treatment contrasts when there are more than one outlier among the observations. It appears that symmetry and balance play an important role in this study; it is seen that as we deviate from them, designs deviate from robustness. [ABSTRACT FROM AUTHOR]

Remove unwanted variation (RUV) is an estimation and normalization system in which the underlying correlation structure of a multivariate dataset is estimated from negative control measurements, typically gene expression values, which are assumed to stay constant across experimental conditions. In this paper we derive the weight matrix which is estimated and incorporated into the generalized least squares estimates of RUV‐inverse, and show that this weight matrix estimates the average covariance matrix across negative control measurements. RUV‐inverse can thus be viewed as an estimation method adjusting for an unknown experimental design. We show that for a balanced incomplete block design (BIBD), RUV‐inverse recovers intra‐ and interblock estimates of the relevant parameters and combines them as a weighted sum just like the best linear unbiased estimator (BLUE), except that the weights are globally estimated from the negative control measurements instead of being individually optimized to each measurement as in the classical, single measurement BIBD BLUE. [ABSTRACT FROM AUTHOR]

Field experiments are subjected to spatial variability due to factors such as soil moisture, fertility, pH, and structure, as well as the pressure of diseases and pests. Soybean yields are highly variable across fields. Controlling spatial variability could decrease the risk of erroneous inferences in breeding trials. This study aims at evaluating the spatial variability of furrow-irrigated soybean for seed yield, wilting, and maturity under four different irrigation levels. The field experiment was conducted in four environmzents (location-year combination). A total of 165 soybean lines of similar relative maturity (maturity group 5) along with commercial checks were planted in an augmented strip plot design. Irrigation treatment decisions were triggered using an atmometer based on a threshold at a designated growth stage. Data were analyzed via Analysis of Variance as a linear mixed model using a blocking structure (block model) and spatial covariances using range and column. Two different spatial models were used: exponential and Gaussian. Results showed that the spatial models displayed better data fitting (lower AIC and/or BIC) than the block model in each different irrigation level across different environments and traits. Indeed, genotype ranking for seed yield was different between the block model and the best spatial model, suggesting that spatial adjustment may be necessary for soybean breeding operations under furrow irrigation. Further validation in a breeding yield trial demonstrated similar results of the effectiveness in terms of AIC and/or BIC of the spatial model compared to the block model for soybean seed yield. [ABSTRACT FROM AUTHOR]

Balanced Bipartite Block (BBPB) designs resistant against the trend are used when the interest of the experimenter is in making comparisons between two sets of treatments that are disjoint, and there is the presence of systematic trend within a block. This paper deals with the bipartite block model incorporating trend component. The general methodology has been described related to BBPB designs incorporating trend effect. The conditions for a BBPB design to be trend resistant are also obtained. Further, methods of constructing trend resistant BBPB designs are discussed. The designs so obtained are trend resistant and are more efficient for estimating the contrasts pertaining to two treatments from different sets. [ABSTRACT FROM AUTHOR]

In this paper we give a method for constructing transitive q-analogs of designs, and illustrate the method by giving some examples. We also show how this method can be used to construct q-analogs of 2-designs admitting an automorphism group that acts transitively on 1-subspaces, but have more than one orbit on the set of blocks. The q-analogs of designs obtained by the method given in this paper yield a special kind of constant dimension subspace codes, called orbit codes. [ABSTRACT FROM AUTHOR]

Block designs have an important historical footing in the design of experiments. Let θ be the treatment mean vector in the statistical model with fixed block effects. It is desirable to have the covariance of the least squares estimator of the treatment effects, Cov (θ ̂) , be a completely symmetric matrix. When this occurs, we have a variance balanced design (VBD). It is known that a pairwise balanced design can be converted into a VBD by choosing blocks with a multiplicity inversely proportional to the block size. This assumes that experimental errors are uncorrelated. However, this need not be the case, especially in ecological experiments where blocks have spatial correlation or laboratory settings with temporal correlation. This paper proposes the use of graph decompositions as a generalization of balanced incomplete block designs for the construction of VBDs in the presence of correlated errors. A general result is obtained to construct VBDs for various error correlation structures. Several applications are given to illustrate the relationship between graph decompositions and VBDs. • Variance-balanced designs give equal variance to the contrasts of treatment effects. • When errors are correlated, a block design based on graph decomposition can be used. • Conditions are found for a graph decomposition to produce a variance-balanced design. • Examples of variance-balanced designs based on graph decompositions are explored. [ABSTRACT FROM AUTHOR]

For positive integers n and m, consider a multiset of nonempty subsets of [m] such that there is a unique partition of these subsets into n partitions of [m]. We study the maximum possible size g(n,m) of such a multiset. We focus on the regime n≤2m-1-1 and show that g(n,m)≥Ω(nmlog2n). When n=2cm for any c∈(0,1), this lower bound simplifies to Ω(nc), and we show a matching upper bound g(n,m)≤O(nclog2(1c)) that is optimal up to a factor of log2(1c). We also compute g(n,m) exactly when n≥2m-1-O(2m2). [ABSTRACT FROM AUTHOR]

OBJECTIVE: Neuropsychiatric assessment is essential part of child and adolescent psychiatry clinic practice, also provides important information about central nervous system dysfunctions. In studies conducted to date, it has been known that both the high frequency of psychiatric comorbidity in epileptic patients and that epilepsy comorbidity is quite common in neurodevelopmental disorders. In fact, considering the high comorbidity of epileptic abnormalities and psychiatric disorders, it has been very important to determine predictors for epileptic abnormalities in a clinical sample of child and adolescent psychiatry. In this retrospective study, we aim to determine possible predictive factors for epileptic abnormalities in a clinical sample of child and adolescent psychiatry according to Weschler Intelligence Scale for Children (WISC-R) results. METHODS: We identified patients who had two or more rotation errors in the block design subtest of WISC-R by retrospectively scanning the system records of 2609 cases who were applied WISC-R with different prediagnoses at Gazi University Child and Adolescent Psychiatry Outpatient Clinic between January 2013 and December 2020 (n=71). After the first step identification, we selected the ones who had a previous electroencephalography (EEG) recording available for our own re-review (n=60). RESULTS: We found 15% EEG abnormalities and ADHD is the most common diagnosis in both normal and abnormal EEG groups. Due to correlation analysis, there was a positive-mild correlation between presence of EEG abnormality and WISC-R performance (r=0.56) in intellectual disability (ID) group and a positive-strong correlation between presence of EEG abnormality and WISC-R performance-verbal scores (r=0.74) in ID group. CONCLUSION: This study has shown that many different abnormal EEG patterns can be found in patients who have rotation errors in the block design test of WISC-R, suggesting diagnoses of ID, and having notable performance-verbal subtests scores difference and rotation errors in the block design subtest of WISC-R should be predicitive factors for epileptic abnormalities. [ABSTRACT FROM AUTHOR]

The building envelope is a crucial element in the regulation of thermal energy in the indoor environment, from which comfortable living inevitably depends. Designing a low-dispersion envelope represents a fundamental strategy to minimize the energy demand and HVAC systems' consumption. To this end, the need to select suitable insulation has become increasingly important, and the search for new solutions is constantly evolving. This justifies the great interest in the study of energy-efficient and sustainable insulation materials that are able to provide the low thermal transmittance values of multilayer components. To date, 3D printing has experienced a growing popularity for the research of alternative building materials (e.g., concrete). Conversely, it still appears to be very uncommon for the research of purely energy-efficient solutions. The aim of this work is to compare the thermal performance of three 3D-printed PLA (polylactic acid) blocks, characterized by different internal geometries and air cavities: (i) a multi-row structure; (ii) a square structure; (iii) a honeycomb structure. The study was conducted theoretically, with two-dimensional heat transfer modeling, and experimentally, by means of a heat flow meter and infrared thermography. The results showed that the configurations of the 3D-printed blocks reduced the flow of heat exchange. In addition, as the complexity of the blocks' internal structure increased, a heat flow reduction could be observed. In particular, the honeycomb structure showed a better behavior than the other two blocks did, with an experimental transmittance value that was equal to 1.22 ± 0.04 W/m2K. This behavior, which was mainly due to an attenuation of convective and radiative internal heat exchanges, suggests that the 3D printing has great potential in this field. [ABSTRACT FROM AUTHOR]

In this paper we consider r-regular graphs G that admit the vertex set partition such that one of the induced subgraphs is the join of an s-vertex clique and a t-vertex co-clique and represents a star complement for an eigenvalue μ of G. The cases in which one of the parameters s, t is less than 2 or μ = r are already resolved. It is conjectured in Wang et al. (Linear Algebra Appl 579:302–319, 2019) that if s , t ≥ 2 and μ ≠ r , then μ = - 2 , t = 2 and G = (s + 1) K 2 ¯ . For μ = - t we verify this conjecture to be true. We further study the case in which μ ≠ - t and confirm the conjecture provided t 2 - 4 μ 2 t - 4 μ 3 = 0 . For the remaining possibility we determine the structure of a putative counterexample and relate its existence to the existence of a particular 2-class block design. It occurs that the smallest counterexample would have 1265 vertices. [ABSTRACT FROM AUTHOR]

The block design task (BDT) is a visuospatial measure that individuals with Williams syndrome (WS) perform poorly on. However, it is unclear what underlies their impaired performance. This study investigated whether poorer performance is a result of visuospatial difficulties, executive function (EF) difficulties, atypical looking strategies, or a combination of these. Eleven individuals with WS participated alongside mental age (MA)- and chronological age (CA)-matched control groups. Eye movements were recorded while they took the BDT. Dwell times and visits to areas of interest in WS differed from CA, but not MA, groups. Findings suggest that BDT abilities of individuals with WS are delayed, but not atypical. Delays result from visuospatial and attention-switching difficulties rather than atypical looking strategies. [ABSTRACT FROM AUTHOR]

We propose a method of constructing block designs which combine genetic algorithm and a method for constructing designs with a prescribed automorphism group using tactical decompositions (i.e., orbit matrices). We apply this method to construct new Steiner systems with parameters S(2,5,45) $S(2,5,45)$ and new symmetric designs with parameters (71, 15, 3). [ABSTRACT FROM AUTHOR]

In this paper, we introduce a switching for 2-designs, which defines a type of trade. We illustrate this method by applying it to some symmetric (64, 28, 12) designs, showing that the switching introduced in this paper in some cases can be applied directly to orbit matrices. In that way we obtain six new symmetric (64, 28, 12) designs. Further, we show that this type of switching (of trades) can be applied to any symmetric design related to a Bush-type Hadamard matrix and construct symmetric designs with parameters (36, 15, 6) leading to new Bush-type Hadamard matrices of order 36, and symmetric (100, 45, 20) designs yielding Bush-type Hadamard matrices of order 100. [ABSTRACT FROM AUTHOR]

In an equireplicate graph decomposition, every vertex of the host graph appears in the same number of blocks. We propose the use of colored loops as a framework for unifying various other types of local regularity conditions in graph decompositions. In the basic case where a single graph with colored loops is used as a block, an existence theory for such decompositions follows as a straightforward generalization of previous work on graph decompositions. [ABSTRACT FROM AUTHOR]

Let H be a connected subgraph of a graph G. An H-factor of G is a spanning subgraph of G whose components are isomorphic to H. Given a set H of mutually non-isomorphic graphs, a uniform H -factorization of G is a partition of the edges of G into H-factors for some H ∈ H . In this article, we give a complete solution to the existence problem for uniform (C k , P k + 1) -factorizations of K n − I in the case when k is even. [ABSTRACT FROM AUTHOR]

In this paper our focus is on regular signed graphs with exactly 3 (distinct) eigenvalues. We establish certain basic results; for example, we show that they are walk-regular. We also give some constructions and determine all the signed graphs with 3 eigenvalues, under the constraint that they are either signed line graphs or have vertex degree 3. We also report our result of computer search on those with at most 10 vertices.

This paper considers the balanced resampling design approach of generating bootstrap samples to handle the simulation error problem in bootstrap estimation of mean and variance of a sample statistic of interest. A class of balanced n-arry block design, slightly different from the definition of Tocher (1952), is defined and its necessary conditions for the existence of these designs are derived. In particular, an infinite series of balanced n-arry block designs are found to be efficiency balanced, i.e., every contrast of element (observation) totals has the same loss of information. As an application in bootstrap method, the eccentric class of efficiency balanced n-arry block design (termed Efficient Bootstrap Sample Design (EBSD(n)) can be used to generate 4 n 2 + 1 resamples of sample size n to achieve an exact bootstrap estimation of mean and variance of statistic "sample average", i.e., a collection of bootstrap data samples and corresponding bootstrap sample averages where mean and variance of this empirical collection of sample averages match the first two theoretical central moments i.e., moments about the sample average. The EBSD(n) solely depends on the existence of balanced incomplete block design B[ 2 n , 4n-2, 2n-1, n, n-1] for n ≥ 2. Thus the implementation of computer algorithm for spawning bootstrap samples using EBSD(n) is simple and straightforward for recapitulating sampling characteristics such as standard error of predefined computable symmetric and non symmetric sample statistic of interest. [ABSTRACT FROM AUTHOR]

Das and Gupta constructed optimal block designs for triallel crosses through Nested balanced block designs. In the present paper we are constructing three series of optimal partial triallel cross designs through complete diallel cross designs which have been obtained by nested balanced incomplete block designs. [ABSTRACT FROM AUTHOR]

First we investigate net-biregular signed graphs with spectrum of the form [ ρ , μ m , λ l ] where λ is non-main; such graphs are necessarily biregular with exactly two main eigenvalues. We provide two constructions of signed graphs with three eigenvalues, where the graphs that arise include net-biregular and net-regular signed graphs having spectrum [ ρ , μ , λ l ] , with λ non-main. Secondly we determine all the connected signed graphs with spectrum [ ρ , μ 2 , λ l ] (l ≥ 2) where λ is non-main: these include a new infinite family of signed graphs which are neither net-regular nor net-biregular. Thus, in contrast to the situation for graphs, a signed graph with two main eigenvalues and one non-main eigenvalue is not necessarily net-biregular. [ABSTRACT FROM AUTHOR]

For integers n > 2 and k > 0 , an (n × n) ∕ k semi-Latin square is an n × n array of k -subsets (called blocks) of an n k -set (of treatments), such that each treatment occurs once in each row and once in each column of the array. A semi-Latin square is uniform if every pair of blocks, not in the same row or column, intersect in the same positive number of treatments. It is known that a uniform (n × n) ∕ k semi-Latin square is Schur optimal in the class of all (n × n) ∕ k semi-Latin squares, and here we show that when a uniform (n × n) ∕ k semi-Latin square exists, the Schur optimal (n × n) ∕ k semi-Latin squares are precisely the uniform ones. We then compare uniform semi-Latin squares using the criterion of pairwise-variance (PV) aberration, introduced by J. P. Morgan for affine resolvable designs, and determine the uniform (n × n) ∕ k semi-Latin squares with minimum PV aberration when there exist n − 1 mutually orthogonal Latin squares of order n. These do not exist when n = 6 , and the smallest uniform semi-Latin squares in this case have size (6 × 6) ∕ 10. We present a complete classification of the uniform (6 × 6) ∕ 10 semi-Latin squares, and display the one with least PV aberration. We give a construction producing a uniform ((n + 1) × (n + 1)) ∕ ((n − 2) n) semi-Latin square when there exist n − 1 mutually orthogonal Latin squares of order n , and determine the PV aberration of such a uniform semi-Latin square. Finally, we describe how certain affine resolvable designs and balanced incomplete-block designs can be constructed from uniform semi-Latin squares. From the uniform (6 × 6) ∕ 10 semi-Latin squares we classified, we obtain (up to block design isomorphism) exactly 16875 affine resolvable designs for 72 treatments in 36 blocks of size 12 and 8615 balanced incomplete-block designs for 36 treatments in 84 blocks of size 6. In particular, this shows that there are at least 16875 pairwise non-isomorphic orthogonal arrays OA (72 , 6 , 6 , 2). • Uniform semi-Latin squares with least pairwise-variance aberration are determined. • The uniform 6 by 6 semi-Latin squares with block size 10 are classified. • New uniform semi-Latin squares are constructed. • New affine resolvable designs and orthogonal arrays are obtained. • New balanced incomplete-block designs are obtained. [ABSTRACT FROM AUTHOR]

Cell-based biological assays (also called bioassays) are an essential analytical tool used for quality assessment of biologic drug substances and drug products. In particular, they are used to determine the potency compared against a standard preparation under assumptions of similarity. In the design of bioassays, orthogonality between preparations and nuisance factors is desired. Block designs are an efficient way to assay multiple preparations simultaneously and mitigate bias from multiple sources, such as plates, locations within plates, and operators. The construction of a block design of a bioassay is challenging because of the treatment/control setup and the presence of multiple block effects. In many cases, absolute orthogonality is not feasible, and consequently, we need a design that achieves "near-orthogonality." We propose an extended Youden design with mathematical construction such that near-orthogonality can be achieved in the presence of these multiple confounding effects. We also provide an efficient algorithm implementation with R. Numerical results show that the extended Youden design is the optimal design for the given scenario when absolute orthogonality is not achievable. [ABSTRACT FROM AUTHOR]

In this note we point out an error in a recent paper on flag-transitive block designs with gcd (r , λ) = 1 , and we prove a result correcting the error. [ABSTRACT FROM AUTHOR]

In this paper we study the problem of finding neighbor optimal designs for a general correlation structure. We give universal optimality conditions for nearest-neighbor (NN) balanced block designs when observations on the same block are modeled by an autoregressive AR(m) process with arbitrary order m. The cases m = 1 , 2 have been studied by Grondona and Cressie (Sankhyā Indian J Stat Ser A 55(2):267–284, 1993) for AR(2) and by Gill and Shukla (Biometrika 72(3):539–544, 1985a, Commun Stat Theory Methods 14(9):2181–2197, 1985b) and Kunert (Biometrika 74(4):717–724, 1987) for AR(1); we extend these results to the cases m ≥ 3 . [ABSTRACT FROM AUTHOR]

Several studies investigated the neuropsychological bases of spatial construction in developmental samples. However, no study directly tested whether the pattern of the neuropsychological processes implied in spatial construction changed depending on whether a block building or a figure drawing task is considered. Here, we used the path analysis to test the direct and indirect effects of verbal abilities (naming and verbal knowledge), executive functions, figure disembedding and mental rotation on two classical spatial construction tasks: the Rey-Osterrieth Complex Figure (ROCF) and the Block Design (BD). We recruited a sample of 186 typically developing children (age range: 7–12 years). Results showed that ROCF copying was directly influenced by age and figure disembedding, and it was indirectly affected by executive functions, naming and verbal knowledge, whereas BD was influenced in a direct way by verbal knowledge, figure disembedding and mental rotation and indirectly affected by executive functions and naming skills. Moreover, the results showed a full measurement invariance of the path model between sexes, whereas only partial invariance was found for age. Thus, we tested the model in two age groups (age ranges: 7–9.5 and 9.6–12 years) and found that the relationships between the variables of the model changed across development. Although other variables might be relevant to spatial construction, the present findings demonstrate different neuropsychological bases of drawing figures and building blocks in typically developing children. [ABSTRACT FROM AUTHOR]