Splitting Balanced Incomplete Block Designs with Block Size 2×k

This paper investigated the existence of splitting balanced incomplete block designs with blck size 2× k .The necessary conditions for such a design are λ(v-1) ≡0(mod k ),and λv(v- 1)≡0(mod 2 k 2).It will show that the above necessary conditions are also sufficient for k =3 with the definite exception( v,λ )=(10,1) and with several possible exceptions.

Some Properties of Weak Block Designs

The necessary conditions for the existence of weak designs are given in the form of two inequalities in this paper. The relations among weak block designs (WBDs) , Balanced incomplete block designs ( BIBDs) and differential balanced block designs (DBBDs) are researched.

General Solution of Normal Equations in the Intra-Block Analysis of PBIB Designs with Four Associates

General solution of normal equations in the general intra-block analysis of partially balanced incomplete block designs involving four associates is presented in this talk as they are quite useful in practice. Only intra-block estimates are given as the necessary formulae for inter-block estimates can be derived from them by changing the parameters as discussed in Rao[5]. We have obtained the general formulae for computation of four types of efficiencies, the average efficiency factor and the variance of the estimated elementary treatment contrast of the four types of comparisons irrespective of the type of association scheme a PBIB Design follows.

ORTHOGONAL GEOMETRIES OVER FINITE FIELDS WITH CHARACTERISTIC≠2 AND BLOCK DESIGNS

By taking as blocks certain subspace-pairs of an orthogonal geometry over a finite field with characteristic≠2 we construct some new types of BIB designs and PBIB designs whose parameters are also given.

EMBEDDINGS OF SIMPLE TWO-FOLD BALANCED INCOMPLETE BLOCK DESIGNS WITH BLOCK SIZE FOUR

The necessary and sufficient conditions for the existence of simple incomplete block design （v, ω; 4, 2）-IPBDs are determined. As a consequence, the necessary and sufficient conditions for the embeddings of simple two-fold balanced incomplete block designs with block size 4 are also determined.

Variable Selection in Randomized Block Design Experiment

In the experimental field, researchers need very often to select the best subset model as well as reach the best model estimation simultaneously. Selecting the best subset of variables will improve the prediction accuracy as noninformative variables will be removed. Having a model with high prediction accuracy allows the researchers to use the model for future forecasting. In this paper, we investigate the differences between various variable selection methods. The aim is to compare the analysis of the frequentist methodology (the backward elimination), penalised shrinkage method (the Adaptive LASSO) and the Least Angle Regression (LARS) for selecting the active variables for data produced by the blocked design experiment. The result of the comparative study supports the utilization of the LARS method for statistical analysis of data from blocked experiments.

CONSTRUCTION OF NONSYSTEMATIC LOW-DENSITY PARITY-CHECK CODES BASED ON SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGN

This paper studies the nonsystematic Low-Density Parity-Check(LDPC)codes based onSymmetric Balanced Incomplete Block Design(SBIBD).First,it is concluded that the performancedegradation of nonsystematic linear block codes is bounded by the average row weight of generalizedinverses of their generator matrices and code rate.Then a class of nonsystematic LDPC codes con-structed based on SBIBD is presented.Their characteristics include:both generator matrices andparity-check matrices are sparse and cyclic,which are simple to encode and decode;and almost arbi-trary rate codes can be easily constructed,so they are rate-compatible codes.Because there aresparse generalized inverses of generator matrices,the performance of the proposed codes is only0.15dB away from that of the traditional systematic LDPC codes.

BIMATCHING DESIGNS

A collection of k-matchings of bipartite graph Kn,n with the property thatevery pair of independent edges lies in exactly λ of the k-matchings is called aBIMATCH(n,k,λ)-design. Existences and constructions for various BIMATCH (n,k,λ)designs are given.

Some Construction Methods of Optimum Chemical Balance Weighing Designs III

Methods of constructing the optimum chemical balance weighing designs from symmetric balanced incomplete block designs are proposed with illustration. As a by-product pairwise efficiency and variance balanced designs are also obtained.

PERIODIC COMPLEMENTARY BINARY SEQUENCE PAIRS

A new set of binary sequences-Periodic Complementary Binary Sequence Pair (PCSP) is proposed. A new class of block design-Difference Family Pair (DFP) is also proposed.The relationship between PCSP and DFP, the properties and existing conditions of PCSP and the recursive constructions for PCSP are given.

Patterns of cortical reorganization in facial synkinesis:a task functional magnetic resonance imaging study

Facial synkinesis,a sequela of peripheral facial nerve palsy,is characterized by simultaneous involuntary facial movement during a voluntary desired one.Maladaptive cortical plasticity might be involved in the dysfunction of facial muscles.This cohort study investigated the cortical functional alterations in patients with unilateral facial synkinesis,using the task functional magnetic resonance imaging.Facial motor tasks,including blinking and smiling,were performed by 16 patients（aged 30.6 ± 4.5 years,14 females/2 males） and 24 age-and sex-matched healthy controls（aged 29.1 ± 4.2 years,19 females/5 males）.Results demonstrated that activation in the cortico-facial motor representation area was lower during tasks in patients with facial synkinesis compared with healthy controls.Facial movements on either side performed by patients caused more intensive activation of the supplementary motor area on the contralateral side of the affected face,than those on the unaffected side.Our results revealed that there was cortical reorganization in the primary sensorimotor area and the supplementary motor area.This study was registered in Chinese Clinical Trial Registry（registration number： Chi CTR1800014630）.

A collision recovery algorithm using optimal Q parameter based on BIBD in RFID

In this work,an optimal Q algorithm based on a collision recovery scheme is presented. Tags use BIBD-( 16,4,1) codes instead of RN16 s. Therefore,readers can make a valid recognition even in collision slots. A way of getting the optimal slot-count parameter is studied and an optimal Q algorithm is proposed. The theoretical and simulation results show that the proposed algorithm can improve reading efficiency by 100% more than the conventional Q algorithm. Moreover,the proposed scheme changes little to the existing standard. Thus,it is easy to implement and compatible with ISO 18000-6C.

Block-Transitive 2-(v,k,1) Designs and Groups E_6(q)

This article is a contribution to the study of block-transitive automorphism groups of 2-（v,k,1） block designs. Let D be a 2-（v,k,1） design admitting a block-transitive, pointprimitive but not flag-transitive automorphism group G. Let kr = （k,v-1） and q = pf for prime p. In this paper we prove that if G and D are as above and q （3（krk-kr ＋ 1）f）1/3, then G does not admit a simple group E6（q） as its socle.

On Construction of Optimal Two-Level Designs with Multi Block Variables

When running an experiment, inhomogeneity of the experimental units may result in poor estimations of treatment effects. Thus, it is desirable to select a good blocked design before running the experiment. Mostly, a single block variable was used in the literature to treat the inhomogeneity for simplicity. However, in practice, the inhomogeneity often comes from multi block variables. Recently, a new criterion called B2-GMC was proposed for two-level regular designs with multi block variables. This paper proposes a systematic theory on constructing some B^2-GMC designs for the first time. Experimenters can easily obtain the B^2-GMC designs according to the construction method. Pros of B^2-GMC designs are highlighted in Section 4, and the designs with small run sizes are tabulated in Appendix B for practical use.

Supplementary motor area deactivation impacts the recovery of hand function from severe peripheral nerve injury

Although some patients have successful peripheral nerve regeneration,a poor recovery of hand function often occurs after peripheral nerve injury.It is believed that the capability of brain plasticity is crucial for the recovery of hand function.The supplementary motor area may play a key role in brain remodeling after peripheral nerve injury.In this study,we explored the activation mode of the supplementary motor area during a motor imagery task.We investigated the plasticity of the central nervous system after brachial plexus injury,using the motor imagery task.Results from functional magnetic resonance imaging showed that after brachial plexus injury,the motor imagery task for the affected limbs of the patients triggered no obvious activation of bilateral supplementary motor areas.This result indicates that it is difficult to excite the supplementary motor areas of brachial plexus injury patients during a motor imagery task,thereby impacting brain remodeling.Deactivation of the supplementary motor area is likely to be a serious problem for brachial plexus injury patients in terms of preparing,initiating and executing certain movements,which may be partly responsible for the unsatisfactory clinical recovery of hand function.

Chinese Remainder Codes

Chinese Remainder Codes are constructed by applying weak block designs and Chinese Remainder Theorem of ring theory. The new type of linear codes take the congruence class in the congruence class ring R/I 1∩I 2∩...∩I n for the information bit, embed R/J i into R/I 1∩I 2∩...∩I n, and asssign the cosets of R/J i as the subring of R/I 1∩I 2∩...∩I n and the cosets of R/J i in R/I 1∩I 2∩...∩I n as check lines. There exist many code classes in Chinese Remainder Codes, which have high code rates. Chinese Remainder Codes are the essential generalization of Sun Zi Codes.

Circular neighbor-balanced designs universally optimal for total effects

In many experiments, the performance of a subject may be affected by some previous treatments applied to it apart from the current treatment. This motivates the studies of the residual effects of the treatments in a block design. This paper shows that a circular block design neighbor-balanced at distances up toγ≤k - 1, where k is the block size, is universally optimal for total effects under the linear models containing the neighbor effects at distances up toγamong the class of all circular binary block designs. Some combinatorial approaches to constructing these circular block designs neighbor-balanced at distances up to k - 1 are provided.

The Existence of BIB Designs

Given any positive integers k3 and λ,let c（k,λ）denote the smallest integer such that u ∈ B（k,λ）for every integer uc（k,λ）that satisfies the congruences λv（v-1）≡0（mod k（k-1））and λ（u-1）≡0（mod k-1）.In this article we make an improvement on the bound of c（k,λ）provided by Chang in[4]and prove that c（k,λ）exp{k3k6}.In particular,c（k,1）exp{kk2}.

On the Existence of (v,3×3,λ)-Splitting Balanced Incomplete Block Design with λ between 2 to 9

Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.

Interaction Between Memory Load and Experimental Design on Brain Connectivity and Network Topology

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.