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RS-like locally recoverable (LRC) codes have construction based on the classical construction of Reed–Solomon (RS) codes, where codewords are obtained as evaluations of suitably chosen polynomials. These codes were introduced by Tamo and Barg (IEEE Trans Inf Theory 60(8):4661–4676, 2014) where they assumed that the length n of the code is divisible by r+1 , where r is the locality of the code. They also proposed a construction with this condition lifted to n≠1mod(r+1) . In a recent paper, Kolosov et al. (Optimal LRC codes for all lenghts n≤q , arXiv:1802.00157, 2018) have given an explicit construction of optimal LRC codes with this lifted condition on n. In this paper we remove any such restriction on n completely, i.e., we propose constructions for q-ary RS-like LRC codes of any length n≤q . Further, we show that the codes constructed by the proposed construction are optimal LRC codes for their parameters.

A linear code is called a locally repairable code (LRC) with locality r if one can recover an erased code symbol by accessing at most r other code symbols. Constructions of LRCs have been widely investigated in recent years. In this paper, we give a step forward in this direction. Firstly, we propose a novel concept of perfect LRCs whose size exactly achieves the Hamming-type bound, similar to the perfect codes that achieving the Hamming bound in classical coding theory. By the parity-check matrix approach, we establish some important connections between the existence of LRCs and the existence of some subsets of finite geometry and finite fields with certain properties, respectively. By employing q -Steiner systems and sunflowers in projective geometry and difference sets in finite fields, we obtain two new constructions of perfect LRCs with flexible parameters and present several new constructions of k -optimal LRCs achieving another Hamming-type bound under the integers restriction. Moreover, for fixed q and r , the code lengths of all the q -ary r -LRCs constructed in this paper can be arbitrarily large and the code rates can asymptotically achieve the upper bound r r + 1 .

Inhibitory receptors play a pivotal role in fine-tuning immune responses. The leukocyte receptor complex (LRC) encodes multiple receptor families, including the leukocyte immunoglobulin-like receptor (LILR) family, which next to activating receptors involves several inhibitory receptors. The LILRB1 and LILRB2 receptors are considered immune checkpoint inhibitors, which may interact with MHC class I molecules, and are expressed mainly on monocytes, B- and T-cells. In this study, we characterized and at the genomic and transcriptomic level in three Old World monkey species, namely rhesus and long-tailed macaques and Hamadryas baboon, using SMRT sequencing on PacBio platforms. We describe 71 and 58 alleles in the two macaque species, of which only one allele was previously published. In contrast, less polymorphism is observed in the Hamadryas baboon, with only six and seven alleles characterized. Phylogenetic analysis, including known human data, revealed extensive diversification of the and in macaques, with allelic variation clustering into nine and twelve distinct lineages, respectively. This contrasts with the more conserved repertoires observed in humans and Hamadryas baboons. Compared with our experience analyzing and transcriptome data, the and transcriptomes were dominated by alternatively spliced isoforms. Alternative 3' splice sites near exons 10 and 15 and/or skipping of exon 15, were encountered for most alleles. In , the deletion of exon 9 is the most prominent event, next to deletion of exon 10 and the use of alternative 3' splice sites near exons 10 and 15. The exons that encode the extracellular domains remain largely intact, suggesting that alternative splicing predominantly affects the stem region and the signaling capacity of the LILRB1 and LILRB2 receptors.

In this work, we propose two new types of codes with locality, namely, locally maximal recoverable (LMR) codes and λ -maximally recoverable ( λ -MR) codes. The LMR codes are a subclass of codes with ( r , δ ) -locality such that they can correct h additional erasures in any one local set, in addition to having ( r , δ ) -locality. These codes are a restricted case of maximally recoverable (MR) codes, which enable recovery from all information-theoretically correctable erasure patterns in a local set. The λ -MR codes are a subclass of LMR codes which can also handle λ erasures from any coordinate positions. We give constructions for both of these families of codes. We also study the LMR codes that satisfy the complementary dual property. It is well known that codes with this property are capable of safeguarding communication systems against fault injection attacks. We give a construction of distance-optimal cyclic LMR codes that satisfy the complementary dual property.

Inclusion has been increasingly recognised as a global common goal in education. In China, inclusive education for children with special educational needs and disabilities is currently practised as ‘Learning in Regular Classrooms’ (LRC). However, not only has the inclusion policy frequently been criticised as failing to provide clear, systematic, or consistent strategies, but also the actual practices of LRC have also been found to merely concern children’s physical integration into the mainstream settings. This discussion paper explores key structural barriers to inclusive education through reviewing policies within the wider education ecosystem that are relevant to the theme of inclusion but outside the LRC policy itself. The analysis illustrates how the complex and interlocked structural barriers embedded within the wider context of current education policies pose persisting constraints for inclusion to progress in China, and how these structural barriers unique to the Chinese education system also reflect the common ‘wicked problems’ for practising inclusive education globally. The paper discusses five main education structures: neo-liberal education policies, national college entrance examination system, teacher evaluation system, staffing quota system and the ‘combine medicine and education’ policy. The conclusion illustrates the complexity and main issues facing future inclusion policy reforms and highlights key objectives for policy change. It indicates that, for inclusion reforms to be effective, broader changes are needed within the wider education ecosystem.

Keeping into view the human-brain-like capabilities, a novel adaptive control scheme utilizing a defuzzification module has been designed in an effort to endow the control systems with human-like capabilities of learning and processing human-understandable information. It’s been noted that within real-time systems, uncertain and undefined external disruptions can manifest in various ways due to their ambiguous and unpredictable nature. Consequently, attempting to encapsulate these disturbances within precise closed-form mathematical expressions is often impractical. Therefore, opting to describe such ambiguous and incomplete information using linguistic variables, as opposed to rigid mathematical formulations, is a more suitable approach. In this regard, a novel class of uncertain nonlinear systems in non-strict feedback involving fuzzy variables is introduced in which the fuzzy variables are used to express unknown disturbances. As a result, such class is systems become more general and human-interactable but alongside the control of such class of systems becomes more complicated and difficult. Therefore, the goal of this work is to provide an efficient intelligent control technique for the proposed class of systems which can successfully handle these uncertainties and attributes of fuzziness. The proposed control scheme is therefore consists of (a) a defuzzification module to handle fuzzy variables and (b) radial basis function neural network (RBFNN) to approximate the unknown functions. The existing category of uncertain systems is managed by converting the system into an n-step ahead predictor and applying the suggested control approach. By leveraging Lyapunov theory, it can be demonstrated that the comprehensive closed-loop system achieves semi-global uniform ultimate boundedness (SGUUB), and it is established that the error tends to diminish towards zero. Additionally, the computational complexity of the overall control scheme is also analyzed. The control scheme is validated through numerical simulations for its effectiveness and real-time applicability. A simulation example based on hypersonic flight dynamics model developed by NASA-Langley Research Centre for longitudinal dynamics of a hypersonic vehicle is used to demonstrate the scheme’s reliability and real-time applicability.

The genes of the leukocyte immunoglobulin-like receptor (LILR) family map to the leukocyte receptor complex (LRC) on chromosome 19, and consist of both activating and inhibiting entities. These receptors are often involved in regulating immune responses, and are considered to play a role in health and disease. The human LILR region and evolutionary equivalents in some rodent and bird species have been thoroughly characterized. In non-human primates, the LILR region is annotated, but a thorough comparison between humans and non-human primates has not yet been documented. Therefore, it was decided to undertake a comprehensive comparison of the human and non-human primate LILR region at the genomic level. During primate evolution the organization of the LILR region remained largely conserved. One major exception, however, is provided by the common marmoset, a New World monkey species, which seems to feature a substantial contraction of the number of LILR genes in both the centromeric and the telomeric region. Furthermore, genomic analysis revealed that the killer-cell immunoglobulin-like receptor gene KIR3DX1 , which maps in the LILR region, features one copy in humans and great ape species. A second copy, which might have been introduced by a duplication event, was observed in the lesser apes, and in Old and New World monkey species. The highly conserved gene organization allowed us to standardize the LILR gene nomenclature for non-human primate species, and implies that most of the receptors encoded by these genes likely fulfill highly preserved functions.

Although the maximum carboxylation rate (Vcmax) is an important parameter to calculate the photosynthesis rate for the terrestrial biosphere models (TBMs), current models could not satisfactorily estimate the Vcmax of a crop because the Vcmax is always changing during crop growth period. In this study, the Breathing Earth System Simulator (BESS) and light response curve (LRC) were combined to invert the time-continuous Vm25 (Vcmax normalized to 25 °C) using eddy covariance measurements and remote sensing data in five maize sites. Based on the inversion results, we propose a Two-stage linear model using leaf age to estimate crop Vm25. The leaf age can be readily calculated from the date of emergence, which is usually recorded or can be readily calculated from the leaf area index (LAI), which can be readily obtained from high spatiotemporal resolution remote sensing images. The Vm25 used to calibrate and validate our model was inversely solved by combining the BESS and LRC and using eddy covariance measurements and remote sensing data in five maize sites. Our Two-stage linear model (R2 = 0.71–0.88, RMSE = 5.40–7.54 μmol m−2 s−1) performed better than the original BESS (R2 = 0.01–0.67, RMSE = 13.25–18.93 μmol m−2 s−1) at capturing the seasonal variation in the Vm25 of all of the five maize sites. Our Two-stage linear model can also significantly improve the accuracy of maize gross primary productivity (GPP) at all of the five sites. The GPP estimated using our Two-stage linear model (underestimated by 0.85% on average) is significantly better than that estimated by the original BESS model (underestimated by 12.60% on average). Overall, our main contributions are as follows: (1) by using the BESS model instead of the BEPS model coupled with the LRC, the inversion of Vm25 took into account the photosynthesis process of C4 plants; (2) the maximum value of Vm25 (i.e., PeakVm25) during the growth and development of maize was calibrated; and (3) by using leaf age as a predictor of Vm25, we proposed a Two-stage linear model to calculate Vm25, which improved the estimation accuracy of GPP.

Locally recoverable codes (LRCs) have been introduced as a family of erasure codes that support the repair of a failed storage node by contacting a small number of other nodes in the cluster. Boosted by their applications in distributed storage, LRCs have attracted a lot of attention in recent literature since the concept of codes with locality r was introduced by Gopalan et al. in 2012. Aiming to recover the data from several concurrent node failures, the concept of r -locality was later generalized as ( r , δ ) -locality by Prakash et al. An ( r , δ ) -LRCs in which every code symbol has ( r , δ ) -locality is said to be optimal if it achieves the Singleton-like bound with equality. In present paper, we are interested in optimal ( r , δ ) -LRCs over small fields, more precisely, over quaternary field. We study their parity-check matrices or generator matrices, using the properties of projective space. The classification of optimal quaternary ( r , δ ) -LRCs and their explicit code constructions are proposed by examining all possible parameters.