Gap Sequences Research Articles

An upper bound on asymptotic repetition threshold of balanced sequences via colouring of the Fibonacci sequence

We colour the Fibonacci sequence by suitable constant gap sequences to provide an upper bound on the asymptotic repetition threshold of d-ary balanced sequences. The bound is attained for d=2,4 and 8 and we conjecture that it happens for infinitely many even d's.Our bound reveals an essential difference in behaviour of the repetition threshold and the asymptotic repetition threshold of balanced sequences. The repetition threshold of d-ary balanced sequences is known to be at least 1+1d−2 for each d≥3. In contrast, our bound implies that the asymptotic repetition threshold of d-ary balanced sequences is at most 1+τ32d−3 for each d≥2, where τ is the golden mean.

Kernel Words and Gap Sequences of the Tribonacci Word on an Infinite Alphabet

In this paper, we propose a nuanced variation in the kernel words of the tribonacci sequence. Our primary objective is to investigate the intrinsic properties of the kernel words and associated gap sequences when the tribonacci sequence is expanded over an infinite alphabet.

Near-Chromosomal-Level Genome Assembly of the Sea Urchin Echinometra lucunter, a Model for Speciation in the Sea.

Echinometra lucunter, the rock-boring sea urchin, is a widely distributed echinoid and a model for ecological studies of reproduction, responses to climate change, and speciation. We present a near chromosome-level genome assembly of E. lucunter, including 21 scaffolds larger than 10 Mb predicted to represent each of the chromosomes of the species. The 760.4 Mb assembly includes a scaffold N50 of 30.0 Mb and BUSCO (benchmarking universal single-copy orthologue) single copy and a duplicated score of 95.8% and 1.4%, respectively. Ab-initio gene model prediction and annotation with transcriptomic data constructed 33,989 gene models composing 50.4% of the assembly, including 37,036 transcripts. Repetitive elements make up approximately 39.6% of the assembly, and unresolved gap sequences are estimated to be 0.65%. Whole genome alignment with Echinometra sp. EZ revealed high synteny and conservation between the two species, further bolstering Echinometra as an emerging genus for comparative genomics studies. This genome assembly represents a high-quality genomic resource for future evolutionary and developmental studies of this species and more broadly of echinoderms.

On balanced sequences and their critical exponent

We study aperiodic balanced sequences over finite alphabets. A sequence v of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y′. We show that the language of v is eventually dendric and we focus on return words to its factors. We develop a method for computing the critical exponent and asymptotic critical exponent of balanced sequences, provided the associated Sturmian sequence u has a quadratic slope. The method is based on looking for the shortest return words to bispecial factors in v. We illustrate our method on several examples; in particular we confirm a conjecture of Rampersad, Shallit and Vandomme that two specific sequences have the least critical exponent among all balanced sequences over 9-letter (resp., 10-letter) alphabets.

Gap sequences and Topological properties of Bedford–McMullen sets* *The research of Miao is partially supported by Shanghai Key Laboratory of PMMP (18dz2271000) and NSFC Grant 12071137. The research of Ruan is partially supported by NSFC Grant 11771391, ZJNSF Grant LY22A010023 and the Fundamental Research Funds for the Central Universities of China Grant 2021FZZX001-01.

In this paper, we study the topological properties and the gap sequences of Bedford–McMullen sets. First, we introduce a topological condition, the component separation condition (CSC), and a geometric condition, the exponential rate condition (ERC). Then we prove that the CSC implies the ERC, and that both of them are sufficient conditions for obtaining the asymptotic estimate of gap sequences. We also explore topological properties of Bedford–McMullen sets and prove that all normal Bedford–McMullen sets with infinitely many connected components satisfy the CSC, from which we obtain the asymptotic estimate of the gap sequences of Bedford–McMullen sets without any restrictions. Finally, we apply our result to Lipschitz equivalence.

Driving factors for soil fungal and bacterial community assembly in topical forest of China

Understanding the assembly of soil microbial communities of tropical forest is of great significance for the protection of biodiversity in tropical areas. Many studies have been carried out on biodiversity and its maintenance mechanism in tropical regions. However, the effects of land use and seasonal variation on the assembly of soil fungal and bacterial communities in tropical forests remains unknown. To fill this research gap, 16S rRNA and ITS sequences were used to evaluate the assembly mechanisms of soil bacterial and fungal communities using 260 soil samples collected from tropical rainforest and rubber plantation sites across Hainan Island, South China. A majority (~60%) of observed OTUs conformed with neutral model expectations, indicating that neutral processes were important for the assembly of soil microbial communities. For bacterial communities, the NST (normalized stochasticity ratio) was higher in the tropical rainforest (0.746 in the dry season, 0.684 in the rainy season) versus rubber plantation sites (0.647, 0.584), regardless of season. This indicated rainforest were more stochastic than rubber plantation for soil bacterial community assembly. For fungal communities, rubber plantation communities showed greater stochasticity (NST = 0.578) than rainforest communities (NST = 0.388) in the dry season, but the reverse was true in the rainy season (NST = 0.852 for rubber plantations; NST = 0.978 for rainforest). Both the NST results and structural equation modeling showed that bacterial communities were more stochastic in the dry season, while fungal communities were more stochastic in the rainy season; the effects of seasonal changes on assembly therefore differed between bacterial and fungal communities. More importantly, forest types did not have a direct impact on the assembly of bacterial or fungal communities, but exerted indirect effects via soil pH and soil available potassium.

First report of complete mitochondrial genome in the subfamily Alleculinae and mitochondrial genome-based phylogenetics in Tenebrionidae (Coleoptera: Tenebrionoidea).

Despite worldwide distribution and rich diversity, the knowledge of mitochondrial genome (mtgenome) characteristics within the family Tenebrionidae (Coleoptera) is still very limited, and phylogenetics remain unresolved for the family. In this study, the mtgenomes for 12 species are newly sequenced and annotated. Three of the species represent the first report of complete mtgenomes from the subfamily Alleculinae. Comparative analysis of 36 tenebrionid mtgenomes finds that gene composition and order are the same as a theoretical ancestral insect mtgenome, and AT bias, length variation, and codon usage are consistent with other reported beetle mtgenomes. Some intergenic overlap and gap sequences may contain phylogenetically informative information, whereas neither the conserved nor repeat sequences in the control region do. The subfamilies Lagriinae, Pimeliinae, Stenochiinae, and Alleculinae are found to be monophyletic, and the subfamilies Diaperinae and Tenebrioninae polyphyletic in our study. Furthermore, Lagriinae is sister to the rest of the subfamilies. At the tribal level, the tribes Lagriini in the subfamily Lagrrinae; Strongyliini in Stenochiinae; Cteniopodini in Alleculinae; and Triboliini, Opatrini, and Amarygmini in Tenebrioninae are monophyletic; while Diaperini in Diaperinae, and Tenebrionini in Tenebrioninae are polyphyletic.

A Comparative Study of Several EOF Based Imputation Methods for Long Gap Missing Values in a Single-Site Temporal Time Dependent (SSTTD) Air Quality (PM10) Dataset

Missing values are often a major problem in many scientific fields of environmental research, leading to prediction inaccuracy and biased analysis results. This study compares the performance of existing Empirical Orthogonal Functions (EOF) based imputation methods. The EOF mean centred approach (EOF-mean) with several proposed EOF based methods, which include the EOF-median, EOF-trimmean and the newly applied Regularised Expectation-Maximisation Principal Component Analysis based method, namely R-EMPCA in estimating missing values for long gap sequence of missing values problem that exists in a Single Site Temporal Time-Dependent (SSTTD) multivariate structure air quality (PM10) data set. The study was conducted using real PM10 data set from the Klang air quality monitoring station. Performance assessment and evaluation of the methods were conducted via a simulation plan which was carried out according to four percentages (5, 10, 20 and 30) of missing values with respect to several long gap sequences (12, 24, 168 and 720) of missing points (hours). Based on several performance indicators such as RMSE, MAE, R-Square and AI, the results have shown that R-EMPCA outperformed the other methods. The results also conclude that the proposed EOF-median and EOF-trimmean have better performance than the existing EOF-mean based method in which EOF-trimmean is the best among the three. The methodology and findings of this study contribute as a solution to the problem of missing values with long gap sequences for the SSTTD data set.

MBCL-36. HOW TO INCREASE SURVIVAL IN 7 TO 10% OF PATIENTS WITH AVERAGE-RISK MEDULLOBLASTOMA WITHOUT NEW THERAPIES: EARLY PROSPECTIVE NEURORADIOLOGY SCREENING EXPERIENCE FROM THE CHILDREN’S ONCOLOGY GROUP

BACKGROUNDPrevious Children’s Oncology Group (COG) average-risk medulloblastoma studies retrospectively identified that 7 to 10% of patients were wrongly staged; either due to the presence of unequivocal residual disease greater than 1.5cm2 or metastatic disease. Notably, these patients had an inferior survival. The current COG front-line average-risk study for WNT-driven medulloblastoma patients, ACNS1422, is a reduced-intensity therapeutic protocol. Given the potentially devastating consequences of dose reduction in a wrongly staged patient, ACNS1422 is utilizing optimized MRI sequences, including thin slices with no gap and post contrast T2 FLAIR sequences, combined with a rapid central neuroradiology review.RESULTSThe study opened on October 2 2017. As of 31 December 2019, a total of 34 patients have undergone central neuroradiology review. In 27/34 (79%) repeat scans were requested due to technically inadequate sequences (majority due to missing post contrast T2 FLAIR, slice thickness and gap issues). Of 19 repeat scans received, four patients (12%) were wrongly staged as average-risk; three patients were identified with residual disease >1.5cm2 (in 2 residual disease was confirmed at second resection) and one patient had widespread spinal metastases previously obscured by motion. In addition, metastatic disease was excluded in another patient, reported as having metastatic disease.CONCLUSIONOur data is consistent with previous reports revealing that approximately 10% of patients are wrongly staged as average-risk. The early experience of ACNS1422 reveals that the optimized MRI sequences combined with a rapid central neuroradiology review are very valuable in a cooperative group setting to more accurately stage patients.

A Numerical Study on the Regularity of d-Primes via Informational Entropy and Visibility Algorithms

Let a d -prime be a positive integer number with d divisors. From this definition, the usual prime numbers correspond to the particular case d = 2 . Here, the seemingly random sequence of gaps between consecutive d -primes is numerically investigated. First, the variability of the gap sequences for d ∈ 2,3 , … , 11 is evaluated by calculating the informational entropy. Then, these sequences are mapped into graphs by employing two visibility algorithms. Computer simulations reveal that the degree distribution of most of these graphs follows a power law. Conjectures on how some topological features of these graphs depend on d are proposed.

Codes and Gap Sequences of Hermitian Curves

Hermitian functional and differential codes are AG-codes defined on a Hermitian curve. To ensure good performance, the divisors defining such AG-codes have to be carefully chosen, exploiting the rich combinatorial and algebraic properties of the Hermitian curves. In this paper, the case of differential codes $C_{\Omega }(\mathtt {D},m\mathtt {T})$ on the Hermitian curve $\mathscr {H}_{q^{3}}$ defined over $\mathbb {F}_{q^{6}}$ is worked out where $\mathop {\mathrm {supp}}\nolimits (\mathtt {T}):= \mathscr {H}_{q^{3}}(\mathbb {F}_{q^{2}})$ , the set of all $\mathbb {F}_{q^{2}}$ -rational points of $\mathscr {H}_{q^{3}}$ , while $\mathtt {D}$ is taken, as usual, to be the sum of the points in the complementary set $D = \mathscr {H}_{q^{3}}(\mathbb {F}_{q^{6}})\setminus \mathscr {H} _{q^{3}}(\mathbb {F}_{q^{2}})$ . For certain values of $m$ , such codes $C_{\Omega }(\mathtt {D},m\mathtt {T})$ have better minimum distance compared with true values of 1-point Hermitian codes. The automorphism group of $C_{L}(\mathtt {D},m\mathtt {T})$ , $m\leq q^{3}-2$ , is isomorphic to $PGU(3,q)$ .

DIpartite: A tool for detecting bipartite motifs by considering base interdependencies.

It is extremely important to identify transcription factor binding sites (TFBSs). Some TFBSs are proposed to be bipartite motifs known as two-block motifs separated by gap sequences with variable lengths. While position weight matrix (PWM) is commonly used for the representation and prediction of TFBSs, dinucleotide weight matrix (DWM) enables expression of the interdependencies of neighboring bases. By incorporating DWM into the detection of bipartite motifs, we have developed a novel tool for ab initio motif detection, DIpartite (bipartite motif detection tool based on dinucleotide weight matrix) using a Gibbs sampling strategy and the minimization of Shannon’s entropy. DIpartite predicts the bipartite motifs by considering the interdependencies of neighboring positions, that is, DWM. We compared DIpartite with other available alternatives by using test datasets, namely, of CRP in E. coli, sigma factors in B. subtilis, and promoter sequences in humans. We have developed DIpartite for the detection of TFBSs, particularly bipartite motifs. DIpartite enables ab initio prediction of conserved motifs based on not only PWM, but also DWM. We evaluated the performance of DIpartite by comparing it with freely available tools, such as MEME, BioProspector, BiPad, and AMD. Taken the obtained findings together, DIpartite performs equivalently to or better than these other tools, especially for detecting bipartite motifs with variable gaps. DIpartite requires users to specify the motif lengths, gap length, and PWM or DWM. DIpartite is available for use at https://github.com/Mohammad-Vahed/DIpartite.

GAPPadder: a sensitive approach for closing gaps on draft genomes with short sequence reads

BackgroundClosing gaps in draft genomes is an important post processing step in genome assembly. It leads to more complete genomes, which benefits downstream genome analysis such as annotation and genotyping. Several tools have been developed for gap closing. However, these tools don’t fully utilize the information contained in the sequence data. For example, while it is known that many gaps are caused by genomic repeats, existing tools often ignore many sequence reads that originate from a repeat-related gap.ResultsWe compare GAPPadder with GapCloser, GapFiller and Sealer on one bacterial genome, human chromosome 14 and the human whole genome with paired-end and mate-paired reads with both short and long insert sizes. Empirical results show that GAPPadder can close more gaps than these existing tools. Besides closing gaps on draft genomes assembled only from short sequence reads, GAPPadder can also be used to close gaps for draft genomes assembled with long reads. We show GAPPadder can close gaps on the bed bug genome and the Asian sea bass genome that are assembled partially and fully with long reads respectively. We also show GAPPadder is efficient in both time and memory usage.ConclusionIn this paper, we propose a new approach called GAPPadder for gap closing. The main advantage of GAPPadder is that it uses more information in sequence data for gap closing. In particular, GAPPadder finds and uses reads that originate from repeat-related gaps. We show that these repeat-associated reads are useful for gap closing, even though they are ignored by all existing tools. Other main features of GAPPadder include utilizing the information in sequence reads with different insert sizes and performing two-stage local assembly of gap sequences. The results show that our method can close more gaps than several existing tools. The software tool, GAPPadder, is available for download at https://github.com/Reedwarbler/GAPPadder.

Gap sequences of fractal squares

We discuss gap sequences of a class of fractal squares, which have nontrivial connected components at most in one direction.

A reference genome of the Chinese hamster based on a hybrid assembly strategy.

Accurate and complete genome sequences are essential in biotechnology to facilitate genome‐based cell engineering efforts. The current genome assemblies for Cricetulus griseus, the Chinese hamster, are fragmented and replete with gap sequences and misassemblies, consistent with most short‐read‐based assemblies. Here, we completely resequenced C. griseus using single molecule real time sequencing and merged this with Illumina‐based assemblies. This generated a more contiguous and complete genome assembly than either technology alone, reducing the number of scaffolds by >28‐fold, with 90% of the sequence in the 122 longest scaffolds. Most genes are now found in single scaffolds, including up‐ and downstream regulatory elements, enabling improved study of noncoding regions. With >95% of the gap sequence filled, important Chinese hamster ovary cell mutations have been detected in draft assembly gaps. This new assembly will be an invaluable resource for continued basic and pharmaceutical research.

A Case Study into Microbial Genome Assembly Gap Sequences and Finishing Strategies.

This study characterized regions of DNA which remained unassembled by either PacBio and Illumina sequencing technologies for seven bacterial genomes. Two genomes were manually finished using bioinformatics and PCR/Sanger sequencing approaches and regions not assembled by automated software were analyzed. Gaps present within Illumina assemblies mostly correspond to repetitive DNA regions such as multiple rRNA operon sequences. PacBio gap sequences were evaluated for several properties such as GC content, read coverage, gap length, ability to form strong secondary structures, and corresponding annotations. Our hypothesis that strong secondary DNA structures blocked DNA polymerases and contributed to gap sequences was not accepted. PacBio assemblies had few limitations overall and gaps were explained as cumulative effect of lower than average sequence coverage and repetitive sequences at contig termini. An important aspect of the present study is the compilation of biological features that interfered with assembly and included active transposons, multiple plasmid sequences, phage DNA integration, and large sequence duplication. Our targeted genome finishing approach and systematic evaluation of the unassembled DNA will be useful for others looking to close, finish, and polish microbial genome sequences.

Genome analysis of Hibiscus syriacus provides insights of polyploidization and indeterminate flowering in woody plants.

Hibiscus syriacus (L.) (rose of Sharon) is one of the most widespread garden shrubs in the world. We report a draft of the H. syriacus genome comprised of a 1.75 Gb assembly that covers 92% of the genome with only 1.7% (33 Mb) gap sequences. Predicted gene modeling detected 87,603 genes, mostly supported by deep RNA sequencing data. To define gene family distribution among relatives of H. syriacus, orthologous gene sets containing 164,660 genes in 21,472 clusters were identified by OrthoMCL analysis of five plant species, including H. syriacus, Arabidopsis thaliana, Gossypium raimondii, Theobroma cacao and Amborella trichopoda. We inferred their evolutionary relationships based on divergence times among Malvaceae plant genes and found that gene families involved in flowering regulation and disease resistance were more highly divergent and expanded in H. syriacus than in its close relatives, G. raimondii (DD) and T. cacao. Clustered gene families and gene collinearity analysis revealed that two recent rounds of whole-genome duplication were followed by diploidization of the H. syriacus genome after speciation. Copy number variation and phylogenetic divergence indicates that WGDs and subsequent diploidization led to unequal duplication and deletion of flowering-related genes in H. syriacus and may affect its unique floral morphology.

Explicit Galois representations of automorphisms on holomorphic differentials in characteristic p

We determine the representation of the Galois group for the cyclotomic function fields in characteristic p>0 induced by the natural action on the space of holomorphic differentials via construction of an explicit canonical basis of differentials. This includes those cases which present wild ramification and finite automorphism groups with non-cyclic p-part, which have remained elusive. We also obtain information on the gap sequences of ramified primes and extend these results to rank one Drinfel'd modules.

Gap sequences of McMullen sets

We study the gap sequence of totally disconnected McMullen sets. Our result shows that if every horizontal line in the McMullen set is nonempty, then the gap sequence is unrelated to the box dimension. This implies that in such situations, the separation properties of McMullen sets are quite different from that of self-similar sets.

GAP SEQUENCES OF GRAPH-DIRECTED SETS

This paper studies the gap sequences of graph-directed sets satisfying the strong separation condition. An interesting application is to investigate the gap sequences of self-similar sets with overlaps.