Weak Sequence Research Articles

Pattern Avoidance in Weak Ascent Sequences

In this paper, we study pattern avoidance in weak ascent sequences, giving some results for patterns of length 3. This is an analogous study to one given by Duncan and Steingr\'imsson (2011) for ascent sequences. More precisely, we provide systematically the generating functions for the number of weak ascent sequences avoiding the patterns $001, 011, 012, 021$, and $102$. Additionally, we establish bijective connections between pattern-avoiding weak ascent sequences and other combinatorial objects, such as compositions, upper triangular 01-matrices, and plane trees.

Some aspects of 𝜆-weak convergence using difference operator

Abstract In this paper, we introduce generalized difference weak sequence space classes by utilizing the difference operator Δ ı ȷ \Delta^{\jmath}_{\imath} and the de la Vallée–Poussin mean, denoted as [ ( V , λ ) w , Δ ı ȷ ] m [(\mathscr{V},\lambda)_{w},\Delta^{\jmath}_{\imath}]_{m} for m = 0 m=0 , 1, and ∞. Further, we explore some algebraic and topological properties of these spaces, including their nature as linear, normed, Banach, and BK spaces. Additionally, we examine properties such as solidity, symmetry, and monotonicity. Finally, we define and establish some inclusion relations among generalized difference weak statistical convergence, generalized difference weak 𝜆-statistical convergence, and generalized difference weak [ V , λ ] [\mathscr{V},\lambda] -convergence.

Zinc-finger (ZiF) fold secreted effectors form a functionally diverse family across lineages of the blast fungus Magnaporthe oryzae.

Filamentous plant pathogens deliver effector proteins into host cells to suppress host defence responses and manipulate metabolic processes to support colonization. Understanding the evolution and molecular function of these effectors provides knowledge about pathogenesis and can suggest novel strategies to reduce damage caused by pathogens. However, effector proteins are highly variable, share weak sequence similarity and, although they can be grouped according to their structure, only a few structurally conserved effector families have been functionally characterized to date. Here, we demonstrate that Zinc-finger fold (ZiF) secreted proteins form a functionally diverse effector family in the blast fungus Magnaporthe oryzae. This family relies on the Zinc-finger motif for protein stability and is ubiquitously present in blast fungus lineages infecting 13 different host species, forming different effector tribes. Homologs of the canonical ZiF effector, AVR-Pii, from rice infecting isolates are present in multiple M. oryzae lineages. Wheat infecting strains of the fungus also possess an AVR-Pii like allele that binds host Exo70 proteins and activates the immune receptor Pii. Furthermore, ZiF tribes may vary in the proteins they bind to, indicating functional diversification and an intricate effector/host interactome. Altogether, we uncovered a new effector family with a common protein fold that has functionally diversified in lineages of M. oryzae. This work expands our understanding of the diversity of M. oryzae effectors, the molecular basis of plant pathogenesis and may ultimately facilitate the development of new sources for pathogen resistance.

Genomic surveillance during the first two years of the COVID-19 pandemic - country experience and lessons learned from Türkiye.

Türkiye confirmed its first case of SARS-CoV-2 on March 11, 2020, coinciding with the declaration of the global COVID-19 pandemic. Subsequently, Türkiye swiftly increased testing capacity and implemented genomic sequencing in 2020. This paper describes Türkiye's journey of establishing genomic surveillance as a middle-income country with limited prior sequencing capacity and analyses sequencing data from the first two years of the pandemic. We highlight the achievements and challenges experienced and distill globally relevant lessons. We tracked the evolution of the COVID-19 pandemic in Türkiye from December 2020 to February 2022 through a timeline and analysed epidemiological, vaccination, and testing data. To investigate the phylodynamic and phylogeographic aspects of SARS-CoV-2, we used Nextstrain to analyze 31,629 high-quality genomes sampled from seven regions nationwide. Türkiye's epidemiological curve, mirroring global trends, featured four distinct waves, each coinciding with the emergence and spread of variants of concern (VOCs). Utilizing locally manufactured kits to expand testing capacity and introducing variant-specific quantitative reverse transcription polymerase chain reaction (RT-qPCR) tests developed in partnership with a private company was a strategic advantage in Türkiye, given the scarcity and fragmented global supply chain early in the pandemic. Türkiye contributed more than 86,000 genomic sequences to global databases by February 2022, ensuring that Turkish data was reflected globally. The synergy of variant-specific RT-qPCR kits and genomic sequencing enabled cost-effective monitoring of VOCs. However, data analysis was constrained by a weak sequencing sampling strategy and fragmented data management systems, limiting the application of sequencing data to guide the public health response. Phylodynamic analysis indicated that Türkiye's geographical position as an international travel hub influenced both national and global transmission of each VOC despite travel restrictions. This paper provides valuable insights into the testing and genomic surveillance systems adopted by Türkiye during the COVID-19 pandemic, proposing important lessons for countries developing national systems. The findings underscore the need for robust testing and sampling strategies, streamlined sample referral, and integrated data management with metadata linkage and data quality crucial for impactful epidemiological analysis. We recommend developing national genomic surveillance strategies to guide sustainable and integrated expansion of capacities built for COVID-19 and to optimize the effective utilization of sequencing data for public health action.

Flexible TAM requirement of TnpB enables efficient single-nucleotide editing with expanded targeting scope

TnpBs encoded by the IS200/IS605 family transposon are among the most abundant prokaryotic proteins from which type V CRISPR-Cas nucleases may have evolved. Since bacterial TnpBs can be programmed for RNA-guided dsDNA cleavage in the presence of a transposon-adjacent motif (TAM), these nucleases hold immense promise for genome editing. However, the activity and targeting specificity of TnpB in homology-directed gene editing remain unknown. Here we report that a thermophilic archaeal TnpB enables efficient gene editing in the natural host. Interestingly, the TnpB has different TAM requirements for eliciting cell death and for facilitating gene editing. By systematically characterizing TAM variants, we reveal that the TnpB recognizes a broad range of TAM sequences for gene editing including those that do not elicit apparent cell death. Importantly, TnpB shows a very high targeting specificity on targets flanked by a weak TAM. Taking advantage of this feature, we successfully leverage TnpB for efficient single-nucleotide editing with templated repair. The use of different weak TAM sequences not only facilitates more flexible gene editing with increased cell survival, but also greatly expands targeting scopes, and this strategy is probably applicable to diverse CRISPR-Cas systems.

Alternating parity weak sequencing

AbstractA subset of a group is ‐weakly sequenceable if there is an ordering of its elements such that the partial sums , given by and for , satisfy whenever and . By Costa et al., it was proved that if the order of a group is then all sufficiently large subsets of the nonidentity elements are ‐weakly sequenceable when is prime, and . Inspired by this result, we show that, if is the semidirect product of and and the subset is balanced, then admits, regardless of its size, an alternating parity ‐weak sequencing whenever is prime and . A subset of is balanced if it contains the same number of even elements and odd elements and an alternating parity ordering alternates even and odd elements. Then using a hybrid approach that combines both Ramsey theory and the probabilistic method we also prove, for groups that are semidirect products of a generic (nonnecessarily abelian) group and , that all sufficiently large balanced subsets of the nonidentity elements admit an alternating parity ‐weak sequencing. The same procedure works also for studying the weak sequenceability for generic sufficiently large (not necessarily balanced) sets. Here we have been able to prove that, if the size of a subset of a group is large enough and if does not contain 0, then is ‐weakly sequenceable.

Synthetic self-adjuvanted multivalent Mucin 1 (MUC1) glycopeptide vaccines with improved in vivo antitumor efficacy.

The tumor-associated glycoprotein Mucin 1 (MUC1) is aberrantly glycosylated on cancer cells and is considered a promising target for antitumor vaccines. The weak immunogenicity and low sequence homology of mouse mucins and human MUC1 are the main obstacles for the development of vaccines. Herein, a self-adjuvanted strategy combining toll-like receptor 2 lipopeptide ligands and T-cell epitopes and the multivalent effect were used to amplify the immune response and evade the unpredictable immunogenicity, generating two self-adjuvanted three-component MUC1 vaccines (mono- and trivalent MUC1 vaccines). To simulate the aberrantly glycosylated MUC1 glycoprotein, the MUC1 tandem repeat peptide was bounded with Tn antigens at T9, S15, and T16, and served as B-cell epitopes. Results showed that both vaccines elicited a robust antibody response in wild-type mice compared with a weaker response in MUC1 transgenic mice. The trivalent vaccine did not elevate the antibody response level compared with the monovalent vaccine; however, a more delayed tumor growth and prolonged survival time was realized in wild-type and transgenic mouse models treated with the trivalent vaccine. These results indicate that the self-adjuvanted three-component MUC1 vaccines, especially the trivalent vaccine, can trigger robust antitumor effects regardless of sequence homology, and, therefore, show promise for clinical translation.

WIV, a protein domain found in a wide number of arthropod viruses, which probably facilitates infection.

The most powerful approach to detect distant homologues of a protein is based on structure prediction and comparison. Yet this approach is still inapplicable to many viral proteins. Therefore, we applied a powerful sequence-based procedure to identify distant homologues of viral proteins. It relies on three principles: (1) traces of sequence similarity can persist beyond the significance cutoff of homology detection programmes; (2) candidate homologues can be identified among proteins with weak sequence similarity to the query by using 'contextual' information, e.g. taxonomy or type of host infected; (3) these candidate homologues can be validated using highly sensitive profile-profile comparison. As a test case, this approach was applied to a protein without known homologues, encoded by ORF4 of Lake Sinai viruses (which infect bees). We discovered that the ORF4 protein contains a domain that has homologues in proteins from >20 taxa of viruses infecting arthropods. We called this domain 'widespread, intriguing, versatile' (WIV), because it is found in proteins with a wide variety of functions and within varied domain contexts. For example, WIV is found in the NSs protein of tospoviruses, a global threat to food security, which infect plants as well as their arthropod vectors; in the RNA2 ORF1-encoded protein of chronic bee paralysis virus, a widespread virus of bees; and in various proteins of cypoviruses, which infect the silkworm Bombyx mori. Structural modelling with AlphaFold indicated that the WIV domain has a previously unknown fold, and bibliographical evidence suggests that it facilitates infection of arthropods.

A mitophagy sensor PPTC7 controls BNIP3 and NIX degradation to regulate mitochondrial mass

Mitophagy mediated by BNIP3 and NIX critically regulates mitochondrial mass. Cellular BNIP3 and NIX levels are tightly controlled by SCFFBXL4-mediated ubiquitination to prevent excessive mitochondrial loss and lethal disease. Here, we report that knockout of PPTC7, a mitochondrial matrix protein, hyperactivates BNIP3-/NIX-mediated mitophagy and causes perinatal lethality that is rescued by NIX knockout in mice. Biochemically, the PPTC7 precursor is trapped by BNIP3 and NIX to the mitochondrial outer membrane, where PPTC7 scaffolds assembly of a substrate-PPTC7-SCFFBXL4 holocomplex to degrade BNIP3 and NIX, forming a homeostatic regulatory loop. PPTC7 possesses an unusually weak mitochondrial targeting sequence to facilitate its outer membrane retention and mitophagy control. Starvation upregulates PPPTC7 expression in mouse liver to repress mitophagy, which critically maintains hepatic mitochondrial mass, bioenergetics, and gluconeogenesis. Collectively, PPTC7 functions as a mitophagy sensor that integrates homeostatic and physiological signals to dynamically control BNIP3 and NIX degradation, thereby maintaining mitochondrial mass and cellular homeostasis.

Functional analysis of the AUG initiator codon context reveals novel conserved sequences that disfavor mRNA translation in eukaryotes.

mRNA translation is a fundamental process for life. Selection of the translation initiation site (TIS) is crucial, as it establishes the correct open reading frame for mRNA decoding. Studies in vertebrate mRNAs discovered that a purine at -3 and a G at+4 (where A of the AUG initiator codon is numbered+1), promote TIS recognition. However, the TIS context in other eukaryotes has been poorly experimentally analyzed. We analyzed in vitro the influence of the -3, -2, -1and+4 positions of the TIS context in rabbit, Drosophila, wheat, and yeast. We observed that -3A conferred the best translational efficiency across these species. However, we found variability at the+4 position for optimal translation. In addition, the Kozak motif that was defined from mammalian cells was only weakly predictive for wheat and essentially non-predictive for yeast. We discovered eight conserved sequences that significantly disfavored translation. Due to the big differences in translational efficiency observed among weak TIS context sequences, we define a novel category that we termed 'barren AUG context sequences (BACS)', which represent sequences disfavoring translation. Analysis of mRNA-ribosomal complexes structures provided insights into the function of BACS. The gene ontology of the BACS-containing mRNAs is presented.

Morphisms and extensions between bricks over preprojective algebras of type A

The bricks over preprojective algebras of type A are known to be in bijection with certain combinatorial objects called “arcs”. In this paper, we show how one can use arcs to compute bases for the Hom-spaces and first extension spaces between bricks. We then use this description to classify the “weak exceptional sequences” over these algebras. Finally, we explain how our result relates to a similar combinatorial model for the exceptional sequences over hereditary algebras of type A.

Sediment analysis and historical context of the 2018 Palu-Donggala tsunami deposit, Indonesia

On 28th September 2018, a magnitude 7.5 earthquake occurred on the Palu-Koro strike slip fault near Palu, Indonesia. Shortly after, large tsunami waves generated by the earthquake and the submarine landslides it triggered, washed into Palu Bay. Here, we describe sediment characteristics of the tsunami deposits and present wave height models to provide a modern analogue for tsunamis occurring on strike slip faults. We analyzed 51 sediment samples from 21 sampling points on two transects at Palu City and one transect at Pantaloan. At Palu City, the tsunami inundated between 250 and 270 m inland. Sediments were massive, with landward fining from coarse sands (φ 0) to fine sands (φ 3.7) and weak upward fining sequences (by up to 1 φ). At Pantaloan the tsunami inundated up to 275 m inland. Sediments were massive, with landward fining from a few grains of gravel (φ −2) and coarse sands (φ 0.5) to fine sands (φ 2.5) and weak upward fining sequences (by up to 1 φ). Based on the sediment data the TSUFLIND model predicted: at Palu city flow depths of 1 to 8 m, and flow velocities up to 3.9 m/s; and at Pantoloan flow depths of 2 to 8 m, and flow velocities up 3.8 m/s. The boulder transport model was applied to data from heavy concrete blocks (0.8 to 4.9 tons) deposited by the tsunami between 46 and 125 m inland, and predicted flow depths of 0.8 to 4.3 m and flow velocities up to 5.6 m/s. The rapid attenuation inland of the tsunami flow depth is consistent with the event being partially generated by landslides caused by the Palu-Donggala earthquake. A study of Dutch colonial archives and historical data reveals at least six tsunami events have occurred in or near Palu Bay since 1920, suggesting a very short return period for such events, and a significant tsunami hazard to the area.

Free vibration properties of beetle elytron plate: Composite material, stacked structure and boundary conditions

Beetle elytron plate (BEP), which is derived from the bionics of Trypoxylus dichotomus's elytra, is a typical lightweight and high-strength structure with superior and comprehensive mechanical properties. To promote the engineering application of BEPs, this paper explores the vibration characteristics of foam-filled fiber composite BEPs. Through the finite element method (FEM), structural parameters such as the length-to-width ratio, core height-to-thickness ratio, skin thickness and foam density influence the natural frequency and mode. Furthermore, the influence pattern of parameters (such as boundary conditions and the number of stacked layers) toward the first two orders of natural frequencies and modes of the BEP were investigated under controlled total height and controlled single layer height. The results indicate that 1) the ranking of structural parameters on the 1st order frequency from a strong to weak sequence is as follows: length-to-width ratio, core height-to-thickness ratio, foam density and skin thickness; for the 2nd order natural frequency: length-to-width ratio, skin thickness, foam density and core height-to-thickness ratio. 2) Generally, an increase in the length-to-width ratio will reduce the frequency of the BEP, and increases in the core height-to-thickness ratio and skin thickness will raise its frequency. Additionally, foam filling plays a decisive role in local deformation. 3) When the total height of the sandwich plate is controlled, the improvement of the boundary conditions can effectively boost its 2nd-order frequency (approximately 200%), but the 1st-order frequency can be significantly increased (approximately 140%) only when all four sides are improved. 4) In the case of controlling the height of the single layer of the sandwich plate, its frequency gradually increases with the increase in the number of stacked layers. However, when the constraints are weak or there are few stacked layers, increasing the number of stacked layers can effectively boost the vibration frequency. This paper provides references and suggestions for the design and application of sandwich structures, enriching the research on the mechanical properties of BEPs and establishing groundwork for promoting BEPs in engineering practices.

Isolating all the real roots of a mixed trigonometric-polynomial

Mixed trigonometric-polynomials (MTPs) are functions of the form f(x,sin⁡x,cos⁡x) where f is a trivariate polynomial with rational coefficients, and the argument x ranges over the reals. In this paper, an algorithm “isolating” all the real roots of an MTP is provided and implemented. It automatically divides the real roots into two parts: one consists of finitely many roots in an interval [μ−,μ+] while the other consists of countably many roots in R﹨[μ−,μ+]. For the roots in [μ−,μ+], the algorithm returns isolating intervals and corresponding multiplicities while for those greater than μ+, it returns finitely many mutually disjoint small intervals Ii⊂[−π,π], integers ci>0 and multisets of root multiplicity {mj,i}j=1ci such that any root >μ+ is in the set (∪i∪k∈N(Ii+2kπ)) and any interval Ii+2kπ⊂(μ+,∞) contains exactly ci distinct roots with multiplicities m1,i,...,mci,i, respectively. The efficiency of the algorithm is shown by experiments. The method used to isolate the roots in [μ−,μ+] is applicable to any other bounded interval as well. The algorithm takes advantages of the weak Fourier sequence technique and deals with the intervals period-by-period without scaling the coordinate so to keep the length of the sequence short. The new approaches can easily be modified to decide whether there is any root, or whether there are infinitely many roots in unbounded intervals of the form (−∞,a) or (a,∞) with a∈Q.

A two-step mitochondrial import pathway couples the disulfide relay with matrix complex I biogenesis.

Mitochondria critically rely on protein import and its tight regulation. Here, we found that the complex I assembly factor NDUFAF8 follows a two-step import pathway linking IMS and matrix import systems. A weak targeting sequence drives TIM23-dependent NDUFAF8 matrix import, and en route, allows exposure to the IMS disulfide relay, which oxidizes NDUFAF8. Import is closely surveyed by proteases: YME1L prevents accumulation of excess NDUFAF8 in the IMS, while CLPP degrades reduced NDUFAF8 in the matrix. Therefore, NDUFAF8 can only fulfil its function in complex I biogenesis if both oxidation in the IMS and subsequent matrix import work efficiently. We propose that the two-step import pathway for NDUFAF8 allows integration of the activity of matrix complex I biogenesis pathways with the activity of the mitochondrial disulfide relay system in the IMS. Such coordination might not be limited to NDUFAF8 as we identified further proteins that can follow such a two-step import pathway.

Positively limited sets in Banach lattices

We introduce and study the class of positively limited sets in Banach lattices, that is, sets on which every weak⁎ null sequence of positive functionals converges uniformly to zero. Moreover the relationships between the class of positively limited sets and other known classes of sets such as almost limited sets and (weakly) compact sets are discussed. Some properties of Banach lattices can be characterized in terms of positively limited sets.

A Combinatorial Proof of the Unimodality and Symmetry of Weak Composition Rank Sequences

A Combinatorial Proof of the Unimodality and Symmetry of Weak Composition Rank Sequences

Weak ascent sequences and related combinatorial structures

In this paper we introduce weak ascent sequences, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the following objects: permutations avoiding a particular length-4 bivincular pattern; upper-triangular binary matrices that satisfy a column-adjacency rule; factorial posets that are weakly (3+1)-free. We also show how weak ascent sequences are related to a class of pattern avoiding inversion sequences that has been a topic of recent research by Auli and Elizalde. Finally, we consider the problem of enumerating these new sequences and give a closed form expression for the number of weak ascent sequences having a prescribed length and number of weak ascents.

The GDAP1 p.Glu222Lys Variant-Weak Pathogenic Effect, Cumulative Effect of Weak Sequence Variants, or Synergy of Both Factors?

Charcot–Marie–Tooth disorders (CMT) represent a highly heterogeneous group of diseases of the peripheral nervous system in which more than 100 genes are involved. In some CMT patients, a few weak sequence variants toward other CMT genes are detected instead of one leading CMT mutation. Thus, the presence of a few variants in different CMT-associated genes raises the question concerning the pathogenic status of one of them. In this study, we aimed to analyze the pathogenic effect of c.664G>A, p.Glu222Lys variant in the GDAP1 gene, whose mutations are known to be causative for CMT type 4A (CMT4A). Due to low penetrance and a rare occurrence limited to five patients from two Polish families affected by the CMT phenotype, there is doubt as to whether we are dealing with real pathogenic mutation. Thus, we aimed to study the pathogenic effect of the c.664G>A, p.Glu222Lys variant in its natural environment, i.e., the neuronal SH-SY5Y cell line. Additionally, we have checked the pathogenic status of p.Glu222Lys in the broader context of the whole exome. We also have analyzed the impact of GDAP1 gene mutations on the morphology of the transfected cells. Despite the use of several tests to determine the pathogenicity of the p.Glu222Lys variant, we cannot point to one that would definitively solve the problem of pathogenicity.

Existence of solutions for critical Fractional FitzHugh–Nagumo type systems

AbstractIn this paper we study the existence of radially symmetric solutions for a Fractional FitzHugh–Nagumo type systems where , , denotes the fractional Laplacian operator and is a continuous function which is allowed to have critical growth: polynomial in case and exponential if and . We transform the system into an equation with a nonlocal term. We find a critical point of the corresponding energy functional defined in the space of functions with norm endowed by a scalar product that takes into account such nonlocal term. For that matter, and due to the lack of compactness, we deal with weak convergent minimizing sequences and sequences of Lagrange multipliers of an action minima problem.