Genome-wide analysis of tobacco NtTOM1/TOM3 gene family and identification of NtTOM1a/ NtTOM3a response to tobacco mosaic virus.

BACKGROUND: TOBAMOVIRUS MULTIPLICATION 1 (TOM1) and its homolog TOBAMOVIRUS MULTIPLICATION 3 (TOM3) play a prominent role in the multiplication of tobacco mosaic virus (TMV) in higher plants. Although homologs of NtTOM1/TOM3 genes have been identified in several plant species, little is known about the characteristics and functions of NtTOM1/TOM3 at the genome-wide level in tobacco (Nicotiana tabacum L.). RESULTS: In this study, we performed genome-wide identification and expression pattern analysis of the tobacco NtTOM1/TOM3 gene family. Twelve NtTOM1/TOM3 genes were identified and classified into four groups based on phylogenetic analysis. Sequence and conserved domain analyses showed that all these genes contained a specific DUF1084 domain. Expression pattern analysis showed that NtTOM1a, NtTOM1b, NtTOM1d, NtTOM3a, NtTOM3b, and NtTOM3d were induced by TMV at 1-, 3-, and 9 dpi, whereas the expression of other genes was not responsive to TMV at the early infection stage. TMV virion accumulation showed no obvious difference in either nttom1a or nttom3a mutants compared with the wild type. However, the virus propagation was significantly, but not completely, inhibited in the nttom1atom3a double mutant, indicating that other gene family members may function redundantly, such as NtTOM1b and NtTOM1d. In addition, overexpression of NtTOM1a or NtTOM3a also inhibited the TMV replication to some extent. CONCLUSIONS: The present study performed genome-wide analysis of the NtTOM1/TOM3 gene family in tobacco, and identified NtTOM1a and NtTOM3a as important genes involved in TMV multiplication based on functional analysis. These results provide a theoretical basis for further improving TMV resistance in tobacco.

Arithmetic in two languages: Localizing simple multiplication processing in the adult bilingual brain.

Verbally memorized multiplication tables are thought to create language-specific memories. Supporting this idea, bilinguals are typically faster and more accurate in the language in which they learned math (LA+) than in their other language (LA- ) . No study has yet revealed the underlying neurocognitive mechanisms explaining this effect, or the role of problem size in explaining the recruitment of different brain regions in LA+ and LA- . To fill this gap in the literature, 29 Spanish-English early bilingual adults, proficient in both languages, verified simple multiplication problems in each language while functional magnetic resonance imaging (fMRI) was acquired. More specifically, this study aimed to answer two questions: 1) Does LA+ recruit left superior and middle temporal gyri (STG/MTG) to a greater extent than LA- , reflecting more robust verbal representations of multiplication facts in LA+? In contrast, does LA- recruit the inferior frontal gyrus (IFG), reflecting more effortful retrieval, or the intraparietal sulcus (IPS), reflecting reliance on quantity processes? 2) Is there an interaction between language and problem size, where language differences are more pronounced for less practiced, large multiplication problems (e.g., 8 × 9) in comparison to more familiar, small problems (e.g., 2 × 3). Functional localizer tasks were used to identify hypothesis-driven regions of interest in verbal areas associated with verbal representations of arithmetic facts (left STG/MTG) and with the effortful retrieval of these facts (left IFG) and quantity areas engaged when calculation-based strategies are used (bilateral IPS). In planned analyses, no cluster reached significance for the direct comparison of languages (question 1) or for the interaction between language and problem size (question 2). An exploratory analysis found a main effect of problem size, where small problems recruited left STG/MTG and left IFG to a greater extent than large problems, suggesting greater verbal involvement for these problems in both languages. Additionally, large problems recruited right IPS to a greater extent than small problems, suggesting reliance on quantity processes. Our results suggest that proficient early bilingual adults engage similar brain regions in both languages, even for more difficult, large problems.

A Communication-Efficient Distributed Matrix Multiplication Scheme with Privacy, Security, and Resiliency.

Secure distributed matrix multiplication (SDMM) schemes are crucial for distributed learning algorithms where extensive data computation is distributed across multiple servers. Inspired by the application of repairing Reed-Solomon (RS) codes in distributed storage and secret sharing, we propose SDMM schemes with reduced communication overhead through the use of trace polynomials. Specifically, these schemes are designed to address three critical concerns: (i) ensuring information-theoretic privacy against collusion among servers; (ii) providing security against Byzantine servers; and (iii) offering resiliency against stragglers to mitigate computing delays. To the best of our knowledge, security and resiliency are being considered for the first time within trace polynomial-based approaches. Furthermore, our schemes offer the advantage of reduced sub-packetization and a lower server-count requirement, which diminish the computational complexity and download cost for the user.

Extraction, identification and mass production of arbuscular mycorrhizal fungi (AMF) from faba bean (Vicia faba L.) rhizosphere soils using maize (Zea mays L.) as a host plant.

Ethiopia is the second-largest grower of faba bean in the world next to China. The crop is highly useful with its edible seed serving as an essential protein complement of the Ethiopian diet, especially for those who cannot afford animal protein. Even though faba bean is mycotrophic to Arbuscular Mycorrhizal fungi (AMF), the different genera and species that are associated with the crop are not determined in yet at the maturity time of the crop (harvesting period). Sixteen faba bean rhizospheric soils were collected to isolate and identify AMF. Spores were extracted using the wet-sieving and decanting method. The Glomus genera was the most dominant, followed by the Acaulospora and Gigaspora genera. The highest spore load per 100 g of soil was observed in the sample that contained the lowest soil phosphorus. Furthermore, an inverse relationship between the spore load and soil phosphorus was observed. Three treatments were considered for mass multiplication of AMF, viz, Treatment (1) Glomus aggregatum, treatment (2) Glomus sp.BZ, and treatment (3) Glomus sp.AZ. However, the highest number of AMF's spore and root colonization was seen in treatment 3 with significant difference (P < 0.05) from the others. In conclusion, AMF constituted an important component of the faba bean rhizosphere during its harvesting period (dry season) and its multiplication using maize favored the viability and infectivity of the fungi.

In-Materia Annealing and Combinatorial Optimization Based on Vertical Memristive Array.

Due to its area and energy efficiency, a memristive crossbar array (CBA) has been extensively studied for various combinatorial optimization applications, from network problems to circuit design. However, conventional approaches include heavily burdening software fine-tuning for the annealing process. Instead, this study introduces the "in-materia annealing" method, where the inter-layer interference of vertically stacked memristive CBA is utilized as an annealing method. When mapping combinatorial optimization problems into the configuration layer of the CBA, exponentially decaying annealing profiles are generated in nearby noise layers. Moreover, in-materia annealing profiles can be controlled by changing compliance current, read voltage, and read pulse width. Therefore, the annealing profiles can be arbitrarily controlled and generated individually for each cell, providing rich noise sources to solve the problem efficiently. Consequently, the experimental and simulation of Max-Cut and weighted Max-Cut problems achieve notable results with the minimum software burden.

Toward industry 5.0: Challenges and enablers of intelligent manufacturing technology implementation under the perspective of sustainability.

The advancement of intelligent manufacturing technology in the era of Industry 5.0 has propelled the intelligence and automation of manufacturing production, while also exerting a significant impact on sustainable development of the manufacturing industry. However, the challenges and enablers faced by the transformation of intelligent manufacturing technology in the context of sustainable development of Industry 5.0 are still unclear. Based on literature review and expert opinions, this study uses the Likert scale to determine the challenges and enablers of the implementation of intelligent manufacturing technology in social, environmental and economic sustainability. The fuzzy-DEMETAL and AISM are used to analyze the logical relationship and hierarchical relationship between the above factors, and the MICMAC matrix is used to determine the key influencing factors. The research conclusions show that the most important challenges affecting the implementation of intelligent manufacturing technology are cost and funding, and the most important enabler is social benefits and public service improved. This research will provide insights for industry practitioners and decision makers in the management and decision-making process of implementing the transformation and upgrading of manufacturing intelligent manufacturing, thereby enhancing the sustainability of manufacturing development.

Implementation and optimization of SpMV algorithm based on SW26010P many-core processor and stored in BCSR format.

The irregular distribution of non-zero elements of large-scale sparse matrix leads to low data access efficiency caused by the unique architecture of the Sunway many-core processor, which brings great challenges to the efficient implementation of sparse matrix-vector multiplication (SpMV) computing by SW26010P many-core processor. To address this problem, a study of SpMV optimization strategies is carried out based on the SW26010P many-core processor. Firstly, we design a memorized data storage transformation strategy to transform the matrix in CSR storage format into BCSR (Block Compressed Sparse Row) storage. Secondly, the dynamic task scheduling method is introduced to the algorithm to realize the load balance between slave cores. Thirdly, the LDM memory is refined and designed, and the slave core dual cache strategy is optimized to further improve the performance. Finally, we selected a large number of representative sparse matrices from the Matrix Market for testing. The results show that the scheme has obviously speedup the processing procedure of sparse matrices with various sizes and sizes, and the master-slave speedup ratio can reach up to 38 times. The optimization method used in this paper has implications for other complex applications of the SW26010P many-core processor.

One-step cloning and targeted duplication of Pantoea ananatis chromosomal fragments.

In this study, we describe a novel method for one-step cloning and targeted duplication of P. ananatis chromosomal fragments. According to this method, the chromosomal region of interest is subcloned in vivo via λ Red recombination into the short synthetic non-replicable DNA fragment containing the excisable antibiotic-resistance marker gene and φ80 att-P site. The resulting circular non-replicating DNA molecule was immediately inserted into an alternative chromosomal locus due to φ80-integrase activity. To this end, the specially designed helper plasmid pONI, which can provide both the λ Red recombineering and φ80-integrase-mediated insertion, was constructed. In the described method, PCR amplification of the cloning fragment is unnecessary, making it convenient for manipulation of long-length DNA. Additionally, the possibility of spontaneous mutations occurring is completely precluded. This method was effectively used for the targeted chromosomal integration of additional copies of individual genes and operons up to 16 kb in size.

The Trypanosoma cruzi pleiotropic protein P21 orchestrates the intracellular retention and in-vivo parasitism control of virulent Y strain parasites.

P21 is a protein secreted by all forms of Trypanosoma cruzi (T. cruzi) with recognized biological activities determined in studies using the recombinant form of the protein. In our recent study, we found that the ablation of P21 gene decreased Y strain axenic epimastigotes multiplication and increased intracellular replication of amastigotes in HeLa cells infected with metacyclic trypomastigotes. In the present study, we investigated the effect of P21 in vitro using C2C12 cell lines infected with tissue culture-derived trypomastigotes (TCT) of wild-type and P21 knockout (TcP21-/-) Y strain, and in vivo using an experimental model of T. cruzi infection in BALB/c mice. Our in-vitro results showed a significant decrease in the host cell invasion rate by TcP21-/- parasites as measured by Giemsa staining and cell count in bright light microscope. Quantitative polymerase chain reaction (qPCR) analysis showed that TcP21-/- parasites multiplied intracellularly to a higher extent than the scrambled parasites at 72h post-infection. In addition, we observed a higher egress of TcP21-/- trypomastigotes from C2C12 cells at 144h and 168h post-infection. Mice infected with Y strain TcP21-/- trypomastigotes displayed higher systemic parasitemia, heart tissue parasite burden, and several histopathological alterations in heart tissues compared to control animals infected with scrambled parasites. Therewith, we propose that P21 is important in the host-pathogen interaction during invasion, cell multiplication, and egress, and may be part of the mechanism that controls parasitism and promotes chronic infection without patent systemic parasitemia.

The specifics of the Galois field GF(257) and its use for digital signal processing.

An algorithm of digital logarithm calculation for the Galois field G F ( 257 ) is proposed. It is shown that this field is coupled with one of the most important existing standards that uses a digital representation of the signal through 256 levels. It is shown that for this case it is advisable to use the specifics of quasi-Mersenne prime numbers, representable in the form p = 2 n + 1 , which includes the number 257. For fields G F ( 2 n + 1 ) , an alternating encoding can be used, in which non-zero elements of the field are displayed through binary characters corresponding to the numbers + 1 and - 1. In such an encoding, multiplying a field element by 2 is reduced to a quasi-cyclic permutation of binary symbols (the permuted symbol changes sign). Proposed approach makes it possible to significantly simplify the design of computing devices for calculation of digital logarithm and multiplication of numbers modulo 257. A concrete scheme of a device for digital logarithm calculation in this field is presented. It is also shown that this circuit can be equipped with a universal adder modulo an arbitrary number, which makes it possible to implement any operations in the field under consideration. It is shown that proposed digital algorithm can also be used to reduce 256-valued logic operations to algebraic form. It is shown that the proposed approach is of significant interest for the development of UAV on-board computers operating as part of a group.

High-Coupled Magnetic-Levitation Hybrid Nanogenerator with Frequency Multiplication Effect for Wireless Water Level Alarm.

Hybrid nanogenerators (HNGs) represent a promising avenue for water energy harvesting, yet their commercial viability faces hurdles such as limited power output, poor coupling, and constrained operational lifespans. Here, a highly coupled triboelectric-electromagnetic magnetic-levitation hybrid nanogenerator (ML-HNG) is introduced that shows great potential for water energy harvesting. The ML-HNG fulfills the challenges of high power output, strong coupling, and long operational lifespans. During the contact-separation process of the triboelectric nanogenerator (TENG), the changing magnetic flux in the electromagnetic generator's coils generates a potential difference between the coils and Cu electrodes. The unique design of the ML-HNG employs a shared coil electrode configuration, which enhances the coupling without adding extra volume. This integration allows the ML-HNG to achieve multi-frequency vibrations and multiple output cycles per external longitudinal movement, a phenomenon known as the frequency multiplication effect. With an average power density of 1.69 W m-3 in water, the ML-HNG provides continuous power for a thermo-hygrometer and can quickly drive a wireless water level alarm system within a minute. This groundbreaking hybrid nanogenerator design holds significant promise for the efficient and consistent harvesting of low-frequency ocean wave energy, marking a substantial advancement in blue energy technology.

Meta-Topolin as an Effective Benzyladenine Derivative to Improve the Multiplication Rate and Quality of In Vitro Axillary Shoots of Húsvéti Rozmaring Apple Scion.

In vitro mass propagation of apple plants plays an important role in the rapid multiplication of genetically uniform, disease-free scions and rootstocks with desired traits. Successful micropropagation of apple using axillary shoot cultures is influenced by several factors, the most critical of which is the cytokinin included in the culture medium. The impact of medium composition from single added cytokinins on shoot proliferation of apple scion Húsvéti rozmaring cultured on agar-agar gelled Murashige and Skoog medium fortified with indole butyric acid and gibberellic acid was investigated. The optimum concentration for efficient shoot multiplication differs according to the type of cytokinin. The highest significant multiplication rate (5.40 shoots/explant) was achieved using 2.0 µM thidiazuron while the longest shoots (1.80 cm) were observed on the medium containing benzyladenine at a concentration of 2.0 µM. However, application of either thidiazuron or benzyladenine as cytokinin source in the medium resulted in shoots of low quality, such as stunted and thickened shoots with small leaves. In the case of benzyladenine riboside, the 8 µM concentration was the most effective in increasing the multiplication rate (4.76 shoots/explant) but caused thickened stem development with tiny leaves. In the present study, meta-topolin was shown to be the most effective cytokinin that could be applied to induce sufficient multiplication (3.28 shoots/explant) and high-quality shoots along with shoot lengths of 1.46 cm when it was applied at concentrations of 4 µM. However, kinetin was the least active cytokinin; it practically did not induce the development of new shoots. The superior cytokinin for in vitro axillary shoot development of apple scion Húsvéti rozmaring with high-quality shoots was the meta-topolin, but it may be different depending on the variety/genotype under study.

CRISPR/Cas9-induced knockout of an amino acid permease gene (AAP6) reduced Arabidopsis thaliana susceptibility to Meloidogyne incognita.

BACKGROUND: Plant-parasitic root-knot nematode (Meloidogyne incognita) causes global yield loss in agri- and horticultural crops. Nematode management options rely on chemical method. However, only a handful of nematicides are commercially available. Resistance breeding efforts are not sustainable because R gene sources are limited and nematodes have developed resistance-breaking populations against the commercially available Mi-1.2 gene-expressing tomatoes. RNAi crops that manage nematode infection are yet to be commercialized because of the regulatory hurdles associated with transgenic crops. The deployment of the CRISPR/Cas9 system to improve nematode tolerance (by knocking out the susceptibility factors) in plants has emerged as a feasible alternative lately. RESULTS: In the present study, a M. incognita-responsive susceptibility (S) gene, amino acid permease (AAP6), was characterized from the model plant Arabidodpsis thaliana by generating the AtAAP6 overexpression line, followed by performing the GUS reporter assay by fusing the promoter of AtAAP6 with the ß-glucuronidase (GUS) gene. Upon challenge inoculation with M. incognita, overexpression lines supported greater nematode multiplication, and AtAAP6 expression was inducible to the early stage of nematode infection. Next, using CRISPR/Cas9, AtAAP6 was selectively knocked out without incurring any growth penalty in the host plant. The 'Cas9-free' homozygous T3 line was challenge inoculated with M. incognita, and CRISPR-edited A. thaliana plants exhibited considerably reduced susceptibility to nematode infection compared to the non-edited plants. Additionally, host defense response genes were unaltered between edited and non-edited plants, implicating the direct role of AtAAP6 towards nematode susceptibility. CONCLUSION: The present findings enrich the existing literature on CRISPR/Cas9 research in plant-nematode interactions, which is quite limited currently while compared with the other plant-pathogen interaction systems.

Unpacking the challenges and predictors of elementary-middle school students' use of the distributive property.

The distributive property plays a pivotal role in advancing students' understanding of multiplication, enabling the decomposition of problems and the acquisition of new facts. However, this property of multiplication is difficult for students to understand. We used two unique data sets to explore middle school students' use of the distributive property. Study 1 involved data from 1:1 structured interviews of students (N = 24) discussing worked examples and solving associated practice problems. We examined whether or not students used the distributive property to solve the problems and whether or not interviewers followed the recommended distributive property prompts or defaulted to more conventional methods. Despite exposure to worked examples using the distributive property and a protocol calling for attention to it, students and interviewers favored methods like PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) or long multiplication. Study 2 used a data set with middle school students' (N = 131) item-level responses on Kirkland's (2022; doctoral dissertation, University of Notre Dame) Brief Assessment of Mature Number Sense along with several related measures of domain-general and domain-specific skills. We extracted problems involving the distributive property for analysis. Surprisingly, there was no evidence that students' use of the distributive property improved from sixth grade to eighth grade. However, both grade-level mathematics achievement and cognitive reflection uniquely predicted the correct use of the distributive property. Results suggest that middle school students who exhibit stronger reflective thinking tend to perform better on distributive property problems. Findings highlight cognitive reflection as a potentially important construct involved in the understanding and use of the distributive property.

Efficient Carrier Multiplication in Self-Powered Near-Ultraviolet γ-InSe/Graphene Heterostructure Photodetector with External Quantum Efficiency Exceeding 161.

Carrier multiplication (CM) in semiconductors, the process of absorbing a single high-energy photon to form two or more electron-hole pairs, offers great potential for the high-response detection of high-energy photons in the ultraviolet spectrum. However, compared to two-dimensional semiconductors, conventional bulk semiconductors not only face integration and flexibility bottlenecks but also exhibit inferior CM performance. To attain efficient CM for ultraviolet detection, we designed a two-terminal photodetector featuring a unilateral Schottky junction based on a two-dimensional γ-InSe/graphene heterostructure. Benefiting from a strong built-in electric field, the photogenerated high-energy electrons in γ-InSe, an ideal ultraviolet light-absorbing layer, can efficiently transfer to graphene without cooling. It results in efficient CM within the graphene, yielding an ultrahigh responsivity of 468 mA/W and a record-high external quantum efficiency of 161.2% when it is exposed to 360 nm light at zero bias. This work provides valuable insights into developing next-generation ultraviolet photodetectors with high performance and low-power consumption.

Analysing Hermann Graßmann's works - retrospecting and re-assessing.

The life and work of Hermann Günther Graßmann (1809-1877) attract not only ever again the attention of mathematicians, mathematical historians and those interested in the history of mathematics, they constitute also a challenge for the methodology of historiographical research. This challenge persists since Friedrich Engel's biography of 1911; there, two sources were presented and interpreted in a not legitimate manner which even mislead since then various scholars. This paper faces the intricate task to unravel not only the methodological shortcomings of Engel's biography, but also to re-assess the misinterpretations - particularly of alleged influences on Graßmann's approaches - induced by Engel's misleading claims. Based upon broader historically contextualised analyses of Graßmann's innovative elements in his theory of extension and upon new primary sources for his student times at the Gymnasium and Berlin University, the paper presents a novel assessment of Graßmann's approaches.

Optical frequency multiplication using residual network with random forest regression.

In this work, we present a method for optical frequency multiplication utilizing a hybrid deep learning approach that integrates the Residual Network (ResNet) with the Random Forest Regression (RFR) algorithm. Three different frequency multiplication modulation schemes are adopted to illustrate the method, which can obtain suitable parameters for these schemes. Based on the parameters predicted by the algorithm, the 8-tupling, 12-tupling, and 16-tupling mm-wave signals are generated by numerical simulation. The simulation results show that for 8-tupling frequency multiplication, an OSSR (optical sideband suppression ratio) is 30.73 dB and an RFSSR (radio frequency spurious suppression ratio) of 80 GHz is 42.29 dB. For 12-tupling frequency multiplication, the OSSR is 30.09 dB, and the RFSSR of the 120 GHz mm wave is 36.21 dB. For generating 16-tupling frequency mm-wave, an OSSR of 29.86 dB and an RFSSR of 34.52 dB are obtained. In addition, the impact of amplitude fluctuation and bias voltage drift on the quality of mm-wave signals is also studied.

Minimizing Computation and Communication Costs of Two-Sided Secure Distributed Matrix Multiplication under Arbitrary Collusion Pattern.

This paper studies the problem of minimizing the total cost, including computation cost and communication cost, in the system of two-sided secure distributed matrix multiplication (SDMM) under an arbitrary collusion pattern. In order to perform SDMM, the two input matrices are split into some blocks, blocks of random matrices are appended to protect the security of the two input matrices, and encoded copies of the blocks are distributed to all computing nodes for matrix multiplication calculation. Our aim is to minimize the total cost, overall matrix splitting factors, number of appended random matrices, and distribution vector, while satisfying the security constraint of the two input matrices, the decodability constraint of the desired result of the multiplication, the storage capacity of the computing nodes, and the delay constraint. First, a strategy of appending zeros to the input matrices is proposed to overcome the divisibility problem of matrix splitting. Next, the optimization problem is divided into two subproblems with the aid of alternating optimization (AO), where a feasible solution can be obtained. In addition, some necessary conditions for the problem to be feasible are provided. Simulation results demonstrate the superiority of our proposed scheme compared to the scheme without appending zeros and the scheme with no alternating optimization.

Secure ECDSA SRAM-PUF Based on Universal Single/Double Scalar Multiplication Architecture.

Physically unclonable functions (PUFs) are crucial for enhancing cybersecurity by providing unique, intrinsic identifiers for electronic devices, thus ensuring their authenticity and preventing unauthorized cloning. The SRAM-PUF, characterized by its simple structure and ease of implementation in various scenarios, has gained widespread usage. The soft-decision Reed-Muller (RM) code, an error correction code, is commonly employed in these designs. This paper introduces the design of an RM code soft-decision attack algorithm to reveal its potential security risks. To address this problem, we propose a soft-decision SRAM-PUF structure based on the elliptic curve digital signature algorithm (ECDSA). To improve the processing speed of the proposed secure SRAM-PUF, we propose a custom ECDSA scheme. Further, we also propose a universal architecture for the critical operations in ECDSA, elliptic curve scalar multiplication (ECSM), and elliptic curve double scalar multiplication (ECDSM) based on the differential addition chain (DAC). For ECSMs, iterations can be performed directly; for ECDSMs, a two-dimensional DAC is constructed through precomputation, followed by iterations. Moreover, due to the high similarity of ECSM and ECDSM data paths, this universal architecture saves hardware resources. Our design is implemented on a field-programmable gate array (FPGA) and an application-specific integrated circuit (ASIC) using a Xilinx Virtex-7 and an TSMC 40 nm process. Compared to existing research, our design exhibits a lower bit error rate (2.7×10-10) and better area-time performance (3902 slices, 6.615 µs ECDSM latency).

Directed Self-Assembly of Cylinder-Forming Block Copolymers Using Pillar Topographic Patterns.

We conducted a computational study on the self-assembly behavior of cylinder-forming block copolymers, directed by a guide pattern of hexagonally or tetragonally arrayed pillars, using mesoscale density functional theory simulations. By adjusting the spacing (Lp) and diameter (D) of the pillars in relation to the intrinsic cylinder-to-cylinder distance (L2) of the cylinder-forming block copolymer, we investigated the efficiency of multiple-replicating cylinders, generated by the block copolymer, through the pillar-directed self-assembly process. The simulations demonstrated that at specific values of normalized parameters L˜2=L2/Lp and D˜=D/Lp coupled with suitable surface fields, triple and quadruple replications are achievable with a hexagonally arrayed pillar pattern, while only double replication is attainable with a tetragonally arrayed pillar pattern. This work, offering an extensive structure map encompassing a wide range of possible parameter spaces, including L˜2 and D˜, serves as a valuable guide for designing the contact hole patterning essential in nanoelectronics applications.