Double Group Research Articles

SARAh - web representational analysis.

The online software server SARAh-webRepresentational Analysis is introduced. It replaces the previous Windows-versions of SARAh-Representational analysis and SARAh-Refine, and related theory. The new suite of web apps carries out a range representational analysis calculations, including those based on the works of Kovalev, Bertaut, Izyumov, Bradley, Cracknell, Birman and Landau, for magnetic structures and electronic properties within frameworks based on the crystallographic space groups and point groups. Irreducible representations are sourced from the works of Kovalev, tabulated and computations are carried out on a server using Mathematica.

Spacer-type tibial osteotomy versus open wedge high tibial osteotomy and unicompartmental knee arthroplasty for Kellgren-Lawrence grade 3–4 medial unicompartmental knee osteoarthritis in patients younger than 65 years

BackgroundSpacer-type tibial osteotomy have been proven a novel and effective osteotomy to treat osteoarthritis, while lack of comparison with other surgical methods in younger patients. This study aims to evaluate the short-term clinical outcomes of spacer-type tibial osteotomy versus open wedge high tibial osteotomy (OWHTO) and unicompartmental knee arthroplasty (UKA) for Kellgren-Lawrence (K-L) grade 3–4 osteoarthritis (OA) in patients younger than 65 years.MethodsThis retrospective study analyzed a total of 224 patients with K-L grade 3–4 knee OA treated from March 2018 to November 2020. Three groups were created according to the operation type. The clinical outcomes recorded preoperatively and at 6, 12 and 24 months postoperatively were the range of motion (ROM), visual analogue scale (VAS), American Knee Society Score (KSS), Western Ontario and McMaster Universities Global (WOMAC) score, operation time, length of incision, relevant complications and failures. Radiographic parameters were measured to evaluate the correction of varus deformity.ResultsThe cohort comprised 224 patients; 70 underwent spacer-type tibial osteotomy, 73 underwent OWHTO, and 81 underwent UKA. The spacer group had the shortest incision (P = 0.000), least amount of bleeding (P = 0.000), and shortest operation time (P = 0.000). UKA achieved the most significant pain relief based on VAS (P = 0.014), KSS pain score (0.030), and WOMAC score (P = 0.000) at 6 months postoperatively, but there were no differences between three groups at 12 and 24 months postoperatively. The spacer and OWHTO groups achieved significantly greater ROM changes compared with the UKA group (all P = 0.000). The complication rate did not significantly differ between the three groups. No surgical failures were identified in HTO but two spacer dislocations in spacer group and three polyethylene dislocations in UKA.ConclusionFor younger patients with K-L grade 3–4 OA, OWHTO seems to be the most appropriate method through clinical comparisons. Although spacer-type tibial osteotomy offers shorter operation time and comparable clinical outcomes, it also has extended recovery phase, additional fibular incision and the risk of spacer dislocation, which did not appear to be superior to OWHTO and UKA under the indications outlined in this study.Trial registrationRetrospectively registered, QYFY WZLL 27,021.

Taking time: Auditory statistical learning benefits from distributed exposure.

In an auditory statistical learning paradigm, listeners learn to partition a continuous stream of syllables by discovering the repeating syllable patterns that constitute the speech stream. Here, we ask whether auditory statistical learning benefits from spaced exposure compared with massed exposure. In a longitudinal online study on Prolific, we exposed 100 participants to the regularities in a spaced way (i.e., with exposure blocks spread out over 3 days) and another 100 in a massed way (i.e., with all exposure blocks lumped together on a single day). In the exposure phase, participants listened to streams composed of pairs while responding to a target syllable. The spaced and massed groups exhibited equal learning during exposure, as indicated by a comparable response-time advantage for predictable target syllables. However, in terms of resulting long-term knowledge, we observed a benefit from spaced exposure. Following a 2-week delay period, we tested participants' knowledge of the pairs in a forced-choice test. While both groups performed above chance, the spaced group had higher accuracy. Our findings speak to the importance of the timing of exposure to structured input and also for statistical learning outside of the laboratory (e.g., in language development), and imply that current investigations of auditory statistical learning likely underestimate human statistical learning abilities.

Semiconducting Electrides Derived from Sodalite: A First-Principles Study.

Electrides are ionic crystals, with electrons acting as anions occupying well-defined lattice sites. These exotic materials have attracted considerable attention in recent years for potential applications in catalysis, rechargeable batteries, and display technology. Among this class of materials, electride semiconductors can further expand the horizon of potential applications due to the presence of a band gap. However, there are only limited reports on semiconducting electrides, hindering the understanding of their physical and chemical properties. In recent work, we initiated an approach to derive potential electrides via selective removal of symmetric Wyckoff sites of anions from existing complex minerals. Herein, we present a follow-up effort to design semiconducting electrides from parental complex sodalites. Among four candidate compounds, we found that a cubic Ca4Al6O12 structure with the I-43m space group symmetry exhibits perfect electron localization at the sodalite cages, with a narrow electronic band gap of 1.8 eV, making it suitable for use in photocatalysis. Analysis of the electronic structures reveals that a lower electronegativity of the surrounding cations drives greater electron localization and promotes the formation of an electride band near the Fermi level. Our work proposes an alternative approach for designing new semiconducting electrides under ambient conditions and offers guidelines for further experimental exploration.

Computational self-assembly of a six-fold chiral quasicrystal.

Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under real-space symmetry operations, quasicrystals possess symmetry that requires description by a space group in reciprocal space. In this study, we report the self-assembly of a six-fold chiral quasicrystal using molecular dynamics simulations of a two-dimensional particle system. The particles interact via the Lennard-Jones-Gauss pair potential and are subjected to a periodic substrate potential. We confirm the presence of chiral symmetry through diffraction patterns and order parameters, revealing unique local motifs in both real and reciprocal space. The quasicrystal's properties, including the tiling structure and symmetry and the extent of diffuse scattering, are strongly influenced by substrate potential depth and temperature. Our results provide insights into the mechanisms of chiral quasicrystal formation and the role and potential of external fields in tailoring quasicrystal structures.

Structural Investigation of Chloride Ion-Containing Acrylate-Based Imidazolium Poly(Ionic Liquid) Homopolymers and Crosslinked Networks: Effect of Alkyl Spacer and N-Alkyl Substituents.

Understanding the interplay between the molecular structure of the ionic liquid (IL) subunit, the resulting nanostructure and ion transport in polymerized ionic liquids (PILs) is necessary for the realization of high-performance solid-state electrolytes required in various advanced applications. Herein, we present a detailed structural characterization of a recently synthesized series of acrylate-based PIL homopolymers and networks with imidazolium cations and chloride anions with varying alkyl spacer and terminal group lengths designed for organic solid-state batteries based on X-ray scattering. The impact of the concentrations of both the crosslinker and added tetrabutylammonium chloride (TBACl) conducting salt on the structural characteristics is also investigated. The results reveal that the length of both the spacer and terminal group influence the chain packing and, in turn, the nanophase segregation of the polar domains. Long spacers and terminal groups seem to induce denser polar aggregates sandwiched between more compact alkyl spacer and terminal group domains. However, the large inter-backbone spacing achieved seems to limit the ionic conductivity of these PILs. More importantly, our findings show that the previously reported general relationships between the ionic conductivity and the structural parameters of the nanostructure of PILs are not always attainable for different molecular structures of the IL side group.

Para-Sasakian $$\phi -$$symmetric spaces

AbstractWe study the Boothby–Wang fibration of para-Sasakian manifolds and introduce the class of para-Sasakian $$\phi $$ ϕ -symmetric spaces, canonically fibering over para-Hermitian symmetric spaces. We remark that in contrast to the Hermitian setting the center of the isotropy group of a simple para-Hermitian symmetric space G/H can be either one- or two-dimensional, and prove that the associated metric is not necessarily the G-invariant extension of the Killing form of G. Using the Boothby–Wang fibration and the classification of semisimple para-Hermitian symmetric spaces, we explicitly construct semisimple para-Sasakian $$\phi $$ ϕ -symmetric spaces fibering over semisimple para-Hermitian symmetric spaces. We provide moreover an example of non-semisimple para-Sasakian $$\phi $$ ϕ -symmetric space.

Bifurcation analysis of figure-eight choreography in the three-body problem based on crystallographic point groups

Abstract The bifurcation of figure-eight choreography is analyzed by its symmetry group based on the variational principle of the action. The irreducible representations determine the symmetry and the dimension of the 
Lyapunov-Schmidt reduced action, which yields four types of bifurcations in the sequence of the bifurcation cascade. Type 1 bifurcation, represented by trivial representation, bifurcates two solutions. Type 2, by non-trivial one-dimensional representation, bifurcates two congruent solutions. Type 3 and 4, by two-dimensional irreducible representations, bifurcate two sets of three and six congruent solutions, respectively. We analyze numerical bifurcation solutions previously published and four new ones: 
non-symmetric choreographic solution of type 2, non-planar solution of type 2, y-axis symmetric solution of type 3, and non-symmetric solution of type 4.

Transformation of Matrix Presentation for Bieberbach Groups into Polycyclic Presentations

A Bieberbach group is a torsion free crystallographic group that represents an extension of a free abelian lattice group by a finite point group. This research began by taking the group offered in the Crystallographic Algorithms and Tables (CARAT) package, which is in the matrix form. There are only four Bieberbach groups of dimension six to be isomorphic to the quaternion point group of order eight. In this study, three Bieberbach groups of dimension six with the quaternion point group of order eight that are considered as only the first group has been found its well-defined polycyclic presentation. Every group has eight generators that describe the group. However, the algorithm used in constructing the polycyclic presentation requires a new arbitrary generator to be added into the group. Then the consistency relations need to be checked and the polycyclic presentation is said to be a well-defined construction if it is consistent. Therefore, this study shows the construction of polycyclic presentation with the new arbitrary generator for all three groups. Furthermore, the polycyclic presentation for the second group has been proven to be consistent, which implies that the construction is well-defined.

Electric-Field-Induced Switchable Two-Dimensional Altermagnets.

Altermagnetism, as a recently discovered unconventional antiferromagnetism, allows the lifting of spin degeneracy without net magnetization. The spin splitting of the intrinsic altermagnets is protected by the spin space group symmetry and is therefore difficult to control externally. Here, we propose an extrinsic altermagnet as a complement to the intrinsic altermagnet, whose spin splitting is induced by and can be significantly modulated by the electric field. We then screened intrinsic and extrinsic altermagnets by combining symmetry analysis and high-throughput calculations, identifying 16 intrinsic altermagnets and 24 extrinsic altermagnets. We demonstrate that the spin splitting of extrinsic altermagnets is proportional to the electric field strength, and its sign can be switched by reversing the electric field. Some extrinsic altermagnets exhibit considerable spin splitting, such as CaMnSi with 398 meV under an electric field of 0.1 V/Å. This work provides a realistic material platform for the potential application of 2D altermagnets.

Modulation of Ti3C2Tx interlayer spacing and functional groups by Lewis‐basic halides and their effects on Li+ storage properties

AbstractSurface and interfacial chemistry play a vital role in shaping the properties of two‐dimensional transition metal carbides and nitrides (MXenes). This study focuses on utilizing Lewis‐basic halides (LiCl/KCl) for thermal treatment of multilayered Ti3C2Tx, leading to the simultaneous modulation of interlayer spacing and surface functional groups. Compared to the pristine Ti3C2Tx, the LiCl/KCl treated sample (heating temperature: 450°C, denoted as LK‐Ti3C2Tx‐450) showcases a remarkable increase in the interlayer spacing and synergistic optimization of the functional groups. These modifications endow LK‐Ti3C2Tx‐450 with enhanced electrochemical properties, rendering it as a promising anode candidate for lithium‐ion batteries. The increased interlayer spacing is particularly advantageous, as it facilitates efficient and rapid Li+ diffusion, a vital factor in enhancing the performance of energy storage devices.

Synthesis, characterization, biodegradation, and evaluation of the surface‐active properties of non‐ionic gemini surfactants derived from lauryl diethanolamide

AbstractThe surface activities and application properties of aqueous solution surfactants are greatly influenced by their structure, especially the spacer group that connects the polar head groups. Herein, four new non‐ionic Gemini surfactants with different spacers were designed and synthesized, and their surfactant properties and biodegradability were studied. The synthesis of these compounds involves a two‐step procedure. The first step is the formation of an amide from lauric acid and diethanolamine. The second step is the reaction of lauryl diethanolamide with four different spacers, the latter being flexible‐hydrophilic, and rigid‐hydrophobic in structure, respectively. Their structures were characterized using 1H NMR, 13C NMR, FT‐IR, and ESI‐MS. The critical micelle concentration (CMC), the surface tension at CMC (γCMC), the efficiency of these compounds to reduce the surface tension by 20 mN/m (C20 and pC20), the effectiveness (πCMC), the maximum surface excess (Γmax), and the minimum surface area (Amin) were measured at 20, 40, and 50°C. The molecular architecture of the spacers in these compounds strongly influences the thermodynamic parameters, such as the standard change for Gibbs free energy of adsorption (ΔG°ads) and the standard change for Gibbs free energy of micellization (ΔG°mic). The ability of these surfactants to reduce surface tension is particularly good, but their distinguishing characteristic is their high relative propensity to form micellar aggregates. This aggregation ability improves as the hydrophilicity and flexibility of the spacer increase. Finally, in less than 30 days, all non‐ionic Gemini surfactants were determined to be 99% biodegradable in river water.

Constitutionalisation of the Right to Abortion

Enshrining the right to abortion in the constitution represented an ideal in many states that faced this issue or restrictions that led to the loss of human life. The phenomenon gained momentum in the European space after the decision of the Supreme Court of the United States in the Dobbs v Jackson Women’s Health (Dobbs v Jackson Women’s Health Organization, 2022). I mentioned the decision, by which the Court annulled the right to abortion, offering the possibility to waive this right to the national authorities. The rise of extremist religious groups in the European space made the right to abortion a controversial subject, which is why the phenomenon was left to the discretion of the national state from a decision-making perspective. However, in the EU, the European Parliament alerted in time the threats posed to the rights to abortion requesting that this right be introduced in the EU Convention of Rights (European Parliament Resolution, 2022; European Parliament Resolution, 2024). Rounding off the decision to implement the right to abortion in the constitution generated at the national level a real debate for and against, which in the European space ended with some changes such as states that have adopted this right: France (French legislative proposal no. 293, 2023), Belgium (Parl. doc. 55 2832/001 (2021-2022), Norway, and Sweden (Press release Department of Justice, 2023). Against this reaction, legal experts questioned the necessity, adequacy and added value of the constitutionalisation (Dobner M. Loughlin, 2010) of a right to abortion in European-national contexts.

A Comparative Prospective Study on the Accuracy and Efficiency of Autonomous Robotic System Versus Dynamic Navigation System in Dental Implant Placement.

This study aimed to evaluate the efficiency of and discrepancies between planned and final implant positions using dynamic computer-assisted implant surgery (d-CAIS) and autonomous robotic computer-assisted implant surgery (r-CAIS) in clinical practice. The study included 83 patients, who received 135 implants between December 2022 and March 2024 (r-CAIS group: 43 patients with 71 implants; d-CAIS group: 40 patients with 64 implants). Cone-beam computed tomography scans taken before and after surgery assessed linear and angular deviations between the groups in both 2D and 3D spaces. The duration of surgery was also analysed. The angular deviation between d-CAIS and r-CAIS was 3.61° ± 1.65° versus 1.62° ± 0.93° (p < 0.001), the platform deviation was 1.12 ± 0.51 mm versus 0.50 ± 0.19 mm (p < 0.001) and the apex deviation was 1.36 ± 0.57 mm versus 0.58 ± 0.21 mm (p < 0.001). The d-CAIS group experienced significantly longer drilling and implant placement times compared to the r-CAIS group (10.6 ± 3.8 vs. 8.3 ± 3.4 min, p < 0.01), while preparation time showed no statistical difference between the groups (7.2 ± 3.3 vs. 6.2 ± 2.7 min, p > 0.05). The robotic system demonstrated higher accuracy and efficiency of implant placement than the dynamic navigation system in partially edentulous patients.

Synthesis of zinc oxide-doped reduced graphene oxide (rGO) nanocomposites on visible light-driven photocatalytic and antibacterial activity applications

Abstract In this study, reduced graphene oxide (rGO), ZnO nanocomposites, and zinc oxide-doped reduced graphene oxide (ZnO/rGO) nanocomposites were successfully synthesized via the sol–gel method and investigated for the removal of methyl blue (MB) dye and antibacterial activity under visible light irradiation. The synthesized nanocomposites were characterized using XRD, SEM, EDX, FTIR, UV–vis DRS, and BET techniques to analyze the crystallographic structure, phase, surface morphology, and different functional groups in the prepared catalysts. The ZnO/rGO nanocomposites demonstrated a great photocatalytic performance over 98% degradation of 20 mg L−1 of methylene blue (MB) dye within just 90 min under visible light. A heterojunction material achieved a higher 20% than that of the ZnO single-phase. Among the prepared photocatalysts, the nanocomposite with 0.2 grams rGO demonstrated the best results. Reusability studies revealed that ZnO/rGO catalysts maintained over 90% efficiency up to three cycles, with rGO serving as an effective adsorbent and ZnO providing catalytic activity. In addition, the antibacterial activity of the nanocomposites was evaluated against both Gram-positive and Gram-negative bacteria, showing significant inhibition due to the photocatalytic generation of reactive oxygen species. These findings suggest that ZnO/rGO nanocomposites are promising materials for environmental remediation and antibacterial applications.

Understanding orientational disorder in crystalline assemblies of hard convex polyhedra.

Spontaneous self-assembly of hard convex polyhedra is known to form orientationally disordered crystalline phases, where particle orientations do not follow the same pattern as the positional arrangement of the crystal. A distinct type of orientational phase with discrete rotational mobility has been reported in hard particle systems. In this paper, we present a new analysis method for characterizing the orientational phase of a crystal, which is based on algorithmic detection of unique orientations. Using this method, we collected complete statistics of discrete orientations along the Monte Carlo simulation trajectories and observed that particles were equally partitioned among them, with specific values of pairwise orientational differences. These features remained constant across the pressure range and did not depend on rotational mobility. The discrete mobility was characteristic of a distinct equilibrium thermodynamic phase, qualitatively different from the freely rotating plastic phase with continuous orientations. The high pressure behavior with frozen particle orientations was part of that same description and not a non-equilibrium arrested state. We introduced a precise notion of orientational order and demonstrated that the system was maximally disordered at the level of a unit cell, even though individual particles could only take a few discrete orientations. We report the existence of this phase in five polyhedral shapes and in systematically curated shape families constructed around two of them. The symmetry mismatch between the particle and the crystallographic point groups was found to be a predictive indicator for the occurrence of this phase.

Assessing Cyberattacks in Response to Police Actions in Physical Space

ABSTRACT RThere is little research considering the ways that local events in physical space trigger responses from ideological groups in online spaces. This study attempted to address this gap in the literature through the analysis of information from the Extremist Cybercrime Database (ECCD), a unique open-source repository of cyberattacks performed against U.S. targets from 1998 to 2020. This qualitative study focused on the language used during cyberattacks against police agencies by the hacker collective Anonymous. Evidence suggested that the attackers’ language reflected values observed in the hacker subculture to justify their attacks and incorporated negative language regarding law enforcement. This was particularly evident in cases of police excessive use of force against minority groups and emphasized the need for public protest and social change.

Computational hemodynamic indices to identify Transcatheter Aortic Valve Implantation degeneration

Background and Objectives:Structural Valve Deterioration (SVD) is the main limiting factor to the long-term durability of the bioprosthetic valves used for Transcatheter Aortic Valve Implantation (TAVI), a minimally invasive technique for the treatment of severe aortic stenosis. The aim of this retrospective study is to perform patient-specific computational analyses of blood dynamics shortly after TAVI to identify hemodynamic indices that correlate with a premature onset of SVD which is detected at 5-10 years long-term follow-up exam after TAVI. Methods:The study population comprises fourteen patients: seven cases with SVD at long-term follow-up were identified and seven cases without SVD were randomly extracted from the same cohort. Starting from pre-operative CT images, we created trustworthy post-TAVI scenarios by virtually inserting the bioprosthetic valve (stent and leaflets) and we qualitatively validated such virtual scenarios against post-TAVI CT scans, when available. We then performed numerical simulations imposing personalized inlet conditions based on patient-specific Echo Doppler cardiac output measurements and the numerical results were post-processed to identify suitable hemodynamics indices with the aim of discriminating between the SVD and non-SVD groups of patients. In particular, differences in terms of each individual index were evaluated using a Wilcoxon rank-sum test. Moreover, we defined three synthetic scores, based on suitably scaled hemodynamic indices of stress and vorticity, evaluated in different contexts: on the leaflets, in the ascending aorta, and in the whole domain. Results:We found that the hemodynamic index related to leaflets’ OSI individually shows statistically significant differences (p=0.007) between the SVD and non-SVD groups. Moreover, our proposed synthetic scores are able to clearly isolate the SVD group both in a two-dimensional space given by the aorta and leaflets scores and by only considering the global synthetic score. Conclusion:The results of this computational study suggest that blood dynamics may play an important role in creating the conditions that lead to SVD. Moreover, the proposed synthetic scores could provide further indications for clinicians in assessing and predicting TAVI valves’ long-term performance.

Nano-structured and High-performance Mn-based Positive Electrode Materials for Lithium-ion Batteries

Towards widespread adoption of electric vehicles, Co/Ni-free and high energy density positive electrode materials for lithium-ion batteries are necessary. Among the various positive electrode materials, stoichiometric “zigzag”-type layered LiMnO2 with orthorhombic space-group symmetry has been extensively studied as potential high-energy and low-cost positive electrode materials. Although orthorhombic LiMnO2 delivers a large reversible capacity of over 200 mA h g-1 thorough a phase transition from layered to spinel-like phase during charging and discharging, over 30 cycles are required to obtain such a large reversible capacity due to the sluggish phase transition kinetics. In this study, nanostructured LiMnO2 with both orthorhombic and monoclinic layered domains is synthesized, and its electrochemical performance as positive electrode materials is examined. The nanostructured LiMnO2 delivers a maximum reversible capacity of >200 mA h g-1 within 5 cycles, indicating that the phase transition kinetics to the spinel-like phase upon electrochemical cycling are faster when compared with orthorhombic LiMnO2. Moreover, a significant improvement of cycle performance, i.e., ~90% retention after 100 cycles, is achieved by using a highly concentrated electrolyte solution coupled with lithium phosphate coating through suppression of Mn dissolution into electrolyte. From these results, the feasibility of practical Co/Ni-free high-energy positive electrode materials will be discussed in detail.

Comparison of fusion rate, radiologic and clinical outcome between CaO-SiO2-P2O5-B2O3 bioactive glass-ceramics 7 (BGS-7) spacer and allograft spacer with iliac bone graft in multilevel ACDF.

CaO-SiO2-P2O5-B2O3 bioactive glass-ceramics7 (BGS-7) are known for their strong integration with bone and stability and are commonly used in spinal fusions. This study aimed to compare fusion rates and radiological and clinical outcomes between BGS-7 and allograft spacers with iliac bone grafts (IBG) in multilevel anterior cervical discectomy and fusion (ACDF) surgeries. This retrospective study was conducted at BRM Medical Center. We included patients who underwent multilevel ACDF at BRM Medical Center between January 2012 and December 2023. The patients had symptoms such as cervical radiculopathy and myelopathy due to cervical disc herniation, stenosis, and spondylosis. We evaluated the preoperative and postoperative Japanese Orthopedic Association (JOA) scores, neck disability index (NDI), functional rating index (FRI), and visual analog scale (VAS) scores for the neck, shoulder, and upper extremities at 6 months and 1 year after surgery. Fusion rates were assessed using dynamic radiography and computed tomography (CT) scans at 1 year postoperatively. Radiological measurements were obtained from preoperative and postoperative plain radiographs. At the 1-year follow-up, the fusion rates were 89.5% for BGS-7 and 92.2% for the allograft cage on dynamic radiographs (p=0.156) and 93.4% and 90.4%, respectively, on CT scans (p=0.319), confirming both internal and external osseointegration. Subsidence rates were 4% for BGS-7 and 10% for the allograft spacer group. Both groups showed increased cervical lordosis (CL), segmental lordosis (SL), and segmental height postoperatively, with maintained lower segmental height (LSH) in the BGS-7 group than in the allograft spacer group at postoperatively 1 year. No adjacent segmental disease (ASD) occurred in either group. The JOA, NDI, and FRI showed significant improvements in both groups. The VAS scores decreased significantly in both groups, indicating improved clinical outcomes. In multilevel ACDF, BGS-7 demonstrated fusion rates comparable to those of the allograft spacer with IBG, experiencing fewer instances of subsidence and cage fracture. Therefore, BGS-7 spacer can be safely utilized in multilevel ACDF as a substitute for traditional allograft spacers, without the need for additional IBG.