Non-Enzymatic Glucose Sensors Composed of Polyaniline Nanofibers with High Electrochemical Performance.

The measurement of glucose concentration is a fundamental daily care for diabetes patients, and therefore, its detection with accuracy is of prime importance in the field of health care. In this study, the fabrication of an electrochemical sensor for glucose sensing was successfully designed. The electrode material was fabricated using polyaniline and systematically characterized using scanning electron microscopy, high-resolution transmission electron microscopy, X-ray diffraction, Fourier transform infrared spectroscopy, and UV-visible spectroscopy. The polyaniline nanofiber-modified electrode showed excellent detection ability for glucose with a linear range of 10 µM to 1 mM and a detection limit of 10.6 µM. The stability of the same electrode was tested for 7 days. The electrode shows high sensitivity for glucose detection in the presence of interferences. The polyaniline-modified electrode does not affect the presence of interferences and has a low detection limit. It is also cost-effective and does not require complex sample preparation steps. This makes it a potential tool for glucose detection in pharmacy and medical diagnostics.

Concentration Gradient Induced Delithiation Failure of MoO3 for Li-Ion Batteries.

Electric vehicle manufacturers worldwide are demanding superior lithium-ion batteries, with high energy and power densities, compared to gasoline engines. Although conversion-type metal oxides are promising candidates for high-capacity anodes, low initial Coulombic efficiency (ICE) and poor capacity retention have hindered research on their applications. In this study, the ICE of conversion-type MoO3 is investigated, with a particular focus on the delithiation failure. A computational modeling predicts the concentration gradient of Li+ in MoO3 particles. The highly delithiated outer region of the particle forms a layer with low electronic conductivity, which impedes further delithiation. A comparative study using various sizes of MoO3 particles demonstrated that the electrode failure during delithiation is governed by the concentration gradient and the subsequent formation of a resistive shell. The proposed failure mechanism provides critical guidance for the development of conversion-type anode materials with improved electrochemical reversibility.

Cobalt-ferrite/Ag-fMWCNT hybrid nanocomposite catalyst for efficient degradation of synthetic organic dyes via peroxymonosulfate activation.

The activation of peroxymonosulfate (PMS) by nanocatalysts has shown promise as an effective wastewater treatment protocol. Magnetic CoFe2O4/Ag-nanoparticles (NPs) anchored on functionalized multiwalled carbon nanotubes (fMWCNTs), a support material, were synthesized using a one-pot solvothermal method. The surface morphologies and physicochemical properties of the CoFe2O4/Ag-fMWCNT hybrid nanocomposite catalyst were investigated by powder X-ray diffraction analysis, field-emission scanning electron microscopy, energy-dispersive X-ray spectroscopy, high-resolution transmission electron microscopy, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy, and nitrogen adsorption-desorption isotherms. The activity of the nanocomposite combined with PMS (serving as an activator) toward the degradation of rhodamine B, methylene blue, methyl orange, and methyl red was investigated. The obtained optimal 0.02 g CoFe2O4/Ag-fMWCNTs exhibited the highest PMS activation performance, with a removal percentage of 100% for 20 ppm dye concentration at pH 6.5 within 14 min. In addition, the rhodamine B degradation product was investigated by analyzing the intermediate products by liquid chromatography/mass spectrometry (LC-MS). The homogeneous distribution of CoFe2O4/Ag NPs on fMWCNTs accelerated PMS activation and enhanced the catalytic degradation of dyes. The effects of the reaction parameters on the dye degradation efficiency were investigated by using different nanocatalysts (fMWCNTs, CoFe2O4/fMWCNTs, and CoFe2O4/Ag-fMWCNTs) as well as by varying the pH (3-11), dye concentration (10-50 mg/l), catalyst dose (0.002-0.3 g), and PMS dose (0.02-0.1 g). Quenching experiments revealed that sulfate radicals are primarily responsible for rhodamine B degradation. A plausible mechanism for catalytic PMS activation was also proposed. Complete decolorization occurred within the first few minutes of the reaction. Furthermore, the catalytic activity of the CoFe2O4/Ag-fMWCNT/PMS hybrid nanocomposite remained stable after five successive cycles. This study verifies the applicability of CoFe2O4/Ag-fMWCNTs as an ultrafast catalyst for the complete removal of persistent organic pollutants via PMS activation, revealing their promising application in wastewater treatment.

Bone Resorption During Submerged Healing After Guided Bone Regeneration: A Prospective Case Series.

OBJECTIVE: The aim of this study was to evaluate bone resorption quantitatively during the healing period subsequent to ridge augmentation. MATERIALS AND METHODS: Sixteen patients requiring vertical ridge augmentation before implant placement were recruited in the study. The study used an allograft and nonresorbable membrane. A custom acrylic stent was used to measure changes in bone volume. Augmented bone was compared with remaining bone 6 months after guided bone regeneration (α = 0.05 by means of the paired t test). RESULTS: All sites following the six months post-surgery were analyzed. Overall changes in alveolar bone were observed with a mean resorption rate of 19.8% (p<0.001). The vertical bone measurement indicated a mean resorption rate of 22.8% (range = 18.5% - 26.5%). The horizontal measurement indicated a mean resorption rate of 18.7% (range = 12.6% - 26.0%). Among the sixteen sites, four sites with post-operative complications including membrane exposure showed an average of 42.1% resorption rates. CONCLUSION: Loss in graft quantity was observed after ridge augmentation using an allograft and nonresorbable membrane during submerged healing before implant placement. Further studies with larger sample sizes are recommended to confirm its findings.

Transcriptome sequencing reveals that LPS-triggered transcriptional responses in established microglia BV2 cell lines are poorly representative of primary microglia.

BACKGROUND: Microglia are resident myeloid cells in the CNS that are activated by infection, neuronal injury, and inflammation. Established BV2 microglial cell lines have been the primary in vitro models used to study neuroinflammation for more than a decade because they reduce the requirement of continuously maintaining cell preparations and animal experimentation models. However, doubt has recently been raised regarding the value of BV2 cell lines as a model system. METHODS: We used triplicate RNA sequencing (RNA-seq) to investigate the molecular signature of primary and BV2 microglial cell lines using two transcriptomic techniques: global transcriptomic biological triplicate RNA-seq and quantitative real-time PCR. We analyzed differentially expressed genes (DEGs) to identify transcription factor (TF) motifs (-950 to +50 bp of the 5' upstream promoters) and epigenetic mechanisms. RESULTS: Sequencing assessment and quality evaluation revealed that primary microglia have a distinct transcriptomic signature and express a unique cluster of transcripts in response to lipopolysaccharide. This microglial signature was not observed in BV2 microglial cell lines. Importantly, we observed that previously unidentified TFs (i.e., IRF2, IRF5, IRF8, STAT1, STAT2, and STAT5A) and the epigenetic regulators KDM1A, NSD3, and SETDB2 were significantly and selectively expressed in primary microglia (PM). Although transcriptomic alterations known to occur in BV2 microglial cell lines were identified in PM, we also observed several novel transcriptomic alterations in PM that are not frequently observed in BV2 microglial cell lines. CONCLUSIONS: Collectively, these unprecedented findings demonstrate that established BV2 microglial cell lines are probably a poor representation of PM, and we establish a resource for future studies of neuroinflammation.

Hierarchical superstructures from a star-shaped molecule consisting of a cyclic oligosiloxane with cyanobiphenyl moieties.

Unconventional star-shaped liquid crystals (abbreviated as SiLCs) were successfully synthesized by chemically connecting four cyanobiphenyl anisotropic mesogens to the periphery of a super-hydrophobic and ultra-flexible cyclic tetramethyltetrasiloxane ring with flexible hexyl chains. Based on the combined experimental techniques of differential scanning calorimetry (DSC), cross-polarized optical microscopy (POM), solid-state carbon-13 ((13)C) nuclear magnetic resonance (NMR) spectroscopy and one-dimensional (1D) wide-angle X-ray diffraction (WAXD), it was found that the SiLC molecule exhibited the monotropic phase transition from a LC phase to a crystalline phase. The crystalline phase was only detected during slow heating processes above its glass transition temperature, while a LC phase was formed both during cooling and during heating processes. The hierarchical superstructures were identified from the structure-sensitive 2D WAXD of the macroscopically oriented SiLC film and confirmed by selected area electron diffraction (SAED) of the SiLC single crystals. The molecular packing symmetry in the monoclinic unit cell was further investigated by computer simulations on the real and reciprocal spaces. Macroscopically oriented SiLC hierarchical superstructures on the different length scales may provide the targeted physical properties, which can allow us to apply SiLC molecules in the fields of electro-optical devices and nonlinear optics.

A first-cycle coulombic efficiency higher than 100% observed for a Li2MO3 (M = Mo or Ru) electrode.

The lithiation/de-lithiation behavior of a ternary oxide (Li2MO3, where M = Mo or Ru) is examined. In the first lithiation, the metal oxide (MO2) component in Li2MO3 is lithiated by a conversion reaction to generate nano-sized metal (M) particles and two equivalents of Li2O. As a result, one idling Li2O equivalent is generated from Li2MO3. In the de-lithiation period, three equivalents of Li2O react with M to generate MO3. The first-cycle Coulombic efficiency is theoretically 150% since the initial Li2MO3 takes four Li(+) ions and four electrons per formula unit, whereas the M component is oxidized to MO3 by releasing six Li(+) ions and six electrons. In practice, the first-cycle Coulombic efficiency is less than 150% owing to an irreversible charge consumption for electrolyte decomposition. The as-generated MO3 is lithiated/de-lithiated from the second cycle with excellent cycle performance and rate capability.

Strategies for Enhancing the Stability of Lithium Metal Anodes in Solid-State Electrolytes.

The current commercially used anode material, graphite, has a theoretical capacity of only 372 mAh/g, leading to a relatively low energy density. Lithium (Li) metal is a promising candidate as an anode for enhancing energy density; however, challenges related to safety and performance arise due to Li's dendritic growth, which needs to be addressed. Owing to these critical issues in Li metal batteries, all-solid-state lithium-ion batteries (ASSLIBs) have attracted considerable interest due to their superior energy density and enhanced safety features. Among the key components of ASSLIBs, solid-state electrolytes (SSEs) play a vital role in determining their overall performance. Various types of SSEs, including sulfides, oxides, and polymers, have been extensively investigated for Li metal anodes. Sulfide SSEs have demonstrated high ion conductivity; however, dendrite formation and a limited electrochemical window hinder the commercialization of ASSLIBs due to safety concerns. Conversely, oxide SSEs exhibit a wide electrochemical window, but compatibility issues with Li metal lead to interfacial resistance problems. Polymer SSEs have the advantage of flexibility; however their limited ion conductivity poses challenges for commercialization. This review aims to provide an overview of the distinctive characteristics and inherent challenges associated with each SSE type for Li metal anodes while also proposing potential pathways for future enhancements based on prior research findings.

Unraveling the unknown: Adaptive spatial planning to enhance climate resilience for the endangered Swamp Grass-babbler (Laticilla cinerascens) with habitat connectivity and complexity approach.

The endangered and poorly known Swamp Grass-babbler, Laticilla cinerascens (Passeriformes: Pellorneidae), confronts critical threats and vulnerability due to its specific habitat requirements and restricted populations in the northeastern region of the Indian Subcontinent. This study investigates the distribution of the species, habitat quality, geometry and shape complexity of connectivity among the protected areas (PAs), and responses to climate change in Northeast India under different climate change pathways by utilizing ensemble distribution models, and ecological metrics. From the total distribution extent (1,42,000 km2), approximately 9366 km2 (6.59 %) is identified as the suitable habitat for this threatened species. Historically centered around Dibru Saikhowa National Park (DSNP), the species faced a drastic decline due to anthropogenic activities and alteration in land use and lover cover. The study also reveals a significant decline in suitable habitat for L. cinerascens in future climate scenarios, with alarming reductions under SSP126 (>10 % in the timeframe 2041-2060 and > 30 % from 2061 to 2080), SSP245 (>90 % in both time periods), and SSP585 (>90 % in both timeframes) from the present scenario. At present, DSNP has the most suitable habitat within the distribution range but is projected to decline (>90 %) under more severe climate change scenarios, as observed in other PAs. Landscape fragmentation analysis indicates a shift in habitat geometry, highlighting the intricate impact of climate change. It predicts a substantial 343 % increase (in the SSP126) in small habitat patches in the future. Connectivity analysis among PAs shows a significant shift, with a decline exceeding 20 %. The analysis of shape complexity and connectivity geometry reveals a significant increase of over 220 % in the fragmentation of connectivity among PAs between 2061 and 2080 under the SSP585 climate change scenario compared to the present conditions. The study underscores the urgent need for conservation actions, emphasizing the complex interplay of climate change, habitat suitability, and fragmentation. Prioritizing PAs with suitable habitats and assessing their connectivity is crucial. Adaptive management strategies are essential to address ongoing environmental changes and safeguard biodiversity. Future research in critical areas is needed to establish long-term monitoring programs to lead/extend effective conservation strategies.

Developing centrifugal force real-time digital PCR for detecting extremely low DNA concentration.

Digital PCR (dPCR) is a technique for absolute quantification of nucleic acid molecules. To develop a dPCR technique that enables more accurate nucleic acid detection and quantification, we established a novel dPCR apparatus known as centrifugal force real-time dPCR (crdPCR). This system is efficient than other systems with only 2.14% liquid loss by dispensing samples using centrifugal force. Moreover, we applied a technique for analyzing the real-time graph of the each micro-wells and distinguishing true/false positives using artificial intelligence to mitigate the rain, a persistent issue with dPCR. The limits of detection and quantification were 1.38 and 4.19 copies/µL, respectively, showing a two-fold higher sensitivity than that of other comparable devices. With the integration of this new technology, crdPCR will significantly contribute to research on next-generation PCR targeting absolute micro-analysis.

The effects of radio frequency sputtering of TiO2 on Li[Li0.07Nio.38Co0.15Mn0.4]O2 cathode for lithium ion batteries.

A radio frequency (RF) sputtering system is used to coat nano-thick TiO2 layer on the overlithiated layered metal oxide (OLO) electrode. The X-ray diffraction (XRD) and the field emission-scanning electron microscope (FE-SEM) images indicate amorphous TiO2 is coated on the top surface of the electrode with a thickness of approximately 20 nm for the 40 min sputtered sample. The sample sputtered for 40 minutes cycled at 90 mA g(-1) between 2 and 4.8 V versus Li+/Li has 15 mA h g(-1) more specific capacity at 100th cycle than that of the uncoated sample. In the voltage profiles, additional overpotential is unobservable upon sputtering TiO2 in comparison to that of the reference sample. Further analyses by the electrochemical impedance spectroscopy (EIS) and X-ray photoelectron spectroscopy (XPS) demonstrate the sputtered sample has less electrolyte decomposition products on the surface than that of the reference sample. Moreover, in the case of sputtering, reduced amount of transition metal and Li2O are deposited on the surface of the counter electrode, Li. In summary, the sputtered TiO2 acts as nano-sized artificial solid electrolyte interface (SEI) layer, which protects the surface of the electrode and improves kinetic properties, leading to improved performance.

A three-dimensional image-superimposition CAD/CAM technique to record the position and angulation of the implant abutment screw access channel.

Cement-retained, implant-supported restorations have advantages over screw-retained restorations, but retrievability can be a problem. By using computer-aided design and computer-aided manufacturing (CAD/CAM) technology, a working cast or mouth can be scanned, and a definitive record of the screw hole can be made in 3 dimensions and saved as a file. This information includes not only the position of the opening of the screw hole but also its angulation and orientation, which can be retrieved if required.

The impact of the COVID-19 pandemic on life expectancy by the level of area deprivation in South Korea.

Objective: Comparative evidence suggests that the impact of COVID-19 on life expectancy has been relatively milder in South Korea. This study aims to examine whether the pandemic has universal or unequal impacts on life expectancy across 250 districts with varying levels of deprivation. Methods: Using mortality data from 2012 to 2021 obtained from the Microdata Integrated Service of Statistics Korea, we calculated life expectancy at birth and age 65 for both sexes, by deprivation quintiles, before and during the pandemic. We summarized life expectancy gaps using the slope of the inequality index (SII) and further decomposed the gaps by the contribution of age and cause of death using Arriaga's method. Results: Both men and women experienced consistent improvements in life expectancy from 2012 to 2019, but the trend was disrupted during 2020 and 2021, primarily driven by older people. While men in more deprived areas were initially hit harder by the pandemic, the life expectancy gap across deprivation quintiles remained relatively constant and persistent across the study period [SII: -2.48 (CI: -2.70 from -2.27) for 2019 and - 2.84 (CI: -3.06 from -2.63) for 2020]. Middle-aged men from the most deprived areas were the most significant contributors to the life expectancy gap, with liver disease, liver cancer, transport accidents, and intentional injuries being the leading causes, both in the pre and during the pandemic. While these contributors remained largely similar before and during the pandemic, the contribution of transport accidents and liver cancer to the male life expectancy gap slightly decreased during the pandemic, while that of ischemic heart disease and pneumonia slightly increased. A similar increase was also observed for the female life expectancy gap. Conclusion: This study found no clear evidence of an increased life expectancy gap during the pandemic in South Korea, unlike in other countries, although access to emergency healthcare services may have been slightly more disturbed in deprived areas. This achievement can provide lessons for other countries. However, the persistent regional gaps in life expectancy observed over the past decade indicate the need for more targeted public health policies to address this issue.

Sulfur-doped graphitic carbon nitride: Tailored nanostructures for photocatalytic, sensing, and energy storage applications.

Rapid globalization and industrialization have led to widespread pollution and energy crises, necessitating the development of innovative solutions. Metal-free g-C3N4-based polymeric materials have unique properties but face limitations such as low surface area and inefficient light absorption. Doping, especially sulfur doping, is a prevalent technique to enhance their optical and electronic properties. This comprehensive review focuses on the synthesis techniques employed for sulfur doping of g-C3N4 (S-CN), highlighting the complexities associated with S-doping and the advantages of co-doping. Additionally, the review encompasses the diverse applications of S-CN in catalysis, photocatalysis, sonocatalysis, pollutant remediation, and electrochemical sensing. By incorporating sulfur into the g-C3N4 structure, various desirable properties can be achieved, including improved light absorption efficiency and enhanced charge carrier separation and migration. These advancements have broadened the application potential of S-CN in a range of important fields. S-CN has shown promise as a catalyst, facilitating various chemical reactions, as well as a photocatalyst, harnessing solar energy for environmental remediation and energy conversion processes. Moreover, S-CN exhibits potential in sonocatalysis for ultrasound-mediated reactions, pollutant remediation, and electrochemical sensing applications.

Electrochemical Sensing of H2O2 by Employing a Flexible Fe3O4/Graphene/Carbon Cloth as Working Electrode.

We report the synthesis of Fe3O4/graphene (Fe3O4/Gr) nanocomposite for highly selective and highly sensitive peroxide sensor application. The nanocomposites were produced by a modified co-precipitation method. Further, structural, chemical, and morphological characterization of the Fe3O4/Gr was investigated by standard characterization techniques, such as X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscope (TEM) and high-resolution TEM (HRTEM), Fourier transform infrared (FTIR), and X-ray photoelectron spectroscopy (XPS). The average crystal size of Fe3O4 nanoparticles was calculated as 14.5 nm. Moreover, nanocomposite (Fe3O4/Gr) was employed to fabricate the flexible electrode using polymeric carbon fiber cloth or carbon cloth (pCFC or CC) as support. The electrochemical performance of as-fabricated Fe3O4/Gr/CC was evaluated toward H2O2 with excellent electrocatalytic activity. It was found that Fe3O4/Gr/CC-based electrodes show a good linear range, high sensitivity, and a low detection limit for H2O2 detection. The linear range for the optimized sensor was found to be in the range of 10-110 µM and limit of detection was calculated as 4.79 µM with a sensitivity of 0.037 µA µM-1 cm-2. The cost-effective materials used in this work as compared to noble metals provide satisfactory results. As well as showing high stability, the proposed biosensor is also highly reproducible.

The fabrication of a CAD/CAM ceramic crown to fit an existing partial removable dental prosthesis: a clinical report.

The application of computer-aided design/computer-assisted manufacturing (CAD/CAM) technology to fabricate a retrofit ceramic surveyed crown to an existing partial removable dental prosthesis (PRDP) is described. The fabrication of a surveyed crown by using CAD/CAM technology enables precise and easy replication of the shape and contours as well as the rest seat of the existing abutment tooth, ensuring excellent adaptation to the existing PRDP framework with minimal adjustment.

State-of-the-art developments in carbon quantum dots (CQDs): Photo-catalysis, bio-imaging, and bio-sensing applications.

Carbon quantum dots (CQDs), the intensifying nanostructured form of carbon material, have exhibited incredible impetus in several research fields such as bio-imaging, bio-sensing, drug delivery systems, optoelectronics, photovoltaics, and photocatalysis, thanks to their exceptional properties. The CQDs show extensive photonic and electronic properties, as well as their light-collecting, tunable photoluminescence, remarkable up-converted photoluminescence, and photo-induced transfer of electrons were widely studied. These properties have great advantages in a variety of visible-light-induced catalytic applications for the purpose of fully utilizing the energy from the solar spectrum. The major purpose of this review is to validate current improvements in the fabrication of CQDs, characteristics, and visible-light-induced catalytic applications, with a focus on CQDs multiple functions in photo-redox processes. We also examine the problems and future directions of CQD-based nanostructured materials in this growing research field, with an eye toward establishing a decisive role for CQDs in photocatalysis, bio-imaging, and bio-sensing applications that are enormously effective and stable over time. In the end, a look forward to future developments is presented, with a view to overcoming challenges and encouraging further research into this promising field.

Avoidable Mortality between Metropolitan and Non-Metropolitan Areas in Korea from 1995 to 2019: A Descriptive Study of Implications for the National Healthcare Policy.

This study aims to investigate the trends of avoidable mortality and regional inequality from 1995 to 2019 and to provide evidence for policy effectiveness to address regional health disparities in Korea. Mortality and population data were obtained from the Statistics Korea database. Age-standardized all-cause, avoidable, preventable, and treatable mortality was calculated for each year by sex and region. Changes in mortality trends between metropolitan and non-metropolitan areas were compared with absolute and relative differences. Avoidable mortality decreased by 65.7% (350.5 to 120.2/100,000 persons) in Korea, 64.5% in metropolitan areas, and 65.8% in non-metropolitan areas. The reduction in avoidable mortality was greater in males than in females in both areas. The main causes of death that contribute to the reduction of avoidable mortality are cardiovascular diseases, cancer, and injuries. In preventable mortality, the decrease in non-metropolitan areas (-192.4/100,000 persons) was greater than that in metropolitan areas (-142.7/100,000 persons). However, in treatable mortality, there was no significant difference between the two areas. While inequalities in preventable mortality improved, inequalities in treatable mortality worsened, especially in females. Our findings suggest that regional health disparities can be resolved through a balanced regional development strategy with an ultimate goal of reducing health disparities.

Biological remediation technologies for dyes and heavy metals in wastewater treatment: New insight.

The pollution of the environment caused by dyes and heavy metals emitted by industries has become a worldwide problem. The development of efficient, environmentally acceptable, and cost-effective methods of wastewater treatment containing dyes and heavy metals is critical. Biologically based techniques for treating effluents are fascinating since they provide several benefits over standard treatment methods. This review assesses the most recent developments in the use of biological based techniques to remove dyes and heavy metals from wastewater. The remediation of dyes and heavy metals by diverse microorganisms such as algae, bacteria, fungi and enzymes are depicted in detail. Ongoing biological method's advances, scientific prospects, problems, and the future prognosis are all highlighted. This review is useful for gaining a better integrated view of biological based wastewater treatment and for speeding future research on the function of biological methods in water purification applications.

Facile Fabrication of CuO Nanoparticles Embedded in N-Doped Carbon Nanostructure for Electrochemical Sensing of Dopamine.

In the present study, a highly selective and sensitive electrochemical sensing platform for the detection of dopamine was developed with CuO nanoparticles embedded in N-doped carbon nanostructure (CuO@NDC). The successfully fabricated nanostructures were characterized by standard instrumentation techniques. The fabricated CuO@NDC nanostructures were used for the development of dopamine electrochemical sensor. The reaction mechanism of a dopamine on the electrode surface is a three-electron three-proton process. The proposed sensor's performance was shown to be superior to several recently reported investigations. Under optimized conditions, the linear equation for detecting dopamine by differential pulse voltammetry is I pa (µA) = 0.07701 c (µM) - 0.1232 (R 2 = 0.996), and the linear range is 5-75 µM. The limit of detection (LOD) and sensitivity were calculated as 0.868 µM and 421.1 µA/µM, respectively. The sensor has simple preparation, low cost, high sensitivity, good stability, and good reproducibility.