Let R be a commutative ring with a nonzero identity and Z(R) be the set of zero-divisors of R. The weakly zero-divisor graph of R, denoted by WГ(R), is the graph with the vertex set 〖Z(R)〗^*=Z(R)\\{0}, where two distinct vertices a and b form an edge if ar=bs=rs=0 for r,s∈R\\{0}. For an ideal I of R, the ideal-based zero-divisor graph of R, denoted by Г_I (R), has vertices {a∈R\I:ab∈I for some b∈R\I} and edges {(a,b):ab∈I,a,b∈R\I,a≠b}. In this article, an ideal-based weakly zero-divisor graph of R, denoted by 〖WГ〗_I (R), is introduced which contains Г_I (R) as a subgraph and is identical to the graph WГ(R) when I={0}. The relationship between the graphs WГ_I (R) and WГ(R/I) is investigated and the planar property of 〖WГ〗_I (R) is studied. The results show that WГ(R/I) is isomorphic to a subgraph of 〖WГ〗_I (R). For 〖WГ〗_I (R) to be planar, some restraints are provided on the size of the ideal I and girth of 〖WГ〗_I (R). In conclusion, the results suggest that WГ_I (R) and WГ(R/I) are strongly related and establish necessary and sufficient conditions for WГ_I (R) to be planar. In addition, rings R with planar WГ_I (R) are classified.

We improved the ability of the exponentially weighted moving average (EWMA) control chart to detect small shifts in the mean of a long-memory fractionally integrated autoregressive process with an exogenous variable under exponential white noise. We first designed the structure of the control chart and then evaluated its performance in terms of the average run length (ARL) via a simulation study. We first derived an analytical ARL using explicit formulas by solving integral equations and an approximated ARL derived by utilizing the numerical integral equation approach. Banach's fixed-point theorem proved that the analytical ARL exists and is unique. We then compared the out-of-control ARL values using both methods via a simulation study; the out-of-control ARL results for the analytical and approximated ARLs were similar. Moreover, the methods provided comparable accuracy in terms of the percentage difference in expected ARL and standard deviation of the run length. However, the explicit formula approach proved to be more advantageous in terms of faster computational speed and is thus recommended in this situation. An illustrative example using real data is also provided to demonstrate the practicability of the analytical ARL method.

Fuzzy random graphs offer a powerful framework for modeling uncertain and imprecise relationships in various real-world systems. This study introduces the concept of hesitancy fuzzy random graphs, which incorporate both fuzziness and randomness in edge and vertex memberships. Additionally, this study investigates the beta and gamma products within the context of hesitancy fuzzy random graphs. Leveraging the beta and gamma operations, this study investigates the application of combining and aggregating uncertain information from multiple sources represented by hesitancy fuzzy random graphs.

This study is aimed at assessing the effects of Edible Bird’s Nest (EBN) on subchondral bone, articular cartilage and the expression of proteins in synovial fluid by micro-CT evaluation and histological analysis. 54 New Zealand white rabbits were induced by intra-articular injection of monosodium iodoacetate (8 mg) and divided into four groups: negative control (n=9): non-treated osteoarthritis; positive control (n=15): OA + diclofenac sodium 2 mg/kg daily orally; low dosage (n=15): OA + 75 mg/kg hydrolyzed EBN; and high dosage (n=15): OA + 150 mg/kg hydrolyzed EBN. The joints were harvested and subjected to micro-CT analysis and histological evaluation, and the synovial fluid was subjected to LCMS/MS analysis. Micro-CT analysis showed an increase in bone volume and a decrease in total porosity in the treatment group that showed bone integrity improvement. Histopathological results revealed comparable changes between the positive control group and the EBN treatment group. There was upregulation of proteins involved in the resolution of inflammation and downregulation of proteins associated with the bone resorption process. Morphology evaluation showed that EBN supplementation has a bone-improving effect by inhibiting osteoclastic activity. Protein expression showed chondroprotection and bone improvement through the action of several proteins via various signaling pathways. The morphological and molecular findings suggest the potential use of EBN as beneficial alternative for osteoarthritis treatment by improving bone quality and modulating inflammatory responses.

Air quality forecast is essential in alerting the public, especially those who have respiratory diseases, to take necessary precautions beforehand. The public can be forewarned of any worsening of air quality and be aware of the importance of reducing air pollution. In recent years, forecasting techniques based on deep learning algorithms such as recurrent neural network (RNN) have seen improvements in both accuracy and execution speed. Long short-term memory (LSTM) network and gated recurrent unit (GRU) are among the most popular variants of RNN. In this study, the hourly PM2.5 concentrations at five selected air quality monitoring stations, provided by the Department of Environment Malaysia, are forecasted using LSTM, GRU and vector autoregressive integrated moving average (VARIMA) models respectively. Data containing missing, negative and zero values are pre-processed using an interpolation technique before being split into training and test sets on an 80:20 ratio basis. Optimal combinations of hyperparameter values are selected via manual tuning based on the 10-fold growing window cross-validation results. The model performance is evaluated based on RMSE, MAE and MAPE. The results demonstrate that neural network models significantly outperform the multivariate time series model in which the LSTM and GRU models have comparable performance in forecasting the hourly PM2.5 concentration, with a slightly better prediction in the west coast region for LSTM and the east coast region for GRU. However, due to the complex architecture of neural networks, the computational time to train both LSTM and GRU models is three times longer than that for VARIMA. Additionally, it is observed that a higher percentage of interpolated values leads to lower prediction errors.

Glucose-6-phosphate dehydrogenase deficiency (G6PDD) is a major enzymatic disease affecting human red blood cells (RBCs), causing hemolytic anemia due to the diminish of the nicotinamide adenine dinucleotide phosphate hydrogen (NADPH) synthesis and altered redox balance within erythrocytes. This study sought to correct the defect in G6PDChatham (Ala355Thr) caused by the loss of interactions (hydrogen bonds and salt bridges) by docking the AG1 molecule at the dimer interface, thus restoring these lost interactions. The enzyme conformation was then analyzed before and after AG1 binding using molecular dynamics simulation (MDS). The reasons behind the severity of acute hemolytic anemia (AHA) were explained using several parameters, such as root-mean-square deviation (RMSD), root-mean-square fluctuation (RMSF), hydrogen bonds, salt bridges, radius of gyration (Rg), solvent accessible surface area (SASA), and covariance matrix analysis. Structural alterations in G6PDChatham, including the absence of interactions in a key region of the variant structure, can significantly impact protein stability and function, subsequently contributing to disease severity. Upon AG1 binding, these missing interactions were resorted to correct the structural defect of the variant. This restoration improves dimer stability and restores G6PD function. To develop new G6PD activators, several new analogues (SY7, SY8, SY9, and SY10) were rationally developed by substituting the linker region of the AG1 structure with other functional groups using the Avogadro software. These compounds were successfully synthesized and docked with G6PDChatham where the best binding affinity ranged between -8.0 and -9.1 kcal/mol. SY8, a promising G6PD activator, is predicted to be easily metabolized and excreted, making it less likely to cause toxicity. Its high drug score, drug-likeness, and favorable safety profile make it a strong candidate for synthesis and cellular testing. The toxicity risk assessment supported the overall drug score, increasing confidence in finding additional small-molecule activators for G6PDD disorder. Amidst the absence of effective treatments, such discovery hopes to improve the lives of those with AHA by assisting the development of appropriate pharmaceuticals for G6PDD.

Since the onset of the Covid-19 pandemic, numerous challenges have emerged, including ensuring an adequate supply of personal protective equipment, evaluating the sufficiency of the healthcare workforce, and determining safety measures to sustain businesses and the economy. Consequently, there is a critical need for a computationally competent and realistic model to monitor current caseloads and forecast future cases, thereby enhancing public health awareness, preparation, and response. However, many forecast models currently in use have wide prediction intervals, diminishing their effectiveness as forecasting tools. Thus, this study aims to analyse the trend of Covid-19 cases in Malaysia and develop a forecast model that provides appropriate limits to improve prediction accuracy. This study relied on secondary data of daily Covid-19 cases in Malaysia provided by Ministry of Health from April 12, 2021, to April 24, 2022. Future Covid-19 incidence was predicted using simple, double and Holts-Winter exponential smoothing and SARIMAX models. SARIMAX (0, 1, 1) (1, 0, 2)7 was identified as the best model, exhibiting the lowest error values for forecasting cases. However, the results indicated that SARIMAX's prediction intervals were broad. To address this issue, a new model called hybrid SARIMAX-SARIMA was proposed where the orders from the best SARIMAX model found by using auto.arima() function are extracted and used to specify the order for a SARIMA model. The resulting combined model was then utilized to predict future trends in daily Covid-19 cases and evaluation during cultural festivals and state elections. It was observed that the proposed model outperformed others, demonstrating lower error rates and narrower confidence intervals for future predictions.

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.

Garcinia mangostana Linn., has been studied for its antibacterial properties to augment commercial antibiotics and in the hope of easing reliance on these chemical medications in the future, however, the comparison of the fruit’s bactericidal capabilities relative to different bacterial species requires further analyses. This systematic review and meta-analysis compared the antibacterial activity of ethanolic and methanolic mangosteen extracts against three species that commonly cause Healthcare-Associated Infections (HAIs)—Staphylococcus aureus, Escherichia coli, and Pseudomonas aeruginosa. The results revealed no significant difference [mean difference: 1.42 (CI: -3.53 to 6.37, I2 = 99%, Z = 0.56 (P = 0.57))] between the effectiveness of the extracts against S. aureus and E. coli. But it was contrary when P. aeruginosa was compared with S. aureus [mean difference: 5.00 (CI: 4.48 to 5.52, I2= 0%, Z = 18.97 (P < 0.00001))] and E. coli [mean difference: 3.96 (CI: 2.01 to 5.92, I2 = 94%, Z = 3.97 (P < 0.0001))]. Literature search and screening were done following the PRISMA guidelines. Quality assessments utilized the JBI Critical Appraisal Tool and a remodified Newcastle-Ottawa Scale. A total of 13 studies were included in the review, only 7 of which were eligible for meta-analyses. In conclusion, G. mangostana extracts are indeed effective against multiple microbes, however, relative to the selected bacterial species, inhibition varied. Moreover, this study sheds light on further practical or in vivo applications of mangosteen as a treatment for bacterial infections.

In this paper, an assessment model was developed based on the proposed integrated fuzzy-based evaluation method on students' mathematics learning ability. This model classifies six main attributes that structure the overall evaluation model into several parameters. The weightings of these main attributes and parameters were collected through fuzzy questionnaires among teachers and experts based on triangular fuzzy conjoint and fuzzy Delphi methodology. This highlighted integration contributes to a more reasonable and effective procedure for developing a structured and dynamic assessment model. It can reduce the problem of the measurement results obtained straying from the structure of the developed model due to procedural errors in identifying and analyzing the attributes and parameters of the model when it was developed. In addition, the presented case application also provides an analysis protocol that is simpler and easier compared to other complicated and complex approaches to developing assessment models.