Grid refinement and verification estimates for the RBF construction method of Lyapunov functions

Lyapunov functions are functions with negative orbital derivative, whose existence guarantee the stability of an equilibrium point of an ODE. Moreover, sub-level sets of a Lyapunov function are subsets of the domain of attraction of the equilibrium. In this thesis, we improve an established numerical method to construct Lyapunov functions using the radial basis functions (RBF) collocation method. The RBF collocation method approximates the solution of linear PDE's using scattered collocation points, and one of its applications is the construction of Lyapunov functions. More precisely, we approximate Lyapunov functions, that satisfy equations for their orbital derivative, using the RBF collocation method. Then, it turns out that the RBF approximant itself is a Lyapunov function. Our main contributions to improve this method are firstly to combine this construction method with a new grid refinement algorithm based on Voronoi diagrams. Starting with a coarse grid and applying the refinement algorithm, we thus manage to reduce the number of collocation points needed to construct Lyapunov functions. Moreover, we design two modified refinement algorithms to deal with the issue of the early termination of the original refinement algorithm without constructing a Lyapunov function. These algorithms uses cluster centres to place points where the Voronoi vertices failed to do so. Secondly, we derive two verification estimates, in terms of the first and second derivatives of the orbital derivative, to verify if the constructed function, with either a regular grid of collocation points or with one of the refinement algorithms, is a Lyapunov function, i.e., has negative orbital derivative over a given compact set. Finally, the methods are applied to several numerical examples up to 3 dimensions

Bone Substitutes in Management of Benign Bone Tumors, Review of Literature

Intralesional excision or curettage is commonly used to treat benign and low-grade malignant bone tumors. The resulting defect can be treated with a variety of materials, such as autologous bone grafts, allografts, or synthetic materials like polymethylmethacrylate or composite alternatives. Because it is osteogenic, osteoinductive, and osteoconductive, autologous cancellous bone is often considered the gold standard of transplant material. However, issues including transplant size limitations, wound-related complications, and prolonged donor site pain have limited its usage in clinical practice. Concerns about immunogenicity and infection have also hampered the use of demineralized freeze-dried allografts and xenografts.  As a result, synthetic materials have sparked substantial interest in orthopedics, and a variety of bone graft alternatives are now commercially accessible

Examine the Perceived Risk of Falls Among Patients Receiving Acute Care

Purpose: In an effort to lower the number of falls that occur among hospitalized patients, several facilities have begun introducing various fall prevention programs. However, the efficacy of fall prevention programs is diminished if patients do not consider themselves to be at risk for falls and do not follow recommended procedures. The goal of this study was to characterize how patients in four different acute care specialist services felt about their risk of falling while in the hospital. Methods: One hundred patients admitted to the study hospital with a Morse Fall Scale score of 45 or higher were given the Patient Perception Questionnaire, a tool designed to assess a patient's perception of their own fall risk, fear of falling, and motivation to take part in fall prevention efforts. Scores on the Morse Fall Scale were gathered through a historical assessment of medical records. Descriptive statistics, Pearson's correlation coefficients, and independent sample t tests were used to examine the data. Results: The average age was 65, and around half (52%) were men and half (48%) were women. Based on their ratings on the Morse Fall Scale, all 100 participants were classified as being at high risk for falls. However, only 55.5% of the individuals agreed with this assessment. The likelihood that a patient would seek assistance and the degree to which they feared falling both declined as their faith in their mobility improved. Patients hospitalized after a fall exhibited considerably lower confidence scores and greater fear scores than patients who had not been injured in a fall. Conclusions: Patients who have a high fall risk assessment score may not believe they are at risk for falls and may not take any steps to reduce their risk. The prevalence of falls in hospitals might be mitigated by the creation of a fall risk assessment technique that takes into account both objective and subjective factors

Novel 8-Methoxycoumarin-3-Carboxamides with potent anticancer activity against liver cancer via targeting caspase-3/7 and β-tubulin polymerization

The article processing charge was funded by the Open Access Publication Fund of Humboldt-Universität zu Berlin.In the present study, we explored the potential of coumarin-based compounds, known for their potent anticancer properties, by designing and synthesizing a novel category of 8-methoxycoumarin-3-carboxamides. Our aim was to investigate their antiproliferative activity against liver cancer cells. Toward this, we developed a versatile synthetic approach to produce a series of 8-methoxycoumarin-3-carboxamide analogues with meticulous structural features. Assessment of their antiproliferative activity demonstrated their significant inhibitory effects on the growth of HepG2 cells, a widely studied liver cancer cell line. Among screened compounds, compound 5 exhibited the most potent antiproliferative activity among the screened compounds (IC50 = 0.9 µM), outperforming the anticancer drug staurosporine (IC50 = 8.4 µM), while showing minimal impact on normal cells. The flow cytometric analysis revealed that compound 5 induces cell cycle arrest during the G1/S phase and triggers apoptosis in HepG2 cells by increasing the percentage of cells arrested in the G2/M and pre-G1 phases. Annexin V-FITC/PI screening further supported the induction of apoptosis without significant necrosis. Further, compound 5 exhibited the ability to activate caspase3/7 protein and substantially inhibited β-tubulin polymerization activity in HepG2 cells. Finally, molecular modelling analysis further affirmed the high binding affinity of compound 5 toward the active cavity of β-tubulin protein, suggesting its mechanistic involvement. Collectively, our findings highlight the therapeutic potential of the presented class of coumarin analogues, especially compound 5, as promising candidates for the development of effective anti-hepatocellular carcinoma agents.Peer Reviewe

Prevalence of Comorbidities Associated With Type 2 Diabetes Mellitus In Ksa: A Cross-Sectional Study

Objective: To determine the prevalence of comorbidities associated with type 2 diabetes mellitus among the Saudi adult population. Methods: A cross-sectional study design will be employed to investigate the prevalence of comorbidities associated with Type 2 Diabetes Mellitus (T2DM) within the Kingdom of Saudi Arabia (KSA) population. This design allows for the collection of data at a single point in time, providing insights into the existing relationship between T2DM and comorbidities.Results: The study included 601 participants. The most frequent body mass index BMI value among study participants was overweight 25-29.9 kg/m2 (n= 196, 33%), followed by Normal 18.5-24.9 kg/m2 (n= 177, 29%). The frequent gender among study participants was male years (n= 356, 59%) and female (n= 245, 41%). The most frequent age among study participants was 40-50 years (n= 145, 24%), followed by 18-28 years (n= 140, 23%). The most frequent marital status among study participants was married (n= 360, 60%), followed by single (n= 160, 27%). The perceived physical activity per week among study participants, most of whom did not do any activity (n=231,38%) followed one-time activity (n=98,16%). Conclusion: The results showed that most of the study participants were overweight according to their BMI. The majority of patients had normal blood pressure. Most of the participants suffer from diabetes. In addition, most of the participants do not do any activity, and the majority of participants are non-smokers

The Saudi Critical Care Society practice guidelines on the management of COVID-19 in the ICU: Therapy section

BACKGROUND: The rapid increase in coronavirus disease 2019 (COVID-19) cases during the subsequent waves in Saudi Arabia and other countries prompted the Saudi Critical Care Society (SCCS) to put together a panel of experts to issue evidence-based recommendations for the management of COVID-19 in the intensive care unit (ICU). METHODS: The SCCS COVID-19 panel included 51 experts with expertise in critical care, respirology, infectious disease, epidemiology, emergency medicine, clinical pharmacy, nursing, respiratory therapy, methodology, and health policy. All members completed an electronic conflict of interest disclosure form. The panel addressed 9 questions that are related to the therapy of COVID-19 in the ICU. We identified relevant systematic reviews and clinical trials, then used the Grading of Recommendations, Assessment, Development and Evaluation (GRADE) approach as well as the evidence-to-decision framework (EtD) to assess the quality of evidence and generate recommendations. RESULTS: The SCCS COVID-19 panel issued 12 recommendations on pharmacotherapeutic interventions (immunomodulators, antiviral agents, and anticoagulants) for severe and critical COVID-19, of which 3 were strong recommendations and 9 were weak recommendations. CONCLUSION: The SCCS COVID-19 panel used the GRADE approach to formulate recommendations on therapy for COVID-19 in the ICU. The EtD framework allows adaptation of these recommendations in different contexts. The SCCS guideline committee will update recommendations as new evidence becomes available

Characterization of greater middle eastern genetic variation for enhanced disease gene discovery

The Greater Middle East (GME) has been a central hub of human migration and population admixture. The tradition of consanguinity, variably practiced in the Persian Gulf region, North Africa, and Central Asia1-3, has resulted in an elevated burden of recessive disease4. Here we generated a whole-exome GME variome from 1,111 unrelated subjects. We detected substantial diversity and admixture in continental and subregional populations, corresponding to several ancient founder populations with little evidence of bottlenecks. Measured consanguinity rates were an order of magnitude above those in other sampled populations, and the GME population exhibited an increased burden of runs of homozygosity (ROHs) but showed no evidence for reduced burden of deleterious variation due to classically theorized ‘genetic purging’. Applying this database to unsolved recessive conditions in the GME population reduced the number of potential disease-causing variants by four- to sevenfold. These results show variegated genetic architecture in GME populations and support future human genetic discoveries in Mendelian and population genetics

Examine the Perceived Risk of Falls Among Patients Receiving Acute Care

<p>Purpose: In an effort to lower the number of falls that occur among hospitalized patients, several facilities have begun introducing various fall prevention programs. However, the efficacy of fall prevention programs is diminished if patients do not consider themselves to be at risk for falls and do not follow recommended procedures. The goal of this study was to characterize how patients in four different acute care specialist services felt about their risk of falling while in the hospital. Methods: One hundred patients admitted to the study hospital with a Morse Fall Scale score of 45 or higher were given the Patient Perception Questionnaire, a tool designed to assess a patient's perception of their own fall risk, fear of falling, and motivation to take part in fall prevention efforts. Scores on the Morse Fall Scale were gathered through a historical assessment of medical records. Descriptive statistics, Pearson's correlation coefficients, and independent sample t tests were used to examine the data. Results: The average age was 65, and around half (52%) were men and half (48%) were women. Based on their ratings on the Morse Fall Scale, all 100 participants were classified as being at high risk for falls. However, only 55.5% of the individuals agreed with this assessment. The likelihood that a patient would seek assistance and the degree to which they feared falling both declined as their faith in their mobility improved. Patients hospitalized after a fall exhibited considerably lower confidence scores and greater fear scores than patients who had not been injured in a fall. Conclusions: Patients who have a high fall risk assessment score may not believe they are at risk for falls and may not take any steps to reduce their risk. The prevalence of falls in hospitals might be mitigated by the creation of a fall risk assessment technique that takes into account both objective and subjective factors.</p&gt

Synthesis of biomass-supported CuNi zero-valent nanoparticles through wetness co-impregnation method for the removal of carcinogenic dyes and nitroarene

Stabilization of zero-valent CuNi nanoparticles (NPs) supported on Cicer arietenum (CP) is reported here for the reduction and removal of persistent organic pollutants. The functional groups and interactions of NPs with the CP were determined by ATR-FTIR. The crystallinity, morphology, and the elemental composition of the samples were determined through powder XRD, FESEM, and EDS techniques, respectively. The XRD spectrum displayed a sharp crystalline peak at 43.9 for CuNi. The Cu and Ni zero-valent NPs displayed a peak at almost the same region, and thus, both the peaks are merged and appeared as a single peak. The chemical reduction/degradation of eight model pollutants, viz., 2-nitrophenol (ONP), 3-nitrophenol (MNP), 4-nitrophenol (PNP), 2,4-dinitrophenol (DNP), methyl orange (MO), congo red (CR), methylene blue (MB), and rhodamine B (RB) were carried out in the presence of NaBH4. The kapp value of 0.1 mM 4NP was highest which was 1.8 × 10−1 min−1 while the slowest rate was observed for CR and RB with kapp 5.5 × 10−3 and 5.4 × 10−3 min−1 respectively. This article helps in the removal of toxic organic pollutants through green supported NPs