Singular SPDEs on Homogeneous Lie Groups

The aim of this article is to extend the scope of the theory of regularity structures in order to deal with a large class of singular SPDEs of the form $$\partial_t u = \mathfrak{L} u+ F(u, \xi)\ ,$$ where the differential operator $\mathfrak{L}$ fails to be elliptic. This is achieved by interpreting the base space $\mathbb{R}^{d}$ as a non-trivial homogeneous Lie group $\mathbb{G}$ such that the differential operator $\partial_t -\mathfrak{L}$ becomes a translation invariant hypoelliptic operator on $\mathbb{G}$. Prime examples are the kinetic Fokker-Planck operator $\partial_t -\Delta_v - v\cdot \nabla_x$ and heat-type operators associated to sub-Laplacians. As an application of the developed framework, we solve a class of parabolic Anderson type equations $$\partial_t u = \sum_{i} X^2_i u + u (\xi-c)$$ on the compact quotient of an arbitrary Carnot group

HR Functions Productivity Boost by using AI

In today's fast-paced world, the Human Resources (HR) department plays a pivotal role in the success of any organization. With a plethora of tasks to manage, the HR team often faces the daunting challenge of screening and selecting the best candidates for various positions. To streamline this process, we propose a novel system that integrates the power of Kruskal algorithm for resume screening, conducting a qualifying test called "BTNT," and psychological testing like Emotional Intelligence to analyze the shortlisted candidates. Our proposed system utilizes a Knapsack approach under Dynamic Programming to suggest the most suitable candidates for HR roles. By automating these tedious HR tasks through Artificial Intelligence (AI), we ensure a faster, more accurate, and cost-effective selection process. Our research paper presents a detailed analysis of the proposed system's effectiveness and showcases the benefits of adopting this innovative approach. We believe that this cutting-edge system will revolutionize the HR industry by providing an efficient, objective, and unbiased selection process. The BTNT test's incorporation will help identify candidates' technical skills, while the psychological test will highlight their soft skills. This holistic approach ensures that organizations not only hire the best-fit candidates but also create a positive work environment that fosters growth and development. Our research paper is a must-read for any HR professional looking to optimize their recruitment process and gain a competitive edge in the market. With our proposed system's implementation, companies can attract and retain top talent, improve employee productivity, and ultimately increase their efficiency

Appropriateness of Vancomycin Use and Associated Outcomes

Background: Several studies have documented increased rates of MRSA associated with adverse patient outcomes. Vancomycin remains the primary treatment of choice and use of vancomycin in hospitalized settings is increasing. Inappropriate vancomycin has been shown to lead to the development of vancomycin resistant organisms. Guidelines developed by IDSA have been used to promote appropriate use of vancomycin. However, inappropriate use of vancomycin remains high and its association with patient outcomes has not been well examined. The objective of this study was to examine appropriateness of vancomycin use and associated outcomes based on IDSA guidelines. Methods: A retrospective observational study of patients ≥18 years old who had received one dose of intravenous vancomycin in January 2019 was conducted at the University of Nebraska Medical Center. Appropriateness of vancomycin use was evaluated with criteria established through IDSA guidelines. Vancomycin use was considered appropriate in serious infections due to beta-lactam resistant gram-positive organisms, treatment of infections in the setting of beta-lactam allergy, surgical prophylaxis in patients allergic to beta-lactam antibiotics and empiric treatment for serious infections such as septic shock, bacteremia and infective endocarditis, healthcare-associated pneumonia, osteomyelitis and septic arthritis and central nervous system infections. De-escalation of vancomycin after 72 hours was considered appropriate when used empirically. Any deviation from criteria was deemed inappropriate. Variables reviewed included age, gender, length of stay, mortality, intensive care unit (ICU) admission, and length of vancomycin use. Data is expressed as percentage for nominal variables and as mean with standard deviation for continuous variables. Age, gender, mortality and ICU admission were further analyzed by chi-square tests. Length of stay and vancomycin use days were analyzed using unpaired t-test. A P-value \u3c 0.05 was considered significant for the study. Results: A total of 595 encounters of vancomycin use were included in the study. Overall, 38.2% of all patients were admitted to the ICU, and hospital mortality was 9.24%. Vancomycin use was shown to be inappropriate in 34.3% of all patient encounters. Slightly higher mortality was noted in the appropriate group, but it was not found to be statistically significant (10.74% in appropriate group vs. 6.37% in inappropriate vancomycin use group; p = 0.10). Mean length of stay in patients between the two groups was not found to be statistically significant (12.60 ± 18.23 days for appropriate group vs. 14.01 ± 21.64 days for inappropriate group; p = 0.40). Significantly higher ICU admission was found for the appropriate group (41.43% in appropriate group vs. 32.35% in the inappropriate group, p = 0.0001). The most common indication for appropriate use of vancomycin was for empiric treatment (47.6%), while surgical prophylaxis in the absence of beta-lactam allergy was the most common indication for the inappropriate vancomycin use group (41.7%). Conclusion: The study reveals that there was inappropriate use in about one-third of all vancomycin use encounters. The study also found some outcomes such as ICU admission to be statistically significant between the two groups. The study identified common indications for inappropriate use to target further interventions.https://digitalcommons.unmc.edu/surp2022/1033/thumbnail.jp