Power of kk Choices in the Semi-Random Graph Process

The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then adaptively selects a vertex $v$, and adds the edge $uv$ to the graph. For a fixed monotone graph property, the objective of the player is to force the graph to satisfy this property with high probability in as few rounds as possible. In this paper, we introduce a natural generalization of this game in which $k$ random vertices $u_1, \ldots, u_k$ are presented to the player in each round. She needs to select one of the presented vertices and connect to any vertex she wants. We focus on the following three monotone properties: minimum degree at least $\ell$, the existence of a perfect matching, and the existence of a Hamiltonian cycle.Comment: 18 page

Cutaneous Manifestations of COVID-19: A Systematic Review

Objective: Coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is currently a pandemic. Although pulmonary health has been the primary focus of studies during the early days of COVID-19, development of a comprehensive understanding of this emergent disease requires knowledge of all possible disease manifestations in affected patients. This Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA)-compliant review focuses on cutaneous manifestations reported in COVID-19 patients. Approach: Literature review was conducted using the PubMed database to examine various cutaneous manifestations related to the SARS-CoV-2 infection. Published articles (n = 56) related to search criteria from the onset of the COVID-19 pandemic to June 30, 2020, were included. The primary literature articles included in this study were mainly from France, Spain, Italy, and the United Kingdom. Results: Unique to many other symptoms of COVID-19, its cutaneous manifestations have been found in people of all age groups, including children. The cutaneous manifestations of COVID-19 are varied and include maculopapular, chilblain-like, urticarial, vesicular, livedoid, and petechial lesions. In addition, rashes are common in multisystem inflammatory syndrome in children, a new and serious health condition that shares symptoms with Kawasaki disease and is likely related to COVID-19. In addition, personal protective equipment-related skin wounds are of serious concern since broken cutaneous barriers can create an opening for potential COVID-19 infections. Innovation and Conclusion: As this virus continues to spread silently, mainly through asymptomatic carriers, an accurate and rapid identification of these cutaneous manifestations may be vital to early diagnosis and lead to possible better prognosis in COVID-19 patients. This systematic review and photo atlas provide a detailed analysis of the skin pathologies related to COVID-19. Study of these cutaneous manifestations and their pathogenesis, as well their significance in human health will help define COVID-19 in its entirety, which is a prerequisite to its effective management

Study of the physico-chemical properties of vancomycin hydrochloride for determining its potential applications in formulation development

1113-1119The study of physico-chemical properties of vancomycin hydrochloride is an important parameter in the pre-formulation analysis of a drug. Pre-formulation study provides important information for formulation design or support the need for molecular modification. The main objective of pre-formulation is to develop a stable and an effective drug, with a safe dosage. Therefore, properties like specific conductivity, density, viscosity, velocity of sound and specific gravity are determined which further helps in determination of critical micelle concentration (CMC). Other thermodynamic parameters are calculated from CMC like change in entropy, enthalpy and Gibb’s free energy which indicated that formation of micelles is favourable and exothermic in nature. Along with this, thermo-acoustic parameters such as apparent molar volume and apparent molar compressibility have also been determined. These parameters reveal that electrostatic interactions are favourable at lower concentrations of vancomycin hydrochloride whereas hydrophobic interactions are dominant at higher concentrations. All these studies have proven useful in determining the types of interactions occurring in the system. Moreover, a stable concentration of vancomycin hydrochloride can also be determined which may aid in the topical formulation of this drug

Study of the physico-chemical properties of vancomycin hydrochloride for determining its potential applications in formulation development

The study of physico-chemical properties of vancomycin hydrochloride is an important parameter in the pre–formulation analysis of a drug. Pre-formulation study provides important information for formulation design or support the need for molecular modification. The main objective of pre-formulation is to develop a stable and an effective drug, with a safe dosage. Therefore properties like specific conductivity, density, viscosity, velocity of sound and specific gravity are determined which further helps in determination of critical micelle concentration (CMC). Other thermodynamic parameters are calculated from CMC like change in entropy, enthalpy and Gibb’s free energy which indicated that formation of micelles is favourable and exothermic in nature. Along with this, thermo-acoustic parameters such as apparent molar volume and apparent molar compressibility have also been determined. These parameters revealed that electrostatic interactions were favourable at lower concentrations of vancomycin hydrochloride whereas hydrophobic interactions were dominant at higher concentrations. All these studies have proven useful in determining the types of interactions occurring in the system. Moreover, a stable concentration of vancomycin hydrochloride can also be determined which may aid in the topical formulation of this drug