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For Graph HT ht , there can be no more solutions. Suppose now that Graph HT ht , but Graph HT ht . Now suppose that Graph HT ht . [Extracted from the article]

The COVID-19 pandemic has brought renewed attention to the topic of challenging drug patents in the interest of public health. Pharmaceutical companies have already begun to patent existing medicines for the treatment and prevention of SARS-CoV-2, affording them exclusive manufacturing rights over vital medicines. Advocates have raised concerns regarding the pricing of COVID-19 drugs, as well as patent monopolies on the manufacture of COVID-19 treatments. The HIV/AIDS pandemic provides a useful lens through which we can analyse existing pathways for challenging pharmaceutical patents in the context of global pandemic. In this article, we review three legal pathways for overriding and seizing patents on medicines by describing cases in which they were employed to make antiretroviral drugs more accessible to people living with HIV. Last, we highlight the weaknesses inherent in these pathways and offer advocacy and policy suggestions for how to strengthen these pathways to improve access to COVID-19 treatments as they become available in the United States and globally. [ABSTRACT FROM AUTHOR]

Three modeling approaches, the U.S. Environmental Protection Agency’s (EPA) Community Multiscale Air Quality (CMAQ) zero-out, the Comprehensive Air quality Model with extensions (CAMx) zero-out, and the CAMx probing tools ozone source apportionment tool (OSAT), were used to project the contributions of various source categories to future year design values for summer 8-hr average ozone concentrations at selected U.S. monitors. The CMAQ and CAMx zero-out or brute-force approaches predicted generally similar contributions for most of the source categories, with some small differences. One of the important findings from this study was that both the CMAQ and CAMx zero-out approaches tended to apportion a larger contribution to the “other” category than the OSAT approach. For the OSAT approach, this category is the difference between the total emissions and the sum of the tracked emissions and consists of non-U.S. emissions. For the zero-out approach, it also includes the effects of nonlinearities in the system because the sum of the sensitivities of all sources is not necessarily equal to the sum of their contributions in a nonperturbed environment. The study illustrates the strengths and weaknesses of source apportionment approaches, such as OSAT, and source sensitivity approaches, such as zero-out. The OSAT approach is suitable for studying source contributions, whereas the zero-out approach is suitable for studying response to emission changes. Future year design values of summer 8-hr average ozone concentrations were projected to decrease at all the selected monitors for all the simulations in each city, except at the downtown Los Angeles monitor. Both the CMAQ and CAMx results showed all modeled locations project attainment in 2018 and 2030 to the current National Ambient Air Quality Standards (NAAQS) level of 75 ppb, except the selected Los Angeles monitor in 2018 and the selected San Bernardino monitor in 2018 and 2030.Implications:This study illustrates the strengths and weaknesses of three modeling approaches, CMAQ zero-out, CAMx zero-out, and OSAT to project contributions of various source categories to future year design values for summer 8-hr average ozone concentrations at selected U.S. monitors. The OSAT approach is suitable for studying source contributions, whereas the zero-out approach is suitable for studying response to emission changes. Future year design values of summer 8-hr average ozone concentrations were projected to decrease, except at the downtown Los Angeles monitor. Comparing projections with the current NAAQS (75 ppb) show attainment everywhere, except two locations in 2018 and one location in 2030. [ABSTRACT FROM PUBLISHER]

Glioblastoma multiforme (GBM) is an aggressive tumor with poor survival outcomes and limited treatment options. We conducted a literature review to compare the survival outcomes of intra-arterial (IA) and intravenous (IV) chemotherapy delivery for GBM. Nine studies of IA chemotherapy infusion with 301 total patients met our criteria for inclusion and three studies contained IV treatment groups for comparison (n = 230 for IA, n = 71 for IV). The studies were grouped by either using newly diagnosed or recurrent GBM patients. In the newly diagnosed group, IV chemotherapy produced a statistically higher median overall survival (MOS; 16.3 months) compared with IA treatment (14.02 months). However, the total number of adverse events in IA chemotherapy was 1.08 per patient whereas for IV it was higher at 1.54 events per patient. Our recurrent GBM group includes only patients treated with IA chemotherapy which resulted in an average MOS of 10.84 months. This group had 2.7 adverse events per patient but no IV group is available for comparison. Historically, the survival of patients with recurrent GBM ranges from 3 to 9 months (Gil-Gil et al. Bevacizumab for the treatment of glioblastoma. Clin Med Insights Oncol 2013;7:123-35). For this reason, we believe IA chemotherapy to be a viable methodology in recurrent GBM patients to prolong survival at the risk of procedure-related complications and in newly diagnosed patients with the benefit of decreased complications. [ABSTRACT FROM AUTHOR]

The Community Multiscale Air Quality (CMAQ) modeling system Version 5.0 (CMAQv5.0) was released by the U.S. Environmental Protection Agency (EPA) in February 2012, with an interim release (v5.01) in July 2012. Because CMAQ is a community model, the EPA encourages the development of proven alternative science treatments by external scientists and developers that can be incorporated as part of an official CMAQ release. This paper describes the implementation, evaluation, and testing of a plume-in-grid (PinG) module in CMAQ 5.01. The PinG module, also referred to as Advanced Plume Treatment (APT), provides the capability of resolving sub-grid-scale processes, such as the transport and chemistry of point-source plumes, in a grid model. The new PinG module in CMAQ 5.01 is applied and evaluated for two 15-day summer and winter periods in 2005 to the eastern United States, and the results are compared with those from the base CMAQ 5.01. Eighteen large point sources of NOx in the eastern United States were selected for explicit plume treatment with APT in the PinG simulation. The results show that overall model performance is negligibly affected when PinG treatment is included. However, the PinG model predicts significantly different contributions of the 18 sources to pollutant concentrations and deposition downwind of the point sources compared to the base model.Implications: This study describes the incorporation of a plume-in-grid (PinG) capability within the latest version of the EPA grid model, CMAQ. The capability addresses the inherent limitation of the grid model to resolve processes, such as the evolution of point-source plumes, which occur at scales much smaller than the grid resolution. The base grid model and the PinG version predict different source contributions to ozone and PM2.5 concentrations that need to be considered when source attribution studies are conducted to determine the impacts of large point sources on downwind concentrations and deposition of primary and secondary pollutants. [ABSTRACT FROM AUTHOR]

Glacial erosion patterns on northwest Iceland are quantified using a Geographic Information System (GIS) in order to interpret subglacial characteristics of part of northwest Iceland affected by ice sheet glaciation. Ice scour lake density is used as a proxy for glacial erosion. Erosion classes are interpreted from variations in the density of lake basins. Lake density was calculated using two different methods: the first is sensitive to the total number of lakes in a specific area, and the second is sensitive to total lake area in a specific area. Both of these methods result in a value for lake density, and the results for lake density calculated using the two methods are similar. Areas with the highest density of lakes are interpreted as areas with the most intense erosion with the exception of alpine regions. The highest density of lakes in the study area exceeds 8% and is located on upland plateaus where mean elevations range from 400 to 800 m a.s.l. Low lake density (0-2%) is observed in steep alpine areas where steep topography does not favor lake development. The GIS analysis is combined with geomorphic mapping to provide ground truth for the GIS interpretations and to locate paleo-ice flow indicators and landforms. The patterns identified in this study illustrate distinct regions of glacial erosion and flow paths that are best explained by two independent ice sheets covering northwest Iceland during the Last Glacial Maximum (LGMI. Areas of alpine glacial landforms and the presence of nunataks within the glaciated region support interpretations that ice-free regions or cold-based ice cover existed on parts of northwest Iceland during the LGM. The methods developed in this study are easily transferable to other formerly glaciated regions and provide tools to evaluate subglacial properties of former ice sheets. The data generated yield important subglacial boundary conditions for ice sheet models of Iceland. [ABSTRACT FROM AUTHOR]

In this article, we revisit Zipf's law and test the rank-size rule on US cities for different periods of time and city limits. We show that Zipf 's law holds more closely for urban places in 1900 and recently, in 1990 and 2000, for metropolitan areas. With the evolution of the modern city, the changes in infrastructure and the cost of commuting that have contributed to an urban spread, the metropolitan area is perhaps representing today's communities better, as urban places did 100 years ago. In that sense, the rank-size rule continues to hold with the appropriate redefinition of a city. [ABSTRACT FROM AUTHOR]

In this article, the author reflects on the enumeration of the homomorphisms between two specified cyclic groups. He discusses an example of number of group homomorphism from dihedral group Dm into dihedral group Dn and presents a theorem related to homomorphism. He further states that one can count the number of group homomorphisms between any two dihedral groups with the help of elementary group theory only.