The category ${\rm CM}(B_{k,n}) $ of Cohen-Macaulay modules over a quotient $B_{k,n}$ of a preprojective algebra provides a categorification of the cluster algebra structure on the coordinate ring of the Grassmannian variety of $k$-dimensional subspaces in $\mathbb C^n$, \cite{JKS16}. Among the indecomposable modules in this category are the rank $1$ modules which are in bijection with $k$-subsets of $\{1,2,\dots,n\}$, and their explicit construction has been given by Jensen, King and Su. These are the building blocks of the category as any module in ${\rm CM}(B_{k,n}) $ can be filtered by them. In this paper we give an explicit construction of rank 2 modules. With this, we give all indecomposable rank 2 modules in the cases when $k=3$ and $k=4$. In particular, we cover the tame cases and go beyond them. We also characterise the modules among them which are uniquely determined by their filtrations. For $k\ge 4$, we exhibit infinite families of non-isomorphic rank 2 modules having the same filtration.

Abstract Background Posttraumatic stress disorder (PTSD) and major depressive disorder (MDD) are commonly reported co-occurring mental health consequences of psychological trauma exposure. The disorders have high genetic overlap. Trauma is a complex phenotype but research suggests that trauma sensitivity has a heritable basis. We investigated whether sensitivity to trauma in those with MDD reflects a similar genetic component in those with PTSD. Methods Genetic correlations between PTSD and MDD in individuals reporting trauma and MDD in individuals not reporting trauma were estimated, as well as with recurrent MDD and single-episode MDD, using genome-wide association study (GWAS) summary statistics. Genetic correlations were replicated using PTSD data from the Psychiatric Genomics Consortium and the Million Veteran Program. Polygenic risk scores were generated in UK Biobank participants who met the criteria for lifetime MDD (N = 29 471). We investigated whether genetic loading for PTSD was associated with reporting trauma in these individuals. Results Genetic loading for PTSD was significantly associated with reporting trauma in individuals with MDD [OR 1.04 (95% CI 1.01–1.07), Empirical-p = 0.02]. PTSD was significantly more genetically correlated with recurrent MDD than with MDD in individuals not reporting trauma (rg differences = ~0.2, p < 0.008). Participants who had experienced recurrent MDD reported significantly higher rates of trauma than participants who had experienced single-episode MDD (χ2 > 166, p < 0.001) Conclusions Our findings point towards the existence of genetic variants associated with trauma sensitivity that might be shared between PTSD and MDD, although replication with better powered GWAS is needed. Our findings corroborate previous research highlighting trauma exposure as a key risk factor for recurrent MDD.

This paper shows the use of membrane filters in adsorption of solution of tetracycline hydrochloride on graphene materials. The adsorption process was monitored at different wavelengths, different pH values at certain time intervals. The absorbances of the solutions were measured by UV-Vis spectrophotometry at two wavelengths (275 nm and 356 nm), and three pH values (pH 4, pH 7 and pH 10) every 90 minutes for 6 hours of monitoring, with constant stirring in an ultrasonic bath. The results showed decrease in absorbance at both wavelength and in all three pH values which proved the adsorption of tetracycline hydrochloride on GO and rGO. The largest decrease in absorbance was 98.1%. The most suitable pH value for adsorption was pH 4. This paper used a unique approach to filtration through membrane filters, which in the future could lead to the development of membrane filters based on graphene materials.

Hexavalent chromium (Cr(VI)) is an environmental pollutant with vast mutagenic and carcinogenic potential. Various past and recent studies confirm the deleterious effects of Cr(VI) in different models, from invertebrates to mammalians. However, there is a lack of studies that comprehensively assess and correlate Cr(VI) accumulation patterns and the resulting physiological responses. Here we used an attractive toxicological model, male Japanese quail (Coturnix japonica), as an alternative probing system to evaluate Cr(VI) accumulation in the vital organs, including the brain, heart, kidneys, liver, and testes after 20 days of exposure to 1.2 μg/mL and 2.4 μg/mL potassium dichromate-K2Cr2O7 ingested in the form of drinking water. The observed effects were correlated with the shift in immune system readiness, hematological indices, serum biochemistry and enzyme activity. Regardless of the exposure dose, the Cr(VI) distribution and accumulation pattern in terms of relative Cr(VI) concentration in tissues was: testes > kidneys > liver > heart > brain. Moreover, Cr(VI) triggered the development of microcytic and hypochromic anemia and reduced the immune system's readiness to cope with challenges. Besides, serum biochemistry presented significant shifts, including reduction of serum electrolytes and proteins and an increase in creatine kinase (CK) and lactate dehydrogenase (LDH) activity. Our study provides novel toxicological data that can be translated to higher animal models to help in the extrapolation of Cr(VI) toxicity in humans.

Although COVID-19 vaccines are becoming increasingly available, their ability to effectively control and contain the spread of the COVID-19 pandemic is highly contingent on an array of factors. This paper discusses how limitations to vaccine accessibility, issues associated with vaccine side effects, concerns regarding vaccine efficacy, along with the persistent prevalence of vaccine hesitancy among the public, including health care professionals, might impact the potential of COVID-19 vaccines to curb the pandemic. We draw insights from the literature to identify practical solutions that could boost people’s adoption of COVID-19 vaccines and their accessibility. We conclude with a discussion on health experts’ and government officials’ moral and ethical responsibilities to the public, even in light of the urgency to adopt and endorse “the greatest amount of good for the greatest number” utilitarian philosophy in controlling and managing the spread of COVID-19.