Artinian level algebras of codimension 3

In this paper, we continue the study of which $h$-vectors $\H=(1,3,..., h_{d-1}, h_d, h_{d+1})$ can be the Hilbert function of a level algebra by investigating Artinian level algebras of codimension 3 with the condition $\beta_{2,d+2}(I^{\rm lex})=\beta_{1,d+1}(I^{\rm lex})$, where $I^{\rm lex}$ is the lex-segment ideal associated with an ideal $I$. Our approach is to adopt an homological method called {\it Cancellation Principle}: the minimal free resolution of $I$ is obtained from that of $I^{\rm lex}$ by canceling some adjacent terms of the same shift. We prove that when $\beta_{1,d+2}(I^{\rm lex})=\beta_{2,d+2}(I^{\rm lex})$, $R/I$ can be an Artinian level $k$-algebra only if either $h_{d-1}<h_d<h_{d+1}$ or $h_{d-1}=h_d=h_{d+1}=d+1$ holds. We also apply our results to show that for $\H=(1,3,..., h_{d-1}, h_d, h_{d+1})$, the Hilbert function of an Artinian algebra of codimension 3 with the condition $h_{d-1}=h_d<h_{d+1}$, (a) if $h_d\leq 3d+2$, then $h$-vector \H cannot be level, and (b) if $h_d\geq 3d+3$, then there is a level algebra with Hilbert function \H for some value of $h_{d+1}$.Comment: 15 page

Long-Term Health Effects of Work Trajectories Among Middle-Aged and Older Adults: The Mediating Role of Work, Material, and Social Environments

Using data from 14 waves (2003–2016) of the Korean Labor and Income Panel Study (KLIPS) (N = 1,627 individuals aged 45–64; 22778 observations), in this study, we conducted sequence analysis and a multi-categorical variable mediation analysis (1) to examine to what extent long-term work histories exhibit varying degrees of de-standardization and precariousness using sequence analysis (2) to explore the potential mediating effects of work, material, and social environments in the association between multiple work sequences and self-rated health. We found the coexistence of a relatively stable long-term employment pattern and a high prevalence of precariousness. The health and economic risks of precarious work fall disproportionately on older workers. Future researchers should continue to analyze whether the COVID-19 pandemic will lead to long-term changes in the workforce to improve our understanding of and response to working in later life and its health effects

The Theory of Falling Shadows Applied to -Ideals in -Algebras

On the basis of the theory of a falling shadow which was first formulated by Wang (1985), the notion of falling ∗-ideals in -algebras is introduced, and related properties are investigated. Characterizations of a falling ∗-ideal are established. Relations among falling ∗-ideals, falling -ideals, falling #-ideals, falling -subalgebras, and falling BCK-ideals are discussed

Reinforcing effects of methamphetamine in an animal model of Attention-Deficit/Hyperactivity Disorder-the Spontaneously Hypertensive Rat

Substrains of the Spontaneously Hypertensive rat (SHR), a putative animal model of Attention-Deficit/Hyperactivity Disorder (ADHD), have demonstrated increased sensitivity to many drugs of abuse, including psychostimulants. Therefore, it was suggested that studies in SHR may help elucidate ADHD and comorbidity with substance use disorder (SUD). However, the drug intake profile of the SHR in the most relevant animal model of drug addiction, the self-administration (SA) test, and its response on the conditioned place preference (CPP) paradigm are not yet determined. In the present study, we employed SA and CPP tests to investigate the reinforcing effects of the psychostimulant methamphetamine in an SHR substrain obtained from Charles River, Japan (SHR/NCrlCrlj). Concurrent tests were also performed in Wistar rats, the strain representing "normal" heterogeneous population. To address if the presence of ADHD behaviors further increases sensitivity to the rewarding effect of methamphetamine during adolescence, a critical period for the onset of drug abuse, CPP tests were especially conducted in adolescent Wistar and SHR/NCrlCrlj. We found that the SHR/NCrlCrlj also acquired methamphetamine SA and CPP, indicating reinforcing effects of methamphetamine in this ADHD animal model. However, we did not observe increased responsiveness of the SHR/NCrlCrlj to methamphetamine in both SA and CPP assays. This indicates that the reinforcing effects of methamphetamine may be similar in strains and that the SHR/NCrlCrlj may not adequately model ADHD and increased sensitivity to methamphetamine

Human microglial cells synthesize albumin in brain

Albumin has been implicated in Alzheimer&#x27;s disease since it can bind to and transport amyloid beta, the causative agent; albumin is also a potent inhibitor of amyloid beta polymerization. In a pilot phase study of Human Brain Proteome Project, we found evidence that albumin may be synthesized in immortalized human microglial cells, human primary microglial cells, and human fetal and adult brain tissues. We also found the synthesis and secretion is enhanced upon microglial activation by Amyloid [beta]~1-42~, lipopolysaccharide treatment or human Alzheimer&#x27;s brain