In this note, we give short proofs of three theorems about intersection problems. The first one is a determination of the maximum size of a nontrivial $k$-uniform, $d$-wise intersecting family for $n\ge (1+\frac{d}{2})(k-d+2)$, which improves the range of $n$ of a recent result of O'Neill and Verstraëte. Our proof also extends to $d$-wise, $t$-intersecting families, and from this result we obtain a version of the Erdős-Ko-Rado theorem for $d$-wise, $t$-intersecting families.

Our second result partially proves a conjecture of Frankl and Tokushige about $k$-uniform families with restricted pairwise intersection sizes.

Our third result is about intersecting families of graphs. Answering a question of Ellis, we construct $K_{s,t}$-intersecting families of graphs which have size larger than the Erdős-Ko-Rado-type construction, whenever $t$ is sufficiently large in terms of $s$. The construction is based on nontrivial $(2s)$-wise $t$-intersecting families of sets.

Mathematics Subject Classifications: 05D05, 05D99

Keywords: Nontrivial intersecting family, Hilton-Milner, forbidden intersection, graph intersection

The current study investigated the indirect effect of media multitasking on cognitive performance during subsequent single tasking, mediated through mood. A post-test between-subjects experiment was conducted to investigate the effects of two types of media multitasking, with nonsocial media tasks and with social media tasks, on mood (i.e., valence and arousal), attention filtering (i.e., ability to selectively pay attention to some information), and behavioral inhibition (i.e., ability to control behavior) as compared to single tasking. The results demonstrate that media multitasking with both nonsocial and social tasks decrease pleasant mood valence but increase arousal. Additionally, there is evidence that nonsocial media multitasking may improve behavioral inhibition (i.e., decrease impulsivity) by increasing arousal. The results highlight the potential variation in media multitasking’s task demand depending on the combinations of tasks involved. Further research is necessary to explore the possible benefits of varying task demands for mood and cognitive performance.

A set system $\mathcal{F}$ is $t$-intersecting, if the size of the intersection of every pair of its elements has size at least $t$. A set system $\mathcal{F}$ is $k$-Sperner, if it does not contain a chain of length $k+1$. Our main result is the following: Suppose that $k$ and $t$ are fixed positive integers, where $n+t$ is even and $n$ is large enough. If $\mathcal{F}\subseteq 2^{[n]}$ is a $t$-intersecting $k$-Sperner family, then $|\mathcal{F}|$ has size at most the size of the sum of $k$ layers, of sizes $(n+t)/2,\dots ,(n+t)/2+k-1$. This bound is best possible. The case when $n+t$ is odd remains open.

Mathematics Subject Classifications: 05D05

Keywords: Extremal set theory, Sperner families, intersection theorems

Abstract This dissertation is comprised of three qualitative studies that examine the phenomenon of post-mortem discrimination (PMD). Using an innovative application of the communication theory of identity, this line of research is particularly focused on the process through which agents of the dominant culture become empowered to enact the identities of marginalized individuals after they die. The first two studies explore the persistent practice of families who de-transition their transgender or gender diverse (TGD) family members after they die. Communicative actions associated with this practice were examined through interviews with older (Study 1, aged 40 y. o. and above) and younger (Study 2, ages 18 to 30 y. o.) TGD adults. Findings showed that most TGD individuals had not engaged in end-of-life conversations (EOL) that could help them to preserve their identity after death, nor did they intend to engage in the near future. Other findings revealed a TGD community that is, for the most part, optimistic that their gender identity will be authentically expressed by their family after they die, but concerned regarding the post-mortem expressions of others. Far from a monolith, the communities’ wishes for the enactment of their own gender identity after death proved as varied as their enactment of that identity before death. The third study investigates the articulation of human value as expressed in memorial messages posted by loved ones to the Hart Island Project website. These postings could be seen as an attempt to re-humanize the impoverished, disenfranchised, and unclaimed individuals buried in New York City’s potter’s field. The study particularly highlights the post-mortem negotiation that occurs between CTI’s relational and communal layers of identity – without the participation of the subject. Examined and analyzed through the lens of the CTI, and informed by elements of queer theory, social identity theory, and the writings of Judith Butler on grievability and ungrievability, the data from these three studies reveals an ongoing, oppressive tradition of both interpersonal and systemic acts of post-mortem discrimination that work to reinforce the vulnerability of marginalized individuals and communities. This work suggests that, when the deceased is a member of a marginalized or vulnerable population and the empowered others are associated with the dominant culture, problematic enactments that distort, disrespect, and/or disappear the identity of the deceased can and do occur. Implications of each study and of the entire line of research are identified and discussed.

Censorship has been a heavily investigated topic within the field of Communication, and explanations of why individuals support the censorship of media, particularly pornography, have traditionally relied upon either the third-person effect, or theories of personality, such as authoritarianism. However, recent research within the field of evolutionary psychology has suggested that the generation of particular cultural values have arisen because they indirectly influenced pathogen avoidance. Based upon the parasite model of democratization developed by Thornhill, Fincher and Aran (2009), it was tested whether the reduction of pathogens in decreases authoritarianism and restrictiveness of sexuality, which subsequently decreases support for the censorship of pornography. An analysis of country-level data was undertaken to test whether the historical prevalence of pathogens in a country is related to the legal status of pornography. In addition, an online experiment was administered, in which participants were exposed to either a pathogen prime, a threatening gun prime, or a control. While results did not show a clear link between pathogens and censorship, some interesting results were found.