AM with Multiple Merlins

We introduce and study a new model of interactive proofs: AM(k), or Arthur-Merlin with k non-communicating Merlins. Unlike with the better-known MIP, here the assumption is that each Merlin receives an independent random challenge from Arthur. One motivation for this model (which we explore in detail) comes from the close analogies between it and the quantum complexity class QMA(k), but the AM(k) model is also natural in its own right. We illustrate the power of multiple Merlins by giving an AM(2) protocol for 3SAT, in which the Merlins' challenges and responses consist of only n^{1/2+o(1)} bits each. Our protocol has the consequence that, assuming the Exponential Time Hypothesis (ETH), any algorithm for approximating a dense CSP with a polynomial-size alphabet must take n^{(log n)^{1-o(1)}} time. Algorithms nearly matching this lower bound are known, but their running times had never been previously explained. Brandao and Harrow have also recently used our 3SAT protocol to show quasipolynomial hardness for approximating the values of certain entangled games. In the other direction, we give a simple quasipolynomial-time approximation algorithm for free games, and use it to prove that, assuming the ETH, our 3SAT protocol is essentially optimal. More generally, we show that multiple Merlins never provide more than a polynomial advantage over one: that is, AM(k)=AM for all k=poly(n). The key to this result is a subsampling theorem for free games, which follows from powerful results by Alon et al. and Barak et al. on subsampling dense CSPs, and which says that the value of any free game can be closely approximated by the value of a logarithmic-sized random subgame.Comment: 48 page

Reducing Feelings of Unpreparedness Experienced by Registered Nurses Assigned the Care of Covid-19 Positive Individuals with Intellectual and Developmental Disabilities

Background: Nurses assigned the care of individuals with intellectual and developmental disabilities (IDD) individuals, practice within a fragmented healthcare system. Nurses face barriers of patient competence and capacity to consent, communication challenges, a shortage of specialty providers, and fiscal limitation. The COVID-19 pandemic triggered requests from registered nurses, for guidance related to the care of individuals with IDD and diagnosed with the Severe Acute Respiratory Syndrome Coronavirus-2, the COVID-19 virus. Purpose: The purpose of this project was to reduce, through the administration of in-service, feelings of unpreparedness experienced by registered nurses caring for individuals with intellectual and developmental disabilities and at risk for COVID-19 infection. Method: Nurses enrolled in an IDD course offered by a local university, school of nursing were asked to participate in this research project. The object of the project was to assess the reduction of feelings of unpreparedness experienced by nurses likely to be assigned to care for COVID-19 positive individuals with IDD. The convenience sample of registered nurses enrolled in an IDD course, and consenting to participate in the project, received a 15-item pre- and post- in-service Likert scale survey project. Results: Fourteen of 18 possible professional nurses enrolled in an IDD course, consented to, participate in the study. The participants completed the 15-item pre-post in-service Likert scale survey evaluating feelings of unpreparedness when the care of COVID-19 positive individuals with IDD. The post-in-service Likert scores reflected an improvement in pre- and post-survey scores in the four areas evaluated, knowledge, nursing practice, affective, and implementation. For questions evaluating nurse knowledge, a 0.97-point increase occurred between pre- and post-survey scores, for nursing practice, a one-point increase, for questions evaluating nursing affect, a .13-point increase and for scores evaluating implementation strategies, a 0.57-point increase

SCS 15: Continuous Lattices and Universal Algebra

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.htm

SCS 4: Note on Continuous Lattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.htm

The relationship between Louisiana middle school parent perceptions of school effectiveness and school performance scores

The purpose of this study was to investigate the perception of parents of middle school students in Louisiana about the (a) culture; (b) climate; (c) leadership; (d) curriculum, instruction, and assessment; and (e) level of parental and community involvement at the schools that their children attend as it relates to school performance. The instrument used in this study was the Parent Questionnaire developed for the Louisiana Needs Analysis (LANA). Designed by the Louisiana Department of Education (LDE), LANA is an internet-based tool provided to assist school administrators in evaluating school performance and planning for improvement. During the data analysis, Pearson correlations were calculated. Additionally, the researcher conducted a one-way analysis of variance (ANOVA) followed by a post hoc Tukey HSD. The alpha level for the statistical analyses was p \u3c .05. The findings from this study indicated a significant and positive relationship between school performance and each of the previously mentioned predictor variables. In addition to being highly correlated with school performance, school culture; curriculum, instruction, and assessment; family and community relations; school climate; and school leadership were also found to be highly correlated with each other. The findings from this study support the previous findings of research about effective schools. Due to the focus on parental perceptions, these findings also reveal the impact of communication and collaboration between educators and parents on parental perceptions. These findings further imply that invitations for parental involvement from school personnel may be the key to improving communication between home and school and to building more effective home-school partnerships

Semilattices, Domains, and Computability (Invited Talk)

As everyone knows, one popular notion of Scott domain is defined as a bounded complete algebraic cpo. These are closely related to algebraic lattices: (i) A Scott domain becomes an algebraic lattice with the adjunction of an (isolated) top element. (ii) Every non-empty Scott-closed subset of an algebraic lattice is a Scott domain. Moreover, the isolated ($=$ compact) elements of an algebraic lattice form a semilattice (under join). This semilattice has a zero element, and, provided the top element is isolated, it also has a unit element. The algebraic lattice itself may be regarded as the ideal completion of the semilattice of isolated elements. This is all well known. What is not so clear that is that there is an easy-to-construct domain of countable semilattices giving isomorphic copies of all countably based domains. This approach seems to have advantages over both ``information systems\u27\u27 or more abstract lattice formulations, and it makes definitions of solutions to domain equations very elementary to justify. The ``domain of domains\u27\u27 also has an immediate computable structure