Tackling the Minimal Superpermutation Problem

A superpermutation on $n$ symbols is a string that contains each of the $n!$ permutations of the $n$ symbols as a contiguous substring. The shortest superpermutation on $n$ symbols was conjectured to have length $\sum_{i=1}^n i!$. The conjecture had been verified for $n \leq 5$. We disprove it by exhibiting an explicit counterexample for $n=6$. This counterexample was found by encoding the problem as an instance of the (asymmetric) Traveling Salesman Problem, and searching for a solution using a powerful heuristic solver.Comment: 5 page

Proof equivalence in MLL is PSPACE-complete

MLL proof equivalence is the problem of deciding whether two proofs in multiplicative linear logic are related by a series of inference permutations. It is also known as the word problem for star-autonomous categories. Previous work has shown the problem to be equivalent to a rewiring problem on proof nets, which are not canonical for full MLL due to the presence of the two units. Drawing from recent work on reconfiguration problems, in this paper it is shown that MLL proof equivalence is PSPACE-complete, using a reduction from Nondeterministic Constraint Logic. An important consequence of the result is that the existence of a satisfactory notion of proof nets for MLL with units is ruled out (under current complexity assumptions). The PSPACE-hardness result extends to equivalence of normal forms in MELL without units, where the weakening rule for the exponentials induces a similar rewiring problem.Comment: Journal version of: Willem Heijltjes and Robin Houston. No proof nets for MLL with units: Proof equivalence in MLL is PSPACE-complete. In Proc. Joint Meeting of the 23rd EACSL Annual Conference on Computer Science Logic and the 29th Annual ACM/IEEE Symposium on Logic in Computer Science, 201

Zen Puzzle Garden is NP-complete

Zen Puzzle Garden (ZPG) is a one-player puzzle game. In this paper, we prove that deciding the solvability of ZPG is NP-complete.Comment: Submitte

Finite Products are Biproducts in a Compact Closed Category

If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.Comment: 9 pages. Introduction further expanded, minor errors correcte

The Influence of Prayer on Anxiety in Black Males: A Hermeneutic Phenomenological Study

Prayer is a primary indicator that Christians use to infuse meaning into their lives and navigate life\u27s difficulties. Acquiring the capacity to cope with anxious feelings through spiritual disciplines, practices, and rituals can assist in anxiety relief. The literature indicates that the church has always served as a refuge when life-altering events occur. According to I Corinthians 12:13, the church is one body of believers, unified for a common purpose. Anxiety is defined as a state of distress caused by a perceived social threat. The purpose of this study in Pastoral Care and Counseling was to ascertain why studies have found Black males experience less anxiety than their black female counterparts and what effects prayer has on this phenomenon. The sample and size were taken from the population of Black males near the AME Zion Church, located in Concord, North Carolina. The data was gathered by conducting interviews, observations, and a study group of eight black males. These data sources answered the research questions: (1) What verbalizations best describe Black males\u27 prayer-based strength? What prayer practices produce strength in black males? This qualitative study is a hermeneutic phenomenological approach developed by Martin Heidegger. The research found that prayer is critical in reducing anxiety in Black males. The primary themes that were obtained from the findings included prayer motivations, impact of prayer, attitudes, and knowledge. Participants mentioned COVID-19 and personal problems as some of the motivations for their prayerful life. Their responses underscored the significance of prayer in the reduction of anxiety. One of the implications of this study is that mental health practitioners can use this knowledge to advise religious clients on ways to reduce anxiety through prayer and fellowship

Community Health Workers Can Identify and Manage Possible Infections in Neonates and Young Infants: MINI\u2014A Model from Nepal

The mortality rates of infants and children aged less than five years are declining globally and in Nepal but less among neonates. Most deliveries occur at home without skilled attendants, and most neonates may not receive appropriate care through the existing medical systems. So, a community-based pilot programme\u2014 Morang Innovative Neonatal Intervention (MINI) programme\u2014was implemented in Morang district of Nepal to see the feasibility of bringing the management of sick neonates closer to home. The objective of this model was to answer the question: "Can a team of female community health volunteers and paid facility-based community health workers (collectively called CHWs) within the existing heath system correctly follow a set of guidelines to identify possible severe bacterial infection in neonates and young infants and successfully deliver their treatment?" In the MINI model, the CHWs followed an algorithm to classify sick young infants with possible severe bacterial infection (PSBI). Female Community Health Volunteers (FCHVS) were trained to visit homes soon after delivery, record the birth, counsel mothers on essential newborn care, and assess the newborns for danger-signs. Infants classified as having PSBI, during this or subsequent contacts, were treated with co-trimoxazole and referred to facility-based CHWs for seven-day treatment with injection gentamicin. Additional supervisory support was provided for quality of care and intensified monitoring. Of 11,457 livebirths recorded during May 2005-April 2007, 1,526 (13.3%) episodes of PSBI were identified in young infants. Assessment of signs by the FCHVs matched that of more highly-trained facility-based CHWs in over 90% of episodes. Treatment was initiated in 90% of the PSBI episodes; 93% completed a full course of gentamicin. Case fatality in those who received treatment with gentamicin was 1.5% [95% confidence interval (CI) 1.0-2.3] compared to 5.3% (95% CI 2.6-9.7) in episodes that did not receive any treatment. Within the existing government health infrastructure, the CHWs can assess and identify possible infections in neonates and young infants and deliver appropriate treatment with antibiotics. This will result in improvement in the likelihood of survival and address one of the main causes of neonatal mortality

No proof nets for MLL with units:Proof equivalence in MLL is PSPACE-complete

[Analysis of algorithms and problem complexity]: Nonnumerical algorithms and problems—Complexity of proof procedures Keywords linear logic, proof equivalence, proof nets, constraint logic, PSPACE-completeness MLL proof equivalence is the problem of deciding whether two proofs in multiplicative linear logic are related by a series of inference permutations. It is also known as the word problem for ∗-autonomous categories. Previous work has shown the problem to be equivalent to a rewiring problem on proof nets, which are not canonical for full MLL due to the presence of the two units. Drawing from recent work on reconfiguration problems, in this paper it is shown that MLL proof equivalence is PSPACE-complete, using a reduction from Nondeterministic Constraint Logic. An important consequence of the result is that the existence of a satisfactory notion of proof nets for MLL with units is ruled out (under current complexity assumptions). 1

The effectiveness of digital storytelling in the classrooms: a comprehensive study

In recent years the use of new technologies in educational systems has increased worldwide as digital cameras, personal computers, scanners, and easy-to-use software have become available to educators to harness the digital world. The impact of new technologies in educational contexts has been mostly positive as new technologies have given educators the opportunity to enhance their knowledge, skills, and therefore enhance the standard of education. Researchers have found that student engagement, achievement and motivation are enhanced through integration of such technologies. However, education systems still face many challenges: one of these challenges is how to enhance student engagement to provide better educational outcomes. It has become increasingly important to use innovative pedagogical models to engage learners. Digital storytelling is one of the innovative pedagogical approaches that can engage students in deep and meaningful learning. This research project aimed to create a constructivist learning environment with digital storytelling. The research investigated the pedagogical aspects of digital storytelling and the impact of digital storytelling on student learning when teachers and students use digital stories. A multi-site case study was conducted in one Australian school at primary and secondary levels. In selected classrooms, students and teachers had the opportunity to engage in innovative learning experiences based on digital storytelling. In order to enhance the reliability and validity of the research, multiple methods of data collection and analysis were used. Data was collected with qualitative and quantitative methods. An evaluation rubric was used to collect quantitative data, while interviews and observation were used to collect qualitative data. Data collection was guided by a mixed methods research design in order to evaluate if and how digital storytelling enhances teaching and learning outcomes. The findings from this study suggest that digital storytelling is a powerful tool to integrate instructional messages with learning activities to create more engaging and exciting learning environments. It is a meaningful approach for creating a constructivist learning environment based on novel principles of teaching and learning. Thus, this approach has the potential to enhance student engagement and provide better educational outcomes for learners