Encoding !-tensors as !-graphs with neighbourhood orders

Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to mark repeated structure inside a diagram. This led to !-graphs being implemented in the diagrammatic proof assistant Quantomatic. Having a partially automated program for rewriting diagrams has proven very useful, but being based on !-graphs, only commutative theories are allowed. An enriched abstract tensor notation, called !-tensors, has been used to formalise the notion of !-boxes in non-commutative structures. This work-in-progress paper presents a method to encode !-tensors as !-graphs with some additional structure. This will allow us to leverage the existing code from Quantomatic and quickly provide various tools for non-commutative diagrammatic reasoning.Comment: In Proceedings QPL 2015, arXiv:1511.0118

Tensors, !-graphs, and non-commutative quantum structures

Categorical quantum mechanics (CQM) and the theory of quantum groups rely heavily on the use of structures that have both an algebraic and co-algebraic component, making them well-suited for manipulation using diagrammatic techniques. Diagrams allow us to easily form complex compositions of (co)algebraic structures, and prove their equality via graph rewriting. One of the biggest challenges in going beyond simple rewriting-based proofs is designing a graphical language that is expressive enough to prove interesting properties (e.g. normal form results) about not just single diagrams, but entire families of diagrams. One candidate is the language of !-graphs, which consist of graphs with certain subgraphs marked with boxes (called !-boxes) that can be repeated any number of times. New !-graph equations can then be proved using a powerful technique called !-box induction. However, previously this technique only applied to commutative (or cocommutative) algebraic structures, severely limiting its applications in some parts of CQM and (especially) quantum groups. In this paper, we fix this shortcoming by offering a new semantics for non-commutative !-graphs using an enriched version of Penrose's abstract tensor notation.Comment: In Proceedings QPL 2014, arXiv:1412.810

A first-order logic for string diagrams

Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax called !-box notation. While this does greatly increase the proving power of string diagrams, previous attempts to go beyond equational reasoning have been largely ad hoc, owing to the lack of a suitable logical framework for diagrammatic proofs involving !-boxes. In this paper, we extend equational reasoning with !-boxes to a fully-fledged first order logic called with conjunction, implication, and universal quantification over !-boxes. This logic, called !L, is then rich enough to properly formalise an induction principle for !-boxes. We then build a standard model for !L and give an example proof of a theorem for non-commutative bialgebras using !L, which is unobtainable by equational reasoning alone.Comment: 15 pages + appendi

Audit market concentration and related regulatory measures

Audit markets are highly concentrated and such a situation might have negative consequences on competition, and thus, on price setting, on audit quality and on the functioning of markets. The European regulator recognized some causes for audit market concentration, identified a systemic risk and suggested joint audits and a mandatory rotation of audit firms to reduce concentration. Prominent concentration measures are concentration ratios, the Lorenz curve, the Gini-coefficient and the Herfindahl-Hirschman-Index. An empirical study on the concentration of German Prime Standard market for the period 2010 – 2013 revealed a high concentration which is quite stable over time and a narrow oligopoly with duopolistic tendencies. Nevertheless, competition could still work, e.g. due to the threat of market entrants. Moreover, given the fact that Big4 audit firms provide a higher audit quality, concentration may have positive effects. The mandatory audit firm rotation has a positive effect on auditor independence and a negative effect on auditor competence. This explains why related research output is inconclusive, i.e. the total effect on audit quality remains unclear. Moreover, a positive impact on competition is not ensured. Archival studies reveal that joint audits do not improve audit quality but increase audit costs. On the other hand, joint audits potentially reduce concentration. A combination between audit firm rotation and joint audits might be an optimal solution.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Book Review: Who Needs It: A Review of Instant Art Instant Culture

Book review for Instant Art Instant Culture: The Unspoken Policy for American Schools, Laura Chapman, Teachers College Press, New York, 1982

Contesting Human Rights Coherence: Neoliberalism as an Epoch of Brutality

The end of the Cold War solidified modern human rights’ dependency on neoliberalism. Neoliberal capitalism fosters universal commodification, hyper-individualism, and a standard of excess. A consequence of these developments is that some persons of marginalized populations turn to crime as a means of achieving basic human rights. To particularize, the realization of the self as a rights-holding subject emerges from the brutalization and subsequent de-realization of the other. Furthermore, justifications of such actions may be coherent within the modern human rights discourse. This thesis is contextualized by the historical dynamics and present-day observations of El Salvador, which I take to represent broader global trends in the development of human rights into a discourse of apparently coherent brutality. Given this contradiction, I compare the peril and potential of reclaiming human rights as a popular discourse

Leader Development and Emotional Competence: Authentic Leadership, Self-Awareness, and Personal Integrity

Can leadership be taught? (Doh, 2003) The dramatic growth of leadership academies, institutes, and programs from political science to business and psychology to reserve officer training corps for U.S. military services makes this a compelling question. We say yes and then: How can it be taught? And how are leaders developed? Ours is a developmental theory for teaching leaders and suggests that emotional competence is at the heart of developing authentic leaders with personal integrity

Misogyny, Islamophobia, and Muslim Supression Internal and Abroad

Contrary to assumptions of suppression in Islam, female sexual discourse and agency expresses freedom within the faith. Homosexual Muslim men face identity suppression. While many think Islamophobia hinders Muslims, in many cases it is shown to motivate and propel them. While some believe that Muslims have the right to practice their faith they don’t see what they experience daily to make them feel suppressed. Islamophobia is the perpetuated form of racism against those who practice the Islamic faith and incorrectly associate them with extremism and violence.https://ecommons.udayton.edu/roesch_symposium_content/1040/thumbnail.jp

A discrete slug population model determined by egg production

Slugs are significant pests in agriculture (as well as a nuisance to gardeners), and it is therefore important to understand their population dynamics for the construction of efficient and effective control measures. Differential equation models of slug populations require the inclusion of large (variable) temporal delays, and strong seasonal forcing results in a non-autonomous system. This renders such models open to only a limited amount of rigorous analysis. In this paper, we derive a novel batch model based purely upon the quantity of eggs produced at different times of the year. This model is open to considerable reduction; from the resulting two variable discrete-time system it is possible to reconstruct the dynamics of the full population across the year and give conditions for extinction or global stability and persistence. Furthermore, the steady state temporal population distribution displays qualitatively different behavior with only small changes in the survival probability of slugs. The model demonstrates how small variations in the favorability of different years may result in widely different slug population fluctuations between consecutive years, and is in good agreement with field data