Bonus Symmetry and the Operator Product Expansion of N=4 Super-Yang-Mills

The superconformal group of N=4 super-Yang-Mills has two types of operator representations: short and long. We conjecture that operator product expansions for which at least two of the three operators are short exactly respect a bonus U(1)_Y R-symmetry, which acts as an automorphism of the superconformal group. This conjecture is for arbitrary gauge group G and gauge coupling g_{YM}. A consequence is that n\leq 4-point functions involving only short operators exactly respect the U(1)_Y symmetry, as has been previously conjectured based on AdS duality. This, in turn, would imply that all n\leq 3 -point functions involving only short operators are not renormalized, as has also been previously conjectured and subjected to perturbative checks. It is argued that instantons are compatible with our conjecture. Some perturbative checks of the conjecture are presented and SL(2,Z) modular transformation properties are discussed.Comment: 22 pages, 2 figures, harvma

Maximally Supersymmetric RG Flows and AdS Duality

We discuss four dimensional renormalization group flows which preserve sixteen supersymmetries. In the infra-red, these can be viewed as deformations of the N=4 superconformal fixed points by special, irrelevant operators. It is argued that the gauge coupling beta function continues to vanish identically, for all coupling constants and energy scales, for such RG flows. In addition, the dimensions of all operators in short supersymmetry representations are constant along such flows. It is conjectured that there is a generalization of the AdS/CFT holography correspondence which describes such flows, e.g. the D3 brane vacuum before taking the near-horizon limit, at all energy scales. RG flows in three and six dimensions, preserving 16 supersymmetries, are also briefly discussed, including a conjectured generalized AdS/CFT duality for the M2 and M5 brane cases. Finally, we discuss maximally supersymmetric RG flows associated with non-commutative geometry.Comment: 26 pages, 1 figure. Small typo fixe

On the Relation between Possibilistic Logic and Abstract Dialectical Frameworks

Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, the question poses itself as to whether some and which monotonic three-valued logic underlies ADFs, in the sense that it allows to capture the main semantic concepts underlying ADFs. As an entry-point for such an investigation, we take the concept of model of an ADF, which was originally formulated on the basis of Kleene’s threevalued logic. We show that an optimal concept of a model arises when instead of Kleene’s three-valued logic, possibilistic logic is used. We then show that in fact, possibilistic logic is the most conservative three-valued logic that fulfils this property, and that possibilistic logic can faithfully encode all other semantical concepts for ADFs. Based on this result, we also make some observations on strong equivalence and introduce possibilistic ADFs

Revision and Conditional Inference for Abstract Dialectical Frameworks

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations

Arguing about Complex Formulas: Generalizing Abstract Dialectical Frameworks

Abstract dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex formulas, resulting in conditional abstract dialectical frameworks (in short, cADFs). We define the semantics of cADFs in terms of a non-truth-functional four-valued logic, and study the semantics in-depth, by showing existence results and proving that all semantics are generalizations of the corresponding semantics for ADFs

Online Handbook of Argumentation for AI: Volume 1

This volume contains revised versions of the papers selected for the first volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and this has led to the more recent study of computational models of argument. Argumentation, as a field within artificial intelligence (AI), is highly relevant for researchers interested in symbolic representations of knowledge and defeasible reasoning. The purpose of this handbook is to provide an open access and curated anthology for the argumentation research community. OHAAI is designed to serve as a research hub to keep track of the latest and upcoming PhD-driven research on the theory and application of argumentation in all areas related to AI.Comment: editor: Federico Castagna and Francesca Mosca and Jack Mumford and Stefan Sarkadi and Andreas Xydi

Building Scientific Capability and Reducing Biological Threats: The Effect of Three Cooperative Bio-Research Programs in Kazakhstan.

Cooperative research programs aimed at reducing biological threats have increased scientific capabilities and capacities in Kazakhstan. The German Federal Foreign Office's German Biosecurity Programme, the United Kingdom's International Biological Security Programme and the United States Defense Threat Reduction Agency's Biological Threat Reduction Program provide funding for partner countries, like Kazakhstan. The mutual goals of the programs are to reduce biological threats and enhance global health security. Our investigation examined these cooperative research programs, summarizing major impacts they have made, as well as common successes and challenges. By mapping various projects across the three programs, research networks are highlighted which demonstrate best communication practices to share results and reinforce conclusions. Our team performed a survey to collect results from Kazakhstani partner scientists on their experiences that help gain insights into enhancing day-to-day approaches to conducting cooperative scientific research. This analysis will serve as a basis for a capability maturity model as used in industry, and in addition builds synergy for future collaborations that will be essential for quality and sustainment