Approximate Hagemann-Mitschke co-operations

We show that varietal techniques based on the existence of operations of a certain arity can be extended to n-permutable categories with binary coproducts. This is achieved via what we call approximate Hagemann-Mitschke co-operations, a generalisation of the notion of approximate Mal'tsev co-operation. In particular, we extend characterisation theorems for n-permutable varieties due to J. Hagemann and A. Mitschke to regular categories with binary coproducts.Comment: 11 pages. Dedicated to George Janelidze on the occasion of his sixtieth birthda

Towards Ordinal Data Science

Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason for this is the limited availability of computational resources in the last century that would have been required for ordinal computations. Another reason - particularly important for this line of research - is that order-based methods are often seen as too mathematically rigorous for applying them to real-world data. In this paper, we will therefore discuss different means for measuring and ‘calculating’ with ordinal structures - a specific class of directed graphs - and show how to infer knowledge from them. Our aim is to establish Ordinal Data Science as a fundamentally new research agenda. Besides cross-fertilization with other cornerstone machine learning and knowledge representation methods, a broad range of disciplines will benefit from this endeavor, including, psychology, sociology, economics, web science, knowledge engineering, scientometrics

QNRs: toward language for intelligent machines

Impoverished syntax and nondifferentiable vocabularies make natural language a poor medium for neural representation learning and applications. Learned, quasilinguistic neural representations (QNRs) can upgrade words to embeddings and syntax to graphs to provide a more expressive and computationally tractable medium. Graph-structured, embedding-based quasilinguistic representations can support formal and informal reasoning, human and inter-agent communication, and the development of scalable quasilinguistic corpora with characteristics of both literatures and associative memory. To achieve human-like intellectual competence, machines must be fully literate, able not only to read and learn, but to write things worth retaining as contributions to collective knowledge. In support of this goal, QNR-based systems could translate and process natural language corpora to support the aggregation, refinement, integration, extension, and application of knowledge at scale. Incremental development of QNRbased models can build on current methods in neural machine learning, and as systems mature, could potentially complement or replace today’s opaque, error-prone “foundation models” with systems that are more capable, interpretable, and epistemically reliable. Potential applications and implications are broad

The Necessary Structure of the All-pervading Aether: Discrete or Continuous? Simple or Symmetric?

In this book I investigate the necessary structure of the aether – the stuff that fills the whole universe. Some of my conclusions are. 1. There is an enormous variety of structures that the aether might, for all we know, have. 2. Probably the aether is point-free. 3. In that case, it should be distinguished from Space-time, which is either a fiction or a construct. 4. Even if the aether has points, we should reject the orthodoxy that all regions are grounded in points by summation. 5. If the aether is point-free but not continuous, its most likely structure has extended atoms that are not simples. 6. Space-time is symmetric if and only if the aether is continuous. 7. If the aether is continuous, we should reject the standard interpretation of General Relativity, in which geometry determines gravity. 8. Contemporary physics undermines an objection to discrete aether based on scale invariance, but does not offer much positive support

A Geometric Approach to the Projective Tensor Norm

The main focus of this thesis is on the projective norm on finite-dimensional real or complex tensor products. There are various mathematical subjects with relations to the projective norm. For instance, it appears in the context of operator algebras or in quantum physics. The projective norm on multipartite tensor products is considered to be less accessible. So we use a method from convex algebraic geometry to approximate the projective unit ball by convex supersets, so-called theta bodies. For real multipartite tensor products we obtain theta bodies which are close to the projective unit ball, leading to a generalisation of the Schmidt decomposition. In a second step the method is applied to complex tensor products, in a third step to separable states. In a more general context, the projective norm can be related to binomial ideals, especially to so-called Hibi relations. In this respect, we also focus on a generalisation of the projective unit ball, here called Hibi body, and its theta bodies. It turns out that many statements also hold in this general context

Political economy of climate policy

Die vorliegende Arbeit beschäftigt sich modelltheoretisch, empirisch und experimentell mit dem Thema der Klimapolitik aus einer politökonomischen Perspektive. Der Ansatz der Neuen Politischen Ökonomie versucht, die ökonomischen Modelle um den politischen Prozess zu erweitern. Die Motivation für dieses Vorgehen steht in einem engen Zusammenhang mit der Erkenntnis, dass es unzureichend ist, die ökonomische Analyse auf Probleme des Marktversagens zu reduzieren. Neben Marktversagen können durch den politischen Prozess Probleme generiert werden (sog. Politikversagen). Im Rahmen einer positiven Analyse kann die Neue Politische Ökonomie Erklärungsansätze liefern, die eng mit der Fragestellung verknüpft sind, warum bekannte Ineffizienzen den politischen Prozess überdauern. Dieses Problem lässt sich in vielen Fällen durch Partikularinteressen erklären. Aus einer normativen Perspektive lassen sich die resultierenden Erkenntnisse für Politikempfehlungen heranziehen. Vordergründig sind dabei jene Handlungsalternativen (zum Teil auch Handlungsbeschränkungen z.B. auf konstitutioneller Ebene) die es dem Staat ermöglichen seine Handlungen möglichst unabhängig von Partikularinteressen durchzuführen. Die vorliegende Arbeit gliedert sich in acht Kapitel. Das erste Kapitel dient zur Einleitung. Kapitel zwei bis sieben umfassen den Hauptteil der Arbeit. In Kapitel acht werden die wesentlichen Ergebnisse noch einmal kurz zusammengefasst