Generalized modularity matrices

Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In this paper we put in evidence certain common traits of various modularity matrices and shed light on their spectral properties that are at the basis of various theoretical results and practical spectral-type algorithms for community detection

G(2) Holonomy Spaces from Invariant Three-Forms

We construct several new G(2) holonomy metrics that play an important role in recent studies of geometrical transitions in compactifications of M-theory to four dimensions. In type IIA string theory these metrics correspond to D6 branes wrapped on the three-cycle of the deformed conifold and the resolved conifold with two-form RR flux on the blown-up two-sphere, which are related by a conifold transition. We also study a G(2) metric that is related in type IIA to the line bundle over S^2 x S^2 with RR two-form flux. Our approach exploits systematically the definition of torsion-free G(2) structures in terms of three-forms which are closed and co-closed. Besides being an elegant formalism this turns out to be a practical tool to construct G(2) holonomy metrics.Comment: 29 pages, LaTeX2e, corrected some typo

Taking great pains: critical theory, affective pedagogies and radical democracy

The consolidation of neoliberal capitalism over the past decade has been intense, as has the articulation of critical and creative responses to it. One of the most remarkable is the turn towards forms of political resistance that seek liberation from the logics of state and capital while – or through – simultaneously creating alternative, radically democratic modes of existence. Many of these draw on anarchistic and autonomist traditions of critical theory which assert the possibility of prefiguring alternative political projects as well as critiquing existing ones, thus appearing to transcend what Herbert Marcuse described as a ‘vicious circle’ of liberation (1964, 1967). We have thus seen a proliferation of work on problems of prefigurative politics, autonomy, co-operation and self-valorisation; significantly, there is renewed attention to pedagogy in critical theory and as a political practice. However, there is still little attention to the affective and social labour that this type of prefigurative theory and practice requires, or to the systemic critique of the conditions of possibility for it to constitute a challenge to neoliberalism. My concern is that these lacunae can lead to misinterpretations of the meaning of radical democracy and of its possibilities and limitations as a challenge to the logics of neoliberal capitalism and other forms of dehumanising power. In this paper, I draw on work with British-based cultural workers who are active in radical-democratic projects to illustrate how bringing practical work into conversation with critical theories of political subjectivity, on the one hand, and theories of affective pedagogy and politics, on the other, can contribute to strengthening both theories and practices of radical democracy

EXPRESSing Session Types

To celebrate the 30th edition of EXPRESS and the 20th edition of SOS we overview how session types can be expressed in a type theory for the standard $\pi$-calculus by means of a suitable encoding. The encoding allows one to reuse results about the $\pi$-calculus in the context of session-based communications, thus deepening the understanding of sessions and reducing redundancies in their theoretical foundations. Perhaps surprisingly, the encoding has practical implications as well, by enabling refined forms of deadlock analysis as well as allowing session type inference by means of a conventional type inference algorithm.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.0578

The similarity metric

A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of Kolmogorov complexity, and show that it is in this class and it minorizes every computable distance in the class (that is, it is universal in that it discovers all computable similarities). We demonstrate that it is a metric and call it the {\em similarity metric}. This theory forms the foundation for a new practical tool. To evidence generality and robustness we give two distinctive applications in widely divergent areas using standard compression programs like gzip and GenCompress. First, we compare whole mitochondrial genomes and infer their evolutionary history. This results in a first completely automatic computed whole mitochondrial phylogeny tree. Secondly, we fully automatically compute the language tree of 52 different languages.Comment: 13 pages, LaTex, 5 figures, Part of this work appeared in Proc. 14th ACM-SIAM Symp. Discrete Algorithms, 2003. This is the final, corrected, version to appear in IEEE Trans Inform. T

Group quantization of parametrized systems I. Time levels

A method of quantizing parametrized systems is developed that is based on a kind of ``gauge invariant'' quantities---the so-called perennials (a perennial must also be an ``integral of motion''). The problem of time in its particular form (frozen time formalism, global problem of time, multiple choice problem) is met, as well as the related difficulty characteristic for this type of theory: the paucity of perennials. The present paper is an attempt to find some remedy in the ideas on ``forms of relativistic dynamics'' by Dirac. Some aspects of Dirac's theory are generalized to all finite-dimensional first-class parametrized systems. The generalization is based on replacing the Poicar\'{e} group and the algebra of its generators as used by Dirac by a canonical group of symmetries and by an algebra of elementary perennials. A number of insights is gained; the following are the main results. First, conditions are revealed under which the time evolution of the ordinary quantum mechanics, or a generalization of it, can be constructed. The construction uses a kind of gauge and time choice and it is described in detail. Second, the theory is structured so that the quantum mechanics resulting from different choices of gauge and time are compatible. Third, a practical way is presented of how a broad class of problems can be solved without the knowledge of explicit form of perennials.Comment: After discussions at Imperial College, a great improvement is achieved. I particular, it is shown that many problems can be solved without explicit knowledge of the perennial

Facework and Rhetorical Strategies in Intercultural Argumentation

Intercultural discourse (especially via a lingua franca) adds a new dimension—facework (establishing of culture-sensitive politeness strategies)—to the theory and practice of argumentation from a number of perspectives: its specificity as compared to ordinary argumentational discourse, the interpretation of the concept of incommensurability, and the conduct of international negotiations. Politeness systems relevant for different cultures are not unpredictable, but represent linguistically and cognitively a highly generalised universal system which can be adopted by interlocutors and used in practical discourse. Politeness expressions are governed by linguistic components—by language forms of a certain type and by specific discourse patterns. The proper choice of language forms and discourse patterns adds a special dimension to argumentative schemata. The politeness—relevant packaging of discourse adds a zero-step to the normative stages of an argumentative discussion (establishing hierarchical relations as such), and needs permanent alignment of these relations, by using correct language forms and discourse patterns

Notes on the distinction between diplomatic protection and consular protection

In commonparlance,what is called diplomatic protection means, in most cases, a consular protection action. The generic notion of diplomatic protection is used to define a variety of possible forms of protection of the national abroad. This paper seeks to reflect on what lies behind the recurrent inaccuracy or error in the application of correct semantics to the type of protection of nationals abroad. Using the hypothetical deductive method, we find that in theory diplomatic and consular protection are clearly differentiated by two main axes. In practice, however, these two institutes overlap and confuse each other frequently. The solution to the problem referred to would not be based on doubt about the theory, but on the practical performance of the international actors themselves. The lack of a precise distinction between the two concepts of protection would occur more by the combination of factors resulting from the exercise of protection, than of a hesitation about theory

Type-2 fuzzy alpha-cuts

Type-2 fuzzy logic systems make use of type-2 fuzzy sets. To be able to deliver useful type-2 fuzzy logic applications we need to be able to perform meaningful operations on these sets. These operations should also be practically tractable. However, type-2 fuzzy sets suffer the shortcoming of being complex by definition. Indeed, the third dimension, which is the source of extra parameters, is in itself the origin of extra computational cost. The quest for a representation that allow practical systems to be implemented is the motivation for our work. In this paper we define the alpha-cut decomposition theorem for type- 2 fuzzy sets which is a new representation analogous to the alpha-cut representation of type-1 fuzzy sets and the extension principle. We show that this new decomposition theorem forms a methodology for extending mathematical concepts from crisp sets to type-2 fuzzy sets directly. In the process of developing this theory we also define a generalisation that allows us to extend operations from interval type-2 fuzzy sets or interval valued fuzzy sets to type-2 fuzzy sets. These results will allow for the more applications of type-2 fuzzy sets by expiating the parallelism that the research here affords