Crackling Noise in Fractional Percolation -- Randomly distributed discontinuous jumps in explosive percolation

Crackling noise is a common feature in many systems that are pushed slowly, the most familiar instance of which is the sound made by a sheet of paper when crumpled. In percolation and regular aggregation clusters of any size merge until a giant component dominates the entire system. Here we establish `fractional percolation' where the coalescence of clusters that substantially differ in size are systematically suppressed. We identify and study percolation models that exhibit multiple jumps in the order parameter where the position and magnitude of the jumps are randomly distributed - characteristic of crackling noise. This enables us to express crackling noise as a result of the simple concept of fractional percolation. In particular, the framework allows us to link percolation with phenomena exhibiting non-self-averaging and power law fluctuations such as Barkhausen noise in ferromagnets.Comment: non-final version, for final see Nature Communications homepag

A New Institutionalism? The English School as International Sociological Theory

In this article I engage with the theoretical opening provided by Barry Buzan’s From International to World Society? I present an argument for five functional categories, which should be able to encompass all the institutions identified by English School scholars throughout history. Their introduction should point the way towards a sounder analytical framework for the study of what Buzan believes should be the new subject of the discipline of International Relations (IR). This subject is defined as second-order societies, meaning societies ‘where the members are not individual human beings, but durable collectivities of humans possessed of identities and actor qualities that are more than the sum of their parts’, and where the content of these societies, and the key object of analysis, is primary institutions. The purpose of the five functional categories is to break down this ‘social whole’ and provide a set of lenses through which to potentially analyse international societies throughout history

Counterpart semantics for a second-order mu-calculus

We propose a novel approach to the semantics of quantified μ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of

Quark-Jet model for transverse momentum dependent fragmentation functions

In order to describe the hadronization of polarized quarks, we discuss an extension of the quark-jet model to transverse momentum dependent fragmentation functions. The description is based on a product ansatz, where each factor in the product represents one of the transverse momentum dependent splitting functions, which can be calculated by using effective quark theories. The resulting integral equations and sum rules are discussed in detail for the case of inclusive pion production. In particular, we demonstrate that the 3-dimensional momentum sum rules are satisfied naturally in this transverse momentum dependent quark-jet model. Our results are well suited for numerical calculations in effective quark theories, and can be implemented in Monte-Carlo simulations of polarized quark hadronization processes.Comment: 19 pages, 4 figure

The Use of Proof Planning for Cooperative Theorem Proving

AbstractWe describebarnacle: a co-operative interface to theclaminductive theorem proving system. For the foreseeable future, there will be theorems which cannot be proved completely automatically, so the ability to allow human intervention is desirable; for this intervention to be productive the problem of orienting the user in the proof attempt must be overcome. There are many semi-automatic theorem provers: we call our style of theorem provingco-operative, in that the skills of both human and automaton are used each to their best advantage, and used together may find a proof where other methods fail. The co-operative nature of thebarnacleinterface is made possible by the proof planning technique underpinningclam. Our claim is that proof planning makes new kinds of user interaction possible.Proof planning is a technique for guiding the search for a proof in automatic theorem proving. Common patterns of reasoning in proofs are identified and represented computationally as proof plans, which can then be used to guide the search for proofs of new conjectures. We have harnessed the explanatory power of proof planning to enable the user to understand where the automatic prover got to and why it is stuck. A user can analyse the failed proof in terms ofclam's specification language, and hence override the prover to force or prevent the application of a tactic, or discover a proof patch. This patch might be to apply further rules or tactics to bridge the gap between the effects of previous tactics and the preconditions needed by a currently inapplicable tactic