Minimization via duality

We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the minimal subobject becomes the maximally quotiented object

On the AGN radio luminosity distribution and the black hole fundamental plane

We have studied the dependence of the AGN nuclear radio (1.4 GHz) luminosity on both the AGN 2-10 keV X-ray and the host-galaxy K-band luminosity. A complete sample of 1268 X-ray selected AGN (both type 1 and type 2) has been used, which is the largest catalogue of AGN belonging to statistically well defined samples where radio, X and K band information exists. At variance with previous studies, radio upper limits have been statistically taken into account using a Bayesian Maximum Likelihood fitting method. It resulted that a good fit is obtained assuming a plane in the 3D L_R-L_X-L_K space, namely logL_R= xi_X logL_X + xi_K logL_K + xi_0, having a ~1 dex wide (1 sigma) spread in radio luminosity. As already shown, no evidence of bimodality in the radio luminosity distribution was found and therefore any definition of radio loudness in AGN is arbitrary. Using scaling relations between the BH mass and the host galaxy K-band luminosity, we have also derived a new estimate of the BH fundamental plane (in the L_5GHz -L_X-M_BH space). Our analysis shows that previous measures of the BH fundamental plane are biased by ~0.8 dex in favor of the most luminous radio sources. Therefore, many AGN studies, where the BH fundamental plane is used to investigate how AGN regulate their radiative and mechanical luminosity as a function of the accretion rate, or many AGN/galaxy co-evolution models, where radio-feedback is computed using the AGN fundamental plane, should revise their conclusions.Comment: Submitted to MNRAS. Revised version after minor referee comments. 12 pages, 12 figure

Borrowed contexts for attributed graphs

Borrowed context graph transformation is a simple and powerful technique developed by Ehrig and König that allow us to derive labeled transitions and bisimulation congruences for graph transformation systems or, in general, for pocess calculi that can be defined in terms of graph transformation systems. Moreover, the same authors have also shown how to use this technique for the verification of bisimilarity. In principle, the main results about borrowed context transformation do not apply only to plain graphs, but they are generic in the sense that they apply to all categories tha satisfy certain properties related to the notion of adhesivity. In particular, this is the case of attributed graphs. However, as we show in the paper, the techniques used for checking bisimilarity are not equally generic and, in particular they fail, if we want to apply them to attributed graphs. To solve this problem, in this paper, we define a special notion of symbolic graph bisimulation and show how it can be used to check bisimilarity of attributed graphs.Postprint (published version

The Calculus of Signal Flow Diagrams I: Linear relations on streams

We introduce a graphical syntax for signal flow diagrams based on the language of symmetric monoidal categories. Using universal categorical constructions, we provide a stream semantics and a sound and complete axiomatisation. A certain class of diagrams captures the orthodox notion of signal flow graph used in control theory; we show that any diagram of our syntax can be realised, via rewriting in the equational theory, as a signal flow graph

Rewriting modulo symmetric monoidal structure

String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory. An important role in many such approaches is played by equational theories of diagrams, typically oriented and applied as rewrite rules. This paper lays a comprehensive foundation for this form of rewriting. We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure. We illustrate our approach with a proof of termination for the theory of non-commutative bimonoids

How to kill epsilons with a dagger: a coalgebraic take on systems with algebraic label structure

We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or ϵ-transitions. Our approach employs monads with a parametrized fixpoint operator † to give a semantics to those systems and implement a sound procedure of abstraction of the internal transitions, whose labels are seen as the unit of a free monoid. More broadly, our approach extends the standard coalgebraic framework for state-based systems by taking into account the algebraic structure of the labels of their transitions. This allows to consider a wide range of other examples, including Mazurkiewicz traces for concurrent systems.Funded by the ERDF through the Programme COMPETE and by the Portuguese Foundation for Science and Technology, project ref. FCOMP-01-0124-FEDER-020537 and SFRH/BPD/71956/2010. Acknowledge support by project ANR 12IS0 2001 PACE

Confluence of graph rewriting with interfaces

For terminating double-pushout (DPO) graph rewriting systems confluence is, in general, undecidable. We show that confluence is decidable for an extension of DPO rewriting to graphs with interfaces. This variant is important due to it being closely related to rewriting of string diagrams. We show that our result extends, under mild conditions, to decidability of confluence for terminating rewriting systems of string diagrams in symmetric monoidal categories

Temporal influence over the Last.fm social network

In a previous result, we showed that the influence of social contacts spreads information about new artists through the Last.fm social network. We successfully decomposed influence from effects of trends, global popularity, and homophily or shared environment of friends. In this paper, we present our new experiments that use a mathematically sound formula for defining and measuring the influence in the network. We provide new baseline and influence models and evaluation measures, both batch and online, for real-time recommendations with very strong temporal aspects. Our experiments are carried over the 2-year “scrobble” history of 70,000 Last.fm users. In our results, we formally define and distil the effect of social influence. In addition, we provide new models and evaluation measures for real-time recommendations with very strong temporal aspects. © 2015, Springer-Verlag Wien

The contribution of faint AGNs to the ionizing background at z~4

Finding the sources responsible for the hydrogen reionization is one of the most pressing issues in cosmology. Bright QSOs are known to ionize their surrounding neighborhood, but they are too few to ensure the required HI ionizing background. A significant contribution by faint AGNs, however, could solve the problem, as recently advocated on the basis of a relatively large space density of faint active nuclei at z>4. We have carried out an exploratory spectroscopic program to measure the HI ionizing emission of 16 faint AGNs spanning a broad U-I color interval, with I~21-23 and 3.6<z<4.2. These AGNs are three magnitudes fainter than the typical SDSS QSOs (M1450<~-26) which are known to ionize their surrounding IGM at z>~4. The LyC escape fraction has been detected with S/N ratio of ~10-120 and is between 44 and 100% for all the observed faint AGNs, with a mean value of 74% at 3.6<z<4.2 and -25.1<M1450<-23.3, in agreement with the value found in the literature for much brighter QSOs (M1450<~-26) at the same redshifts. The LyC escape fraction of our faint AGNs does not show any dependence on the absolute luminosities or on the observed U-I colors. Assuming that the LyC escape fraction remains close to ~75% down to M1450~-18, we find that the AGN population can provide between 16 and 73% (depending on the adopted luminosity function) of the whole ionizing UV background at z~4, measured through the Lyman forest. This contribution increases to 25-100% if other determinations of the ionizing UV background are adopted. Extrapolating these results to z~5-7, there are possible indications that bright QSOs and faint AGNs can provide a significant contribution to the reionization of the Universe, if their space density is high at M1450~-23.Comment: Accepted for publication on A&A, 16 pages, 22 figure

Coordination via Interaction Constraints I: Local Logic

Wegner describes coordination as constrained interaction. We take this approach literally and define a coordination model based on interaction constraints and partial, iterative and interactive constraint satisfaction. Our model captures behaviour described in terms of synchronisation and data flow constraints, plus various modes of interaction with the outside world provided by external constraint symbols, on-the-fly constraint generation, and coordination variables. Underlying our approach is an engine performing (partial) constraint satisfaction of the sets of constraints. Our model extends previous work on three counts: firstly, a more advanced notion of external interaction is offered; secondly, our approach enables local satisfaction of constraints with appropriate partial solutions, avoiding global synchronisation over the entire constraints set; and, as a consequence, constraint satisfaction can finally occur concurrently, and multiple parts of a set of constraints can be solved and interact with the outside world in an asynchronous manner, unless synchronisation is required by the constraints. This paper describes the underlying logic, which enables a notion of local solution, and relates this logic to the more global approach of our previous work based on classical logic