On the Luminosity Function of Early--Type Galaxies

In a recent paper Loveday et al. (1992) have presented new results on the luminosity function for a sample of galaxies with $b_J \le 17.15$. After having morphologically classified each galaxy (early--type, late--type, merged or uncertain), they have estimated the parameters of a Schechter luminosity function for early-- and late--type galaxies. However, in their sample there is a bias against identifying early--type galaxies at large distances and/or faint magnitudes: in fact, many of the early--type galaxies at faint magnitudes have probably been classified as ``uncertain". As discussed in Loveday et al., the existence of such a bias is indicated by the fact that for these galaxies $=0.32$. In this paper we show, both theoretically and through the use of simulated samples, that this incompleteness strongly biases the derived parameters of the luminosity function for early--type galaxies. If no correction for such incompleteness is applied to the data (as done by Loveday et al.), one obtains a flatter slope $\alpha$ and a brighter $M^*$ with respect to the real parameters.Comment: accepted for publication on MNRAS, Standard TeX, for tables and figures contact [email protected] BAP 03-1994-04-IR

A Syntactic Model of Mutation and Aliasing

Traditionally, semantic models of imperative languages use an auxiliary structure which mimics memory. In this way, ownership and other encapsulation properties need to be reconstructed from the graph structure of such global memory. We present an alternative "syntactic" model where memory is encoded as part of the program rather than as a separate resource. This means that execution can be modelled by just rewriting source code terms, as in semantic models for functional programs. Formally, this is achieved by the block construct, introducing local variable declarations, which play the role of memory when their initializing expressions have been evaluated. In this way, we obtain a language semantics which directly represents at the syntactic level constraints on aliasing, allowing simpler reasoning about related properties. To illustrate this advantage, we consider the issue, widely studied in the literature, of characterizing an isolated portion of memory, which cannot be reached through external references. In the syntactic model, closed block values, called "capsules", provide a simple representation of isolated portions of memory, and capsules can be safely moved to another location in the memory, without introducing sharing, by means of "affine' variables. We prove that the syntactic model can be encoded in the conventional one, hence efficiently implemented.Comment: In Proceedings DCM 2018 and ITRS 2018 , arXiv:1904.0956

Reconciling positional and nominal binding

We define an extension of the simply-typed lambda calculus where two different binding mechanisms, by position and by name, nicely coexist. In the former, as in standard lambda calculus, the matching between parameter and argument is done on a positional basis, hence alpha-equivalence holds, whereas in the latter it is done on a nominal basis. The two mechanisms also respectively correspond to static binding, where the existence and type compatibility of the argument are checked at compile-time, and dynamic binding, where they are checked at run-time.Comment: In Proceedings ITRS 2012, arXiv:1307.784

Constrained Polymorphic Types for a Calculus with Name Variables

We extend the simply-typed lambda-calculus with a mechanism for dynamic rebinding of code based on parametric nominal interfaces. That is, we introduce values which represent single fragments, or families of named fragments, of open code, where free variables are associated with names which do not obey alpha-equivalence. In this way, code fragments can be passed as function arguments and manipulated, through their nominal interface, by operators such as rebinding, overriding and renaming. Moreover, by using name variables, it is possible to write terms which are parametric in their nominal interface and/or in the way it is adapted, greatly enhancing expressivity. However, in order to prevent conflicts when instantiating name variables, the name-polymorphic types of such terms need to be equipped with simple {inequality} constraints. We show soundness of the type system

Flexible Coinduction in Agda

We provide an Agda library for inference systems, also supporting their recent generalization allowing flexible coinduction, that is, interpretations which are neither inductive, nor purely coinductive. A specific inference system can be obtained as an instance by writing a set of meta-rules, in an Agda format which closely resembles the usual one. In this way, the user gets for free the related properties, notably the inductive and coinductive intepretation and the corresponding proof principles. Moreover, a significant modularity is achieved. Indeed, rather than being defined from scratch and with a built-in interpretation, an inference system can also be obtained by composition operators, such as union and restriction to a smaller universe, and its semantics can be modularly chosen as well. In particular, flexible coinduction is obtained by composing in a certain way the interpretations of two inference systems. We illustrate the use of the library by several examples. The most significant one is a big-step semantics for the ?-calculus, where flexible coinduction allows to obtain a special result (?) for all and only the diverging computations, and the proof of equivalence with small-step semantics is carried out by relying on the proof principles offered by the library

Modeling Infinite Behaviour by Corules

open3openDavide Ancona; Francesco Dagnino; Elena ZuccaAncona, Davide; Dagnino, Francesco; Zucca, Elen

Brightest Cluster Galaxies in the Extended GMRT radio halo cluster sample. Radio properties and cluster dynamics

Brightest Cluster Galaxies (BCGs) show exceptional properties over the whole electromagnetic spectrum. Their special location at the centres of galaxy clusters raises the question of the role of the environment on their radio properties. To decouple the effect of the galaxy mass and of the environment in their statistical radio properties, we investigate the possible dependence of the occurrence of radio loudness and of the fractional radio luminosity function on the dynamical state of the hosting cluster. We studied the radio properties of the BCGs in the Extended GMRT Radio Halo Survey (EGRHS). We obtained a statistical sample of 59 BCGs, which was divided into two classes, depending on the dynamical state of the host cluster, i.e. merging (M) and relaxed (R). Among the 59 BCGs, 28 are radio-loud, and 31 are radio--quiet. The radio-loud sources are located favourably located in relaxed clusters (71\%), while the reverse is true for the radio-quiet BCGs, mostly located in merging systems (81\%). The fractional radio luminosity function (RLF) for the BCGs is considerably higher for BCGs in relaxed clusters, where the total fraction of radio loudness reaches almost 90\%, to be compared to the $\sim$30\% in merging clusters. For relaxed clusters, we found a positive correlation between the radio power of the BCGs and the strength of the cool core, consistent with previous studies on local samples. Our study suggests that the radio loudness of the BCGs strongly depends on the cluster dynamics, their fraction being considerably higher in relaxed clusters. We compared our results with similar investigations, and briefly discussed them in the framework of AGN feedback.Comment: 12 pages, 6 figures, 3 tables, A&A accepte