A notable feature of the TTE approach to computability is the representation of the argument values and the corresponding function values by means of infinitistic names. Two ways to eliminate the using of such names in certain cases are indicated in
the paper. The first one is intended for the case of topological spaces with selected indexed denumerable bases. Suppose a partial function is given from one such space into another one whose selected base has a recursively enumerable index set, and suppose that the intersection of base open sets in the first space is computable in the sense of Weihrauch-Grubba. Then the ordinary TTE computability of the function is characterized by the existence of an appropriate recursively enumerable relation between indices of base sets containing the argument value and indices of base sets containing the corresponding function value.This result can be regarded as an improvement of a result of Korovina and Kudinov. The second way is applicable to metric spaces with selected indexed denumerable dense subsets. If a partial function is given from one such space into another one, then, under a semi-computability assumption concerning these spaces, the ordinary TTE computability of the function is characterized by the existence of an appropriate recursively enumerable set of quadruples. Any of them consists of an index of element from the selected dense subset in the first space, a natural number encoding a rational bound for the distance between this element and the argument value, an index of element from the selected dense subset in the second space and a natural number encoding a rational bound for the distance between this element and the function value. One of the examples in the paper indicates that the computability of real functions can be characterized in a simple way by using the first way of elimination of the infinitistic names.
Over the last years, analyses performed on a stochastic model of catalytic reaction networks have provided some indications about the reasons why wet-lab experiments hardly ever comply with the phase transition typically predicted by theoretical mode
ls with regard to the emergence of collectively self-replicating sets of molecule (also defined as autocatalytic sets, ACSs), a phenomenon that is often observed in nature and that is supposed to have played a major role in the emergence of the primitive forms of life. The model at issue has allowed to reveal that the emerging ACSs are characterized by a general dynamical fragility, which might explain the difficulty to observe them in lab experiments. In this work, the main results of the various analyses are reviewed, with particular regard to the factors able to affect the generic properties of catalytic reactions network, for what concerns, not only the probability of ACSs to be observed, but also the overall activity of the system, in terms of production of new species, reactions and matter.
The Wivace 2013 Electronic Proceedings in Theoretical Computer Science (EPTCS) contain some selected long and short articles accepted for the presentation at Wivace 2013 - Italian Workshop on Artificial Life and Evolutionary Computation, which was he
ld at the University of Milan-Bicocca, Milan, on the 1st and 2nd of July, 2013.
This article considers the problem of storing the paths generated by a particle filter and more generally by a sequential Monte Carlo algorithm. It provides a theoretical result bounding the expected memory cost by $T + C N log N$ where $T$ is the ti
me horizon, $N$ is the number of particles and $C$ is a constant, as well as an efficient algorithm to realise this. The theoretical result and the algorithm are illustrated with numerical experiments.
We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present axiomatizations o
f the monadic second-order logic (MSO), monadic transitive closure logic (FO(TC1)) and monadic least fixed-point logic (FO(LFP1)) theories of this class of structures. These logics can express important properties such as reachability. Using model-theoretic techniques, we show by a uniform argument that these axiomatizations are complete, i.e., each formula that is valid on all finite trees is provable using our axioms. As a backdrop to our positive results, on arbitrary structures, the logics that we study are known to be non-recursively axiomatizable.
We propose an extension of the Restricted Boltzmann Machine (RBM) that allows the joint shape and appearance of foreground objects in cluttered images to be modeled independently of the background. We present a learning scheme that learns this repres
entation directly from cluttered images with only very weak supervision. The model generates plausible samples and performs foreground-background segmentation. We demonstrate that representing foreground objects independently of the background can be beneficial in recognition tasks.
An aspect of fluid dynamics lies in the search of possible statistical models for Navier-Stokes (NS) fluids described by classical solutions of the incompressible Navier-Stokes equations (INSE). This refers in particular to statistical models based o
n the so-called inverse kinetic theory (IKT) . This approach allows the description of fluid systems by means a suitable 1-point velocity probability density function (PDF) which determines, in terms of suitable moments, the complete set of fluid fields which define the fluid state. A fundamental related issue lies in the problem of the unique construction of the initial PDF. The goal of this paper is to propose a solution holding for NS fluids. Our claim is that the initial PDF can be uniquely determined by imposing a suitable set of physical realizability constraints.
