A methodology in choosing a new compatible function in the recovery project of disused religious buildings. Research study in Italy

<p>The phenomenon of abandoned religious buildings is today felt in many countries of the world and particularly in Europe, where the problem has taken on such dimensions as to worry the ecclesiastical institutions, which are encouraging to work with particular caution in order to avoid improper use and to consider each case according to its historical peculiarities. The topic involves many actors (clergy, population, associations, tourists, traders, etc.) since it has several meanings: Social, because religious buildings have held together many generations; Economic, because these places fascinate foreign visitors; Environmental, because their physical presence in the urban or rural landscape revives contexts and traditions; Cultural, because sacred buildings represent the largest portfolio of European historical heritage. From 2018, the Holy See encouraged to produce recommendations especially oriented towards new functional, social and architectural choices able to preserve both the material and spiritual value of the artefacts over time.</p><p>By starting from an analysis of the theme, the contribution provides a methodological approach in searching for a new compatible function, in accordance with the new programmatic guidelines and the principles of the discipline of architectural conservation and recovery, applying it to the case of the old abandoned convents in the historical centre of Salerno in Italy.</p>

Common Fixed Point Theorems on Generalized Ratio Contraction Mapping in Extended Rectangular b-Metric Spaces

In this paper, we propose and prove the common fixed point theorems on generalized contraction mappings in extended rectangular b-metric spaces by utilizing the weakly compatible function property.

Natural Option Critic

The recently proposed option-critic architecture (Bacon, Harb, and Precup 2017) provides a stochastic policy gradient approach to hierarchical reinforcement learning. Specifically, it provides a way to estimate the gradient of the expected discounted return with respect to parameters that define a finite number of temporally extended actions, called options. In this paper we show how the option-critic architecture can be extended to estimate the natural gradient (Amari 1998) of the expected discounted return. To this end, the central questions that we consider in this paper are: 1) what is the definition of the natural gradient in this context, 2) what is the Fisher information matrix associated with an option’s parameterized policy, 3) what is the Fisher information matrix associated with an option’s parameterized termination function, and 4) how can a compatible function approximation approach be leveraged to obtain natural gradient estimates for both the parameterized policy and parameterized termination functions of an option with per-time-step time and space complexity linear in the total number of parameters. Based on answers to these questions we introduce the natural option critic algorithm. Experimental results showcase improvement over the vanilla gradient approach.

On a generalization of u-means

In this paper we present an extension of Bauer's work about u-means. We consider a kind of composition of an admissible function u(x) (described by Bauer) and of a compatible function ϕ(x). This construction allows us to define (u,ϕ)-means. When ϕ(x)=x, the (u,ϕ)-means are the u-means introduced by Bauer. The arithmetic, geometric and harmonic means are special cases.