Carers and careers:Grandparental care investment and its labour market consequences in Europe

Carers and Careers Grandparental care investment and its labour market consequences in Europe Francesca Zanasi Lay Summary As life expectancy increases, grandparents spend a longer part of their lifetime with grandchildren, which opens opportunities for sharing time, resources, and affection. The time grandparents spend with grandchildren has several implications, which were the focal point of the present dissertation. Grandparents differently invest in their grandchildren, according to their socio-economic status: they are active players in the intergenerational transmission of advantages. At the same time, they bear the consequences of their new role, as grandmotherhood influences labour market participation. The extent to which grandmothers reshape their work commitment is determined, on the one hand, by the previous life course, and on the other hand, by the institutional context in which the decisions take place. More specifically, the central findings emerging from the four empirical chapters comprising the present dissertation can be summarized as follows. In Chapter II, I investigate the likelihood of providing care by grandmothers according to their educational level. Empirical results point toward an educational gradient in grandparental childcare: highly educated grandmothers are more likely to provide grandchildren with care than primary educated grandmothers. Most interestingly, they provide more childcare even when their daughters are not in employment, hence less in need of informal support. Furthermore, highly educated grandparents are more likely to engage in activities related to interactive and educational care, for reasons related to the development of grandchildren. The findings could suggest that mechanism of cultural investment could be at work even in the extended family. In Chapter III, I argue that labour supply of grandmothers is jointly determined by the need of support by the younger generation, and the availability of grandmothers themselves as care providers. I found some evidence that grandmotherhood has a negative effect on employment across European countries, although differences exist according to the institutional context: grandmothers are less likely to be employed where there are fewer childcare services for children, where early retirement options are available, and the pension system more generous. In Chapter IV, I concentrate on England to study the relation between the birth of the first grandchild and the probability of labour market withdrawal for mid-life women, with attention paid to differences in terms of work history and economic household situation. Results show that the probability of labour market withdrawal increases after the birth of the first grandchild. Women who had continuous working careers are more likely to withdraw from the labour market after the birth of the first grandchild compared to women with non-continuous careers. The same holds for women living in wealthy households. The explanation probably lies in the lower opportunity cost these women encounter in withdrawing from the labour market. Finally, in Chapter V, I investigated the consequences of grandmotherhood on retirement for Italian mid-life women, accounting for differences in terms of work history, i.e. number of years worked and social class. Results show that there is only a weak relation between the birth of the first grandchild and retirement for Italian grandmothers, and no differences in term of work history. This result could originate from two parallel processes. On the one hand, mid-life women seem to retire before becoming grandmothers in Italy. This could be due to the interplay of the postponement of fertility and availability of early retirement options: women became grandmothers late in life, and they have the possibility to retire early. On the other hand, Italy has an extremely low female labour force participation rate, and many young mothers are not employed due to the difficulty to reconcile work and family; in other words, grandparental childcare might not be needed by many Italian young mothers. Overall, the most important take-home message of the present dissertation is that grandparenthood and its consequences are a multifaceted phenomenon, which must be studied in a multi-generational framework and by considering demographic, social, and institutional trends of current European societies

The Cost of Compositionality A High-Performance Implementation of String Diagram Composition

String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less attention has been given to their algorithmic properties, and efficient implementations of diagrammatic reasoning are almost an unexplored subject. This work intends to be a contribution in such a direction. We introduce a data structure representing string diagrams in terms of adjacency matrices. This encoding has the key advantage of providing simple and efficient algorithms for composition and tensor product of diagrams. We demonstrate its effectiveness by showing that the complexity of the two operations is linear in the size of string diagrams. Also, as our approach is based on basic linear algebraic operations, we can take advantage of heavily optimised implementations, which we use to measure performances of string diagrammatic operations via several benchmarks. © P. Wilson & F. Zanas

Uso de meios alternativos para produção de bioenseticida a base de Bacillus thuringiensis.

IX SINCOBIOL

Coalgebraic semantics for probabilistic logic programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic semantics on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the cofree F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a 'possible worlds' interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming. Furthermore, we show that a similar approach can be used to provide a coalgebraic semantics to weighted logic programming

The Cost of Compositionality: A High-Performance Implementation of String Diagram Composition

String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much fewer attention has been given to their algorithmic properties, and efficient implementations of diagrammatic reasoning are almost an unexplored subject. This work intends to be a contribution in such direction. We introduce a data structure representing string diagrams in terms of adjacency matrices. This encoding has the key advantage of providing simple and efficient algorithms for composition and tensor product of diagrams. We demonstrate its effectiveness by showing that the complexity of the two operations is linear in the size of string diagrams. Also, as our approach is based on basic linear algebraic operations, we can take advantage of heavily optimised implementations, which we use to measure performances of string diagrammatic operations via several benchmarks

Functorial semantics as a unifying perspective on logic programming

Logic programming and its variations are widely used for formal reasoning in various areas of Computer Science, most notably Artificial Intelligence. In this paper we develop a systematic and unifying perspective for (ground) classical, probabilistic, weighted logic programs, based on categorical algebra. Our departure point is a formal distinction between the syntax and the semantics of programs, now regarded as separate categories. Then, we are able to characterise the various variants of logic program as different models for the same syntax category, i.e. structure-preserving functors in the spirit of Lawvere’s functorial semantics. As a first consequence of our approach, we showcase a series of semantic constructs for logic programming pictorially as certain string diagrams in the syntax category. Secondly, we describe the correspondence between probabilistic logic programs and Bayesian networks in terms of the associated models. Our analysis reveals that the correspondence can be phrased in purely syntactical terms, without resorting to the probabilistic domain of interpretation

A coalgebraic perspective on probabilistic logic programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic perspective on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the cofree F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a “possible worlds” interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming

An axiomatic approach to differentiation of polynomial circuits

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model class. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values

A FINITE AXIOMATISATION OF FINITE-STATE AUTOMATA USING STRING DIAGRAMS

We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two notable features. First, the proposed axiomatisation is finite. Second, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks