Superselection Sectors of Gravitational Subregions

Motivated by the problem of defining the entanglement entropy of the graviton, we study the division of the phase space of general relativity across subregions. Our key requirement is demanding that the separation into subregions is imaginary---i.e., that entangling surfaces are not physical. This translates into a certain condition on the symplectic form. We find that gravitational subregions that satisfy this condition are bounded by surfaces of extremal area. We characterise the 'centre variables' of the phase space of the graviton in such subsystems, which can be taken to be the conformal class of the induced metric in the boundary, subject to a constraint involving the traceless part of the extrinsic curvature. We argue that this condition works to discard local deformations of the boundary surface to infinitesimally nearby extremal surfaces, that are otherwise available for generic codimension-2 extremal surfaces of dimension $\geq$ 2.Comment: 17 pages. v4: minor corrections, accepted in JHE

Gravity duals of boundary cones

The replica trick defines Renyi entropies as partition functions on conically singular geometries. We discuss their gravity duals: regular bulk solutions to the Einstein equations inducing conically singular metrics at the boundary. When the conical singularity is supported on a flat or spherical surface, these solutions are rewritings of the hyperbolic black hole. For more general shapes, these solutions are new. We construct them perturbatively in a double expansion in the distance and strength of the conical singularity, and extract the vacuum polarisation due to the cone. Recent results about the structure of logarithmic divergences of Renyi entropies are reproduced ---in particular, $f_b\neq f_c$. We discuss in detail the dynamical resolution of the singularity in the bulk. This resolution is in agreement with a previous proposal, and indicates a non-minimal settling to the `splitting problem': an apparent ambiguity in the holographic entropy formula of certain theories with higher derivatives.Comment: v3: 31 pages. Typos corrected and some clarifications. Matches publishe

Transforming N-ary relationships to database schemas: an old and forgotten problem

The N-ary relationships, have been traditionally a source of confusion and still are. One important source of confusion is that the term cardinality in a relationship has several interpretations, two of them being very popular. But none of the two approaches, nor the two together, allow us to express all the possible cardinality patterns. The transformations from all the possible relationships to database schemas have never been described by the existing literature. Using the 14 ternary patterns as example, we discuss these transformations particularly the transformations from the patterns ignored in the literature.Postprint (published version

Point cloud management techniques for a multihit ladar imaging camera system

Lidar imaging is a powerful measurement technique where a laser pulse is shone onto an object and the beam reflected back is recovered at some solid-state detector. The time elapsed is counted so an automated measurement of the distance to the target is obtained, without any further calculation. The concept is also referred to as ladar or time of-flight imaging. Different scanning mechanisms have been proposed to recover complete 3D images out of this pointwise approach. Most popular recent applications involve landing aids, object recognition, self-guided vehicles and safeWith the incorporation of optical sensors into the machine vision technology, a full new field has emerged to revolutionize different technologies such as self-driving, 3D scanners and printers or virtual reality. However, new technologies come with new techniques and methodologies to manipulate them. Point Clouds were born as the data storage system and a collection of challenges came with them. One of these challenges consists in processing them in order to obtain the best description of the real world. Hence, it is necessary to have a tool to evaluate the quality of those Point Cloud in order to analyze their quality. In this MSc thesis we developed a mathematical approach for Point Cloud quality evaluation and implanted by Matlab. The full mathematical development as well as the structure of the code and the different tools used to acquire and manipulate Point Clouds are described and introduced along the thesis. A final analysis of the methodology showed there is still a lot of work to do. Several questions appeared and need to be solved in order to grow in this field

From ternary relationship to relational tables: a case against common beliefs

The transformation from n-ary relationships to a relational database schema has never been really fully analyzed. This paper presents one of the several ternary cases ignored by the ER-to-RM literature. The case shows that the following common belief is wrong: Given a set of FDs over a table resulting in a non-3NF situation, it is always possible to obtain a fully equivalent set of 3NF tables, without adding other restrictions than candidate keys and inclusion dependencies.Postprint (published version

Wage structures and family economies in the Catalan textile industry in an age of nascent capitalism

This paper deals with changes in managerial practices in Catalonia in an age of nascent capitalism (1830-1925) and adaptive family strategies in order to face the absence of state welfare. During the 19 t h Century and in the absence of recorded labor contracts, human resources of the firm were organized by means of implicit contracts and informal labor markets. With the advent of scientific organization of labor, wage per hour worked began to be recorded. This is why in the 1920s the perfect competition model applies to our case. On the other hand, in the same period, and in the absence of state welfare, ideas stemming from cooperative game theory apply to the pattern of household income formation. Kin related networks were used to improve the living standards of the household. In this particular direction we also show that there was a demonstration effect by means of which migrant’s living standards were higher than those of natives.Labour market, contracts, family strategies, state welfare

Labour market in the Catalan cotton textile sector: Employment and fertility (1850-1913)

This paper deals whit the dynamics of the Catalan textile labour market (the Spanish region that concentrated most of the industrial and factory activity during the 19 Century) and offers hypotheses and results on the impact it had on living standards and fertility levels. We observe the formation of an uneven labour market in which male supply for labour (excluding women and children) grew much faster than the demand. We stress the fact that labour supply is very dependant on institutional factors liked to the transmition of household property between generations. Instead the slow path of growth of adult males demand for labour is witnessing the limits of this industry to expand and to compete in international markets. The strategy of working class families to adapt to scarce opportunities of employment we document here is the diminution of legitimate fertility levels. Fertility control is the direct instrument we think workers have to control their number in a situation that was likely to create labour surpluses in the short and mid run.Labour market, female employment, children employment, fertility

The rise and decline of children's labour participation levels during the early stages of industrialisation. Catalonia (1850-1925)

This article aims to analyse the reasons for the intensive use of child labour in the 19th century and its subsequent decline in the first third of the 20th century in the context of an economy with a highly flexible labour supply like that of Catalonia. During the second half of the 19th century,factors relating to family economies, such as numerous families and low wages for adults, along with the technologies of the time that required manual labour resources, would appear to explain the intensive use of child labour to the detriment of schooling. The technological changes that occurred during the first third of the 20th century, the demographic transition and adult wage increase (for both men and women) explain the schooling of children up to the age of 15 and the consequent practical abolition of child labour in that new era of economic modernisation.Child labour market, human capital, family strategies

Children's work in Spanish textiles during the 19th and 20th Centuries

This essay deals with the reasons explaining children’s work in 19th century textile factories and their removal during the first part of the 20th century. The inadequacy of the structure of incomes and expenditures of the household and the very low economic incentives to educate children can explain why children were in the factories and not in the school. Moreover, the marginal economic contribution to the economy of the household of a child was the same as that of his mother. This normally implied that women and children were perfect substitutes. When the family had a child at working age this allowed to replace the paid work input of the mother. With the beginnings of the 20th century a set of changes leading to the increase of women’s productivity and hourly real wages, switched the situation and involved the new incorporation of women into paid work and the investment in children’s human capital.Children's work, Women's Work, Household Budgets, Education