Wellbeing measures of mortality risks: life-cycle contradictions and ordinal index challenges

The value of a statistical life (VSL) monetizes the expected loss in wellbeing associated with the risk of death. The utility loss resulting from a fatality is central to the empirical framework for estimating the VSL. The VSL trajectory over the life cycle exhibits an inverted-U shape, following a trajectory similar to that of lifetime patterns of consumption. The U-shaped pattern displayed by happiness measures over the life cycle is the opposite of the inverted-U shape pattern displayed by the VSL. It is consequently inappropriate to use happiness measures as ordinal ranking substitutes for the VSL for the purposes of estimating the benefits of mortality risk reduction. Compared to ordinal wellbeing scales, the VSL also offers a variety of additional capabilities by providing a cardinal index of the unit benefits for changes in mortality risks.

Polygonal Numbers

Summary In the article the formal characterization of triangular numbers (famous from [15] and words “EYPHKA! num = Δ+Δ+Δ”) [17] is given. Our primary aim was to formalize one of the items (#42) from Wiedijk’s Top 100 Mathematical Theorems list [33], namely that the sequence of sums of reciprocals of triangular numbers converges to 2. This Mizar representation was written in 2007. As the Mizar language evolved and attributes with arguments were implemented, we decided to extend these lines and we characterized polygonal numbers. We formalized centered polygonal numbers, the connection between triangular and square numbers, and also some equalities involving Mersenne primes and perfect numbers. We gave also explicit formula to obtain from the polygonal number its ordinal index. Also selected congruences modulo 10 were enumerated. Our work basically covers the Wikipedia item for triangular numbers and the Online Encyclopedia of Integer Sequences (http://oeis.org/A000217). An interesting related result [16] could be the proof of Lagrange’s four-square theorem or Fermat’s polygonal number theorem [32].

Winter temperatures in the second half of the sixteenth century in the central area of the Iberian Peninsula

This paper studies the winter temperatures of the second part of the sixteenth century in the central area of the Iberian Peninsula. A large number of historical documents that are stored in many different Spanish archives were consulted in order to carry out this research. The data was first arranged and weighted according to the intensity and significance of the meteorological phenomena described and, subsequently, these values were assigned an ordinal index ranging from +4 to −4. The statistical treatment applied is based on the reconstruction of temperatures equivalent to this ordinal index, expressed as anomalies of the 1961–1990 period, belonging to a reference station located at the approximate geographical center of the area under study. The results show winter thermal conditions different from current ones that, for the most part, stay below the reference average and that occurred with a wide range of variability. The influence that thermal conditions had on the evolution of some environmental aspects are considered based on the forest exploitation problem information and on the wine harvest production.

Winter temperatures in the second half of the XVI century in the central area of the Iberian Peninsula

This paper studies the winter temperatures of the second part of the XVI century in the central area of the Iberian Peninsula. A large number of historical documents that are stored in many different Spanish archives were consulted in order to carry out this research. The data was first arranged and weighted according to the intensity and significance of the meteorological phenomena described and, subsequently, these values were assigned an ordinal index ranging from +4 to −4. The statistical treatment applied is based on the reconstruction of temperatures equivalent to this ordinal index, expressed as anomalies of the 1961–1990 period, belonging to a reference station located at the approximate geographical center of the area under study. The results show winter thermal conditions different from current ones that, for the most part, stay below the reference average and that occurred with a wide range of variability. The influence that thermal conditions had on the evolution of some environmental aspects are considered based on the forest exploitation problem information and on the wine harvest production.

The onset of the Little Ice Age in Andalusia (southern Spain): detection and characterization from documentary sources

In this work the onset of the "Little Ice Age" period in Andalusia (southern Spain) is analysed from documentary data, focusing attention on the evolution of the climate during the 16th and 17th centuries. It is shown that changes in the rainfall regime have been more important than those in the temperature in studying the Andalusian climate change. Analysis of the total annual precipitation is carried out by codifying the documentary data and establishing an ordinal index. Several statistical methods are used to detect and characterize climate changes in the region. The results suggest a fluctuating evolution, without trends or abrupt changes, with a prevailing wet period from 1550 to 1650 AD. Cycles of ~17, 3.5 and 2.1 years are detected. Some possible causal mechanisms are suggested.

Mississippian Period Status Differentiation through Textile Analysis: A Caddoan Example

Specific attributes were recorded for 119 textiles recovered from burial contexts from Craig Mound at the Spiro site and eight southern Ozark bluff shelters. Textile attributes that varied according to status designations of the burial contexts were identified using the following three avenues of investigation. The textiles were rated using an ordinal index of production complexity, and more complex textiles were found to be associated with burial contexts of presumed higher status. Use of a series of contingency tables identified edge finishes, color, patterning, design motif, fiber, and scale as attributes that are individually associated with status differences. When selected attributes were considered together using a classification and pattern-recognition program, color description, scale, fiber, and number of yarn components were identified as the best predictors of status association.

Mississippian Period Status Differentiation through Textile Analysis: A Caddoan Example

Specific attributes were recorded for 119 textiles recovered from burial contexts from Craig Mound at the Spiro site and eight southern Ozark bluff shelters. Textile attributes that varied according to status designations of the burial contexts were identified using the following three avenues of investigation. The textiles were rated using an ordinal index of production complexity, and more complex textiles were found to be associated with burial contexts of presumed higher status. Use of a series of contingency tables identified edge finishes, color, patterning, design motif, fiber, and scale as attributes that are individually associated with status differences. When selected attributes were considered together using a classification and pattern-recognition program, color description, scale, fiber, and number of yarn components were identified as the best predictors of status association.