Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developedto explore patterns in high-dimensional multivariate data. The conventional versionof the algorithm involves the use of Euclidean metric in the process of adaptation ofthe model vectors, thus rendering in theory a whole methodology incompatible withnon-Euclidean geometries.In this contribution we explore the two main aspects of the problem:1. Whether the conventional approach using Euclidean metric can shed valid resultswith compositional data.2. If a modification of the conventional approach replacing vectorial sum and scalarmultiplication by the canonical operators in the simplex (i.e. perturbation andpowering) can converge to an adequate solution.Preliminary tests showed that both methodologies can be used on compositional data.However, the modified version of the algorithm performs poorer than the conventionalversion, in particular, when the data is pathological. Moreover, the conventional ap-proach converges faster to a solution, when data is \well-behaved".Key words: Self Organizing Map; Artificial Neural networks; Compositional data

Weighted Logratio Biplots, Correspondence Analysis and Spectral Maps

Starting with logratio biplots for compositional data, which are based on the principle of subcompositional coherence, and then adding weights, as in correspondence analysis, we rediscover Lewi's spectral map and many connections to analyses of two-way tables of non-negative data. Thanks to the weighting, the method also achieves the property of distributional equivalence

Using vegetation to characterize the avalanche to Canal del Roc Roig, Vall de Núria (Eastern Pyrenees, Spain)

Avalanche hazard maps of high accuracy are difficult to produce. For land-use planning and management purposes, a good knowledge of extreme run-out zones and frequencies of avalanches is required. In the present work, vegetation recognition (especially focused on Pinus uncinata trees) and dendrochronological techniques are used to characterize avalanches that have occurred in historical times, helping to determine both the extent of large or extreme avalanches and their occurrence in time. Vegetation was studied at the Canal del Roc Roig (eastern Pyrenees, Spain) avalanche path. The avalanches descending this path affect the railway that reaches the Vall de Núria resort and the run-up to the opposite slope. During winter 1996, two important avalanches affecting this path were well documented. These are compared with the results of the vegetation study, consisting of an inventory of flora, the recording of vegetation damages along eight transverse profiles at different altitudes on the path and a dendrochronological sampling campaign. The data obtained contributed to a characterization of the predominant snow accumulation in the starting zone, the 1996 avalanches and the range of frequencies of large avalanches. Also, traces of avalanches that increase the path mapped in the avalanche paths map published by the Institut Cartogràfic de Catalunya in 2000 were identified, improving the initial existing information.

Using vegetation to characterize the avalanche to Canal del Roc Roig, Vall de Núria (Eastern Pyrenees, Spain)

Avalanche hazard maps of high accuracy are difficult to produce. For land-use planning and management purposes, a good knowledge of extreme run-out zones and frequencies of avalanches is required. In the present work, vegetation recognition (especially focused on Pinus uncinata trees) and dendrochronological techniques are used to characterize avalanches that have occurred in historical times, helping to determine both the extent of large or extreme avalanches and their occurrence in time. Vegetation was studied at the Canal del Roc Roig (eastern Pyrenees, Spain) avalanche path. The avalanches descending this path affect the railway that reaches the Vall de Núria resort and the run-up to the opposite slope. During winter 1996, two important avalanches affecting this path were well documented. These are compared with the results of the vegetation study, consisting of an inventory of flora, the recording of vegetation damages along eight transverse profiles at different altitudes on the path and a dendrochronological sampling campaign. The data obtained contributed to a characterization of the predominant snow accumulation in the starting zone, the 1996 avalanches and the range of frequencies of large avalanches. Also, traces of avalanches that increase the path mapped in the avalanche paths map published by the Institut Cartogràfic de Catalunya in 2000 were identified, improving the initial existing information.

The geologic and geomorphologic maps of Santa Coloma de Farners (Girona, Spain)

Notice about the geologic and geomorphologic maps of Santa Coloma de Farners, at scale 1:10,000 published by Unitat de Geologia of the Universitat de Girona

Geologic maps published by university de Girona's unity of geodynamics

In 1978 University de Girona's Unity of Geodynamics started publishing geological maps, in several themes and scales, of various areas of the Province of Girona (fig. 1). So far, up to 38 maps, gathered in several collections, have been published

Bifurcations of homoclinic tangency in two-dimensional area-preserving and reversible maps

Report for the scientific sojourn at the Research Institute for Applied Mathematics and Cybernetics, Nizhny Novgorod, Russia, from July to September 2006. Within the project, bifurcations of orbit behavior in area-preserving and reversible maps with a homoclinic tangency were studied. Finitely smooth normal forms for such maps near saddle fixed points were constructed and it was shown that they coincide in the main order with the analytical Birkhoff-Moser normal form. Bifurcations of single-round periodic orbits for two-dimensional symplectic maps close to a map with a quadratic homoclinic tangency were studied. The existence of one- and two-parameter cascades of elliptic periodic orbits was proved.

The Determinants of pricing in pharmaceuticals: are U.S. prices really higher than those of Canada?

This paper studies price determination in pharmaceutical markets using data for 25 countries, six years and a comprehensive list of products from the MIDAS IMS database. We show that market power and the quality of the product has a significantly positive impact of prices. The nationality of the producer appears to have a small and often insignificant impact on prices, which suggests that countries which regulates prices have relatively little power to do it in a way that advances narrow national interest. We produce a theoretical explanation for this phenomenon based on the fact that low negotiated prices in a country would have a knock-on effect in other markets, and is thus strongly resisted by producers. Another key finding is that the U.S. has prices that are not significantly higher than those of countries with similar income levels. This, together with the former observation on the effect of the nationality of producers casts doubt on the ability of countries to purs

Renormalization and α-limit set for expanding Lorenz maps

We establish a one-to-one correspondence between the renormalizations and proper totally invariant closed sets (i.e., α-limit sets) of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. We describe the minimal renormalization by constructing the minimal totally invariant closed set, so that we can define the renormalization operator. Using consecutive renormalizations, we obtain complete topological characteriza- tion of α-limit sets and nonwandering set decomposition. For piecewise linear Lorenz map with slopes ≥ 1, we show that each renormalization is periodic and every proper α-limit set is countable.

Progress Towards to Equity Market Integration in Eastern Europe

The advent of the European Union has decreased the diversification benefits available from country based equity market indices in the region. This paper measures the increase in stock integration between the three largest new EU members (Hungary, the Czech Republic and Poland who joined in May 2004) and the Euro-zone. A potentially gradual transition in correlations is accommodated in a single VAR model by embedding smooth transition conditional correlation models with fat tails, spillovers, volatility clustering, and asymmetric volatility effects. At the country market index level all three Eastern European markets show a considerable increase in correlations in 2006. At the industry level the dates and transition periods for the correlations differ, and the correlations are lower although also increasing. The results show that sectoral indices in Eastern European markets may provide larger diversification opportunities than the aggregate market. JEL classifications: C32; C51; F36; G15 Keywords: Multivariate GARCH; Smooth Transition Conditional Correlation; Stock Return Comovement; Sectoral correlations; New EU Members