Semistable modifications of families of curves and compactified Jacobians

Given a family of nodal curves, a semistable modification of it is another family made up of curves obtained by inserting chains of rational curves of any given length at certain nodes of certain curves of the original family. We give comparison theorems between torsion-free, rank-1 sheaves in the former family and invertible sheaves in the latter. We apply them to show that there are functorial isomorphisms between the compactifications of relative Jacobians of families of nodal curves constructed through Caporaso's approach and those constructed through Pandharipande's approach.Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:1212.112

Some New Approaches to Forecasting the Price of Electricity: A Study of Californian Market

In this paper we consider the forecasting performance of a range of semi- and non- parametric methods applied to high frequency electricity price data. Electricity price time-series data tend to be highly seasonal, mean reverting with price jumps/spikes and time- and price-dependent volatility. The typical approach in this area has been to use a range of tools that have proven popular in the financial econometrics literature, where volatility clustering is common. However, electricity time series tend to exhibit higher volatility on a daily basis, but within a mean reverting framework, albeit with occasional large ’spikes’. In this paper we compare the existing forecasting performance of some popular parametric methods, notably GARCH AR-MAX, with approaches that are new to this area of applied econometrics, in particular, Artificial Neural Networks (ANN); Linear Regression Trees, Local Regressions and Generalised Additive Models. Section 2 presents the properties and definitions of the models to be compared and Section 3 the characteristics of the data used which in this case are spot electricity prices from the Californian market 07/1999-12/2000. This period includes the ’crisis’ months of May-August 2000 where extreme volatility was observed. Section 4 presents the results and ranking of methods on the basis of forecasting performance. Section 5 concludes.Electricty Time Series; Forecasting Performance; Semi- and Non- Parametric Methods

Distributed Parameters Dynamic Model of a Solar Fresnel Collector Field

8th World CongressThe International Federation of Automatic ControlMilano (Italy) August 28 - September 2, 2011This paper describes a dynamic model for a linear Fresnel collector field of a solar refrigeration plant. The collector field concentrates solar radiations on a tube that heats up water that is used by an absorption machine to produce chilled air for refrigeration purposes. The model takes into account the solar radiation losses produced by the mirrors and the absorbing tube structure as well as the temperatures in 64 segments of the receiving tube and water. Although the dynamic model is of high dimension and nonlinear, the identification problem can be expressed as a linear problem in model parameters. The least square method was used for identification. The model was validated comparing the simulation results with the plant data for different operating conditions

An account on the taxonomy and molecular diversity of a marine rock-pool dweller, Tigriopus fulvus (Copepoda, Harpacticoida)

The copepod genus Tigriopus Norman, 1869 is distributed worldwide in coastal rock pools and it is currently considered to include 14 valid species. Tigriopus fulvus (Fischer 1860), with its subspecies Tigriopus fulvus adriaticus Van Douwe 1913 and Tigriopus fulvusalgiricus Monard 1935, and Tigriopus minutus Bozic 1960 are currently reported to occur in the Mediterranean area, but the actual diversity of the genus is currently unknown. We aimed to assess the actual identity of Mediterranean Tigriopus populations and to elucidate their taxonomy and pattern of genetic diversity. In order to reach these goals, a fragment of a mitochondrial DNA gene (cytochrome c oxidase subunit I, COI) was sequenced to be used as a reference marker. Our data suggest the presence of a single species characterized by a noteworthy geographi-cally based genetic structure in the whole study area. The observed diversity pattern is tentatively ascribed here to a strong monopolization of the rock pools by the first immigrants that reached them. However, such a monopolization is periodically disrupted by local extinction events, which are frequent in the intrinsically unstable rock pool habitats. We propose the name “clockwork monopolization” for this pattern.El género de copépodos Tigriopus Norman, 1869 se distribuye en todo el mundo en charcas de rocas costeras y se considera que actualmente incluye 14 especies válidas. Tigriopus fulvus (Fischer 1860), con sus subespecies Tigriopus fulvus adriaticus Van Douwe 1913 y Tigriopus fulvus algiricus Monard 1935, y Tigriopus minutus Bozic 1960 han sido descritos para el área del Mediterráneo, pero la diversidad real del género es desconocida actualmente. El objetivo de este estudio fue evaluar la identidad real de las poblaciones mediterráneas de Tigriopus y dilucidar su taxonomía y patrón de diversidad genética. Con este fin, se secuenció un fragmento del gen de ADN mitocondrial (citocromo c oxidasa subunidad I, COI) como marcador de referencia. Los resultados sugieren la presencia de una sola especie caracterizada por una estructuración genética con una notable base geográfica en toda el área de estudio. El patrón de diversidad observado aquí se atribuye tentativamente a una fuerte monopolización de las charcas de las costas rocosas por parte de los primeros inmigrantes que las alcanzan. Sin embargo, tal monopolización se interrumpe periódicamente por los eventos de extinción local, los cuales son frecuentes en los hábitats de charcas de rocas que son intrínsecamente inestables. Aquí proponemos para este patrón el nombre de “monopolización periódica” (“clockwork monopolization”)

Long memory or shifting means? A new approach and application to realised volatility

It is now recognised that long memory and structural change can be confused because the statistical properties of times series of lengths typical of financial and econometric series are similar for both models. We propose a new set of methods aimed at distinguishing between long memory and structural change. The approach, which utilises the computational efficient methods based upon Atheoretical Regression Trees (ART), establishes through simulation the bivariate distribution of the fractional integration parameter, d, with regime length for simulated fractionally integrated series. This bivariate distribution is then compared with the data for the time series. We also combine ART with the established goodness of fit test for long memory series due to Beran. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average. We show that in these series the value of the fractional integration parameter is not constant with time. The mathematical consequence of this is that the definition of H self-similarity is violated. We present evidence that these series have structural breaks.Long-range dependence; Strong dependence; Global dependence; Hurst phenomena

Quantum density anomaly in optically trapped ultracold gases

We show that the Bose-Hubbard Model exhibits an increase in density with temperature at fixed pressure in the regular fluid regime and in the superfluid phase. The anomaly at the Bose-Einstein condensate is the first density anomaly observed in a quantum state. We propose that the mechanism underlying both the normal phase and the superfluid phase anomalies is related to zero point entropies and ground state phase transitions. A connection with the typical experimental scales and setups is also addressed. This key finding opens a new pathway for theoretical and experimental studies of water-like anomalies in the area of ultracold quantum gases