Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

Regularization Methods for Ill-Posed Problems in Multiple Hilbert Scales

Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a multiple Hilbert scale on a product space is introduced, regularization methods on these scales are defined, both for the case of a single observation and for the case of multiple observations. In the latter case, it is shown how vector-valued regularization functions in these multiple Hilbert scales can be used. In all cases convergence is proved and orders and optimal orders of convergence are shown.Comment: 32 pages, 2 figure

Bathyraja panthera, a new species of skate (Rajidae: Arhynchobatinae) from the western Aleutian Islands, and resurrection of the subgenus Arctoraja Ishiyama

We provide morphological and molecular evidence to recognize a new species of skate from the North Pacific, Bathyraja panthera. We also resurrect the skate subgenus Arctoraja Ishiyama, confirming its monophyly and the validity of the subgenus. Arctoraja was previously recognized as a distinct subgenus of Breviraja and later synonymized with Bathyraja (family Rajidae). Although the nominal species of Arctoraja have all been considered synonyms of Bathyraja parmifera by various authors, on the basis of morphometric, meristic, chondrological, and molecular data we recognize four species, including the new species. Species of Arctoraja are distributed across the North Pacific Ocean and adjacent seas from southern Japan to British Columbia. Bathyraja parmifera is abundant in the eastern Bering Sea, Aleutian Islands, and northern Gulf of Alaska; B. smirnovi is a western Pacific species found in the Sea of Okhotsk and Sea of Japan; B. simoterus is restricted to waters around the northern and eastern coasts of Hokkaido, Japan; and the new species B. panthera is restricted to the western Aleutian Islands. Bathyraja panthera is diagnosed by its color pattern of light yellow blotches with black spotting on a greenish brown background, high thorn and vertebral counts, chondrological characters of the neurocranium and clasper, and a unique nucleotide sequence within the mitochondrial cytochrome oxidase gene. Furthermore, the species presently recognized as Bathyraja parmifera exhibits two haplotypes among specimens from Alaska, suggesting the possibility of a second, cryptic species

Evaluation of Textural and Sensory Properties on Typical Spanish Small Cakes Designed Using Alternative Flours

[EN] The objective of this study was to evaluate the effect of wheat flour substitution with toasted corn, quinoa, and sorghum flours on the overall perception and texture of typical Spanish small cakes named madeleine. In order to evaluate these characteristics, a texture profile analysis (TPA) and a sensory analysis were carried out. TPA showed that the replacement of wheat flour by sorghum flour did not affect significantly texture parameters of cakes. Hedonic sensory tests were also conducted revealing that the cake prepared with sorghum flour was highly appreciated by the consumers as it got scores similar to traditional cakes made with wheat flour.Casas Moreno, MDM.; Barreto Palacios, VJ.; González Carrascosa, R.; Iborra Bernad, MDC.; Andrés Bello, MD.; Martínez Monzó, J.; García-Segovia, P. (2015). Evaluation of Textural and Sensory Properties on Typical Spanish Small Cakes Designed Using Alternative Flours. Journal of Culinary Science and Technology. 13(1):19-28. doi:10.1080/15428052.2014.952475S1928131Baldwin, R. R., Baldry, R. P., & Johansen, R. G. (1972). Fat systems for bakery products. Journal of the American Oil Chemists’ Society, 49(8), 473-477. doi:10.1007/bf02582482Beleia, A., Miller, R. A., & Hoseney, R. C. (1996). Starch Gelatinization in Sugar Solutions. Starch - Starke, 48(7-8), 259-262. doi:10.1002/star.19960480705Brannan, G. L., Setser, C. S., Kemp, K. E., Seib, P. A., & Roozeboom, K. (2001). Sensory Characteristics of Grain Sorghum Hybrids with Potential for Use in Human Food. Cereal Chemistry Journal, 78(6), 693-700. doi:10.1094/cchem.2001.78.6.693Cauvain, S. P., & Young, L. S. (Eds.). (2006). Baked Products. doi:10.1002/9780470995907Chieh, C. (s. f.). Water. Bakery Products, 211-232. doi:10.1002/9780470277553.ch11Conforti, F. D. (s. f.). Cake Manufacture. Bakery Products, 393-410. doi:10.1002/9780470277553.ch22Ghotra, B. S., Dyal, S. D., & Narine, S. S. (2002). Lipid shortenings: a review. Food Research International, 35(10), 1015-1048. doi:10.1016/s0963-9969(02)00163-1Kiosseoglou, V., & Paraskevopoulou, A. (s. f.). Eggs. Bakery Products, 161-172. doi:10.1002/9780470277553.ch8Lai, H.-M., & Lin, T.-C. (s. f.). Bakery Products: Science and Technology. Bakery Products, 3-68. doi:10.1002/9780470277553.ch1Lau, M. ., Tang, J., & Paulson, A. . (2000). Texture profile and turbidity of gellan/gelatin mixed gels. Food Research International, 33(8), 665-671. doi:10.1016/s0963-9969(00)00111-3LINDLEY, M. G. (1987). Sucrose in baked products. Nutrition Bulletin, 12(1), 41-45. doi:10.1111/j.1467-3010.1987.tb00011.xMastromatteo, M., Chillo, S., Iannetti, M., Civica, V., & Del Nobile, M. A. (2011). Formulation optimisation of gluten-free functional spaghetti based on quinoa, maize and soy flours. International Journal of Food Science & Technology, 46(6), 1201-1208. doi:10.1111/j.1365-2621.2011.02613.xOreopoulou, V. (s. f.). Fat Replacers. Bakery Products, 193-210. doi:10.1002/9780470277553.ch10Peressini, D., Pin, M., & Sensidoni, A. (2011). Rheology and breadmaking performance of rice-buckwheat batters supplemented with hydrocolloids. Food Hydrocolloids, 25(3), 340-349. doi:10.1016/j.foodhyd.2010.06.012Sanz, T., Salvador, A., Baixauli, R., & Fiszman, S. M. (2009). Evaluation of four types of resistant starch in muffins. II. Effects in texture, colour and consumer response. European Food Research and Technology, 229(2), 197-204. doi:10.1007/s00217-009-1040-1Taylor, J. R. N., Schober, T. J., & Bean, S. R. (2006). Novel food and non-food uses for sorghum and millets. Journal of Cereal Science, 44(3), 252-271. doi:10.1016/j.jcs.2006.06.009Wilderjans, E., Luyts, A., Brijs, K., & Delcour, J. A. (2013). Ingredient functionality in batter type cake making. Trends in Food Science & Technology, 30(1), 6-15. doi:10.1016/j.tifs.2013.01.001Wilderjans, E., Pareyt, B., Goesaert, H., Brijs, K., & Delcour, J. A. (2008). The role of gluten in a pound cake system: A model approach based on gluten–starch blends. Food Chemistry, 110(4), 909-915. doi:10.1016/j.foodchem.2008.02.079Wilson, N. L. W. (2011). How the Cookie Crumbles: A Case Study of Gluten-Free Cookies and Random Utility. American Journal of Agricultural Economics, 94(2), 576-582. doi:10.1093/ajae/aar081Zhu, J.-H., Yang, X.-Q., Ahmad, I., Li, L., Wang, X.-Y., & Liu, C. (2008). Rheological properties of κ-carrageenan and soybean glycinin mixed gels. Food Research International, 41(3), 219-228. doi:10.1016/j.foodres.2007.11.00