Verified global optimization for estimating the parameters of nonlinear models

Nonlinear parameter estimation is usually achieved via the minimization of some possibly non-convex cost function. Interval analysis allows one to derive algorithms for the guaranteed characterization of the set of all global minimizers of such a cost function when an explicit expression for the output of the model is available or when this output is obtained via the numerical solution of a set of ordinary differential equations. However, cost functions involved in parameter estimation are usually challenging for interval techniques, if only because of multi-occurrences of the parameters in the formal expression of the cost. This paper addresses parameter estimation via the verified global optimization of quadratic cost functions. It introduces tools for the minimization of generic cost functions. When an explicit expression of the output of the parametric model is available, significant improvements may be obtained by a new box exclusion test and by careful manipulations of the quadratic cost function. When the model is described by ODEs, some of the techniques available in the previous case may still be employed, provided that sensitivity functions of the model output with respect to the parameters are available

Private Equity Entities and Conglomerates: What are the Differences?

We compare the characteristics of conglomerates and private equity entities. This is done by examining the differences among their business models. We analyze the relations of the two entity types to their investors on the one hand and to their investments on the other hand. The distinguishing characteristic of private equity entities is that they pursue a stand-alone-perspective with their investment policies, meaning that they treat each investment separately. Therefore, various linkages that exist in conglomerates do not occur in private equity entities. We describe these linkages in detail. We further argue that because of the lack of these linkages in private equity entities the shareholders and debtholders of a private equity entity and its portfolio companies are not faced with the following risks that are specific for a conglomerate: the asset shifting risk, the intra-group profit risk and the capital structure risk. Finally, we define crucial evaluation criteria for identifying a private equity entity and develop a way how regulators and other persons concerned with such a task could do so

Penicillamine Complexes of Nickel, Chromium, and Molybdänum - Structural Particularity and Biological Medical Relevance

Müller A, Johannes KU, Straube M, Krickemeyer E, Bögge H. Penicillamin-Komplexe des Nickels, Chroms und Molybdäns — Strukturelle Besonderheiten und biologische/medizinische Relevanz. Zeitschrift für anorganische und allgemeine Chemie. 1993;619(6):1037-1046.The compounds Tl2[Ni(II)(H2O)6][Ni(II)(D-pen)(L-pen)]2[Ni(II)(SCN)2(H2O)4] 1, TI[Ni(II)(D-pen)2H] . H2O 2, TI[Cr(III)(D-pen)2] 3, and Na2[Mo2(V)O4(pen)2] . 3 CH3OH . 3 H2O 4 have been pre pared by the reaction of nickel nitrate (for 1), nickel acetate (for 2), potassium chromate (for 3), and sodium molybdate (for 4) with D- and D,L-penicillamine, respectively. They were characterized by single-crystal X-ray structure analysis and other physical methods. Whereas penicillamine acts as a bidentate (N, S)-ligand in 1 and 2, Cr(III) (in 3), and Mo(V) (in 4) are coordinated to the three ligand atoms N, O, and S. The presence of three different types of Ni(II)-complexes a cationic, a neutral, and an anionic one in 1 is remarkable. For crystal data see Inhaltstibersicht

Island radiation on a continental scale: Exceptional rates of plant diversification after uplift of the Andes

Species radiations provide unique insights into evolutionary processes underlying species diversification and patterns of biodiversity. To compare plant diversification over a similar time period to the recent cichlid fish radiations, which are an order of magnitude faster than documented bird, arthropod, and plant radiations, we focus on the high-altitude flora of the Andes, which is the most species-rich of any tropical mountains. Because of the recent uplift of the northern Andes, the upland environments where much of this rich endemic flora is found have been available for colonization only since the late Pliocene or Pleistocene, 2–4 million years (Myr) ago. Using DNA sequence data we identify a monophyletic group within the genus Lupinus representing 81 species endemic to the Andes. The age of this clade is estimated to be 1.18–1.76 Myr, implying a diversification rate of 2.49–3.72 species per Myr. This exceeds previous estimates for plants, providing the most spectacular example of explosive plant species diversification documented to date. Furthermore, it suggests that the high cichlid diversification rates are not unique. Lack of key innovations associated with the Andean Lupinus clade suggests that diversification was driven by ecological opportunities afforded by the emergence of island-like habitats after Andean uplift. Data from other genera indicate that lupines are one of a set of similarly rapid Andean plant radiations, continental in scale and island-like in stimulus, suggesting that the high-elevation Andean flora provides a system that rivals other groups, including cichlids, for understanding rapid species diversification