Model selection for density estimation with \mathbb L _2-loss

We consider here estimation of an unknown probability density $s$ belonging to $\mathbb L _2(\mu )$ where $\mu $ is a probability measure. We have at hand $n$ i.i.d. observations with density $s$ and use the squared $\mathbb L _2$ -norm as our loss function. The purpose of this paper is to provide an abstract but completely general method for estimating $s$ by model selection, allowing to handle arbitrary families of finite-dimensional (possibly non-linear) models and any $s\in \mathbb L _2(\mu )$ . We shall, in particular, consider the cases of unbounded densities and bounded densities with unknown $\mathbb L _\infty $ -norm and investigate how the $\mathbb L _\infty $ -norm of $s$ may influence the risk. We shall also provide applications to adaptive estimation and aggregation of preliminary estimators. One major technical tool of our approach is a proof of the existence of suitable tests between $\mathbb L _2$ -balls with centers belonging to $\mathbb L _\infty $ . Although of a purely theoretical nature, our method leads to results that cannot presently be reached by more concrete ones.     

Diaquabis(phen)Ni(II) Complex with Vitamin B13 Counter-ions

Abstract The synthesis and crystal structure of a new Ni(II) complex of stoichiometry [Ni(phen)₂(H₂O)₂](H₂Or)₂ · 2H₂O, where phen is phenanthroline and H₂Or is oratate monoanion, are reported. The complex [Ni(phen)₂(H₂O)₂](H₂Or)₂ · 2H₂O crystallizes in the monoclinic system with space group C2/c and cell parameters a = 16.1661(8) ?, b = 12.5669(7) ? and c = 16.4752(7) ?. The coordination around Ni(II) is a distorted octahedron with two phen ligands perpendicular to each other and two aqua ligands in cis- position. Orotate ions locate themselves out of the coordination sphere and bridge the [Ni(phen)₂(H₂O)₂]²⁺ moieties through hydogen bonding with aqua ligands. The FT-IR spectrum of the complex and thermal decomposition behaviour are also briefly discussed. Graphical Abstract Diaquabis(phen)Ni(II) Complex with Vitamin B13 Counter-ions Dursun Ali K?se, Birgül Zümreoglu-Karan, Başak Koşar, Orhan Büyükgüng?r A new complex where Vitamin B13 monoanions act as counter ions and bridge the [Ni(phen)₂(H₂O)₂]²⁺ units by hydrogen bonds is described CCDC deposition number is 606339.     

A comparison of the statistical treatment of results using concentrations of elements determined by neutron activation and X-ray fluorescence analysis methods

Statistical treatment was carried out using the elements determined both by neutron activation and X-ray fluorescence analysis in order to decide on the method to be used in the future work.     

Chernobyl radioactivity in Turkish tea and its possible health consequences

Like several other European countries, Turkey has been affected by the radioactive clouds arising from the Chemobyl reactor accident. There were two major fronts. The first one affected the western parts of Turkey, namely Thrace, Istanbul and Western Black Sea coast, starting from April 30th 1986. The second cloud affected the Eastern Black Sea coast at the beginning of May 1986. In both regions the clouds left their radioactive content with the heavy rains. Eastern Sea coast is one of the regions receiving highest volume of rainfall almost all year round. However, after the accident, the rains loaded with radioactive contaminants felt just before the tea collection period and the contaminated tea leaves were collected without finding a chance for cleaning with following rains. All of the tea consumed by Turkish people grows on a very narrow coastal line along the Eastern Black Sea. In this study, the results of radioactivity measurement on Turkish tea are summarized. Although there were other affected products in the region, e.g., hazelnuts, tobacco, vegetables, their level of contamination and yearly consumption rates were not as significant as tea. Tea is the major hot beverage consumed by Turkish people of all ages, but unfortunately it turned out to be one of the heavily contaminated products of Turkey. The effect of brewing and rinsing with hot water on tea were also investigated in the present work. The dose estimates from the tea consumption was done following a different approach than previous studies. Instead of using the radioactivity data obtained by measuring only limited number of contaminated tea samples in our laboratories, the data reported by the Turkish Atomic Energy Agency Authority covering all the tea product of 1986 were used for dose estimates. In addition the collective effective dose equivalent in Turkey was estimated. Although in this study contamination only in one product, namely tea, was discussed, it turned out to be important as it was consumed by large populations in Turkey, so contributed to the doses significantly. Precautions to be taken were summarized, one simple precaution rinsing of tea before brewing was sufficient to remove half of the contamination from tea without any drawbacks.Dedicated to the memory of late Olcay Birgül.     

The synthesis, characterization and antimicrobial activity of N,N′-bis(2-thiophenecarboxamido)-1,3-diaminopropane and N,N′-bis (2-furancarboxamido)-1,3-diaminopropane and their Cu(II), Zn(II), Co(III) complexes

Metal complexes derived from amides; N,N′-bis(2-thiophenecarboxamido)-1,3-diamino propane (1) and N,N′-bis(2-furancarboxamido)-1,3-diaminopropane (2) were characterized by elemental analysis, spectral (NMR, FT-IR, LC-MS) methods, magnetic moment, molar conductance, and TGA/DTA studies. The complexes were dimeric and have the general formula [ML.Cl_m.(H₂O)_n]2Cl₂ where M=Cu(II), Zn(II), Co(III); m = 1, 2; n = 0, 1. The antimicrobial activities of the amides and their complexes were studied against the bacteria; Escherichia coli (ATCC 11230), Yersinia enterocolitica (ATCC 1501), Bacillus magaterium (RSKK 5117), Bacillus cereus (RSKK 863), Bacillus subtilis (RSKK 863) and yeast; Candida albicans (ATCC 10239).     

Gaussian model selection

Our purpose in this paper is to provide a general approach to model selection via penalization for Gaussian regression and to develop our point of view about this subject. The advantage and importance of model selection come from the fact that it provides a suitable approach to many different types of problems, starting from model selection per se (among a family of parametric models, which one is more suitable for the data at hand), which includes for instance variable selection in regression models, to nonparametric estimation, for which it provides a very powerful tool that allows adaptation under quite general circumstances. Our approach to model selection also provides a natural connection between the parametric and nonparametric points of view and copes naturally with the fact that a model is not necessarily true. The method is based on the penalization of a least squares criterion which can be viewed as a generalization of Mallows’C _p . A large part of our efforts will be put on choosing properly the list of models and the penalty function for various estimation problems like classical variable selection or adaptive estimation for various types of l _p -bodies. Received February 1, 1999 / final version received January 10, 2001?Published online April 3, 2001     

Synthese und Struktur von Sr6P8‐Polyedern in gemischten Phosphaniden/Phosphandiiden des Strontiums

Synthesis and Structures of Sr₆P₈ Polyhedra in Mixed Phosphanides/Phosphandiides of Strontium The strontiation of H₂PSiⁱPr₃ ( 1 ) with (THF)₂Sr[N(SiMe₃)₂]₂ in THF yields colorless tetrakis(tetrahydrofuran‐O)strontium bis(triisopropylsilylphosphanide) ( 3 ). The central alkaline earth metal atom has an octahedral environment with the phosphanide ligands in trans position. The homometalation in toluene leads to the elimination of 1 and THF. Cooling of this solution gives crystals of colorless tetrakis(tetrahydrofuran‐O)hexastrontium‐tetrakis(triisopropylsilylphosphanide)‐tetrakis(triisopropylsilylphosphandiide) ( 4 ). The equimolar reaction of H₂PSi^tBu₃ ( 2 ) with (THF)₂Sr[N(SiMe₃)₂]₂ in toluene yields in the first step heteroleptic dimeric {(Me₃Si)₂NSr(THF)₂[P(H)Si^tBu₃]}₂ ( 5 )₂. This compounds monomerizes in THF to (Me₃Si)₂N–Sr(THF)₄[P(H)Si^tBu₃] ( 6 ), which forms an equilibrium with the homoleptic dismutation products (THF)₂Sr[N(SiMe₃)₂]₂ and (THF)₄Sr[P(H)Si^tBu₃]₂ ( 7 ). Compound ( 5 )₂ undergoes a intramolecular strontiation and bis(tetrahydrofuran‐O)hexastrontium‐tetrakis[tri(tert‐butyl)silylphosphanide]‐tetrakis[tri(tert‐butyl)silylphosphandiide] ( 8 ) is isolated. The central Sr₆P₈‐polyhedra of 4 and 8 are very similar.     

Phosphopeptide enrichment by IEF

In our efforts to improve the identification of phosphopeptides by MS we have used peptide IEF on IPG strips. Phosphopeptides derived from trypsin digests of single proteins as well as complex cellular protein mixtures can be enriched by IEF and recovered in excellent yields at the acidic end of an IPG strip. IPG peptide fractionation in combination with MS/MS analysis has allowed us to identify phosphopeptides from tryptic digests of a cellular protein extract.