A penalized criterion for variable selection in classification

In this paper, the problem of variable selection in classification is considered. On the basis of recent developments in model selection theory, we provide a criterion based on penalized empirical risk, where the penalization explicitly takes into account the number of variables of the considered models. Moreover, we give an oracle-type inequality that non-asymptotically guarantees the performance of the resulting classification rule. We discuss the optimality of the proposed criterion and present an application of the main result to backward and forward selection procedures.     

Hydrogen Storage Materials: Room‐Temperature Wet‐Chemistry Approach toward Mixed‐Metal Borohydrides

The poor kinetics of hydrogen evolution and the irreversibility of the hydrogen discharge hamper the use of transition metal borohydrides as hydrogen storage materials, and the drawbacks of current synthetic methods obstruct the exploration of these systems. A wet‐chemistry approach, which is based on solvent‐mediated metathesis reactions of precursors containing bulky organic cations and weakly coordinating anions, leads to mixed‐metal borohydrides that contain only a small amount of “dead mass”. The applicability of this method is exemplified by Li[Zn₂(BH₄)₅] and M[Zn(BH₄)₃] salts (M=Na, K), and its extension to other systems is discussed.     

High-Fidelity,Narcissistic Self-Sorting in the Synthesis of Organometallic Assemblies from Poly-NHC Ligands

Highly selective, narcissistic self-sorting has been observed in the one-pot synthesis of three organometallic molecular cylinders of type [M₃{L-(NHC)₃}₂](PF₆)₃ (M=Ag⁺, Au⁺; L=1,3,5-benzene, triphenylamine, or 1,3,5-triphenylbenzene) from L-(NHC)₃ and silver(I) or gold(I) ions. The molecular cylinders contain only one type of tris-NHC ligand with no crossover products detectable. Transmetalation of the tris-NHC ligands from Ag⁺ to Au⁺ in a one-pot reaction with retention of the supramolecular structures is also demonstrated. High-fidelity self-sorting was also observed in the one-pot reaction of benzene-bridged tris-NHC and tetrakis-NHC ligands with Ag₂O. This study for the first time extends narcissistic self-sorting in metal–ligand interactions from Werner-type complexes to organometallic derivatives.     

Inflation of Finite Lattices Along All-or-nothing Sets

We introduce a new generalization of Alan Day’s doubling construction. For ordered sets \(\mathcal {L}\) and \(\mathcal {K}\) and a subset \(E \subseteq \ \leq _{\mathcal {L}}\) we define the ordered set \(\mathcal {L} \star _{E} \mathcal {K}\) arising from inflation of \(\mathcal {L}\) along E by \(\mathcal {K}\). Under the restriction that \(\mathcal {L}\) and \(\mathcal {K}\) are finite lattices, we find those subsets \(E \subseteq \ \leq _{\mathcal {L}}\) such that the ordered set \(\mathcal {L} \star _{E} \mathcal {K}\) is a lattice. Finite lattices that can be constructed in this way are classified in terms of their congruence lattices.A finite lattice is binary cut-through codable if and only if there exists a 0?1 spanning chain \(\left \{\theta _{i}\colon 0 \leq i \leq n \right \}\) in \(Con(\mathcal {L})\) such that the cardinality of the largest block of ?? _i /?? _i?1 is 2 for every i with 1≤i≤n. These are exactly the lattices that can be constructed by inflation from the 1-element lattice using only the 2-element lattice. We investigate the structure of binary cut-through codable lattices and describe an infinite class of lattices that generate binary cut-through codable varieties.     

Analysis of Unsteady Motion with Respect to Noise Sources in a Gas Turbine Combustor: Isothermal Flow Case

In order to evaluate the direct and indirect contributions to the total combustion noise emission, a combustion chamber consisting of a swirl burner and an exit nozzle of Laval-shape, representing a gas turbine combustor, is investigated by means of experiments and large eddy simulation. Focused on the isothermal flow case first and encouraged by a good overall agreement between the LES and the experimental data for the flow field, a first characterisation of the flow with respect to noise sources is performed. To analyse acoustic properties of the flow, time and length scales are evaluated inside the combustor. Furthermore, the evidence for the existence of a precessing vortex core (PVC), typical for configurations with swirl, is revealed. Finally, the effect of the PVC on the flow inside the Laval nozzle is discussed.     

Desch‐Schappacher perturbation of one‐parameter semigroups on locally convex spaces

We prove a Desch‐Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one‐parameter semigroups which are defined on a sequentially complete locally convex space.     

Charging megadalton poly(ethylene oxide)s by electrospray ionization. A charge detection mass spectrometry study

Ions from compounds of megadalton (MDa) molecular weight were produced in an electrospray ionization source from solutions of poly(ethylene oxide) (PEO) samples with average molecular weights ranging from 1,000,000 to 7,000,000 Da. Charge detection mass spectrometry (CDMS) has been used to determine the mass of the MDa PEOs. Simultaneous measurement of the charge and velocity of individual ions allows the mass determination of the ion, after calibration of the instrument with independent samples. In addition to the mass spectra, CDMS generates charge-versus-mass plots, which allow investigation of the charging of electrosprayed ions over a broad range of masses. The experimental charging capacity of MDa PEOs is compared with a simple model based on the affinity of alkali cations for oxygen sites and on the electrostatic potential energy of the charged polymer. The charging capacity of PEOs was also investigated as a function of the concentration of and the type of alkali ions.