Judgement aggregation functions and ultraproducts

The relationship between propositional model theory and social decision making via premise-based procedures is explored. A one-to-one correspondence between ultrafilters on the population set and weakly universal, unanimity-respecting, systematic judgment aggregation functions is established. The proof constructs an ultraproduct of profiles, viewed as propositional structures, with respect to the ultrafilter of decisive coalitions. This representation theorem can be used to prove other properties of such judgment aggregation functions, in particular sovereignty and monotonicity, as well as an impossibility theorem for judgment aggregation in finite populations. As a corollary, Lauwers and Van~Liedekerke's (1995) representation theorem for preference aggregation functions is derived.Judgment aggregation function; ultraproduct; ultrafilter

A simple approach to the correlation of rotovibrational states in four-atomic molecules

The problem of correlation between quantum states of four-atomic molecules in different geometrical configurations is reviewed in detail. A general, still simple rule is obtained which allows one to correlate states of a linear four-atomic molecule with those of any kind of non-linear four-atomic molecule.Comment: 16 pages (+8 figures), Postscript (ready to print!

Reactions of C2_2({\it a}3Piu^3Pi_u) with selected saturated alkanes: A temperature dependence study

We present a temperature dependence study on the gas phase reactions of the C$_2$({\it a}$^3Pi_u$) radical with a selected series of saturated alkanes (C$_2$H$_6$, C$_3$H$_8$, n-C$_4$H$_10$, i-C$_4$H$_10$, and n-C$_6$H$_14$) by means of pulsed laser photolysis/laser-induced fluorescence technique. The bimolecular rate constants for these reactions were obtained between 298 and 673 K. A pronounced negative temperature effect was observed for n-C$_4$H$_10$, i-C$_4$H$_10$, and n-C$_6$H$_14$ and interpreted in terms of steric hindrance of the more reactive secondary or tertiary C-H bonds by less reactive CH$_3$ groups. Detailed analysis of our experimental results reveals quantitatively the temperature dependence of reactivities for the primary, secondary, and tertiary C-H bonds in these saturated alkanes and further lends support to a mechanism of hydrogen abstraction.Comment: 26 pages, 8 figures, 1 table, 30 references; accepted to JC

Predicting and verifying transition strengths from weakly bound molecules

We investigated transition strengths from ultracold weakly bound 41K87Rb molecules produced via the photoassociation of laser-cooled atoms. An accurate potential energy curve of the excited state (3)1Sigma+ was constructed by carrying out direct potential fit analysis of rotational spectra obtained via depletion spectroscopy. Vibrational energies and rotational constants extracted from the depletion spectra of v'=41-50 levels were combined with the results of the previous spectroscopic study, and they were used for modifying an ab initio potential. An accuracy of 0.14% in vibrational level spacing and 0.3% in rotational constants was sufficient to predict the large observed variation in transition strengths among the vibrational levels. Our results show that transition strengths from weakly bound molecules are a good measure of the accuracy of an excited state potential.Comment: 7 pages, 7 figure

Controlled Production of Sub-Radiant States of a Diatomic Molecule in an Optical Lattice

We report successful production of sub-radiant states of a two-atom system in a three-dimensional optical lattice starting from doubly occupied sites in a Mott insulator phase of a quantum gas of atomic ytterbium. We can selectively produce either sub-radiant 1g state or super-radiant 0u state by choosing the excitation laser frequency. The inherent weak excitation rate for the sub-radiant 1g state is overcome by the increased atomic density due to the tight-confinement in a three-dimensional optical lattice. Our experimental measurements of binding energies, linewidth, and Zeeman shift confirm observation of sub-radiant levels of the 1g state of the Yb_2 molecule.Comment: To be published in Phys. Rev. Let

Graph Convolutional Networks for Model-Based Learning in Nonlinear Inverse Problems

The majority of model-based learned image reconstruction methods in medical imaging have been limited to uniform domains, such as pixelated images. If the underlying model is solved on nonuniform meshes, arising from a finite element method typical for nonlinear inverse problems, interpolation and embeddings are needed. To overcome this, we present a flexible framework to extend model-based learning directly to nonuniform meshes, by interpreting the mesh as a graph and formulating our network architectures using graph convolutional neural networks. This gives rise to the proposed iterative Graph Convolutional Newton-type Method (GCNM), which includes the forward model in the solution of the inverse problem, while all updates are directly computed by the network on the problem specific mesh. We present results for Electrical Impedance Tomography, a severely ill-posed nonlinear inverse problem that is frequently solved via optimization-based methods, where the forward problem is solved by finite element methods. Results for absolute EIT imaging are compared to standard iterative methods as well as a graph residual network. We show that the GCNM has strong generalizability to different domain shapes and meshes, out of distribution data as well as experimental data, from purely simulated training data and without transfer training