Reduced local energy as a criterion for the accuracy of approximate H2 wave-functions

The goodness of the local fit of an approximate wave-function, \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document}, to the exact function, ψ₀, is \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. From this quantity the global accuracy of \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \psi $\end{document} is defined and a “working supposition” is presented, which quantitatively relates the global accuracy to the accuracy of expectation values. Two criteria based on the accuracy of the reduced local energy and the density respectively, are presented as alternatives to \documentclass{article}\pagestyle{empty}\begin{document}$ |\tilde \psi - \psi _0 | $\end{document}. The relative global accuracies of eight wave-functions for H₂ are determined using the two criteria. The ‘working supposition’ is applied and predictions are made concerning the relative accuracies of the expectation values of the following operators: z², r², x² + y², 3z² ?; r², ξ, r, r, and E_L (the reduced local energy). The success rate is high (>90%) except for those operators which are sensitive to interelectron coordinates or derivatives of the wave-function.     

A Testable Theory for the Emergence of the Classical World

The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2^N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2^N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments.     

Formalising the Pathways to Life Using Assembly Spaces

Assembly theory (referred to in prior works as pathway assembly) has been developed to explore the extrinsic information required to distinguish a given object from a random ensemble. In prior work, we explored the key concepts relating to deconstructing an object into its irreducible parts and then evaluating the minimum number of steps required to rebuild it, allowing for the reuse of constructed sub-objects. We have also explored the application of this approach to molecules, as molecular assembly, and how molecular assembly can be inferred experimentally and used for life detection. In this article, we formalise the core assembly concepts mathematically in terms of assembly spaces and related concepts and determine bounds on the assembly index. We explore examples of constructing assembly spaces for mathematical and physical objects and propose that objects with a high assembly index can be uniquely identified as those that must have been produced using directed biological or technological processes rather than purely random processes, thereby defining a new scale of aliveness. We think this approach is needed to help identify the new physical and chemical laws needed to understand what life is, by quantifying what life does.     

A compact UHV package for microfabricated ion-trap arrays with direct electronic air-side access

We have demonstrated a new apparatus for operating microfabricated ion-trap arrays in a compact ultra-high-vacuum setup with excellent optical and electrical access. The approach uses conventional components, materials and techniques in a unique fashion. The microtrap chip is mounted on a modified ceramic leadless chip carrier, the conductors of which serve as the vacuum feedthrough. The chip carrier is indium-sealed to stainless-steel components to form vacuum seals, resulting in short electrical path lengths of ≤20 mm from the trap electrodes under vacuum to air side. The feedthrough contains conductors for the radio-frequency trap drive, as well as 42 conductors for DC electrodes. Vacuum pressures of ～1 × 10^?11 mbar are achieved, and ions have been confined and laser cooled in a microtrap chip. The apparatus enables accurate measurements of radio-frequency voltage amplitudes on the trap electrodes, yielding an excellent agreement between measured and modelled trap efficiencies. This feature is of significant use in establishing initial operation of new devices. The principle of the connectivity scheme presented here is applicable to larger ceramic chip carriers containing many more conductors.     

The input impedance of the dielectric resonator antenna

Dielectric cylinders of very high permittivity have been used in the past as resonant cavities, but since the structure is not enclosed by metallic walls, electromagnetic fields do exist beyond the geometrical boundaries of the structure and part of the power is radiated. Through the proper choice of geometry and permittivity this radiation can become the dominant feature of the structure and become an efficient antenna for use at millimeter wave frequencies. Both experimental and theoretical investigations of a variety of these dielectric resonator antennas have been undertaken. In particular, the input impedance of a probe-fed cylindrical structure was examined in detail and a comparison of theoretical and experimental results was made.     

Improved l1-SPIRiT using 3D walsh transform-based sparsity basis

l1-SPIRiT is a fast magnetic resonance imaging (MRI) method which combines parallel imaging (PI) with compressed sensing (CS) by performing a joint l1-norm and l2-norm optimization procedure. The original l1-SPIRiT method uses two-dimensional (2D) Wavelet transform to exploit the intra-coil data redundancies and a joint sparsity model to exploit the inter-coil data redundancies. In this work, we propose to stack all the coil images into a three-dimensional (3D) matrix, and then a novel 3D Walsh transform-based sparsity basis is applied to simultaneously reduce the intra-coil and inter-coil data redundancies. Both the 2D Wavelet transform-based and the proposed 3D Walsh transform-based sparsity bases were investigated in the l1-SPIRiT method. The experimental results show that the proposed 3D Walsh transform-based l1-SPIRiT method outperformed the original l1-SPIRiT in terms of image quality and computational efficiency.     

Neural correlates of intelligibility in speech investigated with noise vocoded speech--a positron emission tomography study

Functional imaging studies of speech perception in the human brain have identified a key role for auditory association areas in the temporal lobes (bilateral superior temporal gyri and sulci) in the perceptual processing of the speech signal. This is extended to suggest some functional specialization within this bilateral system, with a particular role for the left anterior superior temporal sulcus (STS) in processing intelligible speech. In the current study, noise-vocoded speech was used to vary the intelligibility of speech parametrically. This replicated the finding of a selective response to intelligibility in speech in the left anterior superior temporal sulcus, in contrast to the posterior superior temporal sulcus, which showed a response profile insensitive to the degree of intelligibility. These results are related to theories of functional organization in the human auditory system, which have indicated that there are separate processing streams, with different functional roles, running anterior and posterior to primary auditory cortex. Specifically, it is suggested that an anterior stream processing intelligibility can be distinguished from a posterior stream associated with transient representations, important in spoken repetition and working memory.