Exchange and correlation near the nucleus in density functional theory

The near nucleus behavior of the exchange-correlation potential $v_{xc}({\bf r})$ in Hohenberg-Kohn-Sham density functional theory is investigated. It is shown that near the nucleus the linear term of $O(r)$ of the spherically averaged exchange-correlation potential ${\bar v}_{xc}(r)$ is nonzero, and that it arises purely from the difference between the kinetic energy density at the nucleus of the interacting system and the noninteracting Kohn-Sham system. An analytical expression for the linear term is derived. Similar results for the exchange $v_{x}({\bf r})$ and correlation $v_{c}({\bf r})$ potentials are also obtained separately. It is further pointed out that the linear term in $v_{xc}({\bf r})$ arising mainly from $v_{c}({\bf r})$ is rather small, and $v_{xc}({\bf r})$ therefore has a nearly quadratic structure near the nucleus. Implications of the results for the construction of the Kohn-Sham system are discussed with examples.Comment: 10 page

Sequence classification with human attention

Learning attention functions requires large volumes of data, but many NLP tasks simulate human behavior, and in this paper, we show that human attention really does provide a good inductive bias on many attention functions in NLP. Specifically, we use estimated human attention derived from eye-tracking corpora to regularize attention functions in recurrent neural networks. We show substantial improvements across a range of tasks, including sentiment analysis, grammatical error detection, and detection of abusive language

Large Angle Transient Dynamics (LATDYN) user's manual

A computer code for modeling the large angle transient dynamics (LATDYN) of structures was developed to investigate techniques for analyzing flexible deformation and control/structure interaction problems associated with large angular motions of spacecraft. This type of analysis is beyond the routine capability of conventional analytical tools without simplifying assumptions. In some instances, the motion may be sufficiently slow and the spacecraft (or component) sufficiently rigid to simplify analyses of dynamics and controls by making pseudo-static and/or rigid body assumptions. The LATDYN introduces a new approach to the problem by combining finite element structural analysis, multi-body dynamics, and control system analysis in a single tool. It includes a type of finite element that can deform and rotate through large angles at the same time, and which can be connected to other finite elements either rigidly or through mechanical joints. The LATDYN also provides symbolic capabilities for modeling control systems which are interfaced directly with the finite element structural model. Thus, the nonlinear equations representing the structural model are integrated along with the equations representing sensors, processing, and controls as a coupled system

The on-top pair-correlation density in the homogeneous electron liquid

The ladder theory, in which the Bethe-Goldstone equation for the effective potential between two scattering particles plays a central role, is well known for its satisfactory description of the short-range correlations in the homogeneous electron liquid. By solving exactly the Bethe-Goldstone equation in the limit of large transfer momentum between two scattering particles, we obtain accurate results for the on-top pair-correlation density $g(0)$, in both three dimensions and two dimensions. Furthermore, we prove, in general, the ladder theory satisfies the cusp condition for the pair-correlation density $g(r)$ at zero distance $r=0$.Comment: 8 pages, 4 figure

Constraint-based, Single-point Approximate Kinetic Energy Functionals

We present a substantial extension of our constraint-based approach for development of orbital-free (OF) kinetic-energy (KE) density functionals intended for the calculation of quantum-mechanical forces in multi-scale molecular dynamics simulations. Suitability for realistic system simulations requires that the OF-KE functional yield accurate forces on the nuclei yet be relatively simple. We therefore require that the functionals be based on DFT constraints, local, dependent upon a small number of parameters fitted to a training set of limited size, and applicable beyond the scope of the training set. Our previous "modified conjoint" generalized-gradient-type functionals were constrained to producing a positive-definite Pauli potential. Though distinctly better than several published GGA-type functionals in that they gave semi-quantitative agreement with Born-Oppenheimer forces from full Kohn-Sham results, those modified conjoint functionals suffer from unphysical singularities at the nuclei. Here we show how to remove such singularities by introducing higher-order density derivatives. We give a simple illustration of such a functional used for the dissociation energy as a function of bond length for selected molecules.Comment: 16 pages, 9 figures, 2 tables, submitted to Phys. Rev.

Quantitative Sensory Testing in adults with Tourette syndrome

INTRODUCTION: Abnormal sensory perceptions, for instance hypersensitivity to certain external stimuli or premonitory urges preceding tics, are core features in Gilles de la Tourette syndrome (GTS). Aberrant awareness of externally applied stimuli in terms of altered sensory perception thresholds might contribute to these sensory phenomena in GTS. METHODS: We used the well-established and standardized “Quantitative Sensory Testing” (QST) battery (German Research Network on Neuropathic Pain) to investigate 13 sensory parameters including thermal, mechanical/tactile and pain thresholds in 14 GTS patients without clinically significant comorbidities and 14 healthy controls matched for age and gender. RESULTS: There were no relevant group differences in any of the 13 QST parameters and no specific QST pattern in GTS patients. There was no correlation between QST parameters and “Premonitory Urge for Tics scale” (PUTS) scores. CONCLUSION: Our data show that the perceptual threshold detection of externally applied sensory stimuli is normal in adults with GTS. This indicates that other perceptual mechanisms, such as abnormal central sensorimotor processing and/or aberrant interoceptive awareness might underlie the clinically significant sensory abnormalities in GTS

The Effect of Opioid Receptor Blockade on the Neural Processing of Thermal Stimuli

The endogenous opioid system represents one of the principal systems in the modulation of pain. This has been demonstrated in studies of placebo analgesia and stress-induced analgesia, where anti-nociceptive activity triggered by pain itself or by cognitive states is blocked by opioid antagonists. The aim of this study was to characterize the effect of opioid receptor blockade on the physiological processing of painful thermal stimulation in the absence of cognitive manipulation. We therefore measured BOLD (blood oxygen level dependent) signal responses and intensity ratings to non-painful and painful thermal stimuli in a double-blind, cross-over design using the opioid receptor antagonist naloxone. On the behavioral level, we observed an increase in intensity ratings under naloxone due mainly to a difference in the non-painful stimuli. On the neural level, painful thermal stimulation was associated with a negative BOLD signal within the pregenual anterior cingulate cortex, and this deactivation was abolished by naloxone

Grayscale Electron Beam Lithography Direct Patterned Antimony Sulfide

The rise of micro/nanooptics and lab-on-chip devices demands the fabrication of three-dimensional structures with decent resolution. Here, we demonstrate the combination of grayscale electron beam lithography and direct forming methodology to fabricate antimony sulfide structures with free form for the first time. The refractive index of the electron beam patterned structure was calculated based on an optimization algorithm that is combined with genetic algorithm and transfer matrix method. By adopting electron irradiation with variable doses, 4-level Fresnel Zone Plates and metalens were produced and characterized. This method can be used for the fabrication of three-dimensional diffractive optical elements and metasurfaces in a single step manner.Comment: 17 pages, 4 figures, 1 table, 1 scheme. The Supplement Information will be given in a second Arxiv submission or the published journa