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The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn–Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS densityfunctional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.

We present the revM06-L functional, which we designed by optimizing against a larger database than had been used for Minnesota 2006 local functional (M06-L) and by using smoothness restraints. The optimization strategy reduced the number of parameters from 34 to 31 because we removed some large terms that increased the required size of the quadrature grid and the number of self-consistent-field iterations. The mean unsigned error (MUE) of revM06-L on 422 chemical energies is 3.07 kcal/mol, which is improved from 3.57 kcal/mol calculated by M06-L. The MUE of revM06-L for the chemical reaction barrier height database (BH76) is 1.98 kcal/mol, which is improved by more than a factor of 2 with respect to the M06-L functional. The revM06-L functional gives the best result among local functionals tested for the noncovalent interaction database (NC51), with an MUE of only 0.36 kcal/mol, and the MUE of revM06-L for the solid-state lattice constant database (LC17) is half that for M06-L. The revM06-L functional also yields smoother potential curves, and it predicts more-accurate results than M06-L for seven out of eight diversified test sets not used for parameterization. We conclude that the revM06-L functional is well suited for a broad range of applications in chemistry and condensed-matter physics.

Screened-exchange hybrid density functionals are especially recommended for solid-state systems because they combine the advantages of hybrid functionals with the correct physics and lower computational cost associated with the attenuation of Hartree–Fock exchange at long range. We present a screenedexchange hybrid functional, M06-SX, that combines the functional form of the local revM06-L functional with a percentage of short-range nonlocal Hartree–Fock exchange. The M06-SX functional gives good results not only for a large set of training data but also for several databases quite different from the training data. The mean unsigned error (MUE) of the M06-SX functional is 2.85 kcal/mol for 418 atomic and molecular energies (AME418) in Minnesota Database 2019, which is better than all five other screened-exchange hybrid functionals tested in this work. The M06-SX functional also gives especially good results for semiconductor band gaps, molecular dissociation energies, noncovalent interactions, barrier heights, and electronic excitation energies excluding long-range charge transfer excitations. For the LC18 lattice constants database, the M06-SX functional gives an MUE of only 0.034 Å. Therefore, the M06-SX functional is well suited for studying molecular chemistry as well as solid-state physics.

To perform a systematic review and meta-analysis to study the magnitude of the placebo effect associated with sham surgery procedures. We conducted a systematic search for randomized controlled clinical trials comparing any type of surgery to a corresponding sham placebo group and compared improvements in the sham treatment arms in subjective, objective, categorical, and continuous outcomes, as well as complication rates and mortality. Effect sizes were reported as standardized mean differences (SMDs). This is a systematic review and meta-analysis. The overall effect size for pain improvement after sham surgery was SMD = 0.22 (95% confidence interval [CI] = 0.08–0.35) with improvement most marked at 1 month (SMD = 0.34, 95% CI = 0.26–0.43). There was a higher rate of improvement in subjective outcomes compared to objective outcomes for both dichotomized (number of patients with improvement) (42.8% compared to 27.1%) and continuous outcomes (SMD = 0.12, 95% CI = −0.05, 0.30 vs. SMD = −0.01, 95% CI = −0.05, 0.03). There were no deaths in the sham treatment arms and major complications were very rare (0.2%, 95% CI = 0.0–0.6%). Sham surgery is associated with a large improvement in pain and other subjective patient-reported outcomes but with relatively small effect on objective outcomes. Sham surgeries are overwhelmingly safe. The magnitude of this effect should be used when planning future sham-controlled surgery trials.

Neuromodulation through transcranial direct current stimulation (tDCS) has a B recommendation for the treatment of addiction according to therapeutic evidence guidance. We present an intervention, with randomization and placebo, to test the effectiveness of 10 tDCS sessions, without other treatment, spaced over 2 weeks, on tobacco consumption and craving, in 26 healthy smokers. The influence of motivation to quit, self-perceived efficacy, and previous physical dependence was assessed. Active dorsolateral prefrontal cortex (DLPFC, cathode F3/anode F4) tDCS (20 min at 2 mA) was compared to sham through pre-post design with 1-month follow-up. Data analysis included AUCg formulas, ANOVA's and linear regressions. The experimental group showed significantly less consumption than sham during intervention (p = .02, d = .95) but not at follow-up, as well as a significant decrease in craving (р = .04, n° = .15). The most prominent predictors of effectiveness were the number of cigarettes regularly smoked (В = 4.27, р = .001) and self-reported motivation to quit (В = -6.48, р = .05). In sum, tDCS helps to reduce tobacco consumption and craving, but its benefits are not maintained over time. It would be necessary to increase the number of sessions and control motivation and the level of previous consumption.

In this paper, we study a few theoretical issues in the discretized Kohn–Sham (KS) density functional theory. The equivalence between either a local or global minimizer of the KS total energy minimization problem and the solution to the KS equation is established under certain assumptions. The nonzero charge densities of a strong local minimizer are shown to be bounded from below by a positive constant uniformly. We analyze the self-consistent field (SCF) iteration by formulating the KS equation as a fixed point map with respect to the potential. The Jacobian of these fixed point maps is derived explicitly. Both global and local convergence of the simple mixing scheme can be established if the gap between the occupied states and unoccupied states is sufficiently large. This assumption can be relaxed in certain cases. Numerical experiments based on the MATLAB toolbox KSSOLV show that it holds on a few simple examples. Although our assumption on the gap is very stringent, our analysis is still valuable for a better understanding of the KS minimization problem, the KS equation, and the SCF iteration.

•Optimized sham TMS-EEG is introduced and tested.•Sham combined auditory and supramaximal electrical somatosensory stimulation.•Subjects reported equal sensory perception during sham and real TMS.•Subtraction revealed evoked EEG potentials and beta-band power specific to real TMS.•The optimized sham procedure is relevant in research and therapeutic settings. Electroencephalography (EEG) is increasingly used to investigate brain responses to transcranial magnetic stimulation (TMS). A relevant issue is that TMS is associated with considerable auditory and somatosensory stimulation, causing peripherally evoked potentials (PEPs) in the EEG, which contaminate the direct cortical responses to TMS (TEPs). All previous attempts to control for PEPs suffer from significant limitations. To design an optimized sham procedure to control all sensory input generated by subthreshold real TMS targeting the hand area of the primary motor cortex (M1), enabling reliable separation of TEPs from PEPs. In 23 healthy (16 female) subjects, we recorded EEG activity evoked by an optimized sham TMS condition which masks and matches auditory and somatosensory co-stimulation during the real TMS condition: auditory control was achieved by noise masking and by using a second TMS coil that was placed on top of the real TMS coil and produced a calibrated sound pressure level. Somatosensory control was obtained by electric stimulation (ES) of the scalp with intensities sufficient to saturate somatosensory input. ES was applied in both the sham and real TMS conditions. Perception of auditory and somatosensory inputs in the sham and real TMS conditions were compared by psychophysical testing. Transcranially evoked EEG signal changes were identified by subtraction of EEG activity in the sham condition from EEG activity in the real TMS condition. Perception of auditory and somatosensory inputs in the sham vs. real TMS conditions was comparable. Both sham and real TMS evoked a series of similar EEG signal deflections and induced broadband power increase in oscillatory activity. Notably, the present procedure revealed EEG potentials and a transient increase in beta band power at the site of stimulation that were only present in the real TMS condition. The results validate the effectiveness of our optimized sham approach. Despite the presence of typical responses attributable to sensory input, the procedure provided evidence for direct cortical activation by subthreshold TMS of M1. The findings are relevant for future TMS-EEG experiments that aim at measuring regional brain target engagement controlled by an optimized sham procedure.

Renal denervation is a promising new non-pharmacological treatment for resistant hypertension. However, there is a lack of data from Asian patients. The REQUIRE trial investigated the blood pressure-lowering efficacy of renal denervation in treated patients with resistant hypertension from Japan and South Korea. Adults with resistant hypertension (seated office blood pressure ≥150/90 mmHg and 24-hour ambulatory systolic blood pressure ≥140 mmHg) with suitable renal artery anatomy were randomized to ultrasound renal denervation or a sham procedure. The primary endpoint was change from baseline in 24-hour ambulatory systolic blood pressure at 3 months. A total of 143 patients were included (72 renal denervation, 71 sham control). Reduction from baseline in 24-hour ambulatory systolic blood pressure at 3 months was not significantly different between the renal denervation (-6.6 mmHg) and sham control (-6.5 mmHg) groups (difference: -0.1, 95% confidence interval -5.5, 5.3; p = 0.971). Reductions from baseline in home and office systolic blood pressure (differences: -1.8 mmHg [p = 0.488] and -2.0 mmHg [p = 0.511], respectively), and medication load, did not differ significantly between the two groups. The procedure-/device-related major adverse events was not seen. This study did not show a significant difference in ambulatory blood pressure reductions between renal denervation and a sham procedure in treated patients with resistant hypertension. Although blood pressure reduction after renal denervation was similar to other sham-controlled studies, the sham group in this study showed much greater reduction. This unexpected blood pressure reduction in the sham control group highlights study design issues that will be addressed in a new trial. CLINICAL TRIAL REGISTRATION: NCT02918305 ( http://www.clinicaltrials.gov ).

Transcranial Magnetic Stimulation (TMS) excites populations of neurons in the stimulated cortex, and the resulting activation may spread to connected brain regions. The distributed cortical response can be recorded with electroencephalography (EEG). Since TMS also stimulates peripheral sensory and motor axons and generates a loud “click” sound, the TMS-evoked EEG potentials (TEPs) reflect not only neural activity induced by transcranial neuronal excitation but also neural activity due to somatosensory and auditory processing. In 17 healthy young individuals, we systematically assessed the contribution of multisensory peripheral stimulation to TEPs using a TMS-compatible EEG system. Real TMS was delivered with a figure-of-eight coil over the left para-median posterior parietal cortex or superior frontal gyrus with the coil being oriented perpendicularly or in parallel to the target gyrus. We also recorded the EEG responses evoked by realistic sham stimulation over the posterior parietal and superior frontal cortex, mimicking the auditory and somatosensory sensations evoked by real TMS. We applied state-of-the-art procedures to attenuate somatosensory and auditory confounds during real TMS, including the placement of a foam layer underneath the coil and auditory noise masking. Despite these precautions, the temporal and spatial features of the cortical potentials evoked by real TMS at the prefrontal and parietal site closely resembled the cortical potentials evoked by realistic sham TMS, both for early and late TEP components. Our findings stress the need to include a peripheral multisensory control stimulation in the design of TMS-EEG studies to enable a dissociation between truly transcranial and non-transcranial components of TEPs. •Individually adjusted somato-auditory sham stimulation can mimic real TMS.•A realistic sham stimulation is capable to evoke complex EEG potentials.•Real TMS and sham evoked responses strongly correlated at early and late latencies.•Future TMS-EEG studies need to control for the effect of multisensory stimulation.

fMRI Neurofeedback research employs many different control conditions. Currently, there is no consensus as to which control condition is best, and the answer depends on what aspects of the neurofeedback-training design one is trying to control for. These aspects can range from determining whether participants can learn to control brain activity via neurofeedback to determining whether there are clinically significant effects of the neurofeedback intervention. Lack of consensus over criteria for control conditions has hampered the design and interpretation of studies employing neurofeedback protocols. This paper presents an overview of the most commonly employed control conditions currently used in neurofeedback studies and discusses their advantages and disadvantages. Control conditions covered include no control, treatment-as-usual, bidirectional-regulation control, feedback of an alternative brain signal, sham feedback, and mental-rehearsal control. We conclude that the selection of the control condition(s) should be determined by the specific research goal of the study and best procedures that effectively control for relevant confounding factors. •fMRI neurofeedback is an expanding field with no consensus on best control conditions.•Strengths/limitations of different control conditions are discussed in this article.•Multiple control conditions may be ideal, but this has to be balanced against power.•An ideal approach would enable exclusion of as many potential confounds as possible.•Early-phase neurofeedback studies may not need control conditions/groups.