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Laser-induced molecular alignment is well understood within the framework of the Born–Oppenheimer (BO) approximation. Without the BO approximation, however, the concept of molecular structure is lost, making it hard to precisely define alignment. In this work, we demonstrate the emergence of alignment from the first-ever non-BO quantum dynamics simulations, using the HD molecule exposed to ultrashort laser pulses as a few-body test case. We extract the degree of alignment from the non-BO wave function by means of an operator expressed in terms of pseudo-proton coordinates that mimics the BO-based definition of alignment. The only essential approximation, in addition to the semiclassical electric-dipole approximation for the matter–field interaction, is the choice of time-independent explicitly correlated Gaussian basis functions. We use a variational, electric-field-dependent basis-set construction procedure, which allows us to keep the basis-set dimension low while capturing the main effects of electric polarization on the nuclear and electronic degrees of freedom. The basis-set construction procedure is validated by comparing with virtually exact grid-based simulations for two one-dimensional model systems: laser-driven electron dynamics in a soft attractive Coulomb potential and nuclear rovibrational dynamics in a Morse potential. [ABSTRACT FROM AUTHOR]

Children absconding from countries of conflict and war are often not able to document their age. When an age is given, it is frequently untraceable or poorly documented and therefore questioned by immigration authorities. Consequently many countries perform age estimations on these children. Provision of ethical practice during the age estimation investigation of unaccompanied minors is considered from different angles: (1) The UN convention on children’s rights, formulating specific rights, protection, support, healthcare and education for unaccompanied minors. (2) Since most age estimation investigations are based on medical examination, the four basic principles of biomedical ethics, namely autonomy, beneficence, non-malevolence, justice. (3) The use of medicine for non treatment purposes. (4) How age estimates with highest accuracy in age prediction can be obtained. Ethical practice in age estimation of unaccompanied minors is achieved when different but related aspects are searched, evaluated, weighted in importance and subsequently combined. However this is not always feasible and unanswered questions remain. [ABSTRACT FROM AUTHOR]

Counting incremental lines in dental cementum is an accepted method for estimating age in many wild mammals. In human teeth such countings have given variable results, and the aim of the present investigation was to find out if one incremental line is formed per year in human teeth as well. Canines and single-rooted premolars were demineralized, paraffin wax-embedded, sectioned and stained, and the sections were viewed in a fluorescence microscope. Non-fluorescent lines, seen against a fluorescent background, were either counted directly or their number calculated by counting only some of them and computing this on the total width of the cementum. The correlation coefficient between tooth age and the number of lines for the whole material was =0.84 when counted and =0.73 when calculated. This coefficient was stronger in mandibular second premolars but lower in teeth extracted because of dental diseases. The coefficient was only significant in teeth from individuals below the age of 50 yr. The regression formula with tooth age as dependent variable indicated that only incremental lines formed in about every other year stained sufficiently to be counted. [ABSTRACT FROM AUTHOR]

Peritubular dentine is a mineralised deposit formed centripetally in the dentine tubules with advancing age, so that the tubular diameter is smaller in teeth from older persons. The aim of the present study was to investigate the relationship between age in humans and the amount of peritubular dentine and the extent of the consequent obliteration of the tubules, and to find out whether this relationship was strong enough to be used as a parameter for age estimation. Fifty mandibular central and lateral human incisors were ground on the lingual aspect of the root and examined in a scanning electron microscope (SEM). The number of open tubules was counted and the diameter of the tubules measured both before and after etching with 35% orthophosphoric acid. The difference in the number of tubules in unetched and etched specimens was taken to be the number of occluded tubules, and the difference in radii before and after etching to be the thickness of peritubular dentine. The results did not demonstrate a significant relationship between age and the reduction in the number of tubules. One explanation might be that a certain age has to be reached before obliterated dentine tubules can be observed. The correlation between age and the thickness of peritubular dentine was not significant in teeth extracted because of periodontal disease, so these teeth were excluded from the regression analysis with age as the dependent variable.(ABSTRACT TRUNCATED AT 250 WORDS) [ABSTRACT FROM AUTHOR]

In a previous publication [S. E. Schrader et al., J. Chem. Phys. 161, 044105 (2024)], it has been shown that Rothe's method can be used to solve the time-dependent Schrödinger equation for the hydrogen atom in a strong laser field using time-dependent Gaussian wave packets. Here, we generalize these results, showing that Rothe's method can propagate arbitrary numbers of thawed, complex-valued, Explicitly Correlated Gaussian (ECGs) functions with dense correlation matrices for systems with varying dimensionality. We consider the multidimensional Hénon-Heiles potential and show that the dynamics can be quantitatively reproduced using only 30 Gaussians in 2D and that accurate spectra can be obtained using 20 Gaussians in 2D and 30-40 Gaussians in 3D and 4D. Therefore, the relevant multidimensional dynamics can be described at high quality using only a small number of ECGs that give a very compact representation of the wave function. This efficient representation, along with the demonstrated ability of Rothe's method to propagate Gaussian wave packets in strong fields and ECGs in complex potentials, paves the way for accurate molecular dynamics calculations beyond the Born-Oppenheimer approximation in strong fields., (© 2025 Author(s). Published under an exclusive license by AIP Publishing.)

Recent advances in attosecond science have made it increasingly important to develop stable, reliable, and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in attosecond science is high-harmonic generation, which is challenging to model with fixed Gaussian basis sets, as it produces high-energy electrons, with a resulting rapidly varying and highly oscillatory wave function that extends over dozens of ångström. Recently, Rothe's method, where time evolution is rephrased as an optimization problem, has been applied to the one-dimensional Schrödinger equation. Here, we apply Rothe's method to the hydrogen wave function and demonstrate that thawed, complex-valued Gaussian wave packets with time-dependent width, center, and momentum parameters are able to reproduce spectra obtained from essentially exact grid calculations for high-harmonic generation with only 50-181 Gaussians for field strengths up to 5 × 1014 W/cm2. This paves the way for the inclusion of continuum contributions into real-time, time-dependent electronic-structure theory with Gaussian basis sets for strong fields and eventually accurate simulations of the time evolution of molecules without the Born-Oppenheimer approximation., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wave packets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this Article, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential, we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.

We present a numerical approach to magnetic optical rotation based on real-time time-dependent electronic-structure theory. Not relying on perturbation expansions in the magnetic field strength, the formulation allows us to test the range of validity of the linear relation between the rotation angle per unit path length and the magnetic field strength that was established empirically by Verdet 160 years ago. Results obtained from time-dependent coupled-cluster and time-dependent current density-functional theory are presented for the closed-shell molecules H2, HF, and CO in magnetic fields up to 55 kT at standard temperature and pressure conditions. We find that Verdet's linearity remains valid up to roughly 10-20 kT, above which significant deviations from linearity are observed. Among the three current density-functional approximations tested in this work, the current-dependent Tao-Perdew-Staroverov-Scuseria hybrid functional performs the best in comparison with time-dependent coupled-cluster singles and doubles results for the magnetic optical rotation., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

We propose a novel a posteriori error assessment for the single-reference coupled-cluster (SRCC) method called the S -diagnostic. We provide a derivation of the S -diagnostic that is rooted in the mathematical analysis of different SRCC variants. We numerically scrutinized the S -diagnostic, testing its performance for (1) geometry optimizations, (2) electronic correlation simulations of systems with varying numerical difficulty, and (3) the square-planar copper complexes [CuCl 4 ] 2- , [Cu(NH 3 ) 4 ] 2+ , and [Cu(H 2 O) 4 ] 2+ . Throughout the numerical investigations, the S -diagnostic is compared to other SRCC diagnostic procedures, that is, the T 1 , D 1 , max T 2 , and D 2 diagnostics as well as different indices of multideterminantal and multireference character in coupled-cluster theory. Our numerical investigations show that the S -diagnostic outperforms the T 1 , D 1 , max T 2 and D 2 diagnostics and is comparable to the indices of multideterminantal and multireference character in coupled-cluster theory in their individual fields of applicability. The experiments investigating the performance of the S -diagnostic for geometry optimizations using SRCC reveal that the S -diagnostic correlates well with different error measures at a high level of statistical relevance. The experiments investigating the performance of the S -diagnostic for electronic correlation simulations show that the S -diagnostic correctly predicts strong multireference regimes. The S -diagnostic, moreover, correctly detects the successful SRCC computations for [CuCl 4 ] 2- , [Cu(NH 3 ) 4 ] 2+ , and [Cu(H 2 O) 4 ] 2+ , which have been known to be misdiagnosed by T 1 and D 1 diagnostics in the past. This shows that the S -diagnostic is a promising candidate for an a posteriori diagnostic for SRCC calculations.

Three fully variational formulations of the complete-active space coupled-cluster method are derived. The formulations include the ability to approximate the model vectors by smooth manifolds, thereby opening up the possibility for overcoming the exponential wall of scaling for model spaces of complete-active space type. In particular, model vectors of matrix-product states are considered, and it is argued that the present variational formulation allows not only favorably scaling multireference coupled-cluster calculations but also systematic correction of tailored coupled-cluster calculations and of quantum chemical density-matrix renormalization group methods, which are fast and polynomial scaling but lack the ability to properly resolve dynamical correlation at chemical accuracy. The extension of the variational formulations to the time domain is also discussed, with derivations of abstract evolution equations., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Real-time simulations of laser-driven electron dynamics contain information about molecular optical properties through all orders in response theory. These properties can be extracted by assuming convergence of the power series expansion of induced electric and magnetic multipole moments. However, the accuracy relative to analytical results from response theory quickly deteriorates for higher-order responses due to the presence of high-frequency oscillations in the induced multipole moment in the time domain. This problem has been ascribed to missing higher-order corrections. We here demonstrate that the deviations are caused by nonadiabatic effects arising from the finite-time ramping from zero to full strength of the external laser field. Three different approaches, two using a ramped wave and one using a pulsed wave, for extracting electrical properties from real-time time-dependent electronic-structure simulations are investigated. The standard linear ramp is compared to a quadratic ramp, which is found to yield highly accurate results for polarizabilities, and first and second hyperpolarizabilities, at roughly half the computational cost. Results for the third hyperpolarizability are presented along with a simple, computable measure of reliability., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

The coupled cluster method is considered a gold standard in quantum chemistry, reliably giving energies that are exact within chemical accuracy (1.6 mhartree). However, even in the coupled cluster single-double (CCSD) approximation, where the cluster operator is truncated to include only single and double excitations, the method scales as O(N 6 ) in the number of electrons, and the cluster operator needs to be solved for iteratively, increasing the computation time. Inspired by eigenvector continuation, we present here an algorithm making use of the Gaussian processes that provides an improved initial guess for the coupled cluster amplitudes. The cluster operator is written as a linear combination of sample cluster operators that are obtained at particular sample geometries. By reusing the cluster operators from previous calculations in that way, it is possible to obtain a start guess for the amplitudes that surpasses both MP2 guesses and "previous geometry"-guesses in terms of the number of necessary iterations. As this improved guess is very close to the exact cluster operator, it can be used directly to calculate the CCSD energy to chemical accuracy, giving approximate CCSD energies scaling as O(N 5 ).

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

We present a derivation of real-time (RT) time-dependent orbital-optimized Møller-Plesset (TDOMP2) theory and its biorthogonal companion, time-dependent non-orthogonal OMP2 theory, starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in the time-independent molecular electronic structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from RT simulations, comparing the results with those obtained from conventional time-dependent coupled-cluster singles and doubles (TDCCSD) simulations and from its second-order approximation, TDCC2. We also compare our results with those from CCSD and CC2 linear and quadratic response theories. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, including core excitations where optimized orbitals might be particularly important, frequency-dependent polarizabilities and hyperpolarizabilities from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations.

A cornerstone of current-density functional theory (CDFT) in its paramagnetic formulation is proven. After a brief outline of the mathematical structure of CDFT, the lower semicontinuity and expectation-valuedness of the CDFT constrained-search functional is proven, meaning that there is always a minimizing density matrix in the CDFT constrained-search universal density functional. These results place the mathematical framework of CDFT on the same footing as that of standard DFT.

We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster (CC) theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion CC theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for He and Be atoms and for LiH, CH + , and LiF molecules show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by full configuration interaction (FCI) theory, provided that all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorates. Observing that populations computed from the linear response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations.

A state-specific multireference coupled-cluster (MRCC) method based on Arponen's bivariational principle is presented, the bivar-MRCC method. The method is based on single-reference theory and therefore has a relatively straightforward formulation and modest computational complexity. The main difference from established methods is the bivariational formulation, in which independent parameterizations of the wave function (ket) and its complex conjugate (bra) are made. Importantly, this allows manifest multiplicative separability of the state (exact in the extended bivar-MRECC version of the method and approximate otherwise), and additive separability of the energy, while preserving polynomial scaling of the working equations. A feature of the bivariational principle is that the formal bra and ket references can be included as bivariational parameters, which eliminates much of the bias toward the formal reference. A pilot implementation is described, and extensive benchmark calculations on several standard problems are performed. The results from the bivar-MRCC method are comparable to established state-specific multireference methods. Considering the relative affordability of the bivar-MRCC method, it may become a practical tool for non-experts.

We investigate the numerical stability of time-dependent coupled-cluster theory for many-electron dynamics in intense laser pulses, comparing two coupled-cluster formulations with full configuration interaction theory. Our numerical experiments show that orbital-adaptive time-dependent coupled-cluster doubles (OATDCCD) theory offers significantly improved stability compared with the conventional Hartree-Fock-based time-dependent coupled-cluster singles-and-doubles (TDCCSD) formulation. The improved stability stems from greatly reduced oscillations in the doubles amplitudes, which, in turn, can be traced to the dynamic biorthonormal reference determinants of OATDCCD theory. As long as these are good approximations to the Brueckner determinant, OATDCCD theory is numerically stable. We propose the reference weight as a diagnostic quantity to identify situations where the TDCCSD and OATDCCD theories become unstable.

Recent work has established Moreau-Yosida regularization as a mathematical tool to achieve rigorous functional differentiability in density-functional theory. In this article, we extend this tool to paramagnetic current-density-functional theory, the most common density-functional framework for magnetic field effects. The extension includes a well-defined Kohn-Sham iteration scheme with a partial convergence result. To this end, we rely on a formulation of Moreau-Yosida regularization for reflexive and strictly convex function spaces. The optimal L p -characterization of the paramagnetic current density L 1 ∩ L 3/2 is derived from the N-representability conditions. A crucial prerequisite for the convex formulation of paramagnetic current-density-functional theory, termed compatibility between function spaces for the particle density and the current density, is pointed out and analyzed. Several results about compatible function spaces are given, including their recursive construction. The regularized, exact functionals are calculated numerically for a Kohn-Sham iteration on a quantum ring, illustrating their performance for different regularization parameters.

The formulation of the time-dependent Schrödinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced, inducing physical interpretation of coupled-cluster states in the form of transition probabilities, autocorrelation functions, and explicitly real values for observables, solving interpretation issues which are present in time-dependent coupled-cluster theory and in ground-state calculations of molecular systems under the influence of external magnetic fields. The problem of the numerical integration of the equations of motion is considered, and a critical evaluation of the standard fourth-order Runge-Kutta scheme and the symplectic Gauss integrator of variable order are given, including several illustrative numerical experiments. While the Gauss integrator is stable even for laser pulses well above the perturbation limit, our experiments indicate that a system-dependent upper limit exists for the external field strengths. Above this limit, time-dependent coupled-cluster calculations become very challenging numerically, even in the full configuration interaction limit. The source of these numerical instabilities is shown to be rapid increases of the amplitudes as ultrashort high-intensity laser pulses pump the system out of the ground state into states that are virtually orthogonal to the static Hartree-Fock reference determinant.

In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate formal properties of the used method, such as energy size consistency and the equivalence of linked and unlinked formulation. The existing mathematical analysis is here elaborated in a quantum chemical framework. In particular, we highlight the use of what we have defined as a complete active space-external space gap describing the basis splitting between the complete active space and the external part generalizing the concept of a HOMO-LUMO gap. Furthermore, the behavior of the energy error for an optimal basis splitting, i.e., an active space choice minimizing the density matrix renormalization group-tailored coupled-cluster singles doubles error, is discussed. We show numerical investigations on the robustness with respect to the bond dimensions of the single orbital entropy and the mutual information, which are quantities that are used to choose a complete active space. Moreover, the dependence of the ground-state energy error on the complete active space has been analyzed numerically in order to find an optimal split between the complete active space and external space by minimizing the density matrix renormalization group-tailored coupled-cluster error.

A detailed account of the Kohn-Sham (KS) algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy-Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows us to rigorously introduce, in contrast to the common unregularized approach, a well-defined KS iteration scheme. Convergence in a weak sense is then proven. This generalized formulation is applicable to a wide range of different density-functional theories and possibly even to models outside of quantum mechanics.

Computer Tomography (CT) and Magnetic Resonance Imaging (MRI) may be useful tools in assessment of age of an individual. This article presents a review of published studies using CT or MRI in dental age estimation. They were published between July 2004 and September 2017 investigating different types of teeth, methods and formulae for age estimation. Twenty-seven articles were included. The different studies show good results, and it seems that a combination of different types of teeth, methods (depending on the degree of root formation) and cooperation between different disciplines in the same study gives a higher accuracy.

We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional density functional theory and Current-Density Functional Theory (CDFT). In the intermediate theory, which we term linear vector potential-DFT (LDFT), the basic variables are the density, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre-Fenchel transformations are constructed. Many theoretical issues in CDFT find simplified analogs in LDFT. We prove results concerning N-representability, Hohenberg-Kohn-like mappings, existence of minimizers in the constrained-search expression, and a restricted analog to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.

Background: For children with disputed date of birth, age assessments based on skeletal and dental development are recommended., Aim: The aim of this retrospective study was to compare and contrast the results of age assessments from these two methods performed on unaccompanied asylum seeking children in Norway. In addition the aim of the analysis was to see if the skeletal age assessment from hand-wrist was operator sensitive., Materials and Methods: Age assessments performed from January 2010 to December 2014 were analysed. Skeletal development of hand-wrist was graded according to Greulich and Pyle (1959). Dental development of the wisdom teeth was scored on orthopantomograms according to Moorrees, Fanning and Hunt (1963) and age assessed from tables published by Liversidge (2008) and Haavikko (1970). In the statistical analysis agreement between the two age assessments was defined according to the asylum seeker's age being assessed to be older or younger than 18 years. The statistical analysis included 3333 boys and 486 girls., Results: The agreement was 83% for boys and 79% for girls. Approximately 70% of the boys and girls were 18 years or older by both methods. It was more common that the skeletal age was assessed older than 18 years and dental age younger than 18 years for both genders. It could be demonstrated that the age assessment based on skeletal maturation was not operator sensitive., Conclusion: The analyses demonstrate that there is good agreement between the two age assessments, but a method to combine the results would increase the reliability of the age assessments.

Background: The nature of differences in the timing of tooth formation between ethnic groups is important when estimating age., Aim: To calculate age of transition of the mandibular third (M3) molar tooth stages from archived dental radiographs from sub-Saharan Africa, Malaysia, Japan and two groups from London UK (Whites and Bangladeshi)., Materials and Methods: The number of radiographs was 4555 (2028 males, 2527 females) with an age range 10-25 years. The left M3 was staged into Moorrees stages. A probit model was fitted to calculate mean ages for transitions between stages for males and females and each ethnic group separately. The estimated age distributions given each M3 stage was calculated. To assess differences in timing of M3 between ethnic groups, three models were proposed: a separate model for each ethnic group, a joint model and a third model combining some aspects across groups. The best model fit was tested using Bayesian and Akaikes information criteria (BIC and AIC) and log likelihood ratio test., Results: Differences in mean ages of M3 root stages were found between ethnic groups, however all groups showed large standard deviation values. The AIC and log likelihood ratio test indicated that a separate model for each ethnic group was best. Small differences were also noted between timing of M3 between males and females, with the exception of the Malaysian group. These findings suggests that features of a reference data set (wide age range and uniform age distribution) and a Bayesian statistical approach are more important than population specific convenience samples to estimate age of an individual using M3., Conclusion: Some group differences were evident in M3 timing, however, this has some impact on the confidence interval of estimated age in females and little impact in males because of the large variation in age.

Importance: The need to rely on proper, simple, and accurate methods for age estimation in adults is still a world-wide issue. It has been well documented that teeth are more resistant than bones to the taphonomic processes, and that the use of methods for age estimation based on dental imaging assessment are not only less invasive than those based on osseous analysis, but also have shown similar or superior accuracy in adults., Objectives: To summarise the results of some of the recently most recently cited methods for dental age estimation in adults, based on odontometric dental imaging analysis, to establish which is more accurate, accessible, and simple., Evidence Review: A literature search from several databases was conducted from January 1995 to July 2016 with previously defined inclusion criteria., Conclusion: Based on the findings of this review, it could be possible to suggest pulp/tooth area ratio calculation from first, upper canines and other single rooted teeth (lower premolars, upper central incisors), and a specific statistical analysis that considers the non-linear production of secondary dentine with age, as a reliable, easy, faster, and predictable method for dental age estimation in adults. The second recommended method is the pulp/tooth width-length ratio calculation. The use of specific population formulae is recommended, but to include data of individuals from different groups of population in the same analysis is not discouraged. A minimum sample size of at least 120 participants is recommended to obtain more reliable results. Methods based on volume calculation are time consuming and still need improvement., (Copyright © 2017 Elsevier B.V. All rights reserved.)

Objective: To test the variability of the volume measurements when different segmentation methods are applied in pulp volume reconstruction., Materials and Methods: Osirix® and ITK-SNAP software were used. Different segmentation methods (Part A) and volume approaches (Part B) were tested in a sample of 21 dental CBCT's from upper canines. Different combinations of the data set were also tested on one lower molar and one upper canine (Part C) to determine the variability of the results when automatic segmentation is performed., Results: Although the obtained results show correlation among them(r > 0.75), there is no evidence that these methods are sensitive enough to detect small volume changes in structures such as the dental pulp canal (Part A and Part B). Automatic segmentation is highly susceptible to be affected by small variations in the setting parameters (Part C)., Conclusions: Although the volumetric reconstruction and pulp/tooth volume ratio has not shown better results than methods based on dental radiographs, it is worth to persevere with the research in this area with new development in imaging techniques.

The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible density functionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal density functional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.

The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density-in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg-Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau-Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ((ε)E, (ε)F) that converge to (E, F) pointwise everywhere as ε → 0(+), and such that (ε)F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau-Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy (ε)E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ((ε)E, (ε)F). The Moreau-Yosida regularization therefore allows for an exact, differentiable formulation of density-functional theory. In particular, taking advantage of the differentiability of (ε)F, a rigorous formulation of Kohn-Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn-Sham theory.

The curse of dimensionality (COD) limits the current state-of-the-art ab initio propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schrödinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster, and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given.

The clinical art of applying scientific knowledge to a patient's circumstances of suffering is especially challenging when practicing psychotherapy with people who are experiencing chronic pain. Health psychology has made substantial contributions by showing that psychosocial factors are essential in explaining the phenomenon of pain and, particularly, its chronic progression to debilitating degrees. In addition, clinical health psychology has developed empirically supported treatments that improve the lives of chronic pain sufferers across many dimensions. This article is not concerned with reviewing that evidence or the treatment programs, but with noting some issues pain management psychotherapists may face in using this knowledge effectively to improve the lives of their patients.

Rationale: Critics have called into question findings from double-blind placebo-controlled studies because subjects are given drug administration instructions informing them of a placebo condition. The assertion that these drug administration instructions bias estimates of effectiveness has undergone surprisingly little empirical investigation., Objectives: The primary objective of this study was to determine whether drug administration instructions informing subjects of a placebo condition affect the drug response and affect the saliva concentration of the stimulant., Methods: We assessed caffeine responses and levels of saliva concentration of caffeine in 52 subjects who were randomly assigned to receive one of two drug administration instructions: (a) placebo-informed instructions (i.e., individuals informed of the placebo) analogous to those used in double-blind studies and (b) placebo-uninformed instructions (i.e., individuals informed they are taking an active stimulant)., Results: On most measures (systolic blood pressure, heart rate, hand steadiness, reaction time, fatigue, and tension), drug administration instructions did not significantly influence caffeine response. Instructions also had no significant effect on saliva concentration of caffeine. However, only individuals who were uninformed of the placebo condition showed significant diastolic blood pressure and vigor increases with 125 mg caffeine, and significant hand steadiness impairment and vigor increases with 325 mg caffeine compared to placebo., Conclusions: These overall findings suggest that a limited bias is introduced by drug administration instructions. The results do not support any suggestion that information about the existence of a placebo condition dramatically influences conclusions drawn about drug responses in placebo-controlled trials.

In earlier research, Rossini, Wygonik, Barrett, and Friedman (1994) demonstrated that the Thurstone Test of Mental Alertness (TMA) is a valid, brief measure of intelligence by comparing it to the Wechsler Scale of Adult Intelligence-Revised, which was at that time the "gold standard" of IQ assessment. Since that study, the WAIS has again been revised and reissued in a third edition, the WAIS-III. We assessed the relationship between scores on the Thurstone Test of Mental Alertness and this latest WAIS test to see if there is still a predictive relationship between the two tests. Correlations between the two tests and the accuracy of TMA point estimates of IQ indicate that the Thurstone Test of Mental Alertness remains a viable brief measure of adult intelligence.

The Positive and Negative Affect Scale (PANAS), a brief measure of Positive and Negative Affect, may be useful in assessing mood of medical patients because it does not include somatic items frequently confounded with medical conditions. In previous research Positive and Negative Affect have been independent and uncorrelated, and Negative Affect but not Positive Affect has been positively correlated with somatic symptoms. However, relationships between variables may vary in different populations, and there is relatively little information on Positive and Negative Affect in medical patients. In the current study, the PANAS was used to assess the relationships among Positive Affect, Negative Affect, and somatic symptoms and pain in a medically ill hospital population. Positive and Negative Affect scores were positively correlated and for patients reporting pain, Positive Affect scores were positively correlated with pain intensity. Results from this and other studies indicate that Positive and Negative Affect are independent but in some populations may be correlated; positive affects such as hopefulness may co-occur with both somatic complaints and psychological distress.

Research over the last decade has confirmed that facial injuries caused by violence occur most frequently among young males, often under the influence of alcohol, and less frequently in women and children following domestic violence. Evidence of injuries may be used in court or in claims for compensation, and must be carefully documented. Facial asymmetry, deviation of the mandible in opening, altered occlusion and/or abrasions under the chin may be indications of jaw fractures; such patients are referred to oral surgery units for further treatment. Lacerations and ulceration in the oral mucous membrane should be treated as skin wounds. A fractured tooth should be referred to a general dental practitioner. Luxated teeth should be carefully replaced and immediately referred to a dentist for fixation. Completely avulsed teeth should immediately be replaced, preferably at the site of the accident, or immediately upon arrival at the clinic. Prompt referral to a dental practitioner for follow-up treatment is essential for the success of replantations. Additional documentation of the injury may be provided by photographs, radiographs and drawings. The letter of referral to the dentist should contain the following information: data on the patient, the circumstances, clinical findings, treatment performed and prescriptions given, together with advice given to the patient.

Research has identified a relationship between a history of physical and/or sexual abuse and a range of psychological, functional, and physical factors; however, the nature of this relationship has not been tested. We hypothesize two different mechanisms through which an abuse history could influence later life distress and dysfunction. A history of abuse could increase an individual's vulnerability to emotional distress or could increase an individual's tendency to attend, amplify, and over-interpret somatic symptoms. The purpose of this study was to test the influence of emotional distress and somatic focus on the relationship between a history of physical and/or sexual abuse and later chronic painrelated disability in patients with temporomandibular disorders. The subjects were 139 female patients evaluated at a facial pain clinic. Of the 139 subjects, 49% (n = 69) reported a history of physical and/or sexual abuse. Abused subjects reported significantly higher levels of anxiety, depression, and somatic symptoms than nonabused subjects. Path analysis with latent variables, using the LISREL-8 (Scientific Software International, Inc., Chicago, Illinois) statistical program was used to test the hypothesized relationships. When emotional distress and somatic focus were tested as mediators, the path coefficient from somatic focus to physical functioning was significant (beta = -0.38) while the path coefficient from negative emotion to physical functioning was not significant. These results favor somatization as the hypothesized mechanism over the emotional distress vulnerability hypotheses.

Dental age was studied in a sample of 261 Norwegian children by using the maturity standards of Demirjian & Goldstein (1976) to examine the applicability of these standards as a reference for overall dental maturity in a Norwegian population. The sample comprised 128 boys and 133 girls included in 'the Oslo Growth Material', from whom orthopantomograms (total, 783) had been longitudinally obtained, with intervals of about 3 years and covering 3 age spans (5.5-6.5 years, 8.5-9.5 years, and 11.5-12.5 years), each divided into 3 half-year age groups. Reliability was analyzed by repeated assessments of 134 of the radiographs, and the overall mean difference between duplicate dental age determinations was 0.5 months for intra- and 1.8 months for inter-examiner comparisons. The Norwegian children were generally somewhat advanced in dental maturity compared with the French-Canadian reference sample. Among the boys the mean difference between dental age and chronologic age varied in the different age groups from 1.5 to 4.0 months. Among the girls the difference increased with age, varying from 0 to 3.5 months in the younger age groups (5.5 to 9.0 years) and from 4.5 to 7.5 months in the age groups 9.5 years and above. The variability in individual dental age was marked and increased with age. For the older age groups 95% of the individual age estimates were within +/-2 years of the real age. The applied standards appear to be adequate for studying dental age in groups of children from a Norwegian population. Given the considerable individual variation in dental maturity, estimation of chronologic age in individual children should be supplemented by other indicators of biologic maturity.