Equations in the Hadamard ring of rational functions

Let k be a number field. It is well known that the set of sequences composed by Taylor coefficients of rational functions over k is closed under component-wise operations, and so it can be equipped with a ring structure. A conjecture due to Pisot asks if (after enlarging the field) one can take d-th roots in this ring, provided d-th roots of coefficients can be taken in k. This was proved true in a preceding paper of the second author; in this article we generalize this result to more general equations, monic in Y, where the former case can be recovered for g(X,Y)=X^d-Y=0. Combining this with the Hadamard quotient theorem by Pourchet and Van der Poorten, we are able to get rid of the monic restriction, and have a theorem that generalizes both results.Comment: 18 pages, LaTe

Evaluation of the accuracy of a patient-specific instrumentation

Patient-specific instruments (PSI) has been introduced with the aim to reduce the overall costs of the implants, minimizing the size and number of instruments required, and also reducing surgery time. The aim of this study was to perform a review of the current literature, as well as to report about our personal experience, to assess reliability and accuracy of patient specific instrument system in total knee arthroplasty (TKA). A literature review was conducted of PSI system reviewing articles related to coronal alignment, clinical knee and function scores, cost, patient satisfaction and complications. Studies have reported incidences of coronal alignment ≥3° from neutral in TKAs performed with patient-specific cutting guides ranging from 6% to 31%. PSI seem not to be able to result in the same degree of accuracy as for the CAS system, while comparing well with standard manual technique with respect to component positioning and overall lower axis, in particular in the sagittal plane. In cases in which custom-made cutting jigs were used, we recommend performing an accurate control of the alignment before and after any cuts and in any further step of the procedure, in order to avoid possible outliers

Koopmans-compliant spectral functionals for extended systems

Koopmans-compliant functionals have been shown to provide accurate spectral properties for molecular systems; this accuracy is driven by the generalized linearization condition imposed on each charged excitation - i.e. on changing the occupation of any orbital in the system, while accounting for screening and relaxation from all other electrons. In this work we discuss the theoretical formulation and the practical implementation of this formalism to the case of extended systems, where a third condition, the localization of Koopmans' orbitals, proves crucial to reach seamlessly the thermodynamic limit. We illustrate the formalism by first studying one-dimensional molecular systems of increasing length. Then, we consider the band gaps of 30 paradigmatic solid-state test cases, for which accurate experimental and computational results are available. The results are found to be comparable with the state-of-the-art in diagrammatic techniques (self-consistent many-body perturbation theory with vertex corrections), notably using just a functional formulation for spectral properties and the physics of the generalized-gradient approximation; when ionization potentials are compared, the results are roughly twice as accurate.Comment: 9 pages, 3 figures, 1 supporting informatio

Many-body correlations and coupling in benzene-dithiol junctions

Most theoretical studies of nanoscale transport in molecular junctions rely on the combination of the Landauer formalism with Kohn-Sham density functional theory (DFT) using standard local and semilocal functionals to approximate exchange and correlation effects. In many cases, the resulting conductance is overestimated with respect to experiments. Recent works have demonstrated that this discrepancy may be reduced when including many-body corrections on top of DFT. Here we study benzene-dithiol (BDT) gold junctions and analyze the effect of many-body perturbation theory (MBPT) on the calculation of the conductance with respect to different bonding geometries. We find that the many-body corrections to the conductance strongly depend on the metal-molecule coupling strength. In the BDT junction with the lowest coupling, many-body corrections reduce the overestimation on the conductance to a factor two, improving the agreement with experiments. In contrast, in the strongest coupling cases, many-body corrections on the conductance are found to be sensibly smaller and standard DFT reveals a valid approach.Comment: 9 pages, 4 figure

Screening in orbital-density-dependent functionals

Electronic-structure functionals that include screening effects, such as Hubbard or Koopmans' functionals, require to describe the response of a system to the fractional addition or removal of an electron from an orbital or a manifold. Here, we present a general method to incorporate screening based on linear-response theory, and we apply it to the case of the orbital-by-orbital screening of Koopmans' functionals. We illustrate the importance of such generalization when dealing with challenging systems containing orbitals with very different chemical character, also highlighting the simple dependence of the screening on the localization of the orbitals. We choose a set of 46 transition-metal complexes for which experimental data and accurate many-body perturbation theory calculations are available. When compared to experiment, results for ionization potentials show a very good performance with a mean absolute error of $~0.2$ eV, comparable to the most accurate many-body perturbation theory approaches. These results reiterate the role of Koopmans' compliant functionals as simple and accurate quasiparticle approximations to the exact spectral functional, bypassing diagrammatic expansions and relying only on the physics of the local density or generalized-gradient approximation

In-out versus out-in technique for ACL reconstruction. a prospective clinical and radiological comparison

Background: Several studies have recently shown better restoration of normal knee kinematics and improvement of rotator knee stability after reconstruction with higher femoral tunnel obliquity. The aim of this study is to evaluate tunnel obliquity, length, and posterior wall blowout in single-bundle anterior cruciate ligament (ACL) reconstruction, comparing the transtibial (TT) technique and the out–in (OI) technique. Materials and methods: Forty consecutive patients operated on for ACL reconstruction with hamstrings were randomly divided into two groups: group A underwent a TT technique, while group B underwent an OI technique. At mean follow-up of 10 months, clinical results and obliquity, length, and posterior wall blowout of femoral tunnels in sagittal and coronal planes using computed tomography (CT) scan were assessed. Results: In sagittal plane, femoral tunnel obliquity was 38.6 ± 10.2° in group A and 36.6 ± 11.8° in group B (p = 0.63). In coronal plane, femoral tunnel obliquity was 57.8 ± 5.8° in group A and 35.8 ± 8.2° in group B (p = 0.009). Mean tunnel length was 40.3 ± 1.2 mm in group A and 32.9 ± 2.3 mm in group B (p = 0.01). No cases of posterior wall compromise were observed in any patient of either group. Clinical results were not significantly different between the two groups. Conclusions: The OI technique provides greater obliquity of the femoral tunnel in coronal plane, along with satisfactory length of the tunnel and lack of posterior wall compromise. Level of evidence: II, prospective study