Kinetic-Energy Density-Functional Theory on a Lattice

We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn-Sham (keKS) scheme on a lattice and show that by including more observables explicitly in a density-functional approach already simple approximation strategies lead to very accurate results. Here we promote the kinetic-energy density to a fundamental variable along side the density and show for specific cases (analytically and numerically) that there is a one-to-one correspondence between the external pair of on-site potential and site-dependent hopping and the internal pair of density and kinetic-energy density. Based on this mapping we establish two unknown effective fields, the mean-field exchange-correlation potential and the mean-field exchange-correlation hopping, that force the keKS system to generate the same kinetic-energy density and density as the fully interacting one. We show, by a decomposition based on the equations of motions for the density and the kinetic-energy density, that we can construct simple orbital-dependent functionals that outperform the corresponding exact-exchange Kohn-Sham (KS) approximation of standard density-functional theory. We do so by considering the exact KS and keKS systems and compare the unknown correlation contributions as well as by comparing self-consistent calculations based on the mean-field exchange for the keKS and the exact-exchange for the KS system, respectively

Exploring Foundations of Time-Independent Density Functional Theory for Excited-States

Based on the work of Gorling and that of Levy and Nagy, density-functional formalism for many Fermionic excited-states is explored through a careful and rigorous analysis of the excited-state density to external potential mapping. It is shown that the knowledge of the ground-state density is a must to fix the mapping from an excited-state density to the external potential. This is the excited-state counterpart of the Hohenberg-Kohn theorem, where instead of the ground-state density the density of the excited-state gives the true many-body wavefunctions of the system. Further, the excited-state Kohn-Sham system is defined by comparing it's non-interacting kinetic energy with the true kinetic energy. The theory is demonstrated by studying a large number of atomic systems.Comment: submitted to J. Chem. Phy

Local-density approximation for exchange energy functional in excited-state density functional theory

An exchange energy functional is proposed and tested for obtaining a class of excited-state energies using density functional formalism. The functional is the excited-state counterpart of the local-density approximation functional for the ground state. It takes care of the state dependence of the energy functional and leads to highly accurate excitation energies

Exchange and Correlation Kernels at the Resonance Frequency -- Implications for Excitation Energies in Density-Functional Theory

Specific matrix elements of exchange and correlation kernels in time-dependent density-functional theory are computed. The knowledge of these matrix elements not only constraints approximate time-dependent functionals, but also allows to link different practical approaches to excited states, either based on density-functional theory, or on many-body perturbation theory, despite the approximations that have been performed to derive them.Comment: Submitted to Phys. Rev. Lett. (February 4, 1999). Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Immune Checkpoint Inhibitors Targeting the PD-1/PD-L1 Pathway in Advanced, Recurrent Endometrial Cancer: A Scoping Review with SWOT Analysis

Results of recent clinical trials using the immune check point inhibitors (ICI) pembrolizumab or dostarlimab with/without lenvatinib has led to their approval for specific molecular subgroups of advanced recurrent endometrial cancer (EC). Herein, we summarise the clinical data leading to this first tissue-agnostic approval. As this novel therapy is not yet available in the United Kingdom standard care setting, we explore the strengths, weaknesses, opportunities, and threats (SWOT) of ICI treatment in EC. Major databases were searched focusing on clinical trials using programmed cell death protein 1 (PD-1) and its ligand (PD-L1) ICI which ultimately contributed to anti-PD-1 approval in EC. We performed a data quality assessment, reviewing survival and safety analysis. We included 15 studies involving 1609 EC patients: 458 with mismatch repair deficiency (MMRd)/microsatellite instability-high (MSI-H) status and 1084 with mismatch repair proficiency/microsatellite stable (MMRp/MSS) status. Pembrolizumab/dostarlimab have been approved for MMRd ECs, with the addition of lenvatinib for MMRp cases in the recurrent setting. Future efforts will focus on the pathological assessment of biomarkers to determine molecular phenotypes that correlate with response or resistance to ICI in order to identify patients most likely to benefit from this treatment

Imaging cervical cytology with scanning near-field optical microscopy (SNOM) coupled with an IR-FEL

Cervical cancer remains a major cause of morbidity and mortality among women, especially in the developing world. Increased synthesis of proteins, lipids and nucleic acids is a pre-condition for the rapid proliferation of cancer cells. We show that scanning near-field optical microscopy, in combination with an infrared free electron laser (SNOM-IR-FEL), is able to distinguish between normal and squamous low-grade and high-grade dyskaryosis, and between normal and mixed squamous/glandular pre-invasive and adenocarcinoma cervical lesions, at designated wavelengths associated with DNA, Amide I/II and lipids. These findings evidence the promise of the SNOM-IR-FEL technique in obtaining chemical information relevant to the detection of cervical cell abnormalities and cancer diagnosis at spatial resolutions below the diffraction limit (?0.2 \ensuremathμm). We compare these results with analyses following attenuated total reflection Fourier-transform infrared (ATR-FTIR) spectroscopy; although this latter approach has been demonstrated to detect underlying cervical atypia missed by conventional cytology, it is limited by a spatial resolution of ~3 \ensuremathμm to 30 \ensuremathμm due to the optical diffraction limit

Foundations of self-consistent particle-rotor models and of self-consistent cranking models

The Kerman-Klein formulation of the equations of motion for a nuclear shell model and its associated variational principle are reviewed briefly. It is then applied to the derivation of the self-consistent particle-rotor model and of the self-consistent cranking model, for both axially symmetric and triaxial nuclei. Two derivations of the particle-rotor model are given. One of these is of a form that lends itself to an expansion of the result in powers of the ratio of single-particle angular momentum to collective angular momentum, that is essentual to reach the cranking limit. The derivation also requires a distinct, angular-momentum violating, step. The structure of the result implies the possibility of tilted-axis cranking for the axial case and full three-dimensional cranking for the triaxial one. The final equations remain number conserving. In an appendix, the Kerman-Klein method is developed in more detail, and the outlines of several algorithms for obtaining solutions of the associated non-linear formalism are suggested.Comment: 29 page

Feature Selection is Critical for 2-Year Prognosis in Advanced Stage High Grade Serous Ovarian Cancer by Using Machine Learning

Introduction Accurate prediction of patient prognosis can be especially useful for the selection of best treatment protocols. Machine Learning can serve this purpose by making predictions based upon generalizable clinical patterns embedded within learning datasets. We designed a study to support the feature selection for the 2-year prognostic period and compared the performance of several Machine Learning prediction algorithms for accurate 2-year prognosis estimation in advanced-stage high grade serous ovarian cancer (HGSOC) patients. Methods The prognosis estimation was formulated as a binary classification problem. Dataset was split into training and test cohorts with repeated random sampling until there was no significant difference (p = 0.20) between the two cohorts. A ten-fold cross-validation was applied. Various state-of-the-art supervised classifiers were used. For feature selection, in addition to the exhaustive search for the best combination of features, we used the-chi square test of independence and the MRMR method. Results Two hundred nine patients were identified. The model's mean prediction accuracy reached 73%. We demonstrated that Support-Vector-Machine and Ensemble Subspace Discriminant algorithms outperformed Logistic Regression in accuracy indices. The probability of achieving a cancer-free state was maximised with a combination of primary cytoreduction, good performance status and maximal surgical effort (AUC 0.63). Standard chemotherapy, performance status, tumour load and residual disease were consistently predictive of the mid-term overall survival (AUC 0.63–0.66). The model recall and precision were greater than 80%. Conclusion Machine Learning appears to be promising for accurate prognosis estimation. Appropriate feature selection is required when building an HGSOC model for 2-year prognosis prediction. We provide evidence as to what combination of prognosticators leads to the largest impact on the HGSOC 2-year prognosis