Quantal Density Functional Theory of Degenerate States

The treatment of degenerate states within Kohn-Sham density functional theory (KS-DFT) is a problem of longstanding interest. We propose a solution to this mapping from the interacting degenerate system to that of the noninteracting fermion model whereby the equivalent density and energy are obtained via the unifying physical framework of quantal density functional theory (Q-DFT). We describe the Q-DFT of \textit{both} ground and excited degenerate states, and for the cases of \textit{both} pure state and ensemble v-representable densities. This then further provides a rigorous physical interpretation of the density and bidensity energy functionals, and of their functional derivatives, of the corresponding KS-DFT. We conclude with examples of the mappings within Q-DFT.Comment: 10 pages. minor changes made. to appear in PR

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve functional tumour-associated blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation medi- ated by vascular targeting agents that induce occlusion/collapse of tumour blood vessels. In contrast, the therapeutic intention of normalising the abnormal structure and function of tumour vascular net- works, e.g. via alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and radiation therapy efficacy. Although both strategies have shown therapeutic potential, it remains unclear why they often fail to control glioma invasion into the surrounding healthy brain tissue. To shed light on this issue, we propose a mathematical model of glioma invasion focusing on the interplay between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells and modulations of the functional tumour vasculature. Vaso-modulatory interventions are modelled by varying the degree of vaso-occlusion. We discovered the existence of a critical cell proliferation/diffusion ratio that separates glioma invasion re- sponses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the tumour front speed and increase the infiltration width, for those in the other regime the invasion speed increases and infiltration width decreases. We show how these in silico findings can be used to guide individualised approaches of vaso-modulatory treatment strategies and thereby improve success rates

The range of the tangential Cauchy-Riemann system on a CR embedded manifold

We prove that every compact, pseudoconvex, orientable, CR manifold of \C^n, bounds a complex manifold in the $C^\infty$ sense. In particular, the tangential Cauchy-Riemann system has closed range

Variable Selection and Model Averaging in Semiparametric Overdispersed Generalized Linear Models

We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or flexibly. When the variance term is null we obtain a generalized additive model, which becomes a generalized linear model if the predictors enter the mean linearly. The model is estimated using Markov chain Monte Carlo simulation and the methodology is illustrated using real and simulated data sets.Comment: 8 graphs 35 page

Calibrated Generalized Bayesian Inference

We provide a simple and general solution to the fundamental open problem of inaccurate uncertainty quantification of Bayesian inference in misspecified or approximate models, and of generalized Bayesian posteriors more generally. While existing solutions are based on explicit Gaussian posterior approximations, or computationally onerous post-processing procedures, we demonstrate that correct uncertainty quantification can be achieved by substituting the usual posterior with an alternative posterior that conveys the same information. This solution applies to both likelihood-based and loss-based posteriors, and we formally demonstrate the reliable uncertainty quantification of this approach. The new approach is demonstrated through a range of examples, including generalized linear models, and doubly intractable models.Comment: This paper is a substantially revised version of arXiv:2302.06031v1. This revised version has a slightly different focus, additional examples, and theoretical results, as well as different author

Statistical mechanics of Floquet systems: the pervasive problem of near degeneracies

The statistical mechanics of periodically driven ("Floquet") systems in contact with a heat bath exhibits some radical differences from the traditional statistical mechanics of undriven systems. In Floquet systems all quasienergies can be placed in a finite frequency interval, and the number of near degeneracies in this interval grows without limit as the dimension N of the Hilbert space increases. This leads to pathologies, including drastic changes in the Floquet states, as N increases. In earlier work these difficulties were put aside by fixing N, while taking the coupling to the bath to be smaller than any quasienergy difference. This led to a simple explicit theory for the reduced density matrix, but with some major differences from the usual time independent statistical mechanics. We show that, for weak but finite coupling between system and heat bath, the accuracy of a calculation within the truncated Hilbert space spanned by the N lowest energy eigenstates of the undriven system is limited, as N increases indefinitely, only by the usual neglect of bath memory effects within the Born and Markov approximations. As we seek higher accuracy by increasing N, we inevitably encounter quasienergy differences smaller than the system-bath coupling. We therefore derive the steady state reduced density matrix without restriction on the size of quasienergy splittings. In general, it is no longer diagonal in the Floquet states. We analyze, in particular, the behavior near a weakly avoided crossing, where quasienergy near degeneracies routinely appear. The explicit form of our results for the denisty matrix gives a consistent prescription for the statistical mechanics for many periodically driven systems with N infinite, in spite of the Floquet state pathologies.Comment: 31 pages, 3 figure

Electronic structure and magnetism in X_xW_{1-x}O_3 (X=Nb,V,Re) from supercell calculations

Some doped semiconductors have recently been shown to display superconductivity or weak ferromagnetism. Here we investigate the electronic structure and conditions for magnetism in a supercells of cubic XW_{26}O_{81}, where X=Nb,V and Re. The undoped material is an insulator, and although the slightly doped material is a metal, it is far from the Stoner criterion of magnetism. The conditions of a localized density-of-states which varies rapidly with the energy, resemble those of doped hexaborides. The virtual crystal approximation is used to vary the doping level. A small moment appears if the Fermi energy coincides with a large derivative of the DOS.Comment: 5 pages, 5 figures, to appear in JMM

Reconstitution of T cell receptor signaling in ZAP-70-deficient cells by retroviral transduction of the ZAP-70 gene.

A variant of severe combined immunodeficiency syndrome (SCID) with a selective inability to produce CD8 single positive T cells and a signal transduction defect in peripheral CD4+ cells has recently been shown to be the result of mutations in the ZAP-70 gene. T cell receptor (TCR) signaling requires the association of the ZAP-70 protein tyrosine kinase with the TCR complex. Human T cell leukemia virus type I-transformed CD4+ T cell lines were established from ZAP-70-deficient patients and normal controls. ZAP-70 was expressed and appropriately phosphorylated in normal T cell lines after TCR engagement, but was not detected in T cell lines from ZAP-70-deficient patients. To determine whether signaling could be reconstituted, wild-type ZAP-70 was introduced into deficient cells with a ZAP-70 retroviral vector. High titer producer clones expressing ZAP-70 were generated in the Gibbon ape leukemia virus packaging line PG13. After transduction, ZAP-70 was detected at levels equivalent to those observed in normal cells, and was appropriately phosphorylated on tyrosine after receptor engagement. The kinase activity of ZAP-70 in the reconstituted cells was also appropriately upregulated by receptor aggregation. Moreover, normal and transduced cells, but not ZAP-70-deficient cells, were able to mobilize calcium after receptor ligation, indicating that proximal TCR signaling was reconstituted. These results indicate that this form of SCID may be corrected by gene therapy