10,170 research outputs found
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 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
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
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
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
Love kills: Simulations in Penna Ageing Model
The standard Penna ageing model with sexual reproduction is enlarged by
adding additional bit-strings for love: Marriage happens only if the male love
strings are sufficiently different from the female ones. We simulate at what
level of required difference the population dies out.Comment: 14 pages, including numerous figure
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