293 research outputs found
Landau gauge Yang-Mills correlation functions
We investigate Landau gauge Yang-Mills theory in a systematic vertex
expansion scheme for the effective action with the functional renormalisation
group. Particular focus is put on the dynamical creation of the gluon mass gap
at non-perturbative momenta and the consistent treatment of quadratic
divergences. The non-perturbative ghost and transverse gluon propagators as
well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices
are calculated self-consistently with the classical action as only input. The
apparent convergence of the expansion scheme is discussed and within the
errors, our numerical results are in quantitative agreement with available
lattice results.Comment: 20 pages, 13 figure
Diffusing wild type and sterile mosquitoes in an optimal control setting
This paper develops an optimal control framework to investigate the introduction of sterile type mosquitoes to reduce the overal moquito population. As is well known, mosquitoes are vectors of disease. For instance the WHO lists, among other diseases, Malaria, Dengue Fever, Rift Valley Fever, Yellow Fever, Chikungunya Fever and Zika. [http://www.who.int/mediacentre/factsheets/fs387/en/ ] The goal is to establish the existence of a solution given an optimal sterilization protocol as well as to develop the corresponding optimal control representation to minimize the infiltrating mosquito population while minimizing fecundity and the number of sterile type mosquitoes introduced into the environment per unit time. This paper incorporates the diffusion of the mosquitoes into the controlled model and presents a number of numerical simulations
High multipole transitions in NIXS: valence and hybridization in 4f systems
Momentum-transfer (q) dependent non-resonant inelastic x-ray scattering
measurements were made at the N4,5 edges for several rare earth compounds. With
increasing q, giant dipole resonances diminish, to be replaced by strong
multiplet lines at lower energy transfer. These multiplets result from two
different orders of multipole scattering and are distinct for systems with
simple 4f^0 and 4f^1 initial states. A many-body theoretical treatment of the
multiplets agrees well with the experimental data on ionic La and Ce phosphate
reference compounds. Comparing measurements on CeO2 and CeRh3 to the theory and
the phosphates indicates sensitivity to hybridization as observed by a
broadening of 4f^0-related multiplet features. We expect such strong, nondipole
features to be generic for NIXS from f-electron systems
The local electronic structure of alpha-Li3N
New theoretical and experimental investigation of the occupied and unoccupied
local electronic density of states (DOS) are reported for alpha-Li3N. Band
structure and density functional theory calculations confirm the absence of
covalent bonding character. However, real-space full-multiple-scattering
(RSFMS) calculations of the occupied local DOS finds less extreme nominal
valences than have previously been proposed. Nonresonant inelastic x-ray
scattering (NRIXS), RSFMS calculations, and calculations based on the
Bethe-Salpeter equation are used to characterize the unoccupied electronic
final states local to both the Li and N sites. There is good agreement between
experiment and theory. Throughout the Li 1s near-edge region, both experiment
and theory find strong similarities in the s- and p-type components of the
unoccupied local final density of states projected onto an orbital angular
momentum basis (l-DOS). An unexpected, significant correspondence exists
between the near-edge spectra for the Li 1s and N 1s initial states. We argue
that both spectra are sampling essentially the same final density of states due
to the combination of long core-hole lifetimes, long photoelectron lifetimes,
and the fact that orbital angular momentum is the same for all relevant initial
states. Such considerations may be generically applicable for low atomic number
compounds.Comment: 34 pages, 7 figures, 1 tabl
A theoretical study of the response of vascular tumours to different types of chemotherapy
In this paper we formulate and explore a mathematical model to study continuous infusion of a vascular tumour with isolated and combined blood-borne chemotherapies. The mathematical model comprises a system of nonlinear partial differential equations that describe the evolution of the healthy (host) cells, the tumour cells and the tumour vasculature, coupled with distribution of a generic angiogenic stimulant (TAF) and blood-borne oxygen. A novel aspect of our model is the presence of blood-borne chemotherapeutic drugs which target different aspects of tumour growth (cf. proliferating cells, the angiogenic stimulant or the tumour vasculature). We run exhaustive numerical simulations in order to compare vascular tumour growth before and following therapy. Our results suggest that continuous exposure to anti-proliferative drug will result in the vascular tumour being cleared, becoming growth-arrested or growing at a reduced rate, the outcome depending on the drugâs potency and its rate of uptake. When the angiogenic stimulant or the tumour vasculature are targeted by the therapy, tumour elimination can not occur: at best vascular growth is retarded and the tumour reverts to an avascular form. Application of a combined treatment that destroys the vasculature and the TAF, yields results that resemble those achieved following successful treatment with anti-TAF or anti-vascular therapy. In contrast, combining anti-proliferative therapy with anti-TAF or antivascular therapy can eliminate the vascular tumour. In conclusion, our results suggest that tumour growth and the time of tumour clearance are highly sensitive to the specific combinations of anti-proliferative, anti-TAF and anti-vascular drugs
Mathematical Model Creation for Cancer Chemo-Immunotherapy
One of the most challenging tasks in constructing a mathematical model of cancer treatment is the calculation of biological parameters from empirical data. This task becomes increasingly difficult if a model involves several cell populations and treatment modalities. A sophisticated model constructed by de Pillis et al., Mixed immunotherapy and chemotherapy of tumours: Modelling, applications and biological interpretations, J. Theor. Biol. 238 (2006), pp. 841â862; involves tumour cells, specific and non-specific immune cells (natural killer (NK) cells, CD8 T cells and other lymphocytes) and employs chemotherapy and two types of immunotherapy (IL-2 supplementation and CD8 T-cell infusion) as treatment modalities. Despite the overall success of the aforementioned model, the problem of illustrating the effects of IL-2 on a growing tumour remains open. In this paper, we update the model of de Pillis et al. and then carefully identify appropriate values for the parameters of the new model according to recent empirical data. We determine new NK and tumour antigen-activated CD8 T-cell count equilibrium values; we complete IL-2 dynamics; and we modify the model in de Pillis et al. to allow for endogenous IL-2 production, IL-2-stimulated NK cell proliferation and IL-2-dependent CD8 T-cell self-regulations. Finally, we show that the potential patient-specific efficacy of immunotherapy may be dependent on experimentally determinable parameters
Seeking Bang-Bang Solutions of Mixed Immuno-Chemotherapy of Tumors
It is known that a beneficial cancer treatment approach for a single patient often involves the administration of more than one type of therapy. The question of how best to combine multiple cancer therapies, however, is still open. In this study, we investigate the theoretical interaction of three treatment types (two biological therapies and one chemotherapy) with a growing cancer, and present an analysis of an optimal control strategy for administering all three therapies in combination. In the situations with controls introduced linearly, we find that there are conditions on which the controls exist singularly. Although bang-bang controls (on-off) reflect the drug treatment approach that is often implemented clinically, we have demonstrated, in the context of our mathematical model, that there can exist regions on which this may not be the best strategy for minimizing a tumor burden. We characterize the controls in singular regions by taking time derivatives of the switching functions. We will examine these representations and the conditions necessary for the controls to be minimizing in the singular region. We begin by assuming only one of the controls is singular on a given interval. Then we analyze the conditions on which a pair and then all three controls are singular
Optimal fishery with coastal catch
In many spatial resource models, it is assumed that an agent is able to harvest the resource over the complete spatial domain. However, agents frequently only have access to a resource at particular locations at which a moving biomass, such as fish or game, may be caught or hunted. Here, we analyze an infinite timeâhorizon optimal control problem with boundary harvesting and (systems of) parabolic partial differential equations as state dynamics. We formally derive the associated canonical system, consisting of a forwardâbackward diffusion system with boundary controls, and numerically compute the canonical steady states and the optimal timeâdependent paths, and their dependence on parameters. We start with some oneâspecies fishing models, and then extend the analysis to a predatorâprey model of the LotkaâVolterra type. The models are rather generic, and our methods are quite general, and thus should be applicable to large classes of structurally similar bioeconomic problems with boundary controls.
Recommedations for Resource Managers
Just like ordinary differential equationâconstrained (optimal) control problems and distributed partial differential equation (PDE) constrained control problems, boundary control problems with PDE state dynamics may be formally treated by the Pontryagin's maximum principle or canonical system formalism (state and adjoint PDEs).
These problems may have multiple (locally) optimal solutions; a first overview of suitable choices can be obtained by identifying canonical steady states.
The computation of canonical paths toward some optimal steady state yields temporal information about the optimal harvesting, possibly including waiting time behavior for the stock to recover from a lowâstock initial state, and nonmonotonic (in time) harvesting efforts.
Multispecies fishery models may lead to asymmetric effects; for instance, it may be optimal to capture a predator species to protect the prey, even for high costs and low market values of the predators
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