Immobilization of cells by electrostatic droplet generation: a model system for potential application in medicine

The process of electrostatic extrusion as a method for cell immobilization was investigated that could be used for potential applications in medicine. An attempt was made to assess the effects of cell addition and polymer concentration on the overall entrapment procedure, ie, on each stage of immobilization: polymer-cell suspension rheological characteristics, electrostatic extrusion process, and the process of gelation. The findings should contribute to a better understanding of polymer–cell interactions, which could be crucial in possible medical treatments. Alginate–yeast was used as a model system for carrier-cells. The electrostatic extrusion was considered as a complex two-phase flow system and the effects of cell and alginate concentrations on the resulting microbead size and uniformity were assessed. Under investigated conditions, microbeads 50–600 μm in diameter were produced and the increase in both alginate and cell concentrations resulted in larger microbeads with higher standard deviations in size. We attempted to rationalize the findings by rheological characterization of the cell–alginate suspensions. Rheological characterization revealed non-Newtonian, pseudoplastic behavior of cell-alginate suspensions with higher viscosities at higher alginate concentrations. However, the presence of cells even at high concentrations (5×108 and 1×109 cells/mL) did not significantly affect the rheological properties of Na-alginate solution. Lastly, we investigated the kinetics of alginate gelation with respect to the quantity of Ca2+ ions and cell presence. The gelation kinetics were examined under conditions of limited supply with Ca2+ ions, which can be essential for immobilization of highly sensitive mammalian cells that require minimal exposure to CaCl2 solution. The molar ratio of G units to Ca2+ ions of 3.8:1 provided complete crosslinking, while the increase in alginate concentration resulted in prolonged gelation times but higher strength of the resulting gel. The cell presence decreased the rate of network formation as well as the strength of the obtained Ca-alginate hydrogel

Cosmological Histories for the New Variables

Histories and measures for quantum cosmology are investigated through a quantization of the Bianchi IX cosmology using path integral techniques. The result, derived in the context of Ashtekar variables, is compared with earlier work. A non-trivial correction to the measure is found, which may dominate the classical potential for universes on the Planck scale.Comment: 14, CGPG-94/2-

Free-Field Realization of D-dimensional Cylindrical Gravitational Waves

We find two-dimensional free-field variables for D-dimensional general relativity on spacetimes with D-2 commuting spacelike Killing vector fields and non-compact spatial sections for D>4. We show that there is a canonical transformation which maps the corresponding two-dimensional dilaton gravity theory into a two-dimensional diffeomorphism invariant theory of the free-field variables. We also show that the spacetime metric components can be expressed as asymptotic series in negative powers of the dilaton, with coefficients which can be determined in terms of the free fields.Comment: 15 pages, Late

SU(2)-invariant reduction of the 3+1 dimensional Ashtekar's gravity

We consider a space-time with spatial sections isomorphic to the group manifold of SU(2). Triad and connection fluctuations are assumed to be SU(2)-invariant. Thus, they form a finite dimensional phase space. We perform non-perturbative path integral quantization of the model. Contarary to previous claims the path integral measure appeared to be non-singular near configurations admitting additional Killing vectors. In this model we are able to calculate the generating functional of Green functions of the reduced phase space variables exactly.Comment: 12 page

Constants of motion for vacuum general relativity

The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the $SL(2,R)$ principal chiral model with certain `source' terms. Using this formulation, we give a procedure for generating an infinite number of non-local constants of motion for this sector of the Einstein equations. The constants of motion arise as explicit functionals on the phase space of Einstein gravity, and are labelled by sl(2,R) indices.Comment: 10 pages, latex, version to appear in Phys. Rev. D

Warlock: an automated computational workflow for simulating spatially structured tumour evolution

A primary goal of modern cancer research is to characterize tumour growth and evolution, to improve clinical forecasting and individualized treatment. Agent-based models support this endeavour but existing models either oversimplify spatial structure or are mathematically intractable. Here we present warlock, an open-source automated computational workflow for fast, efficient simulation of intratumour population genetics in any of a diverse set of spatial structures. Warlock encapsulates a deme-based oncology model (demon), designed to bridge the divide between agent-based simulations and analytical population genetics models, such as the spatial Moran process. Model output can be readily compared to multi-region and single-cell sequencing data for model selection or biological parameter inference. An interface for High Performance Computing permits hundreds of simulations to be run in parallel. We discuss prior applications of this workflow to investigating human cancer evolution

Functional evolution of quantum cylindrical waves

Kucha{\v{r}} showed that the quantum dynamics of (1 polarization) cylindrical wave solutions to vacuum general relativity is determined by that of a free axially-symmetric scalar field along arbitrary axially-symmetric foliations of a fixed flat 2+1 dimensional spacetime. We investigate if such a dynamics can be defined {\em unitarily} within the standard Fock space quantization of the scalar field. Evolution between two arbitrary slices of an arbitrary foliation of the flat spacetime can be built out of a restricted class of evolutions (and their inverses). The restricted evolution is from an initial flat slice to an arbitrary (in general, curved) slice of the flat spacetime and can be decomposed into (i) `time' evolution in which the spatial Minkowskian coordinates serve as spatial coordinates on the initial and the final slice, followed by (ii) the action of a spatial diffeomorphism of the final slice on the data obtained from (i). We show that although the functional evolution of (i) is unitarily implemented in the quantum theory, generic spatial diffeomorphisms of (ii) are not. Our results imply that a Tomanaga-Schwinger type functional evolution of quantum cylindrical waves is not a viable concept even though, remarkably, the more limited notion of functional evolution in Kucha{\v{r}}'s `half parametrized formalism' is well-defined.Comment: Replaced with published versio

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

Asymptotic behaviour of cylindrical waves interacting with spinning strings

We consider a family of cylindrical spacetimes endowed with angular momentum that are solutions to the vacuum Einstein equations outside the symmetry axis. This family was recently obtained by performing a complete gauge fixing adapted to cylindrical symmetry. In the present work, we find boundary conditions that ensure that the metric arising from this gauge fixing is well defined and that the resulting reduced system has a consistent Hamiltonian dynamics. These boundary conditions must be imposed both on the symmetry axis and in the region far from the axis at spacelike infinity. Employing such conditions, we determine the asymptotic behaviour of the metric close to and far from the axis. In each of these regions, the approximate metric describes a conical geometry with a time dislocation. In particular, around the symmetry axis the effect of the singularity consists in inducing a constant deficit angle and a timelike helical structure. Based on these results and on the fact that the degrees of freedom in our family of metrics coincide with those of cylindrical vacuum gravity, we argue that the analysed set of spacetimes represent cylindrical gravitational waves surrounding a spinning cosmic string. For any of these spacetimes, a prediction of our analysis is that the wave content increases the deficit angle at spatial infinity with respect to that detected around the axis.Comment: 25 pages, accepted for publication in Classical and Quantum Gravit

Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus

Recent work on canonical transformations in quantum mechanics is applied to transform between the Moncrief metric formulation and the Witten-Carlip holonomy formulation of 2+1-dimensional quantum gravity on the torus. A non-polynomial factor ordering of the classical canonical transformation between the metric and holonomy variables is constructed which preserves their classical modular transformation properties. An extension of the definition of a unitary transformation is briefly discussed and is used to find the inner product in the holonomy variables which makes the canonical transformation unitary. This defines the Hilbert space in the Witten-Carlip formulation which is unitarily equivalent to the natural Hilbert space in the Moncrief formulation. In addition, gravitational theta-states arising from ``large'' diffeomorphisms are found in the theory.Comment: 31 pages LaTeX [Important Revision: a section is added constructing the inner product/Hilbert space for the Witten-Carlip holonomy formulation; the proof of unitary equivalence of the metric and holonomy formulations is then completed. Other additions include discussion of relation of canonical and unitary transformations. Title/abstract change.