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

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

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

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.

Singularities of nn-fold integrals of the Ising class and the theory of elliptic curves

We introduce some multiple integrals that are expected to have the same singularities as the singularities of the $n$-particle contributions $\chi^{(n)}$ to the susceptibility of the square lattice Ising model. We find the Fuchsian linear differential equation satisfied by these multiple integrals for $n=1, 2, 3, 4$ and only modulo some primes for $n=5$ and $6$, thus providing a large set of (possible) new singularities of the $\chi^{(n)}$. We discuss the singularity structure for these multiple integrals by solving the Landau conditions. We find that the singularities of the associated ODEs identify (up to $n= 6$) with the leading pinch Landau singularities. The second remarkable obtained feature is that the singularities of the ODEs associated with the multiple integrals reduce to the singularities of the ODEs associated with a {\em finite number of one dimensional integrals}. Among the singularities found, we underline the fact that the quadratic polynomial condition $1+3 w +4 w^2 = 0$, that occurs in the linear differential equation of $\chi^{(3)}$, actually corresponds to a remarkable property of selected elliptic curves, namely the occurrence of complex multiplication. The interpretation of complex multiplication for elliptic curves as complex fixed points of the selected generators of the renormalization group, namely isogenies of elliptic curves, is sketched. Most of the other singularities occurring in our multiple integrals are not related to complex multiplication situations, suggesting an interpretation in terms of (motivic) mathematical structures beyond the theory of elliptic curves.Comment: 39 pages, 7 figure

A Connection Approach to Numerical Relativity

We discuss a general formalism for numerically evolving initial data in general relativity in which the (complex) Ashtekar connection and the Newman-Penrose scalars are taken as the dynamical variables. In the generic case three gauge constraints and twelve reality conditions must be solved. The analysis is applied to a Petrov type \{1111\} planar spacetime where we find a spatially constant volume element to be an appropriate coordinate gauge choice.Comment: 17 pages, LaTe

The effects of chronic SRIH-14 and octreotide administration on the pituitary-adrenal axis in adult male rats

The effects of chronic treatments with SRIH-14 and octreotide on pituitary corticotropes (ACTH cells) and on the adrenal cortex of male Wistar rats were examined. Adult males received two daily s.c. injections of 20 ?g/100 g of body weight of either SRIH-14 or octreotide for 28 consecutive days. ACTH cells were studied using a peroxidaseantiperoxidase immunocytochemical procedure. Morphometry was used to evaluate the changes in cell and nuclear volumes (?m3) and volume densities (%) of ACTHimmunoreactive cells. The adrenal cortex was analyzed by histological and morphometric methods. A significant (p<0.05) decrease in body weight and in the absolute weights of the pituitary and adrenal glands was observed in both treated groups. Morphometric parameters of ACTH cells in both treated groups were not significantly (p>0.05) different than in control rats. The absolute volumes of the adrenal gland and adrenal cortex were significantly (p<0.05) decreased in both treated groups. The absolute and relative volumes of the zona glomerulosa (ZG), as well as the cellular and nuclear volumes of the ZG were significantly (p<0.05) decreased in the both treated groups. In rats treated with SRIH-14 and octreotide, the absolute and relative volumes of the zona fasciculata (ZF) and zona reticularis (ZR), as well as their stereological parameters, did not change significantly (p>0.05). The aldosterone levels in the SRIH-14 and ocreotide-treated groups were significantly (p<0.05) decreased – by 13% and 19%, respectively. The concentration of ACTH and corticosterone did not change significantly. Together, these findings show that SRIH-14 and octreotide administration affected the morphological characteristics of the adrenal ZG in a similar manner, and brought about a decrease in plasma aldosterone concentration. These treatments did not affect pituitary ACTH cells or adrenal ZF and ZR functioning

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.