Modeling Stem/Progenitor Cell-Induced Neovascularization and\ud Oxygenation around Solid Implants

Tissue engineering constructs and other solid implants with biomedical applications, such as drug delivery devices or bioartificial organs, need oxygen (O2) to function properly. To understand better the vascular integration of such devices, we recently developed a novel model sensor containing O2-sensitive crystals, consisting of a polymeric capsule limited by a nano-porous filter. The sensor was implanted in mice with hydrogel alone (control) or hydrogel embedded with mouse CD117/c-kit+ bone marrow progenitor cells (BMPC) in order to stimulate peri-implant neovascularization. The sensor provided local partial O2 pressure (pO2) using non-invasive electron paramagnetic resonance (EPR) signal measurements. A consistently higher level of per-implant oxygenation was observed in the cell-treatment case as compared to the control over a 10-week period. In order to provide a mechanistic explanation of these experimental observations, we present in this paper a mathematical model, formulated as a system of coupled partial differential equations, that simulates peri-implant vascularization. In the control case, vascularization is considered to be the result of a Foreign Body Reaction (FBR) while in the cell-treatment case, adipogenesis in response to paracrine stimuli produced by the stem cells is assumed to induce neovascularization. The model is validated by fitting numerical predictions of local pO2 to measurements from the implanted sensor. The model is then used to investigate further the potential for using stem cell treatment to enhance the vascular integration of biomedical implants. We thus demonstrate how mathematical modeling combined with experimentation can be used to infer how vasculature develops around biomedical implants in control and stem celltreated cases

Dark Energy and the Statistical Study of the Observed Image Separations of the Multiply Imaged Systems in the CLASS Statistical Sample

The present day observations favour a universe which is flat, accelerated and composed of $\sim 1/3$ matter (baryonic + dark) and $\sim 2/3$ of a negative pressure component, usually referred to as dark energy or quintessence. The Cosmic Lens All Sky Survey (CLASS), the largest radio-selected galactic mass scale gravitational lens search project to date, has resulted in the largest sample suitable for statistical analyses. In the work presented here, we exploit observed image separations of the multiply imaged lensed radio sources in the sample. We use two different tests: (1) image separation distribution function $n(\Delta\theta)$ of the lensed radio sources and (2) {\dtheta}_{\mathrm{pred}} vs {\dtheta}_{\mathrm{obs}} as observational tools to constrain the cosmological parameters $w$ and \Om. The results are in concordance with the bounds imposed by other cosmological tests.Comment: 20 pages latex; Modified " Results and Discussion " section, new references adde

Extreme value distributions for weakly correlated fitnesses in block model

We study the limit distribution of the largest fitness for two models of weakly correlated and identically distributed random fitnesses. The correlated fitness is given by a linear combination of a fixed number of independent random variables drawn from a common parent distribution. We find that for certain class of parent distributions, the extreme value distribution for correlated random variables can be related either to one of the known limit laws for independent variables or the parent distribution itself. For other cases, new limiting distributions appear. The conditions under which these results hold are identified.Comment: Expanded, added reference

Quasihole condensates in quantum Hall liquids

We develop a formalism to describe quasihole condensates in quantum Hall liquids and thereby extend the conformal field theory approach to the full hierarchy of spin-polarized Abelian states, and to several classes of non-Abelian hierarchical states. Most previously proposed spin-polarized quantum Hall wave functions appear as special cases. In this paper we explain the physical motivations for the approach, and exemplify it by explicitly constructing the level-two quasihole condensate state at filling fraction 2/3, and the two level-three states at 5/13 and 5/7 which are built from combinations of quasielectron and quasihole condensates.Comment: 16 page

Correlation between dielectric constant and chemical structure of sodium silicate glasses

Journal URL: http://jap.aip.org/jap/staff.js

Criterion for dynamical chiral symmetry breaking

The Bethe-Salpeter equation is related to a generalized quantum-mechanical Hamiltonian. Instability of the presumed vacuum, indicated by a tachyon, is related to a negative energy eigenstate of this Hamiltonian. The variational method shows that an arbitrarily weak long-range attraction leads to chiral symmetry breaking, except in the scale-invariant case when the instability occurs at a critical value of the coupling. In the case of short-range attraction, an upper bound for the critical coupling is obtained.Comment: 10 pages, 2 figures; made minor changes, published versio

Band Structure of the Fractional Quantum Hall Effect

The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides an accurate and complete microscopic description of the strongly correlated many-body states in the low-energy bands. Thus, somewhat like in Landau's fermi liquid theory, there is a one-to-one correspondence between the low energy Hilbert space of strongly interacting electrons in the fractinal quantum Hall regime and that of weakly interacting electrons in the integer quantum Hall regime.Comment: 10 page

Response Function of the Fractional Quantized Hall State on a Sphere I: Fermion Chern-Simons Theory

Using a well known singular gauge transformation, certain fractional quantized Hall states can be modeled as integer quantized Hall states of transformed fermions interacting with a Chern-Simons field. In previous work we have calculated the electromagnetic response function of these states at arbitrary frequency and wavevector by using the Random Phase Approximation (RPA) in combination with a Landau Fermi Liquid approach. We now adopt these calculations to a spherical geometry in order to facilitate comparison with exact diagonalizations performed on finite size systems.Comment: 39 pages (REVTeX 3.0). Postscript file for this paper are available on the World Wide Web at http://cmtw.harvard.edu/~simon/ ; Preprint number HU-CMT-94S0

Composite fermion wave functions as conformal field theory correlators

It is known that a subset of fractional quantum Hall wave functions has been expressed as conformal field theory (CFT) correlators, notably the Laughlin wave function at filling factor $\nu=1/m$ ($m$ odd) and its quasiholes, and the Pfaffian wave function at $\nu=1/2$ and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at $\nu=1/m$ are created by inserting anyonic vertex operators, $P_{\frac{1}{m}}(z)$, that replace a subset of the electron operators in the correlator. The one-quasiparticle wave function is identical to the corresponding CF wave function, and the two-quasiparticle wave function has correct fractional charge and statistics and is numerically almost identical to the corresponding CF wave function. We further show how to exactly represent the CF wavefunctions in the Jain series $\nu = s/(2sp+1)$ as the CFT correlators of a new type of fermionic vertex operators, $V_{p,n}(z)$, constructed from $n$ free compactified bosons; these operators provide the CFT representation of composite fermions carrying $2p$ flux quanta in the $n^{\rm th}$ CF Landau level. We also construct the corresponding quasiparticle- and quasihole operators and argue that they have the expected fractional charge and statistics. For filling fractions 2/5 and 3/7 we show that the chiral CFTs that describe the bulk wave functions are identical to those given by Wen's general classification of quantum Hall states in terms of $K$-matrices and $l$- and $t$-vectors, and we propose that to be generally true. Our results suggest a general procedure for constructing quasiparticle wave functions for other fractional Hall states, as well as for constructing ground states at filling fractions not contained in the principal Jain series.Comment: 26 pages, 3 figure