Mathematical models for cell-matrix interactions during dermal wound healing

This paper contains a review of our recent work on the mathematical modeling of cell interaction with extracellular matrix components during the process of dermal wound healing. The models are of partial differential equation type and allow us to investigate in detail how various mechanochemical effects may be responsible for certain wound healing disorders such as fibrocontractive and fibroproliferative diseases. We also present a model for wound healing angiogenesis. The latter has several features in common with angiogenesis during cancer tumour growth and spread so a deeper understanding of the phenomenon in the context of wound healing may also help in the treatment of certain cancers

Thermodynamic properties of Pb determined from pressure-dependent critical-field measurements

We have carried out extensive low-temperature (1.5 to 10 K) measurements of the critical field, $H_c$, for the element Pb up to a pressure of $P=1.2$ GPa. From this data the electronic entropy, specific heat, thermal expansion coefficient and compressibility is calculated as a function of temperature, pressure and magnetic field. The zero-field data is consistent with direct thermodynamic measurements and the $P$-dependence of $T_c$ and specific heat coefficient, $\gamma(T,P)$ allows the determination of the $P$-dependence of the pairing interaction.Comment: 5 pages, 6 figures, in press Phys. Rev.

Asymmetric Gaussian steering: when Alice and Bob disagree

Asymmetric steering is an effect whereby an inseparable bipartite system can be found to be described by either quantum mechanics or local hidden variable theories depending on which one of Alice or Bob makes the required measurements. We show that, even with an inseparable bipartite system, situations can arise where Gaussian measurements on one half are not sufficient to answer the fundamental question of which theory gives an adequate description and the whole system must be considered. This phenomenon is possible because of an asymmetry in the definition of the original Einstein-Podolsky-Rosen paradox and in this article we show theoretically that it may be demonstrated, at least in the case where Alice and Bob can only make Gaussian measurements, using the intracavity nonlinear coupler.Comment: 5 Pages, 4 Figure

A mathematical model for the capillary endothelial cell-extracellular matrix interactions in wound-healing angiogenesis

Angiogenesis, the process by which new blood capillaries grow into a tissue from surrounding parent vessels, is a key event in dermal wound healing, malignant-tumour growth, and other pathologic conditions. In wound healing, new capillaries deliver vital metabolites such as amino acids and oxygen to the cells in the wound which are involved in a complex sequence of repair processes. The key cellular constituents of these new capillaries are endothelial cells: their interactions with soluble biochemical and insoluble extracellular matrix (ECM) proteins have been well documented recently, although the biological mechanisms underlying wound-healing angiogenesis are incompletely understood. Considerable recent research, including some continuum mathematical models, have focused on the interactions between endothelial cells and soluble regulators (such as growth factors). In this work, a similar modelling framework is used to investigate the roles of the insoluble ECM substrate, of which collagen is the predominant macromolecular protein. Our model consists of a partial differential equation for the endothelial-cell density (as a function of position and time) coupled to an ordinary differential equation for the ECM density. The ECM is assumed to regulate cell movement (both random and directed) and proliferation, whereas the cells synthesize and degrade the ECM. Analysis and numerical solutions of these equations highlights the roles of these processes in wound-healing angiogenesis. A nonstandard approximation analysis yields insight into the travel ling-wave structure of the system. The model is extended to two spatial dimensions (parallel and perpendicular to the plane of the skin), for which numerical simulations are presented. The model predicts that ECM-mediated random motility and cell proliferation are key processes which drive angiogenesis and that the details of the functional dependence of these processes on the ECM density, together with the rate of ECM remodelling, determine the qualitative nature of the angiogenic response. These predictions are experimentally testable, and they may lead towards a greater understanding of the biological mechanisms involved in wound-healing angiogenesis

Travelling waves in wound healing

We illustrate the role of travelling waves in wound healing by considering three different cases. Firstly, we review a model for surface wound healing in the cornea and focus on the speed of healing as a function of the application of growth factors. Secondly, we present a model for scar tissue formation in deep wounds and focus on the role of key chemicals in determining the quality of healing. Thirdly, we propose a model for excessive healing disorders and investigate how abnormal healing may be controlled

Transient excitation and data processing techniques employing the fast fourier transform for aeroelastic testing

The development of testing techniques useful in airplane ground resonance testing, wind tunnel aeroelastic model testing, and airplane flight flutter testing is presented. Included is the consideration of impulsive excitation, steady-state sinusoidal excitation, and random and pseudorandom excitation. Reasons for the selection of fast sine sweeps for transient excitation are given. The use of the fast fourier transform dynamic analyzer (HP-5451B) is presented, together with a curve fitting data process in the Laplace domain to experimentally evaluate values of generalized mass, model frequencies, dampings, and mode shapes. The effects of poor signal to noise ratios due to turbulence creating data variance are discussed. Data manipulation techniques used to overcome variance problems are also included. The experience is described that was gained by using these techniques since the early stages of the SST program. Data measured during 747 flight flutter tests, and SST, YC-14, and 727 empennage flutter model tests are included

Observation of Heteronuclear Feshbach Resonances in a Bose-Fermi Mixture

Three magnetic-field induced heteronuclear Feshbach resonances were identified in collisions between bosonic 87Rb and fermionic 40K atoms in their absolute ground states. Strong inelastic loss from an optically trapped mixture was observed at the resonance positions of 492, 512, and 543 +/- 2 G. The magnetic-field locations of these resonances place a tight constraint on the triplet and singlet cross-species scattering lengths, yielding -281 +/- 15 Bohr and -54 +/- 12 Bohr, respectively. The width of the loss feature at 543 G is 3.7 +/- 1.5 G wide; this broad Feshbach resonance should enable experimental control of the interspecies interactions.Comment: revtex4 + 5 EPS figure

On exponential densities and limit ratios of subsets of N

Funding: National Natural Science Foundation of China (11671189,11971109).Given α,β,γ∈[0,1] with α≤β, we prove that there exists a subset of N such that its lower and upper exponential densities and its lower and upper limit ratios are equal to α, β, γ and 1, respectively. This result provides an affirmative answer to an open problem posed by Grekos et al. (Unif Distrib Theory 6:117–130, 2011).Publisher PDFPeer reviewe

Location-Quality-aware Policy Optimisation for Relay Selection in Mobile Networks

Relaying can improve the coverage and performance of wireless access networks. In presence of a localisation system at the mobile nodes, the use of such location estimates for relay node selection can be advantageous as such information can be collected by access points in linear effort with respect to number of mobile nodes (while the number of links grows quadratically). However, the localisation error and the chosen update rate of location information in conjunction with the mobility model affect the performance of such location-based relay schemes; these parameters also need to be taken into account in the design of optimal policies. This paper develops a Markov model that can capture the joint impact of localisation errors and inaccuracies of location information due to forwarding delays and mobility; the Markov model is used to develop algorithms to determine optimal location-based relay policies that take the aforementioned factors into account. The model is subsequently used to analyse the impact of deployment parameter choices on the performance of location-based relaying in WLAN scenarios with free-space propagation conditions and in an measurement-based indoor office scenario.Comment: Accepted for publication in ACM/Springer Wireless Network

vbyCaHbeta CCD Photometry of Clusters. VI. The Metal-Deficient Open Cluster NGC 2420

CCD photometry on the intermediate-band vbyCaHbeta system is presented for the metal-deficient open cluster, NGC 2420. Restricting the data to probable single members of the cluster using the CMD and the photometric indices alone generates a sample of 106 stars at the cluster turnoff. The average E(b-y) = 0.03 +/- 0.003 (s.e.m.) or E(B-V) = 0.050 +/- 0.004 (s.e.m.), where the errors refer to internal errors alone. With this reddening, [Fe/H] is derived from both m1 and hk, using b-y and Hbeta as the temperature index. The agreement among the four approaches is reasonable, leading to a final weighted average of [Fe/H] = -0.37 +/- 0.05 (s.e.m.) for the cluster, on a scale where the Hyades has [Fe/H] = +0.12. When combined with the abundances from DDO photometry and from recalibrated low-resolution spectroscopy, the mean metallicity becomes [Fe/H] = -0.32 +/- 0.03. It is also demonstrated that the average cluster abundances based upon either DDO data or low-resolution spectroscopy are consistently reliable to 0.05 dex or better, contrary to published attempts to establish an open cluster metallicity scale using simplistic offset corrections among different surveys.Comment: scheduled for Jan. 2006 AJ; 33 pages, latex, includes 7 figures and 2 table