A parallel and adaptive multigrid solver for the solutions of the optimal control of geometric evolution laws in two and three dimensions

We present a problem concerning the optimal control of geometric evolution laws. This is a minimisation problem that aims to find a control η which minimises the objective functional J subject to some imposed constraints. We apply this methodology to an application of whole cell tracking. Given two sets of data of cell morphologies, we may solve the optimal control problem to dynamically reconstruct the cell movements between the time frame of these two sets of data. This problem is solved in two and three space dimensions, using a state-of-the-art numerical method, namely multigrid, with adaptivity and parallelism

An optimal control approach to cell tracking

Cell tracking is of vital importance in many biological studies, hence robust cell tracking algorithms are needed for inference of dynamic features from (static) in vivo and in vitro experimental imaging data of cells migrating. In recent years much attention has been focused on the modelling of cell motility from physical principles and the development of state-of-the art numerical methods for the simulation of the model equations. Despite this, the vast majority of cell tracking algorithms proposed to date focus solely on the imaging data itself and do not attempt to incorporate any physical knowledge on cell migration into the tracking procedure. In this study, we present a mathematical approach for cell tracking, in which we formulate the cell tracking problem as an inverse problem for fitting a mathematical model for cell motility to experimental imaging data. The novelty of this approach is that the physics underlying the model for cell migration is encoded in the tracking algorithm. To illustrate this we focus on an example of Zebrafish (Danio rerio's larvae) Neutrophil migration and contrast an ad-hoc approach to cell tracking based on interpolation with the model fitting approach we propose in this study

Heterogeneity and strong competition in ecology

We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan type evolution equation with effective coefficients. We also perform some numerical simulations in one and two spatial dimensions that suggest that oscillations in motilities are detrimental to invasion behaviour of a species

Multifarious transparent glass nanocrystal composites

Glasses comprising well known ferroelectric crystalline phases have been a subject of curious investigation from the point of view of exploiting these composites for dielectric, pyroelectric, ferroelectric, electro and non-linear optical devices. Transparent glass-ceramics containing ferroelectric crystallites at nano scale have been of much interest owing to their promising physical properties. The advantages that are associated with glass-ceramics include very low levels of porosity and hence high break down voltages. It is of our interest to nanocrystallize Aurivillius family of ferroelectric oxides and tetragonal tungsten bronzes on borate and tellurite based glass matrices and demonstrate their promising optical and nonlinear optical properties. Apart from the above, the nanocrystallites of well known ferroelectric material LiNbO3 was grown in a reactive glass matrix. These nanocrystals of LiNbO3 exhibited intense second harmonic signals in transmission mode when exposed to IR light at 1064 nm. The most interesting result was the demonstration of optical diffraction of the second harmonic signals which was attributed to the presence of self- organized sub-micrometer sized LiNbO3 crystallites that were indeed inscribed by the IR laser light which was used to probe in the NLO property of these materials

Drug resistance in tuberculosis and issues related to multidrug resistance in planning for TB control in India

There is no clear evidence of an increase in the prevalence of initial drug resistance in India over the years. However, relatively high prevalence of acquired resistance has been reported. The level of initial drug resistance is said to be an epidemiological marker to assess the success of the National TB Programme. This also influences the design of the regimens to be employed as well as policy decisions

Drug resistance in tuberculosis in India

The current global concern in the treatment of tuberculosis (TB) is the emergence of resistance to the two most potent drugs viz., isoniazid and rifampicin. The level of initial drug resistance is an epidemiological indicator to assess the success of the TB control programme. Though drug resistance in TB has frequently been reported from India, most of the available information is localized, sketchy or incomplete. A review of the few authentic reports indicates that there is no clear evidence of an increase in the prevalence of initial resistance over the years. However, a much higher prevalence of acquired resistance has been reported from several regions, though based on smaller numbers of patients. A strong TB control programme and continuous surveillance studies employing standardized methodology and rigorous quality control measures will serve as useful parameters in the evaluation of current treatment policies as well as the management of multidrug resistant (MDR) TB cases

Reaction-diffusion patterns in smart sensor networks

technical reportWe introduced the use of Turing?s reaction-diffusion pattern formation to support high-level tasks in smart sensor networks (S-Nets). This has led us to explore various biologically motivated mechanisms. In this paper we address some issues that arise in trying to get reliable, efficient patterns in irregular grids with error in inter-node distances

Electronics and Chemistry: Varying Single Molecule Junction Conductance Using Chemical Substituents

We measure the low bias conductance of a series of substituted benzene diamine molecules while breaking a gold point contact in a solution of the molecules. Transport through these substituted benzenes is by means of nonresonant tunneling or superexchange, with the molecular junction conductance depending on the alignment of the metal Fermi level to the closest molecular level. Electron-donating substituents, which drive the occupied molecular orbitals up, increase the junction conductance, while electron-withdrawing substituents have the opposite effect. Thus for the measured series, conductance varies inversely with the calculated ionization potential of the molecules. These results reveal that the occupied states are closest to the gold Fermi energy, indicating that the tunneling transport through these molecules is analogous to hole tunneling through an insulating film.Comment: 14 pages, 4 figure

Formation and Evolution of Single Molecule Junctions

We analyze the formation and evolution statistics of single molecule junctions bonded to gold electrodes using amine, methyl sulfide and dimethyl phosphine link groups by measuring conductance as a function of junction elongation. For each link, maximum elongation and formation probability increase with molecular length, strongly suggesting that processes other than just metal-molecule bond breakage play a key role in junction evolution under stress. Density functional theory calculations of adiabatic trajectories show sequences of atomic-scale changes in junction structure, including shifts in attachment point, that account for the long conductance plateau lengths observed.Comment: 10 pages, 4 figures, submitte