Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells

Adherent cells exert traction forces on to their environment, which allows them to migrate, to maintain tissue integrity, and to form complex multicellular structures. This traction can be measured in a perturbation-free manner with traction force microscopy (TFM). In TFM, traction is usually calculated via the solution of a linear system, which is complicated by undersampled input data, acquisition noise, and large condition numbers for some methods. Therefore, standard TFM algorithms either employ data filtering or regularization. However, these approaches require a manual selection of filter- or regularization parameters and consequently exhibit a substantial degree of subjectiveness. This shortcoming is particularly serious when cells in different conditions are to be compared because optimal noise suppression needs to be adapted for every situation, which invariably results in systematic errors. Here, we systematically test the performance of new methods from computer vision and Bayesian inference for solving the inverse problem in TFM. We compare two classical schemes, L1- and L2-regularization, with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization. Using artificial data and experimental data, we show that these methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Thus, Bayesian methods can mitigate the considerable uncertainty inherent in comparing cellular traction forces

The Schrodinger equation with Hulthen potential plus ring-shaped potential

We present the solutions of the Schr$\ddot{o}$dinger equation with the Hulth$\acute{e}$n potential plus ring-shape potential for $\ell\neq 0$ states within the framework of an exponential approximation of the centrifugal potential.Solutions to the corresponding angular and radial equations are obtained in terms of special functions using the conventional Nikiforov-Uvarov method. The normalization constant for the Hulth$\acute{e}$n potential is also computed.Comment: Typed with LateX,12 Pages, Typos correcte

A note on q-Bernoulli numbers and polynomials

By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.Comment: 8 page

Exact Solutions of the Duffin Kemmer Petiau Equation for the Deformed Hulthen Potential

Using the Nikiforov Uvarov method, an application of the relativistic Duffin Kemmer Petiau equation in the presence of a deformed Hulthen potential is presented for spin zero particles. We derived the first order coupled differential radial equations which enable the energy eigenvalues as well as the full wavefunctions to be evaluated by using of the Nikiforov Uvarov method that can be written in terms of the hypergeometric polynomials.Comment: 8 pages. submitted to Physica Script

A cost effectiveness analysis of salt reduction policies to reduce coronary heart disease in four Eastern Mediterranean countries.

BACKGROUND: Coronary Heart Disease (CHD) is rising in middle income countries. Population based strategies to reduce specific CHD risk factors have an important role to play in reducing overall CHD mortality. Reducing dietary salt consumption is a potentially cost-effective way to reduce CHD events. This paper presents an economic evaluation of population based salt reduction policies in Tunisia, Syria, Palestine and Turkey. METHODS AND FINDINGS: Three policies to reduce dietary salt intake were evaluated: a health promotion campaign, labelling of food packaging and mandatory reformulation of salt content in processed food. These were evaluated separately and in combination. Estimates of the effectiveness of salt reduction on blood pressure were based on a literature review. The reduction in mortality was estimated using the IMPACT CHD model specific to that country. Cumulative population health effects were quantified as life years gained (LYG) over a 10 year time frame. The costs of each policy were estimated using evidence from comparable policies and expert opinion including public sector costs and costs to the food industry. Health care costs associated with CHDs were estimated using standardized unit costs. The total cost of implementing each policy was compared against the current baseline (no policy). All costs were calculated using 2010 PPP exchange rates. In all four countries most policies were cost saving compared with the baseline. The combination of all three policies (reducing salt consumption by 30%) resulted in estimated cost savings of $235,000,000 and 6455 LYG in Tunisia;$39,000,000 and 31674 LYG in Syria; $6,000,000 and 2682 LYG in Palestine and$1,3000,000,000 and 378439 LYG in Turkey. CONCLUSION: Decreasing dietary salt intake will reduce coronary heart disease deaths in the four countries. A comprehensive strategy of health education and food industry actions to label and reduce salt content would save both money and lives

A note on q-Euler numbers and polynomials

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.Comment: 6 page

Prevalence and Correlates of Common Mental Disorders among Mothers of Young Children in Kilimanjaro Region of Tanzania.

Although poor maternal mental health is a major public health problem, with detrimental effects on the individual, her children and society, information on its correlates in low-income countries is sparse. This study investigates the prevalence of common mental disorders (CMD) among at-risk mothers, and explores its associations with sociodemographic factors. This population-based survey of mothers of children aged 0-36 months used the 14-item Shona Symptom Questionnaire (SSQ). Mothers whose response was "yes" to 8 or more items on the scale were defined as "at risk of CMD." Of the 1,922 mothers (15-48 years), 28.8% were at risk of CMD. Risk of CMD was associated with verbal abuse, physical abuse, a partner who did not help with the care of the child, being in a polygamous relationship, a partner with low levels of education, and a partner who smoked cigarettes. Cohabiting appeared to be protective. Taken together, our results indicate the significance of the quality of relations with one's partner in shaping maternal mental health. The high proportion of mothers who are at risk of CMD emphasizes the importance of developing evidence-based mental health programmes as part of the care package aimed at improving maternal well-being in Tanzania and other similar settings

New identities involving q-Euler polynomials of higher order

In this paper we give new identities involving q-Euler polynomials of higher order.Comment: 11 page

Any l-state improved quasi-exact analytical solutions of the spatially dependent mass Klein-Gordon equation for the scalar and vector Hulthen potentials

We present a new approximation scheme for the centrifugal term to obtain a quasi-exact analytical bound state solutions within the framework of the position-dependent effective mass radial Klein-Gordon equation with the scalar and vector Hulth\'{e}n potentials in any arbitrary $D$ dimension and orbital angular momentum quantum numbers $l.$ The Nikiforov-Uvarov (NU) method is used in the calculations. The relativistic real energy levels and corresponding eigenfunctions for the bound states with different screening parameters have been given in a closed form. It is found that the solutions in the case of constant mass and in the case of s-wave ($l=0$) are identical with the ones obtained in literature.Comment: 25 pages, 1 figur