Interactive System for Similarity-Based Inspection and Assessment of the Well-Being of mHealth Users

Recent digitization technologies empower mHealth users to conveniently record their Ecological Momentary Assessments (EMA) through web applications, smartphones, and wearable devices. These recordings can help clinicians understand how the users’ condition changes, but appropriate learning and visualization mechanisms are required for this purpose. We propose a web-based visual analytics tool, which processes clinical data as well as EMAs that were recorded through a mHealth application. The goals we pursue are (1) to predict the condition of the user in the near and the far future, while also identifying the clinical data that mostly contribute to EMA predictions, (2) to identify users with outlier EMA, and (3) to show to what extent the EMAs of a user are in line with or diverge from those users similar to him/her. We report our findings based on a pilot study on patient empowerment, involving tinnitus patients who recorded EMAs with the mHealth app TinnitusTips. To validate our method, we also derived synthetic data from the same pilot study. Based on this setting, results for different use cases are reported.     

Parallel block iterative method for multiaquifer flow models

Flow in a multiaquifer porous system can be simulated by the so-called “quasi three-dimensional” models. When heterogeneous and/or aquitards with nonlinear hydrogeologic behavior are considered, a fully numerical approach is required for the model solution. If the finite element method is used to integrate the partial differential flow equations, the final solution of large systems is required. In the present article, an original iterative solution strategy is developed. The global system is decoupled into a number of smaller subsystems consistent with the geologic structure (aquitards and aquifers) of the multiaquifer system. The aquifer and the aquitard equations are solved separately with the modified conjugate gradient and the Thomas algorithms, respectively, while the final coupled solution is obtained with an iterative procedure equivalent to a Block Jacobi scheme. The procedure can be efficiently implemented on a parallel super-computer distributing the computational load, so that two successive blocks (related to an aquifer and the underlying aquitard) are solved on the same processor. The procedure is analyzed with linear porous media, where the convergence is theoretically ensured. The results obtained with a realistic linear multiaquifer system, employing a massively parallel computer like the CRAY T3D, have pointed out the high degree of parallelization of the algorithm. Comparison with the parallel implementation of the Block SOR and Block Gauss-Seidel schemes shows that parallel Block Jacobi performs significantly better with a reduction of the elapsed times, which depends on the rate of leakage between neighboring aquifers. © 1997 John Wiley & Sons, Inc.     

Block and graft copolymers based on cationic ring-opening polymerizations

The highly living character of a number of cationic polymerizations has been used to synthesize new, well defined, segmented copolymers. This has been achieved by sequential monomer additions, by grafting reactions, by macromonomer copolymerizations as well as by transfer to polymer. In the present report, a number of examples of such polymers will be presented. The new materials are based on tetrahydrofurane (THF), alkyloxazolines (ROx), cyclic amines, cyclic acetals and cyclic sulfides.     

Large Scale Oscillations in the Continuous Casting Process

Long-term oscillations of the flow in a continuous casting tundish are investigated numerically and experimentally. The numerical model is based on the Reynolds averaged Navier-Stokes equations (URANS). A comparison between numerical results and experimental data from a water model is presented. Frequencies due to long-term oscillations are resolved in the simulation. These frequencies are in satisfactory agreement with the experimental results of LDA measurements. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem

On March 11, 1944, the famous Eremitani Church in Padua (Italy) was destroyed in an Allied bombing along with the inestimable frescoes by Andrea Mantegna et al. contained in the Ovetari Chapel. In the last 60 years, several attempts have been made to restore the fresco fragments by traditional methods, but without much success. One of the authors contributed to the development of an efficient pattern recognition algorithm to map the original position and orientation of the fragments, based on comparisons with an old gray level image of the fresco prior to the damage. This innovative technique allowed for the partial reconstruction of the frescoes. Unfortunately, the surface covered by the colored fragments is only 77 m², while the original area was of several hundreds. This means that we can reconstruct only a fraction (less than 8%) of this inestimable artwork. In particular the original color of the blanks is not known. This begs the question of whether it is possible to estimate mathematically the original colors of the frescoes by making use of the potential information given by the available fragments and the gray level of the pictures taken before the damage. Moreover, is it possible to estimate how faithful such a restoration is? In this paper we retrace the development of the recovery of the frescoes as an inspiring and challenging real-life problem for the development of new mathematical methods. Then we shortly review two models recently studied independently by the authors for the recovery of vector valued functions from incomplete data, with applications to the recolorization problem. The models are based on the minimization of a functional which is formed by the discrepancy with respect to the data and additional regularization constraints. The latter refer to joint sparsity measures with respect to frame expansions, in particular wavelet or curvelet expansions, for the first functional and functional total variation for the second. We establish relations between these two models. As a major contribution of this work we perform specific numerical test on the real-life problem of the A. Mantegna’s frescoes and we compare the results due to the two methods.     

Reaction Rate of Small Diffusing Molecules on a Cylindrical Membrane

Biomembranes consist of a lipid bi-layer into which proteins are embedded to fulfill numerous tasks in localized regions of the membrane. Often, the proteins have to reach these regions by simple diffusion. Motivated by the observation that IP₃ receptor channels (IP₃R) form clusters on the surface of the endoplasmic reticulum (ER) during ATP-induced calcium release, the reaction rate of small diffusing molecules on a cylindrical membrane is calculated based on the Smoluchowski approach. In this way, the cylindrical topology of the tubular ER is explicitly taken into account. The problem can be reduced to the solution of the diffusion equation on a finite cylindrical surface containing a small absorbing hole. The solution is constructed by matching appropriate ‘inner’ and ‘outer’ asymptotic expansions. The asymptotic results are compared with those from numerical simulations and excellent agreement is obtained. For realistic parameter sets, we find reaction rates in the range of experimentally measured clustering rates of IP₃R. This supports the idea that clusters are formed by a purely diffusion limited process.     

Bioactive peptides from libraries

New ligands for a variety of biological targets can be selected from biological or synthetic combinatorial peptide libraries. The use of different libraries to select novel peptides with potential therapeutic applications is reviewed. The possible combination of molecular diversity provided by combinatorial libraries and a rational approach derived from computational modeling is also considered. Advantages and disadvantages of different approaches are compared. Possible strategies to bypass loss of peptide bioactivity in the transition from ligand selection to in vivo use are discussed.