Utilization of inverse approach in the design of materials over nano‐ to macro‐scale

In the light of recent developments in computer technology, a promising and efficient way to design a material with a desired property would be to solve the inverse problem: use a physical property to predict structure. Here, we discuss the basic idea and mathematical foundation of the inverse approach, and proposed strategies for its utilization in the design of materials over nano‐ to macro‐scales. At the nano‐scale, analyzed strategies include scanning of a high‐dimensional space of chemical compounds for those compounds that have a targeted property, and identification of correlations in large databases of materials. However, unlike utilization of inverse approach at nano‐scale where full structural information ‐ atoms and their positions‐ is linked to targeted properties, at the meso‐ and macro‐scale, only partial structural information, manifested via structural motifs or representative volume elements, is available. We discuss the role of partial structural information in the inverse approach to the design of materials at those scales. Risks and limitations of the inverse approach are analyzed and dependence of the approach on factors such as structure parametrization, approximations in theoretical models, and feedback from structural characterization, is addressed.

     

Numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points

We propose a new numerical method for estimating the piecewise constant Robin coefficient in two-dimensional elliptic equation from boundary measurements. The Robin inverse problem is recast into a minimization of an output least-square formulation. A technique based on determining the discontinuous points of the unknown coefficient is suggested, and we investigate the differentiability of the solution and the objective functional with respect to the discontinuous points. Then we apply the Gauss-Newton method for reconstructing the shape of the unknown Robin coefficient. Numerical examples illustrate its efficiency and stability.     

Phase unwrapping by accumulation of residual maps

We present a path independent (global) algorithm for phase unwrapping based on the minimisation of a robust cost function. The algorithm incorporates an outlier rejection mechanism making it robust to large inconsistencies and discontinuities. The proposal consists on an iterative incremental scheme that unwraps a sub-estimation of the residual phase at each iteration. The sub-estimation degree is controlled by an algorithm׳s parameter. We present an efficiently computational multigrid implementation based on a nested strategy: the process is iterated by using multiple resolutions. The proposal׳s performance is demonstrated by experiments with synthetic and real data, and successfully compared with algorithms of the state of the art.     

Magnetic Polymer Composite Particles Via In situ Inverse Miniemulsion Polymerization Process

We aimed at preparing magnetic iron oxide particles by the oxidation-precipitation method in order to encapsulate these particles in polymer matrices composed of poly(acrylamide-styrene sulfonic acid sodium salt). Nanocomposites were synthesized by the incorporation of surface treated magnetic nanoparticles in the synthesized polymers via in situ inverse mini-emulsion polymerization process. The study parameter was the ionic monomer content in the synthesized polymers. The structure and the morphology of the magnetic nanogels were characterized by Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), dynamic light scattering (DLS), thermal gravimetric analysis (TGA) and scanning electron microscopy (SEM). FTIR and XRD showed that pure magnetite was formed and successfully encapsulated in the composite nanoparticles. The polymer encapsulation could reduce the susceptibility to leaching and could protect the magnetite particle surfaces from oxidation. The ionic monomer content had a great effect on the magnetization behavior. Magnetite prepared by the oxidation precipitation method, of 50 nm mean particle size, was embedded successfully into the polymer nanogels with a reasonable magnetic response, as proved by vibrating sample magnetometer measurement. Magnetic nanocomposites were proven to be super-ferromagnetic materials.     

Nonlinear Schrödinger equation in a semi-strip: Evolution of the Weyl–Titchmarsh function and recovery of the initial condition and rectangular matrix solutions from the boundary conditions

Rectangular matrix solutions of the defocusing nonlinear Schrödinger equation (dNLS) are studied in quarter-plane and semi-strip. Evolution of the corresponding Weyl–Titchmarsh (Weyl) function is described in terms of the initial Weyl function and boundary conditions. In the next step, the initial Weyl function is recovered (for the quarter-plane case) from the long-time asymptotics of the wave function considered at the boundary. Thus, it is shown that the evolution of the Weyl function is uniquely defined by the boundary conditions. Moreover, a procedure to recover solutions of dNLS (uniquely defined by the boundary conditions) is given. In a somewhat different way, the same boundary value problem is also dealt with in a semi-strip (for the case of a quasi-analytic initial condition).     

Genotyping of exons 1 to 20 in Duchenne muscular dystrophy by universal multiplex PCR and short‐end capillary electrophoresis

One rapid CE method was established to diagnose Duchenne muscular dystrophy (DMD). DMD is a severe recessive inherited disorder frequently caused by gene deletions. Among them, exons 1–20 account for nearly 30% of occurrences. In this study, the universal multiplex PCR was used to enhance the fluorescently labeling efficiency, which was performed only by one universal fluorescent primer. After PCR, a short‐end injection CE (short‐end CE) speeded up the genotyping of the DMD gene. This method involved no extra purification, and was completed within 9 min. The CE conditions contained a polymer solution of 1.5% hydroxylethylcellulose in 1× TBE buffer at 6 kV for separation. This method was applied to test six DMD patients and one healthy male person. The results showed good agreement with those of multiplex ligation‐dependent probe amplification. This method can be applied for clinical diagnosis of DMD disease. Accurate diagnosis of the DMD gene is the best way to prevent the disease.     

A rapid and effective method for silver staining of PCR products separated in polyacrylamide gels

With the development of molecular quantitative genetics, particularly, genetic linkage map construction, quantitative trait loci mapping or genes fine mapping and association analysis etc., more and more PCR products separated in polyacrylamide gels need to be silver‐stained. However, conventional silver‐staining procedures are complicated and time‐consuming as they require a lot of preparation and handling of several solutions prior to use. In this study, a simple and rapid protocol for silver staining of PCR products was developed. The number of steps was reduced compared to conventional protocols, thus achieving detection of PCR products in 7 min, saving time and resources. Fixation and staining solution and developing solution in present staining procedure allowed a reutilization for 12 and 8 times, respectively, reducing the cost greatly. Meanwhile, the sensitivity was significantly improved with the improved method and the minimum of 0.097 ng/μL of DNA amount can be detected in denaturing polyacrylamide gel. The protocol developed in this study will facilitate the development of molecular quantitative genetics.     

Isometric artifacts from polymerase chain reaction-massively parallel sequencing analysis of short tandem repeat loci: An emerging issue from a new technology?

The recent introduction of polymerase chain reaction (PCR)-massively parallel sequencing (MPS) technologies in forensics has changed the approach to allelic short tandem repeat (STR) typing because sequencing cloned PCR fragments enables alleles with identical molecular weights to be distinguished based on their nucleotide sequences. Therefore, because PCR fidelity mainly depends on template integrity, new technical issues could arise in the interpretation of the results obtained from the degraded samples. In this work, a set of DNA samples degraded in vitro was used to investigate whether PCR-MPS could generate “isometric drop-ins” (IDIs; i.e., molecular products having the same length as the original allele but with a different nucleotide sequence within the repeated units). The Precision ID GlobalFiler NGS STR panel kit was used to analyze 0.5 and 1 ng of mock samples in duplicate tests (for a total of 16 PCR-MPS analyses). As expected, several well-known PCR artifacts (such as allelic dropout, stutters above the threshold) were scored; 95 IDIs with an average occurrence of 5.9 IDIs per test (min: 1, max: 11) were scored as well. In total, IDIs represented one of the most frequent artifacts. The coverage of these IDIs reached up to 981 reads (median: 239 reads), and the ratios with the coverage of the original allele ranged from 0.069 to 7.285 (median: 0.221). In addition, approximately 5.2% of the IDIs showed coverage higher than that of the original allele. Molecular analysis of these artifacts showed that they were generated in 96.8% of cases through a single nucleotide change event, with the C > T transition being the most frequent (85.7%). Thus, in a forensic evaluation of evidence, IDIs may represent an actual issue, particularly when DNA mixtures need to be interpreted because they could mislead the operator regarding the number of contributors. Overall, the molecular features of the IDIs described in this work, as well as the performance of duplicate tests, may be useful tools for managing this new class of artifacts otherwise not detected by capillary electrophoresis technology.