Abstract: Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs.

Abstract: MicroRNAs (miRNAs) are small oligonucleotides (18-25 bases) that play a key role in epigenetic regulation. Since the discovery of miRNAs in 1993, their role in biological processes has been extensively investigated. By now, it has been evidenced that monitoring and detection of miRNAs can improve (early) disease diagnosis. The existing diagnostic approaches have limitations such as the need for complex multistep protocols for sample preparation, analysis, data interpretation, high cost of equipment, the need for highly qualified personnel, and high laboratory standards. As opposed to this, point-of-care biosensors and chips aim to facilitate the procedure and avoid sending samples into centralized laboratories, which saves time, reduces the chance of sample degradation, and enables analysis of patient samples in remote areas, directly at home or primary and secondary care facilities (i.e. general practitioners and specialists). The latter is essential for therapy assessment and follow-up monitoring of patients with chronic diseases and cancer. Nevertheless, the development of such sensors is lagging compared to the projections of 10 – 20 years ago, mainly due to insufficient sensitivity, poor reproducibility, and the complexity of the sensors’ design reported in the research literature. This motivates the development of new detection strategies and technologies such as photoelectrochemical sensors that combine the best features of different sensing approaches. The primary concern when developing detection technologies for miRNA is the need for a highly sensitive and selective platform. This thesis explores a novel photoelectrochemical (PEC) method that is distinctive owing to its sensitive nature and simple and robust design. Firstly, we focused on the usage of recently emerging commercial gold-sputtered electrode systems for the detection of short nucleic acid with enzymatic amplification. Importantly, cleaning such electrodes is a challenge since the standard procedures known for regular disk electrodes such as polishing cannot be employed here, since it will damage the protective layer on the electrode. However, the electrodes can be washed and pretreated chemically and/or electrochemically. Thus, a procedure to effectively clean and modify the gold-sputtered electrode has been developed, resulting in high-performance gold-sputtered nucleic acid sensors. Next, the usage of molecular photosensitizers as an alternative to enzymatic amplification has been evaluated. We took advantage of the singlet oxygen production by photosensitizers upon photoexcitation, leading to a photocurrent response due to the singlet oxygen-induced (electro)chemical conversions. Following the demonstration of the detection strategy, the analytical performance of the sensing system was evaluated using magnetic beads-based nucleic acid assay on disposable electrode platforms, with a focus to enhance the sensitivity and robustness of the technique in detecting complementary nucleic acid targets. Following the fundamental evaluation of the singlet oxygen-based PEC detection of nucleic acids, we further optimized the assay and measurement parameters and employed the sensing strategy for a polymerase chain reaction-free (PCR-free) quantification of miRNAs related to prostate cancer. By successfully detecting and quantifying low-picomolar range concentrations (< 10 pM) in plasma samples from prostate cancer patients, we successfully showed the applicability of the novel sensing strategy. We have also compared and positioned the performance of our developed PEC strategy with an existing state-of-art technique, i.e. electrochemiluminescence (ECL). Our PEC strategy performed on par with ECL, both yielding low-picomolar detection limits in serum matrices, however quicker and cheaper than ECL. Owing to the versatility of this PEC technique, the final study explored its multiplexing capability. As a starting point in this branch of the research, we have investigated two possible ways for multiplexing. To perform multiple measurements at the same time, constructing calibration plots and quantifying unknown miRNA concentrations in patient samples at the same time, we have developed a high-throughput detection with 96X multi-channel electrode systems and in-house designed and constructed 96XLED illumination sources. Secondly, to detect more than one target miRNA in a single measurement, intra-vial multiplexing where the samples were analyzed for different targets in one vial was also explored. Altogether, this thesis presents the fundamentals, development and application of a novel PEC strategy for detecting short (< 25 bases) nucleic acid sequences, in particular, miRNA. With an aim to serve as a distinctive technique to function as a clinical testing platform without any need for PCR, this work adds value to the development of nucleic acid-based sensors for miRNAs and other short-stranded nucleic acid biomarkers, and benefits in the early detection of diseases like cancer.

Abstract: Using first-principles calculations, we investigate the magnetic order in two-dimensional (2D) transition-metal-dichalcogenide (TMD) monolayers: MoS2, MoSe2, MoTe2, WSe2, and WS2 substitutionally doped with period four transition-metals (Ti, V, Cr, Mn, Fe, Co, Ni). We uncover five distinct magnetically ordered states among the 35 distinct TMD-dopant pairs: the non-magnetic (NM), the ferromagnetic with out-of-plane spin polarization (Z FM), the out-of-plane polarized clustered FMs (clustered Z FM), the in-plane polarized FMs (X-Y FM), and the anti-ferromagnetic (AFM) state. Ni and Ti dopants result in an NM state for all considered TMDs, while Cr dopants result in an anti-ferromagnetically ordered state for all the TMDs. Most remarkably, we find that Fe, Mn, Co, and V result in an FM ordered state for all the TMDs, except for MoTe2. Finally, we show that V-doped MoSe2 and WSe2, and Mn-doped MoS2, are the most suitable candidates for realizing a room-temperature FM at a 16-18% atomic substitution.

Abstract: We model transport through two-dimensional topological insulator (TI) nanoribbons. To model the quantum transport, we employ the non-equilibrium Green's function approach. With the presented approach, we study the effect of lattice imperfections on the carrier transport. We observe that the topologically protected edge states of TIs are robust against a high percentage (2%) of vacancy defects. We also investigate tunneling of the edge states in two decoupled TI nanoribbons.