Mathematical modelling of a first order sigma-delta modulator

In this paper an exact model for a basic, first order sigma-delta modulator is derived by means of a difference equation with discontinuous nonlinearity. An explicit solution is given in terms of the greatest integer function under certain boundedness and initial conditions of the input signal. Assumptions are made under which the explicit formula remains a solution of the difference equation although the suppositions of the main theorem are violated.     

Differences in dual-task performance and prefrontal cortex activation between younger and older adults

Background

The purpose of this study was to examine task-related changes in prefrontal cortex (PFC) activity during a dual-task in both healthy young and older adults and compare patterns of activation between the age groups. We also sought to determine whether brain activation during a dual-task relates to executive/attentional function and how measured factors associated with both of these functions vary between older and younger adults.

Results

Thirty-five healthy volunteers (20 young and 15 elderly) participated in this study. Near-infrared spectroscopy (NIRS) was employed to measure PFC activation during a single-task (performing calculations or stepping) and dual-task (performing both single-tasks at once). Cognitive function was assessed in the older patients with the Trail-making test part B (TMT-B). Major outcomes were task performance, brain activation during task (oxygenated haemoglobin: Oxy-Hb) measured by NIRS, and TMT-B score. Mixed ANOVAs were used to compare task factors and age groups in task performance. Mixed ANOVAs also compared task factors, age group and time factors in task-induced changes in measured Oxy-Hb. Among the older participants, correlations between the TMT-B score and Oxy-Hb values measured in each single-task and in the dual-task were examined using a Pearson correlation coefficient. Oxy-Hb values were significantly increased in both the calculation task and the dual-task within patients in both age groups. However, the Oxy-Hb values associated with there were higher in the older group during the post-task period for the dual-task. Also, there were significant negative correlations between both task-performance accuracy and Oxy-Hb values during the dual-task and participant TMT-B scores.

Conclusions

Older adults demonstrated age-specific PFC activation in response to dual-task challenge. There was also a significant negative correlation between PFC activation during dual-task and executive/attentional function. These findings suggest that the high cognitive load induced by dual-task activity generates increased PFC activity in older adults. However, this relationship appeared to be strongest in participants with better baseline attention and executive functions.     

A diffusion-controlled mullite formation reaction model based on tracer diffusivity data for aluminium,silicon and oxygen

This paper compiles all the data from our tracer diffusivity studies in single crystalline 2/1-mullite. As tracers we used the rare stable isotopes ¹⁸O and ³⁰Si and the artificial pseudo-stable isotope ²⁶Al. Secondary-ion mass spectrometry was applied to analyze the depth distribution of the tracer isotopes after the diffusion annealing. An essential result of our tracer diffusivity studies was the very low diffusivity of ³⁰Si compared to the diffusivities of ²⁶Al and ¹⁸O, which are almost equal. Based on this observation, we propose a reaction model for the diffusion-controlled formation of mullite in the solid state, which assumes that the growth kinetics of a mullite layer is mainly controlled by the diffusion of aluminium ions and oxygen ions.     

Weak-coupling treatment of electronic (anti-)ferroelectricity in the extended Falicov-Kimball model

We study the (spinless) Falicov-Kimball model extended by a finite band width (hopping t _f ) of the localized (f-) electrons in infinite dimensions in the weak-coupling limit of a small local interband Coulomb correlation U for half filling. In the case of overlapping conduction- and f-bands different kinds of ordered solutions are possible, namely charge-density wave (CDW) order, electronic ferroelectricity (EFE) and electronic antiferroelectricity (EAFE). The order parameters are calculated as a function of the model parameters and of the temperature. There is a first-order phase transition from the CDW-phase to the EFE- or EAFE-phase. The total energy is calculated to determine the thermodynamically stable solution. The quantum phase diagrams are calculated.     

Mathematical model to reduce loop mediated isothermal amplification (LAMP) false‐positive diagnosis

Loop mediated isothermal amplification (LAMP) is a nucleic acid amplification technique performed under isothermal conditions. The output of this amplification technique includes multiple different sizes of deoxyribonucleic acid (DNA) structures which are identified by a banding pattern on gel electrophoresis plots. Although this is a specific amplification technique, the complexity of the primer design and amplification still lead to the issue of obtaining false‐positive results, especially when a positive reading is determined solely by whether there is any banding pattern in the gel electrophoresis plot. Here, we first performed extensive LAMP experiments and evaluated the DNA structures using microchip electrophoresis. We then developed a mathematical model derived from the various components that make up an entire LAMP structure to predict the full LAMP structure size in base pairs. This model can be implemented by users to make predictions for specific, DNA size dependent, banding patterns on their gel electrophoresis plots. Each prediction is specific to the target sequence and primers used and therefore reduces incorrect diagnosis errors through identifying true‐positive and false‐positive results. This model was accurately tested with multiple primer sets in house and was also translatable to different DNA and RNA types in previously published literature. The mathematical model can ultimately be used to reduce false‐positive LAMP diagnosis errors for applications ranging from tuberculosis diagnostics to E. coli to numerous other infectious diseases.     

Extreme Lagrangian acceleration in confined turbulent flow

A Lagrangian study of two-dimensional turbulence for two different geometries, a periodic and a confined circular geometry, is presented to investigate the influence of solid boundaries on the Lagrangian dynamics. It is found that the Lagrangian acceleration is even more intermittent in the confined domain than in the periodic domain. The flatness of the Lagrangian acceleration as a function of the radius shows that the influence of the wall on the Lagrangian dynamics becomes negligible in the center of the domain, and it also reveals that the wall is responsible for the increased intermittency. The transition in the Lagrangian statistics between this region, not directly influenced by the walls, and a critical radius which defines a Lagrangian boundary layer is shown to be very sharp with a sudden increase of the acceleration flatness from about 5 to about 20.     

Critical threshold behavior for steady-state internal transport barriers in burning plasmas

Burning tokamak plasmas with internal transport barriers are investigated by means of integrated modeling simulations. The barrier sustainment in steady state, differently from the barrier formation process, is found to be characterized by a critical behavior, and the critical number of the phase transition is determined. Beyond a power threshold, alignment of self-generated and noninductively driven currents occurs and steady state becomes possible. This concept is applied to simulate a steady-state scenario within the specifications of the International Thermonuclear Experimental Reactor.     

Adaptive field-of-view imaging for efficient receive beamforming in medical ultrasound imaging systems

Quadrature demodulation-based phase rotation beamforming (QD-PRBF) is commonly used to support dynamic receive focusing in medical ultrasound systems. However, it is computationally demanding since it requires two demodulation filters for each receive channel. To reduce the computational requirements of QD-PRBF, we have previously developed two-stage demodulation (TSD), which reduces the number of lowpass filters by performing demodulation filtering on summation signals. However, it suffers from image quality degradation due to aliasing at lower beamforming frequencies. To improve the performance of TSD-PRBF with reduced number of beamforming points, we propose a new adaptive field-of-view (AFOV) imaging method. In AFOV imaging, the beamforming frequency is adjusted depending on displayed FOV size and the center frequency of received signals. To study its impact on image quality, simulation was conducted using Field II, phantom data were acquired from a commercial ultrasound machine, and the image quality was quantified using spatial (i.e., axial and lateral) and contrast resolution. The developed beamformer (i.e., TSD-AFOV-PRBF) with 1024 beamforming points provided comparable image resolution to QD-PRBF for typical FOV sizes (e.g., 4.6% and 1.3% degradation in contrast resolution for 160 mm and 112 mm, respectively for a 3.5 MHz transducer). Furthermore, it reduced the number of operations by 86.8% compared to QD-PRBF. These results indicate that the developed TSD-AFOV-PRBF can lower the computational requirement for receive beamforming without significant image quality degradation.     

In vitro study of magnetic particle seeding for implant assisted-magnetic drug targeting

The concept of using magnetic particles (seeds) as the implant for implant assisted-magnetic drug targeting (IA-MDT) was analyzed in vitro. Since this MDT system is being explored for use in capillaries, a highly porous (ε∼70%), highly tortuous, cylindrical, polyethylene polymer was prepared to mimic capillary tissue, and the seeds (magnetite nanoparticles) were already fixed within. The well-dispersed seeds were used to enhance the capture of 0.87 μm diameter magnetic drug carrier particles (MDCPs) (polydivinylbenzene embedded with 24.8 wt% magnetite) under flow conditions typically found in capillary networks. The effects of the fluid velocity (0.015–0.15 cm/s), magnetic field strength (0.0–250 mT), porous polymer magnetite content (0–7 wt%) and MDCP concentration (C=5 and 50 mg/L) on the capture efficiency (CE) of the MDCPs were studied. In all cases, when the magnetic field was applied, compared to when it was not, large increases in CE resulted; the CE increased even further when the magnetite seeds were present. The CE increased with increases in the magnetic field strength, porous polymer magnetite content and MDCP concentration. It decreased only with increases in the fluid velocity. Large magnetic field strengths were not necessary to induce MDCP capture by the seeds. A few hundred mT was sufficient. Overall, this first in vitro study of the magnetic seeding concept for IA-MDT was very encouraging, because it proved that magnetic particle seeds could serve as an effective implant for MDT systems, especially under conditions found in capillaries.