Ultrasound imaging is a widely used tool for visualizing human body’s internal organs and quantifying clinical parameters. Due to its advantages such as safety, noninvasiveness, portability, low cost and real-time 2D/3D imaging, diagnostic ultrasound industry has steadily grown. Since the technology advancements such as digital beam-forming, Doppler ultrasound, real-time 3D imaging and automated diagnosis techniques, there are still a lot of demands for image quality improvement, faster and accurate imaging, 3D color Doppler imaging and advanced functional imaging modes. In order to satisfy those demands, mathematics should be used properly and effectively in ultrasound imaging. Mathematics has been used commonly as mathematical modelling, numerical solutions and visualization, combined with science and engineering. In this article, we describe a brief history of ultrasound imaging, its basic principle, its applications in obstetrics/gynecology, cardiology and radiology, domestic-industrial products, contributions of mathematics and challenging issues in ultrasound imaging.

Ultrasound imaging is a widely used tool for visualizing human body's internal organs and quantifying clinical parameters. Due to its advantages such as safety, non-invasiveness, portability, low cost and real-time 2D/3D imaging, diagnostic ultrasound industry has steadily grown. Since the technology advancements such as digital beam-forming, Doppler ultrasound, real-time 3D imaging and automated diagnosis techniques, there are still a lot of demands for image quality improvement, faster and accurate imaging, 3D color Doppler imaging and advanced functional imaging modes. In order to satisfy those demands, mathematics should be used properly and effectively in ultrasound imaging. Mathematics has been used commonly as mathematical modelling, numerical solutions and visualization, combined with science and engineering. In this article, we describe a brief history of ultrasound imaging, its basic principle, its applications in obstetrics/gynecology, cardiology and radiology, domestic-industrial products, contributions of mathematics and challenging issues in ultrasound imaging.

마이크로시뮬레이션 모델은 거시적 수준의 인구, 사회, 경제 변화를 각 개인과 가구 단위의 미시적 수준의 사건들로부터 기술하고자 하는 것을 목적으로 하며, 최근 OECD 국가들을 중심으로 정책 시뮬레이션 도구로서 많은 관심을 받고 있다. 마이크로시뮬레이션 모델의 활용도를 높이기 위해서는 해당 국가의 인구 구조를 잘 반영하는 인구 데이터가 필요한데, 우리는 반복비례갱신 (iterative proportional updating) 방법을 이용하여 한국 가상 인구를 생성하였다. 생성된 가상 인구 데이터의 검증을 위하여 인구센서스 집계 결과와의 오차를 계산하였으며, 가구와 인구 모두에 대해서 실제 집계 결과와 작은 오차를 보이는 것을 확인하였다.

Microsimulation model has aimed to simulate the impact of policy at the level of individual and household. Recently, microsimulation model has been widely accepted in OECD countries for evaluating their economic and social policies. For improving the availability of microsimulation model, the population data which shows good accordance with the official statistics should be required. In this paper, we generate Korean synthetic populations by using the iterative proportional updating method. For the validation of Korean synthetic populations, we compute the difference between the generated synthetic populations and the summary table of Korean census. Then, we confirm that it shows good accordance with the summary table.

In previous studies, we showed that the branch length similarity (BLS) entropy profile could be used successfully for the recognition of shapes such as battle tanks, facial expressions, and butterflies. In the present study, we introduce critical points defined as a set of distinguishing points with high curvature to the BLS entropy profile in order to improve the shape recognition. In order to generate a given number of critical points from the shape, we propose a critical point detection method. Furthermore, we show the invariant properties of the BLS entropy deor. To evaluate the effects of critical points on the shape recognition of the BLS entropy deor, we performed a butterfly classification experiment against a real image data set, and we conducted performance comparisons with other point detection methods. In addition, the performance of the BLS entropy deor computed using the critical points was compared with those of other well-known deors such as the Fourier deor using three machine learning techniques, the Bayesian classifier, the multi-layer perceptron and the support vector machine. The results show that the BLS entropy deor outperforms other well-known deors.

Subterranean termites excavate complicated tunnel networks for foraging below the ground. During foraging activity, termites often encounter many bifurcation nodes generated by the tunnel branching or the tunnel–tunnel interaction. Path selection by termites at the node is likely to affect the foraging efficiency because depending on their selection, the traveling distance from food resources to the nest can vary significantly. To understand the selection mechanism, we artificially constructed Y-shaped tunnels in small arenas and observed the termite behavior at the bifurcation node (i.e. the intersection of the tunnel). At the bifurcation node, the right side tunnel forms 45° with respect to the straight tunnel that a termite advances, while the left side tunnel forms the angle of θ (= 5°, 15°, 30°, and 45°). The experimental results showed that the path selection strongly depends on which termite's antenna touching is first made on the tunnel wall at the bifurcation node. The left (or right) antenna touching tended to cause the right (or left) tunnel selection. As the value of θ increased, the tendency for the left selection ratio decreased. The bias of the advancing termites towards the left (or right) enhanced the tendency of the selection of the left (or right) tunnel but did not affect the spent time of the termites to pass through the node. The results were understood by the location relationship between the advancing termites and the tunnel wall. We briefly discussed the meaning of our finding in relation to the foraging efficiency.

The existence of prey refuges in a predator-prey system is known to be strongly related to the ecosystem’s stability. In this study, we explored how the prey refuge distribution affects the predator-prey system. To do so, we constructed a spatial lattice model to simulate an integrative predator (wolf) - prey (rabbit) - plant (grass) relationship. When a wolf (rabbit) encountered a rabbit (grass), the wolf (rabbit) tended to to the rabbit (grass) for foraging while the rabbit tended to escape from the wolf. These behaviors were mathematically described by the degrees of willingness for hunting (H) and escaping (E). Initially, n refuges for prey were heterogeneously distributed in the lattice space. The heterogeneity was characterized as variable A. Higher values of A equate to higher aggregation in the refuge. We investigated the mean population density for different values of H, E, and A. To simply characterize the refuge distribution effect, we built an H-E grid map containing the population density for each species. Then, we counted the number of grids, N, with a population density ≥ 0.25. Simulation results showed that an appropriate value of A positively affected prey survival while values of A were too high had a negative effect on prey survival. The results were explained by using the trade-off between the staying time of the prey in the refuge and the cluster size of the refuge.

In this study, we constructed a simple ecosystem consisting of one-predator？two-prey escape preferred strategy (EPS)- and hunting preferred strategy (HPS)-prey) ― food for prey relationship to understand how the individual’s strategic behavior, hunting and escaping affects the ecosystem. In the model, when a prey encounters its predator and the food at the same time, either hunting or escaping should be taken as priority. Hunting priority is referred to as a HPS, while escape priority is referred to as an EPS. These strategies are associated with some degree of willingness to either hunt (H) or escape (E). In this model, two prey species were considered. One species (HPS-prey) takes HPS and the other rabbit species (EPS-prey) takes EPS. Predators take only HPS. Simulation results showed that the density of EPS-prey was obviously higher than that of HPS-prey in the appropriate values of 0.2≤E≤0.8                                                 and 0.2≤H≤0.8in the stable state. This means that when a prey individual has appropriate willingness for both hunting and escape, EPS is more beneficial for the survival than HPS. In addition, we briefly discussed the limitation of our model and the possible future improvements.

Microsimulation model has aimed to simulate the impact of policy at the level of individual and household. Recently, microsimulation model has been widely accepted in OECD countries for evaluating their economic and social policies. For improving the availability of microsimulation model, the population data which shows good accordance with the official statistics should be required. In this paper, we generate Korean synthetic populations by using the iterative proportional updating method. For the validation of Korean synthetic populations, we compute the difference between the generated synthetic populations and the summary table of Korean census. Then, we confirm that it shows good accordance with the summary table.

We report here the non-detection of gravitational waves from the merger of binary–neutron star systems and neutron star–black hole systems during the first observing run of the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO). In particular, we searched for gravitational-wave signals from binary–neutron star systems with component masses and component dimensionless spins <0.05. We also searched for neutron star–black hole systems with the same neutron star parameters, black hole mass , and no restriction on the black hole spin magnitude. We assess the sensitivity of the two LIGO detectors to these systems and find that they could have detected the merger of binary–neutron star systems with component mass distributions of 1.35 ± 0.13 M _⊙ at a volume-weighted average distance of ~70 Mpc, and for neutron star–black hole systems with neutron star masses of 1.4 M _⊙ and black hole masses of at least 5 M _⊙, a volume-weighted average distance of at least ~110 Mpc. From this we constrain with 90% confidence the merger rate to be less than 12,600 Gpc⁻³ yr⁻¹ for binary–neutron star systems and less than 3600 Gpc⁻³ yr⁻¹ for neutron star–black hole systems. We discuss the astrophysical implications of these results, which we find to be in conflict with only the most optimistic predictions. However, we find that if no detection of neutron star–binary mergers is made in the next two Advanced LIGO and Advanced Virgo observing runs we would place significant constraints on the merger rates. Finally, assuming a rate of Gpc⁻³ yr⁻¹, short gamma-ray bursts beamed toward the Earth, and assuming that all short gamma-ray bursts have binary–neutron star (neutron star–black hole) progenitors, we can use our 90% confidence rate upper limits to constrain the beaming angle of the gamma-ray burst to be greater than ().

We report results of a deep all-sky search for periodic gravitational waves from isolated neutron stars in data from the S6 LIGO science run. The search was possible thanks to the computing power provided by the volunteers of the Einstein@Home distributed computing project. We find no significant signal candidate and set the most stringent upper limits to date on the amplitude of gravitational wave signals from the target population. At the frequency of best strain sensitivity, between 170.5 and 171 Hz we set a 90% confidence upper limit of $5.5\times {10}^{-25}$, while at the high end of our frequency range, around 505 Hz, we achieve upper limits $？{10}^{-24}$. At 230 Hz we can exclude sources with ellipticities greater than ${10}^{-6}$ within 100 pc of Earth with fiducial value of the principal moment of inertia of ${10}^{38}\mathrm{kg}{m}^2$. If we assume a higher (lower) gravitational wave spin-down we constrain farther (closer) objects to higher (lower) ellipticities.