We present commutation relations depending on the rainbow functions which are slightly different from the well-known results. However, the advantage of these new commutation relations are compatible with the calculation of the Hawking temperature in the rainbow Schwarzschild black hole.

We apply a machine learning algorithm, the artificial neural network, to the search for gravitational-wave signals associated with short gamma-ray bursts (GRBs). The multi-dimensional samples consisting of data corresponding to the statistical and physical quantities from the coherent search pipeline are fed into the artificial neural network to distinguish simulated gravitational-wave signals from background noise artifacts. Our result shows that the data classification efficiency at a fixed false alarm probability (FAP) is improved by the artificial neural network in comparison to the conventional detection statistic. Specifically, the distance at 50% detection probability at a fixed false positive rate is increased about 8%–14% for the considered waveform models. We also evaluate a few seconds of the gravitational-wave data segment using the trained networks and obtain the FAP. We suggest that the artificial neural network can be a complementary method to the conventional detection statistic for identifying gravitational-wave signals related to the short GRBs.

The nature of the phase transition in a system of self-propelling particles has been extensively studied during the past few decades. A theoretical model was proposed by [T. Vicsek et al. Phys. Rev. Lett. 75, 1226 (1995)] with a simple rule for updating the direction of motion of each particle. Based on the model of Vicsek et al., in this paper, we consider a group of animals as particles moving freely in a two-dimensional space. Due to the fact that the viewable area of animals depends on the species, we consider the motion of each individual within an angle $\phi =？/2$ $(？$ is called the angle of view) of a circle centered at its position of radius $R$ . We obtained a phase diagram in the space $\left(\phi ,{\eta }_c\right)$ with ${\eta }_c$ being the critical noise. We show that the phase transition exists only in the case of a wide view's angle $\phi \ge 0.5\pi$ . The flocking of animals is a universal behavior of the species of prey but not the one of the predator. Our simulation results are in good agreement with experimental observation [C. Beccoa et al., Physica A 367, 487 (2006)].

The locomotion behavior of Caenorhabditis elegans has been studied extensively to understand the respective roles of neural control and biomechanics as well as the interaction between them. Constructing a mathematical model is helpful to understand the locomotion behavior in various surrounding conditions that are difficult to realize in experiments. In this study, we built three hidden Markov models (HMMs) for the crawling behavior of C. elegans in a controlled environment with no chemical treatment and in a formaldehyde-treated environment (0.1 and 0.5 ppm). The organism’s crawling activity was recorded using a digital camcorder for 20 min at a rate of 24 frames per second. All shape patterns were quantified by branch length similarity (BLS) entropy and classified into four groups using the self-organizing map (SOM). Comparison of the simulated behavior generated by HMMs and the actual crawling behavior demonstrated that the HMM coupled with the SOM was successful in characterizing the crawling behavior. In addition, we briefly discussed the possibility of using the HMM together with BLS entropy to develop bio-monitoring systems to determine water quality.

A mathematical and computational model combining the heart and circulatory system has been developed to understand the hemodynamics of circulation under normal conditions and ventricular septal defect (VSD). The immersed boundary method has been introduced to describe the interaction between the moving two-dimensional heart and intracardiac blood flow. The whole-heart model is governed by the Navier–Stokes system; this system is combined with a multi-compartment model of circulation using pressure–flow relations and the linearity of the discretized Navier–Stokes system. We investigate the velocity field, flowmeters, and pressure–volume loop in both normal and VSD cases. Simulation results show qualitatively good agreements with others found in the literature. This model, combining the heart and circulation, is useful for understanding the complex, hemodynamic mechanisms involved in normal circulation and cardiac diseases.

In this paper, we present an immersed boundary method for modeling a contractile elastic ring in a three-dimensional Newtonian fluid. The governing equations are the modified Navier–Stokes equations with an elastic force from the contractile ring. The length of the elastic ring is time dependent and the ring shrinks with time because of its elastic nature in our proposed model. We dynamically reduce the number of Lagrangian boundary points when the distance between adjacent points is too small. This point-deleting algorithm helps keep the number of immersed boundary points in a single Cartesian mesh grid from becoming too high. We perform numerical experiments with various initial configurations of the contractile elastic ring, and numerical simulations to investigate the effects of the parameters are also conducted. The numerical results show that the proposed method can model and simulate the time-dependent contractile elastic ring in a three-dimensional Newtonian fluid.

In this study, we present a multidimensional open system for valveless pumping (VP). This system consists of an elastic tube connected to two open tanks filled with a fluid under gravity. The two-dimensional elastic tube model is constructed based on the immersed boundary method, and the tank model is governed by a system of ordinary differential equations based on the work-energy principle. The flows into and out of the elastic tube are modeled in terms of the source/sink patches inside the tube. The fluid dynamics of this system is generated by the periodic compress-and-release action applied to an asymmetric region of the elastic tube. We have developed an algorithm to couple these partial differential equations and ordinary differential equations using the pressure-flow relationship and the linearity of the discretized Navier-Stokes equations. We have observed the most important feature of VP, namely, the existence of a unidirectional net flow in the system. Our computations are focused on the factors that strongly influence the occurrence of unidirectional flows, for example, the frequency, compression duration, and location of pumping. Based on these investigations, some case studies are performed to observe the details of the ow features.

Energy cost of transmitting a single bit of information is approximately the same as that needed for processing a thousand operations in a typical sensor node. Thus, a practical way to prolong a wireless sensor network lifetime is to reduce the sensor energy consumption in data transmissions. Data aggregation is an efficient way to minimize energy consumption on sensors. In this paper, we propose a practical secure data aggregation scheme, Sen-SDA, based on an additive homomorphic encryption scheme, an identity-based signature scheme, and a batch verification technique with an algorithm for filtering injected false data. We then investigate the feasibility of our scheme using low-cost microcontrollers choosing two popular IEEE 802.15.4-compliant wireless sensor network hardware platforms, MICAz and Tmote Sky, used in real-life deployments.

We studied the population structure of South Korea by using the distributions of surnames for all 246 administrative regions. Every 4,177 surnames are distinguished by their bon-gwan which indicates the place of their family clans. Using Fisher’s Alpha, we found that the level of inbreeding increases as the distance from the capital Seoul increases. We introduced the Shannon index to measure the level of spatial diffusion for each surname population, and the geographical clusters based on similarities of the surname compositions among the regions show almost exact agreement with those at the administrative districts.

The Stieltjes transform SA of an infinite lower triangular matrix A with nonzero diagonal entries is defined by SA=A−1A¯ where A¯ is the matrix obtained from A by deleting its initial row. In this paper, we express a sequence of polynomials as the characteristic polynomials of the Stieltjes transforms using a highly structured infinite lower triangular matrix called a Riordan matrix. As a result, computation of the zeros of such polynomials becomes amenable to iterative methods for computing eigenvalues, or to eigenvalue location theorems such as the Geršgorin theorem. We also describe a finite analog of the polynomial correspondence and its relationship to eigenvalue regions. As an application, the recurrence relations for several polynomial sequences are obtained using the Stieltjes transform.