We report on an all-sky search for periodic gravitational waves in the frequency band 20–475 Hz and with a frequency time derivative in the range of [−1.0,+0.1]×10−8  Hz/s. Such a signal could be produced by a nearby spinning and slightly nonaxisymmetric isolated neutron star in our galaxy. This search uses the data from Advanced LIGO’s first observational run, O1. No periodic gravitational wave signals were observed, and upper limits were placed on their strengths. The lowest upper limits on worst-case (linearly polarized) strain amplitude h0 are ∼4×10−25 near 170 Hz. For a circularly polarized source (most favorable orientation), the smallest upper limits obtained are ∼1.5×10−25. These upper limits refer to all sky locations and the entire range of frequency derivative values. For a population-averaged ensemble of sky locations and stellar orientations, the lowest upper limits obtained for the strain amplitude are ∼2.5×10−25.

In Advanced LIGO, detection and astrophysical source parameter estimation of the binary black hole merger GW150914 requires a calibrated estimate of the gravitational-wave strain sensed by the detectors. Producing an estimate from each detector’s differential arm length control loop readout signals requires applying time domain filters, which are designed from a frequency domain model of the detector’s gravitational-wave response. The gravitational-wave response model is determined by the detector’s opto-mechanical response and the properties of its feedback control system. The measurements used to validate the model and characterize its uncertainty are derived primarily from a dedicated photon radiation pressure actuator, with cross-checks provided by optical and radio frequency references. We describe how the gravitational-wave readout signal is calibrated into equivalent gravitational-wave-induced strain and how the statistical uncertainties and systematic errors are assessed. Detector data collected over 38 calendar days, from September 12 to October 20, 2015, contain the event GW150914 and approximately 16 days of coincident data used to estimate the event false alarm probability. The calibration uncertainty is less than 10% in magnitude and 10° in phase across the relevant frequency band, 20 Hz to 1 kHz.

We study the spread of infectious disease based on local- and national-scale mobility networks. We construct a local mobility network using data on urban bus services to estimate local-scale ment of people. We also construct a national mobility network from orientation-destination data of vehicular traffic between highway tollgates to evaluate national-scale ment of people. A metapopulation model is used to simulate the spread of epidemics. Thus, the number of infected people is simulated using a susceptible-infectious-recovered (SIR) model within the administrative division, and inter-division spread of infected people is determined through local and national mobility networks. In this paper, we consider two scenarios for epidemic spread. In the first, the infectious disease only spreads through local-scale ment of people, that is, the local mobility network. In the second, it spreads via both local and national mobility networks. For the former, the simulation results show infected people sequentially spread to neighboring divisions. Yet for the latter, we observe a faster spreading pattern to distant divisions. Thus, we confirm the national mobility network enhances synchronization among the incidence profiles of all administrative divisions.

Given c, a positive integer, we give an asymptotic formula for

It is well known that the symmetric Gaussian function, called the fundamental solution, serves as the Green’s function of the heat equation. In reality, on the other hand, distribution functions obtained empirically often differ from the Gaussian function. This study presents a new solution of the heat equation, satisfying localized initial conditions like the Gaussian fundamental solution. The new solution corresponds to a hetero-mixture distribution, which generalizes the Gaussian distribution function to a skewed and heavy-tailed distribution, and thus provides a candidate for the empirical distribution functions.

Subterranean termites live their tunnel networks constructed below ground. Thus, they often encounter tunnel junctions during traveling in the networks. Directional selection by termites at the junctions is likely to affect foraging efficiency because the selection determines the total traveling distance of the termites in the networks. To understand how termites select their direction at the junctions, we artificially constructed skewed T-junctions (with skew angle, θ = 0°, 10°, 20°, …, and 80°) in small arenas and observed termite behavior at the junctions. When an advancing termite touched the tunnel wall of a junction using left (right) antenna, the termite strongly tended to turn their body to the right (left) side. We measured the ratio of termite's directional selection for right side tunnel (γR). The ratio of the left selection was given as γL = 1 − γR. The value of γR tended to increase gradually as θincreased in the range of 0° ≤ θ ≤ 70° and dramatically decreased at θ = 80°. This experimental result was explained by the relationship between the antenna touching order and the geometry of junction area. Based on the selection behavior, we built a mathematical model and verified it through the comparison with experimental data. In addition, we briefly discussed about the application of the model and the selection mechanism in relation to the foraging efficiency.

We consider the approximation of elliptic eigenvalue problem with an interface. The main aim of this paper is to prove the stability and convergence of an immersed finite element method (IFEM) for eigenvalues using Crouzeix–Raviart $P_1$-nonconforming approximation. We show that spectral analysis for the classical eigenvalue problem can be easily applied to our model problem. We analyze the IFEM for elliptic eigenvalue problems with an interface and derive the optimal convergence of eigenvalues. Numerical experiments demonstrate our theoretical results.

In our previous studies, we suggested equations for describing the hunting and the escaping behaviors employed by predators and prey. The equations were successfully used to understand the stability of the predator-prey system and showed that they had a strong advantage simulating the dynamics of the system. However, in the studies, the equations were simply constituted based on the concepts of probability without a rigorous mathematical proof. We believe that the proof is necessary to not only further expand into other applications but also build more sophisticated models that can be used in characterizing the real animal’s behavior. For this reason, in this study, we show a rigorous derivation with two biological constraints.

The Hodge projection of a vector field is the divergence-free component of its Helmholtz decomposition. In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou–Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition.

In the decomposition by the Gibou–Min method, an important L2$L^2$-orthogonality holds between the gradient field and the solenoidal field, which is similar to the continuous Hodge decomposition.

Using the orthogonality, we present a novel analysis which shows that the convergence order is 1.5$1.5$ in the L2$L^2$-norm for approximating the divergence-free vector field. Numerical results are presented to validate our analyses.

We propose a user-drawn sketch image-based three-dimensional (3D) object recognition method, which automatically learns and optimizes features by using unsupervised algorithm to overcome the difficulty of extracting robust features from the black and white sketch image. As a preprocessing task, both the sketch image database and the projected image database of the 3D objects are built by learning with various user-drawn sketch images and suggestive contour images of the 3D objects respectively, and each sketch image is mapped to the most similar projected database image by measuring the similarity. This enables us to avoid a direct comparison of the sketch query and the projected images of the 3D objects and to use the learned robust sparse features of the trained sketch images in the sketch database, compensating for the difference between the user-drawn sketch image and synthesized images of the 3D mesh model. The locally-enforced feature optimization of the local and global features of the database images reduces the error and retains the feature properties. Furthermore, we quantitatively compared the proposed method to previous remarkable object recognition approaches. Numerous experiments on various challenging 3D objects and sketch images demonstrate that the proposed methodology performs favorably against several state-of-the-art algorithms.