On principal points for location mixtures of spherically symmetric distributions

In this paper, we investigate some properties of 2-principal points for location mixtures of spherically symmetric distributions with focus on a linear subspace in which a set of 2-principal points must lie. Our results can be viewed as an extension of those of Yamamoto and Shinozaki [2000. Two principal points for multivariate location mixtures of spherically symmetric distributions. J. Japan Statist. Soc. 30, 53–63], where a finite location mixture of spherically symmetric distributions is treated. As an extension of their paper, this paper defines a wider class of distributions, and derives a linear subspace in which a set of 2-principal points must exist. A theorem useful for comparing the mean squared distances is also established.     

The dependence of marriage migrations in Japan on personal factors and ecological variables

Marriage is an important migration‐inducing life‐cycle event. This paper uses a nested logit model to explain the interprefectural migration behaviors at marriage by personal factors and prefectural attributes, based on the micro data of the 1986 national migration survey of Japan. Before marriage, each person is considered a potential migrant making a two‐level decision: (1) to stay or depart and (2) to choose a destination. The main findings are as follows.

Destination choice propensities were affected by such attributes of potential destination as income (+), employment growth (+), distance (‐), contiguity (+), and linguistic similarity (+). Non‐natives appeared to be less sensitive to the attraction of economic opportunities. Personal factors were less important than prefectural attributes in affecting destination choice propensities.

Departure propensities were affected by not only such attributes of origin prefecture as income (‐), employment growth (‐), and population density (+) but also the “inclusive variable”; (+), which reflected the attractiveness of the rest of the system. Despite being strongly emphasized in the literature, sibling status was less important than gender, nativity and education in affecting departure propensities. Personal factors were much more important than prefectural attributes in determining the departure propensities.     

Distance-d independent set problems for bipartite and chordal graphs

The paper studies a generalization of the Independent Set problem (IS for short). A distance- $d$ independent set for an integer $d\ge 2$ in an unweighted graph $G = (V, E)$ is a subset $S\subseteq V$ of vertices such that for any pair of vertices $u, v \in S$ , the distance between $u$ and $v$ is at least $d$ in $G$ . Given an unweighted graph $G$ and a positive integer $k$ , the Distance- $d$ Independent Set problem (D $d$ IS for short) is to decide whether $G$ contains a distance- $d$ independent set $S$ such that $|S| \ge k$ . D2IS is identical to the original IS. Thus D2IS is $\mathcal{NP}$ -complete even for planar graphs, but it is in $\mathcal{P}$ for bipartite graphs and chordal graphs. In this paper we investigate the computational complexity of D $d$ IS, its maximization version MaxD $d$ IS, and its parameterized version ParaD $d$ IS( $k$ ), where the parameter is the size of the distance- $d$ independent set: (1) We first prove that for any $\varepsilon >0$ and any fixed integer $d\ge 3$ , it is $\mathcal{NP}$ -hard to approximate MaxD $d$ IS to within a factor of $n^{1/2-\varepsilon }$ for bipartite graphs of $n$ vertices, and for any fixed integer $d\ge 3$ , ParaD $d$ IS( $k$ ) is $\mathcal{W}[1]$ -hard for bipartite graphs. Then, (2) we prove that for every fixed integer $d\ge 3$ , D $d$ IS remains $\mathcal{NP}$ -complete even for planar bipartite graphs of maximum degree three. Furthermore, (3) we show that if the input graph is restricted to chordal graphs, then D $d$ IS can be solved in polynomial time for any even $d\ge 2$ , whereas D $d$ IS is $\mathcal{NP}$ -complete for any odd $d\ge 3$ . Also, we show the hardness of approximation of MaxD $d$ IS and the $\mathcal{W}[1]$ -hardness of ParaD $d$ IS( $k$ ) on chordal graphs for any odd $d\ge 3$ .     

How an ant decides to prey on or to attend aphids

The following results on the behavior decision making of the antLasius niger toward two species of myrmecophilous aphidsLachnus tropicalis andMyzocallis kuricola on chestnut trees have been found. (1) An individual worker consistently attended only one aphid species, even if her nestmates attended other aphid species on the same tree. (2) The ants preyed less on the aphid species which they attended than on other myrmecophilous aphid species. (3) The ants preyed less on the aphids which had been attended by their nestmates, even if both aphids were the same species. (4) The ants preyed less on aphids which had provided honeydew to their nestmates. (5) The increased aphid density per ant led to an increase in the rate of predation on the introduced aphids by the ants. These results suggest that each worker ofL. niger chooses aphid species to attend from her experience. In addition, the workers can recognize whether an aphid has been attended by their nestmates and whether an aphid has given their nestmates honeydew. Through these processes, each worker decides to attend or to prey on the aphid. As a result, they may realize efficient collective foraging dependent on aphid density per worker.     

A note on Whittaker–Henderson graduation: Bisymmetry of the smoother matrix

Abstract

Whittaker–Henderson (WH) graduation is a popular smoothing method that has been used for mortality table construction in the actuarial sciences and for the trend-cycle decomposition in time series econometrics. This paper proves that the smoother matrix of WH graduation is bisymmetric (i.e., symmetric centrosymmetric). This result implies, for example, that the first row of the smoother matrix is equivalent to the last row of it in reverse order. We also provide some related results.     

Augmenting a Submodular and Posi-modular Set Function by a Multigraph

Given a finite set V and a set function , we consider the problem of constructing an undirected multigraph G = (V,E) such that the cut function together has value at least 2 for all non-empty and proper subsets of V. If f is intersecting submodular and posi-modular, and satisfies the tripartite inequality, then we show that such a multigraph G with the minimum number of edges can be found in time, where is the time to compute the value of f(X) for a subset .     

Amyotrophic lateral sclerosis

In this case study, we describe the symptoms, neurological examination, and pathology of a woman with amyotrophic lateral sclerosis (ALS). ALS is a rare disorder leading to degeneration of the voluntary motor system and death in, on average, 3 to 4 years. The loss of motor neurons in the brain and spinal cord causes the progressive symptoms of muscular weakness, atrophy, fasciculation (muscle twitching), spasticity, and hyperreflexia. Signs of disease in both upper and lower motor neurons are required for a definitive clinical diagnosis. Pathology shows degeneration of the lateral corticospinal tracts, loss of motor neurons and astrogliosis in the brain and brain stem, and neuronal inclusions. This case was marked by the onset of weakness and muscle atrophy in the hand, which spread to involve contiguous muscle segments. Cognition, the extraocular muscles, and the urinary sphincters were spared. Respiratory muscle weakness was a late manifestation.     

Explicit formulas for the smoother weights of the Whittaker–Henderson graduation of order 1

The Whittaker–Henderson (WH) graduation is a widely applied smoothing method. This paper contributes to the literature by providing explicit formulas for the smoother weights of the WH graduation of order 1 along with some related results, which leads to a richer understanding of the filter.     

Development of low-volume,high-intensity,aerobic-type interval training for elderly Japanese men: a feasibility study

Background

The purposes of this study were to identify 1) the feasibility of a novel exercise protocol (elderly Japanese male version of high-intensity interval aerobic training: EJ-HIAT) and 2) its preliminary data (%V?O_2peak, rating of perceived exertion) in comparison with traditional moderate-intensity continuous aerobic training (MICT).

Results

Twenty-one sedentary elderly men, aged 60–69 years, performed two exercise protocols: EJ-HIAT, consisting of 3 sets of 2?3-min cycling at 75?85%V?O_2peak with 1??2-min active rests at 50%V?O_2peak between sets, and MICT, consisting of 40-min cycling at 65%V?O_2peak. The completion rate, defined as the rate of participants who 1) did not demand withdrawal, 2) were not interrupted by the tester, and 3) did not change the workload during either exercise protocol, of EJ-HIAT was similar to that of MICT (EJ-HIAT: 100%, MICT: 95.2%). Maximal perceived exertion ratings assessed by Borg scale were also similar between EJ-HIAT and MICT. However, objectively measured maximal intensity assessed by %V?O_2peak was higher for EJ-HIAT than for MICT (EJ-HIAT: 86.0 ± 5.6%, MICT: 67.1 ± 6.4%).

Conclusion

These results suggested that EJ-HIAT has good feasibility and perceived exertion similar to MICT despite having higher objectively measured intensity than MICT. An intervention aimed as identifying the effects of EJ-HIAT on exercise tolerance should be performed in the future.

Trial registration

UMIN000021185 (February 26, 2016).

     

Influences of the edge radius of curvature of tactile dots and bars on their Discriminability

Tactile dots and bars serve as tactile landmarks so that people with visual impairment can use same consumer products as those used by sighted people. However, reliable age-related data on the appropriate sizes and the shapes was not necessarily available. The purpose of this study is to evaluate influences of edge radius of curvature of tactile dots and bars on their discriminability in younger and older people to determine the appropriate size of tactile bars (as distinguished from tactile dots). Sighted younger and older participants tactually discriminated the tactile dots and bars presented individually, in random order, by a two-alternative forced-choice task. The results showed that both participants discriminated tactile bars from tactile dots faster and more accurately as the dimensional difference between bar length and width increased, regardless of conditions of edge radius of curvature. Therefore, longer dimensional difference between width and length of tactile bars is an important factor to discriminate tactile bars correctly. On the other hand, tactile dots with a larger edge radius of curvature have higher discriminability than tactile dots with a smaller edge radius of curvature in the case of dots of identical height.