Influence of parental density on the distribution pattern of eggs in the common cabbage butterfly,Pieris rapae crucivora

Summary To investigate the relation between the distribution pattern of eggs and the parental density in the common cabbage butterfly,Pieris rapae crucivora, the countings of egg number per plant were made on both cabbage plants cultivated in the farm and planted in the net house in which the female butterflies were released at various densities. The frequency distribution of eggs fits well to the negative binomial excepting the cases where they agree withPoisson series, and the degree of aggregation expressed as the reciprocal of the parameter, 1/k, tends to decrease as the egg or parental density increases. At the same parental density, however, the distribution of eggs can be described by the negative binomial with a common parameter,k _c, regardless of the difference in the density of laid eggs. In the case where a single female butterfly lays eggs, the spatial pattern of egg distribution is always lean, while its frequencies conform toPoisson or the negative binomial series. This lean changes toward patchy with increasing the parental density. From these results, it is concluded that the degree of aggregation in the distribution of eggs decreases with the increase of the parental density.     

Empirical geodesic graphs and CAT(k) metrics for data analysis

Statistics and Computing - A methodology is developed for data analysis based on empirically constructed geodesic metric spaces. For a probability distribution, the length along a path between two...     

TITE‐BOIN‐ET: Time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on both efficacy and toxicity outcomes

One of the primary purposes of an oncology dose‐finding trial is to identify an optimal dose (OD) that is both tolerable and has an indication of therapeutic benefit for subjects in subsequent clinical trials. In addition, it is quite important to accelerate early stage trials to shorten the entire period of drug development. However, it is often challenging to make adaptive decisions of dose escalation and de‐escalation in a timely manner because of the fast accrual rate, the difference of outcome evaluation periods for efficacy and toxicity and the late‐onset outcomes. To solve these issues, we propose the time‐to‐event Bayesian optimal interval design to accelerate dose‐finding based on cumulative and pending data of both efficacy and toxicity. The new design, named “TITE‐BOIN‐ET” design, is nonparametric and a model‐assisted design. Thus, it is robust, much simpler, and easier to implement in actual oncology dose‐finding trials compared with the model‐based approaches. These characteristics are quite useful from a practical point of view. A simulation study shows that the TITE‐BOIN‐ET design has advantages compared with the model‐based approaches in both the percentage of correct OD selection and the average number of patients allocated to the ODs across a variety of realistic settings. In addition, the TITE‐BOIN‐ET design significantly shortens the trial duration compared with the designs without sequential enrollment and therefore has the potential to accelerate early stage dose‐finding trials.     

Gerrymandering in a hierarchical legislature

Theory and Decision - We build a multiple hierarchical model of a representative democracy in which citizens elect ward representatives, ward representatives elect county representatives, county...     

Horn Clause Computation with DNA Molecules

In this paper, we will propose Horn clause computation as an underlying computational framework of DNA computer. Horn clause program is a subclass of the formulas of first order logic and has close relation to PROLOG language. The computational power of Horn clauses was discussed in (Tärnland, 1977) and it was shown that a finite set of Horn clauses is computationally equivalent to Turing Machine. Furthermore, it should be noted that Horn programs are adequate for representing nondeterministic computation. Thus, its parallel implementation with huge number of molecules might have possibility to overcome the computational power of conventional computers. It should also be noted that the clear logical semantics of Horn programs might enable us to accept it as a higher-level programming language of DNA computer. The aim of this paper is to propose an experimental method for implementing deduction with a subclass of Horn programs, called simple Horn programs. The computational power of this model is theoretically investigated and demonstrated with some applications to NP-complete problems.     

Methods for estimating the number of the Cryptomeria red mite, especially with the removal by solutions

Summary We compared the removal by solution, the represented count-area method and the beating, for the purpose of estimating the number of the Cryptomeria red mite. Among them the solution procedure provided the smallest standard error as per cent of the mean. 0.25 per cent unheated solution of sodium hydroxide is used for the summer generation, and also 0.25 per cent boiling one for the winter eggs. The mean proportion removed±standard error for the summer eggs and the winter eggs were 0.8770±0.0316 and 0.7920±0.0281 respectively, while 0.9894±0.0050 for the mites.     

Risk Assessment of the Carbon Nanotube Group

This study assessed the health risks via inhalation and derived the occupational exposure limit (OEL) for the carbon nanotube (CNT) group rather than individual CNT material. We devised two methods: the integration of the intratracheal instillation (IT) data with the inhalation (IH) data, and the “biaxial approach.” A four‐week IH test and IT test were performed in rats exposed to representative materials to obtain the no observed adverse effect level, based on which the OEL was derived. We used the biaxial approach to conduct a relative toxicity assessment of six types of CNTs. An OEL of 0.03 mg/m³ was selected as the criterion for the CNT group. We proposed that the OEL be limited to 15 years. We adopted adaptive management, in which the values are reviewed whenever new data are obtained. The toxicity level was found to be correlated with the Brunauer‐Emmett‐Teller (BET)‐specific surface area (BET‐SSA) of CNT, suggesting the BET‐SSA to have potential for use in toxicity estimation. We used the published exposure data and measurement results of dustiness tests to compute the risk in relation to particle size at the workplace and showed that controlling micron‐sized respirable particles was of utmost importance. Our genotoxicity studies indicated that CNT did not directly interact with genetic materials. They supported the concept that, even if CNT is genotoxic, it is secondary genotoxicity mediated via a pathway of genotoxic damage resulting from oxidative DNA attack by free radicals generated during CNT‐elicited inflammation. Secondary genotoxicity appears to involve a threshold.     

Star-shaped distributions and their generalizations

Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. We generalize elliptically contoured densities to “star-shaped distributions” with concentric star-shaped contours and show that many results in the former case continue to hold in the more general case. We develop a general theory in the framework of abstract group invariance so that the results can be applied to other cases as well, especially those involving random matrices.     

Bayesian longitudinal paired comparison model and its application to sports data using weighted likelihood bootstrap

This article describes a procedure for Bayesian longitudinal paired comparison data analysis to rank stimuli. The proposed model is developed by combining the Bradley–Terry model and a nonlinear model that utilizes an exponential distribution to describe longitudinal changes in scale values. The weighted likelihood bootstrap method (WLB) is used to obtain samples from posterior distributions of parameters. WLB is an effective tool because neither diagnosing parameter convergence nor specifying proposal distributions is required, which decreases both the preparation necessary and the time involved. The proposed model is a simple one with few parameters, so WLB can be effectively accommodated. An actual example using sports data from sumo wrestling is presented to verify the efficacy of the proposed method.