Abstract:
This is a contribution to an on-going debate on animal ethics. It is an epistemological study into the Yorùbá beliefs and perceptions about animals that have existed and still exist in the areas they inhabit. The research sets out to elucidate the Yorùbá perception of animals with regard to their classification, habitat, and their role and position in religious, political, social, economic, and domestic domains of humans. This leads to an appraisal of relationships that exist between the Yorùbá people and animals in their communities. The study explores the Yorùbá folklore in its various dimensions as the paradigm to espouse their ontological perception of animals. The study concludes that the Yorùbá people attach much importance to their animals and that animals occupy an important place and space in human existence and life on the globe.

Abstract:
We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time $t$, satisfy an interesting invariance principle. Namely, together with the age of the renewal process at time $t$, they converge after scaling to the Pitman--Yor distribution. We further discuss how our results extend the classical Dynkin--Lamperti theorem.

Abstract:
Introduction : One of the intensity modulated radiation therapy (IMRT) methods is based on using compensators. The most important factor in designing a compensator is the accurate calculation of its thickness to achieve the intensity modulation of interest. To achieve that, the exact attenuation coefficient of compensator materials must be calculated. However, there are several parameters that are effective in calculating the attenuation coefficient of compensator materials . In this research, the effects of dosimeter and phantom type as well as irradiation dose and measurement depth in the calculation of this compensator characteristic were assessed. Materials and Methods : Using two types of dosimeters (RK & FC65G) and phantoms (RFA300plus & SP34), the effects of radiation dose and measured depth on the estimation of the effective attenuation coefficient was investigated for a 6MV linear accelerator. The value of applied radiation dose was 100, 200, 300 and 400 cGy, and the measured depths were 2, 5, 10, 15 and 20 cm. The measurements were carried out at the reference field size (10×10 cm2) and for a thickness of 1 cm of the compensator. Results: The results indicated that radiation dose has no significant effect in calculating the effective attenuation coefficient of compensator materials. However, altering measured depth from 2 to 20 cm resulted in a change of more than 5% in the calculations. In addition, the type of the dosimeter and phantom used in this study had no significant effect on the calculations. Conclusion: Based on these findings, it is recommended that for more accurate estimation of the effective attenuation coefficient of a compensator material, it is necessary to measure the attenuation coefficient at different depths of the treatment field.

Abstract:
Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t) in the theory of the Riemann zeta-function.

Abstract:
In this work, we propose the kernel Pitman-Yor process (KPYP) for nonparametric clustering of data with general spatial or temporal interdependencies. The KPYP is constructed by first introducing an infinite sequence of random locations. Then, based on the stick-breaking construction of the Pitman-Yor process, we define a predictor-dependent random probability measure by considering that the discount hyperparameters of the Beta-distributed random weights (stick variables) of the process are not uniform among the weights, but controlled by a kernel function expressing the proximity between the location assigned to each weight and the given predictors.

Abstract:
We study the Matsumoto-Yor property in free probability. We prove that the limiting empirical eigenvalue distribution of the GIG matrices and the Marchenko-Pastur distribution have the free Matsumoto-Yor property. Finally we characterize these distributions by a regression properties in free probability.

Abstract:
We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove some theoretical properties of the model and then present two inference methods: a collapsed MCMC sampler which allows us to model uncertainty over tree structures, and a computationally efficient greedy Bayesian EM search algorithm. Both algorithms use message passing on the tree structure. The utility of the model and algorithms is demonstrated on synthetic and real world data, both continuous and binary.

Abstract:
In this paper we study progressive filtration expansions with cadlag processes. Using results from the weak convergence of sigma fields theory, we first establish a semimartingale convergence theorem. Then we apply it in a filtration expansion with a process setting and provide sufficient conditions for a semimartingale of the base filtration to remain a semimartingale in the expanded filtration. Finally, an application to the expansion of a Brownian filtration with a time reversed diffusion is given through a detailed study.

Abstract:
Reincarnation is the belief that after someone dies; his immortal soul separates from the body and lives again in another physical body. The traditional Yorùbá culture holds the belief in reincarnation (atunwaye). Atunwaye is believed to be possible in three different forms which are: ipadawaye (ancestor’s rebirth), akudaaya (die and reappear) and abiku (born to die). Yorùbá people of Akure also hold on to the traditional belief in atunwaye. The article used the philosophical tools of analysis and evaluation to examine reincarnation beliefs among the Yorùbá people in general and Akure people in particular. Oral interviews were also conducted among indigenes of Akure, to understand their beliefs on reincarnation. Findings show that Yorùbá people of Akure also hold on to traditional belief in reincarnation (atunwaye) in its various forms. The research concludes that reincarnation is an established belief among the Yorùbá people in general and the Akure people in particular. It is also noted that this belief has survived despite the influence of Christianity and Islam on the culture of Akure people.