A Periodic Review Inventory Model in a Random Environment

We consider a single product, periodic review inventory model with variable cqacity, random yield, and uncertain demand in a random environment. All model parameters and distributions depend on environmental fluctuations. It is assuumed that the environmental process follows a discrete-time Markov chain. The optimd inventory policy to minimize the total discounted expected cost is derived via dynamic programming. For the finite-horizon model, we show that the objective function is quasi-convex and that the structure of the optimal policy is characterized by a single environmental-dependent critical number for the initial inventory level at each period. Expressions for solving the critical number and the optimal planned ordering are obtained. We further show that the solution for the finite-horizon model converges to that of the infinite-horizon model.

Time evolution of a thin black ring via Hawking radiation

Black objects lose their mass and angular momenta through evaporation by Hawking radiation, and the investigation of their time evolution has a long history. In this paper, we study this problem for a five-dimensional doubly spinning black ring. The black ring is assumed to emit only massless scalar particles. We consider a thin black ring with a small thickness parameter, $\lambda\ll 1$, which can be approximated by a boosted Kerr string locally. We show that a thin black ring evaporates with fixing its thickness parameter $\lambda$. Further, in the case of an Emparan-Reall black ring, we derive analytic formulas for the time evolution, which has one parameter to be evaluated numerically. We find that the lifetime of a thin black ring is shorter by a factor of $O(\lambda^2)$ compared to a five-dimensional Schwarzschild black hole with the same initial mass. We also study detailed properties of the Hawking radiation from the thin black ring, including the energy and angular spectra of emitted particles.Comment: 28 pages, 6 figure

Spectral and Polarization Properties of Photospheric Emission From Stratified Jets

We explore the spectral and polarization properties of photospheric emissions from stratified jets in which multiple components, separated by a sharp velocity shear regions, are distributed in lateral direction. Propagation of thermal photons injected at high optical depth region are calculated until they escape from the photosphere. It is found that presence of the lateral structure within the jet leads to non-thermal feature of the spectra and significant polarization signal in the resulting emission. The deviation from thermal spectra as well as the polarization degree tends to be enhanced as the velocity gradient in the shear region increases. In particular, we show that emissions from multi-component jet can reproduce the typical observed spectra of gamma-ray bursts (GRBs) irrespective to the position of the observer when a velocity shear region is closely spaced in various lateral ($\theta$) positions. The degree of polarization associated in the emission is significant (> few%) at wide range of observer angles and can be higher than 30%.Comment: 21 pages, 12 figures, accepted for publication in Ap

A NOTE ON A PERIODIC REVIEW INVENTORY MODEL WITH UNCERTAIN DEMAND IN A RANDOM ENVIRONMENT

Abstract. This paper is on the analysis of a single product, periodic review inventory model, where the distributions of demands vary with the state of the environment variable. The state of the environment is assumed to follow a discrete-time Markov chain. The optimal inventory policy to minimize the total discounted expected cost is derived via dynamic programming. For the finite-horizon model, we show that an environmental-dependent base-stock policy is optimal, and derive some characteristics of the optimal policy. Under additional conditions, we further derive the monotonicity of the optimal policy. Introduction The inventory control has long focused on managing certain specific types of probability in the demand for the products. But, on the other hand, consumer's liking becomes variously in the real-life. The demand is fluctuated by the economic climate, weather condition, trend of public opinion, and so forth. Mere including a purely random component in the demand process will be impossible to express such situations. So, in this paper, under the assumption that the environmental process follows a discretetime Markov chain, we model a single product inventory system of which the distributions of demands depend on environmental fluctuations, and discuss the management policy. We further investigate the effect of the environmental fluctuations on the optimal policy. The main advantage of the Markov chain approach is that it provides a national and flexible framework for formulating various changes described above. The effect of a randomly changing environment in inventory model received only limited attention in the earlier paper. Kalymon[12] studies a multiple-period inventory model in which the unit cost of the product is determined by a Markov process, and the distribution of demand in each period depends on the current cost. Feldman[8] models the demand environment as a continuous-time Markov chain. The demand is modulated by a compound Poisson process where the parameters are determined by the state of the environment. But he studies only the steady-state distribution of the inventory position. Song and Zipkin[18] present a continuous-review inventory model where the demand process is a Markov modulated Poisson process, and they derive some basic characteristics of the optimal policy and algorithms for computing the optimal policy. In recent articles,Özekici and Parlar The purpose of this paper is to show that the environmental-dependent base-stock policy is optimal, and that the optimal policy have the monotonicity for review periods by analyzing finite-horizon periodic-review inventory model where the demand distribution depen

Novel metric for hyperbolic phylogenetic tree embeddings

Advances in experimental technologies, such as DNA sequencing, have opened up new avenues for the applications of phylogenetic methods to various fields beyond their traditional application in evolutionary investigations, extending to the fields of development, differentiation, cancer genomics, and immunogenomics. Thus, the importance of phylogenetic methods is increasingly being recognized, and the development of a novel phylogenetic approach can contribute to several areas of research. Recently, the use of hyperbolic geometry has attracted attention in artificial intelligence research. Hyperbolic space can better represent a hierarchical structure compared to Euclidean space, and can therefore be useful for describing and analyzing a phylogenetic tree. In this study, we developed a novel metric that considers the characteristics of a phylogenetic tree for representation in hyperbolic space. We compared the performance of the proposed hyperbolic embeddings, general hyperbolic embeddings, and Euclidean embeddings, and confirmed that our method could be used to more precisely reconstruct evolutionary distance. We also demonstrate that our approach is useful for predicting the nearest-neighbor node in a partial phylogenetic tree with missing nodes. Furthermore, we proposed a novel approach based on our metric to integrate multiple trees for analyzing tree nodes or imputing missing distances. This study highlights the utility of adopting a geometric approach for further advancing the applications of phylogenetic methods