Generation, Ranking and Unranking of Ordered Trees with Degree Bounds

We study the problem of generating, ranking and unranking of unlabeled ordered trees whose nodes have maximum degree of $\Delta$. This class of trees represents a generalization of chemical trees. A chemical tree is an unlabeled tree in which no node has degree greater than 4. By allowing up to $\Delta$ children for each node of chemical tree instead of 4, we will have a generalization of chemical trees. Here, we introduce a new encoding over an alphabet of size 4 for representing unlabeled ordered trees with maximum degree of $\Delta$. We use this encoding for generating these trees in A-order with constant average time and O(n) worst case time. Due to the given encoding, with a precomputation of size and time O(n^2) (assuming $\Delta$ is constant), both ranking and unranking algorithms are also designed taking O(n) and O(nlogn) time complexities.Comment: In Proceedings DCM 2015, arXiv:1603.0053

Numerical Analysis of a Photovoltaic Module Integrated with Various Water Cooling Systems

As the main drawback of a photovoltaic module is its high operating temperature, various designs for cooling the module are presented in this study. Computational fluid dynamics (CFD) software is used for simulating the presented models. In these models, water channels are placed above or below the panel to cool the module and heat the water at the same time. In two designs, aluminium fins are attached to the bottom side of the panel inside the water channel. The water outlet temperature, pressure drop and heat flux from the panel are calculated at various Reynolds numbers. The results show that as the Reynolds number increases, the heat flux and the pressure drop increase while the coolant average outlet temperature decreases. The highest amount of heat flux is obtained from Model A, which indicates that this model has a better cooling capacity than other models investigated in the study

A general class of spreading processes with non-Markovian dynamics

In this paper we propose a general class of models for spreading processes we call the $SI^*V^*$ model. Unlike many works that consider a fixed number of compartmental states, we allow an arbitrary number of states on arbitrary graphs with heterogeneous parameters for all nodes and edges. As a result, this generalizes an extremely large number of models studied in the literature including the MSEIV, MSEIR, MSEIS, SEIV, SEIR, SEIS, SIV, SIRS, SIR, and SIS models. Furthermore, we show how the $SI^*V^*$ model allows us to model non-Poisson spreading processes letting us capture much more complicated dynamics than existing works such as information spreading through social networks or the delayed incubation period of a disease like Ebola. This is in contrast to the overwhelming majority of works in the literature that only consider spreading processes that can be captured by a Markov process. After developing the stochastic model, we analyze its deterministic mean-field approximation and provide conditions for when the disease-free equilibrium is stable. Simulations illustrate our results