Parallel Algorithms for Generating Random Networks with Given Degree Sequences

Random networks are widely used for modeling and analyzing complex processes. Many mathematical models have been proposed to capture diverse real-world networks. One of the most important aspects of these models is degree distribution. Chung--Lu (CL) model is a random network model, which can produce networks with any given arbitrary degree distribution. The complex systems we deal with nowadays are growing larger and more diverse than ever. Generating random networks with any given degree distribution consisting of billions of nodes and edges or more has become a necessity, which requires efficient and parallel algorithms. We present an MPI-based distributed memory parallel algorithm for generating massive random networks using CL model, which takes $O(\frac{m+n}{P}+P)$ time with high probability and $O(n)$ space per processor, where $n$, $m$, and $P$ are the number of nodes, edges and processors, respectively. The time efficiency is achieved by using a novel load-balancing algorithm. Our algorithms scale very well to a large number of processors and can generate massive power--law networks with one billion nodes and $250$ billion edges in one minute using $1024$ processors.Comment: Accepted in NPC 201

Fundamentals of PV Efficiency Interpreted by a Two-Level Model

Elementary physics of photovoltaic energy conversion in a two-level atomic PV is considered. We explain the conditions for which the Carnot efficiency is reached and how it can be exceeded! The loss mechanisms - thermalization, angle entropy, and below-bandgap transmission - explain the gap between Carnot efficiency and the Shockley-Queisser limit. Wide varieties of techniques developed to reduce these losses (e.g., solar concentrators, solar-thermal, tandem cells, etc.) are reinterpreted by using a two level model. Remarkably, the simple model appears to capture the essence of PV operation and reproduce the key results and important insights that are known to the experts through complex derivations.Comment: 7 pages, 6 figure

The Relevant Operators for the Hubbard Hamiltonian with a magnetic field term

The Hubbard Hamiltonian and its variants/generalizations continue to dominate the theoretical modelling of important problems such as high temperature superconductivity. In this note we identify the set of relevant operators for the Hubbard Hamiltonian with a magnetic field term.Comment: 19 pages, RevTe