On Frankl and Furedi's conjecture for 3-uniform hypergraphs

The Lagrangian of a hypergraph has been a useful tool in hypergraph extremal problems. In most applications, we need an upper bound for the Lagrangian of a hypergraph. Frankl and Furedi in \cite{FF} conjectured that the $r$-graph with $m$ edges formed by taking the first $m$ sets in the colex ordering of ${\mathbb N}^{(r)}$ has the largest Lagrangian of all $r$-graphs with $m$ edges. In this paper, we give some partial results for this conjecture.Comment: 19 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1211.650

Negatively Correlated Search

Evolutionary Algorithms (EAs) have been shown to be powerful tools for complex optimization problems, which are ubiquitous in both communication and big data analytics. This paper presents a new EA, namely Negatively Correlated Search (NCS), which maintains multiple individual search processes in parallel and models the search behaviors of individual search processes as probability distributions. NCS explicitly promotes negatively correlated search behaviors by encouraging differences among the probability distributions (search behaviors). By this means, individual search processes share information and cooperate with each other to search diverse regions of a search space, which makes NCS a promising method for non-convex optimization. The cooperation scheme of NCS could also be regarded as a novel diversity preservation scheme that, different from other existing schemes, directly promotes diversity at the level of search behaviors rather than merely trying to maintain diversity among candidate solutions. Empirical studies showed that NCS is competitive to well-established search methods in the sense that NCS achieved the best overall performance on 20 multimodal (non-convex) continuous optimization problems. The advantages of NCS over state-of-the-art approaches are also demonstrated with a case study on the synthesis of unequally spaced linear antenna arrays

A Parallel Divide-and-Conquer based Evolutionary Algorithm for Large-scale Optimization

Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to solve the emerging large-scale problems both effectively and efficiently. In this paper, we propose a novel Divide-and-Conquer (DC) based EA that can not only produce high-quality solution by solving sub-problems separately, but also highly utilizes the power of parallel computing by solving the sub-problems simultaneously. Existing DC-based EAs that were deemed to enjoy the same advantages of the proposed algorithm, are shown to be practically incompatible with the parallel computing scheme, unless some trade-offs are made by compromising the solution quality.Comment: 12 pages, 0 figure

High-dimensional Black-box Optimization via Divide and Approximate Conquer

Divide and Conquer (DC) is conceptually well suited to high-dimensional optimization by decomposing a problem into multiple small-scale sub-problems. However, appealing performance can be seldom observed when the sub-problems are interdependent. This paper suggests that the major difficulty of tackling interdependent sub-problems lies in the precise evaluation of a partial solution (to a sub-problem), which can be overwhelmingly costly and thus makes sub-problems non-trivial to conquer. Thus, we propose an approximation approach, named Divide and Approximate Conquer (DAC), which reduces the cost of partial solution evaluation from exponential time to polynomial time. Meanwhile, the convergence to the global optimum (of the original problem) is still guaranteed. The effectiveness of DAC is demonstrated empirically on two sets of non-separable high-dimensional problems.Comment: 7 pages, 2 figures, conferenc

On the Properties of Gromov Matrices and their Applications in Network Inference

The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a heuristic procedure for general graphs by (usually randomly) choosing a spanning tree in the graph to apply the approach developed for trees. However, there are an intractable number of spanning trees in a dense graph. In this paper, we represent a weighted tree with a matrix, which we call a Gromov matrix. We propose a method that constructs a family of Gromov matrices using convex combinations, which can be used for inference and estimation instead of a randomly selected spanning tree. This procedure increases the size of the candidate set and hence enhances the performance of the classical spanning tree heuristic. On the other hand, our new scheme is based on simple algebraic constructions using matrices, and hence is still computationally tractable. We discuss some applications on network inference and estimation to demonstrate the usefulness of the proposed method

Three-terminal normal-superconductor junction as thermal transistor

We propose a thermal transistor based on a three-terminal normal-superconductor (NS) junction with superconductor terminal acting as the base. The emergence of heat amplification is due to the negative differential thermal conductance (NDTC) effect for the NS diode in which the normal side maintains a higher temperature. The temperature dependent superconducting energy gap is responsible for the NDTC. By controlling quantum dot levels and their coupling strengths to the terminals, a huge heat amplification factor can be achieved. The setup offers an alternative tuning scheme of heat amplification factor and may find use in cryogenic applications.Comment: 6 pages, 3 figure