Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

A parallel random forest algorithm for big data in a spark cloud computing environment

With the emergence of the big data age, the issue of how to obtain valuable knowledge from a dataset efficiently and accurately has attracted increasingly attention from both academia and industry. This paper presents a Parallel Random Forest (PRF) algorithm for big data on the Apache Spark platform. The PRF algorithm is optimized based on a hybrid approach combining data-parallel and task-parallel optimization. From the perspective of data-parallel optimization, a vertical data-partitioning method is performed to reduce the data communication cost effectively, and a data-multiplexing method is performed is performed to allow the training dataset to be reused and diminish the volume of data. From the perspective of task-parallel optimization, a dual parallel approach is carried out in the training process of RF, and a task Directed Acyclic Graph (DAG) is created according to the parallel training process of PRF and the dependence of the Resilient Distributed Datasets (RDD) objects. Then, different task schedulers are invoked for the tasks in the DAG. Moreover, to improve the algorithm's accuracy for large, high-dimensional, and noisy data, we perform a dimension-reduction approach in the training process and a weighted voting approach in the prediction process prior to parallelization. Extensive experimental results indicate the superiority and notable advantages of the PRF algorithm over the relevant algorithms implemented by Spark MLlib and other studies in terms of the classification accuracy, performance, and scalability.

Variations in MIMO-OFDM channel capacity due to random human movement in an indoor environment

Channel measurements and simulations have been carried out to observe the effects of pedestrian movement on multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) channel capacity. An in-house built MIMO-OFDM packet transmission demonstrator equipped with four transmitters and four receivers has been utilized to perform channel measurements at 5.2 GHz. Variations in the channel capacity dynamic range have been analysed for 1 to 10 pedestrians and different antenna arrays (2 × 2, 3 × 3 and 4 × 4). Results show a predicted 5.5 bits/s/Hz and a measured 1.5 bits/s/Hz increment in the capacity dynamic range with the number of pedestrian and the number of antennas in the transmitter and receiver array.

Random Indexing K-tree

Random Indexing K-tree is the combination of two algorithms suited for large scale document clustering.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Can't see the water for the trees

The work was both conceived and constructed in-situ within Gnombup Swamp a seasonal water body at Bremer Bay, Western Australia. The work interacts with site-specific conditions including wind patterns and a datum of seasonal water levels marks. The work is the result of collaboration between soil scientist Paula Deegan and Ian Weir. The installation was documented with a series of 30 still digital photographs, later animated in Microsoft Powerpoint.

The relationship between culture, attitude, social networks and quality of life in midlife Australian and Taiwanese citizens

Objectives: The objectives of this study were to specifically investigate the differences in culture, attitudes and social networks between Australian and Taiwanese men and women and identify the factors that predict midlife men and women’s quality of life in both countries. Methods: A stratified random sample strategy based on probability proportional sampling (PPS) was conducted to investigate 278 Australian and 398 Taiwanese midlife men and women’s quality of life. Multiple regression modelling and classification and regression trees (CARTs) were performed to examine the potential differences on culture, attitude, social networks, social demographic factors and religion/spirituality in midlife men and women’s quality of life in both Australia and Taiwan. Results: The results of this study suggest that culture involves multiple functions and interacts with attitudes, social networks and individual factors to influence a person’s quality of life. Significant relationships were found between the interaction between cultural circumstances and a person’s internal and external factors. The research found that good social support networks and a healthy optimistic disposition may significantly enhance midlife men and women’s quality of life. Conclusion: The study indicated that there is a significant relationship between culture, attitude, social networks and quality of life in midlife Australian and Taiwanese men and women. People who had higher levels of horizontal individualism and collectivism, positive attitudes and better social support had better psychological, social, physical and environmental health, while it emerged that vertical individualists with competitive characteristics would experience a lower quality of life. This study has highlighted areas where opportunities exist to further reflect upon contemporary social health policies for Australian and Taiwanese societies and also within the global perspective, in order to provide enhanced quality care for growing midlife populations.