A CENTER OF A POLYTOPE: AN EXPOSITORY REVIEW AND A PARALLEL IMPLEMENTATION

ABSTRACT. The solution space of the rectangular linear system Az b, subject to x> 0, is called a polytope. An attempt is made to provide a deeper geometric insight, with numerical examples, into the condensed paper by Lord, et al. [1], that presents an algorithm to compute a center of a polytope. The algorithm is readily adopted for either sequential or parallel computer implementation. The computed center provides an initial feasible solution (interior point) of a linear programming problem. KEY WORDS AND PHRASES. Center of a polytope, consistency check, Euclidean distance, initial feasible solution, linear programming, Moore-Penrose inverse, nonnegative solution

Antipodean Theory for Educational Research

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Backprojection for Training Feedforward Neural Networks in the Input and Feature Spaces

After the tremendous development of neural networks trained by backpropagation, it is a good time to develop other algorithms for training neural networks to gain more insights into networks. In this paper, we propose a new algorithm for training feedforward neural networks which is fairly faster than backpropagation. This method is based on projection and reconstruction where, at every layer, the projected data and reconstructed labels are forced to be similar and the weights are tuned accordingly layer by layer. The proposed algorithm can be used for both input and feature spaces, named as backprojection and kernel backprojection, respectively. This algorithm gives an insight to networks with a projection-based perspective. The experiments on synthetic datasets show the effectiveness of the proposed method.Comment: Accepted (to appear) in International Conference on Image Analysis and Recognition (ICIAR) 2020, Springe

Load-settlement modelling of axially loaded drilled shafts using CPT-based recurrent neural networks

The design of pile foundations requires good estimation of the pile load-carrying capacity and settlement. Design for bearing capacity and design for settlement have been traditionally carried out separately. However, soil resistance and settlement are influenced by each other, and the design of pile foundations should thus consider the bearing capacity and settlement inseparably. This requires the full load–settlement response of piles to be well predicted. However, it is well known that the actual load–settlement response of pile foundations can be obtained only by load tests carried out in situ, which are expensive and time-consuming. In this paper, recurrent neural networks (RNNs) were used to develop a prediction model that can resemble the full load–settlement response of drilled shafts (bored piles) subjected to axial loading. The developed RNN model was calibrated and validated using several in situ full-scale pile load tests, as well as cone penetration test (CPT) data. The results indicate that the developed RNN model has the ability to reliably predict the load–settlement response of axially loaded drilled shafts and can thus be used by geotechnical engineers for routine design practice

Characterization of clastic sedimentary enviroments by clustering algorithm and several statistical approaches — case study, Sava Depression in Northern Croatia

Abstract This study demonstrates a method to identify and characterize some facies of turbiditic depositional environments. The study area is a hydrocarbon field in the Sava Depression (Northern Croatia). Its Upper Miocene reservoirs have been proved to represent a lacustrine turbidite system. In the workflow, first an unsupervised neural network was applied as clustering method for two sandstone reservoirs. The elements of the input vectors were the basic petrophysical parameters. In the second step autocorrelation surfaces were used to reveal the hidden anisotropy of the grid. This anisotropy is supposed to identify the main continuity directions in the geometrical analyses of sandstone bodies. Finally, in the description of clusters several parametric and nonparametric statistics were used to characterize the identified facies. Obtained results correspond to the previously published interpretation of those reservoir facies

The effects of meteorological factors on the occurrence of Ganoderma sp. spores in the air

Ganoderma sp. is an airborne fungal spore type known to trigger respiratory allergy symptoms in sensitive patients. Aiming to reduce the risk for allergic individuals, we analysed fungal spore circulation in Szczecin, Poland, and its dependence on meteorological conditions. Statistical models for the airborne spore concentrations of Ganoderma sp.—one of the most abundant fungal taxa in the area—were developed. Aerobiological sampling was conducted over 2004–2008 using a volumetric Lanzoni trap. Simultaneously, the following meteorological parameters were recorded: daily level of precipitation, maximum and average wind speed, relative humidity and maximum, minimum, average and dew point temperatures. These data were used as the explaining variables. Due to the non-linearity and non-normality of the data set, the applied modelling techniques were artificial neural networks (ANN) and mutlivariate regression trees (MRT). The obtained classification and MRT models predicted threshold conditions above which Ganoderma sp. appeared in the air. It turned out that dew point temperature was the main factor influencing the presence or absence of Ganoderma sp. spores. Further analysis of spore seasons revealed that the airborne fungal spore concentration depended only slightly on meteorological factors

Comparative genomics of 10 new Caenorhabditis species

Abstract The nematode Caenorhabditis elegans has been central to the understanding of metazoan biology. However, C. elegans is but one species among millions and the significance of this important model organism will only be fully revealed if it is placed in a rich evolutionary context. Global sampling efforts have led to the discovery of over 50 putative species from the genus Caenorhabditis, many of which await formal species description. Here, we present species descriptions for 10 new Caenorhabditis species. We also present draft genome sequences for nine of these new species, along with a transcriptome assembly for one. We exploit these whole‐genome data to reconstruct the Caenorhabditis phylogeny and use this phylogenetic tree to dissect the evolution of morphology in the genus. We reveal extensive variation in genome size and investigate the molecular processes that underlie this variation. We show unexpected complexity in the evolutionary history of key developmental pathway genes. These new species and the associated genomic resources will be essential in our attempts to understand the evolutionary origins of the C. elegans model