dCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS

We provide a numerical package for the computation of a d-variate near G-optimal polynomial regression design of degree m on a finite design space X ⊂ R d , by few iterations of a basic multiplicative algorithm followed by Tchakaloff-like compression of the discrete measure keeping the reached G-efficiency, via an accelerated version of the Lawson-Hanson algorithm for Non-Negative Least Squares (NNLS) problems. This package can solve on a personal computer large-scale problems where c a r d ( X ) × dim ( P 2 m d ) is up to 10 8 – 10 9 , being dim ( P 2 m d ) = 2 m + d d = 2 m + d 2 m . Several numerical tests are presented on complex shapes in d = 3 and on hypercubes in d > 3 .

Cross-entropy optimal dimensionality reduction with condition on information capacity

Using a data leads to a problem of its sufficiency to solve specific task. Proposed paper is devoted to a modification of direct-inverse projection method (DIP-method) based on an idea of information capacity. DIP-method is updated with a condition on maintaining the information capacity in given ranges. Modified dimensionality reduction method (mDIP) based on the problem of minimization cross-entropy function on a set defined by linear inequality. Minimization of the function is suggested to perform by the first-order multiplicative algorithm. There obtained conditions of local convergence.

Selmer's Multiplicative Algorithm

The behavior of the multiplicative acceleration of Selmer's algorithm is widely unknown and no general result on convergence has been detected yet. Solely for its 2-dimensional, periodic expansions, there exist some results on convergence and approximation due to Fritz Schweiger. In this paper we show that periodic expansions of any dimension do in fact converge and that the coordinates of the limit points are rational functions of the largest eigenvalue of the periodicity matrix.

Distributed mass-balance modelling on two neighbouring glaciers in Ortles-Cevedale, Italy, from 2004 to 2009

A 6 year application of an enhanced temperature-index mass-balance model to Careser and La Mare glaciers, Eastern Italian Alps, is presented. The two glaciers exhibit very different characteristics, and a comprehensive dataset of distributed mass-balance measurements was used to test the model performance. The model was run using meteorological data acquired outside the glaciers. The work was focused on two main aspects: (1) the development of a morphological redistribution procedure for snow, and (2) the comparison of three different melt algorithms proposed in the literature. The results show that the simple method proposed for snow redistribution can greatly improve simulation of winter balance, and further improvements would be achievable by collecting data on inaccessible and high-altitude areas. All three melt formulations displayed a good skill level and very similar results in modelling the mass-balance distribution over glacier areas, with slightly better results from a multiplicative algorithm in capturing the vertical balance gradient. The simulation errors are related to aspect and elevation, and tend to be spatially aggregated. Some assumptions concerning the spatial and temporal distribution of air temperature and incoming solar radiation, although reasonable and widely used in the literature, may be responsible for this aggregation. Hence, there is a need to further investigate the processes that regulate the distribution of melt energy, and that appear to control the current deglaciation phase in this area.