CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions

We introduce a general framework for active learning in regression problems. Our framework extends the standard setup by allowing for general types of data, rather than merely pointwise samples of the target function. This generalization covers many cases of practical interest, such as data acquired in transform domains (e.g., Fourier data), vector-valued data (e.g., gradient-augmented data), data acquired along continuous curves, and, multimodal data (i.e., combinations of different types of measurements). Our framework considers random sampling according to a finite number of sampling measures and arbitrary nonlinear approximation spaces (model classes). We introduce the concept of generalized Christoffel functions and show how these can be used to optimize the sampling measures. We prove that this leads to near-optimal sample complexity in various important cases. This paper focuses on applications in scientific computing, where active learning is often desirable, since it is usually expensive to generate data. We demonstrate the efficacy of our framework for gradient-augmented learning with polynomials, Magnetic Resonance Imaging (MRI) using generative models and adaptive sampling for solving PDEs using Physics-Informed Neural Networks (PINNs)

A unified framework for learning with nonlinear model classes from arbitrary linear samples

This work considers the fundamental problem of learning an unknown object from training data using a given model class. We introduce a unified framework that allows for objects in arbitrary Hilbert spaces, general types of (random) linear measurements as training data and general types of nonlinear model classes. We establish a series of learning guarantees for this framework. These guarantees provide explicit relations between the amount of training data and properties of the model class to ensure near-best generalization bounds. In doing so, we also introduce and develop the key notion of the variation of a model class with respect to a distribution of sampling operators. To exhibit the versatility of this framework, we show that it can accommodate many different types of well-known problems of interest. We present examples such as matrix sketching by random sampling, compressed sensing with isotropic vectors, active learning in regression and compressed sensing with generative models. In all cases, we show how known results become straightforward corollaries of our general learning guarantees. For compressed sensing with generative models, we also present a number of generalizations and improvements of recent results. In summary, our work not only introduces a unified way to study learning unknown objects from general types of data, but also establishes a series of general theoretical guarantees which consolidate and improve various known results

Field Activity of Reticulitermes grassei (Isoptera: Rhinotermitidae) in Oak Forests of the Southern Iberian Peninsula

This paper presents preliminary data on the field activity of Reticulitermes grassei Clément in oak forests of the southern Iberian Peninsula. Recent research has provided information on the nature and intensity of termite damage to cork oaks (Quercus suber, L.) in northern Andalusia (Spain). Taking that information into account, the present study sought to determine annual field activity pattern in R. grassei, with a view to identifying more precisely the best time for applying control techniques. Data were obtained from field monitoring experiments conducted over a complete one-year cycle using termite-specific baited traps. Results for relative termite numbers at different periods indicated that forest activity was most intense in mid-summer, whilst the surface foraging area was greatest from late summer to early fall, peaking after the first autumnal rains. The findings of this study may help to enhance the efficacy of termite bait treatments in natural environments, since baits decay and lose effectiveness over time, and are also dispersed by the termites themselves. Accurate information on peak termite activity periods would enable products to be applied in most favorable timing, thus optimizing the results of treatment

Effect of surface structure of platinum single crystal electrodes on the electrochemical reduction of CO2 in methanol-water mixtures

The reduction of CO2 on platinum single crystal electrodes has been investigated in methanol/water mixtures. The reaction is sensitive to the crystallographic structure of the surface, with the (111) triangular arrangement of atoms being the most active site. Use of stepped surfaces revealed that long range order has little effect on the reaction rate. On the other hand, the (100) site is the less active. The combination of the results of a voltammetric study using different scan rate and the use of a hanging meniscus rotating disk electrode configuration with different rotation speeds suggests the reaction rate is limited by a chemical step at large overvoltages. The nature of this chemical step is uncertain but different possibilities are discussed. The Tafel slope suggests that the rate determining step is the first electron transfer at low overvoltages while at high overvoltages the rate of the first chemical step limits the rate of CO2 reduction.Financial support from MINECTO through projects CTQ2013-44083-P and PCIN-2013-046 is greatly acknowledged. B. Cardenas also acknowledges the Generalitat Valenciana for the award of a Santiago Grisolia Grant

Network models of soil porous structure

Soils sustain life on Earth. In times of increasing anthropogenic demands on soils [1] there is growing need to seek for novel approaches to understand the relationships between the soil porous structure and specific soil functions. Recently [2-4], soil pore structure was described as a complex network of pores using spatially embedded varying fitness network model [2] or heterogeneous preferential attachment scheme [3-4], both approaches revealing the apparent scale-free topology of soils. Here, we show, using a large set of soil images of structures obtained by X-ray computed tomography that both methods predict topological similar networks of soil pore structures. Furthermore, by analyzing the node-node link correlation properties of the obtained networks we suggest an approach to quantify the complexity of soil pore structur

Typological analysis of slidequakes emitted from landslides : experiments on an expander body pile and Sobradinho landslide (Brasilia, Brazil)

Reactivation of a landslide is usually accompanied by microseismic signals emitted from the deforming soil mass. The reproduction of similar signals in a physical model test conducted under control conditions can allow researchers to explore and test such complicated signals to improve the prediction of full-scale failure. The present study investigates the similarity between the slidequakes (microseismicity) naturally emitted from an existing colluvial landslide (Sobradinho, Brazil) in response to rainfalls and the emissions generated by a pullout test of an expander body (EB) pile in tropical soil under controlled conditions. The microseismic signals emitted from both experimental sites (i.e. the landslide and the EB pile test) were recorded and compared. Data were acquired by mini-arrays of four short-period seismometers. For the signal nomenclature, a typological scheme was adopted, in which sonograms/spectral contents of the signals were used. As a result, short duration microseismic signals were observed during the pullout test. In contrast, at the Sobradinho landslide, the testing detected signals of different characteristics whose source mechanisms have remained ambiguous, mainly because of the short duration of the data campaigns. However, at the landslide, propagating events were observed that might be attributed to the energies generated by the river bedload during the heavy rains. The present study offers some insight into the pre-collapse dynamic behavior of unstable slopes in clayey formations

Impact of Dragon Fruit Waste in Microbial Fuel Cells to Generate Friendly Electric Energy

Pollution generated by the misuse of large amounts of fruit and vegetable waste has become a major environmental and social problem for developing countries due to the absence of specialized collection centers for this type of waste. This research aims to generate electricity in an eco-friendly way using red dragon fruit (pitahaya) waste as the fuel in single-chamber microbial fuel cells on a laboratory scale using zinc and copper electrodes. It was possible to generate voltage and current peaks of 0.46 ± 0.03 V and 2.86 ± 0.07 mA, respectively, with an optimum operating pH of 4.22 ± 0.09 and an electrical conductivity of 175.86 ± 4.72 mS/cm at 8 °Brix until the tenth day of monitoring. An internal resistance of 75.58 ± 5.89 Ω was also calculated with a maximum power density of 304.33 ± 16.51 mW/cm2 at a current density of 5.06 A/cm2, while the FTIR spectra showed a decrease in the initial compounds and endings, especially at the 3331 cm−1 peaks of the O–H bonds. Finally, the yeast-like fungus Geotrichum candidum was molecularly identified (99.59%). This research will provide great opportunities for the generation of renewable energy using biomass as fuel through electronic devices with great potential to generate electricity