$$\alpha $$-Firmly nonexpansive operators on metric spaces

We extend to p-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise averaged mappings. Our main contribution is establishing a calculus for these mappings in p-uniformly convex spaces, showing in particular how the property is preserved under compositions and convex combinations. This is of central importance to splitting algorithms that are built by such convex combinations and compositions, and reduces the convergence analysis to simply verifying that the individual components have the required regularity pointwise at fixed points of the splitting algorithms. Our convergence analysis differs from what can be found in the previous literature in that the regularity assumptions are only with respect to fixed points. Indeed we show that, if the fixed point mapping is pointwise nonexpansive at all cluster points, then these cluster points are in fact fixed points, and convergence of the sequence follows. Additionally, we provide a quantitative convergence analysis built on the notion of gauge metric subregularity, which we show is necessary for quantifiable convergence estimates. This allows one for the first time to prove convergence of a tremendous variety of splitting algorithms in spaces with curvature bounded from above.

Formation Grain Size Profile Prediction Model Considering the Longitudinal Continuity of Reservoir Using Artificial Intelligence Tools

Grain size characteristics (d50, UC) of formation sands are crucial parameters in a sand control design. UC and d50 are commonly derived from sieve or laser particle size analysis (LPSA) techniques on a limited number of core samples in the process of drilling, which cannot represent the variations of grain sizes in the formation by the limited number of core samples. Moreover, staged and hierarchic design of sand control usually needs the whole longitudinal distribution profile of grain size. The grain size characteristics of the reservoir are formed in the process of a long history and have a good correlation with the formation environment of the sediments. Sand control design can only use test well data, because of lacking actual producing position cores. The vertical and horizontal anisotropy and heterogeneity of reservoirs bring difficulties and greater risks to the design of sand control schemes. Therefore, it is very important to find a simple and effective reservoir granularity prediction method. The existing prediction models by artificial intelligence method use single point logging data as eigenvalues to predict d50 and UC without considering the longitudinal continuity of data. This paper presents an efficient solution to predict grain size profile based on conventional logging curves by using four machine learning method (ANN, Random forest, XGBoost, SVM). In order to make full use of the geological continuity of the reservoir, the longitudinal continuous points according to the spatial correlation are adopted as the machine learning feature parameters from the perspective of geological analysis and the data-driven grain size profile prediction model are established by using the logging curve trend and background information, which further improves the prediction accuracy of the model and provides basic data for sand control. The ANN model of five point mapping has the best prediction effect in predicting d50 with a highest correlation coefficient 0.819 and a lowest error MAE 9.59. The XGBoost model of five point mapping has the best prediction effect in predicting UC with a highest correlation coefficient 0.402 and a lowest error RMSE 1.15. This method has been successfully used in offshore oil field in sand control optimization.

Extending and paralleling Stechkin's category theorem

We strengthen one of Stechkin's theorems. We also obtain results in the same spirit regarding the farthest point mapping. We work in length spaces, sometimes without bifurcating geodesics, sometimes with geodesic extendability.

Exploiting spatio-spectral aberrations for rapid synchrotron infrared imaging

The Infrared Microspectroscopy Beamline at the Australian Synchrotron is equipped with a Fourier transform infrared (FTIR) spectrometer, which is coupled with an infrared (IR) microscope and a choice of two detectors: a single-point narrow-band mercury cadmium telluride (MCT) detector and a 64 × 64 multi-pixel focal plane array (FPA) imaging detector. A scanning-based point-by-point mapping method is commonly used with a tightly focused synchrotron IR beam at the sample plane, using an MCT detector and a matching 36× IR reflecting objective and condenser (NA = 0.5), which is time consuming. In this study, the beam size at the sample plane was increased using a 15× objective and the spatio-spectral aberrations were investigated. A correlation-based semi-synthetic computational optical approach was applied to assess the possibilities of exploiting the aberrations to perform rapid imaging rather than a mapping approach.

Point mapping method in investigating the dynamics of relay stabilization with account for nonlinearity of the speed sensor, delays, and time-independent perturbation

Using the point mapping method, we obtained analytical expressions for the first return functions for determining simple and complex attractors in the stabilization mode by a general-purpose relay controller with the linear formation of the control signal. We investigated self-oscillations with account for the operating members’ aftereffect, the dead zone of the speed sensor, and the time-independent perturbation action. The study shows that the dead zone of the speed sensor introduces significant changes in the behavior of the system, giving it new properties. The analysis of dynamic processes on a three-sheet phase surface revealed a wide variety of limit cycles and their dependence on the system’s parameters. Complex limit cycles are represented by combining simple cycles of two types, which allowed for a simplifying approach to their search based on the theory of multidimensional transformations of Yu.I. Neymark. A more complete result was obtained in comparison with the well-known literary sources.

Walking Wheel

A hypothesis was proposed that during the bipedal walking, there appear stable periodic movements in certain variables (self-oscillations). In this case, it is possible to easily change parameters of this periodic locomotion using open (without feedback) control loops with respect to some of the variables. As the first stage in testing this hypothesis, dynamics of the walking wheel downward movement along an inclined plane was analytically studied. Walking wheel is the simplest model of passive bipedal walking. When it moves, energy is supplied to the system due to the force of gravity action. It is shown that point mapping of the wheel angular speed alteration per step (Poincare map) in the overwhelming majority of cases has one fixed point. This fixed point corresponds either to stable periodic solution (self-oscillation), which is the wheel rolling down an inclined plane, or to the wheel movement ending with its termination as a result of the endless series of impacts with swinging on two legs. In the degenerate case, the Poincare map has two fixed points. One of them corresponds to the unstable limiting cycle matching the wheel rolling, and the second corresponds to a wheel stop. In this case, the limiting cycle is stable outside and unstable inside itself

Modification of Experimental Design and Statistical Method for Mapping Imprinted QTLs Based on Immortalized F2 Population

Genomic imprinting is an epigenetic phenomenon, which plays important roles in the growth and development of animals and plants. Immortalized F2 (imF2) populations generated by random cross between recombinant inbred (RI) or doubled haploid (DH) lines have been proved to have significant advantages for mapping imprinted quantitative trait loci (iQTLs), and statistical methods for this purpose have been proposed. In this paper, we propose a special type of imF2 population (R-imF2) for iQTL mapping, which is developed by random reciprocal cross between RI/DH lines. We also propose two modified iQTL mapping methods: two-step point mapping (PM-2) and two-step composite point mapping (CPM-2). Simulation studies indicated that: (i) R-imF2 cannot improve the results of iQTL mapping, but the experimental design can probably reduce the workload of population construction; (ii) PM-2 can increase the precision of estimating the position and effects of a single iQTL; and (iii) CPM-2 can precisely map not only iQTLs, but also non-imprinted QTLs. The modified experimental design and statistical methods will facilitate and promote the study of iQTL mapping.

Multilayer fabrication of durable catheter-deployable soft robotic sensor arrays for efficient left atrial mapping

Devices that perform cardiac mapping and ablation to treat atrial fibrillation provide an effective means of treatment. Current devices, however, have limitations that either require tedious point-by-point mapping of a cardiac chamber or have limited ability to conform to the complex anatomy of a patient’s cardiac chamber. In this work, a detailed, scalable, and manufacturable technique is reported for fabrication of a multielectrode, soft robotic sensor array. These devices exhibit high conformability (~85 to 90%) and are equipped with an array of stretchable electronic sensors for voltage mapping. The form factor of the device is intended to match that of the entire left atrium and has a hydraulically actuated soft robotic structure whose profile facilitates deployment from a 13.5-Fr catheter. We anticipate that the methods described in this paper will serve a new generation of conformable medical devices that leverage the unique characteristics of stretchable electronics and soft robotics.

Long-term Treatment Leads to Reduction of Tree-of-Heaven (Ailanthus altissima) Populations in the Buffalo National River

In this case study, we used point mapping data to evaluate long-term treatment of invasive tree-of-heaven (Ailanthus altissima). This study at the Buffalo National River included 21 project areas ranging in size from 0.02 to 11.3 ha and spanned five to eight years depending on the site. The control techniques varied depending on the year and included the application of herbicide, which also varied over the course of the study and included imazapyr, triclopyr, and triclopyr+fluroxypyr. Treatments during the first year reduced local A. altissima populations by an average of 66%. Long-term repeated treatments led to decreases of at least 90% in 70% of the project areas and at least 73% in 95% of the project areas. Only one project area was found to support no plants during the final treatment year. A. altissima increased at most project areas during an unusually wet year and was more likely to increase than decrease in intervals > 1 year with no treatment. Over the temporal and spatial scales of this case study, we observed high levels of control that will likely meet the specified levels and ecological benefits required in many similar efforts. Land managers must, however, make a long-term commitment of resources to achieve lasting control of this invasive species.