N. Belknap's Four-Valued Logic, Belknap Computer and New Proximity Functions for Comparing Discrete Objects

The idea of ​​Belknap's four-valued logic is that modern computers should function normally not only with the true values ​​of the input information, but also under the conditions of inconsistency and incompleteness of true failures. Belknap's logic introduces four true values: T (true - true), F (false - false), N (none - nobody, nothing, none), B (both - the two, not only the one but also the other). For ease of work with these true values, the following designations are introduced: (1, 0, n, b). Belknap's logic can be used to obtain estimates of proximity measures for discrete objects, for which the functions Jaccard and Needhem, Russel and Rao, Sokal and Michener, Hamming, etc. are used. In this case, it becomes possible to assess the proximity, recognition and classification of objects in conditions of uncertainty when the true values ​​are taken from the set (1, 0, n, b). Based on the architecture of the Hamming neural network, neural networks have been developed that allow calculating the distances between objects described using true values ​​(1, 0, n, b). Keywords: four-valued Belknap logic, Belknap computer, proximity assessment, recognition and classification, proximity function, neural network.

An Evertse–Ferretti Nevanlinna constant and its consequences

In this paper, we introduce the notion of an Evertse–Ferretti Nevanlinna constant and compare it with the birational Nevanlinna constant introduced by the authors in a recent joint paper. We then use it to recover several previously known results. This includes a 1999 example of Faltings from his Baker’s Garden article. We also extend the theory of these Nevanlinna constants to what we call “multidivisor Nevanlinna constants,” which allow the proximity function to involve the maximum of Weil functions for finitely many divisors.

Enhanced low-rank matrix estimation for simultaneous denoising and reconstruction of five-dimensional seismic data

Noise and missing traces usually influence the quality of multidimensional seismic data. It is, therefore, necessary to e stimate the useful signal from its noisy observation. The damped rank-reduction (DRR) method has emerged as an effective method to reconstruct the useful signal matrix from its noisy observation. However, the higher the noise level and the ratio of missing traces, the weaker the DRR operator becomes. Consequently, the estimated low-rank signal matrix includes a unignorable amount of residual noise that influences the next processing steps. This paper focuses on the problem of estimating a low-rank signal matrix from its noisy observation. To elaborate on the novel algorithm, we formulate an improved proximity function by mixing the moving-average filter and the arctangent penalty function. We first apply the proximity function to the level-4 block Hankel matrix before the singular value decomposition (SVD), and then, to singular values, during the damped truncated SVD process. The relationship between the novel proximity function and the DRR framework leads to an optimization problem, which results in better recovery performance. The proposed algorithm aims at producing an enhanced rank-reduction operator to estimate the useful signal matrix with a higher quality. Experiments are conducted on synthetic and real 5-D seismic data to compare the effectiveness of our approach to the DRR approach. The proposed approach is shown to obtain better performance since the estimated low-rank signal matrix is cleaner and contains less amount of artifacts compared to the DRR algorithm.

The MINC proximity function for fractured reservoirs flow modeling with non-uniform block distribution

Reservoir simulation is a powerful technique to predict the amount of produced hydrocarbon. After a solid representation of the natural fracture geometry, an accurate simulation model and a physical reservoir model that account for different flow regimes should be developed. Many models based on dual-continuum approaches presented in the literature rely on the Pseudo-Steady-State (PSS) assumption to model the inter-porosity flow. Due to the low permeability in such reservoirs, the transient period could reach several years. Thus, the PSS assumption becomes unjustified. The numerical solution adopted by the Multiple INteracting Continua (MINC) method was able to simulate the transient effects previously overlooked by dual-continuum approaches. However, its accuracy drops with increasing fracture network complexity. A special treatment of the MINC method, i.e., the MINC Proximity Function (MINC–PF) was introduced to address the latter problem. And yet, the MINC–PF suffers a limitation that arises from the existence of several grid-blocks within a studied cell. In this work, this limitation is discussed and two possible solutions (transmissibility recalculation/adjusting the Proximity Function by accounting for nearby fractures) are put forward. Both proposed methods have demonstrated their applicability and effectiveness once compared to a reference solution.

Seismic productivity of blasts: A case-study of the Khibiny Massif

The authors study the property of production-scale blasts to induce seismic events classified as micro shocks, rock bursts and earthquakes caused by sudden slips along faults. The study area is the production performance zone of Apatit’s Kirovsk Branch. It is situated in the southeast of the Khibiny Massif on the Kola Peninsula and is subjected to continuous autonomous seismicity monitoring. The subject of the research is the production blasts and seismic events recorded by the seismic monitoring station of Apatit’s Kirovsk Branch between January 1996 and June 2019. Blasting-induced seismic events were identified using the nearest neighbor method and the seismicity-dependent proximity function of the space–time–magnitude (energy), calculated with respect to the blasts. The threshold of the proximity function to assume a seismic event as the blast-induced event was selected using the model-independent method of seismic catalog randomization. It is shown that the number of blasting-induced seismic events—blasting productivity—obeys an exponential distribution irrespective of magnitudes or occurrence depths of the studied events. The obtained result conforms with the earlier determined productivity law for natural earthquakes on a global and regional scale, as well as for mining-induced seismicity in the Khibiny Massif. Accordingly, the productivity distribution is governed by the properties of a medium and is independent of the source mechanism of a triggering event (explosion, seismicity). The paper presents the research findings supported by the Russian Foundation for Basic Research, Project No. 19-05-00812, and in the framework of State Contract No. 007-00186-18-00 with the Kola Branch of the Geophysical Service of the Russian Academy of Sciences.

Determination of the Most Stable Configuration Pair(s) of the Constituent Matrix Shells and the Set of Most Stable Configurations of the Corresponding Matrix Shell System

The present article addresses the issue of determining the most stable configuration pair(s) of a Matrix Shell, and thereby, of determining the set of most stable configurations of the associated Matrix Shell System. The problem is resolved using the criteria of spectral proximity w.r.t. the Ordered Eigenspectrum of a defined Baseline Matrix (both for Individual constituent Matrix Shells and the Matrix Shell System) and quantified in terms of an appropriate Proximity Function, the article presents the analytic expressions of the Matrix Shell Baseline elements, corresponding to A n A n A n A n (0,2 ), (0,2 1), (1,2 ), (1,2 1)   and A t n A t n ( ,2 ), ( ,2 1)  where t  2 , type Matrix Shells and defines the Baseline Matrices in terms of these Baseline elements, the article then provides a mathematical framework to determine the most stable Configuration pair(s) of constituent Matrix Shells and the set of most stable configurations of the Matrix Shell System and concludes with demonstration of the working of the presented framework through hypothetical examples based case studies

Model of Recognition Operators Based on the Formation of Representative Objects

Parametric representations of the model of recognition operators based on the selection of representative objects are considered. The main idea of the proposed model is to build a family of proximity functions in the parameter space. In this case, the proximity function is determined within the framework of the radial function. A distinctive feature of the proposed model is the formation of preferred features with respect to selected representative objects when constructing recognition operators. To verify the performance of the proposed model, experimental studies were carried out to solve the model problem.

Accelerometer-Measured Patterns of Shared Physical Activity Among Mother–Young Child Dyads

Background:Many mothers and young children are not meeting physical activity guidelines. Parent–child coparticipation in physical activity (ie, shared physical activity) provides opportunities for social modeling and might be associated with child physical activity. There is very little information about shared physical activity using objective measures.Methods:Participants (N = 17 mother–young child dyads) completed a demographic survey and height/weight measurements, and wore a Bluetooth® accelerometer for 1 week. Accelerometers were initialized using the proximity function to yield both individual and proximity [a minute-by-minute log of whether the 2 accelerometers were in- or out-of-range (∼50 m or less)] data. Shared physical activity was calculated in MATLAB by overlaying individual and proximity accelerometer data.Results:Mother–child dyads spent approximately 2 hours per day in shared time that was mostly shared sedentary activities. Less than 1% of shared minutes per day were spent in shared moderate to vigorous physical activity.Conclusions:Mothers and young children spent a small portion of their day in shared activities. Most mother–child shared time was spent in sedentary or light activities rather than moderate to vigorous physical activity. This method for objectively measuring shared physical activity provides novel information about the context in which physical activity occurs and could be used to understand patterns of physical activity among other dyads.