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We consider the bond percolation problem on a transient weighted graph induced by the excursion sets of the Gaussian free field on the corresponding cable system. Owing to the continuity of this setup and the strong Markov property of the field on the one hand, and the links with potential theory for the associated diffusion on the other, we rigorously determine the behavior of various key quantities related to the (near-)critical regime for this model. In particular, our results apply in case the base graph is the three-dimensional cubic lattice. They unveil the values of the associated critical exponents, which are explicit but not mean-field and consistent with predictions from scaling theory below the upper-critical dimension. |
We explore the separability of point sets in the plane by a restricted-orientation convex hull, which is an orientation-dependent, possibly disconnected, and non-convex enclosing shape that generalizes the convex hull. Let R and B be two disjoint sets of red and blue points in the plane, and O be a set of k≥2 lines passing through the origin. We study the problem of computing the set of orientations of the lines of O for which the O-convex hull of R contains no points of B. For k=2 orthogonal lines we have the rectilinear convex hull. |
This research reflects on using mathematics for processing and interpreting data obtained from digital surveying. The experiments outlined in this study demonstrate how mathematical algorithms, which can be written in computational environments like Wolfram Mathematica, can reveal the geometric structure of an architectural artifact. |
Global Value Chains (GVC) have reshaped the landscape of international trade. The quality and intensity of regulation significantly impacts firms' competitiveness and their ability to engage in GVC. Economic literature suggests that regulation of product market competition has a detrimental effect on trade by decreasing productivity, innovation, and economic growth. This paper expands existing knowledge on this relationship by examining the influence of product market regulation (PMR) on value-added trade flows in an augmented gravity model. We constructed a data panel with trade data from 40 OECD and BRICS countries in the period from 2000 to 2015 and combined it with an extensive multi-level indicator set on PMR developed by the OECD. |
Utilizing fog computing and explainable deep learning techniques for gestational diabetes prediction Gestational diabetes mellitus (GDM) is one of the pregnancy complications that poses a significant risk on mothers and babies as well. GDM usually diagnosed at 22–26 of gestation. However, the early prediction is desirable as it may contribute to decrease the risk. The continuous monitoring for mother’s vital signs helps in predicting any deterioration during pregnancy. The originality of this paper is to provide comprehensive framework for pregnancy women monitoring. The proposed Data Replacement and Prediction Framework consists of three layers which are: (i) IoT Layer, (ii) Fog Layer, and (iii) Cloud Layer. |
We study optional projections of G-adapted strict local martingales on a smaller filtration F under changes of equivalent martingale measures. General results are provided as well as a detailed analysis of two specific examples given by the inverse Bessel process and a class of stochastic volatility models. This analysis contributes to clarify the absence of arbitrage opportunities of market models under restricted information. |
In order to improve the starved lubrication condition of rolling bearings, three kinds of textures, namely dimple, groove texture, and gradient groove texture, were developed on the guiding surface of thrust ball bearings in this study. The results show that gradient groove texture has the one-way self-driving function of liquid droplets. The root mean square (RMS) value of vibration acceleration of gradient groove textured bearing (GGB) decreased by 49.1% and the kurtosis decreased by 24.6% compared with non-textured bearing (NB) due to the directional spreading effect of gradient groove textures on oil. |
The supraclavicular plexus block (SCB) and interscalene plexus block (ISB) have the potential to pulmonary function, the duration of the potential remains uncertain. So, we compared the effect of SCB and ISB on pulmonary function, especially the duration time. |
Markov introduced his triples in 1879 in relation to the Diophantine properties of the binary quadratic forms that can be interpreted as the description of the “most irrational” numbers. Since then, many surprising connections have been discovered between Markov triples and hyperbolic geometry, combinatorics of words, and, more recently, the theory of Frobenius manifolds, algebraic geometry, and cluster mutations (see [1, 2] and the references therein). This makes the Markovian theme one of the most fascinating stories in mathematics, which because of a still unproven uniqueness conjecture [1] is far from being finished. |
We claim that human mathematics is only a limited part of the consequences of the chosen basic axioms. Properly human mathematics varies with time but appears to have universal features which we try to analyse. In particular, the functioning of the human brain privileges concept naming and short formulations. This leads to organising mathematical knowledge structurally. We consider briefly the problem of non-mathematical sciences. |
