Abstract: In this work, we provide a procedure that allows us to transform certain kinds of deterministic Boolean networks on minterm or maxterm functions into symmetric ones, so inferring that such symmetrizable networks can present only periodic points of periods 1 or 2. In particular, we deal with generalized parallel (or synchronous) dynamical systems (GPDS) over undirected graphs, i. e., discrete parallel dynamical systems over undirected graphs where some of the self-loops may not appear. We also study the class of anti-symmetric GPDS (which are non-symmetrizable), proving that their periodic orbits have period 4. In addition, we introduce a class of non-symmetrizable systems which admit periodic orbits with arbitrary large periods.

Abstract: We introduce Neural Network (NN for short) approximation architectures for the numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN approach for the boundary reduction of the potential problem in two spatial dimensions. We adopt a Galerkin formulation-based method, in polygonal domains with a finite number of straight sides. Trial spaces used in the Galerkin discretization of the BIEs are built by using NNs that, in turn, employ the so-called Rectified Linear Units (ReLU) as the underlying activation function. The ReLU-NNs used to approximate the solutions to the BIEs depend nonlinearly on the parameters characterizing the NNs themselves. Consequently, the computation of a numerical solution to a BIE by means of ReLU-NNs boils down to a fine tuning of these parameters, in network training. We argue that ReLU-NNs of fixed depth and with a variable width allow us to recover well-known approximation rate results for the standard Galerkin Boundary Element Method (BEM). This observation hinges on existing well-known properties concerning the regularity of the solution of the BIEs on Lipschitz, polygonal boundaries, i.e. accounting for the effect of corner singularities, and the expressive power of ReLU-NNs over different classes of functions. We prove that shallow ReLU-NNs, i.e. networks having a fixed, moderate depth but with increasing width, can achieve optimal order algebraic convergence rates. We propose novel loss functions for NN training which are obtained using computable, local residual a posteriori error estimators with ReLU-NNs for the numerical approximation of BIEs. We find that weighted residual estimators, which are reliable without further assumptions on the quasi-uniformity of the underlying mesh, can be employed for the construction of computationally efficient loss functions for ReLU-NN training. The proposed framework allows us to leverage on state-of-the-art computational deep learning technologies such as TENSORFLOW and TPUs for the numerical solution of BIEs using ReLU-NNs. Exploratory numerical experiments validate our theoretical findings and indicate the viability of the proposed ReLU-NN Galerkin BEM approach.

Abstract: We establish two-point distortion theorems for sense-preserving planar harmonic map -pings f = h + g in the unit disk D which satisfy harmonic versions of the univalence criteria due to Becker and Nehari. In addition, we also find two-point distortion theo-rems for the cases when h is a normalized convex function and, more generally, when h(D) is a c-linearly connected domain.

Abstract: The constraint satisfaction problem (CSP) is concerned with homomorphisms between two structures. For CSPs with restricted left-hand-side structures, the results of Dalmau, Languages and Programming, Springer, New York, 2007, pp. 279--290] establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by bounded-consistency algorithms (unconditionally) as bounded treewidth modulo homomorphic equivalence. The general-valued constraint satisfaction problem (VCSP) is a generalization of the CSP concerned with homomorphisms between two valued structures. For VCSPs with restricted left-hand-side valued structures, we establish the precise borderline of polynomial-time solvability (subject to complexity-theoretic assumptions) and of solvability by the kth level of the Sherali--Adams LP hierarchy (unconditionally). We also obtain results on related problems concerned with finding a solution and recognizing the tractable cases; the latter has an application in database theory.

Abstract: A Lagrangian model—the Hybrid Single-Particle Lagrangian Integrated Trajectory model (HYSPLIT)—is used to quantify changes in moisture sources and paths for precipitation over North China’s Henan Province associated with tropical cyclone (TC) over the western North Pacific (WNP) during July–August of 1979–2021. During TC-active periods, an anomalous cyclone over the WNP enhances southeasterly and reduces southwesterly moisture transport to Henan. Accordingly, compared to TC-inactive periods, moisture contributions from the Pacific Ocean (PO), eastern China (EC), and the local area (Local) are significantly enhanced by 48.32% (16.73% versus 11.28%), 20.42% (9.44% versus 7.84%), and 2.89% (4.91% versus 4.77%), respectively, while moisture contributions from the Indian Ocean (IO), Southwestern China (SWC), Eurasia (EA), and the South China Sea (SCS) are significantly reduced by −31.90% (8.61% versus 12.64%), −16.27% (4.60% versus 5.50%), −8.81% (19.10% versus 20.95%), and −6.92% (12.18% versus 13.09%). Furthermore, the moisture transport for a catastrophic extreme rainfall event during 17–22 July (“21⋅7” event) influenced by Typhoon Infa is investigated. Compared to the mean state during TC-active periods, the moisture contribution from the PO was substantially increased by 126.32% (37.87% versus 16.73%), while that from IO significantly decreased by −98.26% (0.15% versus 8.61%) during the “21⋅7” event. Analyses with a bootstrap resampling method show that moisture contributions from the PO fall outside the +6σ range, for both the TC-active and TC-inactive probability distributions. Thus, the “21⋅7” event is rare and extreme in terms of the moisture contribution from the PO, with the occurrence probability being less than 1 in 1 million times.
Significance Statement
Henan, one of the most populated provinces in China, experienced a catastrophic extreme precipitation event in July 2021 (the “21⋅7” event), coinciding with the activity of a tropical cyclone (TC) over the western North Pacific, which helps establish the moisture channel. Using a Lagrangian model, we provide a better understanding of how moisture transport changes associated with TC for the mean state of 1979–2021, and reveal how extreme is the moisture transport for the “21⋅7” event with the bootstrap technique. It is found that during active TC periods, the moisture contribution from the Pacific Ocean (the Indian Ocean) is significantly enhanced (reduced). For every 1 000 000 six-day events, less than one instance like the “21⋅7” event should be expected.

Abstract: We provide two new formulas for quasiconformal extension to C for harmonic mappings defined in the unit disk and having sufficiently small Schwarzian derivative. Both are generalizations of the Ahlfors-Weill extension for holomorphic functions.(c) 2023 Elsevier Inc. All rights reserved.

Abstract: The Matern and the Generalized Cauchy families of covariance functions have a prominent role in spatial statistics as well as in a wealth of statistical applications. The Matern family is crucial to index mean-square differentiability of the associated Gaussian random field; the Cauchy family is a decoupler of the fractal dimension and Hurst effect for Gaussian random fields that are not self-similar. Our effort is devoted to prove that a scale-dependent family of covariance functions, obtained as a reparameterization of the Generalized Cauchy family, converges to a particular case of the Matern family, providing a somewhat surprising bridge between covariance models with light tails and covariance models that allow for long memory effect.

Abstract: In this paper we implement a long-term multi-sectoral energy planning model to evaluate the role of green hydrogen in the energy mix of Chile, a country with a high renewable potential, under stringent emission reduction objectives in 2050. Our results show that green hydrogen is a cost-effective and environmentally friendly route especially for hard-to-abate sectors, such as interprovincial and freight transport. They also suggest a strong synergy of hydrogen with electricity generation from renewable sources. Our numerical simulations show that Chile should (i) start immediately to develop hydrogen production through electrolyzers all along the country, (ii) keep investing in wind and solar generation capacities ensuring a low cost hydrogen production and reinforce the power transmission grid to allow nodal hydrogen production, (iii) foster the use of electric mobility for cars and local buses and of hydrogen for long-haul trucks and interprovincial buses and, (iv) develop seasonal hydrogen storage and hydrogen cells to be exploited for electricity supply, especially for the most stringent emission reduction objectives.

Abstract: Consensus is an emergent property of many complex systems, considering this as an absolute majority phenomenon. In this work we study consensus dynamics in grids (in silicon), where individuals (the vertices) with two possible opinions (binary states) interact with the eight nearest neighbors (Moore’s neighborhood). Dynamics emerge once the majority rule drives the evolution of the system. In this work, we fully characterize the sub-neighborhoods on which the consensus may be reached or not. Given this, we study the quality of the consensus proposing two new measures, namely effectiveness and efficiency. We characterize attraction basins through the energy-like and magnetization-like functions similar to the Ising spin model.

Abstract: This research is framed within the study of automatic recognition of emotions in artworks, proposing a methodology to improve performance in detecting emotions when a network is trained with an image type different from the entry type, which is known as the cross-depiction problem. To achieve this, we used the QuickShift algorithm, which simplifies images' resources, and applied it to the Open Affective Standardized Image (OASIS) dataset as well as the WikiArt Emotion dataset. Both datasets are also unified under a binary emotional system. Subsequently, a model was trained based on a convolutional neural network using OASIS as a learning base, in order to then be applied on the WikiArt Emotion dataset. The results show an improvement in the general prediction performance when applying QuickShift (73% overall). However, we can observe that artistic style influences the results, with minimalist art being incompatible with the methodology proposed.