A regularity result for minimal configurations of a free interface problem

We prove a regularity result for minimal configurations of variational problems involving both bulk and surface energies in some bounded open region $$\varOmega \subseteq {\mathbb {R}}^n$$ Ω ⊆ R n . We will deal with the energy functional $${\mathscr {F}}(v,E):=\int _\varOmega [F(\nabla v)+1_E G(\nabla v)+f_E(x,v)]\,dx+P(E,\varOmega )$$ F ( v , E ) : = ∫ Ω [ F ( ∇ v ) + 1 E G ( ∇ v ) + f E ( x , v ) ] d x + P ( E , Ω ) . The bulk energy depends on a function v and its gradient $$\nabla v$$ ∇ v . It consists in two strongly quasi-convex functions F and G, which have polinomial p-growth and are linked with their p-recession functions by a proximity condition, and a function $$f_E$$ f E , whose absolute valuesatisfies a q-growth condition from above. The surface penalization term is proportional to the perimeter of a subset E in $$\varOmega $$ Ω . The term $$f_E$$ f E is allowed to be negative, but an additional condition on the growth from below is needed to prove the existence of a minimal configuration of the problem associated with $${\mathscr {F}}$$ F . The same condition turns out to be crucial in the proof of the regularity result as well. If (u, A) is a minimal configuration, we prove that u is locally Hölder continuous and A is equivalent to an open set $${\tilde{A}}$$ A ~ . We finally get $$P(A,\varOmega )={\mathscr {H}}^{n-1}(\partial {\tilde{A}}\cap \varOmega $$ P ( A , Ω ) = H n - 1 ( ∂ A ~ ∩ Ω ).

A minimal space interferometer configuration for imaging at low radio frequencies

The radio sky at lower frequencies, particularly below 20 MHz, is expected to be a combination of increasingly bright non-thermal emission and significant absorption from intervening thermal plasma. The sky maps at these frequencies cannot therefore be obtained by simple extrapolation of those at higher frequencies. However, due to severe constraints in ground-based observations, this spectral window still remains greatly unexplored. In this paper, we propose and study, through simulations, a novel minimal configuration for a space interferometer system which would enable imaging of the radio sky at frequencies well below 20 MHz with angular resolutions comparable to those achieved at higher radio frequencies in ground-based observations by using the aperture synthesis technique. The minimal configuration consists of three apertures aboard Low Earth Orbit (LEO) satellites orbiting the Earth in mutually orthogonal orbits. Orbital periods for the satellites are deliberately chosen to differ from each other so as to obtain maximum (u,v) coverage in short time spans with baselines greater than 15 000 km, thus, giving us angular resolutions finer than 10 arcsec even at these low frequencies. The sensitivity of the (u,v) coverage is assessed by varying the orbit and the initial phase of the satellites. We discuss the results obtained from these simulations and highlight the advantages of such a system.

On the existence of solutions for the Frenkel-Kontorova models on quasi-crystals

<p style='text-indent:20px;'>This article focuses on recent investigations on equilibria of the Frenkel-Kontorova models subjected to potentials generated by quasi-crystals.</p><p style='text-indent:20px;'>We present a specific one-dimensional model with an explicit potential driven by the Fibonacci quasi-crystal. For a given positive number <inline-formula><tex-math id="M1">\begin{document}$ \theta $\end{document}</tex-math></inline-formula>, we show that there are multiple equilibria with rotation number <inline-formula><tex-math id="M2">\begin{document}$ \theta $\end{document}</tex-math></inline-formula>, e.g., a minimal configuration and a non-minimal equilibrium configuration. Some numerical experiments verifying the existence of such equilibria are provided.</p>

Towards an Optimal Deep Neural Network for SOC Estimation of Electric-Vehicle Lithium-Ion Battery Cells

This paper has identified a minimal configuration of a DNN architecture and hyperparameter settings to effectively estimate SOC of EV battery cells. The results from the experimental work has shown that a minimal configuration of hidden layers and neurons can reduce the computational cost and resources required without compromising the performance. This is further supported by the number of epochs taken to train the best DNN SOC estimations model. Hence, demonstrating that, the risk of overfitting estimation models to training datasets, can also be subsided. This is further supported by the generalisation capability of the best model demonstrated through the decrease in error metrics values from test phase to those in validation phase.

The limits to parapatric speciation 3: evolution of strong reproductive isolation in presence of gene flow despite limited ecological differentiation

Gene flow tends to impede the accumulation of genetic divergence. Here, we determine the limits for the evolution of postzygotic reproductive isolation in a model of two populations that are connected by gene flow. We consider two selective mechanisms for the creation and maintenance of a genetic barrier: local adaptation leads to divergence among incipient species due to selection against migrants, and Dobzhansky–Muller incompatibilities (DMIs) reinforce the genetic barrier through selection against hybrids. In particular, we are interested in the maximum strength of the barrier under a limited amount of local adaptation, a challenge that many incipient species may initially face. We first confirm that with classical two-locus DMIs, the maximum amount of local adaptation is indeed a limit to the strength of a genetic barrier. However, with three or more loci and cryptic epistasis, this limit holds no longer. In particular, we identify a minimal configuration of three epistatically interacting mutations that is sufficient to confer strong reproductive isolation. This article is part of the theme issue ‘Towards the completion of speciation: the evolution of reproductive isolation beyond the first barriers’.

The limits to parapatric speciation 3: Evolution of strong reproductive isolation in presence of gene flow despite limited ecological differentiation

Gene flow tends to impede the accumulation of genetic divergence. Here, we determine the limits for the evolution of postzygotic reproductive isolation in a model of two populations that are connected by gene flow. We consider two selective mechanisms for the creation and maintenance of a genetic barrier: local adaptation leads to divergence among incipient species due to selection against migrants, and Dobzhansky-Muller incompatibilities (DMIs) reinforce the genetic barrier through selection against hybrids. In particular, we are interested in the maximum strength of the barrier under a limited amount of local adaptation, a challenge that may initially face many incipient species. We first confirm that with classical two-locus DMIs, the maximum amount of local adaptation is indeed a limit to the strength of a genetic barrier. However, with three or more loci and cryptic epistasis, this limit holds no longer. In particular, we identify a minimal configuration of three epistatically interacting mutations that is sufficient to confer strong reproductive isolation.

An ML and SMS remote access based model for Anti-theft protection of Android devices

Android phones being stolen is a significant problem that causes concerns to intellectual privacy and property. Always protecting smartphones from being stolen is a problem that remains. The key findings of the survey of existing systems for theft protection are, they provide various efficient functionalities but fail when the internet is unavailable or require specialized equipment to detect thefts. Most of these solutions are not free of charge, inefficient, time-consuming, or/and inflexible. This paper puts forward a system that provides an ML-based real-time anti-theft and remote access system for android devices. It detects theft using SVM-RBF model trained on feature-set extracted from the inertial sensor’s data with an accuracy of 0.76. Whereas remote access is provided using short message services (SMS). The salient feature of this system is minimal configuration without intruding human-assisted tasks. Moreover, it will be an excellent help for authentic smartphone users to realize the theft situation and utilize the remote access features.

Production of linked government datasets using enhanced LIRE architecture

This paper describes the enhanced LIRE (LInked RElations) architecture for creating relations between datasets available on open government portals. The architecture is improved to be applicable on different open government data platforms using minimal configuration at the Data processing layer. We evaluated the applicability of enhanced LIRE, its advantages and disadvantages, which resulted in necessary recommendations for the publication of dataset?s metadata to obtain better associations between datasets. Moreover, we introduced a LINDAT indicator that reflects the percentage of linked data in the total possible number of linked data on open government data portals.

Robust and Accurate Hand–Eye Calibration Method Based on Schur Matric Decomposition

To improve the accuracy and robustness of hand–eye calibration, a hand–eye calibration method based on Schur matric decomposition is proposed in this paper. The accuracy of these methods strongly depends on the quality of observation data. Therefore, preprocessing observation data is essential. As with traditional two-step hand–eye calibration methods, we first solve the rotation parameters and then the translation vector can be immediately determined. A general solution was obtained from one observation through Schur matric decomposition and then the degrees of freedom were decreased from three to two. Observation data preprocessing is one of the basic unresolved problems with hand–eye calibration methods. A discriminant equation to delete outliers was deduced based on Schur matric decomposition. Finally, the basic problem of observation data preprocessing was solved using outlier detection, which significantly improved robustness. The proposed method was validated by both simulations and experiments. The results show that the prediction error of rotation and translation was 0.06 arcmin and 1.01 mm respectively, and the proposed method performed much better in outlier detection. A minimal configuration for the unique solution was proven from a new perspective.