Fast Global Minimization of the Chan–Vese Model for Image Segmentation Problem

The segmentation of weak boundary is still a difficult problem, especially sensitive to noise, which leads to the failure of segmentation. Based on the previous works, by adding the boundary indicator function with L 2,1 norm, a new convergent variational model is proposed. A novel strategy for the weak boundary image is presented. The existence of the minimizer for our model is given, by using the alternating direction method of multipliers (ADMMs) to solve the model. The experiments show that our new method is robust in segmentation of objects in a range of images with noise, low contrast, and direction.

Analysis of Forest Stand Resistance to Insect Attack According to Remote Sensing Data

Methods for analyzing the resistance of large woodlands (such as Siberian taiga forests) to insect attacks based on remote sensing data are proposed. As an indicator of woodland’s resistance, we suggest a function of normalized difference vegetative index (NDVI) susceptibility to changes in the land surface temperature (LST). Both NDVI and LST are obtained via the TERRA/AQUA satellite system. This indicator function was calculated as the spectral transfer function of the response in the integral equation connecting the changes in NDVI and LST. The analysis was carried out for two test sites, both of which are fir stands of the Krasnoyarsk region taiga zone. In the first case, the fir stands have suffered damage inflicted by Siberian silk moth caterpillars, Dendrolimus sibiricus Tschetv. since 2015. Adjacent intact fir forest areas were also analyzed. In the second case, the object of the study was a fir tree site damaged by Black Fir Sawyer Monochamus urussovii Fischer in 2013. It is demonstrated that the above-mentioned indicator function changed significantly 2–3 years prior to the pest population outbreaks, and therefore this indicator function can be used to assess the risk of pest population outbreak. Thereby, the proposed indicator compares favorably with vegetation cover estimates using NDVI, which register significant defoliation of tree stands and cannot be used for forecasting.

Fast Localization of Small Inhomogeneities from Far-Field Pattern Data in the Limited-Aperture Inverse Scattering Problem

In this study, we consider a sampling-type algorithm for the fast localization of small electromagnetic inhomogeneities from measured far-field pattern data in the limited-aperture inverse scattering problem. For this purpose, we designed an indicator function based on the structure of left- and right-singular vectors of a multistatic response matrix, the elements of which were measured far-field pattern data. We then rigorously investigated the mathematical structure of the indicator function in terms of purely dielectric permittivity and magnetic permeability contrast cases by establishing a relationship with an infinite series of Bessel functions of an integer order of the first kind and a range of incident and observation directions before exploring various intrinsic properties of the algorithm, including its feasibility and limitations. Simulation results with synthetic data corrupted by random noise are presented to support the theoretical results.

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

Crecimiento y desempleo en Ecuador: Enfoque asimétrico de la Ley de Okun (período 2004:1-2019:4)

El objetivo de este trabajo es estimar la relación entre crecimiento y desempleo en Ecuador desde una perspectiva asimétrica para el período 2004-2019, a partir de información estadística de periodicidad trimestral. Se estima mediante mínimos cuadrados ordinarios la ecuación de primeras diferencias de Okun que incluye una función indicadora para capturar los coeficientes de asimetría. Los resultados hallados sugieren una relación inversa significativa entre crecimiento y desempleo, pero el efecto es mayor en magnitud cuando el crecimiento es negativo. En este caso, 1 % de caída en el PIB causa un aumento de 0,63 puntos en la tasa de desempleo, mientras que en períodos de crecimiento la respuesta es leve, sugiriendo entonces la preponderancia de efectos asimétricos en la relación estudiada. La principal conclusión es que las autoridades deben diseñar políticas para reducir más aun el desempleo cuando la economía crece, y otras medidas específicas para contener el ascenso del desempleo cuando la economía sufre contracciones severas en términos de crecimiento. Palabras clave: Crecimiento, desempleo, Ecuador, Ley de Okun, asimetría. ABSTRACT The objective of this work is to estimate the relationship between growth and unemployment in Ecuador from an asymmetric perspective for the period 2004-2019, based on statistical information on a quarterly basis. Okun’s first difference equation is estimated using Ordinary Least Squares (OLS), which includes an indicator function to capture the skewness coefficients. The results found affect a significant inverse relationship between growth and unemployment, but the effect is greater in magnitude when growth is negative. In this case, 1% of the fall in GDP causes a decrease of 0.64 points in the unemployment rate, while in the reduction of growth the response is slight, suggesting then the preponderance of the asymmetric effects in the relationship studied. The main conclusion is that the authorities have specific policies to further reduce unemployment when the economy grows, and other specific measures to contain the rise in unemployment when the economy suffers severe contractions in terms of growth. Keywords: Growth, unemployment, Ecuador, Okun’s law, asymmetry.

Laplacian networks: bounding indicator function smoothness for neural networks robustness

For the past few years, deep learning (DL) robustness (i.e. the ability to maintain the same decision when inputs are subject to perturbations) has become a question of paramount importance, in particular in settings where misclassification can have dramatic consequences. To address this question, authors have proposed different approaches, such as adding regularizers or training using noisy examples. In this paper we introduce a regularizer based on the Laplacian of similarity graphs obtained from the representation of training data at each layer of the DL architecture. This regularizer penalizes large changes (across consecutive layers in the architecture) in the distance between examples of different classes, and as such enforces smooth variations of the class boundaries. We provide theoretical justification for this regularizer and demonstrate its effectiveness to improve robustness on classical supervised learning vision datasets for various types of perturbations. We also show it can be combined with existing methods to increase overall robustness.

Stabilization of nonautonomous parabolic equations by a single moving actuator

<p style='text-indent:20px;'>It is shown that an internal control based on a moving indicator function is able to stabilize the state of parabolic equations evolving in rectangular domains. For proving the stabilizability result, we start with a control obtained from an oblique projection feedback based on a finite number of static actuators, then we used the continuity of the state when the control varies in a relaxation metric to construct a switching control where at each given instant of time only one of the static actuators is active, finally we construct the moving control by traveling between the static actuators.</p><p style='text-indent:20px;'>Numerical computations are performed by a concatenation procedure following a receding horizon control approach. They confirm the stabilizing performance of the moving control.</p>

Localization of Small Anomalies via the Orthogonality Sampling Method from Scattering Parameters

We investigate the application of the orthogonality sampling method (OSM) in microwave imaging for a fast localization of small anomalies from measured scattering parameters. For this purpose, we design an indicator function of OSM defined on a Lebesgue space to test the orthogonality relation between the Hankel function and the scattering parameters. This is based on an application of the Born approximation and the integral equation formula for scattering parameters in the presence of a small anomaly. We then prove that the indicator function consists of a combination of an infinite series of Bessel functions of integer order, an antenna configuration, and material properties. Simulation results with synthetic data are presented to show the feasibility and limitations of designed OSM.