Boundary Measures Research Articles

Minority Affirmations and the Boundaries of the Nation: Evidence From Québec

Cultural criteria, like language skills and values, are salient features of nationalism discourse, reflecting imagined boundaries that separate ingroup from outgroup member when thinking about the nation. Despite their salience, the relationship between cultural membership criteria and other civic (attainable) or ethnic (ascriptive) national boundaries, along with their implications for intergroup relations, is contested. Using surveys from N = 6448 majority group members in the Canadian province of Québec, we argue cultural boundaries are empirically distinct from civic and ethnic ones. Cultural and civic criteria are both prominent prerequisites for membership into the Québécois national community, but cultural criteria show markedly divergent relationships with outgroup attitudes. The results underline the importance of conceptualizing cultural boundaries as a distinct set of national membership criteria and question the construct validity of blended ethnocultural boundary measures or approaches that aggregate civic and cultural criteria together as equally “attainable” markers of national membership.

Supplement and Suppression: Both Boundary and Nonboundary are Helpful for Salient Object Detection.

Current methods aggregate multilevel features from the backbone and introduce edge information to get more refined saliency maps. However, little attention is paid to how to suppress the regions with similar saliency appearances in the background. These regions usually exist in the vicinity of salient objects and have high contrast with the background, which is easy to be misclassified as foreground. To solve this problem, we propose a gated feature interaction network (GFINet) to integrate multiple saliency features, which can utilize nonboundary features with background information to suppress pseudosalient objects and simultaneously apply boundary features to supplement edge details. Different from previous methods that only consider the complementarity between saliency and boundary, the proposed network introduces nonboundary features into the decoder to filter the pseudosalient objects. Specifically, GFINet consists of global features aggregation branch (GFAB), boundary and nonboundary features' perception branch (B&NFPB), and gated feature interaction module (GFIM). According to the global features generated by GFAB, boundary and nonboundary features produced by B&NFPB and GFIM employ a gate structure to adaptively optimize the saliency information interchange between abovementioned features and, thus, predict the final saliency maps. Besides, due to the imbalanced distribution between the boundary pixels and nonboundary ones, the binary cross-entropy (BCE) loss is difficult to predict the pixels near the boundary. Therefore, we design a border region aware (BRA) loss to further boost the quality of boundary and nonboundary, which can guide the network to focus more on the hard pixels near the boundary by assigning different weights to different positions. Compared with 12 counterparts, experimental results on five benchmark datasets show that our method has better generalization and improves the state-of-the-art approach by 4.85% averagely in terms of the regional and boundary evaluation measures. In addition, our model is more efficient with an inference speed of 50.3 FPS when processing a 320 x 320 image. Code has been made available at https://github.com/lesonly/GFINet.

Uniform decay estimates for the semi-linear wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic versus frictional dissipative effects

Abstract We are concerned with the stabilization of the wave equation with locally distributed mixed-type damping via arbitrary local viscoelastic and frictional effects. Here, one of the novelties is: the viscoelastic and frictional damping together effect only in a part of domain, not in entire domain, which is only assumed to meet the piecewise multiplier geometric condition that their summed interior and boundary measures can be arbitrarily small. Furthermore, there is no other additional restriction for the location of the viscoelastic-effect region. That is, it is dropped that the viscoelastic-effect region includes a part of the system boundary, which is the fundamental condition in almost all previous literature even if when two types of damping together cover the entire system domain. The other distinct novelty is: in this article we remove the fundamental condition that the derivative of the relaxation function is controlled by relaxation function itself, which is a necessity in the previous literature to obtain the optimal uniform decay rate. Under such weak conditions, we successfully establish a series of decay theorems, which generalize and extend essentially the previous related stability results for viscoelastic model regardless of local damping case, entire damping case and mixed-type damping case.

Ramified Optimal Transportation with Payoff on the Boundary

This paper studies a variant of ramified/branched optimal transportation problems. Given the distributions of production capacities and market sizes, a firm looks for an allocation of productions over factories, a distribution of sales across markets, and a transport path that delivers the product to maximize its profit. Mathematically, given any two measures and on , and a payoff function , the planner wants to minimize among all transport paths from to with and , where is the standard cost functional used in ramified transportation. After proving the existence result, we provide a characterization of the boundary measures of the optimal solution. They turn out to be the original measures restricted on some Borel subsets up to a Delta mass on each connected component. Our analysis further finds that as the boundary payoff increases, the corresponding solution of the current problem converges to an optimal transport path, which is the solution of the standard ramified transportation.

Dynamic properties for a stochastic food chain model

In this paper, Lyapunov exponents of ergodic invariant measures are used to study dynamic properties for a stochastic food chain model, which consists of two competing predators and one prey. Ayala’s experimental result, or rather, competitive coexistence is showed to be possible in this random case. Furthermore, the considered stochastic model have five points of dynamical bifurcation, which happen to be the thresholds (between survival and extinction) of the system or each species. In addition, the necessity of introducing environmental noise is verified by the fact that environmental driving force can drive the system towards extinction from partial extinction or coexistence. Moreover, all the theoretical results are well verified by numerical simulations. It is worth mentioning that we make a first attempt at using meshing method and statistical data to test Lyapunov exponents for two-dimensional boundary measures, and this is an innovation in the numerical methods.

Geographic Boundary Definitions and the Robustness of Common Food Retail Environment Measures

Understanding the relationship between the retail food environment and individual and community health is important for addressing questions about diet-related disease and food security. A wide range of methodological approaches have been used to understand this complex relationship, but the studies have resulted in a lack of consensus on how and whether the food retail environment influences health outcomes and food choice. Inconsistency in measuring the food environment could explain inconsistent results. We calculate five different boundaries of the food retail environment to investigate the robustness of boundary measures. These five boundaries include an administrative boundary (census tract of residence), two Euclidean boundaries, and two network area boundaries. We compare four different aspects of the food retail environment—availability, accessibility, affordability, and realized purchase behavior—across these five fundamentally different geographic boundary definitions. Using the National Food Acquisition and Purchase Survey, Nielsen TDLinx, and Information Resources, Inc. retail and consumer data, we find that food environment measures using administrative boundary definitions are statistically different from all other boundary definitions. We find general similarities within the two Euclidean distance and two network area boundary definitions. Only a small portion of food-at-home purchase events and expenditures by households occur within their own census tract boundary, suggesting the boundary definition has limitations and households are mobile in their food acquisitions.

Both Sides of the Street: Introducing Measures of Physical and Social Boundaries Based on Differences Across Sides of the Street, and Consequences for Crime

Although previous studies have theorized the importance of physical and social boundaries (edges) in understanding crime in place, the relationship between edges and the level of crime has been less studied empirically. The current study examines the effects of physical and social boundaries on crime in street segments. To empirically measure boundaries, we introduce an approach of looking at the differences of land use (physical boundary), socioeconomic status, or racial composition (social boundaries) on both sides of a street segment. We estimated a series of negative binomial regression models in which measures of the physical and social boundaries are included while controlling for the effects of structural characteristic and the conventional physical boundary measures of highways, parks, and rivers. We observed that there are positive relationships between all three of these boundary measures and violent and property crimes. The results indicated that physical and social boundaries are important to consider in understanding the spatial patterns of crime. Moreover, the current study confirmed the moderating effects between social and physical boundaries. Our results indicate that although much empirical research focuses solely on physical boundaries, our measures of social and physical boundaries have important consequences for the spatial location of crime, and therefore are worthy of further research.

On the Relationship Between the Marine Cold Air Outbreak M Parameter and Low‐Level Cloud Heights in the Midlatitudes

AbstractFocusing on conditions of subsidence when low clouds are present, ground‐based observations in both the North Atlantic and the Southern Ocean reveal strong relationships between cloud boundary (base and top heights) and different measures of lower tropospheric instability. The difference in potential temperature between the surface and 800 hPa (a metric called M) provides a stronger relationship than measures of inversion strength such as the lower tropospheric stability and estimated inversion strength. This is because (1) inversion strength itself does not correlate well with cloud boundaries, and (2) M contains information that appears important for cloud boundaries. These include the surface forcing through the use of sea surface rather than near‐surface air temperature and an upper level close to the real cloud top. These results expand upon previous work on the importance of M as a predictor of cloud morphology. However, important differences are found in low‐cloud conditions for the North Atlantic as compared to the Southern Ocean (for a given value of M): stronger inversions, deeper boundary layers, and much larger sea level pressures. Therefore, the relationship between cloud boundaries and M differs between the two regions. A general circulation model provides similar relationships as observed between M and both cloud top height and temperature but tends to place clouds higher and at colder temperatures than observed for a given M. This might cause issues with the representation of precipitation, cloud cover and radiation in the Southern Ocean.

Aerial image semantic segmentation using DCNN predicted distance maps

This paper addresses the challenge of learning spatial context for the semantic segmentation of high-resolution aerial images using Deep Convolutional Neural Networks (DCNNs). The proposed solution involves deriving a signed distance map for each semantic class from a ground truth label map and training a DCNN to predict this distance map instead of a score map for each class. Since the distance between a target pixel and its nearest object boundary measures how far the pixel penetrates an object, the distance maps encode spatial context, particularly spatial smoothness. Positive pixel values in the distance maps correspond to the correct class and negative values correspond to the incorrect class. A final label map is derived from the predicted distance maps by selecting the class with the maximum distance. Since neighboring pixels in the distance maps have similar values, the segmentation results are smoother than current approaches. The results are shown to be even better than performing post-processing using fully connected Conditional Random Fields (CRFs), a common approach to smoothing the segmentations produced DCNNs. Experimental results on the semantic labeling challenge dataset show the proposed approach outperforms most state-of-the-art methods. Our main contribution, though, is the novel idea of replacing the pixel-wise class score maps of DCNNs with distance maps. This is therefore orthogonal and complementary to other techniques employed by the state-of-the-art methods and could therefore be used to improve upon them.

A subclass of boundary measures and the convex combination problem for Herglotz–Nevanlinna functions in several variables

In this paper, we begin by investigating a particular subclass of boundary measures of Herglotz-Nevanlinna functions in two variables. Based on this, we then proceed to solve the convex combination problem for Herglotz-Nevanlinna functions in several variables.

National importance of surveying and ancient linear measures in the history of development of Russia

Issues of rational use of land resources are urgent contemporary problem. It is considered possible to solve it by analyzing centuries-old experience of history of land surveying, geodetic studies and mapping. The purpose of the study is to show the national importance of land surveying and ancient linear-measuring of boundary measures in the history of the state. The tasks of the article are connected with the analysis of types of geodetic surveys, linear measures and instruments during land surveying in different historical periods of development of the state. Historical and archival materials, ancient geodetic tools and maps were used as materials for the study. The study revealed that the development of surveying, the system of linear measurements and geodetic instrumentality had national importance to establish the boundaries of possessions, registration of quantity and quality of the land funds, protection of property rights, and termination of land disputes, valuation of land and establishment on the basis of equitable taxation. The main provisions of this study can add to the history of land relations in Russia and contribute to the further development and improvement of the state system of land surveying.

Hessian boundary measures

We will study certain boundary measures related to [Formula: see text]-subharmonic functions on [Formula: see text]-hyperconvex domains. These measures generalize the boundary measures studied by Wan and Wang (see [Complex Hessian operator and Lelong number for unbounded [Formula: see text]-subharmonic functions, Potential. Anal. 44(1) (2016) 53–69]). For the case of plurisubharmonic functions ([Formula: see text]) the boundary measure has been studied by Cegrell and Kemppe (see [Monge–Ampère boundary measures, Ann. Polon. Math. 96 (2009) 175–196]).

Boundary behavior of solutions to the parabolic p-Laplace equation

We establish boundary estimates for non-negative solutions to the p-parabolic equation in the degenerate range $p>2$. Our main results include new parabolic intrinsic Harnack chains in cylindrical NTA-domains together with sharp boundary decay estimates. If the underlying domain is $C^{1,1}$-regular, we establish a relatively complete theory of the boundary behavior, including boundary Harnack principles and H\"older continuity of the ratios of two solutions, as well as fine properties of associated boundary measures. There is an intrinsic waiting time phenomena present which plays a fundamental role throughout the paper. In particular, conditions on these waiting times rule out well-known examples of explicit solutions violating the boundary Harnack principle.

Философия права как идеологическая предпосылка философского типа понимания права

Introduction. The relevance of the scientific article is due to the ambiguous assessment of the philosophy of law and understanding by scientists of the philosophical type of understanding. The article is based on the analysis of some, in our opinion, fundamental and interrelated provisions of the textbook for masters by the famous Russian scientist, professor O.V. Martyshin “Philosophy of law”, the views of other philosophers and legal theorists concerning the status of philosophy of law in Russia and the philosophical type of understanding of law. Purpose. The aim of the papers is to analyze the positions of scientists who do not recognize the philosophy of law as a science, and give it the status of science; to substantiate the position according to which the philosophy of law is the ideological basis of the philosophical type of understanding of law, which is also understood ambiguously. Methodology. The authors used includes the following methods: general philosophical (dialectical-materialistic); general scientific (analysis and synthesis, logical and historical, comparison, abstraction, etc.); special methods (specifically sociological research, statistical, etc.); private scientific (formal legal, interpretation of law, etc.). Results. Despite the positions of philosophers and jurists about the non-scientific character of the philosophy of law the latter should be regarded as an independent science with its subject, methodology, performing their specific functions, consistent with other legal and social sciences. Legal philosophy serves as the ideological premise of a philosophical type of understanding that defines the scope or boundary measures of human freedom and which should not be confused with natural law type. Conclusion. It is necessary to make joint efforts of scientists related to this branch of knowledge and academic discipline to overcome the existing disagreements on fundamental issues related to the philosophy of law, and to solve the problems arising in the process of its development and improvement.

GIS-BASED DETECTION AND QUANTIFICATION OF PATCH-BOUNDARY PATTERNS FOR IDENTIFYING LANDSCAPE MOSAICS

The study of boundaries between patches allows us to understand the complexity of landscape interactions, especially those involved in the anthropic use of natural resources, which is a common source of environmental problems when harnessing landscape services. The study of the relationships between those two elements makes it possible to identify distinct homogeneous environmental areas in which the same ecological interactions occur. These areas are the mosaics that make up a landscape. This paper presents a GIS-based procedure to identify and quantify the boundaries of land use/cover patches and to record those data in matrices of patches by boundaries. These matrices, by means of a multivariate analysis, allow us to recognize landscape mosaics. This semi-automated procedure contributes to making the concept of landscape mosaics operative and enabling its application to landscape management. To exemplify its possibilities, we tested three alternatives for quantifying boundary measures: presence/absence, frequency and length. They each describe interactions with different details and provide different nuances in interpretations of landscape organization. In the study case, the frequency data provided a more easily understandable interpretation of the mosaic identification and characterization of landscape heterogeneity because these data are less conditioned by the spatial distribution, size or length of rare boundaries. Irrespective of the boundary measure used, a large central mosaic is always identified, highlighting the influence of landscape homogeneity and fragmentation on mosaic identification and the robustness of the tested procedure.

Equivalence relations that act on bundles of hyperbolic spaces

Consider a measured equivalence relation acting on a bundle of hyperbolic metric spaces by isometries. We prove that every aperiodic hyperfinite subequivalence relation is contained in a unique maximal hyperfinite subequivalence relation. We classify elements of the full group according to their action on fields on boundary measures (extending earlier results of Kaimanovich [Boundary amenability of hyperbolic spaces.Discrete Geometric Analysis(Contemporary Mathematics, 347). American Mathematical Society, Providence, RI, 2004, pp. 83–111]), study the existence and residuality of different types of elements and obtain an analog of Tits’ alternative.

Entropy and rotation sets: A toy model approach

Given a continuous dynamical system [Formula: see text] on a compact metric space [Formula: see text] and a continuous potential [Formula: see text], the generalized rotation set is the subset of [Formula: see text] consisting of all integrals of [Formula: see text] with respect to all invariant probability measures. The localized entropy at a point in the rotation set is defined as the supremum of the measure-theoretic entropies over all invariant measures whose integrals produce that point. In this paper, we provide an introduction to the theory of rotation sets and localized entropies. Moreover, we consider a shift map and construct a Lipschitz continuous potential, for which we are able to explicitly compute the geometric shape of the rotation set and its boundary measures. We show that at a particular exposed point on the boundary there are exactly two ergodic localized measures of maximal entropy.

Exponential Boundary Observers for Pressurized Water Pipe

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

A linear algorithm for the identification of a relaxation kernel using two boundary measures**This papers fits into the research program of the GNAMPA-INDAM and has been written in the framework of the ‘Groupement de Recherche en Contrôle des EDP entre la France et l’Italie (CONEDP-CNRS)’.

We consider a distributed system with persistent memory of a type which is encountered in the study of diffusion processes with memory and viscoelasticity for materials of Maxwell–Boltzmann type. The relaxation kernel, i.e. the kernel of the memory term, is scarcely known from first principles, and it has to be inferred from experiments taken on samples of the material. We prove that two boundary measures give a linear Volterra integral equation of the first kind for the unknown kernel. Hence, with two measures, the identification of the kernel, which in principle is a nonlinear problem, is reduced to the solution of a deconvolution problem, hence to an ill-posed but linear problem which can be solved with existing methods.

Boundary measures, generalized Gauss–Green formulas, and mean value property in metric measure spaces

We study mean value properties of harmonic functions in metric measure spaces. The metric measure spaces we consider have a doubling measure and support a (1, 1)-Poincaré inequality. The notion of harmonicity is based on the Dirichlet form defined in terms of a Cheeger differentiable structure. By studying fine properties of the Green function on balls, we characterize harmonic functions in terms of a mean value property. As a consequence, we obtain a detailed description of Poisson kernels. We shall also obtain a Gauss–Green type formula for sets of finite perimeter which posses a Minkowski content characterization of the perimeter. For the Gauss–Green formula we introduce a suitable notion of the interior normal trace of a regular ball.