Notion Of Distance Research Articles

Anchor Distance for 3D Multi-Object Distance Estimation From 2D Single Shot

Visual perception of the objects in a 3D environment is a key to successful performance in autonomous driving and simultaneous localization and mapping (SLAM). In this letter, we present a real time approach for estimating the distances to multiple objects in a scene using only a single-shot image. Given a 2D Bounding Box (BBox) and object parameters, a 3D distance to the object can be calculated directly using 3D reprojection; however, such methods are prone to significant errors because an error from the 2D detection can be amplified in 3D. In addition, it is also challenging to apply such methods to a real-time system due to the computational burden. In the case of the traditional multi-object detection methods, existing works have been developed for specific tasks such as object segmentation or 2D BBox regression. These methods introduce the concept of anchor BBox for elaborate 2D BBox estimation, and predictors are specialized and trained for specific 2D BBoxes. In order to estimate the distances to the 3D objects from a single 2D image, we introduce the notion of anchor distance based on an object's location and propose a method that applies the anchor distance to the multi-object detector structure. We let the predictors catch the distance prior using anchor distance and train the network based on the distance. The predictors can be characterized to the objects located in a specific distance range. By propagating the distance prior using a distance anchor to the predictors, it is feasible to perform the precise distance estimation and real-time execution simultaneously. The proposed method achieves about 30 FPS speed, and shows the lowest RMSE compared to the existing methods.

On Unique and Nonunique Fixed Points and Fixed Circles in M v b -Metric Space and Application to Cantilever Beam Problem

We introduce M v b -metric to generalize and improve M v -metric and unify numerous existing distance notions. Further, we define topological notions like open ball, closed ball, convergence of a sequence, Cauchy sequence, and completeness of the space to discuss topology on M v b -metric space and to create an environment for the survival of a unique fixed point. Also, we introduce a notion of a fixed circle and a fixed disc to study the geometry of the set of nonunique fixed points of a discontinuous self-map and establish fixed circle and fixed disc theorems. Further, we verify all these results by illustrative examples to demonstrate the authenticity of the postulates. Towards the end, we solve a fourth order differential equation arising in the bending of an elastic beam.

Decolonizing anthropology at a distance

Through the notions of distance, double critique, and colonial difference, this essay suggests a decolonization through a novel usage of colonial ethnographies. Analyzing the case of Morocco to reflect on the question of language(s) used in writing ethnography, specifically Arabic, French, and others, and unpacking the notion of colonial difference, the essay attempts to break away from the Western episteme. An “outside” to that episteme is found in the confrontation between knowledge accumulated in the written and the vernacular Arabic on the one hand, and Western knowledge (here, anthropological knowledge), on the other hand. This double critique aims at a reappropriation of colonial ethnography, and restructuring of the anthropological field, thus reframing the question of decolonization. The hope is that this reframing may have some general relevance.

Area Convergence of Monoculus Robots With Additional Capabilities

Abstract This paper considers the area convergence problem, which requires a group of robots to gather in a small area not defined a priori. While it is known that robots can gather at a point if they can precisely measure distances, we, in this paper, show that without any agreement on the coordinate system, it is impossible for robots to converge to an area if they cannot measure distances or angles. We denote these robots without the ability to measure distances or angles as monoculus robots. We present a counterexample showing that monoculus robots fail in area convergence even with the capability of measuring angles. However, monoculus robots with a weak notion of distance or minimal agreement on the coordinate system are sufficient to achieve area convergence. In particular, we present area convergence algorithms in asynchronous model for such monoculus robots with one of the two following simple additional capabilities: (1) locality detection ($\mathcal{L}\mathcal{D}$), a notion of distance or (2) orthogonal line agreement ($\mathcal{O}\mathcal{L}\mathcal{A}$), a notion of direction. We discuss extensions corresponding to multiple dimensions and the termination. Additionally, we validate our findings using simulation and show the robustness of our algorithms in the presence of errors in observation or movement.

Tangible Topology Through the Lens of Limits

ABSTRACT Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this very property makes point set topology perfect for teaching and learning abstract mathematical concepts. It clears our minds of preconceived intuitions and expectations and forces us to think in new and creative ways. In this paper, we present guided investigations into topology through questions and thinking strategies that open up fascinating problems. They are intended for faculty who already teach or are thinking about teaching a class in topology or abstract mathematical reasoning for undergraduates. They can be used to build simple to challenging projects in topology, proofs, honors programs, and research experiences.

Wasserstein distance, Fourier series and applications

We study the Wasserstein metric \(W_p\), a notion of distance between two probability distributions, from the perspective of Fourier Analysis and discuss applications. In particular, we bound the Earth Mover Distance \(W_1\) between the distribution of quadratic residues in a finite field \({\mathbb {F}}_p\) and uniform distribution by \(\lesssim p^{-1/2}\) (the Polya–Vinogradov inequality implies \(\lesssim p^{-1/2} \log {p}\)). We also show that for continuous \(f:{\mathbb {T}} \rightarrow {\mathbb {R}}_{}\) with mean value 0 $$\begin{aligned} (\text{ number } \text{ of } \text{ roots } \text{ of }~f) \cdot \left( \sum _{k=1}^{\infty }{ \frac{ |{\widehat{f}}(k)|^2}{k^2}}\right) ^{\frac{1}{2}} > rsim \frac{\Vert f\Vert ^{2}_{L^1({\mathbb {T}})}}{\Vert f\Vert _{L^{\infty }({\mathbb {T}})}}. \end{aligned}$$Moreover, we show that for a Laplacian eigenfunction \(-\Delta _g \phi _{\lambda } = \lambda \phi _{\lambda }\) on a compact Riemannian manifold \(W_p\left( \max \left\{ \phi _{\lambda }, 0\right\} dx, \max \left\{ -\phi _{\lambda }, 0\right\} dx\right) \lesssim _p \sqrt{\log {\lambda }/\lambda } \Vert \phi _{\lambda }\Vert _{L^1}^{1/p}\), which is at most a factor \(\sqrt{\log {\lambda }}\) away from sharp. Several other problems are discussed.

Multi-View Representation Learning via Dual Optimal Transportation

Recently, multi-view representation learning has gained rapid growth in various fields. Most of previous multi-view learning methods rely on strong notions of distances that often provide no useful gradients in deep network training, which greatly degrades the performance in merging complementary information of views. To address this challenge, a multi-view representation learning network with dual optimal transportation (MDOT-Net) is proposed to capture fusion representations embedded in a common manifold with the weak topology. In MDOT-Net, the multi-view representation learning is modelled as an optimal transportation (OT) problem in manifold fitting, which is further decomposed into the intra-view OT and the inter-view OT. The intra-view OT is implemented by a view-specific adversarial variational network, which accurately captures local manifold structures within views by leveraging fusion knowledge. The inter-view OT is implemented by a view-fusion adversarial inference network, which models fusion representations compatible with diversities of sub-manifolds by utilizing view-specific knowledge. The two OTs boost mutually by providing prior knowledge to each other in multi-view representation learning. Finally, numerous experiments are conducted on four benchmark datasets, and the results demonstrate MDOT-Net achieves the state-of-the-art performance.

Review of Introduction To Property Testing by Oded Goldreich

The area of property testing is concerned with designing methods to decide whether an input object possesses a certain property or not. Usually the problem is described as a promise problem: either the input object has the property or the input object is far from possessing the property. Here, the meaning of object being far from possessing the property is based on a specified and meaningful notion of distance. The main objective of property testing is accomplishing this decision making by developing a super efficient tester. A tester that reads through the entire object can easily determine whether the property is satisfied or not. However, one wishes the tester to probe the input at very few random locations and determine whether the property is satisfied. As such, randomness is a necessary ingredient for testing and having the tester erring on few instances is a necessary price to pay for designing highly efficient methodologies. Much of the literature on property testing has focused on two types of objects: functions and graphs. Naturally they form the major portion of the book: functions are discussed from Chapters 2 to 6 and graph properties are discussed from Chapters 8 to 10. The final three chapters focus on distribution testing, probabilistically checkable proofs (PCPs) and locally testable codes, and ramifications of property testing on other related topics in Computer Science and Statistics. A separate chapter is devoted to query lower bound techniques.

The Virus Covid-19 and Dilemmas of Online Technology.

Commentary on the COVID-19 pandemic must necessarily consider the medical issues in social and political context. This paper discusses one important dimension of the context, the long-term history of human activity as intrinsically technological in its nature. The pandemic has accelerated the use of technology to mediate relations between people at a distance. This involves not only a change in the skills people have (though acquiring these skills has become the central project of work for many people), but changes the sort of person they are. Our notions of closeness and distance, or of touching and being touched, and so on, refer simultaneously to states that are spatial and emotional, factual and evaluative. Inquiry into the differences in human relations where there is physical presence and where there is not raises very significant questions. What are the differences and why are they thought, and felt, to matter? What are the differences when the relationship is supposed to be a therapeutic one? What are the financial and political interests at work in enforcing relations at a distance by new media, i.e., mediated relations? How is a persons agency affected by a lack of freedom to move or a lack of face-to-face contact? What happens to all those human relations for which physical presence was previously the norm, relations such as those performed in the rituals of birth, marriage and death, or in activities like sport and the arts? Can it be said that new technologies involve a loss of soul? The present paper seeks to provide a reflective and open-ended framework for asking such questions.

Non-linear embedding of acoustic cross-spectral density matrices through diffusion maps.

Based on the notion of similarity or "distance" between cross-spectral density matrices (CSDMs), a recent analysis of matched-field source localization in a stochastic ocean waveguide provided evidence that geodesic distances between CSDMs could be employed to estimate the source location in range and depth. For M acoustic sensors configured as a vertical array, these M×M matrices were estimated from source and replica fields propagated to the array and interpreted as points in a Riemannian manifold whose dimension is M2. Because they serve as fundamental constructs for many source localization algorithms, visualizations of CSDM manifolds are illustrated here in an attempt to gain insight into this geometric approach by using simulated acoustic fields propagated through an ocean waveguide with internal wave-induced variability. The manifold is treated as an undirected, weighted graph whose nodes are CSDMs with edges (weights) describing a measure of similarity between nodes. A non-linear dimensionality reduction technique, diffusion maps, is applied to project these high-dimensional matrices onto a three-dimensional subspace using a spectral decomposition of the graph in an attempt to grasp relationships among such matrices. The mapping is designed to preserve the notion of distance between matrices, allowing for a meaningful visualization of the high-dimensional manifold.

« Perspectives »Global Regionalization Processes and (Macro)-Regional Integration. In Favor of Generalization in Geography

Many researchers concur in observing that globalization has abolished neither distance, nor the usefulness of geographical proximity. Spatial constraints continue to shape exchanges, as well as the density and quality of interactions between societies. Even in a globalized world, pervaded with networks that disrupt traditional territorialities, it can be useful and even inevitable to build relationships with one’s neighbors. In this context, the notion of (macro)regional (or multi-state) integration deserves to be exploited. In particular, geographical research has so far eluded this concept, despite this discipline’s recognized expertise on the notions of region, distance, territory and territorial development, which are at the heart of the understanding of regional integration, both theoretically and empirically. This contribution aims to clarify the words, objects and methods of (macro)regional integration from the point of view of geographical semantics, as well as the evolution of theoretical approaches to the notion of region.

Relative-distance-based approaches for ranking intuitionistic fuzzy values

During the uncertain information processing on Atanassov’s intuitionistic fuzzy sets, the ranking for intuitionistic fuzzy values (IFVs) is an important and omnipresent issue. Even though many orders used to compare any two IFVs have been proposed, some shortcomings, such as inadmissibility, nonrobustness, and nondeterminacy, may exist when these orders are utilized. Inspired by the Euclidean approach for ranking IFVs, we present a novel order that can overcome the aforementioned shortcomings using the notion of relative geometric distance. With the help of graphic representation of an IFV, we analyze the existing popular approaches for ranking IFVs and point out their drawbacks. Taking into account these three distances between an IFV and the ideal negative point, ideal positive point and most uncertain point, respectively, we present a relative-distance-based mensuration for describing the favorable degree of the IFV. Accordingly, the boundaries used in the existing ranking approaches for IFVs are replaced by a novel curve. We prove that the proposed method satisfies the admissibility, robustness, and determinacy requirements. Finally, we extend the presented ranking method for IFVs by introducing human attitudes and compare the proposed approach with the existing ones, which indicates its availability and rationality. We then can obtain the conclusion that the relative distance is an effective and reasonable approach for ranking IFVs.

Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces

We consider the problem of model reduction of parametrized PDEs where the goal is to approximate any function belonging to the set of solutions at a reduced computational cost. For this, the bottom line of most strategies has so far been based on the approximation of the solution set by linear spaces on Hilbert or Banach spaces. This approach can be expected to be successful only when the Kolmogorov width of the set decays fast. While this is the case on certain parabolic or elliptic problems, most transport-dominated problems are expected to present a slow decaying width and require to study nonlinear approximation methods. In this work, we propose to address the reduction problem from the perspective of general metric spaces with a suitably defined notion of distance. We develop and compare two different approaches, one based on barycenters and another one using tangent spaces when the metric space has an additional Riemannian structure. Since the notion of linear vectorial spaces does not exist in general metric spaces, both approaches result in nonlinear approximation methods. We give theoretical and numerical evidence of their efficiency to reduce complexity for one-dimensional conservative PDEs where the underlying metric space can be chosen to be theL2-Wasserstein space.

« Importance du rôle de la motricité dans la relation d’objet », de Pierre Marty et Michel Fain

En 1954, Pierre Marty et Michel Fain, psychanalystes récents, présentent un rapport qui ouvre la relation d’objet à sa dimension sensorio-motrice. Leur travail constitue la première étude psychanalytique de ce qu’ils appellent « l’activité motrice pulsionnelle ». Ils envisagent sous cet angle les rapports entre « l’objet extérieur » et « l’objet interne », la notion de « distance » et abordent différentes notions participant à la constitution du Moi comme l’internalisation et l’intellectualisation.

NEW VEGETATION INDICES FOR FULL AND COMPACT POLARIMETRIC SAR DATA: IN PREPARATION FOR THE RADARSAT CONSTELLATION MISSION (RCM)

Abstract. In this paper, we present two radar vegetation indices for full-pol and compact-pol SAR data, respectively. Both are derived using the notion of a geodesic distance between observation and well-known scattering models available in the literature. While the full-pol version depends on a generalized volume scattering model, the compact-pol version uses the ideal depolariser to model the randomness in the vegetation. We have utilized the RADARSAT Constellation Mission (RCM) time-series data from the SAMPVEX16-MB campaign in the Manitoba region of Canada for comparing and assessing the indices in terms of the change in the biophysical parameters as well. The compact-pol data for comparison is simulated from the full-pol RCM time series. Both the indices show better performance at correlating with biophysical parameters such as Plant Area Index (PAI) and Volumetric Water Content (VWC) for wheat and soybean crops, in comparison to the state-of-art Radar Vegetation Index (RVI) of Kim and van Zyl. These indices are timely for the upcoming release of the data from the RCM, which will provide data in both full and compact-pol modes, aimed at better crop monitoring from space.

Homotopic distance between functors

We introduce a notion of categorical homotopic distance between functors by adapting the notion of homotopic distance in topological spaces, recently defined by the authors, to the context of small categories. Moreover, this notion generalizes the work on categorical LS-category of small categories by Tanaka.

A stability result for linear Markovian stochastic optimization problems

In this paper, we propose a semi-metric for Markov processes that allows to bound optimal values of linear Markovian stochastic optimization problems. Similar to existing notions of distance for general stochastic processes, our distance is based on transportation metrics. As opposed to the extant literature, the proposed distance is problem specific, i.e., dependent on the data of the problem whose objective value we want to bound. As a result, we are able to consider problems with randomness in the constraints as well as in the objective function and therefore relax an assumption in the extant literature. We derive several properties of the proposed semi-metric and demonstrate its use in a stylized numerical example.

Highly Local Clostridioides difficile Infection (CDI) Pressure as Risk Factors for CDI

Background. Colonization pressure at the unit level is known to be a risk factor for Clostridioides difficile infections in hospitals. Because C. difficile colonization is not routinely detected in clinical practice, only patients identified as having C. difficile infection (CDI) are included in these pressure calculations. We used data from the University of Iowa Hospitals and Clinics (UIHC) to determine whether highly local CDI pressure, due to patients in nearby rooms, is more strongly correlated with CDI than unit-level CDI pressure. Methods: We designed a base logistic regression model using variables known to be risk factors for CDI: age, antibiotic/gastric acid suppressor use, low albumin, prior hospitalization, comorbidities. To the base model, we add 2 measures, mean colonization pressure (MCP) and sum colonization pressure (SCP) of CDI at the unit level to obtain new models. To the base model, we also added CDI colonization pressure by considering CDI cases at different distance thresholds from the focal patient. Distances between patient rooms were extracted from hospital floor plans. Results: Adding unit-level CDI colonization pressures to the base model improved performance. However, adding CDI colonization pressures due to roommates and due to patients at different distances improved the model much more (Table 1). The top (resp. bottom) row shows in-sample (resp. out-of-sample) C-statistics for the base model, the base model with unit-level MCP, the base model with roommate MCP, and the base model with MCP from patients are different distances added as separate features. C-statistics for the base model and the base model with unit CDI pressure (SCP and MCP) are compared in Fig. 1 with C-statistics from the base model with CDI pressure from patients at distances D = 0, 1, 2, 3, 4, 5, 10, 15, 20 hops (1 hop = 5–6 meters). Conclusions: Our results support the hypothesis that unit CDI colonization pressure is a risk factor for CDI. However, by incorporating spatially granular notions of distances between patients in our analysis, we were able to demonstrate that the true source of CDI pressure at the UIHC is almost exclusively attributable to roommates and patients in adjacent rooms.Funding: NoneDisclosures: None

A Location-and-Form-Based Distance for Geographical Analysis

Location and geometric form constitute a fundamental basis for the characterization of objects in space. The traditional distance-based geographical analysis of objects, however, usually ignores information associated with their forms. In this article, we propose a location-and-form-based distance to simultaneously take into account these basic characteristics. For substantiation, the significance of the proposed distance is examined with respect to its methodological contributions and applicability. In terms of methodology, we use pattern analysis by the L statistic as an example to show the form effect on the conventional geographical analysis, which is based solely on the location-based distance, and show how to generalize point distance–based analyses to the analysis of objects with forms. With respect to applicability, we demonstrate the capability of our proposed distance in improving the performance of matching buildings in OpenStreetMap and the corresponding standard reference of an area. It is also applicable to other real-life problems in which object forms are involved. Generally, the location-and-form-based distance and the associated methods can give us a new perspective on the conceptualization of distance. The proposed distance can be further extended to include other object attributes to study spatial relationships of objects based on a general notion of distance. Therefore, the proposed distance is a powerful concept that can comprehensively reveal the multifaceted nature of geographical relationships. This study advances the frontier of theoretical and applied research in geography where distance plays an important role.

Filosofia da Educação a Distância

O livro “Filosofia da Educação a Distância: conceitos e concepções” é uma obra organizada pela professora doutora Lílian do Valle em parceria com Estrella Bohadana (in memorian), Sônia Ribeiro e Ana Lúcia Gomes. Trata-se de uma coletânea de textos que exploram conceitos pouco (ou nada) visitados na área da educação a distância (EaD), propondo a reflexão conceitual das noções de presença, distância, interatividade, comunicação, mediação, sujeito, atividade, ação, qualidade e autonomia.