metric distance
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2022 ◽  
Vol 6 (POPL) ◽  
pp. 1-31
Author(s):  
Marco Campion ◽  
Mila Dalla Preda ◽  
Roberto Giacobazzi

Imprecision is inherent in any decidable (sound) approximation of undecidable program properties. In abstract interpretation this corresponds to the release of false alarms, e.g., when it is used for program analysis and program verification. As all alarming systems, a program analysis tool is credible when few false alarms are reported. As a consequence, we have to live together with false alarms, but also we need methods to control them. As for all approximation methods, also for abstract interpretation we need to estimate the accumulated imprecision during program analysis. In this paper we introduce a theory for estimating the error propagation in abstract interpretation, and hence in program analysis. We enrich abstract domains with a weakening of a metric distance. This enriched structure keeps coherence between the standard partial order relating approximated objects by their relative precision and the effective error made in this approximation. An abstract interpretation is precise when it is complete. We introduce the notion of partial completeness as a weakening of precision. In partial completeness the abstract interpreter may produce a bounded number of false alarms. We prove the key recursive properties of the class of programs for which an abstract interpreter is partially complete with a given bound of imprecision. Then, we introduce a proof system for estimating an upper bound of the error accumulated by the abstract interpreter during program analysis. Our framework is general enough to be instantiated to most known metrics for abstract domains.


2022 ◽  
Vol 2153 (1) ◽  
pp. 012013
Author(s):  
H A Torres-Mantilla ◽  
L Cuesta-Herrera ◽  
J E Andrades-Grassi ◽  
G Bianchi

Abstract The estimation of the minimum inhibitory concentration is usually performed by a method of serial dilutions by a factor of 2, introducing the overestimation of antimicrobial efficacy, quantified by a simulation model that shows that the variability of the bias is higher for the standard deviation, being dependent on the metric distance to the values of the concentrations used. We use a methodological approach through modeling and simulation for the measurement error of physical variables with censored information, proposing a new inference method based on the calculation of the exact probability for the set of possible samples from nmeasurements that allows quantifying the p-value in one or two independent sample tests for the comparison of censored data means. Tests based on exact probability methods offer a reasonable solution for small sample sizes, with statistical power varying according to the hypothesis evaluated, providing insight into the limitations of censored data analysis and providing a tool for decision making in the diagnosis of antimicrobial efficacy.


2021 ◽  
pp. 103-125
Author(s):  
James Davidson

This chapter introduces and illustrates the concept of a metric (distance measure), and the definition of a metric space. Open, closed, and compact sets are discussed in a general context, and the concepts of separability and completeness introduced. It goes on to look at mappings on metric spaces, examines the important case of function spaces, and treats the Arzelà–Ascoli theorem.


2021 ◽  
Author(s):  
Vijay Kumar ◽  
Rumi De

Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the local rules of interactions among the individuals, namely, metric versus topological interactions as debated over in the current literature. In the case of the metric ruling, the individuals interact with the neighbours within a certain metric distance; in contrast, in the topological ruling, interaction is confined within a number of fixed nearest neighbours. Here, we explore how the range of interaction versus the number of fixed interacting neighbours affects the dynamics of flocking in an unbounded space, as observed in natural scenarios. Our study reveals the existence of a certain threshold value of the interaction radius in the case of metric ruling and a threshold number of interacting neighbours for the topological ruling to reach an ordered state. Interestingly, our analysis shows that topological interaction is more effective in bringing the order in the group, as observed in field studies. We further compare how the nature of the interactions affects the dynamics for various sizes and speeds of the flock.


Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1673
Author(s):  
Aili Wang ◽  
Chengyang Liu ◽  
Dong Xue ◽  
Haibin Wu ◽  
Yuxiao Zhang ◽  
...  

Although hyperspectral data provide rich feature information and are widely used in other fields, the data are still scarce. Training small sample data classification is still a major challenge for HSI classification based on deep learning. Recently, the method of mining sample relationships has been proved to be an effective method for training small samples. However, this strategy requires high computational power, which will increase the difficulty of network model training. This paper proposes a modified depthwise separable relational network to deeply capture the similarity between samples. In addition, in order to effectively mine the similarity between samples, the feature vectors of support samples and query samples are symmetrically spliced. According to the metric distance between symmetrical structures, the dependence of the model on samples can be effectively reduced. Firstly, in order to improve the training efficiency of the model, depthwise separable convolution is introduced to reduce the computational cost of the model. Secondly, the Leaky-ReLU function effectively activates all neurons in each layer of neural network to improve the training efficiency of the model. Finally, the cosine annealing learning rate adjustment strategy is introduced to avoid the model falling into the local optimal solution and enhance the robustness of the model. The experimental results on two widely used hyperspectral remote sensing image data sets (Pavia University and Kennedy Space Center) show that compared with seven other advanced classification methods, the proposed method achieves better classification accuracy under the condition of limited training samples.


2021 ◽  
Vol 8 (9) ◽  
Author(s):  
Vijay Kumar ◽  
Rumi De

Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the local rules of interactions among the individuals, namely, metric versus topological interactions as debated in the current literature. In the case of the metric ruling, the individuals interact with the neighbours within a certain metric distance; by contrast, in the topological ruling, interaction is confined within a number of fixed nearest neighbours. Here, we explore how the range of interaction versus the number of fixed interacting neighbours affects the dynamics of flocking in an unbounded space, as observed in natural scenarios. Our study reveals the existence of a certain threshold value of the interaction radius in the case of metric ruling and a threshold number of interacting neighbours for the topological ruling to reach an ordered state. Interestingly, our analysis shows that topological interaction is more effective in bringing the order in the group, as observed in field studies. We further compare how the nature of the interactions affects the dynamics for various sizes and speeds of the flock.


Author(s):  
B. Erdnüß

Abstract. The one-parameter division undistortion model by (Lenz, 1987) and (Fitzgibbon, 2001) is a simple radial distortion model with beneficial algebraic properties that allows to reason about some problems analytically that can only be handled numerically in other distortion models. One property of this distortion model is that straight lines in the undistorted image correspond to circles in the distorted image. These circles are fully described by their center point, as the radius can be calculated from the position of the center and the distortion parameter only. This publication collects the properties of this distortion model from several sources and reviews them. Moreover, we show in this publication that the space of this center is projectively isomorphic to the dual space of the undistorted image plane, i.e. its line space. Therefore, projective invariant measurements on the undistorted lines are possible by the according measurements on the centers of the distorted circles. As an example of application, we use this to find the metric distance of two parallel straight rails with known track gauge in a single uncalibrated camera image with significant radial distortion.


2021 ◽  
Vol 9 ◽  
Author(s):  
Nicholas T. Ouellette ◽  
Deborah M. Gordon

Local social interactions among individuals in animal groups generate collective behavior, allowing groups to adjust to changing conditions. Historically, scientists from different disciplines have taken different approaches to modeling collective behavior. We describe how each can contribute to the goal of understanding natural systems. Simple bottom-up models that describe individuals and their interactions directly have demonstrated that local interactions far from equilibrium can generate collective states. However, such simple models are not likely to describe accurately the actual mechanisms and interactions in play in any real biological system. Other classes of top-down models that describe group-level behavior directly have been proposed for groups where the function of the collective behavior is understood. Such models cannot necessarily explain why or how such functions emerge from first principles. Because modeling approaches have different strengths and weaknesses and no single approach will always be best, we argue that models of collective behavior that are aimed at understanding real biological systems should be formulated to address specific questions and to allow for validation. As examples, we discuss four forms of collective behavior that differ both in the interactions that produce the collective behavior and in ecological context, and thus require very different modeling frameworks. 1) Harvester ants use local interactions consisting of brief antennal contact, in which one ant assesses the cuticular hydrocarbon profile of another, to regulate foraging activity, which can be modeled as a closed-loop excitable system. 2) Arboreal turtle ants form trail networks in the canopy of the tropical forest, using trail pheromone; one ant detects the volatile chemical that another has recently deposited. The process that maintains and repairs the trail, which can be modeled as a distributed algorithm, is constrained by the physical configuration of the network of vegetation in which they travel. 3) Swarms of midges interact acoustically and non-locally, and can be well described as agents moving in an emergent potential well that is representative of the swarm as a whole rather than individuals. 4) Flocks of jackdaws change their effective interactions depending on ecological context, using topological distance when traveling but metric distance when mobbing. We discuss how different research questions about these systems have led to different modeling approaches.


2021 ◽  
Vol 11 (6) ◽  
pp. 1527-1532
Author(s):  
G. Shobana ◽  
S. Shankar

Prediction of the development risk of some diseases is an important area of Health Care Research. When exploring the personalized care of the patients, precise identification and classification of similarity in patients from their past report is an important process. Electronically stored health information EHRs that has been sampled unevenly as well as which has variable appointment durations, is considered to be unsuitable for measuring the similarity among patients directly, as there is no proper representation that are fitting. In addition, a technique is required that is efficient to evaluate similarities in patient. We propose two new similarities learning environments using deep learning that learn simultaneously the representations of the patients as well as measurement of similarity in pairs. A Convolutional Neural Network (CNN) is used to understand EHRs that contains crucial information which are local thereby providing scholastic illumination in the triplet loss otherwise entropy loss. When the training is completed, distances are calculated as well as similarities scores. Using this similarity information, disease predictions along with patient grouping is performed. Experimentally the results gives an idea that CNN can represent the EHR sequences in a better way and the schema offered are more efficient than the modern metric distance learning.


2021 ◽  
Author(s):  
Ahmed AlSaihati ◽  
Salaheldin Elkatatny ◽  
Ahmed Mahmoud ◽  
Abdulazeez Abdulraheem

Abstract There has been discrepancy between the pre-calculated and actual T&D values, because of the dependence of the model’s predictability on assumed inputs. Therefore, to have a reliable model, the users must adjust the model inputs; mainly friction coefficient in order to match the actual T&D. This, however, can mask downhole conditions such as cutting beds, tight holes and sticking tendencies. This paper aims to introduce a machine learning model to predict the continuous profile of the surface drilling torque to detect the operational issues in advance. Actual data of Well-1, starting from the time of drilling a 5-7/8-inch horizontal section until one day prior to the stuck pipe event, was used to train and test a random forest (RF) model with an 80/20 split ratio, to predict the surface drilling torque. The input variables for the model are the drilling surface parameters, namely: flow rate, hook load, rate of penetration, rotary speed, standpipe pressure, and weight-on-bit. The developed model was used to predict the surface drilling torque, which represents the normal trend for the last day leading up to the stuck pipe incident in Well-1. Then the model was integrated with a multivariate metric distance, Mahalanobis, to be used as a classifier to measure how close an actual observation is from the predictive normal trend. Based on a pre-determined threshold, each actual observation was labeled as "NORMAL" or "ANOMAL".


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