Vectorial integer bootstrapping: flexible integer estimation with application to GNSS

AbstractIn this contribution, we extend the principle of integer bootstrapping (IB) to a vectorial form (VIB). The mathematical definition of the class of VIB-estimators is introduced together with their pull-in regions and other properties such as probability bounds and success rate approximations. The vectorial formulation allows sequential block-by-block processing of the ambiguities based on a user-chosen partitioning. In this way, flexibility is created, where for specific choices of partitioning, tailored VIB-estimators can be designed. This wide range of possibilities is discussed, supported by numerical simulations and analytical examples. Further guidelines are provided, as well as the possible extension to other classes of estimators.

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Typologization of security regulation

Scientific and Informational Bulletin of Ivano-Frankivsk University of Law Named after King Danylo Halytskyi - Scientific and informational bulletin of Ivano-Frankivsk University of Law named after King Danylo Halytskyi ◽

10.33098/2078-6670.2020.9.21.20-27 ◽

2020 ◽

pp. 20-27

Author(s):

Denis Tikhomirov

Keyword(s):

Social Relations ◽

Scientific Literature ◽

Legal Regulation ◽

Procedural Understanding ◽

Limited Ability ◽

Methodological Basis ◽

Wide Range ◽

The Subject ◽

Definition Of ◽

Legal Understanding

The purpose of the article is to typologize terminological definitions of security, to find out the general, to identify the originality of their interpretations depending on the subject of legal regulation. The methodological basis of the study is the methods that made it possible to obtain valid conclusions, in particular, the method of comparison, through which it became possible to correlate different interpretations of the term "security"; method of hermeneutics, which allowed to elaborate texts of normative legal acts of Ukraine, method of typologization, which made it possible to create typologization groups of variants of understanding of the term "security". Scientific novelty. The article analyzes the understanding of the term "security" in various regulatory acts in force in Ukraine. Typological groups were understood to understand the term "security". Conclusions. The analysis of the legal material makes it possible to confirm that the issues of security are within the scope of both legislative regulation and various specialized by-laws. However, today there is no single conception on how to interpret security terminology. This is due both to the wide range of social relations that are the subject of legal regulation and to the relativity of the notion of security itself and the lack of coherence of views on its definition in legal acts and in the scientific literature. The multiplicity of definitions is explained by combinations of material and procedural understanding, static - dynamic, and conditioned by the peculiarities of a particular branch of legal regulation, limited ability to use methods of one or another branch, the inter-branch nature of some variations of security, etc. Separation, common and different in the definition of "security" can be used to further standardize, in fact, the regulatory legal understanding of security to more effectively implement the legal regulation of the security direction.

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Music after the Fall

10.1525/california/9780520283145.001.0001 ◽

2017 ◽

Cited By ~ 14

Author(s):

Tim Rutherford-Johnson

Keyword(s):

New Media ◽

Contemporary Music ◽

The United States ◽

Art Music ◽

Sound Art ◽

Musical Composition ◽

Western Art ◽

Wide Range ◽

Definition Of ◽

The Cold War

By the start of the 21st century many of the foundations of postwar culture had disappeared: Europe had been rebuilt and, as the EU, had become one of the world’s largest economies; the United States’ claim to global dominance was threatened; and the postwar social democratic consensus was being replaced by market-led neoliberalism. Most importantly of all, the Cold War was over, and the World Wide Web had been born. Music After The Fall considers contemporary musical composition against this changed backdrop, placing it in the context of globalization, digitization, and new media. Drawing on theories from the other arts, in particular art and architecture, it expands the definition of Western art music to include forms of composition, experimental music, sound art, and crossover work from across the spectrum, inside and beyond the concert hall. Each chapter considers a wide range of composers, performers, works, and institutions are considered critically to build up a broad and rich picture of the new music ecosystem, from North American string quartets to Lebanese improvisers, from South American electroacoustic studios to pianos in the Australian outback. A new approach to the study of contemporary music is developed that relies less on taxonomies of style and technique, and more on the comparison of different responses to common themes, among them permission, fluidity, excess, and loss.

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Size-adjusted aortic valve area: refining the definition of severe aortic stenosis

European Heart Journal - Cardiovascular Imaging ◽

10.1093/ehjci/jeaa295 ◽

2020 ◽

Author(s):

Branka Vulesevic ◽

Naozumi Kubota ◽

Ian G Burwash ◽

Claire Cimadevilla ◽

Sarah Tubiana ◽

...

Keyword(s):

Aortic Valve ◽

Predictive Accuracy ◽

Severe Aortic Stenosis ◽

Aortic Valve Area ◽

Obese Patients ◽

Derivation Cohort ◽

Wide Range ◽

Definition Of ◽

Diagnostic And Prognostic Value ◽

Valve Area

Abstract Aims Severe aortic valve stenosis (AS) is defined by an aortic valve area (AVA) <1 cm2 or an AVA indexed to body surface area (BSA) <0.6 cm/m2, despite little evidence supporting the latter approach and important intrinsic limitations of BSA indexation. We hypothesized that AVA indexed to height (H) might be more applicable to a wide range of populations and body morphologies and might provide a better predictive accuracy. Methods and results In 1298 patients with degenerative AS and preserved ejection fraction from three different countries and continents (derivation cohort), we aimed to establish an AVA/H threshold that would be equivalent to 1.0 cm2 for defining severe AS. In a distinct prospective validation cohort of 395 patients, we compared the predictive accuracy of AVA/BSA and AVA/H. Correlations between AVA and AVA/BSA or AVA/H were excellent (all R2 > 0.79) but greater with AVA/H. Regressions lines were markedly different in obese and non-obese patients with AVA/BSA (P < 0.0001) but almost identical with AVA/H (P = 0.16). AVA/BSA values that corresponded to an AVA of 1.0 cm2 were markedly different in obese and non-obese patients (0.48 and 0.59 cm2/m2) but not with AVA/H (0.61 cm2/m for both). Agreement for the diagnosis of severe AS (AVA < 1 cm2) was significantly higher with AVA/H than with AVA/BSA (P < 0.05). Similar results were observed across the three countries. An AVA/H cut-off value of 0.6 cm2/m [HR = 8.2(5.6–12.1)] provided the best predictive value for the occurrence of AS-related events [absolute AVA of 1 cm2: HR = 7.3(5.0–10.7); AVA/BSA of 0.6 cm2/m2 HR = 6.7(4.4–10.0)]. Conclusion In a large multinational/multiracial cohort, AVA/H was better correlated with AVA than AVA/BSA and a cut-off value of 0.6 cm2/m provided a better diagnostic and prognostic value than 0.6 cm2/m2. Our results suggest that severe AS should be defined as an AVA < 1 cm2 or an AVA/H < 0.6 cm2/m rather than a BSA-indexed value of 0.6 cm2/m2.

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The Impact of Initial Conditions in N-Body Simulations of Debris Discs

Publications of the Astronomical Society of Australia ◽

10.1017/pasa.2015.41 ◽

2015 ◽

Vol 32 ◽

Cited By ~ 4

Author(s):

E. Thilliez ◽

S. T. Maddison

Keyword(s):

Numerical Simulations ◽

Initial Conditions ◽

Parent Body ◽

Dust Trapping ◽

Physical Context ◽

Disc Width ◽

Wide Range ◽

Belt Width ◽

New Generation ◽

The Impact

AbstractNumerical simulations are a crucial tool to understand the relationship between debris discs and planetary companions. As debris disc observations are now reaching unprecedented levels of precision over a wide range of wavelengths, an appropriate level of accuracy and consistency is required in numerical simulations to confidently interpret this new generation of observations. However, simulations throughout the literature have been conducted with various initial conditions often with little or no justification. In this paper, we aim to study the dependence on the initial conditions of N-body simulations modelling the interaction between a massive and eccentric planet on an exterior debris disc. To achieve this, we first classify three broad approaches used in the literature and provide some physical context for when each category should be used. We then run a series of N-body simulations, that include radiation forces acting on small grains, with varying initial conditions across the three categories. We test the influence of the initial parent body belt width, eccentricity, and alignment with the planet on the resulting debris disc structure and compare the final peak emission location, disc width and offset of synthetic disc images produced with a radiative transfer code. We also track the evolution of the forced eccentricity of the dust grains induced by the planet, as well as resonance dust trapping. We find that an initially broad parent body belt always results in a broader debris disc than an initially narrow parent body belt. While simulations with a parent body belt with low initial eccentricity (e ~ 0) and high initial eccentricity (0 < e < 0.3) resulted in similar broad discs, we find that purely secular forced initial conditions, where the initial disc eccentricity is set to the forced value and the disc is aligned with the planet, always result in a narrower disc. We conclude that broad debris discs can be modelled by using either a dynamically cold or dynamically warm parent belt, while in contrast eccentric narrow debris rings are reproduced using a secularly forced parent body belt.

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Cubical Agda: A dependently typed programming language with univalence and higher inductive types

Journal of Functional Programming ◽

10.1017/s0956796821000034 ◽

2021 ◽

Vol 31 ◽

Author(s):

ANDREA VEZZOSI ◽

ANDERS MÖRTBERG ◽

ANDREAS ABEL

Keyword(s):

Programming Language ◽

Type Theory ◽

Type Checking ◽

Dependent Type Theory ◽

Wide Range ◽

General Schema ◽

Direct Definition ◽

Inductive Types ◽

Definition Of ◽

Cubical Type Theory

Abstract Proof assistants based on dependent type theory provide expressive languages for both programming and proving within the same system. However, all of the major implementations lack powerful extensionality principles for reasoning about equality, such as function and propositional extensionality. These principles are typically added axiomatically which disrupts the constructive properties of these systems. Cubical type theory provides a solution by giving computational meaning to Homotopy Type Theory and Univalent Foundations, in particular to the univalence axiom and higher inductive types (HITs). This paper describes an extension of the dependently typed functional programming language Agda with cubical primitives, making it into a full-blown proof assistant with native support for univalence and a general schema of HITs. These new primitives allow the direct definition of function and propositional extensionality as well as quotient types, all with computational content. Additionally, thanks also to copatterns, bisimilarity is equivalent to equality for coinductive types. The adoption of cubical type theory extends Agda with support for a wide range of extensionality principles, without sacrificing type checking and constructivity.

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Definitions and Prevalence of Multimorbidity in Large Database Studies: A Scoping Review

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph18041673 ◽

2021 ◽

Vol 18 (4) ◽

pp. 1673

Author(s):

Ying Pin Chua ◽

Ying Xie ◽

Poay Sian Sabrina Lee ◽

Eng Sing Lee

Keyword(s):

Scoping Review ◽

Chronic Conditions ◽

Meta Analysis ◽

Epidemiological Studies ◽

Cross Sectional ◽

Coding Systems ◽

Wide Range ◽

Scoping Reviews ◽

Retrospective Cohort Studies ◽

Definition Of

Background: Multimorbidity presents a key challenge to healthcare systems globally. However, heterogeneity in the definition of multimorbidity and design of epidemiological studies results in difficulty in comparing multimorbidity studies. This scoping review aimed to describe multimorbidity prevalence in studies using large datasets and report the differences in multimorbidity definition and study design. Methods: We conducted a systematic search of MEDLINE, EMBASE, and CINAHL databases to identify large epidemiological studies on multimorbidity. We used the Preferred Reporting Items for Systematic Reviews and Meta-analysis Extension for Scoping Reviews (PRISMA-ScR) protocol for reporting the results. Results: Twenty articles were identified. We found two key definitions of multimorbidity: at least two (MM2+) or at least three (MM3+) chronic conditions. The prevalence of multimorbidity MM2+ ranged from 15.3% to 93.1%, and 11.8% to 89.7% in MM3+. The number of chronic conditions used by the articles ranged from 15 to 147, which were organized into 21 body system categories. There were seventeen cross-sectional studies and three retrospective cohort studies, and four diagnosis coding systems were used. Conclusions: We found a wide range in reported prevalence, definition, and conduct of multimorbidity studies. Obtaining consensus in these areas will facilitate better understanding of the magnitude and epidemiology of multimorbidity.

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A Hull Normal Based Approach for Cylindrical Size Assessment

Journal of Manufacturing Science and Engineering ◽

10.1115/1.4003332 ◽

2011 ◽

Vol 133 (1) ◽

Author(s):

Steven Turek ◽

Sam Anand

Keyword(s):

New York ◽

Least Squares ◽

Measured Data ◽

Size Determination ◽

Mathematical Definition ◽

Dimensioning And Tolerancing ◽

Normal Method ◽

Computational Metrology ◽

American Society ◽

Definition Of

Digital measurement devices, such as coordinate measuring machines, laser scanning devices, and digital imaging, can provide highly accurate and precise coordinate data representing the sampled surface. However, this discrete measurement process can only account for measured data points, not the entire continuous form, and is heavily influenced by the algorithm that interprets the measured data. The definition of cylindrical size for an external feature as specified by ASME Y14.5.1M-1994 [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] matches the analytical definition of a minimum circumscribing cylinder (MCC) when rule no. 1 [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] is applied to ensure a linear axis. Even though the MCC is a logical choice for size determination, it is highly sensitive to the sampling method and any uncertainties encountered in that process. Determining the least-sum-of-squares solution is an alternative method commonly utilized in size determination. However, the least-squares formulation seeks an optimal solution not based on the cylindrical size definition [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] and thus has been shown to be biased [Hopp, 1993, “Computational Metrology,” Manuf. Rev., 6(4), pp. 295–304; Nassef, and ElMaraghy, 1999, “Determination of Best Objective Function for Evaluating Geometric Deviations,” Int. J. Adv. Manuf. Technol., 15, pp. 90–95]. This work builds upon previous research in which the hull normal method was presented to determine the size of cylindrical bosses when rule no. 1 is applied [Turek, and Anand, 2007, “A Hull Normal Approach for Determining the Size of Cylindrical Features,” ASME, Atlanta, GA]. A thorough analysis of the hull normal method’s performance in various circumstances is presented here to validate it as a superior alternative to the least-squares and MCC solutions for size evaluation. The goal of the hull normal method is to recreate the sampled surface using computational geometry methods and to determine the cylinder’s axis and radius based upon it. Based on repetitive analyses of random samples of data from several measured parts and generated forms, it was concluded that the hull normal method outperformed all traditional solution methods. The hull normal method proved to be robust by having a lower bias and distributions that were skewed toward the true value of the radius, regardless of the amount of form error.

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Interaction, engagement, and perceived interactivity in single-handed interaction

Internet Research ◽

10.1108/intr-12-2014-0312 ◽

2016 ◽

Vol 26 (5) ◽

pp. 1134-1157 ◽

Cited By ~ 19

Author(s):

Donghee Shin ◽

Myunggoon Choi ◽

Jang Hyun Kim ◽

Jae-gil Lee

Keyword(s):

Behavioral Intention ◽

Interaction Techniques ◽

Content Type ◽

Thumb Movement ◽

Wide Range ◽

Mobile Industry ◽

Perceived Interactivity ◽

The Subject ◽

Definition Of ◽

Practical Implications

Purpose The purpose of this paper is to examine the effects of interaction techniques (e.g. swiping and tapping) and the range of thumb movement on interactivity, engagement, attitude, and behavioral intention in single-handed interaction with smartphones. Design/methodology/approach A 2×2 between-participant experiment (technological features: swiping and tapping×range of thumb movement: wide and narrow) was conducted to study the effects of interaction techniques and thumb movement ranges. Findings The results showed that the range of thumb movement had significant effects on perceived interactivity, engagement, attitude, and behavioral intention, whereas no effects were observed for interaction techniques. A narrow range of thumb movement had more influence on the interactivity outcomes in comparison to a wide range of thumb movement. Practical implications While the subject of actual and perceived interactivity has been discussed, the issue has not been applied to smartphone. Based on the research results, the mobile industry may come up with a design strategy that balances feature- and perception-based interactivity. Originality/value This study adopted the perspective of the hybrid definition of interactivity, which includes both actual and perceived interactivity. Interactivity effect outcomes mediated by perceived interactivity.

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