On the structure of polynomial roots

2021 ◽  
Vol 105 (563) ◽  
pp. 253-262
Author(s):  
R. W. D. Nickalls
Keyword(s):  
Underlying Structure ◽  
Polynomial Roots ◽  
Polynomial Degree

This Article explores how root multiplicity and polynomial degree influence the structure of the roots of a univariant polynomial. After setting up the notation, we draw upon a result derived in [1], and show that all polynomial roots have a common underlying structure comprising just five parameters. Finally we present some examples involving the lower polynomials.

Underlying Structure of Auditory-Visual Consonant Perception by Hearing-Impaired Children and the Influences of Syllabic Compression

1988 ◽  
Vol 31 (2) ◽  
pp. 156-165 ◽  
Author(s):  
P. A. Busby ◽  
Y. C. Tong ◽  
G. M. Clark
Keyword(s):  
Hearing Aids ◽  
Free Field ◽  
Acoustic Parameter ◽  
Hearing Impaired ◽  
Visual Signal ◽  
Underlying Structure ◽  
Choice Procedure ◽  
Release Times ◽  
Impaired Children ◽  
Hearing Impaired Children

The identification of consonants in a/-C-/a/nonsense syllables, using a fourteen-alternative forced-choice procedure, was examined in 4 profoundly hearing-impaired children under five conditions: audition alone using hearing aids in free-field (A),vision alone (V), auditory-visual using hearing aids in free-field (AV1), auditory-visual with linear amplification (AV2), and auditory-visual with syllabic compression (AV3). In the AV2 and AV3 conditions, acoustic signals were binaurally presented by magnetic or acoustic coupling to the subjects' hearing aids. The syllabic compressor had a compression ratio of 10:1, and attack and release times were 1.2 ms and 60 ms. The confusion matrices were subjected to two analysis methods: hierarchical clustering and information transmission analysis using articulatory features. The same general conclusions were drawn on the basis of results obtained from either analysis method. The results indicated better performance in the V condition than in the A condition. In the three AV conditions, the subjects predominately combined the acoustic parameter of voicing with the visual signal. No consistent differences were recorded across the three AV conditions. Syllabic compression did not, therefore, appear to have a significant influence on AV perception for these children. A high degree of subject variability was recorded for the A and three AV conditions, but not for the V condition.

Unravelling the phenotypic tangle of autistic, schizotypal and social anxiety traits: A Network Analysis

2020 ◽  
Author(s):  
Orestis Zavlis ◽  
Myles Jones
Keyword(s):  
Network Analysis ◽  
Social Anxiety ◽  
Factor Structure ◽  
Adult Population ◽  
Autism Spectrum ◽  
Underlying Structure ◽  
Schizotypal Personality ◽  
The Social ◽  
Trait Level ◽  
General Adult Population

Substantial overlap exists between schizophrenia and autism spectrum disorders, with part of that overlap hypothesised to be due to comorbid social anxiety. The current paper investigates the interactions and factor structure of these disorders at a personality trait level, through the lens of a network model. The items of the Autism Quotient (AQ), Schizotypal Personality Questionnaire Brief-Revised (SPQ-BR), and the Liebowitz Social Anxiety Scale (L-SAS) were combined and completed by 345 members of the general adult population. An Exploratory Graph Analysis (EGA) on the AQ-SPQ-BR combined inventory revealed two communities (factors), which reflected the general autism and schizotypal phenotypes. An additional EGA on all inventories validated the AQ-SPQ-BR factor structure and revealed another community, Social Anxiety (L-SAS). A Network Analysis (NA) on all inventories revealed several moderately central subscales, which collectively reflected the social-interpersonal impairments of the three disorders. The current results suggest that a combination of recent network- and traditional factor-analytic techniques may present a fruitful approach to understanding the underlying structure as well as relation of different psychopathologies.

The underlying structure of nonnested hypothesis tests

Biometrika ◽  
1986 ◽  
Vol 73 (2) ◽  
pp. 333-343 ◽  
Author(s):  
JOHN T. KENT
Keyword(s):  
Underlying Structure ◽  
Hypothesis Tests

scholarly journals Effects of Alkyl-Substituted Polybenzoxazines on Tribological Properties of Non-Asbestos Composite Friction Materials

Polymers ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 567
Author(s):  
Anun Wongpayakyotin ◽  
Chanchira Jubsilp ◽  
Sunan Tiptipakorn ◽  
Phattarin Mora ◽  
Christopher W. Bielawski ◽  
...  
Keyword(s):  
Wear Resistance ◽  
Composite Materials ◽  
Coefficient Of Friction ◽  
Aromatic Amines ◽  
Underlying Structure ◽  
Methyl Groups ◽  
Friction Materials ◽  
Wear Rates ◽  
Structure Properties ◽  
Crosslink Densities

A series of substituted polybenzoxazines was synthesized and studied as binders in non-asbestos friction composite materials. The structures of the polybenzoxazines were varied in a systemic fashion by increasing the number and position of pendant alkyl (methyl) groups and was accomplished using the respective aromatic amines during the polymer synthesis step. By investigating the key thermomechanical and tribological characteristics displayed by the composite materials, the underlying structure-properties relationships were deconvoluted. Composite friction materials with higher thermomechanical and wear resistance properties were obtained from polybenzoxazines with relatively high crosslink densities. In contrast, polybenzoxazines with relatively low crosslink densities afforded composite friction materials with an improved coefficient of friction values and specific wear rates.

scholarly journals Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 57
Author(s):  
Max-Olivier Hongler
Keyword(s):  
Burgers Equation ◽  
Higher Order ◽  
Underlying Structure ◽  
Swarm Dynamics ◽  
Special Cases ◽  
Kink Waves ◽  
Systematic Derivation ◽  
Fifth Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.

scholarly journals Frequent Itemset Mining and Multi-Layer Network-Based Analysis of RDF Databases

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 450
Author(s):  
Gergely Honti ◽  
János Abonyi
Keyword(s):  
Climate Change ◽  
Extraction Process ◽  
Knowledge Extraction ◽  
Frequent Itemset ◽  
Frequent Itemset Mining ◽  
Underlying Structure ◽  
Multilayer Network ◽  
Interdisciplinary Science ◽  
Academic Knowledge ◽  
Itemset Mining

Triplestores or resource description framework (RDF) stores are purpose-built databases used to organise, store and share data with context. Knowledge extraction from a large amount of interconnected data requires effective tools and methods to address the complexity and the underlying structure of semantic information. We propose a method that generates an interpretable multilayered network from an RDF database. The method utilises frequent itemset mining (FIM) of the subjects, predicates and the objects of the RDF data, and automatically extracts informative subsets of the database for the analysis. The results are used to form layers in an analysable multidimensional network. The methodology enables a consistent, transparent, multi-aspect-oriented knowledge extraction from the linked dataset. To demonstrate the usability and effectiveness of the methodology, we analyse how the science of sustainability and climate change are structured using the Microsoft Academic Knowledge Graph. In the case study, the FIM forms networks of disciplines to reveal the significant interdisciplinary science communities in sustainability and climate change. The constructed multilayer network then enables an analysis of the significant disciplines and interdisciplinary scientific areas. To demonstrate the proposed knowledge extraction process, we search for interdisciplinary science communities and then measure and rank their multidisciplinary effects. The analysis identifies discipline similarities, pinpointing the similarity between atmospheric science and meteorology as well as between geomorphology and oceanography. The results confirm that frequent itemset mining provides an informative sampled subsets of RDF databases which can be simultaneously analysed as layers of a multilayer network.

scholarly journals On the Move: Principal Components of the Functions and Experiences of Mobile Music Listening

2021 ◽  
Vol 4 ◽  
pp. 205920432110328
Author(s):  
Mia Kuch ◽  
Clemens Wöllner
Keyword(s):  
Life Experiences ◽  
Principal Component ◽  
Underlying Structure ◽  
Music Listening ◽  
Social Dimensions ◽  
Online Questionnaire ◽  
Mood Management ◽  
Five Dimensions ◽  
Mobile Music ◽  
Deep Listening

Mobile music listening is widely recognized as an integral part of everyday music use. It is also a rather peculiar experience, since the listeners are surrounded by strangers in public and at the same time engaged in a solitary and private activity. The current study aimed at investigating the functions and experiences of mobile listening with a quantitative online questionnaire, and collected further information about mobile listening situations and listening habits. Among respondents ( n = 203), 89% reported listening to music while being on the move. We found mood-related and cognitive functions to be most prevalent (e.g., enhancing mood, relaxation, prevention of being bored), whereas least important functions relate to social dimensions (e.g., feeling less lonely, feeling less watched). Regarding experiences of mobile music, respondents most commonly adapted their mood to the music and lost touch with the current surroundings. A principal component analysis on ratings of functions and experiences resulted in an underlying structure of five dimensions, representing different levels of involvement: (1) Mood Management comprises functions to satisfy individual needs; (2) Absorption and Aestheticization encompasses deep listening experiences and altered perception of the surroundings; (3) Social Encapsulation and Self-Focus describe the distancing of oneself and changes in attention; (4) Distraction and Passing Time include the prevention of being bored and making time pass faster; and (5) Auditory Background is defined by a non-attentive and rather unaffected music listening. These results highlight the immersiveness of mobile music listening. By creating an individual soundworld, listeners distance themselves from the surroundings aurally and mentally, and modify their attention, perception, moods, and emotions, leading to an improvement of daily life experiences while moving.

scholarly journals Determination of macro-scale soil properties from pore-scale structures: model derivation

2018 ◽  
Vol 474 (2209) ◽  
pp. 20170141 ◽  
Author(s):  
K. R. Daly ◽  
T. Roose
Keyword(s):  
Pore Space ◽  
Solid Particles ◽  
Underlying Structure ◽  
Pore Scale ◽  
Homogenization Procedure ◽  
Macro Scale ◽  
Model Derivation ◽  
Scale Structures ◽  
Homogenization Scheme

In this paper, we use homogenization to derive a set of macro-scale poro-elastic equations for soils composed of rigid solid particles, air-filled pore space and a poro-elastic mixed phase. We consider the derivation in the limit of large deformation and show that by solving representative problems on the micro-scale we can parametrize the macro-scale equations. To validate the homogenization procedure, we compare the predictions of the homogenized equations with those of the full equations for a range of different geometries and material properties. We show that the results differ by ≲ 2 % for all cases considered. The success of the homogenization scheme means that it can be used to determine the macro-scale poro-elastic properties of soils from the underlying structure. Hence, it will prove a valuable tool in both characterization and optimization.

scholarly journals Functional prediction of environmental variables using metabolic networks

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Adèle Weber Zendrera ◽  
Nataliya Sokolovska ◽  
Hédi A. Soula
Keyword(s):  
Machine Learning ◽  
Growth Temperature ◽  
Environmental Variables ◽  
Metabolic Networks ◽  
Machine Learning Techniques ◽  
Underlying Structure ◽  
Glutathione Biosynthesis ◽  
Additional Information ◽  
Cold Environments ◽  
Novel Approach

AbstractIn this manuscript, we propose a novel approach to assess relationships between environment and metabolic networks. We used a comprehensive dataset of more than 5000 prokaryotic species from which we derived the metabolic networks. We compute the scope from the reconstructed graphs, which is the set of all metabolites and reactions that can potentially be synthesized when provided with external metabolites. We show using machine learning techniques that the scope is an excellent predictor of taxonomic and environmental variables, namely growth temperature, oxygen tolerance, and habitat. In the literature, metabolites and pathways are rarely used to discriminate species. We make use of the scope underlying structure—metabolites and pathways—to construct the predictive models, giving additional information on the important metabolic pathways needed to discriminate the species, which is often absent in other metabolic network properties. For example, in the particular case of growth temperature, glutathione biosynthesis pathways are specific to species growing in cold environments, whereas tungsten metabolism is specific to species in warm environments, as was hinted in current literature. From a machine learning perspective, the scope is able to reduce the dimension of our data, and can thus be considered as an interpretable graph embedding.

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