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17 pages, 11354 KiB  
Article
Complex Discontinuity Structure Beneath the Changbaishan-Tianchi Volcano Revealed by the P-Wave Coda Autocorrelation Method Based on Dense Seismic Array
by Hao Wen, You Tian, Cai Liu and Hongli Li
Remote Sens. 2024, 16(19), 3615; https://doi.org/10.3390/rs16193615 - 27 Sep 2024
Viewed by 280
Abstract
The Changbai volcano, a globally recognized hotspot of volcanic activity, has garnered significant attention due to its persistent seismicity and ongoing magma activity. The volcano’s discontinuities and magma dynamics have raised concerns about the likelihood of future eruptions, which would likely result in [...] Read more.
The Changbai volcano, a globally recognized hotspot of volcanic activity, has garnered significant attention due to its persistent seismicity and ongoing magma activity. The volcano’s discontinuities and magma dynamics have raised concerns about the likelihood of future eruptions, which would likely result in substantial ecological, climatic, and economic impacts. Consequently, a comprehensive understanding of the Changbai volcanic system is essential for mitigating the risks associated with volcanic activity. In recent years, the P-wave coda autocorrelation method has gained popularity in lithosphere exploration as a reliable technique for detecting reflection coefficients. Additionally, the Common Reflection Point stacking approach has been employed to superimpose reflection signals in a spatial grid, enabling continuous observation of reflection coefficients in the study area. However, the accuracy of this approach is heavily reliant on better spatial data coverage. To better understand the internal dynamics of the Changbai volcano, we applied this approach to a densely packed short-period seismic array with an average station spacing of less than 1 km. Our results were constrained using waveform data of reflection coefficients and Moho dip angles. Our findings revealed a discontinuity in the Moho, which may indicate a conduit for mantle magma entering the crust. Furthermore, we identified two low-velocity anomalies within the crust, likely representing a magma chamber comprising molten and crystallized magma. Notably, our results also provided a clear definition of the lithosphere–asthenosphere boundary. Full article
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<p>Location of the Changbai volcano. The gray solid line indicates the active tectonic-block boundary. Abbreviations are the Changbaishan Volcano (CBSV), the Longgang Volcano (LGV), and the Jingpohu Volcano (JPHV). The dashed black line indicates the Dunhua–Mishan Fault (DMF).</p>
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<p>(<b>a</b>) Distribution of the teleseismic events (red stars) used for this study. The black triangle is the location of the center of the study region. (<b>b</b>) The spatial locations of the stations used in this study. The black triangle represents the location of the station deployment.</p>
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<p>(<b>a</b>) Schematic diagram of the Common Reflection Point (CRP), showing the situation where a seismic station receives two different earthquakes. The reflectivity produced by the autocorrelation calculation at the interface position is equivalent to the reflection response of the virtual source at the corresponding position on the surface at this position. When the positions of the reflection points are close enough, they will be superimposed within the same grid, as shown in the red box. (<b>b</b>) The ray paths of earthquakes as received by five different stations.</p>
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<p>(<b>a</b>) The elevation of the location where the profile is located. (<b>b</b>) Reflection point imaging from teleseismic arrivals for the frequency band from 0.3 to 5.0 Hz. The location of station S023 is marked by a gray vertical dashed line. Three regions of anomalous reflectivity are encircled by red dashed circles. (<b>c</b>) Reflection point imaging from teleseismic arrivals for the frequency band from 0.1 to 1.0 Hz. Gray dots indicate the Moho depth estimates derived from the spectral tilting method. The position of station S058 is denoted by a gray vertical dashed line. The red dashed line demarcates the lithosphere–asthenosphere boundary (LAB) as determined by our study.</p>
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<p>Take the average of the energy values at each depth in <a href="#remotesensing-16-03615-f004" class="html-fig">Figure 4</a>b and subtract the average value from all locations to obtain this figure. Compared to <a href="#remotesensing-16-03615-f004" class="html-fig">Figure 4</a>b, this image more clearly reveals the anomaly associated with the shallow magma chamber.</p>
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<p>Velocity scans and dip spectrum results for selected stations ‘S023’ and ‘S097’. The first row illustrates the velocity analysis results at various interface depths, the second row showcases the results of dip scanning, and the third row presents velocity scans post-dip correction. Two red vertical lines mark the approximate position of the Moho, while the black dashed line indicates the USTClitho2.0 velocity model applied to the Changbai volcano study.</p>
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<p>(<b>a</b>) Statistical chart of the Moho depth estimation results. The results show that the Moho depth is approximately 38 km. The brown curve is the result of data fitting, and it can be seen that the Moho at the northern end has a tendency to become shallower. (<b>b</b>) The statistical results of the dip scans of all stations. Most of the blue dots are within the light-colored bands, which range from −30 to 30° and 150 to 210°. This indicates that the morphology of the Moho is mainly tilted in the north–south direction.</p>
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<p>The results from stacking autocorrelation data beneath individual seismic stations are depicted in these figures. Panels (<b>a</b>,<b>b</b>) sequentially illustrate the variations in reflectivity extending from Tianchi towards the south. In panel (<b>a</b>), there is a noticeable decrease in amplitude at the base of the lithosphere beginning at station S058. In panel (<b>b</b>), a significant reduction in amplitude is observed within the crust south of station S023.</p>
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<p>A selection of the single-station stacked data is superimposed on <a href="#remotesensing-16-03615-f004" class="html-fig">Figure 4</a>c. The purple dashed lines mark the approximate location of the Moho interface inferred from the CRP results, while the green dashed lines denote the position of the LAB also derived from the CRP results. As evident in the figure, seismic waveforms corresponding to these interfaces are broadly observed at depths consistent with their predicted positions.</p>
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<p>A simple cartoon diagram illustrating the magma system in this article. Details are described in this article.</p>
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16 pages, 2951 KiB  
Article
Comparative Analysis of Airborne Bacterial and Fungal Communities in South-Eastern Italy and in Albania Using the Compositional Analysis of 16S and ITS rRNA Gene Sequencing Datasets
by Salvatore Romano, Lekë Pepkolaj, Mattia Fragola, Dalila Peccarrisi, Jostina Dhimitri, Alessandro Buccolieri, Adelfia Talà, Pietro Alifano, Gianluca Quarta and Lucio Calcagnile
Atmosphere 2024, 15(10), 1155; https://doi.org/10.3390/atmos15101155 - 26 Sep 2024
Viewed by 466
Abstract
This study investigates airborne bacterial and fungal communities in south-eastern Italy and Albania using advanced DNA-based techniques and compositional data analysis (CoDa). We assess the significance of airborne microbial communities, detailing our methodologies for site selection, sample collection, DNA extraction, and data analysis. [...] Read more.
This study investigates airborne bacterial and fungal communities in south-eastern Italy and Albania using advanced DNA-based techniques and compositional data analysis (CoDa). We assess the significance of airborne microbial communities, detailing our methodologies for site selection, sample collection, DNA extraction, and data analysis. Our results reveal distinct differences in microbial composition between the two regions, driven by local environmental factors. Specifically, Albanian samples showed higher abundances of bacterial species such as Rubellimicrobium roseum and Sphingomonas cynarae, while Italian samples were characterized by a prevalence of Truepera radiovictrix and Rubrobacter radiotolerans. In terms of fungi, Albanian sites exhibited greater abundance of Mycosphaerella tassiana, Aureobasidium pullulans, and Ascochyta herbicola. Aitchison distance-based dendrograms and principal component analysis (PCA) biplots, utilizing singular value decomposition, clearly delineated a geographical separation of microbial communities, underscoring the impact of regional atmospheric conditions on microbial composition. In the discussion, we interpret these findings in the context of regional environmental factors, highlighting their implications for understanding regional differences in airborne microbial communities. The conclusion emphasizes the effectiveness of advanced DNA techniques and CoDa in environmental microbiology, offering insights into how local environmental conditions shape microbial communities and suggesting directions for future research and public health considerations. Full article
(This article belongs to the Section Biosphere/Hydrosphere/Land–Atmosphere Interactions)
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Graphical abstract

Graphical abstract
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<p>(<b>a</b>) Geographical location of the two study areas, i.e., south-eastern Italy and Albania, in the Central Mediterranean basin. The exact locations of the seven monitoring sites in Italy are displayed in (<b>b</b>) by blue dots (GA—Galatone, LE—Lecce, ML—Muro Leccese, NA—Nardò, PA—Parabita, SC1—San Cesario 1, SC2—San Cesario 2). The seven monitoring sites in Albania are reported in (<b>c</b>) by red dots, with a focus on the five sites in Tirana depicted in (<b>d</b>) (MA—Tirana Marashi, NO—Lezha Nord, PU—Tirana Pusi, QI—Tirana Qiriazi, SH—Shkodër, TI—Tirana Center, TO—Tirana Tokat).</p>
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<p>(<b>a</b>) Heatmap defined on the centered log-ratio (CLR) values of the initial dataset (reads) based on the 23 bacterial species with the highest abundances. (<b>b</b>,<b>c</b>) show the Aitchison distance dendrograms pointing out the relations among samples and among species, respectively.</p>
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<p>Two-dimensional principal component analysis biplot via a singular value decomposition of the CLR values of the initial dataset based on the 23 selected bacterial species. The reported biplot illustrates the relationships between samples (score plot, in different colors based on the sampling location: samples collected in Albania are in red, while the ones from Italy are in blue) and species (loading plot, black arrows). The percentages of the total variance explained by the first two principal components are also reported.</p>
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<p>(<b>a</b>) Heatmap defined on the centered log-ratio (CLR) values of the initial dataset (reads) based on the 17 fungal species with the highest abundances. (<b>b</b>,<b>c</b>) show the Aitchison distance dendrograms pointing out the relations among samples and among species, respectively.</p>
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<p>Two-dimensional principal component analysis biplot via a singular value decomposition of the CLR values of the initial dataset based on the 17 selected fungal species. The reported biplot illustrates the relationships between samples (score plot, in different colors based on the sampling location: samples collected in Albania are in red, while the ones from Italy are in blue) and species (loading plot, black arrows). The percentages of the total variance explained by the first two principal components are also reported.</p>
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16 pages, 1171 KiB  
Article
A Longitudinal Exploration of Perception and Production of English Codas in CLIL Settings
by Francisco Gallardo-del-Puerto and Esther Gómez-Lacabex
Languages 2024, 9(9), 303; https://doi.org/10.3390/languages9090303 - 19 Sep 2024
Viewed by 448
Abstract
Second language speech perception and production remain an enduring concern in second language acquisition, as research evidence seems to suggest that there is not a straightforward correspondence between these two speech domains and that their interrelationship seems to be of a complex nature. [...] Read more.
Second language speech perception and production remain an enduring concern in second language acquisition, as research evidence seems to suggest that there is not a straightforward correspondence between these two speech domains and that their interrelationship seems to be of a complex nature. The present proposal intends to contribute to the inspection of such a relationship by observing the development of perception and production skills of English codas longitudinally in a group of secondary school learners in Spain involved in a content and language integrated learning (CLIL) program, which increases exposure and production opportunities. Results point to a slight overall improvement of both sound perception and production skills during a two-year period, the coda sounds exhibiting variable realizations. Many coda sounds were found to be identified and produced at near/ceiling levels while other codas remained at less successful identification and production levels even after two years of CLIL exposure. The correlation analyses performed indicated that the two dimensions tended to correlate when the development for each coda sound was inspected. No correlations were found when students’ individual overall performance in each dimension were examined, attesting individual differences. Full article
(This article belongs to the Special Issue Advances in L2 Perception and Production)
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<p>Correct percentage identification of English codas.</p>
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<p>Correct percentage production of English codas.</p>
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<p>Scatterplot for perception/production for each coda sound in T1.</p>
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<p>Scatterplot for perception/production for each student’s gain scores.</p>
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7 pages, 6370 KiB  
Communication
Recruitment of the Basket Star Astrospartus mediterraneus (Risso, 1826) (Ophiuroidea, Gorgonocephalidae)
by Martina Canessa, Egidio Trainito and Giorgio Bavestrello
Diversity 2024, 16(9), 528; https://doi.org/10.3390/d16090528 - 1 Sep 2024
Viewed by 299
Abstract
The occurrence and abundance of Astrospartus mediterraneus (Risso, 1826) have significantly increased in the last three decades in several areas of the Mediterranean Sea. In the Tavolara–Punta Coda Cavallo Marine Protected Area (NE Sardinia, Tyrrhenian Sea, Mediterranean Sea), 60 specimens were observed mainly [...] Read more.
The occurrence and abundance of Astrospartus mediterraneus (Risso, 1826) have significantly increased in the last three decades in several areas of the Mediterranean Sea. In the Tavolara–Punta Coda Cavallo Marine Protected Area (NE Sardinia, Tyrrhenian Sea, Mediterranean Sea), 60 specimens were observed mainly on the granitic shoals of the Tavolara Channel, an area characterized by very intense currents and high sedimentation. The basket stars were mainly found living as epibionts of gorgonians (Eunicella verrucosa, Paramuricea clavata and Leptogorgia sarmentosa) and massive sponges (Spongia officinalis, S. lamella, Sarcotragus foetidus). We also documented 21 small specimens (3–20 mm in diameter of the oral disc) observed in June 2024 between 27 and 52 m depth on E. verrucosa and P. clavata colonies. The bimodal size-frequency distribution of these specimens suggested that, probably, specimens belong to two different reproductive events occurring in spring 2023 and 2024. Full article
(This article belongs to the Special Issue Deep-Sea Echinoderms of the European Seas)
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<p>Location (black arrow) of the study area within the Tavolara-Punta Coda Cavallo Marine Protected Area and the distribution of <span class="html-italic">Astrospartus mediterraneus</span> (red dots, granitic sites; blue dots, limestone sites).</p>
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<p>Recruitment event of <span class="html-italic">Astrospartus mediterraneus</span>. (<b>a</b>) <span class="html-italic">Eunicella verrucosa</span> (EV1) hosting numerous small specimens of the basket star (red circles); (<b>b</b>,<b>c</b>) small juveniles with arms coiled around the gorgonian branches; (<b>d</b>) large juveniles settled in the upper part of the sea fan (EV2); (<b>e</b>,<b>f</b>) enlargement of these specimens; (<b>g</b>) a specimen on a colony of <span class="html-italic">Paramuricea clavata</span> (PC1). Scale bars: a, d = 5 cm, b, c, 0,5 cm, e–g = 3 cm.</p>
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39 pages, 6630 KiB  
Article
‘No’ Dimo’ par de Botella’ y Ahora Etamo’ Al Garete’: Exploring the Intersections of Coda /s/, Place, and the Reggaetón Voice
by Derrek Powell
Languages 2024, 9(9), 292; https://doi.org/10.3390/languages9090292 - 30 Aug 2024
Viewed by 566
Abstract
The rebranding of reggaetón towards Latin urban has been criticized for tokenizing Afro-Caribbean linguistic and cultural practices as symbolic resources recruitable by non-Caribbean artists/executives in the interest of profit. Consumers are particularly critical of an audible phonological homogeneity in the performances of ethnonationally [...] Read more.
The rebranding of reggaetón towards Latin urban has been criticized for tokenizing Afro-Caribbean linguistic and cultural practices as symbolic resources recruitable by non-Caribbean artists/executives in the interest of profit. Consumers are particularly critical of an audible phonological homogeneity in the performances of ethnonationally distinct mainstream performers, framed as a form of linguistic minstrelsy popularly termed a ‘Caribbean Blaccent’ that facilitates capitalization on the genre’s popularity by tapping into the covert prestige of distinctive phonological elements of Insular Caribbean Spanish otherwise stigmatized. This work pairs acoustic analysis with quantitative statistical modeling to compare the use of lenited coronal sibilant allophones popularly considered indexical of Hispano-Caribbean origins in the spoken and sung speech of four of the genre’s top-charting female performers. A general pattern of style-shifting from interview to sung speech wherein sibilance is favored in the former and phonetic zeros in the latter is revealed. Moreover, a statistically significant increased incidence of [-] across time shows the most recent records to uniformly deploy near-categorical reduction independent of artists’ sociocultural and linguistic backgrounds. The results support the enregisterment of practices popularized by the genre’s San Juan-based pioneers as a stylistic resource—a reggaetón voice—for engaging the images of vernacularity sustaining and driving the contemporary, mainstream popularity of música urbana. Full article
(This article belongs to the Special Issue Interface between Sociolinguistics and Music)
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<p>Proposed diachronic weakening pathway for /s/ [adapted from <a href="#B106-languages-09-00292" class="html-bibr">Lipski</a> (<a href="#B106-languages-09-00292" class="html-bibr">1999</a>)].</p>
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<p>Annotated spectrogram and waveform of sibilance (<b>left</b>) and unmarked deletion (<b>right</b>) in interview speech.</p>
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<p>Annotated spectrogram and waveform of sibilance (<b>left</b>) and trace-marked deletion (<b>right</b>) in the artistic performance speech.</p>
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<p>Visual representation of artists’ averaged reduction rates across corpora.</p>
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<p>Artist s-reduction patterns across time.</p>
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<p>Visual representation of artists’ reduction rates across corpora in 2022.</p>
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17 pages, 1022 KiB  
Article
Financial and ESG Analysis of the Beer Sector Pre- and Post-COVID-19 in Italy and Spain
by Núria Arimany-Serrat and Andrey Felipe Sgorla
Sustainability 2024, 16(17), 7412; https://doi.org/10.3390/su16177412 - 28 Aug 2024
Viewed by 635
Abstract
This study compares the analysis of the financial statements of the brewing sector in Italy and Spain due to its growth in both Mediterranean countries and its relationship with other sectors of activity of great importance in these countries. The web transparency of [...] Read more.
This study compares the analysis of the financial statements of the brewing sector in Italy and Spain due to its growth in both Mediterranean countries and its relationship with other sectors of activity of great importance in these countries. The web transparency of the sustainability indicators of the brewing sector in both countries is also analyzed, following the new regulatory framework, EU Directive 2022/2426, on sustainability information, in order to analyze, in an integrated way, the financial and sustainability information which they report for a sustainable development of the sector, in line with the Sustainable Development Goals and the European Green Deal. The methodology used involved compositional data, which are reliable at an accounting and statistical level; such data allow us to value the financial health of the sector and its relationship with the web exploration of the communication of its environmental, social, and corporate governance indicators. The results indicate a solvency of the sector in the short term, with poor margins, especially in the pandemic, which recovered in 2021 due to the sector’s resilience. On the other hand, there is a clear need to study the costs and margins of the sector in depth to improve the quality of the beers and to project the sector. The web analysis reveals acceptable transparency at the environmental level and poor transparency at the social and corporate governance level, with differences between the two countries and the population under study. Full article
(This article belongs to the Special Issue Sustainability, Accounting, and Business Strategies)
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<p>Mosaic plot of cluster and year. Bar widths show cluster size. Bar heights indicate the importance of the year within the cluster.</p>
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<p>Mosaic plot of cluster and country. Bar widths show cluster size. Bar heights illustrate the importance of the country within the cluster.</p>
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<p>Boxplots of the number of disclosed non-financial indicators per cluster.</p>
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<p>Boxplots of firm size—log(total assets)—per cluster.</p>
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19 pages, 606 KiB  
Article
Agent Mental Models and Bayesian Rules as a Tool to Create Opinion Dynamics Models
by André C. R. Martins
Physics 2024, 6(3), 1013-1031; https://doi.org/10.3390/physics6030062 - 31 Jul 2024
Viewed by 569
Abstract
Traditional models of opinion dynamics provide a simplified approach to understanding human behavior in basic social scenarios. However, when it comes to issues such as polarization and extremism, a more nuanced understanding of human biases and cognitive tendencies are required. This paper proposes [...] Read more.
Traditional models of opinion dynamics provide a simplified approach to understanding human behavior in basic social scenarios. However, when it comes to issues such as polarization and extremism, a more nuanced understanding of human biases and cognitive tendencies are required. This paper proposes an approach to modeling opinion dynamics by integrating mental models and assumptions of individuals agents using Bayesian-inspired methods. By exploring the relationship between human rationality and Bayesian theory, this paper demonstrates the usefulness of these methods in describing how opinions evolve. The analysis here builds upon the basic idea in the Continuous Opinions and Discrete Actions (CODA) model, by applying Bayesian-inspired rules to account for key human behaviors such as confirmation bias, motivated reasoning, and human reluctance to change opinions. Through this, This paper updates rules that are compatible with known human biases. The current work sheds light on the role of human biases in shaping opinion dynamics. I hope that by making the model more realistic this might lead to more accurate predictions of real-world scenarios. Full article
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<p>Schematics for the general use of Bayes’ theorem as a tool for creating opinion update equations, highlighting the role of agent mental models for what others communicate to them (likelihoods).</p>
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<p><b>Upper</b>: size of the steps for agreement, <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>A</mi> </mrow> </semantics></math>, and disagreement, <math display="inline"><semantics> <mrow> <mi>S</mi> <mi>D</mi> </mrow> </semantics></math>, as a function of the estimated proportion, <math display="inline"><semantics> <mi>λ</mi> </semantics></math>, of honest agents among those each agent is biased against when it is believed dishonest agents lie with probability <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>. <b>Lower</b>: ratio <math display="inline"><semantics> <mrow> <mi>s</mi> <mo>=</mo> <mi>S</mi> <mi>A</mi> <mo>/</mo> <mi>S</mi> <mi>D</mi> </mrow> </semantics></math> for two values of <math display="inline"><semantics> <mi>β</mi> </semantics></math>. See text for details.</p>
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<p>Distribution of opinions after these opinions are (<b>upper</b>) measured as disagreement steps and (<b>lower</b>) renormalized to agreement steps. See text for details.</p>
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<p>Typical network formed after applying the rewiring algorithm with an average of twenty rewirings per agent: <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>20</mn> </mrow> </semantics></math>. Brown and blue colors correspond to the two choices, and darker hues show a stronger final opinion obtained after the opinion update phase.</p>
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<p>Distribution of opinions after these opinions are (<b>upper</b>) measured as disagreement steps and (<b>lower</b>) renormalized to agreement steps.</p>
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<p>Distribution of opinions after these opinions opinions are (<b>upper</b>) measured as disagreement steps and (<b>lower</b>) renormalized to agreement steps.</p>
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21 pages, 440 KiB  
Article
Plural Alternations and Word-Final Consonant Syllabification in Brazilian Veneto
by Natália Brambatti Guzzo
Languages 2024, 9(8), 259; https://doi.org/10.3390/languages9080259 - 26 Jul 2024
Viewed by 840
Abstract
In Brazilian Veneto (a heritage variety of Veneto spoken in several areas of Brazil), a stem alternation targets the plurals of masculine nominals ending in a consonant. While nominals with a word-final rhotic or nasal are pluralized by adding the masculine plural suffix [...] Read more.
In Brazilian Veneto (a heritage variety of Veneto spoken in several areas of Brazil), a stem alternation targets the plurals of masculine nominals ending in a consonant. While nominals with a word-final rhotic or nasal are pluralized by adding the masculine plural suffix /i/ ([bi't̑er][bi't̑eri] ‘glass’), pluralization in nominals with a final lateral involves deletion of the consonant (e.g., [ni'sol][ni'soi] ‘bedsheet’). I argue that these differences stem from word-final laterals having a distinct representation from rhotics and nasals: while the latter are represented as codas, the former are represented as onsets of empty-headed syllables. Based on a corpus analysis, I show that (a) speakers’ productions of these plurals are stable, and (b) other patterns of pluralization (namely, in monosyllables and words with final stress on a CV syllable) are consistent with the proposal. In addition, the behaviour of laterals with respect to resyllabification, metaphony and intervocalic consonant deletion further suggest that laterals are represented as onsets word-finally. Full article
(This article belongs to the Special Issue Phonetic and Phonological Complexity in Romance Languages)
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<p>The representation of word-final rhotics and nasals.</p>
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<p>The representation of word-final laterals.</p>
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<p>The representation of the pluralization of masculine participles.</p>
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<p>The representation of the word-final lateral as extrametrical.</p>
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<p>The representation of the word-final lateral as an appendix.</p>
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<p>The representation of the word-final lateral as part of the syllable nucleus.</p>
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<p>The representation of the word-final lateral as linked to both a rhyme and an onset.</p>
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32 pages, 11315 KiB  
Article
Correspondence of Consonant Clustering with Particular Vowels in German Dialects
by Samantha Link
Languages 2024, 9(7), 255; https://doi.org/10.3390/languages9070255 - 22 Jul 2024
Viewed by 614
Abstract
Recent work found a correspondence between consonant clustering probability in monosyllabic lexemes and the three vowel types, short and long monophthong and diphthong, in German dialects. Furthermore, that correspondence was found to be bound to a North–South divide. This paper explores the preferences [...] Read more.
Recent work found a correspondence between consonant clustering probability in monosyllabic lexemes and the three vowel types, short and long monophthong and diphthong, in German dialects. Furthermore, that correspondence was found to be bound to a North–South divide. This paper explores the preferences in consonant clustering of particular vowels by analyzing the PhonD2-Corpus, a large database of phonotactic and morphological information. The clustering probability of the diphthongs is positively correlated with frequency while the other vowels showed particular preferences that are not positively correlated with frequency. However, all of them are determined by a threefold pattern: short monophthongs prefer coda clusters, diphthongs onset clusters and long monophthong are balanced. Furthermore, it was found that this threefold pattern seems to have evolved from an originally twofold pattern (short monophthong prefers coda clusters and long monophthong and diphthong prefer onset clusters) in Middle High and Low German. This result is then further considered under the aspect of the compensation of the syllable weight and moraicity. Furthermore, some interesting parallels with the syllable vs. word-language typology framework are noted. Full article
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<p>Probability of onset (lighter gray) and coda (darker gray) consonant clustering for different vowel types (V, Vː, VV) in dialects of Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG).</p>
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<p>Percentage of onset (lighter gray) and coda (darker gray) CC or CCC consonant clusters for different vowel types (V, Vː, VV) in the dialects of Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG).</p>
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<p>Percentage of short vowels in monosyllabic lexemes without morpheme boundaries for all areas (All), Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG).</p>
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<p>Percentage of long vowels in monosyllabic lexemes without morpheme boundaries for all areas (All), Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG).</p>
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<p>Percentage of diphthongs in monosyllabic lexemes without morpheme boundaries for all areas (All), Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG).</p>
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<p>Consonant clustering probability for the vowels and diphthongs in the five dialect areas Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG).</p>
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<p>Consonant clustering probability for the MHG short and long monophthongs.</p>
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<p>Consonant clustering probabilities for the MHG umlauts and diphthongs.</p>
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<p>MHG words (and MLG words for Low German) with a short vowel that became lengthened and monosyllabic in the five dialect areas. The first word in brackets is MHG and the second is MLG.</p>
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<p>Probability of onset (lighter grey) and coda (darker grey) consonant clustering for different vowel types (V, Vː, VV) in dialects of Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG). The first row repeats <a href="#languages-09-00255-f006" class="html-fig">Figure 6</a> and the second and third rows display the results for the same data split into morphologically simple and complex words.</p>
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<p>Percentage of onset (lighter gray) and coda (darker gray) CC or CCC consonant clusters for different vowel types (V, Vː, VV) in the dialects of Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG). Analysis of morphologically mixed data.</p>
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<p>Percentage of short vowels in monosyllabic lexemes for all areas (All), Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG). Analysis of morphologically mixed data.</p>
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<p>Percentage of long vowels in monosyllabic lexemes for all areas (All), Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG). Analysis of morphologically mixed data.</p>
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<p>Percentage of diphthongs in monosyllabic lexemes for all areas (All), Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG). Analysis of morphologically mixed data.</p>
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<p>Consonant clustering probability for the vowels and diphthongs in the five dialect areas Low German (LG), West Central German (WCG), East Central German (ECG), West Upper German (WUG) and East Upper German (EUG). Analysis of morphologically mixed data.</p>
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<p>Consonant clustering probability for the MHG short and long monophthongs. Analysis of morphologically mixed data.</p>
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<p>Consonant clustering probabilities for the MHG umlauts and diphthongs. Analysis of morphologically mixed data.</p>
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<p>MHG words (and MLG words for Low German) with a short vowel that became lengthened and monosyllabic in the five dialect areas. The first word in brackets is MHG and the second is MLG. Analysis of morphologically mixed data.</p>
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<p>Map of the lemma <span class="html-italic">gesagt</span> from the PhonD2-website. All monosyllabic realizations of the lemma are marked with a black circle. In the South, there are the CV structures CCVCC and CCVCCC. (<a href="https://www.dsa.info/PhonD2/0aakagi42.html" target="_blank">https://www.dsa.info/PhonD2/0aakagi42.html</a> Last accessed: 17 July 2024).</p>
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15 pages, 7415 KiB  
Article
An Improved Method for Calculating Wave Velocity Fields in Fractured Rock Based on Wave Propagation Probability
by Jing Zhou, Lang Liu, Yuan Zhao, Dengdeng Zhuang, Zhizhen Liu and Xuebin Qin
Mathematics 2024, 12(14), 2177; https://doi.org/10.3390/math12142177 - 11 Jul 2024
Viewed by 477
Abstract
Ultrasonic velocity field imaging offers a robust tool for characterizing and analyzing damage and its evolution within fractured rock masses. The combined application of ultrasonic first arrival waves and coda waves can significantly enhance the accuracy and range of velocity field imaging. This [...] Read more.
Ultrasonic velocity field imaging offers a robust tool for characterizing and analyzing damage and its evolution within fractured rock masses. The combined application of ultrasonic first arrival waves and coda waves can significantly enhance the accuracy and range of velocity field imaging. This manuscript introduces an improved imaging method that integrates the propagation probability distribution of the first arrival and coda waves to calculate the velocity field. The proposed method was applied to the velocity field imaging of a medium with multiple scatterers and varying degrees of fracturing. The overall error and calculation unit error of the proposed method were analyzed, and its improvement in calculation accuracy and applicable scope was verified. Additionally, this method was employed to image the velocity field during the damage process of fractured rock masses. The imaging results were compared against digital speckle patterns to confirm the method’s suitability. Finally, we discussed the impact of measurement errors and sensor missing on the accuracy of the computational outcomes presented in this method. These two situations will affect the calculation results, and the influence of reducing the number of sensors is smaller than that of measuring time shifts with error. Full article
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<p>Acoustic wave propagation model.</p>
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<p>The arrival wave and time window. (<b>a</b>) is the first arrival wave, coda wave, and noise wave. (<b>b</b>) is the enlarged image of the first arrival wave. (<b>c</b>) is the time window.</p>
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<p>The calculation process of the improved method.</p>
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<p>(<b>a</b>–<b>c</b>) are the multi-scatterer medium model with cracks. (<b>d</b>–<b>f</b>) are the wave field intensity diagram of acoustic waves propagating to the sensor.</p>
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<p>Results with different methods. (<b>a</b>,<b>b</b>) are the results calculated with the first arrival wave. (<b>c</b>,<b>d</b>) are the results calculated using the improved method.</p>
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<p>The error rate of the calculation unit. (<b>a</b>,<b>b</b>) are the relative error rates of the calculation unit when there are two and four cracks in the multi-scatterer model, respectively.</p>
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<p>Experimental materials and equipment. (<b>a</b>,<b>b</b>) are the photographic surface and acoustic emission monitoring surface of the granite slab specimen, respectively. 1–12 in the (<b>b</b>) are the number of AE sensors. (<b>c</b>) is the experimental system diagram.</p>
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<p>Transmit waveform, transmit time, and receive waveform. (<b>a</b>) is the emitted acoustic waveform. (<b>b</b>) is the variation process of the loading force of the specimen with time. (<b>c</b>) is the waveform of each channel.</p>
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<p>The diffusion coefficient solution process. (<b>a</b>) is the waveform and waveform envelope. (<b>b</b>) is the curve fitting of the waveform.</p>
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<p>Digital speckle results and wave velocity field imaging results. (<b>a</b>) is the results obtained by digital speckle. (<b>b</b>) is the wave velocity field calculated by the improved method.</p>
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<p>The influence of the AE sensor missing on the calculation results. (<b>a</b>) is the error rate and correlation coefficient for different numbers of missing sensors. (<b>b</b>) is the calculation unit error rate for different numbers of missing sensors.</p>
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<p>The impact of the number of error paths on the calculation results. (<b>a</b>) is the average error rate and correlation coefficient with the actual result at different measurement error rate levels. (<b>b</b>) is the calculation unit error rate at different measurement error rate levels.</p>
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17 pages, 5181 KiB  
Article
Forever Becoming: Teaching “Transgender Studies Meets Art History” and Theorizing Trans Joy
by Alpesh Kantilal Patel
Arts 2024, 13(4), 115; https://doi.org/10.3390/arts13040115 - 1 Jul 2024
Viewed by 1205
Abstract
Academics often comment that their teaching affects their research, but how this manifests is often implicit. In this essay, I explicitly explore the artistic, scholarly, and curatorial research instantiated by an undergraduate class titled “Transgender Studies meets Art History,” which I taught during [...] Read more.
Academics often comment that their teaching affects their research, but how this manifests is often implicit. In this essay, I explicitly explore the artistic, scholarly, and curatorial research instantiated by an undergraduate class titled “Transgender Studies meets Art History,” which I taught during the fall of 2022. Alongside personal anecdotes—both personal and connected to the class—and a critical reflection on my pedagogy, I discuss the artwork and public programming connected to a curatorial project, “Forever Becoming: Decolonization, Materiality, and Trans* Subjectivity, I organized at UrbanGlass, New York City in 2023. The first part of the article I examine how “trans” can be applied to thinking about syllabus construction and re-thinking canon formation for a class focused on transgender studies’ relationship to art history. In the second half, I theorize trans joy as a felt vibration between/across multiplicity and singularity, belonging and unbelonging, and world-making and world-unmaking. Overall, I consider trans as a lived experience and its utility as a conceptual tool. As a coda, I consider the precarity of teaching this course in the current political climate of the United States. Full article
(This article belongs to the Special Issue New Articulations of Identity in Contemporary Aesthetics)
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<p>(<b>Left</b>) Carlos Motta, <span class="html-italic">Deseos</span>/رغبات (Desires), (<a href="#B40-arts-13-00115" class="html-bibr">Motta 2015</a>), still, HD video 16:9, color, sound, 32:37. Courtesy of Galeria Filomena Soares, Lisbon and Mor Charpentier Galerie, Paris; (<b>right</b>) Installation view of <span class="html-italic">Deseos</span>/رغبات (Desires), 2015, at Gothenburg International Biennial of Contemporary Art in 2015. Courtesy of Galeria Filomena Soares, Lisbon, and Mor Charpentier Galerie, Paris. Photo: Hendrik Zeitler.</p>
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<p>(<b>Left</b>) folded zine, 2023, by my students: kieran becker, Isabella Darlington, Mihael Artemus Ivashchyshyn, Naz Khoury, Yoona Lee, Brian Leung, and Joshua Ulysses Ribera; (<b>right</b>) unfolded zine. Photo courtesy of author.</p>
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<p>Sebastian Duncan-Portuondo and community participants, <span class="html-italic">Club EXILE Altar</span>, 2023, 9′ × 10′ × 6′, mirror mosaic, photo portraits, neon, fabric flowers, diverse sacred material. Photo courtesy of the artist.</p>
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<p>(<b>Left</b>) Cassils, <span class="html-italic">103 Shots, video still No. 1</span>, 2016. Photo: Cassils with Zen Cohen. Courtesy of the artist; (<b>right</b>) Cassils, <span class="html-italic">103 Shots, video still No. 2</span>, 2016. Photo: Cassils with Zen Cohen. Courtesy of the artist.</p>
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<p>(<b>Left</b>) Erika Diamond, <span class="html-italic">MB Vest</span> (from <span class="html-italic">Imminent Peril Queer Collection</span> series), Kevlar fabric, fabric lining, Kevlar chopped mat collar, embroidery, and applique, 2020. Photo: Terry Brown; (<b>right</b>) Erika Diamond, <span class="html-italic">Imminent Peril Queer Collection</span> at McColl Center for Visual Art. North Carolina. Photo courtesy of the artist.</p>
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<p>(<b>Left</b>) Erika Diamond, <span class="html-italic">In(Visibility) hoodie</span>, 2022. Photo: Echard Wheeler; (<b>right</b>) Erika Diamond, <span class="html-italic">#Saygay</span>, 2022. Photo courtesy of artist.</p>
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24 pages, 1295 KiB  
Article
CODAS–Hamming–Mahalanobis Method for Hierarchizing Green Energy Indicators and a Linearity Factor for Relevant Factors’ Prediction through Enterprises’ Opinions
by Georgina Elizabeth Riosvelasco-Monroy, Iván Juan Carlos Pérez-Olguín, Salvador Noriega-Morales, Luis Asunción Pérez-Domínguez, Luis Carlos Méndez-González and Luis Alberto Rodríguez-Picón
Processes 2024, 12(6), 1070; https://doi.org/10.3390/pr12061070 - 23 May 2024
Viewed by 776
Abstract
As enterprises look forward to new market share and supply chain opportunities, innovative strategies and sustainable manufacturing play important roles for micro-, small, and mid-sized enterprises worldwide. Sustainable manufacturing is one of the practices aimed towards deploying green energy initiatives to ease climate [...] Read more.
As enterprises look forward to new market share and supply chain opportunities, innovative strategies and sustainable manufacturing play important roles for micro-, small, and mid-sized enterprises worldwide. Sustainable manufacturing is one of the practices aimed towards deploying green energy initiatives to ease climate change, presenting three main pillars—economic, social, and environmental. The issue of how to reach sustainability goals within the sustainable manufacturing of pillars is a less-researched area. This paper’s main purpose and novelty is two-fold. First, it aims to provide a hierarchy of the green energy indicators and their measurements through a multi-criteria decision-making point of view to implement them as an alliance strategy towards sustainable manufacturing. Moreover, we aim to provide researchers and practitioners with a forecasting method to re-prioritize green energy indicators through a linearity factor model. The CODAS–Hamming–Mahalanobis method is used to obtain preference scores and rankings from a 50-item list. The resulting top 10 list shows that enterprises defined nine items within the economic pillar as more important and one item on the environmental pillar; items from the social pillar were less important. The implication for MSMEs within the manufacturing sector represents an opportunity to work with decision makers to deploy specific initiatives towards sustainable manufacturing, focused on profit and welfare while taking care of natural resources. In addition, we propose a continuous predictive analysis method, the linearity factor model, as a tool for new enterprises to seek a green energy hierarchy according to their individual needs. The resulting hierarchy using the predictive analysis model presented changes in the items’ order, but it remained within the same two sustainable manufacturing pillars: economic and environmental. Full article
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<p>Research model.</p>
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<p>Data collection diagram flow.</p>
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<p>Average of people employed in a MSMEs and large firms [<a href="#B21-processes-12-01070" class="html-bibr">21</a>].</p>
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<p>Resulting top 10 hierarchy list from an MCDM methodology and a predictive analysis model.</p>
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46 pages, 2878 KiB  
Article
A Stratal Phonological Analysis of Stem-Level and Word-Level Effects in Old French Compensatory Vowel Lengthening upon Coda /s/ Deletion
by Francisco Antonio Montaño
Languages 2024, 9(5), 177; https://doi.org/10.3390/languages9050177 - 13 May 2024
Viewed by 1078
Abstract
The well-known deletion of coda sibilants in Old French (11th–14th centuries) induced a compensatory lengthening effect on the preceding vowel, generally described as applying uniformly where coda /s/ was lost. This study highlights and analyzes phonological contexts where lengthening likely did not occur, [...] Read more.
The well-known deletion of coda sibilants in Old French (11th–14th centuries) induced a compensatory lengthening effect on the preceding vowel, generally described as applying uniformly where coda /s/ was lost. This study highlights and analyzes phonological contexts where lengthening likely did not occur, examining their interaction with stress assignment, vowel quality, schwa adjustment, prothesis, and morphological structure. The Stratal OT analysis formalizes the proposed pattern differentiating the long and short vowel reflexes identified especially for mid vowels: while categorical in tonic syllables and low vowels /a, ɑ/ irrespective of stress, lengthening only prevails in atonic mid vowels when coda /s/ deletion impacts a syllable assigned stress within the specific stratal phonological cycle when /s/ is deleted from input. The resulting length is transmitted and preserved in subsequent stratal cycles regardless of eventual word-level stress reassignment, especially (but not exclusively) because of word-level schwa adjustment, allowing a shift to word-final stress and producing an opacity effect of a long atonic mid vowel inherited from an earlier cycle. The stratal account formalizes observed analogical effects between lexical items and derived forms with respect to vowel quality and length and proposes them to result instead from the interplay of morphology and phonology. Full article
(This article belongs to the Special Issue Phonetic and Phonological Complexity in Romance Languages)
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<p>Stratal phonological account of stress assignment in English <span class="html-italic">accòmmodátionlessness</span> (<a href="#B6-languages-09-00177" class="html-bibr">Bermúdez-Otero 2018</a>). (<math display="inline"><mi>????</mi></math> = phonological function [input–output mapping]; <span class="html-small-caps">sl</span> = stem-level; <span class="html-small-caps">wl = </span>word-level, © = cyclic node [marks boundaries of cyclic domains within a stratum]). (<b>a</b>) Morphosyntactic structure of <span class="html-italic">accommodationlessness</span> in stratal phonology. (<b>b</b>) Morphological structure of <span class="html-italic">accommodationlessness</span> in stratal phonology. (<b>c</b>) Stratal phonological functions on <span class="html-italic">accommodationlessness</span> according to morphosyntactic structure. (<b>d</b>) Stratal phonological derivation of <span class="html-italic">accommodationlessness</span>.</p>
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<p>Effect of <span class="html-small-caps">Max(Root)</span> yielding vowel lengthening upon coda /s/ deletion (<a href="#B37-languages-09-00177" class="html-bibr">Montaño, forthcoming</a>).</p>
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<p>Preliminary constraint ranking for OF in light of stress assignment and long vowel reflex upon coda /s/ deletion.</p>
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<p>Constraint ranking for OF in light of stress assignment, schwa adjustment, and short vs. long vowel reflex upon coda /s/ deletion.</p>
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14 pages, 3379 KiB  
Article
Combinatorial Quantification of Multi-Features of Coda Waves in Temperature-Affected Concrete Beams
by Gang Zheng, Linzheng Song, Wenqi Xue, Zhiyu Zhang and Benniu Zhang
Materials 2024, 17(9), 2147; https://doi.org/10.3390/ma17092147 - 3 May 2024
Viewed by 817
Abstract
Coda waves are highly sensitive to changes in medium properties and can serve as a tool for structural health monitoring (SHM). However, high sensitivity also makes them susceptible to noise, leading to excessive dispersion of monitoring results. In this paper, a coda wave [...] Read more.
Coda waves are highly sensitive to changes in medium properties and can serve as a tool for structural health monitoring (SHM). However, high sensitivity also makes them susceptible to noise, leading to excessive dispersion of monitoring results. In this paper, a coda wave multi-feature extraction method is proposed, in which three parameters, the time shift, the time stretch, and the amplitude variation of the wave trains within the time window, are totally derived. These three parameters are each mapped to the temperature variations of concrete beams, and then combined together with their optimal weight coefficients to give a best-fitted temperature–multi-parameter relationship that has the smallest errors. Coda wave signals were collected from an ultrasonic experiment on concrete beams within an environmental temperature range of 14 °C~21 °C to verify the effectiveness of the proposed method. The results indicate that the combination of multi-features derived from coda wave signals to quantify the medium temperature is feasible. Compared to the relationship established by a single parameter, the goodness-of-fit is improved. During identification, the method effectively reduces the dispersion of identification errors and mitigates the impact of noise interference on structural state assessment. Both the identification accuracy and stability are improved by more than 50%, and the order of magnitude of the identification accuracy is improved from 1 °C to 0.1 °C. Full article
(This article belongs to the Section Construction and Building Materials)
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<p>The multi-features of the scattered waves (the time shift, the time stretch, and the amplitude variation). The red and blue lines represent the coda waveforms formed by scattering in different temperature states of the medium.</p>
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<p>The pulser transmits a high-voltage pulse, which excites the transmitter and generates ultrasonic waves. The scattered ultrasonic waves are input into the receiver and recorded by the saver. The data in the saver are transmitted to the PC end for processing.</p>
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<p>Temperature data were collected during the two phases of the test.</p>
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<p>(<b>a</b>) The original waveform; (<b>b</b>) the waveform erased of the time shift; (<b>c</b>) the waveform erased of the time shift and the time stretch; (<b>d</b>) the waveform erased of the time shift, the time stretch, and the amplitude variation.</p>
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<p>The relationship between the three parameters and temperature variations. (<b>a</b>) <math display="inline"><semantics> <mi>τ</mi> </semantics></math> − <span class="html-italic">T</span>; (<b>b</b>) <math display="inline"><semantics> <mi>ε</mi> </semantics></math> − <span class="html-italic">T</span>; and (<b>c</b>) <math display="inline"><semantics> <mi>θ</mi> </semantics></math> − <span class="html-italic">T</span>.</p>
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<p>Box plots of errors for quantization relations established by feature parameter combinations and decoupled parameters.</p>
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<p>The relationship between independent feature parameters and temperature. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>δ</mi> <mi>v</mi> <mo>/</mo> <mi>v</mi> </mrow> </semantics></math> − <span class="html-italic">T</span>, <math display="inline"><semantics> <mrow> <mi>δ</mi> <mi>v</mi> <mo>/</mo> <mi>v</mi> </mrow> </semantics></math> by CWI; and (<b>b</b>) <math display="inline"><semantics> <mi>θ</mi> </semantics></math> − <span class="html-italic">T</span>, <math display="inline"><semantics> <mi>θ</mi> </semantics></math> by SVD.</p>
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<p>Error box plots of the relationship established between the parameters of the independent features and the temperature variations, and the relationship established between the combination of the three parameters and the temperature variations.</p>
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<p>(<b>a</b>) The combinatorial identification, CWI, and SVD identification results of beam A. (<b>b</b>) Identification results of beam B.</p>
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<p>Identification errors box plot of different methods.</p>
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16 pages, 735 KiB  
Article
Lp-Norm for Compositional Data: Exploring the CoDa L1-Norm in Penalised Regression
by Jordi Saperas-Riera, Glòria Mateu-Figueras and Josep Antoni Martín-Fernández
Mathematics 2024, 12(9), 1388; https://doi.org/10.3390/math12091388 - 1 May 2024
Viewed by 893
Abstract
The Least Absolute Shrinkage and Selection Operator (LASSO) regression technique has proven to be a valuable tool for fitting and reducing linear models. The trend of applying LASSO to compositional data is growing, thereby expanding its applicability to diverse scientific domains. This paper [...] Read more.
The Least Absolute Shrinkage and Selection Operator (LASSO) regression technique has proven to be a valuable tool for fitting and reducing linear models. The trend of applying LASSO to compositional data is growing, thereby expanding its applicability to diverse scientific domains. This paper aims to contribute to this evolving landscape by undertaking a comprehensive exploration of the L1-norm for the penalty term of a LASSO regression in a compositional context. This implies first introducing a rigorous definition of the compositional Lp-norm, as the particular geometric structure of the compositional sample space needs to be taken into account. The focus is subsequently extended to a meticulous data-driven analysis of the dimension reduction effects on linear models, providing valuable insights into the interplay between penalty term norms and model performance. An analysis of a microbial dataset illustrates the proposed approach. Full article
(This article belongs to the Special Issue Multivariate Statistical Analysis and Application)
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<p>The Manhattan distance based on the CoDa <math display="inline"><semantics> <msup> <mi>L</mi> <mn>1</mn> </msup> </semantics></math>-norm in the simplex <math display="inline"><semantics> <msup> <mi mathvariant="bold-italic">S</mi> <mn>3</mn> </msup> </semantics></math>: the distance between two points <math display="inline"><semantics> <mrow> <mi mathvariant="bold">x</mi> <mo>=</mo> <mi mathvariant="script">C</mi> <mfenced separators="" open="[" close="]"> <msup> <mi>e</mi> <mn>3</mn> </msup> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mi>e</mi> </mfenced> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi mathvariant="bold">y</mi> <mo>=</mo> <mi mathvariant="script">C</mi> <mfenced separators="" open="[" close="]"> <mn>1</mn> <mo>,</mo> <msup> <mi>e</mi> <mn>2</mn> </msup> <mo>,</mo> <mi>e</mi> </mfenced> </mrow> </semantics></math> in a grid-based system, where <math display="inline"><semantics> <mrow> <mi mathvariant="script">C</mi> <mfenced open="[" close="]"> <mo>·</mo> </mfenced> </mrow> </semantics></math> is the closure operation, is represented by three paths (red, orange, and blue) of the same length (five units).</p>
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<p><math display="inline"><semantics> <msup> <mi>L</mi> <mn>1</mn> </msup> </semantics></math>-<math display="inline"><semantics> <mi>clr</mi> </semantics></math>: cross-validation MSE curve for different log-transformed values of the penalty parameter (<math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </semantics></math>). The circle (∘) is the arithmetical mean of the ten-fold CV. The red lines (above and below the mean) indicate the mean ± stdev value, where stdev is the standard deviation of the ten-fold CV. The vertical line represents the log-transformed values of lambda.min = 35,769.42.</p>
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<p>Comparison of the <math display="inline"><semantics> <mrow> <mi>clr</mi> <mo>(</mo> <mi mathvariant="bold-italic">β</mi> <mo>)</mo> </mrow> </semantics></math> parameter, with the taxon order maintained on the vertical axis to facilitate comparison: (<b>a</b>) <math display="inline"><semantics> <mi>clr</mi> </semantics></math>-scores for the <math display="inline"><semantics> <msup> <mi>L</mi> <mn>1</mn> </msup> </semantics></math>-<math display="inline"><semantics> <mi>clr</mi> </semantics></math> LASSO estimator, (<b>b</b>) <math display="inline"><semantics> <mi>clr</mi> </semantics></math>-scores for the <math display="inline"><semantics> <msup> <mi>L</mi> <mn>1</mn> </msup> </semantics></math>-CoDa LASSO estimator, and (<b>c</b>) <math display="inline"><semantics> <mi>clr</mi> </semantics></math>-scores for the <math display="inline"><semantics> <msup> <mi>L</mi> <mn>1</mn> </msup> </semantics></math>-plr LASSO estimator.</p>
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<p>CoDa <math display="inline"><semantics> <msup> <mi>L</mi> <mn>1</mn> </msup> </semantics></math>-norm: cross-validation MSE curve for different log-transformed values of the penalty parameter (<math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </semantics></math>). The circle (∘) is the arithmetical mean of the ten-fold CV. The red lines (above and below the mean) represent the value mean ± stdev, where stdev is the standard deviation of the ten-fold CV. The vertical line represents the log-transformed values of lambda.min = 45,582.21.</p>
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<p><math display="inline"><semantics> <msup> <mi>L</mi> <mn>1</mn> </msup> </semantics></math>-plr: cross-validation MSE curve for different log-transformed values of the penalty parameter (<math display="inline"><semantics> <mrow> <mo form="prefix">ln</mo> <mo>(</mo> <mi>λ</mi> <mo>)</mo> </mrow> </semantics></math>). The circle (∘) is the arithmetical mean of the ten-fold CV. The red lines (above and below the mean) represent the value mean ± stdev, where stdev is the standard deviation of the ten-fold CV. The vertical line represents the log-transformed values of lambda.min = 69,669.31.</p>
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