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Search Results (454)

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14 pages, 625 KiB  
Article
Own Typology of Body Posture Based on Research Using the Diers Formetric III 4D System
by Jacek Wilczyński
J. Clin. Med. 2025, 14(2), 501; https://doi.org/10.3390/jcm14020501 - 14 Jan 2025
Viewed by 309
Abstract
Background/Objectives: Body posture is developmentally variable and individually diversified. As a chain of numerous unconditioned and conditioned reflexes, it is, in its essence, a psychomotor habit. The aim of the study was to create an original typology of body posture based on [...] Read more.
Background/Objectives: Body posture is developmentally variable and individually diversified. As a chain of numerous unconditioned and conditioned reflexes, it is, in its essence, a psychomotor habit. The aim of the study was to create an original typology of body posture based on measurements using the Diers Formetric III 4D system. Methods: The research included 303 children aged 10–12. Results: Taking the ranges of standards for the angle of thoracic kyphosis (42–55°) and lumbar lordosis (33–47°) into account, it was shown that there are nine types of body posture. These are as follows: reduced kyphosis, reduced lordosis (K < 42°; L < 33°); reduced kyphosis, normal lordosis (K < 42°; 33° ≤ L ≤ 47°); reduced kyphosis, increased lordosis (K < 42°; L > 47°); normal kyphosis, reduced lordosis (42° ≤ K ≤ 55°; L < 33°); normal kyphosis, normal lordosis (42° ≤ K ≤ 55; 33° ≤ L ≤ 47°); normal kyphosis, increased lordosis (42° ≤ K ≤ 55°; L > 47°); increased kyphosis, reduced lordosis (K > 55°, L < 33°); increased kyphosis, normal lordosis (K > 55°; 33° ≤ L ≤ 47°); and increased kyphosis, increased lordosis (K > 55°; L > 47°). Conclusions: In the final evaluation of the Diers Formetric III 4D examination, the traditional division into round, concave, round-concave, and flat backs should be supplemented and expanded to include the nine posture types mentioned above. This will enable a more precise selection of corrective exercises, which will significantly improve their quality and effectiveness. Full article
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<p>Diers Formetric III 4D system.</p>
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<p>Fixed anatomical points in the sagittal plane—‘Average’ Diers Formetric III 4D analysis.</p>
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<p>Method of determining angle of thoracic kyphosis and lumbar lordosis angles LA—‘Average’ 4D Diers Formetric III 4D analysis.</p>
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12 pages, 277 KiB  
Article
New Analytical Formulas for the Rank of Farey Fractions and Estimates of the Local Discrepancy
by Rogelio Tomás García
Mathematics 2025, 13(1), 140; https://doi.org/10.3390/math13010140 - 2 Jan 2025
Viewed by 493
Abstract
New analytical formulas are derived for the rank and the local discrepancy of Farey fractions. The new rank formula is applicable to all Farey fractions and involves sums of a lower order compared to the searched one. This serves to establish a new [...] Read more.
New analytical formulas are derived for the rank and the local discrepancy of Farey fractions. The new rank formula is applicable to all Farey fractions and involves sums of a lower order compared to the searched one. This serves to establish a new unconditional estimate for the local discrepancy of Farey fractions that decrease with the order of the Farey sequence. This estimate improves the currently known estimates. A new recursive expression for the local discrepancy of Farey fractions is also given. A second new unconditional estimate of the local discrepancy of any Farey fraction is derived from a sum of the Mertens function, again, improving the currently known estimates. Full article
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<p>Illustration of the results in [<a href="#B11-mathematics-13-00140" class="html-bibr">11</a>], showing the upper bounds of the local discrepancy of Farey fractions, <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mover accent="true"> <mi>r</mi> <mo maxsize="90%">^</mo> </mover> <mi>n</mi> </msub> <mrow> <mrow> <mo>(</mo> <mi>α</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>/</mo> <mo>|</mo> </mrow> <msub> <mi>F</mi> <mi>n</mi> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math>, versus the Farey fractions <math display="inline"><semantics> <mi>α</mi> </semantics></math> in <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mo>]</mo> </mrow> </semantics></math> (without respecting the actual separation ratios in the horizontal axis). Note that the red curve for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>≤</mo> <mn>15</mn> <mo>/</mo> <mi>n</mi> </mrow> </semantics></math> has been plotted using expression (<a href="#FD2-mathematics-13-00140" class="html-disp-formula">2</a>), while in [<a href="#B11-mathematics-13-00140" class="html-bibr">11</a>] (page 361) tabulated values are given.</p>
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14 pages, 855 KiB  
Article
Evaluation of Influenza Vaccine Effectiveness from 2021 to 2024: A Guangdong-Based Test-Negative Case–Control Study
by Liyan Zhu, Ying Han, Jiahai Lu, Jianhao Tan, Conghui Liao, Cheng Guo, Qing He, Yajie Qiu, Huahua Lu, Yue Zhou, Jianrui Wei and Dandan Hu
Vaccines 2025, 13(1), 4; https://doi.org/10.3390/vaccines13010004 - 24 Dec 2024
Viewed by 479
Abstract
Background: The influenza virus’s high mutation rate requires the annual reformulation and administration of the vaccine. Therefore, its vaccine effectiveness (VE) must be evaluated annually. Aim: Estimate the effectiveness of the influenza vaccine and analyze the impact of age, seasonal variations, and the [...] Read more.
Background: The influenza virus’s high mutation rate requires the annual reformulation and administration of the vaccine. Therefore, its vaccine effectiveness (VE) must be evaluated annually. Aim: Estimate the effectiveness of the influenza vaccine and analyze the impact of age, seasonal variations, and the vaccination to sample collection interval on VE. Methods: The study used a test-negative case–control (TNCC) design to collect data from patients under 18 years of age who presented with acute respiratory infection (ARI) symptoms and underwent influenza virus testing at a national children’s regional medical center in Guangdong Province between October 2021 and January 2024, spanning three influenza seasons. VE was estimated using unconditional logistic regression. Results: A total of 27,670 patient data entries were analyzed. The VE against all influenza viruses across the three seasons was 37% (95% CI: 31–43), with the lowest VE of 24% (95% CI: 8–37) observed in the 2021–2022 season. In children aged 0.5 to <3 years, the VE was 32% (95% CI: 19–43). The effectiveness for samples collected at intervals of 0.5–2 months, 3–6 months, and over 6 months after vaccination was 39% (95% CI: 32–46), 30% (95% CI: 19–40), and 28% (95% CI: 5–46). Conclusions: Across three influenza seasons, at least one-third of vaccinated individuals were protected from influenza in outpatient settings. Given that children are at high risk, improving vaccination management is recommended, and parents should be encouraged to vaccinate their children before each influenza season. Full article
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<p>Vaccine effectiveness against outpatient cases from October 2021 to January 2024, across different influenza types and age groups. Results were adjusted for gender, age group, and sample collection month. Abbreviations: CI, confidence interval; VE, vaccine effectiveness.</p>
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<p>Vaccine effectiveness against outpatient cases from October 2021 to January 2024, across different influenza seasons and types. Results were adjusted for gender, age group, and sample collection month. Abbreviations: CI, confidence interval; VE, vaccine effectiveness.</p>
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<p>Vaccine effectiveness against outpatient cases of all influenza types from October 2021 to January 2024, across different influenza vaccination characteristics. Results were adjusted for gender, age group, and sample collection month. Abbreviations: CI, confidence interval; VE, vaccine effectiveness.</p>
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12 pages, 803 KiB  
Article
Exploring the Impact of IL-33 Gene Polymorphism (rs1929992) on Susceptibility to Chronic Spontaneous Urticaria and Its Association with Serum Interleukin-33 Levels
by Carmen-Teodora Dobrican-Băruța, Diana Mihaela Deleanu, Mihaela Iancu, Ioana Adriana Muntean, Irena Nedelea, Radu-Gheorghe Bălan, Lucia Maria Procopciuc and Gabriela Adriana Filip
Int. J. Mol. Sci. 2024, 25(24), 13709; https://doi.org/10.3390/ijms252413709 - 22 Dec 2024
Viewed by 467
Abstract
Urticaria is a debilitating skin condition affecting up to 20% of the global population, characterized by erythematous, maculopapular lesions and significant quality of life impairment. This study focused on the role of interleukin 33 (IL-33) and its polymorphisms, particularly SNP rs1929992, in [...] Read more.
Urticaria is a debilitating skin condition affecting up to 20% of the global population, characterized by erythematous, maculopapular lesions and significant quality of life impairment. This study focused on the role of interleukin 33 (IL-33) and its polymorphisms, particularly SNP rs1929992, in chronic spontaneous urticaria (CSU). Using demographic, clinical, and laboratory data from CSU patients and controls, we estimated allele and genotype frequencies, Hardy–Weinberg equilibrium condition, and serum IL-33 levels, using unconditional binomial logistic regression for association analysis. Results revealed that CSU patients had significantly higher frequencies of the minor allele of IL-33 rs1929992 compared to controls (31.25% vs. 17.35%, p = 0.024), and carriers of the GA genotype exhibited increased odds of CSU (adjusted OR = 2.208, p ≤ 0.001). Additionally, serum IL-33 levels were markedly elevated in CSU patients, particularly those with the GA genotype. The findings suggest that the IL-33 SNP is associated with an increased susceptibility to CSU, emphasizing its potential as a diagnostic and therapeutic biomarker. This study underscores the genetic and immunological underpinnings of CSU, paving the way for personalized treatment approaches. Full article
(This article belongs to the Special Issue Skin Diseases: From Molecular Mechanisms to Pathology)
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<p>Distribution of IL-33 values in patients carrying GG and GA genotypes of IL-33 <span class="html-italic">rs1929992</span> gene polymorphism split by group (CSU group is represented in gray while non-CSU group is represented in yellow). Dot plot shows individual IL-33 levels and box-and-whisker plot shows distribution of data based on median and IQR in studied groups.</p>
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<p>Enzymatic digestion of the 529 bp fragment for IL-33- <span class="html-italic">rs1929992</span> identification. Lane 1—pBR HaeIII digest DNA molecular marker V; lanes 2, 4, 5, 10–13—homozygous GG genotype: fragment of 529 bp; lanes 3, 6, 8, 14–18—heterozygous AG genotype: fragments of 529,398 and 131 bp; lanes 7, 9, 19 and 20—homozygous AA genotype: fragment of 398 and 131 bp.</p>
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15 pages, 445 KiB  
Article
Vitamin B1, B2, and B6 Intakes and Risk of Gastric Cancer: Findings from a Case-Control Study
by Ngoan Tran Le, Yen T.-H. Pham, Huy Thanh Dang, Linh Thuy Le, Nhi Y.-N. Huynh, Jennifer Cullen and Hung N. Luu
Nutrients 2024, 16(24), 4370; https://doi.org/10.3390/nu16244370 - 18 Dec 2024
Viewed by 753
Abstract
Background/Objectives: Gastric cancer is one of the leading malignancies worldwide. B vitamins play important roles in DNA synthesis and methylation because they are considered co-enzymes in one-carbon metabolism. There is inconclusive evidence regarding the associations between dietary vitamins B1, B2 [...] Read more.
Background/Objectives: Gastric cancer is one of the leading malignancies worldwide. B vitamins play important roles in DNA synthesis and methylation because they are considered co-enzymes in one-carbon metabolism. There is inconclusive evidence regarding the associations between dietary vitamins B1, B2, and B6 with the risk of gastric cancer in different epidemiologic studies. We, therefore, investigated such associations in a hospital-based case-control study comprising 1182 incident cases of gastric cancer and 2995 controls in Vietnam. Methods: Dietary vitamins B1, B2, and B6 were derived from a semi-quantitative validated food frequency questionnaire. An unconditional logistic regression model was used to calculate the odds ratios (ORs) and 95% confidence intervals (CIs) for the risk of gastric cancer in relation to dietary intake of vitamins B1, B2, and B6. Results: Overall, dietary vitamins B1 (ORper-SD increment = 0.83; 95% CI: 0.78–0.89; Ptrend < 0.001) and B6 (ORper-SD increment = 0.88; 95% CI: 0.81–0.94; Ptrend < 0.001) were associated with a reduced risk of gastric cancer. Compared with the lowest quintile, the ORs (95% CIs) of gastric cancer for quintiles 2, 3, 4, and 5 of the vitamin B1 intake were 0.64 (0.51–0.79), 0.54 (0.43–0.69), 0.57 (0.44–0.74), and 0.42 (0.31–0.55), respectively; for vitamin B6 intake, quintiles 2, 3, 4, and 5 were 0.53 (0.42–0.66), 0.54 (0.42–0.70), 0.61 (0.46–0.81), and 0.46 (0.33–0.63), respectively. This inverse association was not different across sex, BMI, and smoking statuses. No association was found between dietary vitamin B2 and gastric cancer risk. Conclusions: Dietary vitamins B1 and B6 were associated with a reduced risk of gastric cancer in the Vietnamese population. Future studies are warranted to replicate our findings, which also have great implications for gastric cancer prevention and control programs in low- and middle-income countries. Full article
(This article belongs to the Section Micronutrients and Human Health)
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<p>Association between vitamins B<sub>1</sub>, B<sub>2</sub>, and B<sub>6</sub> and the risk of gastric cancer, stratified by BMI, smoking status, alcohol drinking status, and history of type 2 diabetes, in the current study (estimates per SD increment). CI, confidence interval; OR, odds ratio; T2DM, type 2 diabetes mellitus.</p>
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13 pages, 1326 KiB  
Article
Sex and Age Differences in Glucocorticoid Signaling After an Aversive Experience in Mice
by Yun Li, Bin Zhang, Youhua Yang, Ping Su, James Nicholas Samsom, Albert H. C. Wong and Fang Liu
Cells 2024, 13(24), 2041; https://doi.org/10.3390/cells13242041 - 10 Dec 2024
Viewed by 868
Abstract
Background: glucocorticoids may play an important role in the formation of fear memory, which is relevant to the neurobiology of post-traumatic stress disorder (PTSD). In our previous study, we showed the glucocorticoid receptor (GR) forms a protein complex with FKBP51, which prevents translocation [...] Read more.
Background: glucocorticoids may play an important role in the formation of fear memory, which is relevant to the neurobiology of post-traumatic stress disorder (PTSD). In our previous study, we showed the glucocorticoid receptor (GR) forms a protein complex with FKBP51, which prevents translocation of GR into the nucleus to affect gene expression; this complex is elevated in PTSD patients and by fear-conditioned learning in mice, and disrupting this complex blocks the storage and retrieval of fear-conditioned memories. The timing of release of glucocorticoid relative to the formation of a traumatic memory could be important in this process, and remains poorly understood. Methods and Results: we mapped serum corticosterone over time after fear conditioning in cardiac blood samples from male and female mice, as well as adult and aged mice using ELISA. We show a significant alteration in serum corticosterone after conditioning; notably, levels spike after 30 min but drop lower than unconditioned controls after 24 h. We further investigate the effect of glucocorticoid on GR phosphorylation and localization in HEK 293T cells by Western blot. Hydrocortisone treatment promotes phosphorylation and nuclear translocation of GR. Conclusions: these data contribute to our understanding of the processes linking stress responses to molecular signals and fear memory, which is relevant to understanding the shared mechanisms related to PTSD. Full article
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<p>Successful establishment of fear-conditioned mouse model. (<b>A</b>) A schematic illustration schedule for fear conditioning. The conditioned stimulus (CS) was a white light illuminated for 30 s, the unconditioned stimulus (US) was a 1 s 0.5 mA foot shock. Conditioned animals received 5 CS-US pairings, control animals received the CS alone. (<b>B</b>) Time spent freezing during the 3 min CS presentation on day 5 in adult male (8-week-old) mice. Conditioned animals showed significantly more freezing behavior compared to controls. **** <span class="html-italic">p</span> &lt; 0.0001, n = 16, permutation test.</p>
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<p>Fear conditioning affects the time course of corticosterone levels in mice. (<b>A</b>) Corticosterone protein-expression response curves over 24 h in unconditioned (Control) and fear-conditioned animals (Conditioned). Comparison of corticosterone levels over time in conditioned (dashed) and unconditioned (solid) adult (8-week-old) male (<b>B</b>), adult female (<b>C</b>), aged (64-week-old) male (<b>D</b>), and aged female (<b>E</b>) mice. Data are shown as mean ± SEM, 4-way ANOVA (n = 4 *, female aged control n = 3), -corrected post hoc marginal means. Significance indicators: <sup>#</sup> <span class="html-italic">p</span> &lt; 0.05, <sup>##</sup> <span class="html-italic">p</span> &lt; 0.01, <sup>###</sup> <span class="html-italic">p</span> &lt; 0.001, <sup>####</sup> <span class="html-italic">p</span> &lt; 0.0001 relative to 0 h; <sup><span>$</span></sup> <span class="html-italic">p</span> &lt; 0.05, <sup><span>$</span><span>$</span><span>$</span></sup> <span class="html-italic">p</span> &lt; 0.001, <sup><span>$</span><span>$</span><span>$</span><span>$</span></sup> <span class="html-italic">p</span> &lt; 0.0001 relative to 0.5 h; <sup>%%</sup> <span class="html-italic">p</span> &lt; 0.01 relative to 1 h; <sup>^</sup> <span class="html-italic">p</span> &lt; 0.05, <sup>^^</sup> <span class="html-italic">p</span> &lt; 0.01 relative to 2 h, <sup>&amp;&amp;&amp;</sup> <span class="html-italic">p</span> &lt; 0.001 relative to 4 h, <sup>†</sup> <span class="html-italic">p</span> &lt; 0.05, <sup>††</sup> <span class="html-italic">p</span> &lt; 0.005, <sup>††††</sup> <span class="html-italic">p</span> &lt; 0.0001 relative to 8 h; <sup>‡</sup> <span class="html-italic">p</span> &lt; 0.05 relative to 12 h. * Control relative to Conditioned; * <span class="html-italic">p</span> &lt; 0.05, ** <span class="html-italic">p</span> &lt; 0.01, *** <span class="html-italic">p</span> &lt; 0.001, **** <span class="html-italic">p</span> &lt; 0.0001.</p>
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<p>Female mice have increased corticosterone over time, relative to males, after fear conditioning. Comparison of corticosterone levels over time in male (solid) and female (dashed) adult (8-week-old) unconditioned control mice (<b>A</b>), adult conditioned (<b>B</b>), aged (64-week-old) control (<b>C</b>), and aged conditioned (<b>D</b>) mice. Data are shown as mean ± SEM, 4-way ANOVA (n = 4 *, female aged control n = 3), fdr-corrected post hoc marginal means, * <span class="html-italic">p</span> &lt; 0.05, ** <span class="html-italic">p</span> &lt; 0.01, *** <span class="html-italic">p</span> &lt; 0.001.</p>
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<p>Age reduces corticosterone levels and reactivity to fear conditioning. Comparison of corticosterone levels over time in adult (8-week-old) (solid) and aged (64-week-old) (dashed) male unconditioned control mice (<b>A</b>), male conditioned (<b>B</b>), female control (<b>C</b>), and female conditioned (<b>D</b>) mice. Data are shown as mean ± SEM, 4-way ANOVA (n = 4 *, female aged control n = 3), fdr-corrected post hoc marginal means, * <span class="html-italic">p</span> &lt; 0.05, ** <span class="html-italic">p</span> &lt; 0.01, *** <span class="html-italic">p</span> &lt; 0.001.</p>
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<p>Hydrocortisone treatment stimulates Ser211 phosphorylation of glucocorticoid receptor (GR) and promotes nuclear translocation of GR in HEK 293T cells. (<b>A</b>) Representative Western blots (<b>top</b>) and densitometric analysis (<b>bottom</b>) of phosphorylated GR-S211 (pGR<sup>Ser211</sup>) in HEK 293T whole-cell lysates stimulated by different concentrations of hydrocortisone. The level of pGR<sup>Ser211</sup> is expressed as a ratio relative to levels of unphosphorylated GR normalized to the vehicle (DMSO) alone condition. (<b>B</b>) Representative Western blots (<b>top</b>) and densitometric analysis (<b>bottom</b>) of the levels of pGR<sup>Ser211</sup> in HEK 293T cells stimulated by hydrocortisone (100 nM) over time. pGR<sup>Ser211</sup>/GR ratios were normalized to time 0. (<b>C</b>) Representative Western blots (<b>top</b>) and densitometric analysis (<b>bottom</b>) of the changes in cytoplasmic GR protein expression in HEK 293T cells stimulated by different concentrations of hydrocortisone. GR levels expressed relative to α–tubulin and normalized to vehicle (DMSO). (<b>D</b>) Representative Western blots (<b>top</b>) and densitometric analysis (<b>bottom</b>) of the changes in nuclear GR protein expression in HEK 293T cells stimulated by different concentrations of hydrocortisone. GR levels expressed relative to histone H3 and normalized to vehicle (DMSO). Data are shown as mean ± SEM, one-way ANOVA (n = 3), * <span class="html-italic">p</span> &lt; 0.05, ** <span class="html-italic">p</span> &lt; 0.01, *** <span class="html-italic">p</span> &lt; 0.001, **** <span class="html-italic">p</span> &lt; 0.0001.</p>
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<p>Hydrocortisone treatment stimulates Ser211 phosphorylation of glucocorticoid receptor (GR) and promotes nuclear translocation of GR in HEK 293T cells. (<b>A</b>) Representative Western blots (<b>top</b>) and densitometric analysis (<b>bottom</b>) of phosphorylated GR-S211 (pGR<sup>Ser211</sup>) in HEK 293T whole-cell lysates stimulated by different concentrations of hydrocortisone. The level of pGR<sup>Ser211</sup> is expressed as a ratio relative to levels of unphosphorylated GR normalized to the vehicle (DMSO) alone condition. (<b>B</b>) Representative Western blots (<b>top</b>) and densitometric analysis (<b>bottom</b>) of the levels of pGR<sup>Ser211</sup> in HEK 293T cells stimulated by hydrocortisone (100 nM) over time. pGR<sup>Ser211</sup>/GR ratios were normalized to time 0. (<b>C</b>) Representative Western blots (<b>top</b>) and densitometric analysis (<b>bottom</b>) of the changes in cytoplasmic GR protein expression in HEK 293T cells stimulated by different concentrations of hydrocortisone. GR levels expressed relative to α–tubulin and normalized to vehicle (DMSO). (<b>D</b>) Representative Western blots (<b>top</b>) and densitometric analysis (<b>bottom</b>) of the changes in nuclear GR protein expression in HEK 293T cells stimulated by different concentrations of hydrocortisone. GR levels expressed relative to histone H3 and normalized to vehicle (DMSO). Data are shown as mean ± SEM, one-way ANOVA (n = 3), * <span class="html-italic">p</span> &lt; 0.05, ** <span class="html-italic">p</span> &lt; 0.01, *** <span class="html-italic">p</span> &lt; 0.001, **** <span class="html-italic">p</span> &lt; 0.0001.</p>
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12 pages, 447 KiB  
Article
Effect of Low- and Moderate-Intensity Aerobic Training on Body Composition Cardiorespiratory Functions, Biochemical Risk Factors and Adipokines in Morbid Obesity
by Judit Horváth, Ildikó Seres, György Paragh, Péter Fülöp and Zoltán Jenei
Nutrients 2024, 16(23), 4251; https://doi.org/10.3390/nu16234251 - 9 Dec 2024
Viewed by 837
Abstract
Background: Obesity poses an enormous public health and economic burden worldwide. Visceral fat accumulation is associated with various metabolic and cardiovascular consequences, resulting in an increased prevalence of atherosclerotic conditions. We aimed to examine the impact of low-and moderate-intensity aerobic training on several [...] Read more.
Background: Obesity poses an enormous public health and economic burden worldwide. Visceral fat accumulation is associated with various metabolic and cardiovascular consequences, resulting in an increased prevalence of atherosclerotic conditions. We aimed to examine the impact of low-and moderate-intensity aerobic training on several anthropometric and cardiorespiratory parameters and markers of atherosclerosis, including inflammation, serum levels of lipoproteins and adipokines of extremely obese patients in poor condition. Methods: Forty severely obese patients were recruited and randomized into two groups, Group 1 and Group 2, for a six-week inpatient study. Group 1 received moderate-intensity (40–60% heart rate reserve) and Group 2 received low-intensity (30–39% of heart rate reserve) aerobic training combined with resistance training. The patients’ cardiorespiratory functions were assessed by ergospirometry. Anthropometric data were recorded, body composition was analyzed and functional tests were performed. We also investigated serum lipids and high-sensitive C-reactive protein levels and calculated the homeostatic model assessment-insulin resistance indices and adipokine levels as predictive biomarkers. Results: Functional abilities and some biochemical parameters, such as homeostatic model assessment-insulin resistance, serum lipids, apolipoprotein A and apolipoprotein-B improved in both groups in a positive direction. However, cardiorespiratory capacity and the serum levels of high-sensitive C-reactive protein and Lipocalin-2 decreased, while irisin and paraoxonase 1 increased significantly, but only in Group 1. Conclusions: Six weeks of aerobic training, regardless of its intensity, could induce favorable changes in functional tests, body composition and serum lipids, even in severely obese, extremely unconditioned patients in both groups. However, moderate-intensity aerobic training should at least increase cardiorespiratory capacity and yield a better lipid profile oxidative status and inflammation profile. Full article
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<p>Timeline.</p>
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14 pages, 25634 KiB  
Article
Effect of Extreme Environments on Adhesive Joint Performance
by Martin Kadlec, Bohuslav Cabrnoch and Robin Hron
J. Compos. Sci. 2024, 8(12), 511; https://doi.org/10.3390/jcs8120511 - 6 Dec 2024
Viewed by 523
Abstract
The presented research on adhesives was conducted with the aim of supporting the design of composite repairs for composite aircraft structures that can withstand specific environmental conditions. Double-sided strap joint specimens of epoxy-based CFRP adherents and straps were bonded by two types of [...] Read more.
The presented research on adhesives was conducted with the aim of supporting the design of composite repairs for composite aircraft structures that can withstand specific environmental conditions. Double-sided strap joint specimens of epoxy-based CFRP adherents and straps were bonded by two types of adhesives. Room-temperature curing epoxy adhesives EC-9323 and EA-9395 were used for bonding. The specimens’ shear strength and failure modes were evaluated under four different environmental conditions from −72 °C up to 70 °C unconditioned and at 70 °C after humidity conditioning. The results show that EC-9323 performed excellently at room temperature, but very poorly at elevated temperatures after hot–wet conditioning. Adhesive EA-9395 performed consistently well across all tested conditions. The failure mode analysis explained the performance trends and the effect of the environment on the fractured surface. This study will support proper repair design and verification of numerical simulations. The novelty of this article lies in its combined analysis of multiple environmental factors, providing a more realistic assessment of joint performance. Full article
(This article belongs to the Section Polymer Composites)
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<p>Double-sided strap joint specimen geometry.</p>
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<p>Detail of double-sided strap joint bonded by (<b>a</b>) EC-9323 and (<b>b</b>) EA-9395.</p>
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<p>Measured adhesive thickness: (<b>a</b>) average values were 138 μm and 275 μm for EC-9323 and EA-9395, respectively; (<b>b</b>) details of adhesive layer.</p>
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<p>Shear strength results for (<b>a</b>) EC-9323 and (<b>b</b>) EA-9395.</p>
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<p>The typical failure mechanism for double-sided strap joints. One of the laps remains intact as the opposite lap initiates the failure.</p>
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<p>Observed failure modes: (<b>a</b>) schematic diagram; (<b>b</b>) actual fracture surface.</p>
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<p>Observed failure modes: (<b>a</b>) fracture surface of delamination (interlaminar failure) region was dominated by shear cusps (white) in between fibre tracks (black); (<b>b</b>) fracture surface of fibre tear (intralaminar failure) region was dominated by fibres and fibre tracks with less resin/adhesive deformation.</p>
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<p>Observed failure mode transition: (<b>a</b>) from debonding to fibre tear; (<b>b</b>) from cohesive failure to fibre tear; (<b>c</b>) from fibre tear to delamination. Propagation from left to right.</p>
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<p>Failure mode analysis of EC-9323 at various test temperatures: (<b>a</b>) −72 °C; (<b>b</b>) 21 °C; (<b>c</b>) 70 °C; and (<b>d</b>) 70 °C after wet conditioning. Initiation occurred on top side of imaged surfaces.</p>
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<p>Failure mode analysis of EA-9395 at various test temperatures: (<b>a</b>) −72 °C; (<b>b</b>) 21 °C; (<b>c</b>) 70 °C; and (<b>d</b>) 70 °C after wet conditioning. Initiation occurred on top side of imaged surfaces.</p>
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<p>Differences in fracture surfaces at low and high temperatures for delamination and fibre tear: (<b>a</b>,<b>c</b>) relatively smooth surface at −72 °C, and (<b>b</b>,<b>d</b>) significant fibre pull-out at 70 °C. Propagation from left to right.</p>
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<p>Failure mode analysis of EC-9323 adhesive joints. The significant impact of adhesive failure on shear strength is apparent.</p>
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<p>Failure mode analysis of EA-9395 adhesive joints. Wet environment degradation caused an increase in the adhesive failure ratio.</p>
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<p>Delamination failure ratio relationship with shear strength. Linear increase in strength with delamination ratio observed for both adhesives.</p>
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17 pages, 2999 KiB  
Article
Lightweight Multi-Scales Feature Diffusion for Image Inpainting Towards Underwater Fish Monitoring
by Zhuowei Wang, Xiaoqi Jiang, Chong Chen and Yanxi Li
J. Mar. Sci. Eng. 2024, 12(12), 2178; https://doi.org/10.3390/jmse12122178 - 28 Nov 2024
Viewed by 541
Abstract
In the process of gradually upgrading aquaculture to the information and intelligence industries, it is usually necessary to collect images of underwater fish. In practical work, the quality of underwater images is often affected by water clarity and light refraction, resulting in most [...] Read more.
In the process of gradually upgrading aquaculture to the information and intelligence industries, it is usually necessary to collect images of underwater fish. In practical work, the quality of underwater images is often affected by water clarity and light refraction, resulting in most fish images not fully displaying the entire fish body. Image inpainting helps infer the occluded fish image information based on known images, thereby better identifying and analyzing fish populations. When using existing image inpainting methods for underwater fish images, limited by the small datasets available for training, the results were not satisfactory. Lightweight Multi-scales Feature Diffusion (LMF-Diffusion) is proposed to achieve results closer to real images when dealing with image inpainting tasks from small datasets. LMF-Diffusion is based on guided diffusion and flexibly extracts features from images at different scales, effectively capturing remote dependencies among pixels, and it is more lightweight, making it more suitable for practical deployment. Experimental results show that our architecture uses only 48.7% of the parameter of the guided diffusion model and produces inpainting results closer to real images in our dataset. Experimental results show that LMF-Diffusion enables the Repaint method to exhibit better performance in underwater fish image inpainting. Underwater fish image inpainting results obtained using our LMF-Diffusion model outperform those produced by current popular image inpainting methods. Full article
(This article belongs to the Section Marine Aquaculture)
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<p>Example of underwater fish image collection.</p>
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<p>The forward process and the reverse process of DDPM.</p>
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<p>Underwater fish video shooting schematic.</p>
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<p>Results of underwater fish image inpainting using the guided diffusion model as a prior in the Repaint method.</p>
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<p>An example of 256 × 256 images input through the proposed LMF-Diffusion.</p>
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<p>Comparison of standard convolution and depthwise separable convolution.</p>
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<p>Comparison of the guided diffusion architecture [<a href="#B42-jmse-12-02178" class="html-bibr">42</a>] and LMF-Diffusion in underwater image inpainting (fish mask setting).</p>
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<p>Comparison of the guided diffusion architecture [<a href="#B42-jmse-12-02178" class="html-bibr">42</a>] and the LMF-Diffusion in underwater image inpainting (other mask settings).</p>
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<p>Results of inpainting underwater fish images. Comparison against other inpainting methods (DSI [<a href="#B17-jmse-12-02178" class="html-bibr">17</a>], AOT [<a href="#B18-jmse-12-02178" class="html-bibr">18</a>], Repaint with guided diffusion [<a href="#B42-jmse-12-02178" class="html-bibr">42</a>]) for the over fish mask setting.</p>
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<p>Results of inpainting obscured fish images.</p>
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23 pages, 6469 KiB  
Article
Spatio-Temporal Evolution and Interactive Relationship Between Digital Economy and Green Development in China
by Tingting Chen, Chunyan Lu, Yuting Lai, Mengxing Zhou, Qingping Hu, Tingyan Wang and Lingxin Bao
Appl. Sci. 2024, 14(23), 11030; https://doi.org/10.3390/app142311030 - 27 Nov 2024
Viewed by 531
Abstract
A digital economy parallel with green development holds profound significance for achieving sustainability. The primary objective of this study was to explore the synergistic interaction effects between the digital economy and green development in China and forecast their future development. This study analyzed [...] Read more.
A digital economy parallel with green development holds profound significance for achieving sustainability. The primary objective of this study was to explore the synergistic interaction effects between the digital economy and green development in China and forecast their future development. This study analyzed the spatio-temporal characteristics of provincial digital economy and green development in China by integrating a combined assignment method, an unconditional spatial kernel density estimation method, and a standard deviation ellipse model. The interplay between the digital economy and green development was examined using a panel vector autoregression model. Additionally, digital economy and green development levels were forecasted using univariate time series and radial basis function kernel ε-support vector regression models. The results indicate that both the digital economy and green development levels in China exhibited an upward trend from 2013 to 2021, with the digital economy increasing at a faster rate. However, both domains demonstrated regional disparities in their development processes. The mutual interaction between the digital economy and green development intensified as the lag period increased. The digital economy contributed 21% to green development, whereas green development contributed 18% to the digital economy. The initial effect of the digital economy on green development was negative, however, this impact gradually diminished over time. Additionally, the influence of green development on the digital economy was shown to follow a consistent trend of transitioning from negative to positive across the eastern, central, and western regions. Therefore, it can be seen that the digital economy exerts a sustainable impact on green development, albeit with a one-phase lag. This research provides a scientific basis for the deep integration of the digital economy and green development, thereby fostering sustainable socioeconomic growth. Full article
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<p>Spatial distribution of the DE and GD levels in 2013, 2017, and 2021. (<b>a</b>) Spatial distribution of the DE level in 2013, 2017, and 2021. (<b>b</b>) Spatial distribution of the GD level in 2013, 2017, and 2021.</p>
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<p>Spatial kernel density and density contours of the DE level in different periods. (<b>a</b>) Spatial kernel density and density contours of the DE level in 2013–2017. (<b>b</b>) Spatial kernel density and density contours of the DE level in 2017–2021.</p>
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<p>Spatial kernel density and density contours of the GD level in different periods. (<b>a</b>) Spatial kernel density and density contours of the GD level in 2013–2017. (<b>b</b>) Spatial kernel density and density contours of the GD level in 2017–2021.</p>
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<p>Standard deviation ellipse and gravity center shifted the trajectory of the DE and GD levels from 2013 to 2021. (<b>a</b>) Standard deviation ellipse and gravity center shifted the trajectory of the DE level from 2013 to 2021. (<b>b</b>) Standard deviation ellipse and gravity center shifted the trajectory of the GD level from 2013 to 2021.</p>
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<p>Impulse response function in the eastern region. (<b>a</b>) Impulse response function of DE to DE. (<b>b</b>) Impulse response function of DE to GD. (<b>c</b>) Impulse response function of GD to DE. (<b>d</b>) Impulse response function of GD to GD. (The black solid line is an impulse response curve that reflects the response effect of the variable to an impact, and the upper and lower black dashed lines represent confidence intervals of two standard deviations, estimates of 95% and 5% quantiles, respectively. The red dashed line represents the position where the response level is 0. The same is true for other impulse response graphs).</p>
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<p>Impulse response function in the central region. (<b>a</b>) Impulse response function of DE to DE. (<b>b</b>) Impulse response function of DE to GD. (<b>c</b>) Impulse response function of GD to DE. (<b>d</b>) Impulse response function of GD to GD.</p>
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<p>Impulse response function in the western region. (<b>a</b>) Impulse response function of DE to DE. (<b>b</b>) Impulse response function of DE to GD. (<b>c</b>) Impulse response function of GD to DE. (<b>d</b>) Impulse response function of GD to GD.</p>
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<p>Change in the 2020–2023 provincial DE level.</p>
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<p>Results of the linear regression correlation coefficients between the training set and test set in each province.</p>
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<p>Changes in the GD level in provincial areas from 2021 to 2023.</p>
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12 pages, 723 KiB  
Article
Pregnancy-Associated Plasma Protein A (PAPP-A) as a Predictor of Third Trimester Obesity: Insights from the CRIOBES Project
by Inmaculada Gabaldón-Rodríguez, Carmen de Francisco-Montero, Inmaculada Menéndez-Moreno, Álvaro Balongo-Molina, Ana Isabel Gómez-Lorenzo, Rubén Rodríguez-García, Ángel Vilches-Arenas and Manuel Ortega-Calvo
Pathophysiology 2024, 31(4), 631-642; https://doi.org/10.3390/pathophysiology31040046 - 15 Nov 2024
Viewed by 721
Abstract
Introduction: Our objective in this article was to develop a predictive model for obesity in the third trimester of pregnancy using the plasma and clinical biomarkers that are managed within the Chromosomopathies Programme in the Andalusian Public Healthcare System. Methods: The epidemiological design [...] Read more.
Introduction: Our objective in this article was to develop a predictive model for obesity in the third trimester of pregnancy using the plasma and clinical biomarkers that are managed within the Chromosomopathies Programme in the Andalusian Public Healthcare System. Methods: The epidemiological design was observational, of the unmatched case–control type. The geographical environment was the Seville Primary Healthcare District (DSAP Sevilla). The information was collected between 2011 and 2021. The reference cohort consisted of women who had carried a pregnancy to term. The variables and biomarkers studied correspond to those managed within the primary-care Pregnancy Integrated Care Pathway (ICP). Unconditional binary logistic regression (BLR) models were created, with the outcome variable being whether or not the women were obese in their third trimester of pregnancy. Results: A total of 423 controls and 104 cases of obesity were obtained for women in their third trimester who had not been obese in their first trimester. The average age for the sample group (P50) was 34 years old. The final, most parsimonious model included the variables PAPP-A (p = 0.074), beta-hCG (p = 0.1631), and systolic blood pressure (SBP) (p = 0.085). ROC curve = 0.75 (C.I. at 95%: 0.63–0.86). Discussion: The results of this research can only be extrapolated to primary care and to pregnancies with no complications. PAPP-A has been shown in our research to be a significant predictor of obesity risk in the third trimester of pregnancies with no complications (OR = 0.53; C.I. at 95%: 0.39–0.66; p = 0.04 in the single-variant study; OR = 0.58; C.I. at 95%: 0.29–0.93; p = 0.074 in the multi-variant analysis). This predictive capacity is further enhanced from an operational perspective by beta-hCG and 12-week SBP. Full article
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<p>Week of pregnancy when screening was performed (discrete quantitative variable). Measured according to information from DIRAYA or the chromosomal screening. A total of 409 records were taken between the 10th and 11th week of pregnancy (78.8%).</p>
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<p>Model ROC curve from <a href="#pathophysiology-31-00046-t005" class="html-table">Table 5</a> (most parsimonious).</p>
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<p>Calibration graph of most parsimonious model shown in <a href="#pathophysiology-31-00046-t005" class="html-table">Table 5</a> (three predictor variables; <span class="html-italic">x</span>-axis predicted probabilities; <span class="html-italic">y</span>-axis observed data).</p>
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19 pages, 1393 KiB  
Article
Compact ADI Difference Scheme for the 2D Time Fractional Nonlinear Schrödinger Equation
by Zulayat Abliz, Rena Eskar, Moldir Serik and Pengzhan Huang
Fractal Fract. 2024, 8(11), 658; https://doi.org/10.3390/fractalfract8110658 - 12 Nov 2024
Viewed by 709
Abstract
In this paper, we will introduce a compact alternating direction implicit (ADI) difference scheme for solving the two-dimensional (2D) time fractional nonlinear Schrödinger equation. The difference scheme is constructed by using the L123 formula to approximate the Caputo [...] Read more.
In this paper, we will introduce a compact alternating direction implicit (ADI) difference scheme for solving the two-dimensional (2D) time fractional nonlinear Schrödinger equation. The difference scheme is constructed by using the L123 formula to approximate the Caputo fractional derivative in time and the fourth-order compact difference scheme is adopted in the space direction. The proposed difference scheme with a convergence accuracy of O(τ1+α+hx4+hy4)(α(0,1)) is obtained by adding a small term, where τ, hx, hy are the temporal and spatial step sizes, respectively. The convergence and unconditional stability of the difference scheme are obtained. Moreover, numerical experiments are given to verify the accuracy and efficiency of the difference scheme. Full article
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<p>Contour plots of the numerical errors when <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mi>N</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> for different values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>Contour plots of the numerical errors when <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mi>N</mi> <mo>=</mo> <mn>100</mn> </mrow> </semantics></math> for different values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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20 pages, 2860 KiB  
Article
Experimental Investigation of Indirect Tensile Strength of Hot Mix Asphalt with Varying Hydrated Lime Content at Low Temperatures and Prediction with Soft-Computing Models
by Mustafa Sinan Yardım, Betül Değer Şitilbay and Mehmet Ozan Yılmaz
Buildings 2024, 14(11), 3569; https://doi.org/10.3390/buildings14113569 - 9 Nov 2024
Viewed by 714
Abstract
If asphalt pavements are exposed to cold weather conditions and high humidity for long periods of time, cracking of the pavement is an inevitable consequence. In such cases, it would be a good decision to focus on the filler material, which plays an [...] Read more.
If asphalt pavements are exposed to cold weather conditions and high humidity for long periods of time, cracking of the pavement is an inevitable consequence. In such cases, it would be a good decision to focus on the filler material, which plays an important role in the performance variation in the hot asphalt mixtures used in the pavement. Although the use of hydrated lime as a filler material in hot asphalt mixtures is a common method frequently recommended to eliminate the adverse effects of low temperature and to keep moisture sensitivity under control in asphalt pavements, the sensitivity of the quantities of the material cannot be ignored. Therefore, in this study, an amount of filler in the mixture was replaced with hydrated lime (HL) filler additive at different rates of 0%, 1%, 2%, 3% and 4%. These asphalt briquettes, designed according to the Marshall method, have optimum asphalt contents for samples with specified HL content. In this study, where the temperature effect was examined at five different levels of −10 °C, −5 °C, 0 °C, 5 °C and 25 °C, the samples were produced in two different groups, conditioned and unconditioned, in order to examine the effect of water. The indirect tensile strength (ITS) test was applied on the produced samples. Experimental study showed that HL additive strengthened the material at low temperatures and made it more resistant to cold weather conditions and humidity. In the second part of the study, two different prediction models with varying configurations were introduced using nonlinear regression and feed-forward neural networks (FFNNs) and the best prediction performance among these was investigated. Examination of the performance measures of the prediction models indicated that ITS can be accurately predicted using both methods. As a result of comparing the developed models with the experimental data, the model provides significant contributions to the evaluation of the relationship between the ITS values obtained with the specified conditioning, temperature changes and HL contents. Full article
(This article belongs to the Section Building Materials, and Repair & Renovation)
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<p>Gradation curve of the aggregates used in the specimens and specification limits.</p>
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<p>Experimental setup for indirect tensile strength test.</p>
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<p>Specimens tested in the experimental program.</p>
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<p>Process of preparation of asphalt briquettes and application of indirect tensile strength test.</p>
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<p>Comparison of void ratio of hydrated lime and mineral filler.</p>
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<p>Experimental ITS results of 150 specimens (50 unique sets) with varying temperature, conditioning status and HL content.</p>
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<p>Comparison of the predicted indirect tensile strength and predicted values by regression models with varying exponents.</p>
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<p>Illustrative scheme of FFNN with 3 inputs and 1 output.</p>
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<p>Illustration of data partition for 5-fold cross-validation.</p>
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<p>Comparison of the predicted results by FFNN with experimental observations.</p>
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23 pages, 1969 KiB  
Article
A Novel Fourth-Order Finite Difference Scheme for European Option Pricing in the Time-Fractional Black–Scholes Model
by Xin Cai and Yihong Wang
Mathematics 2024, 12(21), 3343; https://doi.org/10.3390/math12213343 - 25 Oct 2024
Viewed by 826
Abstract
This paper addresses the valuation of European options, which involves the complex and unpredictable dynamics of fractal market fluctuations. These are modeled using the α-order time-fractional Black–Scholes equation, where the Caputo fractional derivative is applied with the parameter α ranging from 0 [...] Read more.
This paper addresses the valuation of European options, which involves the complex and unpredictable dynamics of fractal market fluctuations. These are modeled using the α-order time-fractional Black–Scholes equation, where the Caputo fractional derivative is applied with the parameter α ranging from 0 to 1. We introduce a novel, high-order numerical scheme specifically crafted to efficiently tackle the time-fractional Black–Scholes equation. The spatial discretization is handled by a tailored finite point scheme that leverages exponential basis functions, complemented by an L1-discretization technique for temporal progression. We have conducted a thorough investigation into the stability and convergence of our approach, confirming its unconditional stability and fourth-order spatial accuracy, along with (2α)-order temporal accuracy. To substantiate our theoretical results and showcase the precision of our method, we present numerical examples that include solutions with known exact values. We then apply our methodology to price three types of European options within the framework of the time-fractional Black–Scholes model: (i) a European double barrier knock-out call option; (ii) a standard European call option; and (iii) a European put option. These case studies not only enhance our comprehension of the fractional derivative’s order on option pricing but also stimulate discussion on how different model parameters affect option values within the fractional framework. Full article
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<p>The convergence order of the <math display="inline"><semantics> <msup> <mi>l</mi> <mn>2</mn> </msup> </semantics></math> norm. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.4</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.8</mn> </mrow> </semantics></math>.</p>
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<p>TFPS for <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.25</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.5</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.75</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> at <span class="html-italic">t</span> = 1. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.25</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.5</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.75</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1</mn> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>. (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>The convergence order of the <math display="inline"><semantics> <msup> <mi>l</mi> <mn>2</mn> </msup> </semantics></math> norm. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.4</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.6</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.8</mn> </mrow> </semantics></math>.</p>
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<p>TFPS for <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.25</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.5</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.75</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1</mn> </mrow> </semantics></math>. (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> at <span class="html-italic">t</span> = 1. (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>0.25</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.5</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>0.75</mn> <mo>,</mo> <mspace width="0.166667em"/> <mn>1</mn> </mrow> </semantics></math>. (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> at <span class="html-italic">t</span> = 1. (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>Double barrier option prices obtained by TFPS. (<b>a</b>) Different <math display="inline"><semantics> <mi>α</mi> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>σ</mi> <mo>=</mo> <mn>0.45</mn> </mrow> </semantics></math>. (<b>b</b>) Different <math display="inline"><semantics> <mi>σ</mi> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>,<b>b</b>) call option prices for different <math display="inline"><semantics> <mi>α</mi> </semantics></math> values. (<b>c</b>,<b>d</b>) put option prices for different <math display="inline"><semantics> <mi>α</mi> </semantics></math> values.</p>
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<p>(<b>a</b>) call option price with different <math display="inline"><semantics> <mi>σ</mi> </semantics></math> values. (<b>b</b>) put option price with different <math display="inline"><semantics> <mi>σ</mi> </semantics></math> values. (<b>c</b>) call option price with different <span class="html-italic">r</span> values. (<b>d</b>) put option price with different <span class="html-italic">r</span> values; (<b>e</b>) call option price with different <span class="html-italic">K</span> values. (<b>f</b>) put option price with different <span class="html-italic">K</span> values.</p>
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<p>(<b>a</b>,<b>b</b>) the numerical solution of the TFPS for call option prices in <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>. (<b>c</b>,<b>d</b>) the numerical solution of the TFPS for put option prices in <math display="inline"><semantics> <mrow> <mi>T</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
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15 pages, 333 KiB  
Review
Critical Points in the Noiseberg Achievable Region of the Gaussian Z-Interference Channel
by Max H. M. Costa, Chandra Nair and David Ng
Entropy 2024, 26(11), 898; https://doi.org/10.3390/e26110898 - 23 Oct 2024
Viewed by 547
Abstract
The Gaussian signaling strategy with power control for the Gaussian Z-interference channel with weak interference is reviewed in this paper. In particular, we study the various communication strategies that may arise at various points of the capacity region and identify the locations of [...] Read more.
The Gaussian signaling strategy with power control for the Gaussian Z-interference channel with weak interference is reviewed in this paper. In particular, we study the various communication strategies that may arise at various points of the capacity region and identify the locations of the phase transitions between the various strategies. The Gaussian Z-interference channel with weak interference is known to have two critical points in its capacity region, where the slope of the region shows a sudden change. They occur at the points of the unconditional maximum rate for one of the users and the maximum rate that can be accommodated by the other user. In this paper, we discuss additional critical points (locations of phase transitions) in the achievable region of this channel. These turn out to be second-order phase transitions, i.e., we do not observe a discontinuous slope in the achievable rate region, but there is a discontinuity in the second derivative of the rate contour of the achievable region. This review paper is mainly based on some of our ITA (Information Theory and Applications Workshop, UCSD, San Diego, CA, USA) papers since 2011. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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Figure 1

Figure 1
<p>Gaussian <span class="html-italic">Z</span>-interference channel.</p>
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<p>Degraded Gaussian interference channel.</p>
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<p>Critical points of the capacity region.</p>
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<p>Phase 1 (Sato’s corner point).</p>
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<p>Phase 2 (Pure superposition strategy).</p>
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<p>Phase 3 (Backoff corner point).</p>
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<p>Phase 4 (The noiseberg strategy).</p>
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<p>Phase 5 (The overflow region).</p>
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<p>Phase 6 (The top boundary of the admissible (<math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>,</mo> <mi>h</mi> </mrow> </semantics></math>) parameter region).</p>
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<p>Phase 7 (Essentially, a portion of the so-called non-naïve time sharing).</p>
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<p>Contour of admissible region for a Z-interference channel with <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, i.e., a degraded channel with <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>Contourof the admissible region (blue lines) and optimized points (red lines; obtained numerically) for a Z-interference channel with <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <msqrt> <mn>2</mn> </msqrt> <mn>2</mn> </mfrac> </mstyle> </mrow> </semantics></math>, i.e., a degraded channel with <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Admissible region (blue lines) and optimized points (red lines; obtained numerically) for a Z-interference channel with <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1.25</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <msqrt> <mn>2</mn> </msqrt> </mfrac> </mstyle> </mrow> </semantics></math>, i.e., a degraded channel with <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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<p>Admissible region (blue lines) and optimized points (red lines; obtained numerically) for a Z-interference channel with <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>Q</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0.25</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> </semantics></math>, i.e., a degraded channel with <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>.</p>
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<p>Boundaries between pure superposition and multiplex regions for different values of <math display="inline"><semantics> <msub> <mi>Q</mi> <mn>1</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>Q</mi> <mn>2</mn> </msub> </semantics></math>.</p>
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<p>The noiseberg achievable region for <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p>
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