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19 pages, 10997 KiB  
Article
Re-(De)fined Level of Detail for Urban Elements: Integrating Geometric and Attribute Data
by Benjamin Boswick, Zachary Pankratz, Matthew Glowacki and Yuhao Lu
Architecture 2025, 5(1), 1; https://doi.org/10.3390/architecture5010001 - 25 Dec 2024
Viewed by 289
Abstract
The level of detail (LOD) differentiates multi-scale representations of virtual 3D city models; however, the LOD tends to relay primarily the geometric details of buildings. When the LOD extends to other datasets, such as vegetation, transportation, terrain, water bodies, and city furniture, their [...] Read more.
The level of detail (LOD) differentiates multi-scale representations of virtual 3D city models; however, the LOD tends to relay primarily the geometric details of buildings. When the LOD extends to other datasets, such as vegetation, transportation, terrain, water bodies, and city furniture, their LODs are not as clearly defined. Despite the general acceptance of this categorization, existing LOD formats also neglect non-geometric attributes. Integrating geometric and attribute data enables geometrically accurate and data-rich 3D models, ensuring that representations are as accurate as possible and that analyses contain as much information as possible. This paper proposes a family of LOD definitions considering both geometric and attribute data based on the geometric complexity and difficulty of obtaining, archiving, processing, and distributing the data. These definitions are intended to apply to all datasets by determining divisions in the LOD typically experienced across urban 3D model elements and their associated datasets, including buildings, vegetation, roads, relief, water bodies, and city furniture. Universally applicable definitions for datasets allow individuals to recreate studies or representations of 3D models to ensure the relevant data are present. These definitions also assist data providers in evaluating their data infrastructure and further strategizing and prioritizing updates or upgrades. Full article
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Figure 1
<p>Geometric and attribute data LOD conceptual matrix.</p>
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<p>LOD graphical definitions of buildings. In addition to geometric form, different examples of attributes are represented by different colour palettes and gradients. The model spans a 30 by 30 m area to represent a variety of buildings of (<b>a</b>) LOD 0.0, (<b>b</b>) LOD 1.1, (<b>c</b>) LOD 2.2 and (<b>d</b>) LOD 3.3.</p>
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<p>LOD graphical definitions of vegetation. In addition to geometric form, different examples of attributes are represented by different colour palettes and gradients. The model spans a 30 by 30 m area to represent the spatial distribution of street vegetation of (<b>a</b>) LOD 0.0, (<b>b</b>) LOD 1.1, (<b>c</b>) LOD 2.2 and (<b>d</b>) LOD 3.3.</p>
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<p>LOD graphical definitions of transportation (roads) of (<b>a</b>) LOD 0.0, (<b>b</b>) LOD 1.1, (<b>c</b>) LOD 2.2 and (<b>d</b>) LOD 3.3. In addition to geometric form, different examples of attributes are represented by different colour palettes and gradients. The model spans a 30 by 30 m area to represent the spatial layout of a typical street.</p>
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<p>LOD graphical definitions of relief (terrain) of (<b>a</b>) LOD 0.0 (not applicable in this case), (<b>b</b>) LOD 1.1, (<b>c</b>) LOD 2.2 and (<b>d</b>) LOD 3.3. In addition to geometric form, different examples of attributes are represented by different colour palettes and gradients. The model represents a 100 m by 100 m area to accurately depict topographical variations and avoid a featureless appearance.</p>
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<p>LOD graphic definition of water bodies of (<b>a</b>) LOD 0.0, (<b>b</b>) LOD 1.1, (<b>c</b>) LOD 2.2 and (<b>d</b>) LOD 3.3. In addition to geometric form, different examples of attributes are represented by different colour palettes and gradients. The model spans a 100 by 100 m area to accurately depict a permanent water body.</p>
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<p>LOD graphical definitions of city furniture of (<b>a</b>) LOD 0.0, (<b>b</b>) LOD 1.1, (<b>c</b>) LOD 2.2 and (<b>d</b>) LOD 3.3. In addition to geometric form, different examples of attributes are represented by different colour palettes and gradients. The model spans a 30 by 30 m area to represent the spatial distribution and arrangement of city furniture along a typical street.</p>
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<p>An example of an urban canopy density model featuring multiple tree types.</p>
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<p>An example of a building density distribution model featuring multiple building types.</p>
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17 pages, 352 KiB  
Article
Parametric Inference in Biological Systems in a Random Environment
by Manuel Molina-Fernández and Manuel Mota-Medina
Axioms 2024, 13(12), 883; https://doi.org/10.3390/axioms13120883 - 20 Dec 2024
Viewed by 346
Abstract
This research focuses on biological systems with sexual reproduction in which female and male individuals coexist together, forming female–male couples with the purpose of procreation. The couples can originate new females and males according to a certain probability law. Consequently, in this type [...] Read more.
This research focuses on biological systems with sexual reproduction in which female and male individuals coexist together, forming female–male couples with the purpose of procreation. The couples can originate new females and males according to a certain probability law. Consequently, in this type of biological systems, two biological phases are involved: a mating phase in which the couples are formed, and a reproduction phase in which the couples, independently of the others, originate new offspring of both sexes. Due to several environmental factors of a random nature, these phases usually develop over time in a non-predictable (random) environment, frequently influenced by the numbers of females and males in the population and by the number of couples participating in the reproduction phase. In order to investigate the probabilistic evolution of these biological systems, in previous papers, by using a methodology based on branching processes, we had introduced a new class of two-sex mathematical models. Some probabilistic properties and limiting results were then established. Additionally, under a non-parametric statistical framework, namely, not assuming to have known the functional form of the offspring law, estimates for the main parameters affecting the reproduction phase were determined. We now continue this research line focusing the attention on the estimation of such reproductive parameters under a parametric statistical setting. In fact, we consider offspring probability laws belonging to the family of bivariate power series distributions. This general family includes the main probability distributions used to describe the offspring dynamic in biological populations with sexual reproduction. Under this parametric context, we propose accurate estimates for the parameters involved in the reproduction phase. With the aim of assessing the quality of the proposed estimates, we also determined optimal credibility intervals. For these purposes, we apply the Bayesian estimation methodology. As an illustration of the methodology developed, we present a simulated study about the demographic dynamics of Labord’s chameleon populations, where a sensitivity analysis on the prior density is included. Full article
(This article belongs to the Special Issue Advances in Mathematical Modeling and Related Topics)
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Figure 1
<p>Evolution of the numbers of females (left plot, black line) and males (left plot, red line), couples (right plot, black line), and progenitor couples (right plot, red line).</p>
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<p>Evolution of estimations (solid lines with points) and 95% HPD intervals (dashed lines) of <math display="inline"><semantics> <msubsup> <mi>μ</mi> <mn>1</mn> <mn>1</mn> </msubsup> </semantics></math> (upper-left plot) and <math display="inline"><semantics> <msubsup> <mi>μ</mi> <mn>2</mn> <mn>1</mn> </msubsup> </semantics></math> (upper-right plot) and <math display="inline"><semantics> <msubsup> <mi>μ</mi> <mn>1</mn> <mn>2</mn> </msubsup> </semantics></math> (bottom-left plot) and <math display="inline"><semantics> <msubsup> <mi>μ</mi> <mn>2</mn> <mn>2</mn> </msubsup> </semantics></math> (bottom-right plot). Calculations made with prior (a) appear in black color, and those made with prior (b) appear in red color. Horizontal black lines show the true values for the parameters.</p>
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<p>Evolution of estimations (solid lines with points) and 95% HPD intervals (dashed lines) of <math display="inline"><semantics> <msubsup> <mi>σ</mi> <mrow> <mn>11</mn> </mrow> <mn>1</mn> </msubsup> </semantics></math> (upper-left plot) and <math display="inline"><semantics> <msubsup> <mi>σ</mi> <mrow> <mn>11</mn> </mrow> <mn>2</mn> </msubsup> </semantics></math> (upper-right plot), <math display="inline"><semantics> <msubsup> <mi>σ</mi> <mrow> <mn>22</mn> </mrow> <mn>1</mn> </msubsup> </semantics></math> (middle-left plot) and <math display="inline"><semantics> <msubsup> <mi>σ</mi> <mrow> <mn>22</mn> </mrow> <mn>2</mn> </msubsup> </semantics></math> (middle-right plot), and <math display="inline"><semantics> <msubsup> <mi>σ</mi> <mrow> <mn>12</mn> </mrow> <mn>1</mn> </msubsup> </semantics></math> (bottom-left plot) and <math display="inline"><semantics> <msubsup> <mi>σ</mi> <mrow> <mn>12</mn> </mrow> <mn>2</mn> </msubsup> </semantics></math> (bottom-right plot). Calculations made with prior (a) appear in black color, and those made with prior (b) appear in red color. Horizontal black lines show the true values of the parameters.</p>
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35 pages, 3685 KiB  
Review
Molecular Basis of Na, K–ATPase Regulation of Diseases: Hormone and FXYD2 Interactions
by Bárbara Martins Cordeiro, Carlos Frederico Leite Fontes and José Roberto Meyer-Fernandes
Int. J. Mol. Sci. 2024, 25(24), 13398; https://doi.org/10.3390/ijms252413398 - 13 Dec 2024
Viewed by 620
Abstract
The Na, K–ATPase generates an asymmetric ion gradient that supports multiple cellular functions, including the control of cellular volume, neuronal excitability, secondary ionic transport, and the movement of molecules like amino acids and glucose. The intracellular and extracellular levels of Na+ and [...] Read more.
The Na, K–ATPase generates an asymmetric ion gradient that supports multiple cellular functions, including the control of cellular volume, neuronal excitability, secondary ionic transport, and the movement of molecules like amino acids and glucose. The intracellular and extracellular levels of Na+ and K+ ions are the classical local regulators of the enzyme’s activity. Additionally, the regulation of Na, K–ATPase is a complex process that occurs at multiple levels, encompassing its total cellular content, subcellular distribution, and intrinsic activity. In this context, the enzyme serves as a regulatory target for hormones, either through direct actions or via signaling cascades triggered by hormone receptors. Notably, FXYDs small transmembrane proteins regulators of Na, K–ATPase serve as intermediaries linking hormonal signaling to enzymatic regulation at various levels. Specifically, members of the FXYD family, particularly FXYD1 and FXYD2, are that undergo phosphorylation by kinases activated through hormone receptor signaling, which subsequently influences their modulation of Na, K–ATPase activity. This review describes the effects of FXYD2, cardiotonic steroid signaling, and hormones such as angiotensin II, dopamine, insulin, and catecholamines on the regulation of Na, K–ATPase. Furthermore, this review highlights the implications of Na, K–ATPase in diseases such as hypertension, renal hypomagnesemia, and cancer. Full article
(This article belongs to the Special Issue The Na, K-ATPase in Health and Disease)
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Figure 1

Figure 1
<p><b>Crystal structure of the Na, K–ATPase in the E1.Mg<sup>2+</sup> state</b>. Panels (<b>A</b>,<b>B</b>) show the Na, K–ATPase from pig kidney viewed from two orthogonal directions. The enzyme consists of a catalytic α-subunit (orange), a glycosylated β-subunit (maroon), and a regulatory FXYD protein, specifically FXYD2 (yellow), located behind the α-subunit. The α-subunit comprises three well-defined cytoplasmic domains (A-blue, N-red, and P-gray) and 10 transmembrane helices (M1–M10). The helices are not labeled with numbers. Panel (<b>C</b>) highlights residues (pink) in the M9 region of the α subunit that interact with the corresponding FXYD peptides and are important for forming a stable complex [<a href="#B13-ijms-25-13398" class="html-bibr">13</a>]. Panel (<b>D</b>) shows the RRNS motif of the Na, K–ATPase α1 isoform, where Ser936 is phosphorylated by PKA [<a href="#B13-ijms-25-13398" class="html-bibr">13</a>]. Protein Data Bank (PDB) ID: 8JBL.</p>
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<p><b>Scheme of catalytic cycle of Na, K–ATPase</b>. Panel (<b>A</b>,<b>B</b>) represent the simplified Post–Albers model [<a href="#B11-ijms-25-13398" class="html-bibr">11</a>] that outlines the process of ATP hydrolysis and ion transport by the Na, K–ATPase. This enzyme alternates between two conformations, E1 and E2. In the forward cycle (clockwise), the Na, K–ATPase first binds intracellular Na<sup>+</sup> and MgATP with high affinity, forming the Na3E1ATP complex (Mg ions are not shown). The γ-phosphate of ATP is then transferred to the enzyme, and Na<sup>+</sup> ions become occluded (represented by parentheses). The resulting (Na3)E1-P<sup>•</sup>ADP complex has a high-energy phosphate bond, making the reaction reversible. After ADP is released, Na<sup>+</sup> ions are deoccluded and expelled into the extracellular space following or alongside the enzyme’s conformational shift in the enzyme to E2-P. This E2-P conformation also serves as the binding site for OUA, a well-known inhibitor of Na, K–ATPase. Extracellular K<sup>+</sup> then binds to E2-P, promoting Pi release and K<sup>+</sup> occlusion as they travel to the cytosol (protons, which are thought to bind to the “third Na<sup>+</sup> site” with two K<sup>+</sup> ions, are not shown). ATP, acting with low apparent affinity, accelerates K<sup>+</sup> deocclusion and intracellular release. The enzyme then shifts back from E2 to E1 and is ready to begin the cycle again.</p>
Full article ">Figure 2 Cont.
<p><b>Scheme of catalytic cycle of Na, K–ATPase</b>. Panel (<b>A</b>,<b>B</b>) represent the simplified Post–Albers model [<a href="#B11-ijms-25-13398" class="html-bibr">11</a>] that outlines the process of ATP hydrolysis and ion transport by the Na, K–ATPase. This enzyme alternates between two conformations, E1 and E2. In the forward cycle (clockwise), the Na, K–ATPase first binds intracellular Na<sup>+</sup> and MgATP with high affinity, forming the Na3E1ATP complex (Mg ions are not shown). The γ-phosphate of ATP is then transferred to the enzyme, and Na<sup>+</sup> ions become occluded (represented by parentheses). The resulting (Na3)E1-P<sup>•</sup>ADP complex has a high-energy phosphate bond, making the reaction reversible. After ADP is released, Na<sup>+</sup> ions are deoccluded and expelled into the extracellular space following or alongside the enzyme’s conformational shift in the enzyme to E2-P. This E2-P conformation also serves as the binding site for OUA, a well-known inhibitor of Na, K–ATPase. Extracellular K<sup>+</sup> then binds to E2-P, promoting Pi release and K<sup>+</sup> occlusion as they travel to the cytosol (protons, which are thought to bind to the “third Na<sup>+</sup> site” with two K<sup>+</sup> ions, are not shown). ATP, acting with low apparent affinity, accelerates K<sup>+</sup> deocclusion and intracellular release. The enzyme then shifts back from E2 to E1 and is ready to begin the cycle again.</p>
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<p><b>Representation of the chemical structures of hormones that regulate Na, K–ATPase</b>. The structures are represented as follows: Angiotensin II in green, dopamine in pink, epinephrine in yellow, norepinephrine in salmon, thyroxine in purple, and the three-dimensional structure of insulin (PDB: 1WAV). Oxygen atoms are shown in red, nitrogen atoms in blue, and iodine-123 in purple. The small molecule structures were obtained from ChemSpider, with CSIDs 150504, 661, 5611, 388394, and 64880242, respectively.</p>
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<p><b>Ang II induces multiple signaling pathways that regulate Na, K–ATPase activity</b>. In the adenylate cyclase–cAMP–PKA pathway, the phosphorylation of the α subunit by PKA inhibits Na, K–ATPase activity. Stimulatory effect of Ang II via the AT1R. The GRK4 increased phosphorylation of AT2R is associated with the inhibition of Na, K–ATPase. A signaling pathway involving PKC and the interaction of Na, K–ATPase with the adaptor protein 1 (AP1) recruits Na, K–ATPase molecules to the plasma membrane.</p>
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<p><b>Schematic diagram of the role of Na, K–ATPase in cell adhesion in different cancer types</b>. Blue line shows that Na<sup>+</sup> pump inhibition by CTS reduces cell adhesion in renal cells, leading to decreased expression and enzymatic activity, which is linked to cancer progression. Pink line shows that the overexpression β<sub>2</sub> isoform increased cellular adhesion on glia and ovary, arresting cancer progression.</p>
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<p><b>Signaling pathways of Na, K–ATPase and their consequences in cancer</b>. The inhibition of Na, K–ATPase by ouabain (red boxes) and the combined treatment with digoxin and cisplatin (green boxes) activate the Src/EGFR pathway, which leads to the activation of ERK and increased ROS production in mitochondria. This activates NF-κB, resulting in transcriptional regulation. EGFR phosphorylated activates the PKC pathway. Ouabain decreases the expression of alpha and beta subunits, while the combined treatment with digoxin and cisplatin has antitumoral effects. Solid arrows indicate experimentally supported events induced by inhibitors mentioned, while broken arrows indicate events with limited or indirect support.</p>
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16 pages, 4260 KiB  
Article
Comparative Study of (Fe,Nb)MoTaTiZr High Entropy Alloys in Ringer Grifols Solution
by Miguel Lopez-Rios, Santiago Brito-Garcia, Julia Mirza-Rosca and Ionelia Voiculescu
Metals 2024, 14(12), 1430; https://doi.org/10.3390/met14121430 - 13 Dec 2024
Viewed by 476
Abstract
High-entropy alloys (HEAs) are a family of materials that, because of their particular characteristics and possible uses in a variety of industries, have garnered a lot of interest recently. One such promising HEA is the MoNbTaTiZr high-entropy alloy, which displays excellent corrosion resistance [...] Read more.
High-entropy alloys (HEAs) are a family of materials that, because of their particular characteristics and possible uses in a variety of industries, have garnered a lot of interest recently. One such promising HEA is the MoNbTaTiZr high-entropy alloy, which displays excellent corrosion resistance and biocompatibility alongside good mechanical properties. Another promising HEA that has attracted researchers for its potential applications in various fields is FeMoTaTiZr. Exchanging one of the elements may result in important variation of properties of a material. This work studies two different samples of high-entropy alloys, MoNbTaTiZr (named NbHEA) and FeMoTaTiZr (named FeHEA), both generated in a laboratory context using electric-arc remelting technology, keeping similar atomic percentage of the elements in both alloys. Optical microscopy and scanning electron microscopy techniques were used to characterize the microstructure of the alloys. Replacing Nb for Fe affects the distribution proportion of the other four elements, since Fe has a higher tendency than Nb to form part of the inter-dendrite region. An evaluation of the properties related to the corrosion process was accomplished using the polarization method along with electrochemical impedance spectroscopy (EIS), performed under a simulated biological environment. As a result, FeHEA showed a higher corrosion rate in simulated body fluid than NbHEA. Full article
(This article belongs to the Special Issue Feature Papers in Entropic Alloys and Meta-Metals)
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Figure 1
<p>Optical microscopy at 20× magnification of (<b>a</b>) FeHEA microstructure and (<b>b</b>) NbHEA microstructure.</p>
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<p>(<b>a</b>) SEM and EDS analysis for Area 1, Area 2, and Area 3 of MoNbTaTiZr high-entropy alloy; (<b>b</b>) compositional spectrum in dendritic areas; (<b>c</b>) compositional spectrum in interdendritic areas.</p>
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<p>(<b>a</b>) SEM and EDS analysis for Area 1, Area 2, and Area 3 of FeMoTaTiZr high-entropy alloy; (<b>b</b>) compositional spectrum in dendritic areas; (<b>c</b>) compositional spectrum in interdendritic areas.</p>
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<p>Open circuit potential variation with time for the two samples FeHEA and NbHEA in Ringer solution.</p>
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<p>Tafel curves for the two samples of FeHEA and NbHEA after 24 h immersion in Ringer solution.</p>
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<p>Nyquist vs. Eocp curves for the two samples of FeHEA and NbHEA.</p>
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<p>Bode Z vs. Eocp curves for the two samples of FeHEA and NbHEA.</p>
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<p>Bode Theta vs. Eocp curves for the two samples of FeHEA and NbHEA.</p>
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<p>Equivalent circuit used for the EIS experimental data and its interpretation in the interface for the two samples of FeHEA and NbHEA.</p>
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<p>HV<sub>0</sub>.<sub>01</sub> microhardness test results for sample of (<b>a</b>) FeHEA and (<b>b</b>) NbHEA.</p>
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16 pages, 6827 KiB  
Article
Habitat Suitability of Danaus genutia Based on the Optimized MaxEnt Model
by Jun Yao, Chengli Zhou, Wenquan Wang, Yangyang Li, Ting Du and Lei Shi
Insects 2024, 15(12), 971; https://doi.org/10.3390/insects15120971 - 5 Dec 2024
Viewed by 723
Abstract
Danaus genutia, commonly known as the tiger butterfly, is a visually appealing species in the Danaidae family. As it is not currently classified as endangered, it is excluded from key protected species lists at national and local levels, limiting focus on its [...] Read more.
Danaus genutia, commonly known as the tiger butterfly, is a visually appealing species in the Danaidae family. As it is not currently classified as endangered, it is excluded from key protected species lists at national and local levels, limiting focus on its population and habitat status, which may result in it being overlooked in local butterfly conservation initiatives. Yunnan, characterized by high butterfly diversity, presents an ideal region for studying habitat suitability for D. genutia, which may support the conservation of regional biodiversity. This study employs the MaxEnt ecological niche model, predictions regarding suitable habitat distribution, and trends for D. genutia and identifying primary environmental factors influencing their distribution. The results indicate that the niche model that includes interspecies relationships provides a distribution prediction closely aligned with the observed range of D. genutia. Under current climatic conditions, highly suitable habitats for both D. genutia and its host plant, Cynanchun annularium, are located predominantly in the Yuanjiang River Valley. Optimal conditions occur at average annual temperatures of 19.80–22 °C for D. genutia and 22–24 °C for C. annularium. The distribution range of C. annularium is a vital biological factor limiting D. genutia’s habitat. By 2040, projections under four future climate scenarios indicate a potential increase in the total area of suitable habitats for D. genutia, with a general trend of northward expansion. Full article
(This article belongs to the Section Insect Ecology, Diversity and Conservation)
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<p>The distribution records of <span class="html-italic">Danaus genutia</span> and <span class="html-italic">Cynanchum annularium</span> in Yunnan.</p>
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<p>Optimization of MaxEnt model parameters using the ENMeval package in R.</p>
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<p>Optimization results for the model by ENMeval (H—Hinge, L—Linear, Q—Quadratic, P—Product, T—Threshold).</p>
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<p>ROC evaluation curve of MaxEnt.</p>
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<p>Prediction of potential suitable habitat distribution of <span class="html-italic">C. annularium</span> and <span class="html-italic">D. genutia</span> with different model structures under current climate conditions in Yunnan.</p>
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<p>Evaluation of the importance of different environmental factors based on the Jackknife test.</p>
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<p>Response curves of existence probability for <span class="html-italic">C. annularium</span> and <span class="html-italic">D. genutia</span> to dominant climatic factors.</p>
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<p>Habitat suitability for <span class="html-italic">D. genutia</span> under future climate scenarios.</p>
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<p>Habitat suitability for <span class="html-italic">D. genutia</span> under future climate change scenarios.</p>
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14 pages, 235 KiB  
Article
Is It Really a Failure? A Survey About Foster Animal Adoption
by Laura A. Reese
Animals 2024, 14(23), 3498; https://doi.org/10.3390/ani14233498 - 4 Dec 2024
Viewed by 466
Abstract
The widespread use of the term “foster fail” in animal rescue suggests that it happens often, but no research has explored the prevalence of volunteers adopting their foster animals or whether the phenomenon is really a “failure”. This survey-based study focused on the [...] Read more.
The widespread use of the term “foster fail” in animal rescue suggests that it happens often, but no research has explored the prevalence of volunteers adopting their foster animals or whether the phenomenon is really a “failure”. This survey-based study focused on the following questions: 1. How common are foster fails among volunteers on shelter and rescue lists and why do they occur? 2. What types of volunteers are most likely to adopt their foster animals? 3. Do different attachment styles to pets affect foster adoption? 4. Is the adoption of foster animals a way to deal with the potential grief of letting them go to adoption? 5. What are the impacts of foster fails on animal shelters in terms of longevity of volunteers and satisfaction with the volunteer experience? Data were collected through surveys of foster volunteers. Two nonprofit organizations, the Pedigree Foundation and Shelter Animals Count, distributed information about the survey and shelter directors distributed the survey link to their population of foster volunteers. Nine hundred and forty-seven individuals responded. To address the research questions, frequency, correlation, and regression analyses were employed. A total of 38% of volunteers had not adopted a foster in the past ten years, and another 38% had adopted one or two; 90 (11%) and 103 (13%) had adopted three to four or more than four, respectively. Volunteers that had significantly higher numbers of foster fails were those that were older (r = 0.22, p < 0.001), retired (chi-squared = 9.05, p = 0.029), lower on educational attainment (r = −0.13, p < 0.001), female with their own cats (r = 0.16, p < 0.001), and part of a fostering family (r = 0.08, p = 0.043). Volunteers that expressed higher levels of both people-substituting (r = 0.16, p = 0.003) and general (r = 0.13, p = 0.017) attachment to their fosters were more likely to adopt them, as were those that more frequently fostered animals with special medical or behavioral needs (r = 0.25, p < 0.001). Volunteers that had longer tenures (r = 0.43, p < 0.001), fostered more frequently (r = 0.24, p < 0.001), and reported greater resilience (r = 0.10, p = 0.009) had adopted significantly more animals. Finally, there was a significant and positive relationship between satisfaction with fostering and adopting more foster animals (r = 0.16, p < 0.001). The findings indicated that instead of being a “failure,” foster adoptions can be a positive force for the animal in question, their adopters, and shelters and rescues because they have more resilient, satisfied, and active volunteers. Full article
(This article belongs to the Section Companion Animals)
14 pages, 5114 KiB  
Article
Immediate Response of Carabids to Small-Scale Wildfire Across a Healthy-Edge-Burnt Gradient in Young Managed Coniferous Forest in Central Europe
by Václav Zumr, Jiří Remeš and Oto Nakládal
Fire 2024, 7(12), 436; https://doi.org/10.3390/fire7120436 - 26 Nov 2024
Viewed by 555
Abstract
Wildfire is a type of disturbance that plays a critical role in affecting forest ecosystems. Wildfires also have a significant effect on shaping arthropods communities. Carabids (family Carabidae) are often used as a bioindicator group of altered biocenoses. Methods: For carabid sampling, pitfall [...] Read more.
Wildfire is a type of disturbance that plays a critical role in affecting forest ecosystems. Wildfires also have a significant effect on shaping arthropods communities. Carabids (family Carabidae) are often used as a bioindicator group of altered biocenoses. Methods: For carabid sampling, pitfall traps were used in three habitats, healthy-edge-burnt, fifteen days after the suppression of wildfire. Seven traps were evenly placed on each transect. In total, twenty-one traps were used for the study. Aim of the study: (i) evaluate the overall diversity of carabids, (ii) sex change and distribution within the studied habitats, (iii) dynamics of pyrophilous carabids. Results: In total, 1051 individuals within 42 species were recorded. The total number of species was higher in the edge and burnt habitats and differed from the healthy habitat. The abundance of carabids did not differ significantly across the three habitats. However, the healthy habitat exhibited both lower species numbers and abundance. Communities, species richness, and diversity indices were similar in the edge and burnt habitats, while the healthy habitat had lower species richness, diversity indices, and more homogenized communities. The overall sex ratio was nearly equal, with females comprising 519 individuals (49.4%) and males 532 individuals (50.6%), showing nonsignificant differences among study habitats. Among the nine most dominant species, a general trend of female dominance was observed. Many species showed different patterns in sex distribution in relation to the study habitats. Pyrophilous species accounted for the majority of individuals, comprising 55% of all carabids in the burnt habitat, predominantly represented by Pterostichus quadrifoveolatus. The rare species Sericoda quadripunctata was observed infrequently with only twenty-three individuals recorded. These two species are highly correlated, potentially indicating their near-habitat requirements. Males of pyrophilous species in general colonize the area in the earliest post-fire period. Conclusions: The immediate response of carabids to forest wildfire is significant, primarily influencing species richness and communities. While wildfire did not affect overall sex distribution, it shaped interspecies sex distribution across the study habitats. Full article
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<p>Location of the study area with the distribution of forest stands affected by the wildfire. Points indicate the location of pitfall traps. The photos show the typical appearance of the study stands.</p>
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<p>A pitfall trap installed in the ground, with dimensions of its parts (cm).</p>
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<p>Number of species (<b>A</b>) and individuals (<b>B</b>) per trap of carabid beetles. Boxes indicate the interquartile range 1–3Q, the solid line in the box represents the median, and the error lines are min–max values. The letters above the bars indicate differences.</p>
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<p>Non-metric multidimensional scaling (NMDS) shows differences in carabid communities between study habitats. Ellipses indicate 95% confidence interval. (*) Indicate sampling units. Solid points are centroids of carabid communities.</p>
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<p>Sample coverage-based rarefaction and extrapolation of species richness (q = 0), the exponential of Shannon’s entropy index (q = 1), and the inverse of Simpson’s concentration index (q = 2). Solid points indicate observed sample coverage with the number of recorded species. Dashed lines indicate extrapolation to 100% sample coverage. Shaded area represents 95% confidence intervals.</p>
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<p>Numbers of individuals per sex (F—female, M—male) among dominant carabid species recorded in the study in three habitats.</p>
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<p>Dominant carabid activity (catches per day over sampling period; events) categorized by sex and study habitats (represented by colored lines). The number of events indicates the intervals of trap exposition and days after the end of wildfire. (1. = 15.5–28.5 (15–28); 2. = 28.5–18.6 (28–49); 3. = 18.6–6.7 (49–67); 4. = 6.7–25.7 (67–86); 5. = 25.7–13.8 (86–105); 6. = 13.8–23.9 (105–146).</p>
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<p>Relationship between two pyrophilous carabid species recorded in the burnt habitat. The shaded area represents the 95% confidence interval.</p>
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25 pages, 6473 KiB  
Article
Birds as Cultural Ambassadors: Bridging Ecosystem Services and Biodiversity Conservation in Wetland Planning
by Michela Ingaramo, Anna Rita Bernadette Cammerino, Vincenzo Rizzi, Maurizio Gioiosa and Massimo Monteleone
Sustainability 2024, 16(23), 10286; https://doi.org/10.3390/su162310286 - 24 Nov 2024
Viewed by 1083
Abstract
Coastal wetlands deliver essential ecosystem services, including cultural services, which provide non-material benefits such as recreation, education, and spiritual enrichment that are crucial for human well-being. This study investigates the cultural ecosystem services provided by a 40 ha coastal wetland in the Gulf [...] Read more.
Coastal wetlands deliver essential ecosystem services, including cultural services, which provide non-material benefits such as recreation, education, and spiritual enrichment that are crucial for human well-being. This study investigates the cultural ecosystem services provided by a 40 ha coastal wetland in the Gulf of Manfredonia, southern Italy, within the Gargano National Park. By integrating an ecological survey of the bird community with a social survey of visitors to the King’s Lagoon Nature Reserve, the content of tailored planning strategies and management tools for the conservation of wetland biodiversity was developed. An ecological analysis of the bird community was carried out on the assumption that it could be representative of the total biodiversity observed in the wetland. On the other hand, a questionnaire was used to collect information from visitors to the reserve, highlighting the aspects of the wetland that they found most interesting and attractive according to their judgement and beliefs, and thus targeting a specific set of cultural ecological services. The two approaches were then combined to develop a comprehensive strategy. The bird community analysis led to the identification of the mixed biotope category (a combination of wetlands, aquatic/riparian ecosystems, semi-natural vegetated areas, and meadows together with agricultural areas) as the reference biotope for prioritizing wetland management. The Ardeidae family was chosen as a bird flagship group because of its high visibility, ease of identification, attractiveness to visitors, wide local distribution, and fairly constant presence in the study area throughout the year. Flagship species have a dual function: to guide conservation measures and actions by wetland managers, and to attract the interest, curiosity and active participation of potential visitors to the wetland. Based on the results, a list of guidelines for improving the birds’ habitats and providing them with resources (feeding, breeding, shelter, roosting, etc.) has been proposed. The aim of these measures is to optimize the presence and abundance of Ardeidae as flagship species, thereby preserving the biodiversity heritage in general and increasing the provision of cultural ecosystem services in the wetland. The resulting dynamic interplay ensures that both natural and cultural resources are fully and appropriately valued, protected, and maintained for the benefit of present and future generations. Full article
(This article belongs to the Topic Mediterranean Biodiversity)
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<p>Methodological planning of the research work. The flow chart was designed by the authors to show the relationships between the three pillars considered in a wetland strategic plan: nature, economy, and culture. Each green arrow indicates the path being studied and the red arrows indicate the links and relationships between them. Two positive loops are generated by matching the ecological analysis with the socio-cultural analysis: feedback (A) a better strategy for ecological conservation and feedback (B) a better strategy for the provision of cultural services.</p>
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<p>Satellite image and planimetric map of King’s Lagoon, the coastal wetland considered in the study case. (<b>A</b>) Location of the study area within the Gargano National Park (southern Italy). (<b>B</b>) Planimetric map displaying the following landcover classes: AGR (agricultural areas); BUILT (built-up areas); NAT (semi-natural vegetation areas and meadows); and WET (wetlands and aquatic/riparian ecosystems). (<b>C</b>) Satellite image of King’s Lagoon.</p>
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<p>Satellite image showing the overlaid regular grid of 67 reference units (one hectare each) used to survey land cover and monitor bird communities in King’s Lagoon, the coastal wetland under study.</p>
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<p>Flow chart showing the overall processing of the statistical data.</p>
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<p>Clustering (circle) of the four wetland biotope categories and display of the wetland cells (dots) according to a principal component plot. The shaded colored area of each cluster encloses the 50% of the observations, while the size of each black line circle is proportional to the count of the observations. Different colors specify the four identified clusters corresponding to the biotope categories: 1. WET (26 cells); 2. NAT (13 cells); 3. MIXED (21 cells), and 4. AGR (4 cells).</p>
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<p>Principal Component Analysis (PCA) performed on the membership values of each taxonomic order of birds (CA, CL, PA, GR, CH, AF, SU, AN, CI, PO, and LS) to their respective categories of biotope (WET, AGR, NAT, and MIXED) identified in the wetland. The list of the bird order code is reported in <a href="#sustainability-16-10286-t004" class="html-table">Table 4</a>.</p>
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<p>(A) Trends in the scores (from 1 to 5) given by visitors to the four selected biotope categories (AGR, NAT, MIXED, and WET) and (B) corresponding average score. Levels not connected with the same letter are significantly different (<span class="html-italic">p</span> &lt; 0.05).</p>
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15 pages, 732 KiB  
Article
It Is Better to Be Semi-Regular When You Have a Low Degree
by Theodore Kolokolnikov
Entropy 2024, 26(12), 1014; https://doi.org/10.3390/e26121014 - 23 Nov 2024
Viewed by 322
Abstract
We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity as well as the full spectrum distribution. For an integer d3,7, we find [...] Read more.
We study the algebraic connectivity for several classes of random semi-regular graphs. For large random semi-regular bipartite graphs, we explicitly compute both their algebraic connectivity as well as the full spectrum distribution. For an integer d3,7, we find families of random semi-regular graphs that have higher algebraic connectivity than random d-regular graphs with the same number of vertices and edges. On the other hand, we show that regular graphs beat semi-regular graphs when d8. More generally, we study random semi-regular graphs whose average degree is d, not necessarily an integer. This provides a natural generalization of a d-regular graph in the case of a non-integer d. We characterize their algebraic connectivity in terms of a root of a certain sixth-degree polynomial. Finally, we construct a small-world-type network of an average degree of 2.5 with relatively high algebraic connectivity. We also propose some related open problems and conjectures. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
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<p>Types of graphs considered in this work. Colour is used for emphasis, with blue vertices having degree 3 and red vertices having degree 2. (<b>a</b>) Random semi-regular bipartite graph with <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>b</b>) Random semi-regular graph with <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <mi>p</mi> <mo>,</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>0.4</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </semantics></math> Both graphs have the same average degree of <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>2.4</mn> </mrow> </semantics></math>. (<b>c</b>) Small-world network consisting of a ring and with edges added at random between the odd-numbered vertices. It has an average degree of <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>2.5</mn> </mrow> </semantics></math>.</p>
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<p>(<b>a</b>) Full spectrum of random semi-regular bipartite graph with <math display="inline"><semantics> <mrow> <mfenced separators="" open="(" close=")"> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> </mfenced> <mo>=</mo> <mfenced separators="" open="(" close=")"> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mfenced> </mrow> </semantics></math>. Numerics correspond to the histogram of eigenvalues of one of such a graph with 1000 vertices, computed numerically using Matlab. Asymptotics correspond to Formula (<a href="#FD3-entropy-26-01014" class="html-disp-formula">3</a>). The height of the lollipop corresponds to the weight delta function at the origin. (<b>b</b>) Comparison of algebraic connectivity between <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mn>3</mn> <mo>,</mo> <mn>3</mn> </mfenced> </semantics></math> regular bipartite, <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mn>2</mn> <mo>,</mo> <mn>6</mn> </mfenced> </semantics></math> semi-regular bipartite graphs, and the asymptotic theory. The two classes have the same number of vertices and edges, and <math display="inline"><semantics> <mfenced separators="" open="(" close=")"> <mn>2</mn> <mo>,</mo> <mn>6</mn> </mfenced> </semantics></math> is 15% better than (3,3) (both for asymptotics and numerics).</p>
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<p>Comparison between RSR, RSRB asymptotics, and RSR numerics, with average degree <math display="inline"><semantics> <mrow> <mn>2</mn> <mo>&lt;</mo> <mi>d</mi> <mo>≤</mo> <mn>3</mn> <mo>.</mo> </mrow> </semantics></math> Numerics represent the AC of 1000 randomly chosen RSR graphs with <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>∈</mo> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </semantics></math>. Here, <math display="inline"><semantics> <mi>μ</mi> </semantics></math> is plotted against <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>2</mn> <mo>+</mo> <mi>p</mi> </mrow> </semantics></math>. Asymptotics for RSR correspond to roots of (<a href="#FD8-entropy-26-01014" class="html-disp-formula">8</a>). Asymptotics for RSRB are given by (<a href="#FD5-entropy-26-01014" class="html-disp-formula">5</a>).</p>
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<p>Distribution of AC for RSR graphs with <math display="inline"><semantics> <mrow> <mfenced separators="" open="(" close=")"> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>d</mi> <mn>2</mn> </msub> </mfenced> <mo>=</mo> <mfenced separators="" open="(" close=")"> <mn>2</mn> <mo>,</mo> <mn>6</mn> </mfenced> </mrow> </semantics></math> and with <span class="html-italic">p</span> as indicated. Average degree <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>2</mn> <mo>+</mo> <mn>4</mn> <mi>p</mi> </mrow> </semantics></math> is also indicated. We used <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>500</mn> </mrow> </semantics></math> nodes and 1000 simulations. <math display="inline"><semantics> <msub> <mi>μ</mi> <mi>numeric</mi> </msub> </semantics></math> is the average of the distribution, whereas <math display="inline"><semantics> <msub> <mi>μ</mi> <mi>asym</mi> </msub> </semantics></math> is the asymptotics according to Main Result 2. Note the multi-peaked shape of the distribution, and the fact that the distribution does not concentrate around the mean when <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>≤</mo> <mn>5</mn> </mrow> </semantics></math>.</p>
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29 pages, 1927 KiB  
Article
Fast Proxy Centers for the Jeffreys Centroid: The Jeffreys–Fisher–Rao Center and the Gauss–Bregman Inductive Center
by Frank Nielsen
Entropy 2024, 26(12), 1008; https://doi.org/10.3390/e26121008 - 22 Nov 2024
Viewed by 489
Abstract
The symmetric Kullback–Leibler centroid, also called the Jeffreys centroid, of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks, including information retrieval, information fusion, and clustering. However, the [...] Read more.
The symmetric Kullback–Leibler centroid, also called the Jeffreys centroid, of a set of mutually absolutely continuous probability distributions on a measure space provides a notion of centrality which has proven useful in many tasks, including information retrieval, information fusion, and clustering. However, the Jeffreys centroid is not available in closed form for sets of categorical or multivariate normal distributions, two widely used statistical models, and thus needs to be approximated numerically in practice. In this paper, we first propose the new Jeffreys–Fisher–Rao center defined as the Fisher–Rao midpoint of the sided Kullback–Leibler centroids as a plug-in replacement of the Jeffreys centroid. This Jeffreys–Fisher–Rao center admits a generic formula for uni-parameter exponential family distributions and a closed-form formula for categorical and multivariate normal distributions; it matches exactly the Jeffreys centroid for same-mean normal distributions and is experimentally observed in practice to be close to the Jeffreys centroid. Second, we define a new type of inductive center generalizing the principle of the Gauss arithmetic–geometric double sequence mean for pairs of densities of any given exponential family. This new Gauss–Bregman center is shown experimentally to approximate very well the Jeffreys centroid and is suggested to be used as a replacement for the Jeffreys centroid when the Jeffreys–Fisher–Rao center is not available in closed form. Furthermore, this inductive center always converges and matches the Jeffreys centroid for sets of same-mean normal distributions. We report on our experiments, which first demonstrate how well the closed-form formula of the Jeffreys–Fisher–Rao center for categorical distributions approximates the costly numerical Jeffreys centroid, which relies on the Lambert W function, and second show the fast convergence of the Gauss–Bregman double sequences, which can approximate closely the Jeffreys centroid when truncated to a first few iterations. Finally, we conclude this work by reinterpreting these fast proxy Jeffreys–Fisher–Rao and Gauss–Bregman centers of Jeffreys centroids under the lens of dually flat spaces in information geometry. Full article
(This article belongs to the Special Issue Information Theory in Emerging Machine Learning Techniques)
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<p>Application of centroids and centers in signal processing. (<b>Left</b>): information fusion and mixture model simplification, a 2D Gaussian mixture model (GMM) is simplified to a single bivariate normal distribution. (<b>Right</b>): distributed estimation, a data set is split among <span class="html-italic">p</span> processes <math display="inline"><semantics> <msub> <mi>P</mi> <mi>i</mi> </msub> </semantics></math>s, which first estimate the statistical model parameters <math display="inline"><semantics> <msub> <mover accent="true"> <mi>θ</mi> <mo stretchy="false">^</mo> </mover> <mi>i</mi> </msub> </semantics></math>s. Then, the processus models are aggregated to yield a single consolidated model <math display="inline"><semantics> <mover accent="true"> <mi>θ</mi> <mo stretchy="false">^</mo> </mover> </semantics></math>.</p>
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<p>Visualizing the arithmetic and normalized geometric and numerical Jeffreys, Jeffreys–Fisher–Rao, and Gauss–Bregman centroids/centers in red, blue, green, purple, and yellow, respectively. (<b>Left</b>): input set consists of <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> trinomial distributions (black) with parameters chosen randomly. (<b>Right</b>): input set consists of <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>32</mn> </mrow> </semantics></math> trinomial distributions (black) with parameters <math display="inline"><semantics> <mrow> <mo>(</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> <mo>,</mo> <mstyle scriptlevel="0" displaystyle="true"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0.99</mn> <mo>,</mo> <mn>0.005</mn> <mo>,</mo> <mn>0.005</mn> <mo>)</mo> </mrow> </semantics></math>. The numerical Jeffreys centroid (green) is time consuming to calculate using the Lambert <span class="html-italic">W</span> function. However, the Jeffreys centroid can be well approximated by either the Jeffreys–Fisher–Rao center (purple) or the inductive Gauss–Bregman center (yellow). Point centers are visualized with different radii in order to distinguish them easily.</p>
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<p>(<b>Left</b>): Displaying the arithmetic and normalized geometric and numerical Jeffreys, Jeffreys–Fisher–Rao, and Gauss–Bregman centroids/centers in red, blue, green, purple, and yellow, respectively. Input sets are two normalized histograms with <math display="inline"><semantics> <mrow> <mi>d</mi> <mo>=</mo> <mn>256</mn> </mrow> </semantics></math> bins plotted as polylines with 255 line segments (black). Observe that the Jeffreys–Fisher–Rao center (purple) and Gauss–Bregman center (yellow) approximates the Jeffreys centroid (green) well, which is more computationally expensive to calculate. (<b>Right</b>): close-up window on the first left bins of normalized histograms.</p>
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<p>Geometric illustration of the double sequence inducing a Gauss–Bregman center in the limit.</p>
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<p>Illustration of the double sequence convergence for scalar Gauss–Bregman <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>A</mi> <mo>,</mo> <msub> <mi>m</mi> <mrow> <mo>∇</mo> <mi>F</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> mean.</p>
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<p>Visualization of the Jeffreys–Fisher–Rao center and Gauss–Bregman center of two univariate normal distributions (black circle). The exponential geodesic and mixture geodesics are shown in red and blue, respectively, with their corresponding midpoints. The Jeffreys–Fisher–Rao is the Fisher–Rao midpoint (green) lying on the Fisher–Rao geodesics (purple). The inductive Gauss–Bregman center is displayed in yellow with double size in order to ease its comparison with the Jeffreys–Fisher–Rao center.</p>
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<p>Centroids and centers between a pair of bivariate normal distributions (black). Each normal distribution <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>(</mo> <mi>μ</mi> <mo>,</mo> <mo>∑</mo> <mo>)</mo> </mrow> </semantics></math> (parameterized by a 5D parameter <math display="inline"><semantics> <mi>θ</mi> </semantics></math>) is displayed as a 2D ellipsoid <math display="inline"><semantics> <mrow> <mi mathvariant="script">E</mi> <mrow> <mo>(</mo> <mi>μ</mi> <mo>,</mo> <mo>∑</mo> <mo>)</mo> </mrow> <mo>=</mo> <mo>{</mo> <msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mi>μ</mi> <mo>)</mo> </mrow> <mo>⊤</mo> </msup> <msup> <mo>∑</mo> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>−</mo> <mi>μ</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>l</mi> <mo>}</mo> </mrow> </semantics></math> for a prescribed level <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math> in the sample space <math display="inline"><semantics> <msup> <mi mathvariant="double-struck">R</mi> <mn>2</mn> </msup> </semantics></math>. Blue, red, purple, yellow, and green ellipsoids correspond to <span class="html-italic">m</span>-geodesic midpoint, <span class="html-italic">e</span>-geodesic midpoint, Jeffreys–Fisher–Rao midpoint, Gauss–Bregman inductive mean, and numerical Jeffreys centroid (symmetrized Bregman centroid), respectively.</p>
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<p>Centroids and centers between a pair of bivariate centered normal distributions (black). Each normal distribution <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>(</mo> <mi>μ</mi> <mo>,</mo> <mo>∑</mo> <mo>)</mo> </mrow> </semantics></math> with a prescribed <math display="inline"><semantics> <mi>μ</mi> </semantics></math> (parameterized by a 3D parameter <math display="inline"><semantics> <mi>θ</mi> </semantics></math>) is displayed as a 2D ellipsoid. The red and blue ellipsoids correspond to the <span class="html-italic">e</span>-geodesic and <span class="html-italic">m</span>-geodesic midpoints, respectively. The green ellipsoid is the exact Jeffreys centroid which coincide perfectly with the inductive Gauss–Bregman center (yellow) and Jeffreys–Fisher–Rao center (purple). Thus these three green, yellow, and purple matching ellipsoids are rendered superposed in an overall shade of brown.</p>
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<p>Centroids and centers between a pair of bivariate-centered normal distributions (black). Each normal distribution <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>(</mo> <mi>μ</mi> <mo>,</mo> <mo>∑</mo> <mo>)</mo> </mrow> </semantics></math> with a prescribed covariance matrix <math display="inline"><semantics> <mo>∑</mo> </semantics></math> (parameterized by a 2D parameter <math display="inline"><semantics> <mi>θ</mi> </semantics></math>) is displayed as a 2D ellipsoid. The red and blue ellipsoids correspond to the <span class="html-italic">e</span>-geodesic and <span class="html-italic">m</span>-geodesic midpoints, respectively. The inductive Gauss–Bregman (yellow) and Jeffreys–Fisher–Rao center (purple) do not coincide.</p>
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<p>Illustration on a dually flat space of the double sequence inducing a Gauss–Bregman center in the limit.</p>
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<p>Illustration of the Jeffreys–Fisher–Rao and Gauss–Bregman centers a dually flat space. <math display="inline"><semantics> <mi>γ</mi> </semantics></math> denotes the Riemannian geodesic.</p>
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28 pages, 1718 KiB  
Article
Advancing Continuous Distribution Generation: An Exponentiated Odds Ratio Generator Approach
by Xinyu Chen, Zhenyu Shi, Yuanqi Xie, Zichen Zhang, Achraf Cohen and Shusen Pu
Entropy 2024, 26(12), 1006; https://doi.org/10.3390/e26121006 - 22 Nov 2024
Viewed by 505
Abstract
This paper presents a new methodology for generating continuous statistical distributions, integrating the exponentiated odds ratio within the framework of survival analysis. This new method enhances the flexibility and adaptability of distribution models to effectively address the complexities inherent in contemporary datasets. The [...] Read more.
This paper presents a new methodology for generating continuous statistical distributions, integrating the exponentiated odds ratio within the framework of survival analysis. This new method enhances the flexibility and adaptability of distribution models to effectively address the complexities inherent in contemporary datasets. The core of this advancement is illustrated by introducing a particular subfamily, the “Type 2 Gumbel Weibull-G family of distributions”. We provide a comprehensive analysis of the mathematical properties of these distributions, including statistical properties such as density functions, moments, hazard rate and quantile functions, Rényi entropy, order statistics, and the concept of stochastic ordering. To test the robustness of our new model, we apply five distinct methods for parameter estimation. The practical applicability of the Type 2 Gumbel Weibull-G distributions is further supported through the analysis of three real-world datasets. These real-life applications illustrate the exceptional statistical precision of our distributions compared to existing models, thereby reinforcing their significant value in both theoretical and practical statistical applications. Full article
(This article belongs to the Special Issue Number Theoretic Methods in Statistics: Theory and Applications)
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<p>MSE of parameters in <a href="#entropy-26-01006-t003" class="html-table">Table 3</a>.</p>
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<p>(<b>left</b>): The pdf of the T2GWE distribution for different parameters. (<b>right</b>): The hrf of the T2GWE for different parameter values.</p>
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<p>(<b>left</b>): Pdf of T2GWU distribution for different values of parameters <math display="inline"><semantics> <mi>α</mi> </semantics></math>, <math display="inline"><semantics> <mi>β</mi> </semantics></math>, and <math display="inline"><semantics> <mi>γ</mi> </semantics></math>. (<b>right</b>): Hrf of T2GWU for selected parameters <math display="inline"><semantics> <mi>α</mi> </semantics></math>, <math display="inline"><semantics> <mi>β</mi> </semantics></math>, and <math display="inline"><semantics> <mi>γ</mi> </semantics></math>.</p>
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<p>(<b>left</b>): The pdf of the T2GWP distribution for selected values of <math display="inline"><semantics> <mi>α</mi> </semantics></math>, <math display="inline"><semantics> <mi>β</mi> </semantics></math>, <math display="inline"><semantics> <mi>θ</mi> </semantics></math>, and <span class="html-italic">k</span>. (<b>right</b>): The hrf of the T2GWP for various <math display="inline"><semantics> <mi>α</mi> </semantics></math>, <math display="inline"><semantics> <mi>β</mi> </semantics></math>, <math display="inline"><semantics> <mi>θ</mi> </semantics></math>, and <span class="html-italic">k</span>.</p>
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<p>(<b>left</b>): Fitted density superposed on the histogram and observed probability for the Aarset data. (<b>right</b>): Expected probability plots for the Aarset data.</p>
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<p>Fitted K-M survival curve, theoretical and empirical cdfs, the TTT statistics, and the hrf for the Aarset data.</p>
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<p>(<b>left</b>): Fitted density superposed on the histogram and observed probability for the Aarset data. (<b>right</b>): Expected probability plots for the Meeker and Escobar data.</p>
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<p>Fitted K-M survival curve, theoretical and empirical cdf, the TTT statistics, and the hrf for the Meeker and Escobar data.</p>
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<p>(<b>left</b>): Fitted density superposed on the histogram and observed probability for the Chemotherapy data. (<b>right</b>): Expected probability plots for the Chemotherapy data.</p>
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<p>Fitted K-M survival curve, theoretical and empirical cdfs, the TTT statistics, and the hrf for the Chemotherapy data.</p>
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11 pages, 1000 KiB  
Article
Genome Insights and Identification of Sex Determination Region and Sex Markers in Argyrosomus japonicus
by Yike Liu, Wanbo Li, Dinaer Yekefenhazi, Xianfeng Yang, Qihui Zhu, Kun Ye, Fang Han and Dongdong Xu
Genes 2024, 15(12), 1493; https://doi.org/10.3390/genes15121493 - 21 Nov 2024
Viewed by 759
Abstract
Background: Argyrosomus japonicus, a member of the Sciaenidae family, is widely distributed across the sea areas near China, Japan, Australia, and South Africa. The aim of this study is to provide a high-quality genome with new technology and to understand the sex [...] Read more.
Background: Argyrosomus japonicus, a member of the Sciaenidae family, is widely distributed across the sea areas near China, Japan, Australia, and South Africa. The aim of this study is to provide a high-quality genome with new technology and to understand the sex determination mechanism of this species. Methods: We generated a high-quality chromosome-level genome for Argyrosomus japonicus using PacBio HiFi and Hi-C sequencing technologies. To map the sex determination region, we employed re-sequencing data from 38 A. japonicus and conducted genome-wide association studies (GWASs) on sex phenotypes. Results: Utilizing Hifiasm, we assembled a 708.8 Mb genome with a contig N50 length of 30 Mb. Based on Hi-C data, these contigs were organized into 24 chromosomes. The completeness of the assembly was assessed to be 99% using BUSCO, and over 98% according to Merqury. We identified a total of 174.57 Mb of repetitive elements and annotated 24,726 protein-coding genes in the genome. We mapped a 2.8 Mb sex determination region on chromosome 9, within which we found two sex-linked markers. Furthermore, we confirmed that the XX-XY sex determination system is adopted in A. japonicus. Conclusions: The findings of this study provide significant insights into genetic breeding, genome evolution research, and sex control breeding in A. japonicus. Full article
(This article belongs to the Special Issue Omic Study and Genes in Fish Sex Determination and Differentiation)
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<p>Location of sex determination region in <span class="html-italic">A. japonicus</span>. (<b>A</b>) Manhattan plot of <span class="html-italic">A. japonicus</span> association analysis. (<b>B</b>) Manhattan plot of chromosome 9 association analysis and scatter plot with a coincidence of more than 90%. The blue dots indicate all SNPs on chromosome 9, the red dots indicate SNPs on chromosome 9 that exceed the threshold line, and the purple box indicates SNPs with a compliance greater than 90%. If a purple square resides in an annotated gene, the gene name is labeled.</p>
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<p>Verification of two molecular markers in random samples. (MFS-1) Verification of 18 bp deletion. (MFS-2) Verification of 14 bp deletion.</p>
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16 pages, 7947 KiB  
Article
Genome-Wide Analysis of the Multidrug and Toxic Compound Extrusion Gene Family in the Tea Plant
by Tao Xie, Yumei Qian, Deyan Wang, Xiadong Yan, Ying Jiang, Min Li, Hao Rong and Tao Xia
Agronomy 2024, 14(11), 2718; https://doi.org/10.3390/agronomy14112718 - 18 Nov 2024
Viewed by 557
Abstract
The multidrug and toxic compound extrusion (MATE) family is the latest class of novel secondary transporters discovered in plants. However, there is currently no comprehensive analysis of the MATE gene family in the tea plant. In this study, 68 CsMATE genes were identified [...] Read more.
The multidrug and toxic compound extrusion (MATE) family is the latest class of novel secondary transporters discovered in plants. However, there is currently no comprehensive analysis of the MATE gene family in the tea plant. In this study, 68 CsMATE genes were identified from the tea plant genome using bioinformatic methods. In general, we analyzed the evolutionary relationships, intron–exon structure, distribution in chromosomes, conserved domains, and gene expression patterns in different tissues and stresses of the CsMATE gene family. The 68 CsMATEs were phylogenetically divided into four major clusters (Class I to Class IV). The CsMATE genes within the same class exhibit similar structural features, while displaying certain distinctions across different classes. Evolutionary analysis indicated that the CsMATE gene family expanded mainly through gene duplication events, in addition to proximal duplication. Through the analysis of cis-acting elements, it was found that CsMATE genes may be involved in the growth, development, and stress response. Furthermore, we observed that certain CsMATE genes could be induced to exhibit expression under abiotic stress conditions such as low temperature, high salinity (NaCl), osmotic stress (PEG), and methyl jasmonate treatment (MeJA). The findings presented herein offer a crucial theoretical foundation for elucidating the biological functions of CsMATE genes, particularly in response to abiotic stress, and furnish valuable potential genetic resources for tea plant resistance breeding. Full article
(This article belongs to the Section Horticultural and Floricultural Crops)
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<p>Phylogenetic relationships of MATE proteins of <span class="html-italic">Arabidopsis</span> and the tea plant. Blue dots represent MATE proteins from the tea plant and red dots represent MATE proteins from <span class="html-italic">Arabidopsis</span>. Branch colors represent different classes. The numbers assigned to branches indicate the reliability.</p>
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<p>Intron–exon and motif composition of CsMATEs. (<b>A</b>) Phylogenetic tree of CsMATEs. (<b>B</b>) 10 conserved motifs in CsMATE proteins. (<b>C</b>) Intron–exon composition of <span class="html-italic">CsMATEs</span>.</p>
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<p>The distribution of <span class="html-italic">CsMATEs</span> on tea plant chromosomes. Font colors represent different classes. MB, megabase.</p>
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<p>Synteny of <span class="html-italic">CsMATEs</span> in <span class="html-italic">C. sinensis</span>. Grey and red lines represent synteny blocks and <span class="html-italic">CsMATE</span> gene pairs, respectively.</p>
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<p>The collinearity of <span class="html-italic">MATE</span> genes in <span class="html-italic">C. sinensis</span> and three other species. (<b>A</b>) <span class="html-italic">C. sinensis</span> and <span class="html-italic">A. thaliana</span>; (<b>B</b>) <span class="html-italic">C. sinensis</span> and <span class="html-italic">C. canephora</span>; (<b>C</b>) <span class="html-italic">C. sinensis</span> and <span class="html-italic">A. chinensis</span>. Grey lines represent collinear blocks among <span class="html-italic">C. sinensis</span>, <span class="html-italic">A. thaliana</span>, <span class="html-italic">C. canephora,</span> and <span class="html-italic">A. chinensis</span>; red lines represent the syntenic <span class="html-italic">MATE</span> gene pairs.</p>
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<p><span class="html-italic">Cis</span>-acting elements in <span class="html-italic">CsMATE</span> promoters.</p>
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<p>Spatiotemporal expression pattern of <span class="html-italic">CsMATE</span> genes. The heatmap of <span class="html-italic">CsMATEs</span> expression with log<sub>2</sub> (FPKM + 1).</p>
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<p>Expression analysis of <span class="html-italic">CsMATE</span> genes under diverse abiotic stress and hormone treatment (<b>A</b>–<b>D</b>).</p>
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16 pages, 511 KiB  
Article
On the Discretization of the Weibull-G Family of Distributions: Properties, Parameter Estimates, and Applications of a New Discrete Distribution
by Abeer Balubaid, Hadeel Klakattawi and Dawlah Alsulami
Symmetry 2024, 16(11), 1519; https://doi.org/10.3390/sym16111519 - 13 Nov 2024
Viewed by 808
Abstract
In this article, we introduce a new three-parameter distribution called the discrete Weibull exponential (DWE) distribution, based on the use of a discretization technique for the Weibull-G family of distributions. This distribution is noteworthy, as its probability mass function presents both symmetric and [...] Read more.
In this article, we introduce a new three-parameter distribution called the discrete Weibull exponential (DWE) distribution, based on the use of a discretization technique for the Weibull-G family of distributions. This distribution is noteworthy, as its probability mass function presents both symmetric and asymmetric shapes. In addition, its related hazard function is tractable, exhibiting a wide range of shapes, including increasing, increasing–constant, uniform, monotonically increasing, and reversed J-shaped. We also discuss some of the properties of the proposed distribution, such as the moments, moment-generating function, dispersion index, Rényi entropy, and order statistics. The maximum likelihood method is employed to estimate the model’s unknown parameters, and these estimates are evaluated through simulation studies. Additionally, the effectiveness of the model is examined by applying it to three real data sets. The results demonstrate that, in comparison to the other considered distributions, the proposed distribution provides a better fit to the data. Full article
(This article belongs to the Section Mathematics)
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<p>PMF plots of the DWE model.</p>
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<p>HRF plots of the DWE model.</p>
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<p>The MSE of <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>θ</mi> <mo stretchy="false">^</mo> </mover> <mo>,</mo> <mover accent="true"> <mi>β</mi> <mo stretchy="false">^</mo> </mover> <mo>,</mo> <mover accent="true"> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </semantics></math> for the DWE (0.5, 0.6, 1.1).</p>
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<p>The MSE of <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>θ</mi> <mo stretchy="false">^</mo> </mover> <mo>,</mo> <mover accent="true"> <mi>β</mi> <mo stretchy="false">^</mo> </mover> <mo>,</mo> <mover accent="true"> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </semantics></math> for the DWE (0.2, 0.5, 2.4).</p>
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<p>The MSE of <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>θ</mi> <mo stretchy="false">^</mo> </mover> <mo>,</mo> <mover accent="true"> <mi>β</mi> <mo stretchy="false">^</mo> </mover> <mo>,</mo> <mover accent="true"> <mi>α</mi> <mo stretchy="false">^</mo> </mover> </mrow> </semantics></math> for the DWE (0.05, 0.4, 1.3).</p>
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<p>p-p plots for the DWE and other considered distributions for the first data set.</p>
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<p>Plots of the empirical CDFs of the DWE and other considered distributions for the first data set.</p>
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<p>p-p plots of the DWE and other considered distributions for the second data set.</p>
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<p>Plots of the empirical CDFs of the DWE and other considered distributions for the second data set.</p>
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<p>p-p plots of the DWE and other considered distributions for the third data set.</p>
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<p>Plots of the empirical CDFs of the DWE and other considered distributions for the third data set.</p>
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20 pages, 7684 KiB  
Article
Genome-Wide Analysis of Heat Shock Protein Family and Identification of Their Functions in Rice Quality and Yield
by Hong Wang, Sidra Charagh, Nannan Dong, Feifei Lu, Yixin Wang, Ruijie Cao, Liuyang Ma, Shiwen Wang, Guiai Jiao, Lihong Xie, Gaoneng Shao, Zhonghua Sheng, Shikai Hu, Fengli Zhao, Shaoqing Tang, Long Chen, Peisong Hu and Xiangjin Wei
Int. J. Mol. Sci. 2024, 25(22), 11931; https://doi.org/10.3390/ijms252211931 - 6 Nov 2024
Cited by 1 | Viewed by 980
Abstract
Heat shock proteins (Hsps), acting as molecular chaperones, play a pivotal role in plant responses to environmental stress. In this study, we found a total of 192 genes encoding Hsps, which are distributed across all 12 chromosomes, with higher concentrations on chromosomes 1, [...] Read more.
Heat shock proteins (Hsps), acting as molecular chaperones, play a pivotal role in plant responses to environmental stress. In this study, we found a total of 192 genes encoding Hsps, which are distributed across all 12 chromosomes, with higher concentrations on chromosomes 1, 2, 3, and 5. These Hsps can be divided into six subfamilies (sHsp, Hsp40, Hsp60, Hsp70, Hsp90, and Hsp100) based on molecular weight and homology. Expression pattern data indicated that these Hsp genes can be categorized into three groups: generally high expression in almost all tissues, high tissue-specific expression, and low expression in all tissues. Further analysis of 15 representative genes found that the expression of 14 Hsp genes was upregulated by high temperatures. Subcellular localization analysis revealed seven proteins localized to the endoplasmic reticulum, while others localized to the mitochondria, chloroplasts, and nucleus. We successfully obtained the knockout mutants of above 15 Hsps by the CRISPR/Cas9 gene editing system. Under natural high-temperature conditions, the mutants of eight Hsps showed reduced yield mainly due to the seed setting rate or grain weight. Moreover, the rice quality of most of these mutants also changed, including increased grain chalkiness, decreased amylose content, and elevated total protein content, and the expressions of starch metabolism-related genes in the endosperm of these mutants were disturbed compared to the wild type under natural high-temperature conditions. In conclusion, our study provided new insights into the HSP gene family and found that it plays an important role in the formation of rice quality and yield. Full article
(This article belongs to the Special Issue Gene Mining and Germplasm Innovation for the Important Traits in Rice)
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<p>Conservative domains of 6 Hsp subfamilies in rice: (<b>A</b>) 23 small Hsp (sHsp) members: protein name suffix is subcellular localization, and each protein has the α-crystallin domain, which is the characteristic domain of sHsp; (<b>B</b>) 104 Hsp40 members, including three types, A (DjA1-DjA12), B (DjB1-DjB9), and C (DjC1-DjC83); each member has the DnaJ domain; (<b>C</b>) 22 Hsp60 members: each protein has a GroEL domain, and these proteins were named according to their positions on the chromosome; (<b>D</b>) 32 Hsp70 members, including 18 proteins whose name contain Hsp70, 6 Bips (Binding immunoglobulin proteins), and 8 Hsp110 members, each with an Hsp70 domain; (<b>E</b>) 8 Hsp90 members, each containing the Hsp90 domain; (<b>F</b>) 3 Hsp100 members, each harboring the ClpB domain specific to Hsp100. The scale at the bottom represents the number of amino acids. The conserved domain data of sHsp, Hsp70, and Hsp90 were downloaded from the Pfam database and visualized using the TBtools-II software. For Hsp40, Hsp60, and Hsp100, the conserved domain data were obtained from NCBI and visualized using a website.</p>
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<p>Phylogenetic tree and chromosomal localization analysis of 6 Hsp subfamilies. (<b>A</b>) Phylogenetic tree illustrating relationships among 192 Hsps. (<b>B</b>) Chromosomal distribution of 192 <span class="html-italic">Hsp</span> genes. The scale on the left is chromosome physical distance.</p>
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<p>Gene structure of 192 <span class="html-italic">Hsp</span> genes in rice. (<b>A</b>–<b>F</b>) Gene structure depicting <span class="html-italic">sHsp</span>, <span class="html-italic">Hsp40</span>, <span class="html-italic">Hsp60</span>, <span class="html-italic">Hsp70</span>, <span class="html-italic">Hsp90</span>, and <span class="html-italic">Hsp100</span>. CDS indicates coding sequence for protein; UTR denotes untranslated region. The scale is the number of gene bases.</p>
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<p>Expression pattern of 15 <span class="html-italic">Hsp</span> genes and subcellular localization analysis of 15 Hsp proteins. (<b>A</b>) The relative expression levels of 15 <span class="html-italic">Hsps</span> in roots, stems, leaves, panicles, and seeds at 5, 10, 15, 20, and 25 days after flowering. The heat map shows the expression level determined by TBtools-II (<a href="https://github.com/CJ-Chen/TBtools-II" target="_blank">https://github.com/CJ-Chen/TBtools-II</a>, (accessed on 31 March 2024)); the range of blue to red indicates the expression levels from low to high. Clustering is according to the expression level in each tissue. (<b>B</b>–<b>E</b>) Subcellular localization of Hsp proteins. Free green fluorescent protein (GFP) and full-length Hsp fusion proteins (Hsp-GFP) were transiently expressed in rice protoplasts. Hsp60-11-GFP co-localized with the chloroplast autofluorescence, Hsp16.9A and DjB7 localized in the cytoplasm (<b>B</b>). mtHsp70-1 and mtHsp70-3 co-localized with mitochondria, and the yellow signal represents the mitochondria dyed by Mito-Tracker Red (<b>C</b>). DjB6, DjC43, DjC79, Hsp110-2, Hsp110-8, Hsp90-1, and Hsp90-4 co-localized with HDEL-mCherry signals of the endoplasmic reticulum (<b>D</b>). cHsp70-6, cHsp70-7 and Hsp110-7 co-localized with the cytoplasm and DAPI signals of the nucleus (<b>E</b>). Scale bars, 5 μm.</p>
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<p>The induced expression levels of 15 <span class="html-italic">Hsp</span> genes in the seedlings of ZH11 under different stresses. ZH11-CK represents the normal seedlings as control with no treatment. HT-10min and HT-60min represent the seedlings that were moved to a high temperature of 42 °C from normal temperature for 10 and 60 min. HT-6h-Rec represents the seedlings that recovered at a normal temperature for 6 h after 60 min of heat shock. LT-6h represents the seedlings that were treated at 5 °C for 6 h. NaCl-6h represents the seedlings that were treated with high salt stress for 6 h (100 mmol/L NaCl). PEG6000-6h represents the seedlings that were treated at 20% PEG stress for 6 h. The expression levels of <span class="html-italic">Hsps</span> were detected in the above treated seedlings and ZH11-CK. Data are means ± SD (n = 3). Different letters indicate significant differences at <span class="html-italic">p</span> &lt; 0.05 by ANOVA and Duncan’s test.</p>
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<p>Grain size- and yield-related traits of ZH11 and the <span class="html-italic">hsp</span> mutants. (<b>A</b>–<b>C</b>) Comparison of the grain length (<b>A</b>), grain width (<b>B</b>), and grain thickness (<b>C</b>) of ZH11 and <span class="html-italic">hsp</span> mutants; scale bars = 1 cm. (<b>D</b>–<b>I</b>) Grain length (<b>D</b>), grain width (<b>E</b>), grain thickness (<b>F</b>), 1000-grain weight (<b>G</b>), seed setting rate (<b>H</b>), and yield per plant (<b>I</b>) of ZH11 and the mutants. The investigated plants were grown in natural high-temperature conditions in fields in Hangzhou in 2023. Data are means ± SD; n = 20 in (<b>D</b>–<b>F</b>), n = 3 in (<b>G</b>), and n = 10 in (<b>H</b>,<b>I</b>), and no less than 200 grains per replication in (<b>G</b>). Asterisks show statistical significance between the WT and the mutants, as determined by Student’s <span class="html-italic">t</span>-test (* <span class="html-italic">p</span> &lt; 0.05; ** <span class="html-italic">p</span> &lt; 0.01).</p>
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<p>Grain quality of ZH11 and <span class="html-italic">hsp</span> mutants under natural high temperature in the Hangzhou field in 2023. (<b>A</b>) Appearance of mature grains of ZH11 and 15 <span class="html-italic">hsp</span> mutants. Scale bars = 1 cm. (<b>B</b>,<b>C</b>) Chalkiness rate and chalkiness degree of ZH11 and 15 <span class="html-italic">hsp</span> mutants grains. (<b>D</b>–<b>F</b>) Total starch, amylose, and total protein contents of ZH11 and the mutant grains. Data are means ± SD (n = 3); no less than 200 grains per replication in (<b>B</b>,<b>C</b>). Asterisks show the statistical significance between the WT and the mutants, as determined by Student’s <span class="html-italic">t</span>-test (* <span class="html-italic">p</span> &lt; 0.05; ** <span class="html-italic">p</span> &lt; 0.01).</p>
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<p>The expression levels of starch synthesis-related genes in developing endosperm of the wild type (WT) and 7 mutants (<span class="html-italic">hsp16.9a</span>, <span class="html-italic">chsp70-6</span>, <span class="html-italic">chsp70-7</span>, <span class="html-italic">hsp110-7</span>, <span class="html-italic">hsp110-8</span>, <span class="html-italic">djc79</span>, and <span class="html-italic">hsp90-4</span>). (<b>A</b>–<b>G</b>) The relative expression level of starch synthesis-related genes in endosperm at 10d after flowering under natural high temperature in the Hangzhou field in 2023. The data presented here are the relative expression levels of the genes that are expressed differently between mutants and the wild type. The rice UBIQUITIN gene was used as the internal control. Data are means ± SD of three individual replicates. Asterisks show the statistical significance between the WT and the mutants, as determined by Student’s <span class="html-italic">t</span>-test (** <span class="html-italic">p</span> &lt; 0.01).</p>
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