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17 pages, 5521 KiB  
Article
Versican Proteolysis by ADAMTS: Understanding Versikine Expression in Canine Spontaneous Mammary Carcinomas
by Maria Carolina Souza, Simone Nunes, Samantha Hellen Santos Figuerêdo, Bruno Sousa de Almeida, Isac Patrick Conceição Santos, Geovanni Dantas Cassali, Sérgio Marcos Arruda, Thiago Marconi de Souza Cardoso, Alessandra Estrela-Lima and Karine Araújo Damasceno
Cancers 2024, 16(23), 4057; https://doi.org/10.3390/cancers16234057 - 4 Dec 2024
Viewed by 496
Abstract
Background: The present study investigates VKINE, a bioactive proteolytic fragment of the proteoglycan VCAN, as a novel and significant element in the tumor extracellular matrix (ECM). Although VKINE has been recognized for its immunomodulatory potential in certain tumor types, its impact on ECM [...] Read more.
Background: The present study investigates VKINE, a bioactive proteolytic fragment of the proteoglycan VCAN, as a novel and significant element in the tumor extracellular matrix (ECM). Although VKINE has been recognized for its immunomodulatory potential in certain tumor types, its impact on ECM degradation and prognostic implications remains poorly understood. Objectives: This study aimed to evaluate VCAN proteolysis and its association with ADAMTS enzymes involved in extracellular matrix remodeling in spontaneous canine mammary gland cancer. Methods: The expression levels of VKINE, ADAMTS enzymes, and collagen fibers were comparatively analyzed in situ and in invasive areas of carcinoma in mixed tumor (CMT) and carcinosarcoma (CSS) with different prognoses. Results: VKINE was notably expressed in the stroma adjacent to the invasion areas in CMT, whereas ADAMTS-15 was identified as the enzyme associated with VCAN proteolysis. Inverse correlations were observed between type III collagen and VCAN expression in in situ areas. Conclusions: Our findings suggest that VKINE and ADAMTS-15 play crucial roles in the tumor microenvironment, influencing invasiveness and type III collagen deposition. This study contributes to a better understanding of the dynamics within the ECM, paving the way for potential new tools in diagnosing and treating human and canine mammary tumors. Full article
(This article belongs to the Section Tumor Microenvironment)
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Graphical abstract

Graphical abstract
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<p>Immunohistochemical VCAN and VKINE expressions. (<b>A</b>) Moderate positive expression of VCAN in the stroma adjacent to carcinomatous areas in situ in CMT, 400×, bar 100 µm. (<b>B</b>) Moderate positive cytoplasmic expression of VCAN in carcinoma cells (black arrow) and strong expression in the stroma adjacent to areas of invasion in CMT, 400×, bar 100 µm. (<b>C</b>) Moderate positive expression of VKINE in the in situ area of CMT, 200×, bar 100 µm. (<b>D</b>) Strong positive expression of VKINE in the area of invasion, 200×, bar 100 µm. (<b>A</b>–<b>D</b>) Counterstaining with Mayer’s hematoxylin. (<b>E</b>) Difference in VCAN expression in stroma between in situ and invasive carcinomatous in CTM types (*** <span class="html-italic">p</span> ≤ 0.0001, Wilcoxon test). (<b>F</b>) Difference in VCAN expression in the stroma between in situ and invasion areas in CMT (*** <span class="html-italic">p</span> ≤ 0.0001, Wilcoxon test). (<b>G</b>) Difference in VKINE expression in the stroma between in situ and invasive carcinomatous areas in CMT (** <span class="html-italic">p</span> ≤ 0.0048, Wilcoxon test). (<b>H</b>) Intensity of VCAN staining in carcinoma cells in the analyzed cases. Primary antibody used: VCAN (1:50, clone 12C5, DSHB, Iowa City, IA, USA). <span class="html-italic">p</span>-values ≤ 0.05 were considered significant.</p>
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<p>VKINE immunostaining in canine mammary tumors. (<b>A</b>) VKINE expression in the cytoplasm in carcinosarcoma (black arrow), 400×, bar 20 µm. (<b>B</b>) VKINE labeling on epithelial cell membrane with squamous differentiation into mixed tumor carcinoma, 400×, bar 20 µm. (<b>C</b>) VKINE expression in stroma adjacent to carcinomatous invasion areas in carcinosarcoma, 200×, bar 20 µm. (<b>D</b>) VKINE expression in a myxoid matrix in CMT (black arrow), 200×, bar 50 µm. (<b>A</b>–<b>D</b>) Counterstaining with Mayer’s hematoxylin. (<b>E</b>) Table illustrating the number of cases with cellular stain according to intensity. Primary antibody used: VKINE (neo-epitope DPEAAE, polyclonal, ThermoFisher Scientific, Waltham, MA, USA).</p>
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<p>Immunostaining pattern of ADAMTS 1, 5, 8, 9, and 15. (<b>A</b>) Moderate positive ADAMTS-1 staining of stromal and inflammatory cells near the in situ area in CMT, 200×, bar 20 µm. (<b>B</b>) Strong positive cytoplasmic ADAMTS-1 staining of macrophages around invasive carcinoma cells (black arrow), 200×, bar 20 µm. (<b>C</b>) In situ area in CMT revealing predominant moderate positive cytoplasmic staining and absent or weak stromal ADAMTS-5 staining, 400×, bar 50 µm. (<b>D</b>) ADAMTS-5 in an area with chondromyxoid matrix in the CSS, showing moderate positive stromal and cellular staining, 200×, bar 20 µm. (<b>E</b>) In situ area of CMT showing expressive nuclear and weak cytoplasmatic ADAMTS-8 staining, 400×, bar 50 µm. (<b>F</b>) Invasive carcinomatous areas in CSS, nuclear staining pattern in ADAMTS-8 staining 400×, bar 50 µm. (<b>G</b>) In situ areas showing strong positive cytoplasmic ADAMTS-9 staining in carcinomatous and immune cells in CMT, 200×, bar 20 µm. (<b>H</b>) Area of invasion with strong positive cytoplasmic and stromal ADAMTS-9 staining in CMT, 200×, bar 20 µm. (<b>I</b>) Strong positive nuclear staining in carcinoma cells and moderate cytoplasmic immunolabeling in immune cells of ADAMTS-15 in CMT, 400×, bar 50 µm. (<b>J</b>) Strong positive nuclear and cytoplasmic staining in carcinoma cells and stromal staining of ADAMTS-15 in CMT, 200×, bar 20 µm. (<b>A</b>–<b>J</b>) Counterstaining with Mayer’s hematoxylin. Antibodies used: ADAMTS1 (clone 3C8F4, Santa Cruz, Dallas, TX, USA), ADAMTS-5 (clone Ab41037, Abcam, Cambridge, UK), ADAMTS8 (clone 31G7, Invitrogen, Vacaville, CA, USA), ADAMTS-9 (polyclonal, Invitrogen, Vacaville, CA, USA), and ADAMTS-15 (clone 561819, Invitrogen, Vacaville, CA, USA).</p>
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<p>Heat map matrix of Spearman correlation analysis showing the correlation coefficients among ADAMTS enzymes and Versican expression in different areas in canine mammary tumors (in situ, invasion, epithelial, and stromal areas). Legend: AD = ADAMTS; VCAN = versican; IS = in situ; IN = invasion; EP = epithelial; EST = stromal; <span class="html-italic">p</span>-value: * = &lt;0.05; ** = &lt;0.01; *** = &lt;0.001.</p>
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<p>Heat map matrix of Spearman correlation analysis showing the correlation coefficients among ADAMTS enzymes and versikine expression in different areas in canine mammary tumors (in situ, invasion, epithelial, and stromal areas). Legend: AD = ADAMTS; VKINE = versikine; IS = in situ; IN = invasion; EP = epithelial; EST = stromal; <span class="html-italic">p</span>-value: * = &lt;0.05; ** = &lt;0.01; *** = &lt;0.001.</p>
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<p>Relationship between VCAN proteolysis and desmoplasia. (<b>A</b>) Masson’s Trichrome staining revealing collagen deposition in the stroma adjacent to the in situ areas in CMT, 200×, bar 50 µm. (<b>B</b>) Masson’s Trichrome staining in the invasion areas in CMT, 200×, bar 50 µm. (<b>C</b>) Invasion areas in CSS stained with Masson’s Trichrome, 400×, bar 50 µm. (<b>D</b>) Picrosirius Red staining revealing the deposition of type I (in red) and type III (in green) collagen in the stroma adjacent to the in situ areas in the CMT, under polarized light, 200×, bar 50 µm. (<b>E</b>) Picrosirius Red staining in the areas of invasion in the CMT, under polarized light, 200×, bar 50 µm. (<b>F</b>) Picrosirius Red staining in the areas of invasion in the CSS, under polarized light, 100×, bar 50 µm. (<b>G</b>) Collagem area (CA) difference between CTM and CSS. (<b>H</b>) Collagen difference between in situ and invasion areas in CMT. (<b>I</b>) Collagen intensity (CI) on invasion and in situ area in CMT. (<b>J</b>) Type III collagen difference between CMT and CSS. Legend: <span class="html-italic">p</span>-value: * = &lt;0.05; ** = &lt;0.01; *** = &lt;0.001.</p>
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24 pages, 3274 KiB  
Article
Adjacency List Algorithm for Traffic Light Control Systems in Urban Networks
by Sergio Rojas-Blanco, Alberto Cerezo-Narváez, Manuel Otero-Mateo and Sol Sáez-Martínez
Systems 2024, 12(12), 539; https://doi.org/10.3390/systems12120539 - 3 Dec 2024
Viewed by 552
Abstract
The increasing complexity of urban road networks has driven the development of Intelligent Transportation Systems (ITS) to optimize vehicle flow. To address this challenge, this paper presents an algorithm and MATLAB function that generates an adjacency list of traffic signals to provide detailed [...] Read more.
The increasing complexity of urban road networks has driven the development of Intelligent Transportation Systems (ITS) to optimize vehicle flow. To address this challenge, this paper presents an algorithm and MATLAB function that generates an adjacency list of traffic signals to provide detailed information about the relationships between all signals within a network. This list is based on stable structural road and traffic lights data and offers a crucial global perspective for signal coordination, especially in managing multiple intersections. An adjacency list is more efficient than matrices in terms of space and computational cost, allowing for the identification of critical signals before applying advanced optimization techniques such as neural networks or hypergraphs. We successfully tested the proposed method on three networks of varying complexity extracted from VISSIM and VISUM, demonstrating its effectiveness even in networks with up to 8372 links and 547 traffic lights. This tool provides a solid foundation for improving urban traffic management and coordinating signals across intersections. Full article
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Figure 1
<p>Example schema of a road network (<b>a</b>) and its corresponding graph representation (<b>b</b>).</p>
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<p>Flowchart of the general algorithm.</p>
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<p>Urban road network example.</p>
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<p>Map and road network of London (GB).</p>
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<p>Map and road network of Boise (US).</p>
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<p>Map and road network of Luxembourg (LU).</p>
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27 pages, 8131 KiB  
Article
Formation Conditions of Unusual Extremely Reduced High-Temperature Mineral Assemblages in Rocks of Combustion Metamorphic Complexes
by Igor S. Peretyazhko and Elena A. Savina
Crystals 2024, 14(12), 1052; https://doi.org/10.3390/cryst14121052 - 3 Dec 2024
Viewed by 444
Abstract
New data, including Raman spectroscopy, characterize unusual mineral assemblages from rocks of the Naylga and Khamaryn–Khyral–Khiid combustion metamorphic complexes in Mongolia. Several samples of melilite–nepheline paralava and other thermally altered (metamorphosed) sedimentary rocks contain troilite (FeS), metallic iron Fe0, kamacite α-(Fe,Ni) [...] Read more.
New data, including Raman spectroscopy, characterize unusual mineral assemblages from rocks of the Naylga and Khamaryn–Khyral–Khiid combustion metamorphic complexes in Mongolia. Several samples of melilite–nepheline paralava and other thermally altered (metamorphosed) sedimentary rocks contain troilite (FeS), metallic iron Fe0, kamacite α-(Fe,Ni) or Ni-bearing Fe0, taenite γ-(Fe,Ni) or Ni-rich Fe0, barringerite or allabogdanite Fe2P, schreibersite Fe3P, steadite Fe4P = eutectic α-Fe + Fe3P, wüstite FeO, and cohenite Fe3C. The paralava matrix includes a fragment composed of magnesiowüstite–ferropericlase (FeO–MgO solid solution), as well as of spinel (Mg,Fe)Al2O4 and forsterite. The highest-temperature mineral assemblage belongs to a xenolithic remnant, possibly Fe-rich sinter, which is molten ash left after underground combustion of coal seams. The crystallization temperatures of the observed iron phases were estimated using phase diagrams for the respective systems: Fe–S for iron sulfides and Fe–P ± C for iron phosphides. Iron monosulfides (high-temperature pyrrhotite) with inclusions of Fe0 underwent solid-state conversion into troilite at 140 °C. Iron phosphides in inclusions from the early growth zone of anorthite–bytownite in melilite–nepheline paralava crystallized from <1370 to 1165 °C (Fe2P), 1165–1048 °C (Fe3P), and <1048 °C (Fe4P). Phase relations in zoned spherules consisting of troilite +Fe0 (or kamacite + taenite) +Fe3P ± (Fe3C, Fe4P) reveal the potential presence of a homogeneous Fe–S–P–C melt at T~1350 °C, which separated into two immiscible melts in the 1350–1250 °C range; namely, a dense Fe–P–C melt in the core and a less dense Fe–S melt in the rim. The melts evolved in accordance with cooling paths in the Fe–S and Fe–P–C phase diagrams. Cohenite and schreibersite in the spherules crystallized between 988 °C and 959 °C. The crystallization temperatures of minerals were used to reconstruct redox patterns with respect to the CCO, IW, IM, and MW buffer equilibria during melting of marly limestone and subsequent crystallization and cooling of melilite–nepheline paralava melts. The origin of the studied CM rocks was explained in a model implying thermal alteration of low-permeable overburden domains in reducing conditions during wild subsurface coal fires, while heating was transferred conductively from adjacent parts of ignited coal seams. The fluid (gas) regime in the zones of combustion was controlled by the CCO buffer at excess atomic carbon. Paralava melts exposed to high-temperature extremely reducing conditions contained droplets of immiscible Fe–S–P–C, Fe–S, Fe–P, and Fe–P–C melts, which then crystallized into reduced mineral assemblages. Full article
(This article belongs to the Collection Topic Collection: Mineralogical Crystallography)
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Figure 1

Figure 1
<p>Raman spectra of several minerals from CM rocks in Mongolia.</p>
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<p>(<b>a</b>) Raman spectra of iron monosulfide (pyrrhotite or troilite) and its oxidation products collected at a laser power of 1, 5, 7, and 17 mW, 150 accumulations to 1 s, groove density 1800 g/mm; (<b>b</b>) Raman spectrum of troilite acquired at 1 mW laser power, 5400 accumulations to 2 s (3 h), 1800 g/mm.</p>
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<p>Phase diagram of the Fe–S system, after Shishin et al. [<a href="#B31-crystals-14-01052" class="html-bibr">31</a>] with additions (see text).</p>
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<p>(<b>a</b>) Raman spectra of schreibersite Fe<sub>3</sub>P and (<b>b</b>) cohenite Fe<sub>3</sub>C. Operation conditions: (<b>a</b>) laser power 5 mW, 600 accumulations to 1 s, groove density 600 g/mm and (<b>b</b>) laser power 5 mW, 1000 accumulations to 1 s, groove density 600 g/mm.</p>
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<p>Fragments of a coarse troilite grain in sample MN-1287, with enlarged symplectitic zones. Scale bars: 10 µm in panels (<b>c</b>,<b>e</b>) and 100 µm in panels (<b>a</b>,<b>b</b>,<b>d</b>,<b>f</b>). Abbreviations are as follows: Tro = troilite, Mag = magnetite, Wüs = wüstite, Mrc = marcasite, Gth = goethite, Sd = siderite, Cal = calcite, Cpx = clinopyroxene, Pl = plagioclase, Kir = kirschsteinite.</p>
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<p>(<b>a</b>) Raman spectra of magnetite and wüstite from sample MN-1287 and (<b>b</b>) ferropericlase–magnesiowüstite from sample MN-1133. Operation conditions: (<b>a</b>) laser power 1–5 mW, 600 accumulations to 1 s, 1800 g/mm groove density and (<b>b</b>) laser power 5 mW, 1000 accumulations to 1 s, 600 g/mm groove density.</p>
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<p>(<b>a</b>–<b>d</b>) Fragments of a coarse troilite grain in sample MN-1133, with some enlarged zones and (<b>e</b>–<b>g</b>) mineral assemblages with magnesiowüstite–ferropericlase. Scale bars: 10 µm in panels (<b>e</b>,<b>f</b>) and 40 µm in panels (<b>a</b>–<b>d</b>,<b>g</b>) for BSE images. Abbreviations are as follows: Tro = troilite, Fe = metallic iron, Wüs–Per = magnesiowüstite–ferropericlase, Mfr = magnesioferrite, Mag = magnetite, Mrc = marcasite, Gth = goethite, Fo = forsterite, Ol = Mg-Fe olivine, Pl = plagioclase, Cpx = clinopyroxene, Mll = melilite, Spl = spinel, Sd = siderite, Cal = calcite.</p>
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<p>(<b>a</b>–<b>c</b>) Matrix fragments of sample MN-1417, with enlarged vitreous zones containing grains of detrital quartz, zircon, troilite spherules, and newly formed mullite; (<b>d</b>) vitreous zone with iron spherules, microlites and phases of mullite and Fe-mullite; (<b>e</b>) grain of ferropseudobrookite–pseudobrookite with rutile inclusions. Scale bars: 100 µm for (<b>b</b>,<b>c</b>), and 10 µm for (<b>d</b>,<b>e</b>) for BSE images. Abbreviations are as follows: Gl = glass, Mul = mullite, Fe = metallic iron, Qz = quartz, Pbrk = pseudobrookite, Fe-Pbrk = ferropseudobrookite, Rt = rutile.</p>
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<p>Globules and spherules in vitreous parts of sample MN-1417. (<b>a</b>–<b>c</b>) Thorilite globules with inclusions and (<b>d</b>–<b>i</b>) zoned spherules with troilitic rim. Scale bars: 10 µm for BSE images. Abbreviations are as follows: Gl = glass, Tro = troilite, Scb = schreibersite, Fe<sub>4</sub>P = steadite, Coh = cohenite, Fe = metallic iron, Kmc = kamacite, Tae = taenite, Gth = goethite.</p>
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<p>Zoned spherule in sample MN-1417 with schreibersite and cohenite. Scale bars: 10 µm in panel (<b>a</b>) and 1 µm in panels (<b>b</b>–<b>e</b>); (<b>c</b>–<b>e</b>) discrete color images for elements: carbon (<b>c</b>), phosphorus (<b>d</b>), iron (<b>e</b>); (<b>f</b>) EDS spectra for Fe<sub>3</sub>C, α-Fe, and Fe<sub>3</sub>P. Abbreviations are as follows: Gl = glass, Tro = troilite, Scb = schreibersite, Coh = cohenite, Fe = metallic iron.</p>
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<p>Compositional variations of kamacite and taenite in zoned spherules (MN-1417 and MN-1412 samples).</p>
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<p>Matrix fragments of melilite–nepheline paralava, sample MN-1420. Scale bars: 10 µm in panels (<b>a</b>–<b>c</b>,<b>e</b>,<b>f</b>) and 1 µm in panel (<b>d</b>) for BSE images. Abbreviations are as follows: Nph = Na-Ca nepheline (davidsmithite), Mll = melilite, Pl = plagioclase, Pyh = pyrrhotite, Tro = troilite, Fe = metallic iron, Gl = glass, Spl = spinel, Prv = perovskite, Cal = calcite, Nng = ninengerite (Mg,Fe)S.</p>
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<p>Matrix fragments of melilite-nepheline paralava, sample MN-1412. Scale bars: 50 µm for all BSE images, 5 µm for insets in panels (<b>e</b>,<b>f</b>,<b>h</b>), and 1 µm for insets in panel (<b>g</b>). (<b>a</b>–<b>d</b>) Spherules of Fe<sup>0</sup>, intergrown Fe<sup>0</sup> and troilite, Fe<sup>0</sup> inclusions in troilite and (<b>i</b>) troilite encloses of cubanite veinlets. Abbreviations are as follows: Nph = Na-Ca nepheline (davidsmithite), Mll = melilite, Pl = plagioclase, Cpx = clinopyroxene, Kur = kuratite, Spl = spinel, Tro = troilite, Fe = metallic Fe, Gth = goethite, Scb = schreibersite, Fe<sub>2</sub>P = barringerite or allabogdanite, Fe<sub>4</sub>P = steadite, Cbn = cubanite CuFe<sub>2</sub>S<sub>3</sub>, Cal = calcite.</p>
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<p>Matrix fragments of plagioclase–orthopyroxene paralava, sample MN-1406. Scale bars: 10 µm in panels (<b>a</b>,<b>b</b>) and 1 µm in panels (<b>c</b>–<b>f</b>) for BSE images. Abbreviations are as follows: Gl = glass, Opx = orthopyroxene, Pl = plagioclase, Crd-Sec = cordierite–sekaninaite, Tro = troilite, Fe = metallic iron, Scb = schreibersite, Std = steadite, Bn = bornite (?), Ccp = chalcopyrite, Cu-Fe-S = non-identified Cu-Fe sulfides.</p>
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<p>FeO–MgO and FeO–MgO–Al<sub>2</sub>O<sub>3</sub> phase diagrams according to thermodynamic modeling by Samoilova and Markovets [<a href="#B38-crystals-14-01052" class="html-bibr">38</a>]. Lines with arrows are crystallization paths of Mg–Fe and Mg–Fe–Al melts, which produced (<b>a</b>) magnesiowüstite–ferropericlase with Mg# 0.6–0.3 in the 1800–1600 °C temperature range and (<b>b</b>) a solid solution of spinel cotectic assemblage (Fe,Mg)Al<sub>2</sub>O<sub>4</sub> + MgO–FeO.</p>
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<p>Simplified Fe–P phase diagram at 1 bar, after Miettinen and Vassilev [<a href="#B44-crystals-14-01052" class="html-bibr">44</a>]. with additions (see text). Arrows are three crystallization paths of an Fe–P melt with different P contents. Path I: 1370 °C to 1165 °C, formation of Fe<sub>2</sub>P and then Fe<sub>2</sub>P + Fe<sub>3</sub>P; Path II: 1165 °C to 1048 °C, formation of Fe<sub>3</sub>P and then α-Fe + Fe<sub>3</sub>P; Path III: 1530 °C to 1048 °C, formation of α-Fe and then α-Fe + Fe<sub>3</sub>P.</p>
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<p>(<b>a</b>): Fe-rich corner of the Fe–S–P diagram, after Jones and Drake [<a href="#B45-crystals-14-01052" class="html-bibr">45</a>]. The solid line shows the location of the two-liquids solvus. M<sub>1</sub> and M<sub>1</sub><sup>1</sup> are invariant points (shown connected by dashed lines) where the next condensed phases stably coexist: M<sub>1</sub> and M<sub>1</sub><sup>1</sup> (Fe, Fe<sub>3</sub>P, two liquids) at ~1000 °C; E<sub>1</sub> (Fe, Fe<sub>3</sub>P, FeS) at 970 °C; M<sub>2</sub> and M<sub>2</sub><sup>1</sup> (Fe<sub>3</sub>P, Fe<sub>2</sub>P, two liquids) at 1150 °C; U<sub>2</sub> (Fe<sub>3</sub>P, Fe<sub>2</sub>P, FeS); (<b>b</b>): Fe–S–P phase diagram in the P–S section. The solid line is a boundary between the miscibility domains of liquids, and the dashed line limits the field of a homogeneous Fe–P–S melt at 1350 °C (IW buffer) and the field of two (phosphide and sulfide) liquids at 1250 °C (IW and QFI buffers), after Chabot and Drake [<a href="#B47-crystals-14-01052" class="html-bibr">47</a>].</p>
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<p>(<b>a</b>) Liquidus surface projection in the Fe-rich part of the ternary Fe–P–C system (1, 2, and 3 and lines with arrows show three evolution paths of the melt) and (<b>b</b>) vertical section in the ternary Fe–P–C system at 2.4 wt% C, after thermodynamic assessment by Bernhard et al. [<a href="#B50-crystals-14-01052" class="html-bibr">50</a>].</p>
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<p>Redox evolution (heavy arrow) during crystallization of magnesiowüstite–ferropericlase, iron phosphides (Fe<sub>2</sub>P, Fe<sub>3</sub>P), metallic iron, cohenite, wüstite, and magnetite (see text for explanation). Colored fields refer to hypothetical crystallization conditions of reducing mineral assemblages, in <span class="html-italic">T</span>–Lg<span class="html-italic">P</span><sub>O2</sub> coordinates: grey for melilite-nepheline paralavas and blue for mineral assemblage containing magnesiowüstite–ferropericlase (<a href="#crystals-14-01052-f006" class="html-fig">Figure 6</a>b and <a href="#crystals-14-01052-f007" class="html-fig">Figure 7</a>e–g). CCO, IW, IM, WM, FMQ, and MH are buffers. Buffers equilibria intersections are at 720 °C for CCO and IW and at 550 °C for IW and WM.</p>
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14 pages, 4606 KiB  
Article
Research on Multi-Scale Spatio-Temporal Graph Convolutional Human Behavior Recognition Method Incorporating Multi-Granularity Features
by Yulin Wang, Tao Song, Yichen Yang and Zheng Hong
Sensors 2024, 24(23), 7595; https://doi.org/10.3390/s24237595 - 28 Nov 2024
Viewed by 403
Abstract
Aiming at the problem that the existing human skeleton behavior recognition methods are insensitive to human local movements and show inaccurate recognition in distinguishing similar behaviors, a multi-scale spatio-temporal graph convolution method incorporating multi-granularity features is proposed for human behavior recognition. Firstly, a [...] Read more.
Aiming at the problem that the existing human skeleton behavior recognition methods are insensitive to human local movements and show inaccurate recognition in distinguishing similar behaviors, a multi-scale spatio-temporal graph convolution method incorporating multi-granularity features is proposed for human behavior recognition. Firstly, a skeleton fine-grained partitioning strategy is proposed, which initializes the skeleton data into data streams of different granularities. An adaptive cross-scale feature fusion layer is designed using a normalized Gaussian function to perform feature fusion among different granularities, guiding the model to focus on discriminative feature representations among similar behaviors through fine-grained features. Secondly, a sparse multi-scale adjacency matrix is introduced to solve the bias weighting problem that amplifies the multi-scale spatial domain modeling process under multi-granularity conditions. Finally, an end-to-end graph convolutional neural network is constructed to improve the feature expression ability of spatio-temporal receptive field information and enhance the robustness of recognition between similar behaviors. The feasibility of the proposed algorithm was verified on the public behavior recognition dataset MSR Action 3D, with a accuracy of 95.67%, which is superior to existing behavior recognition methods. Full article
(This article belongs to the Special Issue AI-Based Computer Vision Sensors & Systems)
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Figure 1
<p>Adjacency matrix topology diagram. (<b>a</b>–<b>c</b>) respectively represent the topological graphs of first-order, second-order, and third-order adjacency matrices used to connect human skeletal joints, while (<b>d</b>–<b>f</b>) respectively represent the topological graphs after constructing multi-scale adjacency matrices.</p>
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<p>Framework of multi-scale spatio-temporal graph convolutional network model incorporating multi-granularity features. (<b>a</b>) represents the overall framework of the proposed network, and (<b>b</b>) represents the framework of the multi-scale spatio-temporal convolutional module.</p>
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<p>Three granularity representation methods for MSR Action 3D. The blue nodes represent the original coarse-grained joints, and the red nodes represent the newly added fine-grained joints.</p>
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<p>The structure of cross-scale feature fusion layer (CSFL).</p>
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<p>Skeleton graphs of different granularities.</p>
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<p>The confusion matrix of the MSR Action 3D dataset. The darker the background color of each grid in the figure, the higher the recognition rate it represents.</p>
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22 pages, 13858 KiB  
Article
Large-Scale Origin–Destination Prediction for Urban Rail Transit Network Based on Graph Convolutional Neural Network
by Xuemei Wang, Yunlong Zhang and Jinlei Zhang
Sustainability 2024, 16(23), 10190; https://doi.org/10.3390/su162310190 - 21 Nov 2024
Viewed by 433
Abstract
Due to data sparsity, insufficient spatial relationships, and the complex spatial and temporal characteristics of passenger flow, it is very challenging to achieve a high prediction accuracy on Origin–Destination (OD) in a large urban rail transit network. This paper proposes a two-stage prediction [...] Read more.
Due to data sparsity, insufficient spatial relationships, and the complex spatial and temporal characteristics of passenger flow, it is very challenging to achieve a high prediction accuracy on Origin–Destination (OD) in a large urban rail transit network. This paper proposes a two-stage prediction network GCN-GRU, using a Graph Convolutional Network (GCN) with a Gated Recursive Unit (GRU). The GCN can obtain the adjacency relationship between different stations by selecting the adjacent neighborhoods and interacting neighborhoods of a station and capturing the spatial characteristics of the OD passenger flow. Then, an advanced weighted aggregator is employed to gather important information from the two above-mentioned types of neighborhoods to capture the spatial relationship of the network OD passenger flow and to perceive the sparsity and range of the OD data. On the other hand, the GRU can extract the temporal relationship, such as periodicity and other time-varying trends. The effectiveness of GCN-GRU is tested with a real-world urban rail transit dataset. The experimental results show that whether it is the OD passenger flow matrix of each period (one hour) on weekdays and weekends or the single-pair OD passenger flow between stations, the proposed GCN-GRU models perform better than the benchmark models. This study provides an important theoretical basis and practical applications for operators, thus promoting the sustainable development of urban rail transit systems. Full article
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<p>Heat map of OD passenger flow distribution of a metro network from 8:00 to 9:00 in the morning peak.</p>
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<p>GRU network structure.</p>
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<p>Large-scale OD passenger flow prediction process based on GCN-GRU.</p>
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<p>GCN network framework diagram.</p>
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<p>GRU network framework diagram.</p>
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<p>Urban railway transit network topology.</p>
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<p>The reduction percentage of prediction error indicators of GCN-GRU and HA on different days.</p>
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<p>The reduction of prediction error indicators of GCN-GRU and HA on different stations.</p>
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<p>The prediction effect picture of OD passenger flow GCN-GRU from 8:00 to 9:00 in the morning peak of a weekday (April 20).</p>
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<p>The prediction effect picture of OD passenger flow GCN-GRU from 18:00 to 19:00 in the evening peak of a weekday (April 23).</p>
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<p>The prediction effect picture of OD passenger flow GCN-GRU from 14:00 to 15:00 on a weekend (April 24).</p>
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<p>The OD passenger flow prediction effect picture of various models from station 35 to station 26.</p>
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<p>The OD passenger flow prediction effect picture of various models from station 0 to station 35.</p>
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<p>The OD passenger flow prediction effect picture of various models from station 51 to station 53.</p>
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<p>The OD passenger flow prediction effect picture of various models from station 23 to station 16.</p>
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14 pages, 283 KiB  
Article
Bounds for the Energy of Hypergraphs
by Liya Jess Kurian and Chithra Velu
Axioms 2024, 13(11), 804; https://doi.org/10.3390/axioms13110804 - 19 Nov 2024
Viewed by 347
Abstract
The concept of the energy of a graph has been widely explored in the field of mathematical chemistry and is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of a hypergraph is the trace [...] Read more.
The concept of the energy of a graph has been widely explored in the field of mathematical chemistry and is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of a hypergraph is the trace norm of its connectivity matrices, which generalize the concept of graph energy. In this paper, we establish bounds for the adjacency energy of hypergraphs in terms of the number of vertices, maximum degree, eigenvalues, and the norm of the adjacency matrix. Additionally, we compute the sum of squares of adjacency eigenvalues of linear k-hypergraphs and derive its bounds for k-hypergraph in terms of number of vertices and uniformity of the k-hypergraph. Moreover, we determine the Nordhaus–Gaddum type bounds for the adjacency energy of k-hypergraphs. Full article
(This article belongs to the Special Issue Recent Developments in Graph Theory)
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<p>Example for hypergraphs with <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mo>∥</mo> <mi>A</mi> <mo>∥</mo> </mrow> <mi>F</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>m</mi> <mfenced separators="" open="(" close=")"> <mi>m</mi> <mo>(</mo> <mi>k</mi> <mo>−</mo> <mn>2</mn> <mo>)</mo> <mo>+</mo> <mn>2</mn> </mfenced> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msubsup> <mrow> <mo>∥</mo> <mi>A</mi> <mo>∥</mo> </mrow> <mi>F</mi> <mn>2</mn> </msubsup> <mo>&lt;</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> </mrow> <mi>m</mi> <mfenced separators="" open="(" close=")"> <mi>m</mi> <mo>(</mo> <mi>k</mi> <mo>−</mo> <mn>2</mn> <mo>)</mo> <mo>+</mo> <mn>2</mn> </mfenced> </mrow> </semantics></math>.</p>
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14 pages, 4040 KiB  
Article
Analysis of the Radial Force of a Piezoelectric Actuator with Interdigitated Spiral Electrodes
by Yateng Wang, Tianxing Ren, Yuan Ren, Ruijie Gu and Yonggang Liu
Micromachines 2024, 15(11), 1378; https://doi.org/10.3390/mi15111378 - 15 Nov 2024
Viewed by 629
Abstract
The actuator is a critical component of the micromanipulator. By utilizing the properties of expansion and contraction, the piezoelectric actuator enables the manipulator to handle and grasp miniature objects during micromanipulation. However, in piezoelectric ceramic disc actuators with conventional surface electrode configurations, the [...] Read more.
The actuator is a critical component of the micromanipulator. By utilizing the properties of expansion and contraction, the piezoelectric actuator enables the manipulator to handle and grasp miniature objects during micromanipulation. However, in piezoelectric ceramic disc actuators with conventional surface electrode configurations, the actuating force generated in the radial direction is relatively limited. When used as the actuation element of the manipulator, achieving regulation over a wide range of operating strokes becomes challenging. Therefore, altering the electrode structure is necessary to generate a greater radial force, thus enhancing the positioning and grasping capabilities of the operating arm. This paper investigates a piezoelectric actuator with interdigitated spiral electrodes, featuring a constant pitch between adjacent electrodes. The radial force was tested under mechanical clamping conditions, and the influence of the electrical signal was examined. The characteristics of the electrode structure were described, and the working principles of the piezoelectric actuators were analyzed. Theoretical equations were derived for the macroscopic characterization of the radial clamping force of the actuator, based on the piezoelectric constitutive equation, geometric principles, and Bond matrix transformation relationships. A finite element model was developed, reflecting the features of the electrode structure, and finite element simulations were employed to verify the theoretical equations for radial force. To prepare the samples, encircled interdigitated spiral electrode lines were printed on the PZT-52 piezoelectric ceramic disc using a screen printing method. The clamping force experimental platform was established, and experiments on the clamping radial force were conducted with electrical signals of varying waveforms, frequencies, and voltages. The experimental results show that the piezoelectric ceramic disc actuator with an interdigitated spiral electrode line structure, when excited by a stable sine wave operating at 200 V and 0.2 Hz, generated a peak force of 0.37 N. It was 1.76 times greater than that produced by a previously utilized piezoelectric disc with conventional electrode structures. Full article
(This article belongs to the Special Issue Soft Actuators: Design, Fabrication and Applications, 2nd Edition)
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<p>Structure of the piezoelectric actuator with spiral electrodes.</p>
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<p>The deformation diagram of the electrode spacing sub-body.</p>
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<p>Overall model and segmentation models.</p>
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<p>Diagram of the finite element meshing model.</p>
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<p>Radial stress distribution.</p>
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<p>Flowchart for polarization and preparation of samples.</p>
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<p>Schematic diagram of the force test.</p>
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<p>Clamping force experimental device: 1. Antai ATA-2021 High Voltage Amplifier (Aigtek Electronic Technology Ltd., Xian, China); 2. Tektronix AFG1022 Signal Generator (Tektronix, Inc., Johnston, IA, USA); 3. Samples; 4. Digital force gauge (YueQing Handpi Instruments Co., Ltd., Yueqing, China); 5. Computer; 6. Damping block.</p>
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<p>Influence of the electrical signal waveform on the radial force: (<b>a</b>) Force–time history versus the signals; (<b>b</b>) Force response versus the signals.</p>
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<p>Influence of the voltage on the radial force: (<b>a</b>) Force–time history versus the voltage; (<b>b</b>) Force response versus the voltage.</p>
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<p>Influence of the frequency on the radial force: (<b>a</b>) Force–time history versus the frequency of the electrical signal; (<b>b</b>) Force response versus the frequency of the electrical signal.</p>
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16 pages, 2966 KiB  
Article
Integrated Extraction of Entities and Relations via Attentive Graph Convolutional Networks
by Chuhan Gao, Guixian Xu and Yueting Meng
Electronics 2024, 13(22), 4373; https://doi.org/10.3390/electronics13224373 - 8 Nov 2024
Viewed by 602
Abstract
For information security, entity and relation extraction can be applied in sensitive information protection, data leakage detection, and other aspects. The current approaches to entity relation extraction not only ignore the relevance and dependency between name entity recognition and relation extraction but also [...] Read more.
For information security, entity and relation extraction can be applied in sensitive information protection, data leakage detection, and other aspects. The current approaches to entity relation extraction not only ignore the relevance and dependency between name entity recognition and relation extraction but also may result in the cumulative propagation of errors. To solve this problem, it is proposed that an end-to-end joint entity and relation extraction model based on the Attention mechanism and Graph Convolutional Network (GCN) to simultaneously extract named entities and their relationships. The model includes three parts: the detection of entity span, the construction of an entity relation weighted graph, and the inference of entity relation type. Firstly, the detection of entity spans is viewed as a sequence labeling problem, and a multi-feature fusion approach for word embedding representation is designed to calculate all entity spans in a sentence to form an entity span matrix. Secondly, the entity span matrix is employed in the Multi-Head Attention mechanism for constructing the weighted adjacency matrix of the entity relation graph. Finally, for the inference of entity relation type, considering the interaction between entities and relations, the entity span matrix and relation connection matrix are simultaneously fed into the GCN for integrated extraction of entities and relations. Our model is evaluated on the public NYT dataset, attaining a precision of 66.4%, a recall of 63.1%, and an F1 score of 64.7% for joint entity and relation extraction, significantly outperforming other approaches. Experiments demonstrate that the proposed model is helpful for inferring entities and relations, considering the interaction between entities and relations through the Attention mechanism and GCN. Full article
(This article belongs to the Special Issue Network Security Management in Heterogeneous Networks)
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<p>The integrated extraction frame of entities and relations.</p>
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<p>Diagram of entity span detection.</p>
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<p>Structure of the Multi-Head Attention.</p>
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<p>Structure of the Scaled Dot-Product Attention.</p>
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<p>Construction of relation weight graph.</p>
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<p>The architecture of the GCN.</p>
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<p>Precision of different entity relation extraction models.</p>
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<p>Recall of various entity relation extraction models.</p>
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<p>F1 of different entity relation extraction models.</p>
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<p>Comparison of different entity relation extraction models.</p>
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<p>Comparison of various word embedding.</p>
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<p>Comparison of different extraction models.</p>
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<p>Comparison of various GCN layers.</p>
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22 pages, 7112 KiB  
Article
A New Encryption Algorithm Utilizing DNA Subsequence Operations for Color Images
by Saeed Mirzajani, Seyed Shahabeddin Moafimadani and Majid Roohi
AppliedMath 2024, 4(4), 1382-1403; https://doi.org/10.3390/appliedmath4040073 - 4 Nov 2024
Viewed by 641
Abstract
The computer network has fundamentally transformed modern interactions, enabling the effortless transmission of multimedia data. However, the openness of these networks necessitates heightened attention to the security and confidentiality of multimedia content. Digital images, being a crucial component of multimedia communications, require robust [...] Read more.
The computer network has fundamentally transformed modern interactions, enabling the effortless transmission of multimedia data. However, the openness of these networks necessitates heightened attention to the security and confidentiality of multimedia content. Digital images, being a crucial component of multimedia communications, require robust protection measures, as their security has become a global concern. Traditional color image encryption/decryption algorithms, such as DES, IDEA, and AES, are unsuitable for image encryption due to the diverse storage formats of images, highlighting the urgent need for innovative encryption techniques. Chaos-based cryptosystems have emerged as a prominent research focus due to their properties of randomness, high sensitivity to initial conditions, and unpredictability. These algorithms typically operate in two phases: shuffling and replacement. During the shuffling phase, the positions of the pixels are altered using chaotic sequences or matrix transformations, which are simple to implement and enhance encryption. However, since only the pixel positions are modified and not the pixel values, the encrypted image’s histogram remains identical to the original, making it vulnerable to statistical attacks. In the replacement phase, chaotic sequences alter the pixel values. This research introduces a novel encryption technique for color images (RGB type) based on DNA subsequence operations to secure these images, which often contain critical information, from potential cyber-attacks. The suggested method includes two main components: a high-speed permutation process and adaptive diffusion. When implemented in the MATLAB software environment, the approach yielded promising results, such as NPCR values exceeding 98.9% and UACI values at around 32.9%, demonstrating its effectiveness in key cryptographic parameters. Security analyses, including histograms and Chi-square tests, were initially conducted, with passing Chi-square test outcomes for all channels; the correlation coefficient between adjacent pixels was also calculated. Additionally, entropy values were computed, achieving a minimum entropy of 7.0, indicating a high level of randomness. The method was tested on specific images, such as all-black and all-white images, and evaluated for resistance to noise and occlusion attacks. Finally, a comparison of the proposed algorithm’s NPCR and UAC values with those of existing methods demonstrated its superior performance and suitability. Full article
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<p>DNA subsequence elongation and truncation processes.</p>
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<p>The schematic of the utilized procedure: (<b>a</b>) The schematic of the image encryption method, (<b>b</b>) The schematic of the decryption method.</p>
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<p>Encryption and decryption of images: (<b>a</b>–<b>d</b>): Plain images. (<b>e</b>–<b>h</b>): Respective encryption of images. (<b>i</b>–<b>l</b>): Respective decryption of images.</p>
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<p>(<b>a</b>) Original color image of Daryasar; (<b>b</b>–<b>d</b>) plain image histograms for R, G, and B, respectively; (<b>e</b>) cipher image; (<b>f</b>–<b>h</b>) cipher image histograms, respectively.</p>
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<p>Correlation histograms. (<b>a</b>,<b>c</b>,<b>e</b>) show the histograms for the original image, while (<b>b</b>,<b>d</b>,<b>f</b>) display the histograms for the encrypted image.</p>
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<p>Correlation histograms. (<b>a</b>,<b>c</b>,<b>e</b>) show the histograms for the original image, while (<b>b</b>,<b>d</b>,<b>f</b>) display the histograms for the encrypted image.</p>
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<p>Encrypted images with correct and incorrect initial keys, and their differences from the original encrypted images: (<b>a</b>–<b>e</b>) depict five newly encrypted images using the specified keys, while (<b>f</b>–<b>j</b>) illustrate the differences between the incorrectly encrypted images and the original image.</p>
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<p>Evaluation with selected plain images for uniform color patterns: (<b>a</b>) image with all-white pixels, (<b>b</b>) encrypted version of the all-white image, (<b>c</b>) histogram of the red channel for the all-white image, (<b>d</b>) image with all-black pixels, (<b>e</b>) encrypted version of the all-black image, (<b>f</b>) histogram of the red channel for the all-black image.</p>
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<p>Outcomes of the noise attack evaluation for the “Guangzhou” image ((<b>a</b>,<b>b</b>): 10% noise attack, (<b>c</b>,<b>d</b>): 15% noise attack, (<b>e</b>,<b>f</b>): 20% noise attack).</p>
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19 pages, 4846 KiB  
Article
Development of Hybrid Implantable Local Release Systems Based on PLGA Nanoparticles with Applications in Bone Diseases
by Maria Viorica Ciocîlteu, Andreea Gabriela Mocanu, Andrei Biță, Costel Valentin Manda, Claudiu Nicolicescu, Gabriela Rău, Ionela Belu, Andreea Silvia Pîrvu, Maria Balasoiu, Valentin Nănescu and Oana Elena Nicolaescu
Polymers 2024, 16(21), 3064; https://doi.org/10.3390/polym16213064 - 31 Oct 2024
Viewed by 696
Abstract
The current strategy for treating osteomyelitis includes surgical procedures for complete debridement of the formed biofilm and necrotic tissues, systemic and oral antibiotic therapy, and the clinical use of cements and three-dimensional scaffolds as bone defect fillers and delivery systems for therapeutic agents. [...] Read more.
The current strategy for treating osteomyelitis includes surgical procedures for complete debridement of the formed biofilm and necrotic tissues, systemic and oral antibiotic therapy, and the clinical use of cements and three-dimensional scaffolds as bone defect fillers and delivery systems for therapeutic agents. The aim of our research was to formulate a low-cost hybrid nanoparticulate biomaterial using poly(lactic-co-glycolic acid) (PLGA), in which we incorporated the therapeutic agent (ciprofloxacin), and to deposit this material on titanium plates using the matrix-assisted pulsed laser evaporation (MAPLE) technique. The deposited material demonstrated antibacterial properties, with all analyzed samples inhibiting the growth of tested bacterial strains, confirming the release of active substances from the investigated biocomposite. The poly(lactic-co-glycolic acid)-ciprofloxacin (PLGA-CIP) nanoparticle scaffolds displayed a prolonged local sustained release profile over a period of 45 days, which shows great promise in bone infections. Furthermore, the burst release ensures a highly efficient concentration, followed by a constant sustained release which allows the drug to remain in the implant-adjacent area for an extended time period. Full article
(This article belongs to the Special Issue Polymer Materials for Drug Delivery and Tissue Engineering II)
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<p>Biomaterial evolution in bone repair and regeneration.</p>
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<p>Formulation of PLGA-CIP and PLGA-CIP implantable local release systems.</p>
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<p>FTIR spectra of (<b>A</b>) PLGA-CIP and PLGA–CIP films deposited by MAPLE on titanium supports; (<b>B</b>) CIP; (<b>C</b>) PLGA.</p>
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<p>Volume distribution of PLGA-CIP (500 rpm) (<b>A</b>); number distribution of PLGA-CIP (500 rpm) (<b>B</b>); volume distribution of PLGA-CIP (1500 rpm) (<b>C</b>); number distribution of PLGA-CIP (1500 rpm) (<b>D</b>).</p>
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<p>Volume distribution of PLGA-CIP (500 rpm) (<b>A</b>); number distribution of PLGA-CIP (500 rpm) (<b>B</b>); volume distribution of PLGA-CIP (1500 rpm) (<b>C</b>); number distribution of PLGA-CIP (1500 rpm) (<b>D</b>).</p>
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<p>Scanning electron microscopy images of (<b>A</b>) PLGA-CIP (1500 rpm) and (<b>B</b>) PLGA-CIP (500 rpm).</p>
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<p>CIP release from the control sample: mechanical mixture CIP:HA (<span class="html-italic">w</span>:<span class="html-italic">w</span>) (25:75).</p>
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<p>CIP release from PLGA-CIP scaffolds.</p>
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<p>Release profile of CIP from implantable PLGA-CIP LRS.</p>
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<p>Korsmeyer–Peppas model for the mechanism of drug release.</p>
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<p>Higuchi release model or the mechanism of drug release.</p>
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<p>Antibacterial activity of scaffolds over tested germs.</p>
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<p>The zone of inhibition obtained for (<b>A</b>) PLGA-CIP scaffolds on Staphylococcus aureus; (<b>B</b>) PLGA-CIP scaffolds (1500 rpm) on methicillin-resistant Staphylococcus aureus using the disk diffusion agar method.</p>
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<p>The zone of inhibition obtained for implantable PLGA-CIP LRS (1500 rpm) on <span class="html-italic">Staphylococcus aureus.</span></p>
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29 pages, 11619 KiB  
Article
MSA-GCN: Multistage Spatio-Temporal Aggregation Graph Convolutional Networks for Traffic Flow Prediction
by Ji Feng, Jiashuang Huang, Chang Guo and Zhenquan Shi
Mathematics 2024, 12(21), 3338; https://doi.org/10.3390/math12213338 - 24 Oct 2024
Viewed by 568
Abstract
Timely and accurate traffic flow prediction is crucial for stabilizing road conditions, reducing environmental pollution, and mitigating economic losses. While current graph convolution methods have achieved certain results, they do not fully leverage the true advantages of graph convolution. There is still room [...] Read more.
Timely and accurate traffic flow prediction is crucial for stabilizing road conditions, reducing environmental pollution, and mitigating economic losses. While current graph convolution methods have achieved certain results, they do not fully leverage the true advantages of graph convolution. There is still room for improvement in simultaneously addressing multi-graph convolution, optimizing graphs, and simulating road conditions. Based on this, this paper proposes MSA-GCN: Multistage Spatio-Temporal Aggregation Graph Convolutional Networks for Traffic Flow Prediction. This method overcomes the aforementioned issues by dividing the process into different stages and achieves promising prediction results. In the first stage, we construct a latent similarity adjacency matrix and address the randomness interference features in similarity features through two optimizations using the proposed ConvGRU Attention Layer (CGAL module) and the Causal Similarity Capture Module (CSC module), which includes Granger causality tests. In the second stage, we mine the potential correlation between roads using the Correlation Completion Module (CC module) to create a global correlation adjacency matrix as a complement for potential correlations. In the third stage, we utilize the proposed Auto-LRU autoencoder to pre-train various weather features, encoding them into the model’s prediction process to enhance its ability to simulate the real world and improve interpretability. Finally, in the fourth stage, we fuse these features and use a Bidirectional Gated Recurrent Unit (BiGRU) to model time dependencies, outputting the prediction results through a linear layer. Our model demonstrates a performance improvement of 29.33%, 27.03%, and 23.07% on three real-world datasets (PEMSD8, LOSLOOP, and SZAREA) compared to advanced baseline methods, and various ablation experiments validate the effectiveness of each stage and module. Full article
(This article belongs to the Topic New Advances in Granular Computing and Data Mining)
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<p>MSA-GCN model framework.</p>
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<p>Stage 1 flowchart.</p>
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<p>Pearson threshold screening experiment.</p>
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<p>Comparisonof average prediction performance over 12 time steps. (<b>a</b>) PEMSD8, (<b>b</b>) LOSLOOP, (<b>c</b>) SZAREA.</p>
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<p>Ablation experiments: specific RMSE values for each time step. (<b>a</b>) PEMSD8, (<b>b</b>) LOSLOOP, (<b>c</b>) SZAREA.</p>
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<p>Convergence process of loss values for different datasets, training time consumed, number of parameters statistics. (<b>a</b>) PEMSD8—loss convergence process, (<b>b</b>) PEMSD8—training time and number of parameters, (<b>c</b>) LOSLOOP—loss convergence process, (<b>d</b>) LOSLOOP—training time and number of parameters, (<b>e</b>) SZAREA—loss convergence process, (<b>f</b>) SZAREA—training time and number of parameters.</p>
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<p>Fitted plots of predicted and true values of some nodes for different datasets. (<b>a</b>) Real and predicted features of PEMSD8 dataset node 12, (<b>b</b>) real and predicted features of PEMSD8 dataset node 70, (<b>c</b>) real and predicted features of LOSLOOP dataset node 43, (<b>d</b>) real and predicted features of LOSLOOP dataset node 83, (<b>e</b>) real and predicted features of SZAREA dataset node 7, (<b>f</b>) real and predicted features of SZAREA dataset node 63.</p>
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14 pages, 313 KiB  
Article
The Singularity of Three Kinds of New Tricyclic Graphs
by Haicheng Ma, Yanbo Gao and Xiaojie You
Symmetry 2024, 16(11), 1416; https://doi.org/10.3390/sym16111416 - 24 Oct 2024
Viewed by 821
Abstract
A graph G is singular if its adjacency matrix is singular. The starting vertices of two paths Pb1 and Pb2 are simultaneously bound to the ending vertex of the path Ps1, and the ending vertices of [...] Read more.
A graph G is singular if its adjacency matrix is singular. The starting vertices of two paths Pb1 and Pb2 are simultaneously bound to the ending vertex of the path Ps1, and the ending vertices of the paths Pb1 and Pb2 are bound to the starting vertex of path Ps2. Meanwhile, the starting vertex of the path Ps1 is bound to a vertex of the cycle Ca1, and the ending vertex of the path Ps2 is bound to a vertex of the cycle Ca2. Thus, the resulting graph is written as ξ(a1,a2,b1,b2,s1,s2). This is denoted by ζ(a1,a2,b1,b2,s)=ξ(a1,a2,b1,b2,1,s) and ε(a1,a2,b1,b2)=ζ(a1,a2,b1,b2,1), which are referred to as the ξ-graph, ζ-graph and ε-graph for short, respectively. It is known that there are 15 kinds of tricyclic graphs. The purpose of this paper is to study the necessary and sufficient conditions for ξ-graphs, ζ-graphs and ε-graphs to be singular graphs. We analyzed the structure of the elementary spanning subgraphs of the graph G=ξ(a1,a2,b1,b2,s1,s2). By calculating the determinant of the adjacency matrix of the graph G, the necessary and sufficient conditions for the determinant of the graph G to be zero is obtained, and so the necessary and sufficient conditions for graph ξ(a1,a2,b1,b2,s1,s2) to be singular are obtained. As the corollaries, the necessary and sufficient conditions for graphs ζ(a1,a2,b1,b2,s) and ε(a1,a2,b1,b2) to be singular are also obtained. Full article
(This article belongs to the Section Mathematics)
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<p>Graph <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>s</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Graph <math display="inline"><semantics> <mrow> <mi>ζ</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>,</mo> <mi>s</mi> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Graph <math display="inline"><semantics> <mrow> <mi>ε</mi> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>The connected tricyclic graphs without pendant vertices.</p>
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<p>Graph <span class="html-italic">X</span> and graph <span class="html-italic">Y</span>.</p>
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<p>Graphs <span class="html-italic">Z</span> and <span class="html-italic">W</span>, and the structure of elementary spanning subgraphs of graph <span class="html-italic">Z</span>.</p>
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21 pages, 4945 KiB  
Article
An Enhanced Fault Localization Technique for Distribution Networks Utilizing Cost-Sensitive Graph Neural Networks
by Zilong Wang, Birong Huang, Bingyang Zhou, Jianhua Chen and Yichen Wang
Processes 2024, 12(11), 2312; https://doi.org/10.3390/pr12112312 - 22 Oct 2024
Viewed by 771
Abstract
Accurate and timely fault diagnosis is of great significance for the stable operation of a distribution network. Traditional artificial intelligence-based localization methods rely heavily on large-scale labeled datasets, making them prone to being affected by distributed generators. To address this issue, this study [...] Read more.
Accurate and timely fault diagnosis is of great significance for the stable operation of a distribution network. Traditional artificial intelligence-based localization methods rely heavily on large-scale labeled datasets, making them prone to being affected by distributed generators. To address this issue, this study proposes a fault location method for distribution systems using a cost-sensitive graph attention network model. In this approach, the physical structure of the distribution network is considered a crucial constraint for model training, thereby enhancing its information perception capabilities. Specifically, the electrical nodes and lines of the distribution network are mapped to the vertices and edges within the graph attention network, with the attention weights determined by the correlation of adjacent node fault characteristics, thus improving the sensitivity to grounding faults. Additionally, a cost-sensitive matrix is used to balance class distribution, enhancing the robustness and generalization ability of the model. Fault localization experiments were conducted on the IEEE-33 bus distribution system to validate the effectiveness of the proposed fault localization method. Factors such as data disturbance, varying fault grounding resistances, and distributed power supply access were employed to assess the model’s anti-interference performance. The experimental results demonstrate that the fault location method exhibits high positioning accuracy and excellent robustness. Full article
(This article belongs to the Section Process Control and Monitoring)
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<p>Graph structure of IEEE-33 bus distribution system.</p>
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<p>Influence of DG access on node voltage and node current.</p>
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<p>Power flow of distribution network with DGs.</p>
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<p>Structure of proposed fault location framework.</p>
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<p>Graph attention layer.</p>
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<p>Multi-head graph attention mechanism (<math display="inline"><semantics> <mrow> <mi>M</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>).</p>
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<p>The process of transforming graph relationships into adjacency matrices.</p>
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<p>Model structure.</p>
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<p>Fault location selection in IEEE-33 bus distribution network.</p>
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<p>Batch training of <span class="html-italic">n</span>-group graph data.</p>
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<p>Training loss of different fault location models.</p>
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<p>Testing confusion matrix of the GAT and proposed model.</p>
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<p>Impact of data disturbances on model performance.</p>
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<p>Impact of fault resistance on model performance.</p>
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<p>Comparison of the effects of DG integration on the model.</p>
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25 pages, 15710 KiB  
Article
TG-PGAT: An AIS Data-Driven Dynamic Spatiotemporal Prediction Model for Ship Traffic Flow in the Port
by Jianwen Ma, Yue Zhou, Yumiao Chang, Zhaoxin Zhu, Guoxin Liu and Zhaojun Chen
J. Mar. Sci. Eng. 2024, 12(10), 1875; https://doi.org/10.3390/jmse12101875 - 18 Oct 2024
Viewed by 807
Abstract
Accurate prediction of ship traffic flow is essential for developing intelligent maritime transportation systems. To address the complexity of ship traffic flow data in the port and the challenges of capturing its dynamic spatiotemporal dependencies, a dynamic spatiotemporal model called Temporal convolutional network-bidirectional [...] Read more.
Accurate prediction of ship traffic flow is essential for developing intelligent maritime transportation systems. To address the complexity of ship traffic flow data in the port and the challenges of capturing its dynamic spatiotemporal dependencies, a dynamic spatiotemporal model called Temporal convolutional network-bidirectional Gated recurrent unit-Pearson correlation coefficient-Graph Attention Network (TG-PGAT) is proposed for predicting traffic flow in port waters. This model extracts spatial features of traffic flow by combining the adjacency matrix and spatial dynamic coefficient correlation matrix within the Graph Attention Network (GAT) and captures temporal features through the concatenation of the Temporal Convolutional Network (TCN) and Bidirectional Gated Recurrent Unit (BiGRU). The proposed TG-PGAT model demonstrates higher prediction accuracy and stability than other classic traffic flow prediction methods. The experimental results from multiple angles, such as ablation experiments and robustness tests, further validate the critical role and strong noise resistance of different modules in the TG-PGAT model. The experimental results of visualization demonstrate that this model not only exhibits significant predictive advantages in densely trafficked areas of the port but also outperforms other models in surrounding areas with sparse traffic flow data. Full article
(This article belongs to the Special Issue Management and Control of Ship Traffic Behaviours)
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<p>Gridded results of the study waters.</p>
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<p>Spatial influencing factors of ship traffic flow in port waters.</p>
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<p>VMD time-series decomposition of ship traffic flow in the port.</p>
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<p>Thermal map of spatial nodes related to ship traffic flow in the port.</p>
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<p>Architecture of the TG-PGAT model.</p>
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<p>The calculation of the spatial attention coefficient of ship traffic flow in the port using GAT.</p>
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<p>Fusion strategy for spatial features of ship traffic flow in the port.</p>
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<p>The architecture of the TCN model for extracting time-series features of ship traffic flow in the port (<span class="html-italic">a</span> represents the TCN neural network architecture, <span class="html-italic">b</span> represents the residual block, and <span class="html-italic">c</span> represents the dilated causal convolution).</p>
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<p>Extraction steps of temporal features of ship traffic flow in the port using BiGRU.</p>
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<p>Loss values of different loss functions.</p>
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<p>Loss values of different optimizers.</p>
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<p>Error values of different random dropout parameters. (<b>a</b>) <span class="html-italic">MAE</span>; (<b>b</b>) <span class="html-italic">RMSE</span>.</p>
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<p>Training set effect of the TG-PGAT model.</p>
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<p>Testing set effect of the TG-PGAT model.</p>
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<p>Distribution of error indicators for each model under different prediction durations. (<b>a</b>) prediction duration of 1 h; (<b>b</b>) prediction duration of 2 h; (<b>c</b>) prediction duration of 3 h.</p>
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<p>The training process of ablation experiment.</p>
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<p>Comparison of error indicators for prediction effects in ablation experiments. (<b>a</b>) <span class="html-italic">MAE</span> error; (<b>b</b>) <span class="html-italic">RMSE</span> error; (<b>c</b>) <span class="html-italic">MAPE</span> error.</p>
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<p>Comparison of error indicators for prediction effects in ablation experiments. (<b>a</b>) <span class="html-italic">MAE</span> error; (<b>b</b>) <span class="html-italic">RMSE</span> error; (<b>c</b>) <span class="html-italic">MAPE</span> error.</p>
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<p>Variations in evaluation indicators after adding Gaussian noise for different prediction durations.</p>
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<p>Comparison of traffic flow prediction by different models at various temporal nodes within a day. (<b>a</b>) node x5y5; (<b>b</b>) node x10y4.</p>
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<p>Distribution of traffic flow prediction error values by different models at various spatial nodes in port waters. (<b>a</b>) CNN-LSTM; (<b>b</b>) SDSTGNN; (<b>c</b>) STA-BiLSTM; (<b>d</b>) TG-PGAT.</p>
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<p>Distribution of traffic flow prediction error values by different models at various spatial nodes in port waters. (<b>a</b>) CNN-LSTM; (<b>b</b>) SDSTGNN; (<b>c</b>) STA-BiLSTM; (<b>d</b>) TG-PGAT.</p>
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15 pages, 425 KiB  
Article
Sequence of Bounds for Spectral Radius and Energy of Digraph
by Jietong Zhao, Saira Hameed, Uzma Ahmad, Ayesha Tabassum and Leila Asgharsharghi
Symmetry 2024, 16(10), 1386; https://doi.org/10.3390/sym16101386 - 18 Oct 2024
Viewed by 923
Abstract
The graph spectra analyze the structure of the graph using eigenspectra. The spectral graph theory deals with the investigation of graphs in terms of the eigenspectrum. In this paper, the sequence of lower bounds for the spectral radius of digraph D having at [...] Read more.
The graph spectra analyze the structure of the graph using eigenspectra. The spectral graph theory deals with the investigation of graphs in terms of the eigenspectrum. In this paper, the sequence of lower bounds for the spectral radius of digraph D having at least one doubly adjacent vertex in terms of indegree is proposed. Particularly, it is exhibited that ρ(D)αj=p=1m(χj+1(p))2p=1m(χj(p))2, such that equality is attained iff D=G+ {DE Cycle}, where each component of associated graph is a k-regular or (k1,k2) semiregular bipartite. By utilizing the sequence of lower bounds of the spectral radius of D, the sequence of upper bounds of energy of D, where the sequence decreases when eUαj and increases when eU>αj, are also proposed. All of the obtained inequalities are elaborated using examples. We also discuss the monotonicity of these sequences. Full article
(This article belongs to the Special Issue Symmetry in Combinatorics and Discrete Mathematics)
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<p>(2, 3) semi-regular bipartite digraph (<math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">D</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </semantics></math>.</p>
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<p><math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">D</mi> <mn>2</mn> </msub> <mo>=</mo> <mover accent="true"> <msub> <mi mathvariant="script">K</mi> <mn>3</mn> </msub> <mo>↔</mo> </mover> <mo>+</mo> <mi mathvariant="bold">e</mi> </mrow> </semantics></math>.</p>
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<p><math display="inline"><semantics> <mrow> <msub> <mi mathvariant="script">D</mi> <mn>3</mn> </msub> <mo>=</mo> <mover accent="true"> <msub> <mi mathvariant="script">K</mi> <mn>4</mn> </msub> <mo>↔</mo> </mover> </mrow> </semantics></math>.</p>
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<p><math display="inline"><semantics> <msub> <mi mathvariant="script">D</mi> <mn>4</mn> </msub> </semantics></math>.</p>
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