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Search Results (1,709)

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15 pages, 527 KB  
Review
Physiological Bio-Regeneration in Aesthetic Medicine: A Conceptual Framework and Narrative Review of PEGDE-HA and CaHA-Based Formulations
by Maurizio Cavallini, Raquel Fernández de Castro Isalguez, Francesco Marchetti, Izumrud Ramazanova Kurbankadieva, Ricardo Augusto Sandoval Vásquez, Diogo Pereira Forjaz, Silvia Zimbres and Dissapong Panithaporn
Cosmetics 2026, 13(2), 67; https://doi.org/10.3390/cosmetics13020067 - 12 Mar 2026
Viewed by 527
Abstract
Aesthetic medicine has progressed from the early 2000s fascination with bio-stimulation to the current dominance of hyaluronic acid (HA) fillers, prized for immediate, predictable, and reversible volumizing effects. Recently, demand for more natural results, stronger emphasis on skin quality, and increased post-pandemic self-scrutiny [...] Read more.
Aesthetic medicine has progressed from the early 2000s fascination with bio-stimulation to the current dominance of hyaluronic acid (HA) fillers, prized for immediate, predictable, and reversible volumizing effects. Recently, demand for more natural results, stronger emphasis on skin quality, and increased post-pandemic self-scrutiny have renewed interest in regenerative strategies, sometimes called the “second wave of bio-stimulation.” This trend highlights the need for clearer terminology and a cautious, evidence-based reading of proposed biological mechanisms. This narrative review proposes a framework in which bio-regeneration denotes a hypothesized, controlled induction of physiological processes, fibroblast activation, collagen and elastin synthesis, extracellular matrix remodeling, and immune modulation, potentially producing sustained improvements in dermal structure and function beyond simple filling. Among emerging technologies, polyethylene glycol diglycidyl ether (PEGDE) cross-linking is reported to create a stable, flexible HA scaffold with homogeneous tissue integration, favorable rheology, thermal stability, and a reduced inflammatory profile, supporting safer multimodal use with energy-based devices. The framework is illustrated with PEGDE-crosslinked HA combined with low-concentration calcium hydroxyapatite (CaHA), exemplified by a PEGDE-HA filler containing CaHA microspheres plus glycine and L-proline. These formulations aim to deliver immediate correction via HA and delayed stimulatory effects possibly driven by gradual CaHA exposure and macrophage-associated signaling. Available clinical, imaging, and histological observations, including prospective ultrasound and biopsy assessments, suggest progressive dermal thickening and predominant type I collagen expression, without pathological inflammation or granuloma formation. Although evidence remains preliminary and largely non-comparative, findings are compatible with controlled remodeling and resolving inflammation; however, the underlying mechanism and any ‘regenerative’ versus ‘reparative’ classification require controlled comparative studies. Full article
(This article belongs to the Section Cosmetic Dermatology)
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27 pages, 2343 KB  
Article
Democratizing Urban Well-Being: A Virtual Reality and Eye-Tracking Analysis of Biophilic Interventions Across Socioeconomic Contexts
by Cleiton Ferreira, Marina Guil-Jiménez, Paula Latorre, Aurora Molina-Muñoz, Sergio Castaño-Castaño and Francisco Nieto-Escamez
Computers 2026, 15(3), 149; https://doi.org/10.3390/computers15030149 - 1 Mar 2026
Viewed by 272
Abstract
In this pilot study, we investigate the psychological and attentional impact of biophilic urban interventions using an immersive virtual reality (VR) framework integrated with real-time eye-tracking. Specifically, it examines whether bio-esthetic enhancements can mitigate perceptual inequalities across neighborhoods of varying socioeconomic status (SES). [...] Read more.
In this pilot study, we investigate the psychological and attentional impact of biophilic urban interventions using an immersive virtual reality (VR) framework integrated with real-time eye-tracking. Specifically, it examines whether bio-esthetic enhancements can mitigate perceptual inequalities across neighborhoods of varying socioeconomic status (SES). Sixteen participants viewed original and digitally enhanced fixed-viewpoint 360° videos of Low-, Medium-, and High-SES environments while a comprehensive suite of oculomotor dynamics and psychometric responses were recorded. Results confirmed a significant Condition × SES interaction across both subjective preference (Liking) and esthetic evaluation (η2p = 0.41), suggesting a role for biophilic design as a “socio-perceptual equalizer”: while baseline ratings consistently favored High-SES areas, interventions in Low-SES contexts yielded the highest marginal gains, effectively bridging the gap with privileged environments. Eye-tracking metrics revealed that this convergence was associated with active visual engagement, with Enhanced Low-SES scenes eliciting the highest fixation counts and visual coverage. However, a critical dissociation emerged between immediate affective improvement and self-reported stress reduction. Elevated saccadic velocities in Enhanced Low-SES scenes are consistent with a state of “hard fascination” or novelty-induced arousal. This pattern implies that while biophilia elements boost positive affect, physiological restoration may be a dose-dependent process, requiring sufficient exposure duration to transition from curiosity-driven scanning to the “soft fascination” linked to stress recovery. These findings provide preliminary evidence for integrated XR analytics as a tool for evidence-based urban design and are discussed in the context of the equigenesis hypothesis. Full article
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37 pages, 6774 KB  
Article
Evaluating WELL-Informed Biophilic Façades in Automated Retail Environments: A Multimodal Eye-Tracking and Facial Expression Analysis
by Jie Yun and Nayeon Kim
Buildings 2026, 16(4), 876; https://doi.org/10.3390/buildings16040876 - 22 Feb 2026
Viewed by 443
Abstract
Global urbanization redirects attention toward the sensory quality of the built environment as a decisive factor in public health and psychological resilience. In automated retail, façades function as sensory interfaces to mitigate the psychological alienation and sensory deprivation inherent in automated nodes. This [...] Read more.
Global urbanization redirects attention toward the sensory quality of the built environment as a decisive factor in public health and psychological resilience. In automated retail, façades function as sensory interfaces to mitigate the psychological alienation and sensory deprivation inherent in automated nodes. This preliminary study proposes and empirically validates a multimodal evaluation framework for assessing WELL-informed, AI-generated biophilic façade designs in automated retail contexts. Grounded in Environment-Based Design (EBD) theory, the framework systematically integrates health-oriented design logic with generative AI–based façade synthesis and multimodal human-response evaluation. To evaluate the effectiveness of the proposed methodology, this study pursued three specific objectives: (1) to utilize a curated series of architectural façade variations with calibrated biophilic complexity derived from an environment-based AI generative framework, as experimental stimuli, (2) to quantify subconscious responses represented by gaze patterns and behavioral indicators elicited by these configurations, and (3) to analyze the correlation and potential divergence between implicit physiological responses and explicit conscious aesthetic appraisals. The multimodal experiment involving 30 participants integrated eye-tracking, facial expression analysis, and Semantic Differential (SD) scales. Area of Interest (AOI)-based visual attention analysis indicated that biophilic complexity, particularly the integration of organic patterns and natural materials, significantly enhanced subconscious visual interest and sustained engagement within specific design zones. The findings unveiled a complexity–aesthetic paradox where subconscious physiological and behavioral indicators exhibited peak engagement with high-complexity patterns while conscious aesthetic preference favored material-driven structural clarity. Statistical verification via repeated measures correlation analysis revealed a lack of significant linear association between instinctive physiological engagement and explicit aesthetic appraisal, highlighting a notable divergence between implicit and explicit responses. In conclusion, grounded in an EBD–driven evaluation framework, this research establishes a systematic evaluation methodology for health-conscious design, recommending a material-first strategy with pattern as an enhancement to align subconscious fascination with psychological comfort. Full article
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35 pages, 37297 KB  
Article
Heterogeneous Acoustofluidic Distributions Induced by Different Radiation Surface Arrangements in Various Pseudo-Sierpiński-Carpet-Shaped Chambers
by Qiang Tang, Boyang Li, Chen Li, Junjie Wang, Huiyu Huang, Yulong Hu, Kan Zhu, Hao Chen, Xu Wang and Songfei Su
Micromachines 2026, 17(2), 259; https://doi.org/10.3390/mi17020259 - 16 Feb 2026
Viewed by 624
Abstract
In this research, an innovative scheme to generate heterogeneous acoustofluidic distributions in various pseudo-Sierpiński-carpet-shaped chambers with different filling fractions and cross-sectional configurations has been proposed and calculated for topographical manipulation of large-scale micro-particles. All of the structural components positioned in the pseudo-fractal chambers [...] Read more.
In this research, an innovative scheme to generate heterogeneous acoustofluidic distributions in various pseudo-Sierpiński-carpet-shaped chambers with different filling fractions and cross-sectional configurations has been proposed and calculated for topographical manipulation of large-scale micro-particles. All of the structural components positioned in the pseudo-fractal chambers are symmetrically distributed in space, and all ultrasonic radiation surfaces hold the unified settings of input frequency point, oscillation amplitude, and initial phase distribution along their respective normal directions. A large number of fascinating acoustofluidic patterns can be generated in the originally-static pseudo-Sierpiński-carpet-shaped chambers at different recursion levels without complicated vibration parameter modulation. The simulation results of acoustofluidic distributions and particle motion trajectories under different radiation surface arrangements further demonstrate the manipulation performance of these specially designed devices, and indicate that controllable spatial partitioning and intensity modulation of the acoustofluidic field can be achieved by adjusting the hierarchical order, cross-sectional configuration and combination mode of the radiation surfaces. Unlike the existing device construction method of miniaturized microfluidic systems, the artificial introduction of fractal elements like Sierpiński carpet/triangle, Koch snowflake, Mandelbrot set, Pythagoras tree, etc., can provide extraordinary perspectives and expand the application range of the acoustofluidic effect, which also makes ultrasonic micro/nano-scale manipulation technology more abundant and diversified. This exploratory research indicates the potential possibility of applying fractal structures as alternative component parts to purposefully customize acoustofluidic distributions for the further research of patterned manipulation of bio-organisms and navigation of micro-robot swarms in brand new ways that cannot be achieved through traditional methods. Full article
(This article belongs to the Special Issue Acoustic-Microfluidic Integration and Biological Applications)
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18 pages, 332 KB  
Article
Neuroscience and the Non-Elimination of Theology
by Paul C. Knox
Religions 2026, 17(2), 236; https://doi.org/10.3390/rel17020236 - 15 Feb 2026
Viewed by 651
Abstract
The scientific activity and outputs of the neurosciences are fascinating and, for the most part, uncontroversial. However, there have been sustained claims that neuroscientific findings represent a powerful challenge to historic, orthodox Christian teaching concerning human ontology. While philosophers had long debated the [...] Read more.
The scientific activity and outputs of the neurosciences are fascinating and, for the most part, uncontroversial. However, there have been sustained claims that neuroscientific findings represent a powerful challenge to historic, orthodox Christian teaching concerning human ontology. While philosophers had long debated the “mind/brain” problem, the rise of “eliminative materialism” (in the specific form of “neurophilosophy”) in the last quarter of the 20th century evoked various responses to the proposition that a mature neuroscience would forever banish familiar “folk science” entities like beliefs and desires as well as immaterial souls or minds. These would all be shown to play no role in a thoroughly materialistic, mature, neuroscientific understanding of ourselves. One aspect of the response to such claims within Christian scholarship was a turn to non-reductive physicalism and theological monism prompting a reassessment of biblical teaching concerning human ontology, seeking a position that would be consistent both with neuroscience (or its alleged implications) and Christian teaching. The aim of this paper is to review neuroscientific, philosophical and theological developments in order to establish where theological anthropology currently stands. In part this requires an assessment of contemporary neuroscience (including the subfield of “consciousness studies”) because while the science continues to generate intriguing hypotheses and data, it has fallen some way short of the eliminative materialists’ hopes of forty years ago. Additionally, important methodological criticisms of the science have emerged concerning such issues as reproducibility and participant selection. This may have contributed to the twenty-first century resurgence of interest in the sort of dualism long a key component of theological orthodoxy, as well as highlighting the need for a reassertion of theological values, methods and perspectives. The apparent non-elimination of theology indicates a need to rebalance theological and neuroscientific perspectives in developing our understanding of the person. Full article
28 pages, 2374 KB  
Article
The Psychologically Restorative Effects of Blue-Green Spaces in Universities: A Deep Learning-Based Analysis of Visual Elements
by Weihong Guo, Qingyi Li and Hongyan Wen
Sustainability 2026, 18(4), 1780; https://doi.org/10.3390/su18041780 - 9 Feb 2026
Viewed by 409
Abstract
In the context of accelerating urbanization, university students face mounting academic stress and increasingly severe psychological health challenges. University blue-green spaces are critical environments for fostering restorative experiences. They highlight the urgent need for targeted strategies to enhance their restorative potential. This study [...] Read more.
In the context of accelerating urbanization, university students face mounting academic stress and increasingly severe psychological health challenges. University blue-green spaces are critical environments for fostering restorative experiences. They highlight the urgent need for targeted strategies to enhance their restorative potential. This study used three universities in Guangzhou as case studies, based on image collection and deep learning-based semantic segmentation methods, and employed the Perceived Restorativeness Scale (PRS) and Restoration Outcome Scale (ROS) to explore the hypothesized pathways and threshold characteristics through which visual elements of blue-green spaces are associated with university students’ psychological restoration within everyday campus environments. The results indicate: (1) the restorative effects of different space types follow a clear gradient: waterfront spaces > planar vegetation spaces > linear vegetation spaces > point vegetation spaces; (2) perceived restorativeness acts as a key mediator between visual elements and psychological restoration. The mediating pathways vary across space types. Waterfront spaces show polarized effects. Planar vegetation spaces rely on a dual pathway of being away and compatibility, supplemented by a secondary role of fascination. Linear vegetation spaces exhibit complex pathway patterns in which multidimensional positive support coexists with both positive and negative influences; (3) several visual elements display nonlinear threshold effects. This study deepens the understanding of the “environment–perception–psychology” pathway in the context of sustainable campus environments. It also proposes a three-level optimization framework (macro–meso–micro) that provides empirical references for evidence-informed planning and design of university blue-green spaces, with potential implications for sustainable campus environments and student well-being. Full article
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25 pages, 1052 KB  
Review
Gut Microbiota Impact on Cognitive Function in Humans
by Soghra Bagheri, Ireneusz Ryszkiel and Agata Stanek
Nutrients 2026, 18(3), 369; https://doi.org/10.3390/nu18030369 - 23 Jan 2026
Viewed by 1298
Abstract
The human gut microbiome and its relationship with both physiological and pathological functions have long intrigued researchers. One of the most fascinating and important areas within this domain is cognitive function. Given that a substantial number of studies, especially interventional ones, have been [...] Read more.
The human gut microbiome and its relationship with both physiological and pathological functions have long intrigued researchers. One of the most fascinating and important areas within this domain is cognitive function. Given that a substantial number of studies, especially interventional ones, have been conducted on animal models, the findings of which are not fully generalizable to humans and may therefore be misinterpreted, the purpose of this study is to synthesize evidence from the most recent human research. Current evidence indicates that the gut microbiota is linked to cognitive function in both healthy and diseased states, with numerous studies suggesting a potential causal relationship between the two. Although the majority of these studies associate changes in cognitive function with differences in the composition of the gut microbiota, some findings also indicate an inverse relationship. Full article
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16 pages, 415 KB  
Article
Investigations of Compactness-Type Attributes in Interval Metric Spaces
by Rukhsar Khatun, Maryam G. Alshehri, Md Sadikur Rahman and Asoke Kumar Bhunia
Axioms 2026, 15(1), 57; https://doi.org/10.3390/axioms15010057 - 13 Jan 2026
Viewed by 257
Abstract
Discovering the compactness properties in generalized-type metric spaces opens up a fascinating area of research. The present study tries to develop a theoretical framework for compactness with key properties in the recently developed interval metric space. This work begins with explaining the covers [...] Read more.
Discovering the compactness properties in generalized-type metric spaces opens up a fascinating area of research. The present study tries to develop a theoretical framework for compactness with key properties in the recently developed interval metric space. This work begins with explaining the covers and open covers to define compact interval metric spaces and their main features. Next, a similar definition of compactness using the finite intersection property is introduced. Then, the famous Heine–Borel theorem for compactness is extended in the case of interval metric spaces. Also, the concepts of sequential-type compactness and Bolzano–Weierstrass (BW)-type compactness for interval metric spaces are introduced with their equivalency relationship. Finally, the notion of total boundedness in interval metric spaces and its connection with compactness is introduced, providing new insights into these mathematical concepts. Full article
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6 pages, 7659 KB  
Interesting Images
When Consumption Comes from Beneath: A Visual Record of Slow-Moving Consumers and Abrupt Lower Distribution Limits of Sessile Intertidal Species
by Ricardo A. Scrosati
Diversity 2026, 18(1), 40; https://doi.org/10.3390/d18010040 - 13 Jan 2026
Viewed by 412
Abstract
This article documents abrupt lower distribution limits of sessile invertebrates and seaweeds from rocky intertidal habitats on Pacific and Atlantic shores from both hemispheres. The common feature of these striking patterns is that they are caused primarily by slow-moving predators or herbivores coming [...] Read more.
This article documents abrupt lower distribution limits of sessile invertebrates and seaweeds from rocky intertidal habitats on Pacific and Atlantic shores from both hemispheres. The common feature of these striking patterns is that they are caused primarily by slow-moving predators or herbivores coming from lower elevations. This contribution aims at stimulating comparative studies on these fascinating systems as well as providing visual materials of educational value. Full article
(This article belongs to the Collection Interesting Images from the Sea)
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21 pages, 2284 KB  
Article
Synthesis, Characterization and Anticancer Activities of Zn2+, Ni2+, Co2+, and Cu2+ Complexes of 4-Benzopyranone-2-carboxylic Acid
by Qianqian Kang, Qasim Umar, Wenjie Zhang, Xianggao Meng, Hao Yin, Mei Luo and Yanmin Zhang
Inorganics 2026, 14(1), 26; https://doi.org/10.3390/inorganics14010026 - 12 Jan 2026
Viewed by 416
Abstract
Coordination complexes play a crucial role in modern research. 4-benzopyranone-2-carboxylic acid is a fascinating class of molecules with numerous applications, including the synthesis of pharmaceuticals and valuable chiral compounds. Antibacterial and tuberculostatic medicines, HIV protease inhibitors, intermediates in organic synthesis, and organic catalysis [...] Read more.
Coordination complexes play a crucial role in modern research. 4-benzopyranone-2-carboxylic acid is a fascinating class of molecules with numerous applications, including the synthesis of pharmaceuticals and valuable chiral compounds. Antibacterial and tuberculostatic medicines, HIV protease inhibitors, intermediates in organic synthesis, and organic catalysis are only a few of the biological applications of chiral complexes. In this study, the synthesis of four metal complexes, C30H28N2NiO12 [Ni(bzpyr)2(py)2(H2O)2] (I), C30H24CoN2O10 [Co(bzpyr)2(py)2(H2O)2] (II), C20H20O13Zn [Zn(bzpyr)2(H2O)3] (III), and C30H22CuN2O9 [Cu(bzpyr)2(py)2(H2O)] (IV), is reported via direct reactions of 4-benzopyranone-2-carboxylic acid with metal salts and pyridine in anhydrous ethanol. Single-crystal X-ray diffraction analysis revealed that complexes I and II crystallize in the chiral space group P-1, whereas III and IV crystallize in the centrosymmetric space group P21/c. The structures of these complexes were further characterized by infrared spectroscopy, UV-Visible Diffuse Reflectance Spectroscopy, electrospray ionization mass spectrometry (ESI-MS), elemental analysis, nuclear magnetic resonance, electron paramagnetic resonance spectroscopy and single-crystal X-ray diffraction. In addition, the cytotoxic activities of complexes I–IV were evaluated against the human tumor cell lines K562, A549, HepG2, MDA-MB-231, and SW480, and molecular docking studies were conducted on the four complexes. Full article
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6 pages, 480 KB  
Editorial
Editorial—The Lifelong Continuum of Pediatric Cardiovascular Care: New Insights from a Growing Field
by Sara Moscatelli, Giorgia Rocchetti and Massimo Mapelli
Children 2026, 13(1), 101; https://doi.org/10.3390/children13010101 - 10 Jan 2026
Viewed by 358
Abstract
Pediatric cardiology remains a fascinating yet challenging niche within medicine [...] Full article
(This article belongs to the Special Issue Research Progress of the Pediatric Cardiology: 3rd Edition)
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12 pages, 4677 KB  
Article
Preparation of Robust Superhydrophobic Surfaces Based on the Screen Printing Method
by Yinyu Sun, Qing Ding, Qiaoqiao Zhang, Yuting Xie, Zien Zhang, Yudie Pang, Zhongcheng Ke and Changjiang Li
Nanomaterials 2026, 16(2), 86; https://doi.org/10.3390/nano16020086 - 8 Jan 2026
Viewed by 541
Abstract
The bioinspired superhydrophobic surfaces have demonstrated many fascinating performances in fields such as self-cleaning, anti-corrosion, anti-icing, energy-harvesting devices, and antibacterial coatings. However, developing a low-cost, feasible, and scalable production approach to fabricate robust superhydrophobic surfaces has remained one of the main challenges in [...] Read more.
The bioinspired superhydrophobic surfaces have demonstrated many fascinating performances in fields such as self-cleaning, anti-corrosion, anti-icing, energy-harvesting devices, and antibacterial coatings. However, developing a low-cost, feasible, and scalable production approach to fabricate robust superhydrophobic surfaces has remained one of the main challenges in the past decades. In this paper, we propose an uncommon method for the fabrication of a durable superhydrophobic coating on the surface of the glass slide (GS). By utilizing the screen printing method and high-temperature curing, the epoxy resin grid (ERG) coating was uniformly and densely loaded on the surface of GS (ERG@GS). Subsequently, the hydrophobic silica (H-SiO2) was deposited on the surface of ERG@GS by the impregnation method, thereby obtaining a superhydrophobic surface (H-SiO2@ERG@GS). It is demonstrated that the micro-grooves in ERG can provide a large specific surface area for the deposition of low surface energy materials, while the micro-columns can offer excellent protection for the superhydrophobic coating when it is subjected to mechanical wear. It is important to note that micro-columns, micro-grooves, and nano H-SiO2 jointly form the micro–nano structure, providing a uniform and robust rough structure for the superhydrophobic surface. Therefore, the combination of a micro–nano rough structure, low surface energy material, and air cushion effect endow the material with excellent durability and superhydrophobic property. The results show that H-SiO2@ERG@GS possesses excellent self-cleaning property, mechanical durability, and chemical stability, indicating that this preparation method of the robust superhydrophobic coating has significant practical application value. Full article
(This article belongs to the Section Synthesis, Interfaces and Nanostructures)
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37 pages, 1157 KB  
Review
Deploying LLM Transformer on Edge Computing Devices: A Survey of Strategies, Challenges, and Future Directions
by Endah Kristiani, Vinod Kumar Verma and Chao-Tung Yang
AI 2026, 7(1), 15; https://doi.org/10.3390/ai7010015 - 7 Jan 2026
Cited by 1 | Viewed by 3167
Abstract
The intersection of edge computing, Large Language Models (LLMs), and the Transformer architecture is a very active and fascinating area of research. The core tension is that LLMs, which are built on the Transformer architecture, are massive and computationally intensive, while edge devices [...] Read more.
The intersection of edge computing, Large Language Models (LLMs), and the Transformer architecture is a very active and fascinating area of research. The core tension is that LLMs, which are built on the Transformer architecture, are massive and computationally intensive, while edge devices are resource-constrained in terms of power, memory, and processing capabilities. Therefore, LLMs based on the Transformer architecture are inherently unsuitable for edge computing in their original, full-sized form. They were designed for powerful, resource-rich cloud data centers. However, there is a massive and growing effort to make them suitable for edge devices. Implementing Transformer-based LLMs on edge computing devices is a complex but crucial task that requires a multi-faceted strategy. This paper reviews LLM deployment strategies for Transformer models on edge computing devices, examines the challenges, and estimates future directions. To address these challenges, researchers are exploring methods to compress LLMs and optimize their inference capabilities, making them more efficient for edge environments. Recent advancements in compact LLMs have shown promise in enhancing their deployment on edge devices, enabling improved performance while addressing the limitations of traditional models. This approach not only reduces computational costs but also enhances user privacy and security. Full article
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14 pages, 5202 KB  
Article
9,10-Difluoro-9,10-disila-9,10-dihydroanthracene
by Mirei Kawamoto and Takahiro Sasamori
Inorganics 2026, 14(1), 23; https://doi.org/10.3390/inorganics14010023 - 7 Jan 2026
Viewed by 548
Abstract
9,10-Disila-9,10-dihydroanthracenes have attracted significant attention due to their unique electronic structures, characterized by an extended π-system facilitated by σ-π conjugation. Here, we report the synthesis of 9,10-bis(p-methoxyphenyl)-9,10-disila-9,10-dihydroanthracene, which serves as a crucial precursor for the preparation of the corresponding difluoro derivative. [...] Read more.
9,10-Disila-9,10-dihydroanthracenes have attracted significant attention due to their unique electronic structures, characterized by an extended π-system facilitated by σ-π conjugation. Here, we report the synthesis of 9,10-bis(p-methoxyphenyl)-9,10-disila-9,10-dihydroanthracene, which serves as a crucial precursor for the preparation of the corresponding difluoro derivative. This conversion is achieved through a selective deanisyl-fluorination at the silicon centers using HBF4. A key finding is the successful isolation of the cis-isomer of 9,10-difluoro-9,10-disila-9,10-dihydroanthracenes as a crystalline compound. This allowed for definitive structural characterization by single-crystal X-ray diffraction (SC-XRD) analysis, providing precise geometric insights into this electronically fascinating framework. Full article
(This article belongs to the Section Organometallic Chemistry)
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18 pages, 307 KB  
Article
Structural Properties of Pascal Pyramids and Pascal Simplexes: Classical Results and Some Extensions
by Hui Li
Symmetry 2026, 18(1), 97; https://doi.org/10.3390/sym18010097 - 5 Jan 2026
Viewed by 613
Abstract
Pascal’s Triangle, renowned for its geometric elegance and profound applications across combinatorics, algebra, and probability, has fascinated mathematicians for centuries. While its origins can be traced to Chinese, Persian, and European mathematical traditions, the study of its higher-dimensional analogues remains notably underexplored. This [...] Read more.
Pascal’s Triangle, renowned for its geometric elegance and profound applications across combinatorics, algebra, and probability, has fascinated mathematicians for centuries. While its origins can be traced to Chinese, Persian, and European mathematical traditions, the study of its higher-dimensional analogues remains notably underexplored. This paper offers a systematic and self-contained study of Pascal Pyramids and Pascal Simplexes with their proofs. It encompasses both classical results (such as multinomial identities) and novel contributions (including boundary and scaling properties), as well as fresh perspectives (such as graph-theoretic interpretations) that are rarely documented in the existing literature. Full article
(This article belongs to the Section Computer)
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