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Article
Biology and Life Sciences
Horticulture

Huanhuan Li

,

Yage Chen

,

Zhipeng Xie

,

Qian Su

,

Bingqi Chen

,

Yue Yang

,

Guifang Ma

,

Yizhu Yang

,

Xinwen Shan

,

Junjie Wang

+2 authors

Abstract: Penicillium expansum inflicts significant economic damage in the fruit and vegetable industry due to its wide distribution and ability to infect a diverse range of hosts. Therefore, developing safe and environmentally sustainable strategies to suppress the growth of this pathogen is of critical importance. Bacillus subtilis, recognized for its broad antimicrobial activity and widespread occurrence, has been widely utilized in the biological management of plant diseases. This research seeks to assess the inhibitory potential of B. subtilis against P. expansum. The cell-free supernatant (CFS) derived from B. subtilis significantly suppresses the germination spores, germ tube extension, and hyphal development of P. expansum. It also reduces disease incidence in grapes and citrus and suppresses the expansion of lesions. Further investigate had shown that it can induced mycelium reactive oxygen species (ROS) accumulation, destroyed the cell membrane integrity, led to leakage of cytoplasmic contents and induced membrane lipid peroxidation. Moreover, exposure to high concentrations of CFS results in mycelial contraction and morphological abnormalities, triggering the disintegration of intracellular organelles and markedly upregulating the expression of apoptosis-associated genes. The self-protective response elicited by 5% CFS is insufficient to counteract the extent of cellular damage, ultimately driving cells toward a dynamic, multistage, and disintegrative form of cell death. The findings of this study offer a theoretical foundation for managing P. expansum after harvest.

Article
Computer Science and Mathematics
Applied Mathematics

Gaotsiwe Joel Rampho

Abstract: This paper presents modified Lagrange-Jacobi functions derived from the sine, exponential, and hyperbolic tangent coordinate transformations. The resulting Lagrange-Jacobi functions and their respective matrix elements for observables can be reduced to their respective Lagrange-Legendre, Lagrange-Chebyshev, and Lagrange-Gegenbauer functions. Furthermore, this paper postulates that the Lagrange-mesh functions form approximate complete set of basis, a property implied by their approximate orthogonality.

Article
Physical Sciences
Astronomy and Astrophysics

Tongfeng Zhao

Abstract: This perspective article proposes and systematically develops a phenomenological framework centered on the correlation between dark energy dynamics and cosmic structure growth. Building upon the foundational linear relation w(a) = -1 + η(γ(a) - 0.55), where w is the dark energy equation of state and γ is the structure growth index, we extend it to allow for redshift-dependent couplings and provide a complete roadmap for empirical testing. We establish its theoretical basis as an interacting dark energy-dark matter model that respects energy-momentum conservation. A key advancement is our complete parameterization w(z)=−1+η(z)[γ(z)− 0.55]+Δwbg(z), which separates structure-dependent coupling from possible background evolution and allows for redshift-dependent interactions. This work introduces a novel, phenomenologically motivated piecewise parameterization for the coupling strength η(z), designed to capture potential variations across distinct cosmic epochs (z < 0.5, 0.5 ≤ z ≤ 1.5, z > 1.5) based on the history of structure formation.​ We provide a comprehensive testing roadmap using hierarchical Bayesian model comparison, detailing the specific observational data, analysis methods, and systematic error treatments required. Using Fisher matrix forecasts based on detailed survey specifications, we demonstrate that upcoming surveys (DESI, Euclid, Roman Space Telescope) will provide decisive tests, capable of detecting coupling strengths |η| ≳0.05 with strong evidence. This framework offers a unified approach to addressing both the Hubble and S8​ tensions while making distinctive, testable predictions that differentiate it from other proposed solutions. We conclude with specific recommendations for observational teams and theoretical directions for further development.

Article
Biology and Life Sciences
Food Science and Technology

Sakhi Ghelichi

,

Behdad Shokrollahi Yancheshmeh

,

Mona Hajfathalian

,

Seyed Hossein Helalat

,

Arpan Shrestha

,

Saroj Katwal

,

Charlotte Jacobsen

Abstract: Docosahexaenoic acid (DHA), an omega-3 fatty acid essential for human health, is highly prone to oxidation in nanoemulsions due to their large interfacial area and presence of transition metal ions. This study investigated macroalgal chelators for stabilizing DHA-rich nanoemulsions. Sequential enzymatic–alkaline extraction using Alcalase® produced an extract with the strongest Fe2+-chelating activity (IC50 = 1.22 mg/mL), protein content of 10.11 ± 0.15%, and total phenolics ≈17 µg GAE/mL. This extract was incorporated into nanoemulsions (5 wt% DHA oil, 1 wt% Tween® 20) at 0.61, 1.22, and 2.44 mg/mL and compared with controls containing EDTA (0.025 mg/mL) or no antioxidant. Droplet size remained stable (D3,2 ≈ 77-80 nm; D4,3 ≈ 199-215 nm) and zeta potential averaged -17 to -19 mV, confirming physical stability. Confocal microscopy revealed concentration-dependent interfacial adsorption of extract components. During iron-accelerated storage, extract-treated nanoemulsions slowed hydroperoxide formation and delayed tocopherol depletion compared to the control, while reducing volatile oxidation markers such as 1-penten-3-ol by up to 40%. However, EDTA consistently provided superior protection against oxidation. These findings highlight the potential of macroalgal extracts as clean-label, natural chelators for mitigating metal-driven oxidation in DHA nanoemulsions, though synthetic chelators remain more effective under severe prooxidant conditions.

Article
Environmental and Earth Sciences
Remote Sensing

Xiaofan Li

,

Shuangxun Li

,

Bin Deng

,

Qiang Fu

,

Hongqiang Wang

Abstract: Terahertz waves are located in the "transition zone" between millimeter waves and infrared light. Terahertz video synthetic aperture radar utilizes the high operating frequency, strong radar cross-section intensity, and high azimuth repetition frequency of terahertz waves to detect and track ground moving targets. The conventional methods for detecting moving targets do not take into account the imaging characteristics of moving targets in terahertz video synthetic aperture radar. The Constant False Alarm Rate (CFAR) detection method is used together with other methods to detect moving targets, resulting in unsatisfactory detection performance. This article proposes a new detection method for single channel slow-moving targets in terahertz video SAR based on shadows and light spots, which extracts the features of the shadow and spot areas of the moving target, and determines the position and direction of the moving target through the identification of the shadow and spot areas. The progressiveness of this method is verified by simulation and experimental tests.

Article
Biology and Life Sciences
Biophysics

Khushboo Singh

,

Roon Banerjee

,

Chandrakanta Potdar

,

Anisha Shaw

,

Rakshith V

,

Nitish Kamble

,

Vikram Holla

,

Ravi Yadav

,

Pramod Kumar Pal

,

Indrani Datta

Abstract: Mutations in leucine-rich repeat kinase 2 (LRRK2) are among the most common genetic causes of Parkinson’s disease (PD), yet substantial heterogeneity exists among pathogenic variants. How mutations in distinct functional domains of LRRK2 differentially perturb cellular homeostasis remains incompletely understood. Here, we compared two pathogenic LRRK2 mutations—G2019S in the kinase domain and I1371V in the GTPase domain—across multiple cellular models, including SH-SY5Y and U87 cells, and healthy human iPSC-derived floor plate cells. We demonstrate that the I1371V mutation induces markedly more severe cellular dysfunction than G2019S. I1371V-expressing cells exhibited elevated LRRK2 autophosphorylation at S1292 and robust hyperphosphorylation of Rab8A and Rab10, indicating enhanced downstream signaling. These alterations impaired sterol trafficking, leading to selective depletion of plasma membrane cholesterol without changes in total cellular cholesterol. Consequently, I1371V cells displayed increased membrane fluidity, disrupted microdomain organization, altered membrane topology, reduced Caveolin-1 expression, and impaired dopamine transporter surface expression and dopamine uptake. Lipidomic profiling further revealed broad disruption of lipid homeostasis, including reductions in cholesteryl esters, sterols, sphingolipids, and glycerophospholipids, whereas G2019S cells showed comparatively modest changes. Pharmacological intervention revealed mutation-specific responses, with the non-selective LRRK2 modulator GW5074 outperforming the kinase-selective inhibitor MLi-2 in restoring Rab8A phosphorylation, membrane integrity, and dopaminergic function. Collectively, these findings identify membrane lipid dysregulation as a central cell-biological mechanism in LRRK2-associated PD and underscore the importance of variant-specific therapeutic strategies.

Article
Medicine and Pharmacology
Ophthalmology

Daniela Oehring

Abstract: This study quantified the analytical performance of an automated videotopography system for dry eye disease (DED) and evaluated a novel multivariate composite score to improve diagnostic accuracy. In a prospective, repeated-measures study, 35 adults completed three visits involving automated (Keratograph 5M) and manual (fluorescein break-up time; slit-lamp meniscus height) assessments. Data were analysed using linear mixed-effects models and Bland–Altman plots, while a logistic regression-based Objective Symptom Risk Score (Objective-SRS) was derived to predict symptom status. Results showed that automated meniscus height (NIKTMH) had excellent precision (CV 8.8%) and reliability (ICC 0.727), whereas non-invasive break-up times were highly variable (CV &gt; 40%). Automated and manual measures demonstrated wide limits of agreement and systematic bias, precluding interchangeability. While individual objective tests failed to differentiate symptom groups, the composite Objective-SRS achieved good accuracy (AUC 0.768) and superior net clinical benefit. The study concludes that diagnostically useful information is distributed across multiple signals; thus, automated and manual measures should be used complementarily, with multivariate models offering superior discrimination of DED symptom burden.

Review
Physical Sciences
Optics and Photonics

Etienne Brauns

Abstract: Optical precision measurement is fundamental to space technology and physics. For over a century, the “ray-of-light” paradigm and the Equivalence Principle have underpinned both theoretical and applied optics. However, recent theoretical and experimental work demonstrates that these paradigms are fundamentally flawed when applied to photon-level phenomena. This manuscript synthesizes a trilogy of research—spanning theoretical falsification, experimental confirmation, and practical application—to show that photons do not inherit the velocity vector of their source, and that the Equivalence Principle does not hold for photon propagation. We introduce the Real Velocity Measuring Device (RVMD), a novel instrument enabling direct measurement of real velocity vectors in real space. The potential implications for spacecraft navigation and metrology (including our planet) are profound, necessitating a paradigm shift in optical science.

Article
Engineering
Electrical and Electronic Engineering

Saurav Chaudhari

,

Ketan Pise

,

Dinesh Fukate

,

Shantanu Gawande

Abstract: This pilot study evaluates whether Wi-Fi Channel State Information (CSI)-derived micro-movements can reflect autonomic patterns associated with Heart Rate Variability (HRV). CSI-estimated inter-beat intervals were compared with smartwatch-derived HRV metrics during relaxation and mild stress tasks involving 14 volunteers. While absolute HRV values differed, CSI-derived LF/HF variations showed directional alignment with physiological state changes (r = 0.84, p < 0.001), with mean absolute error of 5.8 ms for SDNN and 4.1 ms for RMSSD. Results underscore potential for contactless autonomic monitoring and motivate further clinical investigation, avoiding any claim of diagnostic utility. The findings suggest CSI-based passive wireless analytics may complement existing wearable methods for stress monitoring and autonomic assessment in ecologically valid settings.

Article
Environmental and Earth Sciences
Environmental Science

António Rochette Cordeiro

,

André Lucas

,

José Miguel Lameiras

Abstract: Topography plays a crucial role in shaping local urban microclimates and can drive the formation of cold-air pools in valley bottoms. This study examines the Eiras Valley (Coimbra, Portugal), a rapidly growing peri-urban area, to identify the conditions under which cold-air pools form and to characterize their spatial and vertical dynamics. Field measurements were carried out using Tinytag Plus 2 data loggers at the surface (≈1.5 m above ground) and mounted on an unmanned aerial vehicle (UAV) for vertical profiles, complemented by high-resolution thermal mapping through Empirical Bayesian Kriging. The results show that a nocturnal cold-air pool develops within the valley under clear, anticyclonic winter conditions, persisting into the early morning hours and dissipating after sunrise due to solar heating. In contrast, under overcast or summer conditions, no cold-air pooling was observed. The temperature inversion capping the cold-air pool was found at approximately 275 m altitude, inhibiting vertical mixing and trapping pollutants near the ground. These findings underscore the importance of topoclimatology in urban and regional planning, with implications for thermal comfort, air quality, and public health. The study contributes to urban climate research by highlighting how local topography and seasonal atmospheric stability govern cold-air pool formation in valley environments, supporting the development of mitigation strategies aligned with urban sustainability goals.

Article
Medicine and Pharmacology
Dietetics and Nutrition

Nathan Ryder

,

Ulf Bronas

,

Jason Westra

,

Jieqi Tu

,

Evan De Jong

,

Yosef Bodovski

,

Kiarri N. Kershaw

,

Nathan L. Tintle

Abstract: People in mid-life interact with several different environments during their daily life in-cluding employment, leisure, commuting, and various family responsibilities, a concept defined as activity space. However, little is known about how these activity spaces contrib-ute to individuals’ daily health behavior choices. The Everyday Environments and Expe-riences (E3) study was conducted to explore these relationships. In this paper, we provide a reproducible GPS processing workflow to generate time-weighted exposure measures (activity spaces) inferred from 21 days of continuous GPS monitoring among 340 mid-life adults in Cook County, Illinois (N=340) from the E3 study. Data from waist-mounted GPS devices that recorded one-minute location epochs were aggregated after excluding time spent within an 800-meter buffer around the home. For each epoch, we derived proximity and kernel density measures for eleven food and physical-activity-related location types (e.g., supermarkets, fitness facilities), along with twenty-six environmental context varia-bles (e.g., land use, crime, population density). Time-weighted averages characterized each participant’s typical non-home environmental exposure. After adjustment for envi-ronmental context, age and gender were generally unrelated to activity-space measures. However, Black and Hispanic participants (as compared to White participants) spent less time near both food and physical-activity resources, suggesting systemic inequities in ac-cess beyond neighborhood composition.

Review
Public Health and Healthcare
Public Health and Health Services

Lysanne Veerle Michels

,

Lucy Smith

,

Jacob Keast

,

Hajira Dambha-Miller

Abstract: Physical activity (PA) improves health and well-being, and helps prevent long-term conditions. Yet opportunities to be active are not evenly distributed, with social, economic, and environmental disadvantages constraining access to PA among populations who may benefit most. Since the extent to which PA interventions incorporate equity considerations remains insufficiently characterised, risking exacerbation of health inequity, this scoping review aims to synthesise trial evidence on interventions of PA to improve health outcomes in populations at risk of health inequity as defined by the PROGRESS-Plus and CORE20PLUS5 frameworks. PubMed, Web of Science, and Scopus were searched for randomised controlled trials of PA interventions with at-risk populations published between 2020 and 2025. Study characteristics, intervention design, and equity-relevant factors were extracted. Two reviewers independently screened and synthesised findings narratively. Results indicate that of 2,480 articles identified, 23 trials met eligibility criteria. Most reported positive effect of PA on health outcomes amongst at-risk populations, including weight loss, improved motor skills and gait speed, reduced anxiety and PTSD, and fewer fractures or hospital visits. Interventions commonly included strength and balance training, group exercise, stretching, and aerobic fitness. UK-based studies and subgroup analyses by e.g. sex or age were largely absent, and many populations at risk of health inequity were underrepresented. Explicit equity considerations throughout design, implementation, or evaluation were rare across trials and few assessed differential effects between social or economic groups. Integrating equity frameworks and engaging with at-risk populations is recommended in future physical activity interventions to mitigate exacerbation of health inequity.

Article
Medicine and Pharmacology
Ophthalmology

Cord Huchzermeyer

,

Friedrich Kruse

,

Jan Kremers

Abstract: Head-mounted (“virtual reality”) perimeters (HMPs), based on standard consumer electronic hardware, are a cheaper alternative to standard automated perimetry. They have not been validated in patients with inherited retinal disease (IRDs), yet. We evaluated the Iowa-HMP in a first pilot study. It consists of a legacy smartphone, a headset, and freely available, open-source software. We used the 10-2 grid, the ZEST algorithm, and a background of 10 cd/m^2 to measure central visual fields in one normal subject, and in patients with occult macular dystrophy (n = 2), Stargardt’s disease (n=3) and retinitis pigmentosa (n = 6). Results were compared with those from an Octopus 900 perimeter. The typical patterns of visual field loss were clearly discernible, but head-mounted perimeters generally have a limited dynamic range. Within the dynamic range of the Iowa-HMP (14 to 30 dB Octopus sensitivity), the Limits of Agreement (Bland-Altman) were ±7.5 dB. The Iowa-HMP had a diagnostic sensitivity of 0.67 for detecting locations with low perimetric sensitivity (< 14 dB in the Octopus perimetry) with a diagnostic specificity of 0.95. Although the Iowa-HMP cannot be directly compared to standard perimetry in IRDs, open software greatly facilitates research in this area.

Article
Public Health and Healthcare
Public Health and Health Services

Paulo Acácio Egger

,

Matheus Henrique Arruda Beltrame

,

Makcileni Paranho de Souza

,

Cristiane de Oliveira Riedo

,

Amanda de Carvalho Dutra

,

Wagner Sebastião Salvarani

,

Sandra Marisa Pelloso

,

Maria Dalva de Barros Carvalho

Abstract:

This population-based study aimed to analyze the annual incidence and case fatality trends, and the clinical-epidemiological profile of gastroschisis in the state of Paraná, Brazil, between 2013 and 2024. Specifically, temporal trends in annual incidence and mortality rates related to gastroschisis were examined. Maternal, gestational, and neonatal characteristics were analyzed. Data from the Live Birth Information System and the Mortality Information System were analyzed using polynomial regression modeling. During the study period, 1,798,727 live births were recorded, including 491 cases of gastroschisis and 179 related deaths. The mean incidence was 2.73 per 10,000 live births. A significant 39.5% decrease over the study period was observed (p < 0.001). The case fatality rate was 36.5%. The predominant profile included young mothers (< 25 years; 77%), low educational attainment (87.7%), and no partner (59.1%). High frequencies of cesarean deliveries (84.3%), prematurity (57.3%), low birth weight (63.7%), and low Apgar scores were also observed. Gastroschisis incidence in Paraná declined significantly from 2013 to 2024. While the annual incidence showed a decreasing trend, mortality fluctuated. The persistently high case fatality rate underscores the need for public policies focused on prenatal care and specialized neonatal management.

Article
Computer Science and Mathematics
Artificial Intelligence and Machine Learning

Wen Ding

,

Yi Han

,

Mujiangshan Wang

Abstract: Detecting coordinated inauthentic behavior on social media remains a critical challenge, as many existing methods rely on correlation-based heuristics, fixed configurations, and heavy manual annotation. From the perspective of symmetry and asymmetry, coordinated campaigns often exhibit repeatable temporal and structural invariances (e.g., synchronized bursts and stable influence motifs), whereas adversarial adaptation and noisy environments introduce symmetry breaking and context-dependent deviations. To address this issue, we propose Adaptive Causal Coordination Detection (ACCD), a three-stage progressive framework with memory-guided adaptation. In Stage 1, ACCD introduces an adaptive Convergent Cross Mapping (CCM) module that learns embedding parameters across scenarios to recover invariant causal dependencies. In Stage 2, ACCD integrates active learning with semi-supervised classification to reduce labeling effort while preserving robust discrimination under asymmetric user behaviors. In Stage 3, ACCD employs an experience-driven validation module to self-verify detection results and mitigate spurious correlations across varying contexts. We evaluate ACCD on real-world benchmarks, including the Twitter IRA dataset, Reddit coordination traces, and TwiBot-20. Experimental results show that ACCD achieves an F1-score of 87.3% on coordinated attack detection, outperforming the strongest baseline by 15.2%, while reducing manual annotation by 68% and delivering a 2.8× speedup via hierarchical clustering optimization. Overall, ACCD 19 provides an accurate and scalable end-to-end solution that explicitly leverages symmetry (invariant coordination signatures) and asymmetry (evolving adversarial behaviors) for practical coordination detection.

Article
Physical Sciences
Astronomy and Astrophysics

Yuxuan Zhang

,

Weitong Hu

,

Wei Zhang

Abstract: We propose an algebraic framework constructed from a finite-dimensional 19-dimensional Z3-graded Lie superalgebra g = g0 ⊕ g1 ⊕ g2 (dimensions 12+4+3), featuring exact closure of the graded Jacobi identities (verified symbolically in key sectors and numerically in a faithful matrix representation, with residuals ≲ 10−12 across 107 random combinations) and a unique (up to scale) invariant cubic form on the grade-2 sector, driving a triality symmetry on the vacuum sector. Interpreting the grade-2 sector as the physical vacuum state, we explore whether representation-theoretic invariants and contractions within this algebraic structure can account for observed Standard Model parameters—including fermion masses, mixing angles, and gauge couplings—as well as the magnitude of the cosmological constant, black-hole entropy scaling, and certain qualitative features of quantum entanglement. The framework yields twelve quantitative predictions amenable to experimental scrutiny at forthcoming facilities such as the High-Luminosity LHC, Hyper-Kamiokande, DARWIN/XLZD, and LiteBIRD.

Article
Engineering
Control and Systems Engineering

Adilton Lopes da Silva

,

Cristiano Hora Fontes

,

Marcelo Embiruçu

Abstract: This work presents a strategy for implementing advanced control in a real Linear Low-Density PolyEthylene (LLDPE) production unit (“Sclairtech” technology) followed by a systematic evaluation of economic benefits in accordance with best international practices. Melt Index (MI), density and conversion were considered as controlled variables. The analysis considered two different situations (with and without hydrogen as process input) and comprised groups/ families of polyethylene (rotational molding, low-density injection, octene film and high-density injection). The proposed control strategy is capable of efficiently addressing two of the main problems associated with “Sclairtech” technology, namely, the generation of out-of-specification product during grade transitions and wide specification ranges. The benefits analysis involved using real process data, a statistical analysis of key variables to identify the dispersion and percentage of out-of-specification products, and the calculation of the net present value of financial indicators capable of validating the investment. An annual gain of US$ 791,812 was estimated, with US$ 494,883 coming from the reduction in catalyst consumption and US$ 296,929 from other sources (reduction in out-of-specification product and production losses associated with grade transitions).

Review
Engineering
Chemical Engineering

Miza Syahmimi Haji Rhyme

,

Dk Nur Hayati Amali Pg Haji Omar Ali

,

Hazwani Suhaimi

,

Pg Emeroylariffion Abas

Abstract: With the increasing demand for clean energy and the uncertainty surrounding the application of renewables, recent years have seen ammonia emerging as a viable way to store and transport hydrogen on a large scale. Its increasing importance in national hydrogen policies, as in the case of Brunei, highlights the need to look into technological readiness and global paths of innovation for this novel fuel. This study analyzes the global development of ammonia-based hydrogen production technologies from a methodological perspective and has shown that 708 granted patents to that were systematically screened, sorted and analyzed. A statistically sound retrieval method and screening process, following the PRISMA guidelines, have been employed to categorize the patents by synthesis processes, types of catalyst, and technological field. The results indicate that electrochemical, plasma-based, photocatalysis, and hybrid systems are becoming common paths as low-temperature alternatives, while thermal catalytic breakdown remains the most popular and well-known path to pursue. A range of reactor engineering, system integration, and catalyst design efforts have been undertaken, particularly in Asia. This indicates a high level of industrial and research interest in advancing ammonia-to-hydrogen technologies. These findings offer a clear overview of current technological maturity and emerging innovation trends, supporting long-term transitions toward cleaner hydrogen pathways.

Article
Physical Sciences
Particle and Field Physics

Tejinder P. Singh

Abstract: Over the last few years, we have attempted to develop an \( E_8 \times E_8 \) theory of unification to combine the standard model with general relativity. In the present new work, we give a self-contained construction in which the two extra \( SU(3) \) factors that appear in the maximal subgroup chain \( E_8\supset E_6\times SU(3) \) on each side of \( E_8\times \omega E_8 \) generate: (i) a six-dimensional base \( (M_6,g) \) of signature \( (3,3) \); (ii) two embedded Lorentzian 4D spacetimes; and (iii) per side, a canonical real 4-dimensional internal fibre naturally identified with the tangent of \( \mathbb{C}P^2=SU(3)/S(U(2)\times U(1)) \). The key algebraic ingredient is the octonionic split \( O=H\oplus H\varepsilon \) with \( \varepsilon\perp H \), by which the branch AdjSU(3) →\( \mathbf{3}_0\oplus \mathbf{2}_{+1}\oplus\overline{\mathbf{2}}_{-1}\oplus \mathbf{1}_0 \) is realised as ℑ\( H\oplus (H\varepsilon)_{\mathbb{R}}\oplus R \). The two \( U(1) \) factors play the role of Spin\( ^c \) connections on the \( \mathbb{C}P^2 \) fibres.

Article
Computer Science and Mathematics
Mathematics

Rafael Garcia-Sandoval

Abstract: It is posited that the two balanced ternary systems, (-1, 0, 1) and (-i, 0, i), are positioned on the line of real numbers and on the axis of complex numbers, respectively. In the event that the system is reduced to a single entity, the digits of the resulting system will be as follows: { -1, -i, 0, i, 1} The set (-1, -i, 0, i, 1) is transformed into a base five system. In this article and the following ones, I will outline the aforementioned relationship and its considerable potential for implementation in the domains of computer technology and a novel programming language. In addition to laying the groundwork for the trivalent system, which was clearly and brilliantly developed by Jan Łukasiewicz, we can expand beyond the {third middle defined by Aristotle in Chapter 9 of his treatise "De Interpretatione", which was written in opposition to the Stoics' determinism. This perspective enables us to extend the law of middles to the fourth, fifth, sixth, and so on, while adhering to the principles of polyvalent systems. This generates a proliferating field of probabilities where we can establish a chain of closely related probabilities, link by link, where each one is equally likely to be true or false. This allows us to approach or separate from the local truth or lie. I understand that the concepts of truth and falsehood, as developed by mathematical logic in a bivalent system, refer to a particular truth or lie. Thus, absolute truth is universal and impossible to know. However, it is not necessary to know absolute truth because what affects us in our daily lives is local truth or local falsehood. Then, it is appropriate to discern between a local truth universally accepted and a falsehood that can also be accepted as true, as well as the distinction between a true truth and a falsehood that could also be a true lie. In this article, we will analyze up to the third dimension (3D) which is composed by the following structures: i. A polyvalent system of "fifth truth degree", where the fifth middle is introduced. ii. A balanced system of base seven, in which seven coordinated points are introduced. iii. This balanced system operates within the Ternary Balanced system. iv. The Ternary base number defines the lowest and highest limits. v. Every volumetric body is founded on its complex plane, but empty space, between the volumetric bodies is a volume of its respective dimension. vi. Every mathematical operation can be developed directly as (ST110i0)(1T0S1) or (ST110i0)/(1T0S1) without requiring the complex polynomial form. A polyvalent system allows us to construct volumes of bodies, then surface of volumetric bodies, then volumes of volumetric bodies, then surface of volumes of volumetric bodies, and so forth. I briefly glance beyond the seventh base to the eleventh, thirteenth, and fifteenth bases.

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