In contemporary design practices, there is a disconnect between the design techniques used for early-stage design experimentation and performance analysis, and those used for the manufacture and construction. This study addresses the problems in developing an integrated digital design workflow and provides a research framework for integrating environmental performance requirements with robotic manufacturing processes on a construction site. The proposed method enables the user to import a design surface, identify design parameters, set several environmental performance goals, and thereafter simulate and select a robotic building strategy. Based on these inputs, design alternatives are developed and evaluated, considering their robotically simulated constructibility, in terms of their performance criteria. To validate the proposed method, the design is evaluated in an experiment wherein a double-skin facade perforation is generated using the proposed methodology. Initial results suggest a heuristic feature to improve the simulated robotic constructibility. Moreover, the functionality of the prototype is demonstrated.

The study delved into the impact of two extrusion processing parameters—screw speed (SS at 400, 600, 800 RPM) and material moisture content in the extruder barrel (M at 12, 15, 18%) at constant feed rate (50 kg/h)—on reducing the content of alternariol (AOH), alternariol monomethyl ether (AME), tenuazonic acid (TeA), and tentoxin (TEN) in whole-grain red sorghum flour. Ultra-performance liquid chromatography coupled with a triple-quadrupole mass spectrometer (UPLC-MS/MS) was used for determination of Alternaria toxin levels. The extruder die temperature ranged between 136 and 177 °C, the pressure at the die was from 0.16 to 6.23 MPa, the specific mechanical energy ranged from 83.5 to 152.3 kWh/t, the torque ranged between 88 to 162.8 Nm, while the mean retention time of material in the barrel was between 5.6 and 13 s. Optimal parameters for reducing the concentration of all Alternaria toxins with the satisfactory quality of sorghum snacks were: SS=400 RPM, M= 12%, with a reduction of 61.4, 76.4, 12.1 and 50.8% for AOH, AME, TeA and TEN, respectively.

Current trends in industrial development strive for maximum digitalization. The digital industrial revolution has been going on for more than a dozen years, Industry 4.0 and the idea of digital twins (DT) is becoming the focus of virtually all industrial sectors. Some sectors are more predisposed to digitalization, for others the process is much more difficult. This depends mainly on the specific characteristics and susceptibility of a given industry, including the current degree of digitalization of enterprises, as well as the knowledge and mental readiness of employees. The individual characteristics of an industry are important. Shipyards belong to the industry with a traditional approach, where the degree of digitalization remains low. As a result, the efficiency of shipbuilding processes and the quality of ships built are not sufficiently controlled. The article addresses this problem, reviews work in the field of digitalization of shipbuilding processes and points out the needs and challenges in this area. The article proposes the concept of a DT system for the entire ship design and production process. Key areas of digitalization of actual processes were defined, and a division was made into planning, monitoring and process analysis activities. Special attention was paid to the area of dimensional quality control and the Dimensional Quality Management Metasystem (DQMM) was featured in the comprehensive DT system. The requirements were defined and the limitations of the proposed solution were identified, taking into account a number of external factors including the degree of readiness of the manufacturer – the shipyard. The developed DT system concept was tested on the example of the construction process of a simplified ship. Practical aspects of the implementation of the proposed solution, in particular DQMM, were indicated.

The final assembly of appliances and automotive industries is a rigorous process, that has limited capabilities of full traceability associated with: (1) the parts installed, (2) their fabrication processes, and (3) the assembly work. This is also the case for each of its sub-assemblies The many parts and sub-assemblies that compose the final assembly, make full traceability a challenging fit, that is almost unsurmountable. Such full traceability along the entire supply-chain is not existent today and must be based on documentation of most assembled parts, assembly tasks, and inspection tasks that compose the full assembled product. In addition, security measures are needed to prevent hostile hacking and unauthorized approach to the assembly documentation throughout the entire supply chain. The related documentation and repeated verifications require considerable effort and have many chances for human errors. So, automating these processes has a great value. This article expounds a framework that harnesses block-chain and smart-contract technology to offer traceable and protected documentation of the assembly process. We expand the concept of a Bill-Of-Assembly (BOA) to incorporate data from the bill of materials (BOM), the associated assembly activities, the associated activities’ specification parameters and materials, and the associated assembly resources (machines and/or operators). The paper defines the operation of the BOA with blockchain and smart-contract technology, for attaining full traceability, safety, and security, for the entire assembled product. Future research could extend the proposed approach to facilitate the usage of the BOA data structure in constructing a digital twin of the entire simulated system.

Fundamental science and applied research and technology development (RTD) are facing significant challenges that particularly compound to the notorious credibility, reproducibility, funding and sustainability crises. The underlying, serious shortcomings are substantially amplified by a metrics-obsessed publication culture, and a growing cohort of academics fishing for fairly stagnant (public) funding budgets. This work presents, for the first time, a groundbreaking strategy to successfully address these severe issues; the novel strategy proposed here leverages the distributed ledger technology (DLT) “blockchain” to capitalize on cryptoeconomic mechanisms, such as tokenization, consensus, crowdsourcing, smart contracts, reputation systems as well as staking, reward and slashing mechanisms. This powerful toolbox, which is so far widely unfamiliar to traditional scientific and RTD communities (“TradSci”), is synergistically combined with the exponentially growing computing capabilities for virtualizing experiments through digital twin methods in a future scientific “metaverse”. Project contributions, such as hypotheses, methods, experimental data, modelling, simulation, assessment, predictions and directions are crowdsourced using blockchain, and captured by so-called non-fungible tokens (“NFTs”). The so enabled, highly integrative approach, termed decentralized science (“DeSci”), is destined to move research out of its present silos, and to markedly enhance quality, credibility, efficiency, transparency, inclusiveness, sustainability, impact, and sustainability of a wide spectrum of academic and commercial research initiatives.

A homogenization of billets from Al-Cu-Li-Mg-Sc-Zr alloys should be accomplished at high annealing temperatures exceeding 500 °C. This type of aluminum alloy is susceptible to the depletion of surface layers from Li. Therefore, choosing a suitable homogenization temperature and duration is a crucial step in assuring a homogeneous distribution of alloying elements and optimal exploitation of the potential of the alloy. In-situ heating in an electron microscope was performed on a twin-roll cast Al-Cu-Li-Mg-Sc-Zr alloy to understand the peculiarities of the homogenization process. Four types of primary phase particles rich in Cu, Li, Mg, and Fe were identified in the as-cast material. They appear as coarse particles at the boundaries of eutectic cells. Their partial dissolution occurs at temperatures above 450 °C. They are almost fully dissolved at 550 °C, except for complex phases containing Fe and Cu. Small dimensions of eutectic cells in the range of 10 µm assure a homogeneous distribution of main alloying elements within the matrix after 20 min of annealing. Direct comparison with the same material prepared by mold-casting indicates that such short annealing times result in the dissolution of main primary phase particles but do not assure a homogeneous distribution of alloying elements in the whole volume of the specimen.

Drone imagery has the potential to enrich urban planning and preservation, especially where it converges with the growing creation and use of 3D models. The authors have conducted a systematic literature review of articles published between 2002 and 2022, drawing from reputable academic repositories including Science Direct, Web of Science, and China National Knowledge Infrastructure (CNKI), to identify current gaps in existing research in the application of UAVs to the creation of 3D models in urban planning and preservation. Findings indicate five research shortcomings: limited participation of planning experts, research focus imbalance, lack of usage for special scenarios, lack of integration with smart city planning, and limited interdisciplinary collaboration. The study also acknowledges current limitations with UAV applications and discusses possible countermeasures as well as future prospects.

In the last decades, climate and environmental changes have highlighted the fragility and vulnerability of the landscape, especially in mountain areas where the effects are most severe. The strategy for hazard mitigation must deploy synergistic actions based on a thorough knowledge of the territory and its phenomena to enable integrated and effective land planning and management through suitable communication tools. This study promotes the methodological setup of a Landscape Digital Twin to establish a multi-disciplinary and multi-scalar hazards overview according to a matrix framework implementable over time and space. The original contribution to the research addresses a holistic vision that combines meaningfully qualitative with quantitative approaches to generate risk maps by integrating various indicators within a multi-hazard framework from the socio-economic perspective. This contribution presents road network risk analysis by exploiting flooding and landslide scenarios. The critical road segments or nodes most vulnerable or impacted by network performance and accessibility can be identified with minimal preprocessing from credible open-source sources. The method's applicability is tested in a Piedmont Region, northern Italy case study. The integration proposed will help generate comprehensive risk analysis maps that effectively portray the interconnectedness among natural hazards, infrastructure, and socio-economic factors fostering more resilient decision-making processes.

Microturbines can be used not only in models and education but also to propel UAVs. However, their wider adoption is limited by their relatively low efficiency and durability. Validated simulation models are required to monitor their performance, improve their lifetime, and design engine control systems. This study aims at developing a numerical model of a micro gas turbine for prediction and prognostics of engine performance. To build a reliable zero-dimensional model, the available compressor and turbine maps were scaled to the available test bench data with the least squares method, to meet the performance of the engine achieved during bench and flight tests. A steady-state aeroengine model was implemented in GSP and compared with experimental operating points. The selected flight data was then used as input for the transient engine model. The exhaust gas temperature (EGT) and fuel flow were chosen as the two key parameters to validate the model, comparing the numerical predicted values with the experimental ones. The observed difference between the model and the flight data was lower than 3% for both EGT and fuel flow.

This paper is an attempt to forecast the potential application of Digital Twin in an industrial environment by adopting scenario analysis as part of technology monitoring. In recent years Digital Twin has become one of the most emerging topics in both the tech industry and academia. This field is the latest addition to industry 4.0. It has paved a great growth opportunity in the fields of Healthcare, manufacturing, and smart city areas. The Digital twin can be defined as mirroring the physical entities into a virtual environment where the status, health, and control of these entities can be monitored and controlled. It is a field where Artificial intelligence and the Internet of Things play a major role in the handshake between the two environments. In this paper we have done a thorough analysis to find out the possible future outcome of this technology in the manufacturing industry from the perspective of our fictious company. These scenarios expose various challenges and opportunities our organization may face in our future endeavour.

Thin twin-roll cast strips from a model Al-Cu-Mg-Li-Zr alloy with a small addition of Sc were prepared. A combination of a fast solidification rate and a favorable effect of Sc microalloying impacts the size and distribution of primary phase particles and the dimension of eutectic cells. Small interdendritic spacing in the range of 10-15 um enables substitution of the initial long-term homogenization annealing by a two-step annealing at 300 and 450 °C and a short solution treatment at 530 °C before quenching and the final age-hardening procedure. A dense dispersion of small Al3(Sc,Zr) precipitates intensively inhibiting recrystallization forms during this treatment. Further refining and fragmentation of the structure were performed using constrained groove pressing before the solution treatment. Small pre-straining of quenched specimens and subsequent age-hardening simulating T8 temper were used to promote the formation of a homogeneous distribution of strengthening particles and to suppress preferential heterogeneous precipitation on subgrain and grain boundaries. Microstructural features and microhardness evolution during annealing were critically examined and confronted with microstructural characteristics observed on reference mold cast alloy or alloys without Sc alloying. The proposed treatment represents a model near net shape procedure for manufacturing thicker sheets for the aerospace industry.

Construction 4.0 is witnessing exponential growth in Digital Twin (DT) technology developments and applications, revolutionizing the adoption of Building Information Modelling (BIM) and other emerging technologies used throughout the lifecycle of the built environment. BIM provides technologies, procedures, and data schemas representing building components and systems. At the same time, DT enhances this with real-time data for cyber-physical integration, enabling live asset monitoring and better decision-making. Despite being in the early stages of development, DT applications have rapidly progressed in the AEC sector, resulting in a diverse literature landscape due to the various technologies and parameters involved in fully developing the DT technology. The intricate complexities inherent in digital twin advancements have confused professionals and researchers. This confusion arises from the nuanced distinctions between the two technologies, i.e., BIM and DT, causing a convergence that hinders realizing their potential. To address this confusion and lead to a swift development of DT technology, this study presents a holistic review of the existing research focusing on the critical components responsible for developing DT applications in the construction industry. The study identifies five crucial elements: technologies, maturity levels, data layers, enablers, and functionalities. Additionally, it identifies research gaps and proposes future avenues for streamlined DT developments and applications in the AEC sector. Future researchers and practitioners can target data integrity, integration and transmission, bi-directional interoperability, nontechnical factors, and data security to achieve mature digital twin applications for AEC practices. This study highlights the growing significance of DTs in construction and provides a foundation for further advancements in this field to harness its potential to transform built environment practices.

Since its inception in the late 2000s, blockchain has emerged as a powerful tool for creating trust without intermediaries to incentivize global communities for working for a common goal, such as the improvement of its very ecosystem, its applications and community adoption. While first blockchains were mainly devised for confirming transactions of their innate cryptocurrencies like Bitcoin, smart-contract blockchains like Ethereum can interface with the real-world through so-called “oracles”, which feed trustful off-chain information. This paper introduces digital twins of physical objects and processes as computational oracles to effectively unleash the tremendous opportunity offered by blockchain to the realm of fundamental science, research and technology development (RTD). The crowdsourcing concept is illustrated with the example of centrifugal flow control in microfluidic “Lab-on-a-Disc” (LoaD) systems.

Climate analogues provide forestry practice empirical evidence of how forests are managed in “twin” regions, i.e. regions where the current climate is comparable to the expected future climate at a site of interest. But the uncertain future climate creates uncertainty in how to adapt the forests. We therefore investigate how the uncertainty in future climate affects tree species suitability and whether there is a common underlying pattern. Like most studies we employ different ensemble variants of RCP 4.5 and 8.5. But instead of focusing on a single point in future time, we resolve each variant in a climate trajectory from 2000 to 2100. We calculate climatic distances between the climate trajectories of our site of interest and the current climate in Europe, generating maps with twin regions from 2000 to 2100. Forest inventories from the twin regions allow us to trace the changes in the prevalence of 23 major tree species. We find that it is not the direction but rather the velocity of the change that differs between the scenarios. We use this pattern to propose a tree species suitability concept that integrates the uncertainty in future climate. Twin regions provide further information on silvicultural practices, pest management, product chains etc.

Seniors safety is a compelling need, which necessitates 24/7 real-time monitoring and timely dangerous action recognition. Being able to mirror characteristics of physical objects (PO) to corresponding logical objects (LO) and seamlessly monitor their footprints thus detect anomaly parameters, Digital Twins (DT) has been considered a practical way to provide virtual health services for seniors safety. Meanwhile, widely adopted Internet of Medical Things (IoMT) consisting of wearable sensors and non-contact optical cameras for self and remote health data monitoring also raises concerns on information security and privacy violation. Therefore, security of POs, LOs and reliable data sharing among healthcare professionals are challenging as constructing trust and privacy-preserving virtual health services. Thanks to characteristics of decentralization, traceability and unalterability, Blockchain is promising to enhance security and privacy properties in many areas like data analysis, finance and healthcare. This paper envisions a lightweight authentication framework (LAF) to enable secure and privacy-preserving virtual healthcare services. Leveraging Non-Fungible Token (NFT) technology to tokenize LOs and data streams on blockchain, anyone can certify the authenticity of a digital LO along with its synchronized data between PO without relying on a third-party agency. In addition, the NFT-based tokenization not only allows owners fully control their IoMT devices and data, but it also enables verifiable ownership and traceable transferability during data sharing process. Moreover, NFT only contains references to encrypted raw data that are saved on off-chain storage like local files or distributed databases, such a hybrid storage strategy ensures privacy-preservation for sensitive information. A proof-of-concept prototype is implemented and tests are conducted on a case study of seniors safety. The experimental evaluation shows the feasibility and effectiveness of the proposed LAF solution.

Some concepts/hypotheses have been proposed to explain the general rules behind the complexity of tumorigenesis. Characterization of the property of cancer cells and neural stem cells indicates that neural stemness underlies tumorigenicity and pluripotency, leading to the proposal that tumorigenesis represents a process of progressive loss of original cell identity and gain of neural stemness. This reminds of a most fundamental process required for the development of the nervous system and body axis during embryogenesis, i.e., embryonic neural induction. The principle of neural induction is that, in response to extracellular signals that are secreted by the Spemann-Mangold organizer in amphibians or the node in mammals and inhibit epidermal fate in ectoderm, the ectodermal cells assume the neural default fate and turn into neuroectodermal cells. These cells further differentiate into the nervous system and also some non-neural cells via interaction with adjacent tissues. Failure in neural induction leads to failure of embryogenesis, and ectopic neural induction due to ectopic organizer or node activity or activation of embryonic neural genes causes a formation of secondary body axis or conjoined twins. A similar principle underlies tumorigenesis. Increasing evidence has demonstrated that the core property of cancer cells is neural stemness. Therefore, cancer cells are cells with the loss of original cell identity and gain of neural stemness, and consequently tumorigenicity and pluripotency, due to various intra-/extracellular insults in postnatal animals. Unlike that pluripotent cells (embryonic pluripotent cells, neural stem cells and cancer cells) can differentiate and integrate into embryonic development, cancer cells are capable of self-renewal and differentiation, but cannot integrate into normal tissues in a 2 postnatal animal, ultimately leading to tumor formation. Neural induction and the unique property of neural stemness provide an inclusive explanation for embryogenesis, conjoined twin formation and tumorigenesis. Based on these findings, I discuss about some confusion in cancer research, e.g., epithelial-mesenchymal transition, and propose to distinguish the causality and associations, and the causal and supporting factors involved in tumorigenesis, and suggest revisiting the focus of cancer research. Integration of evidence from developmental and cancer biology indicates that neural stemness determines tumorigenicity and pluripotency, and neural induction drives embryogenesis in gastrulating embryos but a similar process drives tumorigenesis in a postnatal animal.

Rapid post-earthquake damage diagnosis of bridges can guide decision-making for emergency response management and recovery. This can be facilitated using digital technologies to remove the barriers of manual post-event inspections. Prior mechanics-based Finite Element (FE) models can be used for post-event response simulation using the measured ground motions at nearby stations; however, the damage assessment outcomes would suffer from uncertainties in structural and soil material properties, input excitations, etc. For instrumented bridges, these uncertainties can be reduced by integrating sensory data with prior models through a model updating approach. This study presents a sequential Bayesian model updating technique, through which a linear/nonlinear FE model, including soil-structure interaction effects, and the foundation input motions are jointly identified from measured acceleration responses. The efficacy of the presented model updating technique is first examined through a numerical verification study. Then, seismic data recorded from the San Rogue Canyon Bridge in California are used for a real-world case study. Comparison between the free-field and the foundation input motions reveals valuable information regarding the soil-structure interaction effects at the bridge site. Moreover, the reasonable agreement between the recorded and estimated bridge responses shows the potentials of the presented model updating technique for real-world applications. The updated FE model is considered as the digital twin of the bridge and can be used to analyze the bridge and monitor the structural response at element, section, and fiber levels to diagnose the location and severity of any potential damage mechanism.

As an important follow-up report on the latest study of the first author (H.S.) on an off-shell quantum field causing a dressed photon and dark energy, we further discuss a couple of intriguing subjects based on our new theory. One is the dressed photon constant. If we use it, in addition to h¯ and c, as the third component of natural units, then it is defined as the geometric mean of the smallest and the largest lengths: Planck length and that relating to the cosmological constant. Interestingly, this length (≈ 50 nanometers) seems to give a rough measure of the Heisenberg cut for electromagnetic phenomena. The other is a new perspective on cosmology that combines two original notions, i.e., twin universes and conformal cyclic cosmology, proposed respectively by Petit and Penrose, into one novel picture where universes expand self-similarly. We show the possibility that twin universes having a dual structure of [matter with (dark energy & matter)] vs. corresponding anti-entities, separated by an event horizon embedded in the geometric structure of de Sitter space, undergo endless cyclic processes of birth and death, as in the case of the pair creation and annihilation of elementary particles through the intervention of a conformal light field.

The absolute time and relative time are defined in terms of the 4-D Euclidean space. Our universe is the 3-D x₁x₂x₃ quantized photon space which follows the absolute time simultaneity when the universe moves along the absolute time axis of ct. The length expansion of Dx = gDx₀ is derived under the condition of the absolute time (ct) simultaneity. From the similarity between this length expansion of Dx = gDx₀ and the energy increasing of E = gE₀, it is assumed that the energy is proportional to the particle size of Dx. The extension of this assumption to the 4-D Euclidean space gives the new definition that the particle energy (E) is the 4-D volume. Then, the particle mass energy is defined as E= mc² = cDtDV = gE₀. The masses of the elementary particles are originated from the 4-D warped volume of the photon space because the particle is the warped photon space with the velocity of v < c. Therefore, the Higgs boson concept in the standard model (SM) is not needed in the present 3-D quantized space model (TQSM). The scalar boson with the spin of zero, photon with the spin of 1 and graviton with the spin of 2 are the two-boson states. Therefore, the observed Higgs boson is reinterpreted as the two-boson state of the scalar boson with the spin of zero. The cosmic muon observation and twin paradox are explained by using the absolute time and relative time. The relative time is the observed time in the twin paradox and cosmic muon observation. In the twin paradox, a person who travels the long distance is more aged than a person on the earth in terms of the relative time ages because of the space and time conversion effect (STCE effect) of the moving space distance (x). But twins are in the same ages in terms of the absolute time without STCE effect. The fast-moving cosmic muon has the expanded half-life from the time expansion of the relative time. Also, the quantum entanglement and Pauli exclusion principle are explained. The quantum base of the photon space line connects two entangled particles. Two particles and quantum base system is fluctuated along the absolute time axis by the time clicking when one particle is measured. Another particle is instantly selected by the time clicking. This is called as the quantum entanglement. The photons which are the flat photon space with the constant speed of c along the space axis and absolute time axis have the 4-D photon velocity of c_eff = 2^0.5 c. Total 10-D Euclidean space including three 3-D quantized spaces and one absolute time axis is required for the electric charges (EC), lepton charges (CC) and color charges (CC) of the elementary particles. The 3-D photon space is very stiff along the absolute time (ct) axis and very soft along the space axes. The Coulomb force through the photons (2EM waves) of the space fluctuations is much stronger than the Gravitational force through the gravitons (G waves) of the time fluctuations between two electrons.

In this research a neccessary and sufficient condition for the proof of the Binary Goldbach conjecture is established. It is established that the square of all natural numbers greater or equal to 2 have an additive partition equal to the sum of the square of a natural number greater or equal to zero and a Goldbach partition semiprime. All Goldbach partition semiprimes are odd except 4. This finding is in itself proof all composite even numbers have at least Goldbach partition. The result of the proof of the Binary Goldbach conjecture is used to prove the Andrica and Legendre conjectures. The Riemann hypothesis is examined and sources of non trivial zeroes outside the critical strip are discussed. An example example of a non-trivial zero outside the critical strip is given

Fluidic larger-scale integration (LSI) resides at the heart of comprehensive sample-to-answer automation and parallelization of assay panels for frequent and ubiquitous bioanalytical testing in decentralized the point-of-use / point-of-care settings. This paper develops a novel “digital twin” strategy with an emphasis on rotational, centrifugo-pneumatic flow control. The underlying model systematically connects retention rates of rotationally actuated valves as a key element of LSI to experimental input parameters; for the first time, the concept of band widths in frequency space as the decisive quantity characterizing operationally robustness is introduced, a set of quantitative performance metrics guiding algorithmic optimization of disc layouts is defined, and the engineering principles of advanced, logical flow control and timing are elucidated. Overall, the digital twin enables efficient design for automating multiplexed bioassay protocols on such “Lab-on-a-Disc” (LoaD) systems featuring high packing density, reliability, configurability, modularity and manufacturability to eventually minimize cost, time and risk of development and production.

Gyroscopes are fascinating instruments with a history of about 200 years. When J.G.F. Bohnenberger presented his machine to his students in 1810 at the University of Tuebingen, Germany, nobody could have foreseen that this fascinating development would be used for complex orientation and positioning. At the University of Stuttgart, Germany, a collection of 160 exhibits is available and in transition for a sustainable future. Here, the systems are digitized in 2D, 2.5D and 3D and are made available for a world-wide community using OpenAccess platforms. The technologies being used are Computed Tomography, Computer Vision, Endoscopy and Photogrammetry. The workflows for combining voxel representations and colored point clouds are described, to create Digital Twins of the tangible assets. Advantages and disadvantages are discussed und work for near future is outlined in this new and challenging field of Tech Heritage digitization.

Let {$\Gamma(k)$} denote {$(k-1)!$}, and let {$\Gamma_{n}(k)$} denote {$(k-1)!$}, where {$n \in \{3,\ldots,16\}$} and {$k \in \{2\} \cup [2^{\textstyle 2^{n-3}}+1,\infty) \cap \mathbb N$}. For an integer {$n \in \{3,\ldots,16\}$}, let $\Sigma_n$ denote the following statement: if a system of equations {${\mathcal S} \subseteq \{\Gamma_{n}(x_i)=x_k:~i,k \in \{1,\ldots,n\}\} \cup \{x_i \cdot x_j=x_k:~i,j,k \in \{1,\ldots,n\}\}$} with $\Gamma$ instead of $\Gamma_{n}$ has only finitely many solutions in positive integers {$x_1,\ldots,x_n$}, then every tuple {$(x_1,\ldots,x_n) \in (\mathbb N \setminus \{0\})^n$} that solves the original system ${\mathcal S}$ satisfies {$x_1,\ldots,x_n \leqslant 2^{\textstyle 2^{n-2}}$}. Our hypothesis claims that the statements {$\Sigma_{3},\ldots,\Sigma_{16}$} are true. The statement {$\Sigma_6$} proves the following implication: if the equation {$x(x+1)=y!$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(1,2),(2,3)\}$}. The statement {$\Sigma_6$} proves the following implication: if the equation {$x!+1=y^2$} has only finitely many solutions in positive integers $x$ and $y$, then each such solution {$(x,y)$} belongs to the set {$\{(4,5),(5,11),(7,71)\}$}. The statement {$\Sigma_9$} implies the infinitude of primes of the form {$n^2+1$}. The statement {$\Sigma_9$} implies that any prime of the form {$n!+1$} with {$n \geqslant 2^{\textstyle 2^{9-3}}$} proves the infinitude of primes of the form {$n!+1$}. The statement {$\Sigma_{14}$} implies the infinitude of twin primes. The statement {$\Sigma_{16}$} implies the infinitude of Sophie Germain primes.

Structural health monitoring (SHM) is critical for ensuring the safety of infrastructures like bridges. This article presents a digital twin solution for SHM of railway bridges using low-cost wireless accelerometers and Machine Learning (ML). The system architecture combines edge on-premises computing and cloud analytics to enable efficient real-time monitoring and complete storage of relevant time-history datasets. After train crossings, accelerometers stream raw vibration data, which is processed in the frequency domain and analyzed via machine learning to detect anomalies indicating potential structural issues. The digital twin approach is demonstrated on an in-service railway bridge, where vibration data was collected over two years under normal operating conditions. By learning allowable ranges for vibration patterns, the digital twin model identifies abnormal spectral peaks, suggesting changes in structural integrity. The long-term pilot proves that this affordable SHM system can provide automated and real-time warning of bridge damage and also supports the use of in-house designed sensors of lower-cost and edge computing capabilities than those used in the demonstration. The successful on-premises-cloud hybrid implementation provides a cost effective and scalable model for expanding monitoring to thousands of railway bridges, democratizing SHM to improve safety by avoiding catastrophic failures.