In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{F}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We show that the public, secret and channel keys become indistinguishable to the eavesdropper under matrix multiplication. Remarkably, for achieving a 512-bit security level, the public key is 1024 bits and the private key is 768 bits, making them the smallest keys among post-quantum key exchange algorithms. Also, we discuss how to achieve key authentication, interdomain certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{Z}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We claim that the unique eavesdropper's opportunity to get the secret/private key is by means of an exhaustive search which is equivalent to the unsorted database search problem. Furthermore, we show that the secret/private keys become indistinguishable to the eavesdropper. Remarkably, to achieve a 512-bit security level, the keys (public/private) are of the same size when matrix multiplication is done over a reduced 8-bit size modulo. Also, we discuss how to achieve key certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.

The primary motivation for this work is to develop the concept of Marshall's quotient (\cite{ribeiro2016functorial}) applicable to non-commutative multirings endowed with involution, expanding the main ideas of the classical (= commutative, without involution) case presented in Marshall's seminal paper \cite{marshall2006real}. We define two multiplicative properties to deal with the involutive case and characterize their Marshall quotient. Besides, this article presents various cases showing that the ''multi'' version of rings with involution offers many examples, applications, and relatives in (multi) algebraic structures.

Recognizing the need to enhance immune cells' ability to target and eliminate tumor cells by focusing on tumor-associated antigens is crucial for the success of immunotherapy. Numerous cell-based therapies, such as CAR-T cell therapy, tumor-infiltrating lymphocyte (TIL) therapy, CAR-NK cell therapy, and T-cell receptor (TCR)-based therapies, are currently undergoing clinical and pre-clinical evaluation across various cancer types. However, a significant challenge lies in managing the inflammatory responses that are harmful to cancer patients. To overcome this, developing advanced strategies to target tumor cells precisely while preserving immune balance in cancer patients is imperative. One promising approach involves using modified tumor-associated macrophages (TAMs), which constitute approximately 50% of the tumor microenvironment (TME) and play a pivotal role in tumor progression. CAR-Macrophage (CAR-M) therapy is an emerging potential asset of immunotherapy for a wide range of tumors.

In the paper we suggest an implementation of the non-commutative logic and apply its operators for decision-making in the group of autonomous agents. The suggested operators extend the uninorm and absorbing norm aggregators and use an additional asymmetry parameter that defines the “level of non-commutativity”. The value of this parameter is specified using the perception bias of humans measured in the experiments. The suggested operators and decision-making method are illustrated by simulated behavior of mobile robots in the group.

The European Green Deal poses a two-pronged challenge for the automotive industry: migrating to solutions based in light structures, requiring light weight concepts and light materials, while at the same time avoiding dependence towards the importation of these advanced materials. Aluminium alloys are lightweight and cost-effective materials that can successfully cover the requirements of many structural applications, however their production requires from bauxite and other Critical Raw Materials (CRM), such as Si and Mg. Aluminium alloys are fully recyclable, but scrap is usually contaminated and its use is related to an increment of impurities, tramp element and undesired inclusions. Traditionally, the use of secondary alloys has been restricted to low performance applications. The present work analyses the effect that the use of scrap has in the quantity of inclusions present in the alloy and in other properties relevant for the material processing. The study was carried out for common alloys belonging to 3 of the most common aluminium processes used in the car manufacturing industry: High Pressure Die Casting (HPDC) (EN AC-43500), extrusion (6063) and sheet metal forming (5754 and 6181). Reference alloy were mixed with different level of scrap (0, 20, 40, 60, 80 and 100%) trying to keep the chemical composition as unaffected as possible. The inclusions level of the alloy was characterized with the Prefil Foot-printer® test. In addition, the obtained materials, after being cast in an open mould, were subjected to metallographic characterization. Relevant properties to assess the formability quality of the alloys for the corresponding transforming process, were obtained: flowability test for HPDC alloy and high temperature compression for extrusion alloys. The results obtained suggest that the number of inclusions present in the melt highly increase with the amount of scrap used to produce the alloy. These inclusions are also related with an important lost of flowability, but do not have a noticeable impact on microstructure.

The article presents the author’s works in the field of modifications and modeling of the PQC CSIDH algorithm on non-cyclic supersingular Edwards curves and its predecessor CRS scheme on ordinary non-cyclic Edwards curves are reviewed. Lower estimates of the computational speed gains of the modified algorithms over the original ones are obtained. The most significant results were obtained by choosing classes of non-cyclic Edwards curves connected as quadratic twist pairs instead of cyclic complete Edwards curves, as well as the method of algorithm randomization as an alternative to “constant time CSIDH.” It is shown that in the CSIDH and CSIKE algorithms, there are two independent cryptosystems with the possibility of parallel computation, eliminating the threat of side-channel attacks. For the CRS scheme, there are four such cryptosystems. Integral lower bound estimates of the performance gain of the modified CSIDH algorithm are obtained at 1.5 ∙ 29, and for the CRS scheme are 3 ∙ 29.

While the beneficial effects of using magnetic and electromagnetic treatment (ET) of brackish and saline waters on soil salinity reduction in the root zone were widely reported more studies are needed to answer questions about the soil salt leaching efficiency and the effect of the duration of the exposure to ET. For this aim, pot experiments were conducted using an Aqua-4DR physical water treatment device. The first experiment included two trials. The first considered 5 concentrations: C0:1.0; C1:4.5; C2:9; C3:13.5; and C4:18 dSm-1. The results revealed that the volume and the salt concentrations of the drained waters were significantly higher under irrigation with ET saline waters than those provided by untreated waters. The drained fraction of water varied from 20 to 26% under irrigation with untreated water and increased from 33 to 56% under irrigation with electromagnetized water indicating an improvement of salt leaching. The second trial was carried out with different irrigation doses. The result showed that the higher the dose, the more obvious and significant ET effect. The different treatment durations of water exposure revealed that the volume and salinity of drained water significantly increase as the ET duration increases. An increase in ET duration induces also an increase in soil water content of around 2.5%. Based on the experimental findings, we may conclude that the ET of saline water can reduce the adverse effect of salinity on the top soil, but these leached salts are carried away in depth and there is no concentration limit of water to the effect of the ET.

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB = C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB = C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB = C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.

The combination of encryption and digital watermarking technologies is a trend to achieve full lifecycle data protection. Recently, reversible data hiding in encrypted domain (RDHED) has greatly aroused the interests of many scholars. But the fixed order of first encryption and then watermarking makes this kind of algorithms unsuitable to many applications. Commutative encryption and watermarking (CEW) technology realizes the flexible combination of encryption and watermarking, and suits more applications. However, most existing CEW schemes for vector maps are not reversible and unsuitable to high precision maps. To solve this problem, here we propose a commutative encryption and reversible watermarking (CERW) algorithm for vector maps based on virtual coordinates which are uniformly distributed on the number axis. The CERW algorithm consists of virtual interval step based encryption scheme and coordinate difference based reversible watermarking scheme. In the encryption scheme, the map coordinates are moved randomly by multiples of virtual interval step defined as distance between two adjacent virtual coordinates. In the reversible watermarking scheme, difference expansion (DE) technique is used to embed the watermark bit into the coordinate difference computed based on the relative position of a map coordinate in a virtual interval. Since the relative position of a map coordinate in a virtual interval keeps unchanged during the coordinate scrambling encryption process, the watermarking operation and the encryption operation don’t interfere with each other and the commutativity between encryption and watermarking achieves. Results show that: proposed method has high security, high capacity and good invisibility. In addition, the algorithm is not only applicable to polyline and polygon vector data, but also can be applied to sparsely distributed point data which the traditional DE watermarking algorithm often fails to watermark.

In this paper, we investigate the effects of certain variants of the commutative laws on properties of several families of algebras which are in general not commutative, such as groups, linear algebras, or actually quite anti-commutative, such as $BCK$-algebras and $d$-algebras among others. From results obtained it becomes clear that by considering these variants in the presence of yet other axioms it is to be expected that a quite rich and varied set of results may be obtained both in the general and the particular setting of which what has been accomplished in this paper is a substantial sample.

There is great current interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed with an emphasis on their geometrical thermodynamics properties.

There is great current interest in systems represented by non-Hermitian Hamiltonians, including a wide variety of real systems that may be dissipative and whose behaviour can be represented by a "phase" parameter that characterises the way "exceptional points" (singularities of various sorts) determine the system. These systems are briefly reviewed with an emphasis on their geometrical thermodynamics properties.

In this work, studies were carried out on the extraction of silver and gold from cakes of pressure oxidation leaching of sulfide concentrate containing pyrite and arsenopyrite. The addition of gypsum at a consumption of 0.1 g/g of concentrate helps to increase silver extraction from 13.4 to 95–98% at the cyanidation stage, with no conditioning operation. Gold recovery was 99%. An increase in gypsum consumption contributes to the formation of BFAS with an increased content of sulfate sulfur, and a decrease in the As/S(sulfate) molar ratio in the cake from 3.7 down to 0.88 contributes to an increase in silver extraction at the cyanidation stage up to 98%, and its further decrease from 0.88 down to 0.58 leads to a gradual reducing silver transfer into solution from 98 down to 75.1% at the cyanidation stage. Basic ferric sulfate (BFS) is not formed in this case, since according to EDS mapping the distribution of arsenic and sulfur over iron-containing particles is uniform. According to TCLP analysis, the cake obtained after pressure oxidation leaching with the addition of gypsum and cyanidation is stable and suitable for disposal, since the final concentration of arsenic in the solution was 0.45 mg/dm3.

In the field of railroad safety, effective detection of surface cracks is critical, necessitating reliable, high-speed non-destructive testing (NDT) methods. This study introduces a hybrid Eddy Current Testing (ECT) probe, specifically engineered for railroad inspection, to address the common issue of ’lift-off noise’ due to varying distances between the probe and test material. Unlike traditional ECT methods, this probe integrates transmit and differential receiver coils, aiming to enhance detection sensitivity and minimize lift-off impact. The study optimizes ECT probes employing different driver coils, emphasizing three main objectives: a) quantitatively evaluating each probe using signal- to-noise ratio (SNR) and outlining a real-time data processing algorithm based on SNR methodology; b) exploring the frequency range proximal to the electrical resonance of the receiver coil; c) examining sensitivity variations across varying lift-off distances. The experimental outcomes indicate that the newly designed probe with figure 8-shape driver coil significantly improves sensitivity in detecting surface cracks on railroads. It achieves an impressive SNR exceeding 100 for defects with minimal dimensions of 1 mm in width and depth. Simulation results closely align with experimental findings, validating the investigation of optimal operational frequency and lift-off distance for selected probe performance, determined to be 0.3 MHz and 0.5 mm, respectively. The realization of this project would lead to notable advancements in enhancing railroad safety by improving crack detection efficiency.

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. To illustrate our main findings, we present two numerical algorithms and examples in this paper.

Students have historically fared poorly on the West African Examinations Council’s (WAEC) mathematics exam. This study investigated senior high school students’ difficulties with studying Geometry in the Cape Coast Metropolis, Central Region, Ghana. Using the descriptive survey design, data were collected from 300 Senior High School Two (SHS 2) students using simple random sampling. Students responded to the questionnaire and a 30-item multiple-choice achievement test on geometry. Four geometry concepts students perceived difficult to study are Circle theorems, Perpendicularity of Tangent and radius of a circle, Angle between Tangent and a chord and Tangents from an external point. The reasons for the difficulty in studying geometry topics are the unavailability of instructional materials, the geometry topics being complex, and teachers not teaching geometry concepts to the students’ understanding. Students’ gender did not influence the learning of concepts in geometry at a 0.05 level of significance. There was an insignificantly weak positive correlation between the students’ performance and their perceived difficult geometry concepts. It was concluded that the Ministry of Education does not provide relevant instructional materials to the various schools to teach geometry concepts. Schools do not organise workshops and seminars for teachers on effectively teaching geometry concepts in mathematics.

The reasons for the circular sense of human color perception generated by two sorts of color opponent neurons and three cone types are not well understood. Here we use geometrical analysis to examine the hypothesis that opponency, the recursive nature of color perception, and trichromacy arise as the most efficient ways of distinguishing spectrally different points on a plane using a minimum of color classes and receptor types.

Mechanically homogenized composite of expanded graphite and cobalt(II) rhenate(VII) has been described. Cobalt(II) rhenate(VII) was obtained in a reaction of perrhenic acid with cobalt(II) nitrate. A simple mortar homogenization method was used to enhance intercalation of cobalt species within carbon matrix. The specific capacity of composite was enhanced by 50% in comparison to bare expanded graphite. The electrochemical characteristic was significantly improved including better cyclability, lower resistance of electrode material, lower iR drop, with respect to expanded graphite without cobalt(II) rhenate(VII) active species. Expanded graphite with its unique specific surface area and pore size diameter was proved as potential and cheap carbon support.

Sialylated milk oligosaccharides (SMOs) is the most important oligosaccharides in human milk oligosaccharides (HMOs), and have a multifunctional health benefit, and the most abundant SMOs are sialyllactose (SLs). The previous studies indicate that the growth of tumor cells, and angiogenesis on tumor tissues with Lewis lung carcinoma, melanoma, and colon carcinoma cells could be prevented by SL. Thus, it has been proposed that SL might be an ideal candidate for the development of anti-angiogenic drugs without any side effects. It has been proposed that the Sialic acid (Sia) can be produced through SL’s hydrolysis, and the dietary Sia is further transported to the brain and other tissues though blood for formation of CMP-Sia, the activated precursor of Sia, and then is catalyzed by polysialyltransferases (polySTs) for synthesis of polysialic acid (polySia) or polysialylation of neural cell adhesion molecule (NCAM). Thus, it’s necessary to study and develop new inhibitors, which not only modulate a proper balance between the gut health and neuros system development, but also inhibit the overexpression of polySia, and thus block the tumor cell migration. In this study, we proposed that 3’-SL and 6’-SL may be more ideal inhibitors comparing with two previous inhibitors, the low molecular weight heparin (LMWH) and cytidine monophosphate (CMP) in the previous studies.

Let R be a commutative ring with identity and m, n be positive integers. In this paper, we introduce the class of (m,n)-prime ideals which lies properly between the classes of prime and (m,n)-closed ideals. A proper ideal I of R is called (m,n)-prime if for a,b∈R, a^{m}b∈I implies either aⁿ∈I or b∈I. Several characterizations of this new class with many examples are given. Analougus to primary decomposition, we define the (m,n)-decomposition of ideals and show that every ideal in an n-Noetherian ring has an (m,n)-decomposition. Furthermore, the (m,n)-prime avoidance theorem is proved.

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium, given uncertainty inherent in the systems. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic systems and information geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time, and is called the information length. By using this concept, we investigate the information geometry of non-equilibrium processes involved in disorder-order transitions between the critical and subcritical states in a bistable system. Specifically, we compute time-dependent PDFs, information length, the rate of change in information length, entropy change and Fisher information in disorder-to-order and order-to-disorder transitions, and discuss similarities and disparities between the two transitions. In particular, we show that the total information length in order-to-disorder transition is much larger than that in disorder-to-order transition, and elucidate the link to the drastically different evolution of entropy in both transitions. We also provide the comparison of the results with those in the case of the transition between the subcritical and supercritical states and discuss implications for fitness.

In this paper, we study semiconic idempotent commutative residuated lattices. After giving some properties of such residuated lattices, we obtain a structure theorem for semiconic idempotent com- mutative residuated lattices. As an application, we make use of the structure theorem to prove that the variety of strongly semiconic idempotent commutative residuated lattices has the amalgamation property.

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. The purpose of this paper is to introduce the concept of weakly S-primary ideals as a new generalization of weakly primary ideals. An ideal I of R disjoint with S is called a weakly S-primary ideal if there exists s∈S such that whenever 0≠ab∈I for a,b∈R, then sa∈√I or sb∈I. The relationships among S-prime, S-primary, weakly S-primary and S-n-ideals are investigated. For an element r in any general ZPI-ring, the (weakly) S_{r}-primary ideals are charctarized where S={1,r,r²,⋯}. Several properties, characterizations and examples concerning weakly S-primary ideals are presented. The stability of this new concept with respect to various ring-theoretic constructions such as the trivial ring extension and the amalgamation of rings along an ideal are studied. Furthermore, weakly S-decomposable ideals and S-weakly Laskerian rings which are generalizations of S-decomposable ideals and S-Laskerian rings are introduced.

The expression of polysialic acid (polySia) on the neuronal cell adhesion molecule (NCAM), is called NCAM-polysialylation, which is strongly related to the migration and invasion of tumor cells and with aggressive in the clinic. Thus, it’s important to select a proper drug to block tumor cell migration for clinic treatment. In this study, we proposed that lactoferrin (LFcinB11) may be a more ideal candidate for inhibition of NCAM polysialylation comparing with CMP and low molecular weight heparin (LMWH), which were determined based on our NMR studies. On the other hand, because neutrophil extracellular traps (NET) is the most dramatic stage in cell death process, and NETs’ release are related to pathogenesis of autoimmune and inflammatory disorders, with proposed involvement in glomerulonephritis, chronic lung disease, sepsis and vascular disorders. In this study, the molecular mechanism of inhibition of NETs’ release using LFcinB11 as inhibitor was also determined. Based on these results, LFcinB11 is proposed to be bifunctional inhibitor for inhibiting both NCAM polysialylation and NETs releases.

We propose novel spectrometer designs that aim to enhance the measured spectral range 1 of ions on a finite-sized detector. In contrast to the traditional devices that use uniform magnetic 2 field, in which the deflection of particles increases inversely proportional to their momentum, in a 3 gradient magnetic field, the deflection of particles will be decreased due to the reduction of the 4 magnetic field along their propagation. Low energy ions are particularly impacted, as they are 5 deflected less and are more likely to reach the detector compared to being driven out of it while 6 using a uniform magnetic field. By the means of a gradient magnetic field, the nonlinear dispersion 7 of ions in a homogeneous magnetic field can approach a nearly linear dispersion. Nonetheless, 8 the dispersion of low energy ions in a homogeneous magnetic field remains unnecessarily high. 9 In this article, we explore linear, quadratic, and higher-order field profiles in comparison to the 10 homogeneous field case. We discuss the employed methodology and present simulation results of 11 the spectrometer with an extended ion spectral range, focusing on the minimum detectable energy 12 (energy dynamic range) and energy resolution

Let $R$ be a commutative ring with identity. A proper ideal $I$ of a ring $R$ is called a square-difference factor absorbing primary ideal of $R$ if for $a,b\in R$, whenever $a^{2}-b^{2}\in I$, then $a+b\in\sqrt{I}$ or $a-b\in I$. Several characterizations and properties of this class of ideals are presented.Various examples are provided to illustrate the obtained results and demonstrate the applicability of our findings. Furthermore, the properties of this class of ideals are investigated in extensions of rings.

Let R be a commutative ring and m, n be positive integers. We define a proper submodule N of an R-module M to be (m,n)-closed if for r∈R and b∈M, r^{m}b∈N implies rⁿ∈(N:_{R}M) or b∈N. This class of submodules lies properly between the classes of prime and primary submodules. Many characterizations, properties and supporting examples concerning this class of submodules are provided. The notion of (m,n)-modules is introduced and characterized. Furhermore, the (m,n)-closed avoidance theorem is proved. Finally, the (m,n)-closed submodules in amalgamated modules are studied.

This work is devoted to the construction and study of commutative gates for a two-qubit quantum system. Using four-dimensional algebra developed by the Kazakh mathematician Abenov M.M. all groups of commutative gates have been constructed, and among all states of a two-qubit quantum system, unitary states with which a specific gate is connected have been identified. An explicit type of gate is described that transfers a quantum system from one unitary state to another unitary state. The proposed approach opens up new possibilities for the design of quantum algorithms not only for two-qubit quantum systems, but also for $n$-qubit quantum systems.

A way of systematizing different geometries by geometrical transformations is presented by using Klein’s perspective. Symmetry is considered the basic precedent, and different groups of transformations are introduced by using Erlangen program ideas. So, to focus on the importance of geometric transformations, two purposes are shown: first, the classification of geometries is based on the invariants of geometric transformations; and second, the construction of geometry unlike the theory of deduction can be done by means of geometric transformations.

As one of the typical deposits in Sichuan-Yunnan-Guizhou Pb-Zn metallogenic province, the Daliangzi Pb-Zn deposit has a close genetic relation with the structural system of “black/fracture zone” formed under the action of NWW-approx. EW strike-slip structures in the metallogenic province, but the mechanism of rock and ore-controlling action of the structural system remains unclear. Based on detailed analysis of tectonite-mineralized alteration lithofacies of R1 “black/fracture zone”, the tectonite-mineralized alteration lithofacies zones can be divided into 4 types in succession outward from the Pb-Zn mineralization center, i.e., ① brecciated and stockwork-like Pb-Zn mineralization-complex breccia facies zone, ② stockwork-like Pb-Zn mineralization-simple breccia and cataclasite facies zone, ③ veined pyrite-sulfide-dolomitic cataclasite facies zone, and ④ fine-veined calcite-black carbonized dolomite facies zone; Cl- and SO42--rich high-temperature oxidizing ore-bearing fluid mixes with reducing fluid in Zone ① while migration and precipitation occur in Zone ④. With the evolution of ore-forming fluid, the homogenization temperature decreases from Zone ① to Zone ④, the salinity increases from Zone ① to Zone ② and then decreases to Zones ③ and ④, and the fluid density has little change on the whole; the contents of Zn, Pb, Cu, Ga, Ge, Cd, Ag, and other metallogenic elements, the Zn/Pb ratio, and the CaO/MgO mole ratio decrease gradually from Zone ① to Zone ④; and REE fractionation, calcilization, silicification, and pyritization enhance gradually from Zone ① to Zone ④. This series of changes are the product of diapirism (cryptoexplosion) of strike-slip structures and “black/fracture zone”, among which the second-order structures (F5, F100, and other faults) derived from NWW-approx. EW striking dextral shear-tension faults F1 and F15 control the brecciated and stockwork-like Pb-Zn mineralized complex breccia facies zones and the stockwork-like Pb-Zn mineralized simple breccia and cataclasite facies zones. Therefore, this paper establishes the zoning mode of tectonite-mineralized alteration lithofacies of “black/fracture zone” and proposes that Zones ① and ② are important prospecting criteria. conclusions.

The unexploited unification of general relativity and quantum physics is a painstaking issue that prevents physicists to properly understanding the whole of Nature. Here we propose a pure mathematical approach that introduces the problem in terms of group theory. Indeed, we build a cyclic groupoid (a nonempty set with a binary operation defined on it) that encompasses both the theories as subsets, making it possible to join together two of their most dissimilar experimental results, i.e., the commutativity detectable in our macroscopic relativistic world and the noncommutativity detectable in the quantum, microscopic world. This approach, combined with the Connes fusion operator, leads to a mathematical framework useful in the investigation of relativity/quantum mechanics relationships.

We apply the Ramsey theory to the analysis of geometrical properties of closed contours. Consider a set of six points placed on a closed contour. The straight lines connecting these points are yikx=αikx+βik i,k=1...6, αik≠0. We color the edges connecting the points for which αik>0 holds with red, and the edges for which αik<0 with green with red. At least one monochromic triangle should necessarily appear within the curve (according to the Ramsey number R3,3=6). This result is immediately applicable for the analysis of dynamical billiards. The second theorem emerges from the combination of the Jordan curve and Ramsey theorem. The closed curve is considered. We connect the points located within the same region with green links and the points placed within the different regions with red links. In this case, transitivity/intransitivity of the relations between the points should be considered. Ramsey constructions arising from the differential geometry of closed contours are discussed.

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic processes and geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate classical and quantum systems and demonstrate the utility of the information length as a unique Lagrangian diagnostic to quantify the information change as a system continuously evolves in time and to map out attractor structure. We further elucidate quantum effects (uncertainty relation) and the dual role of the width of PDF in quantum systems.

With the advancement of technology, signal modulation types are becoming increasingly diverse and complex. The phenomenon of signal time-frequency overlap during transmission poses significant challenges for the classification and recognition of mixed signals, including poor recognition capabilities and low generality. This paper presents a recognition model for fine-grained analysis of mixed signal characteristics, proposing a Geometry Coordinate attention mechanism and introducing a low-rank bilinear pooling module to more effectively extract signal features for classification. The model employs a residual neural network as its backbone architecture and utilizes the Geometry Coordinate attention mechanism for time-frequency weighted analysis based on information geometry theory. This analysis targets multiple-scale features within the architecture, producing time-frequency weighted features of the signal. These weighted features are further analyzed through a low-rank bilinear pooling module, combined with the backbone features, to achieve fine-grained feature fusion. This results in a fused feature vector for mixed signal classification. Experiments were conducted on a simulated dataset comprising 39,600 mixed signal time-frequency plots. The model was benchmarked against a baseline using a residual neural network. The experimental outcomes demonstrated an improvement of 9% in the exact match ratio and 5% in the Hamming score. These results indicate that the proposed model significantly enhances the recognition capability and generalizability of mixed signal classification.

Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, represented by a set of physical equations such as the Navier-Stokes equations, energy balances and hydrological cycle among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal dimensions, which are non-integer values that represent the complexity of variables like the precipitation. However, observed precipitation is measured as an aggregate variable over time, thus physical analysis of the observed fluxes is very limited. Therefore, this review aims to go through the different approaches used in the identification and analysis of the complexity of the observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for classification of climatic features, including monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy and time scaling in intensity-duration-frequency curves.

We survey the main results emerging in the rapidly developing field that considers the geometry of thermodynamics and statistical mechanics. Our ideas of stability depend on variational principles – Maximum Entropy together with Least Action (and the isomorphic Least Exertion) – and this stability (invariance in time) indicates the centrality of the geometries of the systems. We explore a variety of examples of the application of thermodynamics in both macro- and micro-systems, and propose that irreversibility is an intrinsic and fundamental property of the physical realm (instead of being merely emergent). Using the concept of complex time, we examine the underlying mathematical unity of quantum mechanics, statistical mechanics, and geometrical thermodynamics. We show how the Planck and Boltzmann constants provide the fundamental quantum units for the phenomenological characteristics of the two Noether-conserved quantities controlling overall thermodynamic behaviour: respectively, energy and entropy production. We discuss the far-reaching isomorphisms (between all of complex time, temperature and the system symmetry) that always exist for Maximum Entropy systems, even as they exhibit either irreversible (dissipative, yet still dynamically stable) or reversible (including stable and static geometries) behaviours.

Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of symmetry is controlled by numerical parameters, which act in analogy with a biological organism's DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional design parameters and shape symmetry for visual or tactile shape sensation, and for perception-based decision making in populations of experts and non-experts. Thereafter, results from a pilot study on the effects of fractal symmetry, referred to herein as the symmetry of things in a thing, on aesthetic judgments and visual preference are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from "symmetry of things in a thing" significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion.

Orbit and clock products are used in real-time GNSS precise point positioning without knowing their quality. This study develops a new approach to detect orbit and clock errors through comparing geometry-free and geometry-based wide-lane ambiguities in PPP model. The reparameterization and estimation procedures of the geometry-free and geometry-based ambiguities are described in detail. The effects of orbit and clock errors on ambiguities are given in analytical expressions. The numerical similarity and differences of geometry-free and geometry-based wide-lane ambiguities are analyzed using different orbit and clock products. Furthermore, two types of typical errors in orbit and clock are simulated and their effects on wide-lane ambiguities are numerically produced and analyzed. The contribution discloses that the geometry-free and geometry-based wide-lane ambiguities are equivalent in terms of their formal errors. Although they are very close in terms of their estimates when the used orbit and clock for geometry-based ambiguities are precise enough, they are not the same, in particular, in the case that the used orbit and clock, as a combination, contain significant errors. It is discovered that the discrepancies of geometry-free and geometry-based wide-lane ambiguities are coincided with the actual time-variant errors in the used orbit and clock at the line-of-sight direction. This provides a quality index for real-time users to detect the errors in real-time orbit and clock products, which potentially improves the accuracy of positioning.

Due to the optical properties of the Electron Transport Layer (ETL) and Hole Transport Layer (HTL), inverted perovskite solar cells can perform better than traditional perovskite solar cells. It is essential to compare both types to understand their efficiencies. In this article, we studied inverted perovskite solar cells with NiOx/CH3NH3Pb3/ETL (ETL = MoO3, TiO2, ZnO) structures. Our results showed that the optimal thickness of NiOx is 80 nm for all structures. The optimal perovskite thickness is 600 nm for solar cells with ZnO and MoO3, and 800 nm for those with TiO2. For the ETLs, the best thicknesses are 100 nm for ZnO, 80 nm for MoO3, and 60 nm for TiO2. We found that the efficiencies of inverted perovskite solar cells with ZnO, MoO3, and TiO2 as ETLs, and with optimal layer thicknesses, are 30.16%, 18.69%, and 35.21%, respectively. These efficiencies are 1.5%, 5.7%, and 1.5% higher than those of traditional perovskite solar cells. Our study highlights the potential of optimizing layer thicknesses in inverted perovskite solar cells to achieve higher efficiencies than traditional structures.

We introduce the Symplectic Structure of Information Geometry based on Souriau’s Lie Group Thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using Geometric (Planck) Temperature of Souriau model and Symplectic cocycle notion, the Fisher metric is identified as a Souriau Geometric Heat Capacity. Souriau model is based on affine representation of Lie Group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie Group Thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant-Kirillov-Souriau) 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of Information Geometry for the action of an affine Group for exponentiel families, and provide some illustrations of use cases for multivariate Gaussian densities. Information Geometry is presented in the context of seminal work of Fréchet and his Clairaut-Legendre equation. Souriau model of Statistical Physics is validated as compatible with Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

The wave energy converter (WEC) technology constantly develops new designs and models. To encourage its development within the energy sector, research is required to improve current designs and create durable and effective devices. However, it is also crucial to investigate the suitability of a WEC to a site-specific sea condition as this can impact its optimal power absorption and constructability. This study evaluates and compares the efficiency of a heaving buoy with varied geometries in one of the most energetic places along the Mexican coast. A statistical analysis of the wave climate on the coast of Ensenada during the last 42 years is performed to define the conditions to which the device is subjected. The location of the WEC in shallow waters is chosen using a computational model which solves the modified mild slope equation in its elliptic shape. The heaving buoy floater is studied using three distinct geometries: a semi-sphere, a cylinder, and a proposed rounded semi-rectangle. The hydrodynamic response of the three geometries is then analysed in the frequency and time domain using ANSYS AQWA. The hydrodynamic study involves the assessment of the floating body dynamics, exerted forces, the power absorbed as well as the suitability of the proposed power take-off (PTO) system. Findings reveal that the proposed geometry absorbs the most energy, with an annual power of 135.11 MW, and that the transmission PTO design is appropriate for this type of technology.

We study Cartan-Schouten metrics, explore invariant dual connections, and propose them as models for Information Geometry. Based on the underlying Riemannian barycenter and the biinvariant mean of Lie groups, we subsequently propose a new parametric mean for data science and machine learning which comes with several advantages compared to traditional tools such as the arithmetic mean, median, mode, expectation, least square method, maximum likelihood, linear regression. We call a metric on a Lie group, a Cartan-Schouten metric, if its Levi-Civita connection is biinvariant, so every 1-parameter subgroup through the unit is a geodesic. Except for not being left or right invariant in general, Cartan-Schouten metrics enjoy the same geometry as biinvariant metrics, since they share the same Levi-Civita connection. To bypass the non-invariance apparent drawback, we show that Cartan-Schouten metrics are completely determined by their value at the unit. We give an explicit formula for recovering them from their value at the unit, thus making them much less computationally demanding, compared to general metrics on manifolds. Furthermore, Lie groups with Cartan-Schouten metrics are complete Riemannian or pseudo-Riemannian manifolds. We give a complete characterization of Lie groups with Riemannian or Lorentzian Cartan-Schouten metrics. Cartan-Schouten metrics are in abundance on 2-nilpotent Lie groups. Namely, on every 2-nilpotent Lie group, there is a 1-1 correspondence between the set of left invariant metrics and that of Cartan-Schouten metrics.

Generative Adversarial Networks (GANs) are powerful models for generative tasks but face significant challenges such as instability, mode collapse, and inefficient convergence. This paper introduces a theoretical framework leveraging Fermi-Dirac statistics, Ruppeiner geometry, phase transition dynamics, and graph theory to address these issues. The proposed theorems provide a robust mathematical foundation for enhancing GAN stability, diversity, and convergence. Experimental validation on the MNIST dataset demonstrates that the application of these theorems results in improved Inception Scores, reduced Fr´echet Inception Distances, and stable training dynamics, as indicated by Ruppeiner curvature analysis. The findings suggest that these theoretical insights offer a comprehensive solution to the persistent challenges in GAN training, paving the way for more reliable and effective generative models.

The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance based risk analysis. Considering the Solvency II Standard Formula from the viewpoint of linear geometry, we immediately find that it defines a norm and therefore provides a homogeneous and sub-additive tool for risk aggregation. Hence Euler's Principle for the reallocation of risk capital applies and yields explicit formulas for capital allocation in the framework given by the Solvency II Standard Formula. This gives rise to the definition of diversification functions, which we define as monotone, subadditive, and homogeneous functions on a convex cone. Diversification functions constitute a class of models for the study of the aggregation of risk, and diversification. The aggregation of risk measures using a diversification function preserves the respective properties of these risk measures. Examples of diversification functions are given by seminorms, which are monotone on the convex cone of non-negative vectors. Each L^p norm has this property, and any scalar product given by a non-negative positive semidefinite matrix does as well. In particular, the Standard Formula is a diversification function and hence a risk measure that preserves homogeneity, subadditivity, and convexity.

Lung cancer (LC) continues to be an important public health problem being the most common form of cancer and a major cause of cancer deaths worldwide. Despite the great bulk of research to identify genetic susceptibility genes by genome-wide association studies, only few loci associated to nicotine dependence have been consistently replicated. Our previously published study in few phenotypically discordant sib-pairs identified a combination of germline truncating mutations in known cancer susceptibility genes in never smoker early-onset LC patient does not present in their healthy sib. These results firstly demonstrated the presence of an oligogenic combination of disrupted cancer predisposing genes in non-smokers patients, giving experimental support to a model of a “private genetic epidemiology”. Here, we used a combination of whole-exome and RNA sequencing coupled with a discordant sib’s model in a novel cohort of pairs of never-smokers early-onset LC patients and in their healthy sibs used as controls. We selected rare germline variants predicted as deleterious by CADD and SVM bio-informatics tools and absent in the healthy sib. Overall, we identified an average of 200 variants per patient, about 10 of which in cancer predisposing genes. In most of them, RNA sequencing data reinforced the pathogenic role of the identified variants showing: i) downregulation in LC tissue (indicating “second hit” in tumor suppressor genes); ii) upregulation in cancer tissue (likely oncogene); iii) downregulation in both normal and cancer tissue (indicating transcript instability). The combination of the two techniques demonstrates that each patient has an average of six (with a range from four to eight) private mutations with functional effect in tumor predisposing genes. The presence of a unique combination of disrupting events in the affected subjects may explain the absence of familial clustering of non-small cell lung cancer. In conclusion, these findings indicate that each patient has his/her own “predisposing signature” to cancer development and suggest the use of personalized therapeutic strategies in lung cancer.

Currently, the majority of industrial metal processing involves the use of taps for cutting. However, existing tap machines require relocation to specialized inspection stations and only assess the con-dition of the cutting edges for defects. They do not evaluate the quality of the cutting angles and the amount of removed material. Machine vision, a key component of smart manufacturing, is com-monly used for visual inspection. Taps are employed for processing various materials. Traditional tap replacement relies on the technician's accumulated empirical experience to determine the ser-vice life of the tap. Typically, inspecting tooth wear involves removing the tap and evaluating the degree of wear to determine if regrinding or replacement is necessary. Therefore, we propose the use of visual inspection of the tap's external features to determine whether replacement or regrinding is needed. We examined the bearing surface of the tap and utilized single images to identify the cutting angle, clearance angle, and cone angles. By inspecting the side of the tap, we calculated the wear of each cusp. We further investigated whether the cutting portion affected the length of the tool by measuring changes in tooth surface area and the amount of removed thread. This inspection process can facilitate the development of a tap life system, allowing for the estimation of the durability and wear of taps and nuts made of different materials. Statistical analysis can be employed to predict the lifespan of taps in production lines.

As paradigm of complex behavior, multifractals describe the underlying geometry of self-similar objects or processes. Building on the connection between entropy and multifractals, we show here that the generalized dimension of geodesic trajectories in General Relativity coincides with the four-dimensionality of classical spacetime.

The focus of this work lies in the construction of monitoring system designed in the form of a patch using a long-lasting potentiometric electrolyte concentration sensor from metal electrodes, in a galvanic cell configuration Mg(s)|NaCl(aq)|Cu(s). Initially, a mathematical analysis was conducted on the expected sensor output through the Nernst equation. The experimental phase involved conducting controlled tests in the laboratory using various molar concentrations of sodium chloride (NaCl) in aqueous solution. Results showed that the electrolyte sensor allows for monitoring electrolyte levels in NaCl in the range of 0.02 to 1 M/L, with electrode lifespan exceeding 10 days. On the other hand, when patch is using human sweat during controlled exercise routines, it showed the sensor's capability for monitoring changes in the subjects' hydration levels in real time. The sensor output potential is greater than 1.7 volts when the sensor electrodes are in contact with human sweat, which is equivalent to measuring molar concentrations at normal hydration and moderately high hydration levels. Sensor results indicate that the system can function in a self-powered manner without external batteries. Additionally, the extended lifespan of its electrodes allows for continuous monitoring of imbalances in the human body, showcasing the system capability for long-term health assessment.

Microplastics (plastic particles < 5 mm) are ubiquitous pollutants that pose the ability to carry microbiota, including pathogens. Microbial adhesion is usually a sign of pathogenicity, thus we investigated the adherent strains found on 4 mm nylon strips, which were ingested and excreted by wild fish specimens. Polymer analysis of the excreted samples shown no signs of degradation, nor have their controls, represented by the nylon strips submerged in the same water tanks. Both the ingested samples and controls presented pathogens in large numbers, revealing the fact that nylon microplastics can be physical carriers for pathogens in the aquatic environment.

Background/Objectives: Periodontitis (P), a chronic inflammatory condition that affects the supportive tissues around the teeth, is 3 to 4 times more prevalent in individuals with diabetes mellitus (DM), with a direct correlation between its severity and the levels of glycosylated haemoglobin (HbA1c). This study aimed to evaluate the periodontal clinical parameters following non-surgical periodontal treatment (NSPT) in patients with and without type 2 DM and P. Methods: Forty patients with P were divided into two groups: Group DM/P and Group P. All patients were assessed at baseline, and 90 and 180 days after receiving NSPT. The parameters evaluated included HbA1c levels, plaque index (PI), probing pocket depth (PPD), clinical attachment level (CAL), and bleeding on probing (BoP). Statistical analysis was performed with a significance level set at α = 5%. Results: There were significant differences in HbA1c levels between the DM/P and P groups at baseline, 90, and 180 days, as expected. Importantly, HbA1c levels did not change after NSPT. Group P showed a significant reduction in both PI and BoP values at 90 and 180 days (p < 0.05). In contrast, group DM/P demonstrated a significant increase in the percentage of sites with PPD ≥ 5mm at 180 days (p < 0.05). Additionally, group P exhibited an increase in sites with PPD ≤ 4mm and a decrease in sites with PPD ≥ 5mm at both 90 and 180 days (p < 0.05). Conclusions: Our findings suggest that DM may compromise the effectiveness of NSPT, potentially hindering favorable outcomes during the follow-up period.

Epithelial ovarian cancer (EOC) has not significantly benefited from advances in immunotherapy, mainly because of the lack of well-defined actionable antigen targets. Using proteogenomic analyses of primary EOC tumors, we previously identified 91 aberrantly expressed tumor-specific antigens (TSAs) originating from unmutated genomic sequences. Most of these TSAs derive from non-exonic regions, and their expression results from cancer-specific epigenetic changes. The present study aimed to evaluate the immunogenicity of 48 TSAs selected according to two criteria: presentation by highly prevalent HLA allotypes and expression in a significant fraction of EOC tumors. Using targeted mass spectrometry analyses, we found that pulsing with synthetic TSA peptides leads to a high-level presentation on dendritic cells. TSA abundance correlated with the predicted binding affinity to the HLA allotype. We stimulated naïve CD8 T cells from healthy blood donors with TSA-pulsed dendritic cells and assessed their expansion with two assays: MHC-peptide tetramer staining and TCR Vβ CDR3 sequencing. We report that these TSAs can expand sizeable populations of CD8 T cells and, therefore, represent attractive targets for EOC immunotherapy.

Descriptive geometry has indispensable applications in many engineering activities, some of which are presented in the first chapter of this paper in order to place the development presented here among them. As a result of the continuous variability of the technological environment according to various optimization aspects, the engineering activities must also be continuously adapted to the changes, which an appropriate approach and formulation are required from the practitioners of descriptive geometry, and can even lead to improvement in the field of descriptive geometry. The imaging procedures are always based on the methods and theorems of descriptive geometry. Resolving contradictions in spatial geometry reconstruction research is a constant challenge, to which a possible answer in many cases is the search for the right projection direction. A special method of enumerating the possible infinite viewpoints for the representation of the surface edge curves is presented in another part of the paper. The procedure for determining the correct directions in a mathematically exact way is also presented through examples. The analysis and some of the results of the Monge mapping, which is suitable for the solution of a mechanical engineering task to be solved in a specific technical environment, are also presented.

Fractals and multifractals are well-known trademarks of nonlinear dynamics and classical chaos. The goal of this work is to tentatively uncover the unforeseen path from multifractals and selfsimilarity to the framework of effective field theory (EFT). An intriguing finding is that the partition function of multifractal geometry includes a signature analogous to that of gravitational interaction. Our results also suggest that multifractal geometry may offer insights into the non-renormalizable interactions presumed to develop beyond the Standard Model scale.

In this paper, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area and volume, and unifies the calculus of scalar, spinor, vector and tensor, so that it is able to naturally describe all variables and calculus in geometry and physics. Clifford algebra unifies and generalizes real number, complex, quaternion and vector algebra, converts complicated relations and operations into intuitive matrix algebra independent of coordinate systems. By localizing the basis or frame of space-time and introducing differential and connection operators, Clifford algebra also contains Riemann geometry. Clifford algebra provides a unified, standard, elegant and open language and tools for numerous complicated mathematical and physical theories. Clifford algebra calculus is an arithmetic-like operation that can be well understood by everyone. This feature is very useful for teaching purposes, and popularizing Clifford algebra in high schools and universities will greatly improve the efficiency of students to learn fundamental knowledge of mathematics and physics. So Clifford algebra can be expected to complete a new big synthesis of scientific knowledge.

In recent experimental studies, we reported the aggravating effects of Asian sand dust (ASD) on male reproductive function in mice. However, the effects of fetal ASD exposure on male reproductive function have not been investigated. The present study investigated the effects of fetal ASD exposure on reproductive function in male offspring. Using pregnant CD-1 mice, ASD was administered intratracheally on days 7 and 14 of gestation, and the reproductive function of male offspring was determined at 5, 10, and 15 weeks after birth. The secondary sex ratio was significantly lower in the fetal ASD-exposed mice than in the controls. Histologic examination showed partial vacuolation of seminiferous tubules in immature mice. Moreover, daily sperm production (DSP) was significantly less in the fetal ASD-exposed mice than in the controls. DSP in the fetal ASD-exposed mice was approximately 10% less than the controls at both 5 and 10 weeks. However, both the histologic changes and the DSP decrease were reversed as the mice matured. These findings suggest that ASD exposure affects both the fetal development and the reproductive function of male offspring. In the future, it will be necessary to clarify the onset mechanisms of ASD-induced male fetus death and male reproductive disorders.

This paper investigates the constructability of angles multiples of 3 within the framework of Euclidean geometry. It makes a significant contribution by presenting the first geometric construction for all such angles, offering a rigorous solution to a longstanding geometric problem. The paper reaffirms the efficacy of Euclidean geometry in providing precise constructions and robust proofs for these angles, demonstrating the enduring strength of Euclidean principles from classical to modern times. The presented workflow goes beyond Euclidean geometry to examine non-Euclidean methods, particularly analytical approaches, revealing misconceptions that compromise the genetic and geometric rigor of Euclidean principles. The paper exposes incongruities when algebraic proofs related to angle constructability are applied to the Euclidean system, emphasizing the misalignment of fundamental geometric concepts. A notable result in the paper is the construction of a angle, introducing the “ angle chord” as a novel geometric property. This property challenges assumptions made by non-Euclidean methods and highlights the nuanced geometric properties crucial for rigorous constructions. The paper refutes the fallacy of relying solely on algebra for solutions to angles multiples of , emphasizing the necessity of embracing Euclidean geometry for geometric discoveries. The paper underscores the merits and resilience of Euclidean geometry, showcasing its independence and depth across historical and modern perspectives. The newly presented geometric construction not only resolves a longstanding question but also emphasizes the intrinsic strength and uniqueness of Euclidean principles in contrast to alternative methodologies.

The dynamic factors in the environment violate the static environment assumption of the SLAM algorithm, leading to a decrease in the accuracy of camera positioning. In recent years, many studies have attempted to address dynamic objects by combining semantic constraints and geometric constraints, but issues such as poor real-time performance, the potential for mistakenly treating humans as rigid objects, and subpar performance in high-dynamic scenes still persist. This paper proposes a dynamic scene visual SLAM algorithm called Dynamic SLAM based on target tracking and multi-view geometry (TKG-SLAM), based on object detection, Kalman filters, and multi-view geometry. This algorithm takes into consideration both real-time performance and algorithm accuracy. It combines semantic constraints and multi-view geometry constraints, selectively running the algorithm in different scenarios, filtering and preserving static points for camera pose estimation. Experimental results demonstrate that, compared to current state-of-the-art dynamic SLAM methods, our approach achieves optimal performance in some scenarios and exhibits stronger real-time capabilities.

This paper proposes an interpretable geometry solution based on the formal language set of text and diagram. Geometry problems are solved by machines, which still poses challenges in natural language processing and computer vision. Significant progress promotes existing methods in the extraction of geometric formal languages. However, the neglect of the graph structure information in the formal language and the lack of further refinement of the extracted language set can lead to the poor effect of the theorem prediction and affect the accuracy in problem solving. In this paper, the formal language graph is constructed by the extracted formal language set and used to theorem prediction by graph convolutional network. So as to better extract the relationship set of diagram elements, an improved diagram parser was proposed. The test results indicate that the improved method has good results in solving the problem with interpretability geometry.

The paper considers coherent states for the representation of Weyl commutation relations over a field of $p$-adic numbers. A geometric object, a lattice in vector space over a field of p-adic numbers, corresponds to the family of coherent states. It is proved that the bases of coherent states corresponding to different lattices are mutually unbiased, and the operators defining the quantization of symplectic dynamics are Hadamard operators.

In this paper we investigate the geometric structure and control of exponential families depending on additional parameters, called external parameters. These generalized exponential families emerges naturally when one applies the maximum entropy formalism to derive the equilibrium statistical mechanics framework. We study the associated statistical model, compute the Fisher metric and introduce a natural fibration of the parameter space over the external parameter space. The Fisher Riemannian metric allows to endow this fibration with an Ehresmann connection and to study the geometry and control of these statistical models. As an example, we show that horizontal lift of paths in the external parameter space corresponds to an isentropic evolution of the system. We apply the theory to the example of a ideal gas in a rotating rigid container. Most of the results are expressed in local coordinates; in the appendices we hint at possible global extensions of the theory.

In this article, a generalization of the geometry of Grassmannian chain complex of free abelian groups generated by the projective configuration of points and Cathelineau's infinitesimal complex of polylogarithmic groups is proposed. Firstly, homomorphisms for weight n =2 up to weight n=6 will be introduced to connect sub-complexes of Grassmannian and Cathelineau. Lately, generalization of these morphisms will be shown for weight n=N. The associated diagrams will also be proven to be commutative and bi-complex.

Recently, historians have discussed the relevance of the nineteenth-century mathematical discipline of projective geometry for early modern classical logic in relation to possible solutions to semantic problems facing it. In this paper I consider Hegel’s Science of Logic as an attempt to provide a projective geometrical alternative to the implicit Euclidean underpinnings of Aristotle’s syllogistic logic. While this proceeds via Hegel’s acceptance of the role of the three means of Pythagorean music theory in Plato’s cosmology, the relevance of this can be separated from any fanciful “music of the spheres” approach by the fact that common mathematical structures underpin both music theory and projective geometry, as suggested in the name of projective geometry’s principal invariant, the “harmonic cross-ratio”. Here I demonstrate this common structure in terms of the phenomenon of “inverse foreshortening”. As with recent suggestions concerning the relevance of projective geometry for logic, Hegel’s modifications of Aristotle respond to semantic problems of his logic.

The paper describes an algorithm for semantic representation of behavioral contexts relative to a dichotomic decision alternative. The contexts are represented as quantum qubit states in two-dimensional Hilbert space visualized as points on the Bloch sphere. The azimuthal coordinate of this sphere functions as a one-dimensional semantic space in which the contexts are accommodated according to their subjective relevance to the considered uncertainty. The contexts are processed in triples defined by knowledge of a subject about a binary situational factor. The obtained triads of context representations function as stable cognitive structure at the same time allowing a subject to model probabilistically-variative behavior. The developed algorithm illustrates an approach for quantitative subjectively-semantic modeling of behavior based on conceptual and mathematical apparatus of quantum theory.

Starting from Thomas Friedrich’s work “Weak Spin(9) structures on 16-dimensional Riemannian manifolds”, we review several interactions between Spin(9) and geometries related to octonions. Several topics are discussed in this respect: explicit descriptions of the Spin(9) canonical 8-form and its analogies with quaternionic geometry, the role of Spin(9) both in the classical problems of vector fields on spheres and in the geometry of the octonionic Hopf fibration. Next, we deal with locally conformally parallel Spin(9) manifolds in the framework of intrinsic torsion. Finally, we discuss applications of Clifford systems and Clifford structures to Cayley-Rosenfeld planes and to three series of Grassmannians.

Aim of expressional space is to facilitate the public to explore their hobby and talent in autodidact. The space for expression in Makassar City is necessary for the mural artist and the youngsters who has a hobby to play a skateboard. Their talent is insufficient attention by the government and create negative attitude because there no space to accommodate their activity. Therefore, this paper presents a design idea of expressional space by implementing the architectural geometry. The architectural geometry design principle is based on simple geometry form application as a realization of form from the space. An experience of the space for the user realizes by the relationship between the space and the interaction with the environment through geometry and form processing as the basic of the creation process in the architectural works. Content analysis method providing a landscape layout and transformation of form and building mass in form of the implementation of architectural geometry principles. The principles are pure geometry, composition of geometry, direction wall, and opening for the transformation process of expressional space form to produce and increase aesthetic value of the environment.

In this paper we suggest a first ever construction of fractional integral and differential operators based on signed measures including a vector-valued case. The study focuses on constructing the fractional power of the Riemann-Stieltjes integral with a signed measure, using semigroup theory. The main result is a theorem that provides the exact form of a semigroup for the Riemann-Stieltjes integral with a measure having a countable number of extrema. The article provides examples of semigroups based on integral operators with signed measures and discusses the fractional powers of differential operators with partial derivatives.

Heart failure is a prevalent cardiovascular condition with significant health implications, necessitating effective diagnostic strategies for timely intervention. This study explores the potential of continuous monitoring of non-invasive signals, specifically integrating Photoplethysmogram (PPG) and Electrocardiogram (ECG), for enhancing early detection and diagnosis of heart failure. Leveraging a dataset from the MIMIC-III database, encompassing 682 heart failure patients and 954 controls. Feature selection techniques were used to systematically select key features which were identified for their clinical relevance and significance in capturing cardiovascular dynamics and to reduce computational complexity and to decrease the chance of overfitting the ML algorithms. These features are then utilized to train and evaluate machine learning algorithms, resulting in a model with an impressive accuracy of 98%, sensitivity of 97.60%, specificity of 96.90%, and precision of 97.20%. The integrated approach outperforms single-signal strategies, showcas-ng its potential for early, precise, and non-invasive heart failure diagnosis. Furthermore, the study underscores the significance of continuous monitoring through wearables, emphasizing the benefits of integrating multiple signals for a comprehensive evaluation of cardiovascular health. The proposed approach holds promise for implementation in hardware systems to enable continuous monitoring, aiding in early detection and prevention of critical health conditions.

This study presents a novel approach for quantifying the dynamics of monthly hydraulic geometry relationships in the Jingjiang reach of the Yangtze River by integrating leaf area index (LAI) data as an indicator of riparian vegetation. A comprehensive system of ordinary differential equations (ODEs) couples traditional power-law hydraulic geometry equations with LAI, capturing the influence of erosion control on channel morphology. The periodic delayed response theory and automatic differentiation techniques are employed to enhance the modeling framework's capabilities. Calibration and verification demonstrate the models' effectiveness in capturing overall trends in discharge, width, and depth dynamics, outperforming traditional constant-parameter approaches. However, model predictive abilities are limited under extreme climate conditions due to training on normal climate data. Key assumptions, including the periodic delayed response theory's neglect of peak discharges, simplified representation of artificial cut-offs, and reliance on remotely sensed data with limited local validation, introduce uncertainties. The proposed modeling framework shows potential for broader application to other river systems with appropriate adjustments. Future research could incorporate additional environmental factors, integrate models across scales, couple with advanced simulation techniques, and expand stability assessments beyond the riverbed index. By addressing related challenges, this integrated approach lays a foundation for enhancing understanding of river morphodynamics and channel stability.

Corrugated board, widely used in the packing industry, is a recyclable and durable material. Its strength and cushioning, influenced by geometry, environmental conditions like humidity and temperature, and paper quality, make it versatile. Double-walled (or five-ply) corrugated board, comprising two flutes and three liners, enhances these properties. This study introduces a novel approach to analyze 5-layered corrugated board, extending a previously published algorithm for single-walled boards. Our method focuses on measuring layer and overall board thickness, flute height, and center lines of each layer. Integrating image processing and genetic algorithms, the research successfully developed an algorithm for precise geometric feature identification of double-walled boards. Images were recorded using a special device with a sophisticated camera and image sensor for detailed corrugated board cross-sections. Demonstrating high accuracy, the method faced limitations only with very deformed or damaged samples. This research contributes significantly to quality control in the packaging industry and paves the way for further automated material analysis using advanced machine learning and image sensors. It emphasizes the importance of sample quality and suggests areas for algorithm refinement to enhance robustness and accuracy.

Non-isocyanate polyurethane synthesis by non-Sn catalysis is an essential challenge toward green polyurethane synthesis. Bismuth compounds are attractive candidates due to their low cost, low toxicity, and availability to urethane chemistry. We applied various Bi catalysts to the self-polycondensation of a bishydroxyurethane monomer and found BiCl3 to be an excellent catalyst through optimization. The catalytic activity and price of BiCl3 are comparable to those of Bu2SnO, while its toxicity is significantly low. BiCl3 is, therefore, a promising alternative to Sn-based catalysts in non-isocyanate polyurethane synthesis.

The aim of this randomized controlled clinical trial was to compare the 2-year clinical performance of resin composite restorations placed at non-caries cervical lesions (NCCL) with one-step self-etch, total-etch, and selective enamel etch & self-etch adhesive techniques. Thirty-two patients received three resin composite restorations each at NCCLs (Tetric EvoCeram/Ivoclar/Vivadent), bonded with a total-etch adhesive agent (ExciTE F/Ivoclar/Vivadent) and a self-etch (AdheSE One F/Ivoclar/Vivadent) without and with selective enamel etching. All restorations were evaluated by two examiners at baseline, 6-, 12-, 18- and 24-months post-operation regarding retention, caries occurrence, marginal adaptation, and marginal staining. A logistic regression analysis with generalized estimating equations was used. After 2 years, the retention rate was 86,8% for total-etch, 92.26% for self-etch, and 93.63% for selective enamel etching & self-etch. No caries were detected during all the restorations. Concerning marginal adaptation, the clinically perfect restorations were 26.9% for the total-etch technique, 16% for self-etch, and 25,9% for selective enamel etch & self-etch. All three adhesive strategies provided restorations with no significant differences in the retention rate and the marginal adaptation, whereas the total etch yielded better performance for marginal staining. All the restorations were assessed as clinically acceptable after 2 years.

The Heisenberg Lie algebra (HA) plays an important role in mathematics with Fourier transforms, as well as for the foundations of quantum theory where it expresses the operators of space-time, X, and their commutation rules with the momentum operators, D, that execute infinitesimal translations in X. Yet it is known that space-time is curved and thus the D operators must interfere thus giving “structure constants” that vary with location which suggests a mathematical generalization of the concept of a Lie algebra to allow for “structure constants” that are functions of X. We here investigate the mathematics of such a “generalized Heisenberg algebra” (GHA) which has “structure constants” that are functions of X and thus are in the enveloping algebra rather than constants. As expected, the Jacobi identity no longer holds globally but only in small regions of space-time where the [D, X] commutator can be considered locally constant and thus where one has a true Lie algebra. We show that one is able to reframe Riemannian geometry in this GHA. As an example, it is then shown that one can express the Einstein equations of general relativity as commutation rules. If one requires that the GHA commutator reduces to the HA of quantum theory in the limit of no curvature, then there are observable effects for quantum theory in this curved space time.

The state-of-the-art smart city has been calling for an economic but efficient energy management over large-scale network, especially for the electric power system. It is a critical issue to monitor, analyze and control electric loads of all users in system. In this paper, we employ the popular computer vision techniques of AI to design a non-intrusive load monitoring method for smart electric energy management. First of all, we utilize both signal transforms (including wavelet transform and discrete Fourier transform) and Gramian Angular Field (GAF) methods to map one-dimensional current signals onto two-dimensional color feature images. Second, we propose to recognize all electric loads from color feature images using a deep neural network with multi-scale feature extraction and attention mechanism. Third, we design our method as a cloud-based, non-intrusive monitoring of all users, thereby saving energy cost during electric power system control. Experimental results on both public and our private datasets have demonstrated our method achieves superior performances than its peers, and thus supports efficient energy management over large-scale Internet of Things.

Meat serves as a vital component of the human diet, offering a rich source of protein and essential trace elements. China stands as both a significant producer and consumer of meat on a global scale, leading the world in terms of total meat production and consumption. As the standard of living within the country continues to rise, there is a growing emphasis on the nutritional value and safety of meat consumption. The tenderness of meat is a critical factor influencing its overall quality. Traditionally, tenderness has been assessed through shear force testing, a method that is inherently destructive, inefficient, and results in considerable sample wastage. In light of these drawbacks, non-destructive testing techniques have emerged as a preferred alternative, promising greater accuracy, efficiency, and convenience without compromising the integrity of the samples. This paper delves into the application of five advanced non-destructive testing technologies in the realm of meat tenderness assessment. These include near-infrared spectroscopy, hyperspectral imaging, Raman spectroscopy, airflow optical fusion detection, and nuclear magnetic resonance detection. Each technology is scrutinized for its respective strengths and limitations, providing a comprehensive overview of their current utility and potential for future development. Moreover, the integration of these techniques with the latest advancements in artificial intelligence (AI) technology is explored. The fusion of AI with non-destructive testing offers a promising avenue for the development of more sophisticated, rapid, and intelligent systems for meat tenderness evaluation. This integration is anticipated to significantly enhance the efficiency and accuracy of quality assessment in the meat industry, ensuring a higher standard of safety and nutritional value for consumers. The paper concludes with a set of technical recommendations aimed at guiding the future direction of non-destructive, AI-enhanced meat tenderness detection, thereby contributing to the ongoing improvement of the meat industry in China and beyond.

The effect of the heterogeneity in sex factor is considered in the Markovian manpower modeling model. The estimation of the transition probability matrix of the staff flow was done using the maximum likelihood method. The expected future durations of the individuals in the manpower system were obtained under the aggregated and disaggregated (male and female) staff flow as well as their variances. Test for the heterogeneity of the staff based on sex factor was performed and the result of the heterogeneity test shows that there is difference between the disaggregated staff flows. The computed entrant probabilities also indicate that the male group has higher probabilities of attaining higher grades than the female group.

MicroRNAs (miRNA) exert regulatory actions via base-pairing with their binding sites on target mRNAs. Cooperative-binding, i.e., synergism, among binding sites on a mRNA is biochemically well-characterized. We studied whether this synergism is reflected in global relationship between miRNA-mediated regulatory activity and miRNA-binding-site count on the target mRNAs, i.e., leading to a non-linear relationship between the two. Recently, using our own and public datasets, we have enquired into miRNA regulatory actions: first, we analyzed the power-law distribution pattern of miRNA binding sites; second, strikingly, mRNAs for core miRNA regulatory apparatus proteins have extra-ordinarily high binding site counts, forming self-feedback-control loops; third, we revealed that tumor suppressor mRNAs generally have more sites than oncogene mRNAs; and fourth, we characterized enrichment of miRNA target mRNAs in translationally less-active polysomes relative to more-active polysomes. In these four studies, obvious correlation was observed qualitatively between the extent to which a mRNA is miRNA-regulated and its binding sites count. This paper summarizes the used datasets. We also re-analyzed the correlation by comparative linear and non-linear regression analyses. The results support a non-linear, instead of linear, relationship between the two parameters, conceivably a transcriptome-level reflection of cooperative-binding/synergism among miRNA binding sites on a target mRNA.

This paper presents a theory on graph topological structure and graph coloring, proving that for any N-order graph structure (with a topological structure similar to ), the maximum number of colors required for coloring is less than or equal to . The Four Color Theorem is just one special case of this theory, with the maximum structure size for a four-color graph being a 4-order structure graph, hence requiring only a maximum of 4 colors for coloring.

Glucose is a simple sugar molecule. The sugar molecule is chemically symbolised as C6H12O6. This means that the glucose molecule contains 6 carbon atoms (C), 12 hydrogen atoms (H) and 6 oxygen atoms (O). In human blood, the molecule glucose circulates as blood sugar. Normally after eating or drinking, our body breaks down the sugars in food and uses them to obtain energy for our cells. To do this, our pancreas produces insulin. Insulin "pulls" sugar from the blood and puts it into the cells for use. If someone has diabetes, their pancreas can't produce enough insulin. As a result, the level of glucose in the blood rises. This can lead one to many potential complications, including blindness, disease, nerve damage, amputation, stroke, heart attack and damage to blood vessels etc. In this study, a non-invasive method for monitoring blood glucose has been developed and is therefore easily usable. The device developed can measure the glucose level continuously and eliminates the disadvantages of the invasive system. Near-IR sensors (optical sensors) were used to estimate the concentration of glucose in the blood; these sensors have a wavelength of 940 nm. The sensor is placed on the tip of the finger and the output of the optical sensor is then connected to the microcontroller at the analogue input. Another sensor used, but only to provide more medical information was the heartbeat sensor. After processing and regression analysis, the glucose level is predicted, and data is sent via the Bluetooth network to a developed APP. The results of the implemented device were compared with available invasive methods. The study consists of a hardware platform inserted into an armband and then a small black parallelepiped-shaped box in which the optical sensors are inserted. The hardware consists of a microcontroller, a Near-IR optical sensor, a heartbeat sensor and a Bluetooth module.

A cyclic antipodal points of a circle is a pair of points that are the intersection of the circle with a diameter of the circle. A recent proof of Ptolemy’s Theorem, simultaneously in both (i) Euclidean geometry; and (ii) the relativistic model of hyperbolic geometry (which is identified with the Klein model of hyperbolic geometry), motivates in this article the study of four cyclic antipodal points of a circle, ordered arbitrarily counterclockwise. The translation of results from Euclidean geometry into hyperbolic geometry is obtained by means of hyperbolic trigonometry, called gyrotrigonometry, to which Einstein addition gives rise. Formulas that extend the Pythagorean formula in both Euclidean and hyperbolic geometry are obtained as byproducts

Bifacial PV modules have become the pervasive choice for utility-scale solar photovoltaic (PV) installations. Understanding bifacial PV performance for commercial deployments is, therefore, critically important. Although there have been studies on the modeling of Bifacial PV performance, to the best of our knowledge, the comprehensive integration of racking and mounting geometry for Bifacial PV performance simulation is yet to be reported. In this work, we modeled the racking and mounting geometry for a field-deployed operational PV array. We then applied optical ray-trace simulation to study the impact of those structures on array performance. The study reveals that the support structures have a considerable impact on the rear surface irradiance and overall bifacial PV performance, amounting to as much as 30% shading in certain situations. The work analyzes the impact of installation parameters such as tilt, height, and row spacing on the bifacial PV array’s performance. Thus, a novel holistic approach to studying the sensitivity of various installation parameters’ impact on bifacial PV array performance, with the racking and mounting structure’s geometry integrated, has been demonstrated through the work. This knowledge and its practice enables site-specific design optimization for utility-scale bifacial solar PV arrays and synergistic PV applications such as agrivoltaics and carports, where maximizing power generation is not necessarily the sole objective.

In this research, we investigate the bending of photon light and/or time-like geodesics within the context of four-dimensional space-time geometry, specifically in the presence of topological defects. These topological defects manifest as cosmic string space-time configurations, encompassing screw dislocation, spiral dislocation, and spacelike dislocation. Our primary objective is to determine the extent of deflection experienced by light-like and time-like geodesics and analyze how this deflection is affected by the cosmic string parameter, screw dislocation parameter, and spacelike dislocation parameter. To accomplish this, we employ a derivation technique that centers on the observation that photon rays (light-like geodesics) and/or time-like geodesics follow paths parallel to the z-axis while maintaining a constant radius along the cylinder.

The present paper provides a new definition for dual spline curves in a geometric intuitive way based on adaptive curve refinement techniques. The dual spline is an implementation of the interpolatory subdivision scheme for curve modeling, which is comprised of polynomial segments of different degrees. Specially, the dual spline curves are mainly aims to solve the difficult geometry defeaturing problems in the existing computer-aided technology. Dual spline curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, continuous and discontinuous boundary approximation. By adding fictitious and intrinsic nodes inside or at the vertices of interpolation elements, the dual spline is flexible and convenient for approximating a set of ordered points or discrete segments. Combined with the Lagrange interpolation polynomial and meshless method, the proposed approach is capable of approximating the non-smooth boundary for geometry defeaturing. Experimental results are given to verify the validity, robustness, and accuracy of the proposed method.

Cells are influenced by several biomechanical aspects of their microenvironment, such as substrate geometry. According to the literature, substrate geometry influences the behavior of muscle cells; in particular, the curvature feature improves cell proliferation. However, the effect of the substrate geometry on the myogenic differentiation process is not clear and needs to be further investigated. Here, we show that the 3D co-printing technique allows the realization of substrates. To test the influence of the co-printing technique on cellular behavior we realized linear polycaprolactone substrates with channels in which a fibrinogen-based hydrogel loaded with C2C12 cells was deposited. Cell viability and differentiation were investigated up to 21 days in culture. The results suggest that this technology significantly improves the differentiation at 14 days. Therefore, we investigate the substrate geometry influence by comparing three different co-printed geometries – linear, circular, and hybrid structures (linear and circular features combined). Based on our results, all structures exhibit optimal cell viability (> 94%) but the linear pattern allows to increase the in-vitro cell differentiation, in particular after 14 days of culture. This study proposes an endorsed approach for creating artificial muscles for future skeletal muscle tissue engineering applications.

Computer extended Descriptive Geometry (CeDG) is a new approach to solve and build computer models of three dimensional (3D) geometrical systems through descriptive geometry procedures that have demonstrated reliability and accuracy. CeDG may calculate a parametric algebraic exact form for the spatial curves generated in the intersection of two surfaces, as well as of the flattened pattern of any developable surface involved in those encounters. This study presents first the theoretical foundations and methodology to calculate those parametric algebraic curves. Secondly, a compound hopper is defined and modelled through CeDG (implemented in GeoGebra) and CAD (Solid Edge 2023) approaches to evaluate the advantages of CeDG against CAD. The results demonstrate the robustness and accuracy of the CeDG technique for surfaces intersection and flattening and the advantages of CeDG against Solid Edge 2023 in solving the hopper case study.

A new framework in quantum chemistry has been proposed recently ("An approach to first principles electronic structure calculation by symbolic-numeric computation'' by A. Kikuchi). It is based on the modern technique of computational algebraic geometry, viz. the symbolic computation of polynomial systems. Although this framework belongs to molecular orbital theory, it fully adopts the symbolic method. The analytic integrals in the secular equations are approximated by the polynomials. The indeterminate variables of polynomials represent the wave-functions and other parameters for the optimization, such as atomic positions and contraction coefficients of atomic orbitals. Then the symbolic computation digests and decomposes the polynomials into a tame form of the set of equations, to which numerical computations are easily applied. The key technique is Grröbner basis theory, by which one can investigate the electronic structure by unraveling the entangled relations of the involved variables. In this article, at first, we demonstrate the featured result of this new theory. Next, we expound the mathematical basics concerning computational algebraic geometry, which are necessitated in our study. We will see how highly abstract ideas of polynomial algebra would be applied to the solution of the definite problems in quantum mechanics. We solve simple problems in "quantum chemistry in algebraic variety'' by means of algebraic approach. Finally, we review several topics related to polynomial computation, whereby we shall have an outlook for the future direction of the research.

The effect of divergence of chute sidewalls with three different baffle block geometries namely USBR, trihedral and semicircular blocks, as well as the depth and dimensions of the scour hole downstream of the chute were studied using a physical model. For this purpose, 9 models of baffled chutes were designed and constructed with divergence ratios of 1.45, 1.75, and 2.45 and without divergence (with a divergence ratio of 1). Comparing the results on the effect of block geometry at different divergence ratios revealed that the use of blocks proposed in this study instead of standard USBR blocks reduced the mean and maximum scour hole by 50%. For a given block geometry, the mean depth, maximum depth, and length of scour hole were reduced by 75%, 58%, and 50%, respectively.

The evaluation of geometric defects is necessary in order to maintain the integrity of structures over time. These assessments are designed to detect damages of structures and ideally help inspectors to estimate the remaining life of structures. Current methodologies for monitoring structural systems, while providing useful information about the current state of a structure, are limited in the monitoring of defects over time and in linking them to predictive simulation. This paper presents a new approach to the predictive modeling of geometric defects. A combination of segmented from point clouds are parametrized using the convex hull algorithm to extract features from detected defects, and a stochastic dynamic model is then adapted to these features to model the evolution of the hull over time. Describing a defect in terms of its parameterized hull enables consistent temporal tracking for predictive purposes, while implicitly reducing data dimensionality and complexity as well. In this study, 2D point clouds analogous to information derived from point clouds were first generated over simulated life-cycles. The evolutions of point cloud hull parameterizations were modeled as stochastic dynamical processes via autoregressive integrated moving average (ARIMA) and vectorized autoregression (VAR) and compared against ground truth. The results indicate that this convex hull approach provides consistent and accurate representations of defect evolution across a range of defect topologies and is reasonably robust to noisy measurements, however assumptions regarding the underlying dynamical process play a significant the role in predictive accuracy. The results were then validated on experimental data from fatigue testing with high accuracy. Longer term, the results of this work will support finite element model updating for predictive analysis of structural capacity.

Alzheimer's disease (AD) is a multifaceted neurodegenerative disorder characterized by cognitive decline and neuronal loss, representing a most challenging health issue. We present a computational analysis of transcriptomic data of AD tissues vs. healthy controls, focused on elucidation of functional roles played by long non-coding RNAs (lncRNAs) throughout the AD progression. We first assembled our own lncRNA transcripts from the raw RNA-Seq data generated from 527 samples of dorsolateral prefrontal cortex, resulting in the identification of 31,574 novel lncRNA genes. Based on co-expression analyses between mRNAs and lncRNAs, a co-expression network is constructed. Maximal subnetworks with dense connections are identified as functional clusters. Pathway enrichment analyses are conducted over mRNAs and lncRNAs in each cluster, which serve as the basis for the inference of functional roles played by lncRNAs involved in each of the key steps in an AD development model that we have previously build based on transcriptomic data of protein-encoding genes. Detailed information is presented about the functional roles by lncRNAs in activities related to stress response, reprogrammed metabolism, cell-polarity, and development. Our analyses have also revealed that lncRNAs have discerning power in distinguishing between AD samples of each stage and healthy controls. This study represents the first of its kind.

A great deal of studies have assessed the expression of noncoding RNAs (ncRNAs) as well as their relevant molecular functions and biological mechanisms in the individuals of alcohol dependence. Alcohol dependence is one of the most prevalent neuropsychological disorders worldwide, and its pathogenesis is intricate and inadequately understood. There is considerable evidence demonstrating substantial links between multiple genetic factors and the development of alcohol dependence. Critical roles of ncRNAs have been emphasized in the pathophysiology of mental diseases including alcohol dependence. In the comprehension of ncRNAs action and their mechanisms of modification, they have emerged as therapeutic targets for a variety of psychiatric illness including alcohol dependence. Worth mentioning, dysregulated expression of ncRNAs has been regularly detected in individuals of alcohol dependence. An in-depth knowledge of roles of ncRNAs and m6A modification may be valuable for the development of a novel treatment against alcohol dependence. In general, a deeper comprehension of functional roles ncRNAs may make significant contributions to the precise diagnosis and/or actual treatment of alcohol dependence. Here in this review, we mostly focused on the up-to-date knowledge regarding alterations and/or modifications in the expression of ncRNAs in alcohol dependence, and then, presented their prospects for future research and therapeutic application with a novel concept of engram-system.

Non-toroidal shape primary pass through protection current transformers (CTs) are used to measure high currents. Their design provides them with a big airgap that allow passing several cables per phase though them, which is the main advantage versus toroidal types, as the number of CTs required to measure the whole phase current is drastically reduced. The cables pass through the transformer window can be in several positions. As the isolines of the magnetic field generated by the primary currents are centered in the cables, if these cables are not centered in the transformer window, the magnetic field will be non-uniform along the transformer core. Consequently, local saturations can appear if the cables are not properly disposed causing the malfunction of the CT. In this paper, the performance of a non-toroidal shape protection CT is studied. The research is focused on the cable position influence in possible partial saturations of the CT when it is operating near to its accuracy limit. Depending on the cable position, the ratio of the primary and secondary currents can depart from assigned ratio. The validation of this phenomenon has been carried out via Finite Element Analysis (FEA) showing that partial transformer core saturations appears in areas of the magnetic core close to the cable. Applying FEA, also the admissible accuracy region for cable positioning inside the CT is delimited. Finally, the simulation results are ratified with experimental tests performed in non-toroidal protection CTs varying the primary cables’ positions, which are subjected to currents up to 5 kA, achieving satisfactory results. From this analysis, installation recommendations are given.

To date, the percentage composition of the lung microbiome in bronchopulmonary cancer has not been summarized. Existing studies on identifying the lung microbiome in bronchopulmonary cancer through 16S rRNA sequencing have shown variable results regarding the abundance of bacterial taxa. Objectives: To identify the predominant bacteria in the lung microbiome of bronchopulmonary cancer from samples collected through bronchoalveolar lavage and to assess their potential role in the diagnosis of bronchopulmonary cancers. Data Sources: A systematic review of English articles using MEDLINE, Embase, and Web of Science. Search terms included lung microbiome, lung cancer, bronchoalveolar lavage. Study Selection: Randomized clinical trials that investigated the lung microbiome in bronchopulmonary cancer with samples collected via bronchoalveolar lavage. Data Extraction: Independent extraction of articles using predefined data fields, including study quality indicators. Data Synthesis: Nine studies met the inclusion criteria, focusing on those that utilized a percentage expression of the microbiome at the phylum or genus level. There was noted heterogeneity between studies, both in terms of phylum and genus, with a relatively constant percentage of the Firmicutes phylum and the genera Streptococcus and Veillonella being mentioned. Significant differences were also observed regarding the inclusion criteria for study participants, the method of sample collection, and data processing. Conclusions: To date, there is no consistent percentage pattern at the phylum or genus level in bronchopulmonary cancer, with the predominance of a phylum or genus varying across different patient cohorts, resulting in non-overlapping outcomes.

Discovered as an apparent pattern, a universal relation between geometry and information called the holographic principle has yet to be explained. This relation is unfolded in the present paper. As it is demonstrated there, the origin of the holographic principle lies in the fact that a geometry of physical space has only a finite number of points. Furthermore, it is shown that the puzzlement of the holographic principle can be explained by a magnification of grid cells used to discretize geometrical magnitudes such as areas and volumes into sets of points. To wit, when grid cells of the Planck scale are projected from the surface of the observable universe into its interior, they become enlarged. For that reason, the space inside the observable universe is described by the set of points whose cardinality is equal to the number of points that constitute the universe’s surface.

Effective development of digital twins of real-world objects requires sophisticated data collection techniques and algorithms for automated modeling of individual objects. In City Information Modeling (CIM) systems, individual buildings can be modeled automatically at the second Level Of Detail or LOD 2. Similarly, automated solutions for 3D modeling of individual trees at different levels of details are required for Tree Information Modeling (TIM) and building Forest Digital Twins (FDT). The existing algorithms support the automated modeling of trees by generating models of the canopy and the lower part of the trunk. Our work in this paper is based on the assumption that, similar to the canopy shape, the structure of tree trunk and branches is also an important consideration. An algorithm for automated modeling of tree trunks is proposed. Aiming to generate 3D models of tree trunks, the suggested approach starts by extracting the trunk point cloud, which is then segmented into single stems. Finally, the individual stems are modeled by dividing them into slices. The geometry of the developed tree models is represented in a matrix format. This solution enables automatic comparisons of tree elements over time, which is necessary for monitoring changes in forest stands and promoting sustainable forest management. Despite the huge variation of trunk geometric forms, the proposed modeling approach can gain an accuracy of better than 4 cm in the constructed tree trunk models.

The number of Internet of Things (IoT) applications is increasing at a fast-paced and so is the interest in blockchain-enabled IoT ecosystem. IoT applications make our day-to-day life more efficient, while integrating blockchain into the IoT ecosystem (blockchain-IoT) brings security, transparency, trust, and privacy to IoT applications. Perhaps, smart logistics, smart health, and smart city are some of the potential blockchain-enabled IoT application domains. One of the reasons that is hindering the mass adoption of blockchain-IoT into mainstream applications is the lack of a dedicated governance. Without proper governance and regulations, and because of the obfuscated and concealed cryptographic nature of blockchain, blockchain can be used for various illicit activities such as ransomware, money laundering, fraud and so on. Furthermore, blockchain and IoT are relatively contemporary technologies and paucity of exclusive governance can ultimately lead to lack of confidence in these technologies. Therefore, in order to fully avail from blockchain and IoT integration (blockchain-IoT) and as well as further prevail this integration, governance can play an important role. Proper regulations and standarization are required to benefit from the novel characteristics of blockchain-IoT and avoid blockchain being used for malicious purposes. In this research, we address the role of blockchain in governance mechanisms, governance for blockchain, and finally proposed a vigorous governance framework for blockchain-enabled IoT ecosystem. We also demonstrate the applications of our proposed governance framework through a smart logistics case study. We anticipate that our proposed governance framework can facilitate and encourage blockchain and IoT integration in various application domains.

Recently, we studied CR-slant warped products B1×fM⊥, where B1=MT×Mθ is the Riemannian product of holomorphic and proper slant submanifolds and M⊥ is a totally real submanifold in a nearly Kaehler manifold. In the continuation, in this paper, we study B2×fMθ, where B2=MT×M⊥ is a CR-product of a nearly Kaehler manifold and establish Chen’s inequality for the squared norm of the second fundamental form. Some special cases of Chen’s inequality are given.

In this work, generalized geometry of second-order tangent groups and affine configuration complexes is proposed. Initially, geometry for higher weights n=4 and weights n=5 is presented through some interesting and suitable homomorphisms, finally, this geometry is extended and generalized for any weight n.

The geometry of Poincare disk itself is interpreted without any mapping to dierent spaces. Our approach might be one of the shortest and is intended for educational contribution.

We study impact of geometry on leakage loss in negative curvature fibers made with As₂Se₃ chalcogenide and As₂Se₃ chalcogenide glasses for carbon dioxide (CO₂) laser transmission. The minimum leakage loss decreases when the core diameter increases both for fibers with six and for fibers with eight cladding tubes. The optimum gap corresponding to the minimum loss increases when the core diameter increases for negative curvature fibers with six cladding tubes. For negative curvature fibers with eight cladding tubes, the optimum gap is always less than 20 μm when the core diameter ranges from 300 μm to 500 μm. The influence of material loss on fiber loss is also studied. When material loss exceeds 10² dB/m, it dominates the fiber leakage loss for negative curvature fiber at a wavelength of 10.6 μm.