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.

In this article we compute many topological indices for the family of Möbius ladder. At first we give general closed form of M-polynomial of this family and recover many degree based topological indices out of it. We also compute Zagreb indices and Zagreb polynomials of this family.

Titania is one of the most comprehensively studied nanostructures due to its widespread applications in production of catalytic, gas- sensing and corrosion- resistance materials [1]. M-polynomial of nanotubes has been vastly investigated as it produces many degree-based topological indices which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules are correlated with their structure like boiling point, stability, strain energy etc of chemical compounds. In this paper, we determine M-polynomials of single-walled titanium (SW TiO2) nanotubes and recover important topological degree based indices of them to theoretically judge these nanotubes. We also use Maple to plot surfaces associated to different types of single-walled titanium (SW TiO2) nanotubes.

M-polynomial of different molecular structures helps to calculate many topological indices. A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR) quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of Octagonal network. From the M-polynomial we recover some degree-based topological indices for Octagonal network. Moreover, we give a graphical representation of our results.

The part of this article dealing with topological insulators and topological superconductors was first written about two years ago - the ideas in the part about the topological universe originated six years ago or more. It’s rather strange that I never put the two parts together in writing before. My belief in unification is unshakeable - I’ve been convinced for years that the universe must be composed of topology. Since Earth is part of the cosmos, entanglement means it must have topological materials. The reverse is also true: topological materials on Earth are well known to science - so in a unification, space and time inevitably possess topological composition. Topological materials (topological insulators, topological superconductors) can be less mystifying if they’re related to the paradigm-shifting deterministic view of quantum mechanics which is described in the universal topology (the “rubber-sheet geometry” of the cosmos): see my previous submission “Hypothesis of Quantum Gravity - Resulting from a Static, Topological Universe Resulting from the Positives and Negatives of the Steady State and Big Bang Theories" at https://www.preprints.org/manuscript/202105.0239/v1 (the first section of this present article is a quick summary of the relevant parts).

We study the coupling of two topologcal subsystems in distinct topological states, and show that it leads to a precursor behavior of the topological phase transition in the overall system. This behavior is solely determined by the symmetry classes of the subsystem Hamiltonians and coupling terms, and is marked by the persistent existence of subgap states within the bulk energy gap. By investigating the critical current of Josephson junctions involving topological superconductors, we also illustrate that such subgap states play crucial roles in physical properties of nanoscale devices or materials.

We recently proposed that topological quantum computing might be based on $SL(2,\mathbb{C})$ representations of the fundamental group $\pi_1(S^3\setminus K)$ for the complement of a link $K$ in the $3$-sphere. The restriction to links whose associated $SL(2,\mathbb{C})$ character variety $\mathcal{V}$ contains a Fricke surface $\kappa_d=xyz -x^2-y^2-z^2+d$ is desirable due to the connection of Fricke spaces to elementary topology. Taking $K$ as the Hopf link $L2a1$, one of the three arithmetic two-bridge links [the Whitehead link $5_1^2$, the Berge link $6_2^2$, the double-eight link $6_3^2$] or the link $7_3^2$, the $\mathcal{V}$ for those links contains the reducible component $\kappa_4$, the so-called Cayley cubic. In addition, the $\mathcal{V}$ for the later two links contains the irreducible component $\kappa_3$, or $\kappa_2$, respectively. Taking $\rho$ to be a representation with character $\kappa_d$ ($d<4$), with $|x|,|y|,|z| \le 2$, then $\rho(\pi_1)$ fixes a unique point in the hyperbolic space $\mathcal{H}_3$ and is conjugate to a $SU(2)$ representation (a qubit). Even though details on the physical implementation remain open, more generally, we show that topological quantum computing may be developed from the point of view of three-bridge links, the topology of the $4$-punctured sphere and Painlev\'e VI equation. The $0$-surgery on the $3$ circles of the Borromean rings L6a4 is taken as an example.

We study the Kelvinons: monopole ring solutions to the Euler equations, regularized as the Burgers vortex in the viscous core. There is finite anomalous dissipation in the inviscid limit. However, in the anomalous Hamiltonian, some terms are growing as logarithms of Reynolds number; these terms come from the core of the Burgers vortex. In our theory, the turbulent multifractal phenomenon is similar to asymptotic freedom in QCD, with these logarithmic terms summed up by an RG equation. The small effective coupling does not imply small velocity; on the contrary, velocity is large compared to its fluctuations, which opens the way for a quantitative theory. In the leading order in the perturbation theory in this effective coupling constant, we compute running multifractal dimensions for high moments of velocity circulation, in good agreement with the data for quantum Turbulence and available data for classical Turbulence. The logarithmic dependence of fractal dimensions on the loop size comes from the running coupling in anomalous dimensions. This slow logarithmic drift of fractal dimensions would be barely observable at Reynolds numbers achievable at modern DNS.

.With the increasing use of carbon fiber reinforced plastics in various area, carbon fiber composites based on prepregs have attracted attention in industries and academia research. However, prepreg manufacturing processes are costly, and the strength of structures varies depending on the orientation and defects (pores and delamination). For non-contact evaluation of internal defects, we proposed lock-in infrared thermography to investigate orientation angles after a compression test. We also conducted a drop-weight impact test to study the behaviour of the composites after impact according the fibers orientation for composite fabricated using unidirectional carbon fiber prepregs. Using CAI tests, we determined the residual compressive strength and confirmed the damage modes using a thermal camera. The results of the drop weight impact tests show that the specimen laminated at 0° suffered the largest damage because of susceptibility of the resin to impact. In contrast, the specimens oriented in of 0°/90° and +45°/–45° directions transferred more than 90% of the impact energy back to the impactor because of the lamination of fibers in the orthogonal directions. Furthermore, the specimens that underwent complete damage in the impact tests were subjected to the lock-in method and showed internal delamination and cut fibers. With the finite elements analysis, the damage of each ply could be observed. Moreover, the temperature differences in the residual compression tests were not significant.

Patients with predominantly antibody deficiencies (PAD) display hypogammaglobulinemia with a high prevalence of infections, along with autoimmune manifestations, benign and malignant lymphoproliferation and granulomatous disease. It is noteworthy that PAD patients, even those with defects in the same causative genes display a variable clinical phenotype, suggesting that additional genetic polymorphisms, located in either immune-related or non-immune-related genes, may affect their clinical and laboratory phenotype. In this context, we analyzed 80 PAD patients, including 70 with common variable immunodeficiency (CVID) for SERPINA1 defects, in order to investigate their possible contribution to PAD clinical phenotype. Eight CVID patients carried heterozygous pathogenic SERPINA1 defects with normal alpha-1 antitrypsin levels. Interestingly, the presence of the Z allele (rs28929474) which was found in three patients, was significantly associated with liver disease; hepatic complications were also observed in patients carrying the p.Leu23Gln (rs1379209512) and the p.Phe76del (rs775982338) alleles. Conversely, no correlation of SERPINA1 defective variants with respiratory complications was observed, although patients with pathogenic variants exhibit a reduced probability of developing autoimmune diseases. Therefore, we recommend SERPINA1 genetic analysis in PAD, in order to identify patients with a higher risk for liver disease.

Topological indices are invariant numerical fields of a graph that give facts about the structure of graphs and are found to be very helpful in predicting the physical properties of aluminophosphates. The characteristics of the aluminophosphates are similar to those of zeolites. Two examples of current applications are natural gas dehydration and humidity sensor. New frameworks are being synthesised by researchers in chemistry and materials science. There are many layers and holes in these substances. In this study, Vertex version of distance-based topological indices, the entropy of topological indices and their numerical analysis are explained.

Damaged connective tissues between the bone and tendons or ligaments are common among adults regardless of activity level. Achilles tendinosis is one of the most common tissue defects and enthesopathies. The patient in this study is a 54-year-old female with chronic Achilles tendinosis from chronic enthesopathy at the Achilles tendon insertion with a retrocalcaneal exostosis for three years who has failed standard-of-care practices for over two years. The patient received extracorporeal pulsed-activated therapy (EPAT) before applying 2ml of CryoText, a Wharton’s jelly tissue allograft. The patient then received class IV laser therapy treatments twice weekly for three weeks. The patient started with a 10/10 VAS at the initial visit. At five weeks post-application, the patient’s score had improved by 80% at 2/10 VAS. By week 13, the patient rated her pain as 0/10 VAS. The improvement in patient-reported pain and functionality reported in this study after the application of Wharton’s Jelly, EPAT, and class IV laser therapy warrants future research studying the safety and efficacy of these patient care modalities together.

Chromium (Cr) metal has garnered significant attention in alloy systems owing to its exceptional properties, such as high melting point, low density, and superior oxidation and corrosion resistance. However, its processing capabilities are hindered by the high Ductile-Brittle Transition Temperature (DBTT). Recently, powder bed fusion-laser beam for metals (PBF-LB/M) has emerged as a promising technique, offering the fabrication of net shapes and precise control over crystallographic texture. Nevertheless, research investigating the mechanism underlying crystallographic texture development in pure Cr via PBF-LB/M still needs to be conducted. This study explores the impact of scan speed on relative density and crystallographic texture. At the optimal scan speed, an increase in grain size attributed to epitaxial growth was observed, resulting in the formation of cubic texture. Consequently, a reduction in High Angle Grain Boundaries (HAGB) was achieved, suppressing defects such as cracks and enhancing relative density up to 98.1%. Furthermore, with increasing densification, Vickers hardness also exhibited a corresponding increase. These findings underscore the efficacy of PBF-LB/M for processing metals with high DBTT properties.

The experimental realization of twisted bilayer graphene strongly pushed the inspection of bilayer systems. In this context, it was recently shown that a two layer Haldane model with a thirty degree rotation angle between the layers represents a higher order topological insulator, with zero-dimensional states isolated in energy and localized at the physical vertices of the nanostructure. We show, within a numerical tight binding approach, that the energy of the zero dimensional states strongly depends on the geometrical structure of the vertices. In the most extreme cases, once a specific band gap is considered, these bound states can even disappear just by changing the vertex structure.

We propose a method for creating parallel Bessel-like vortical optical needles with an arbitrary axial intensity distribution via superposition of different cone-angle Bessel vortices. We analyze the interplay between the separation of individual optical vortical needles and their respective lengths and introduce a super-Gaussian function as their axial profile. We also analyze the physical limitations to observe well-separated optic needles, as they are influenced by mutual interference of the individual beams. To verify our theoretical and numerical results, we generate controllable spatial arrays of individual Bessel beams with various numbers and spatial separations by altering the spectrum of the incoming laser beam via the spatial light modulator. We demonstrate experimentally how to implement such beams using a diffractive mask. The presented method facilitates the creation of diverse spatial intensity distributions in three dimensions, potentially finding applications in specific microfabrication tasks or other contexts. These beams may have benefits in laser material processing applications such as nanochannel machining, glass via production, modification of glass refractive indices, and glass dicing.

The results of a study of the processes of formation of macro- and micro-inhomogeneity of ingots and rolled sheets are presented. To study the nature and sources of surface defects in rolled sheets, a comparative method of structural-concentration analysis of metal at the end-to-end metallurgical process of ingot - slab - sheet metal has been developed, based on the metallographic method of studying the structure and qualitative analysis of non-metallic inclusions. The research results showed that the quality of the surface of rolled sheets is determined mainly by the physical heterogeneity of the crust zone of the ingots, and the internal defects of thin rolled sheets largely depend on the contamination of the metal with non-metallic inclusions and off-axis segregation. A mechanism for transforming defects in the casting cortical zone into surface and internal defects in rolled sheets is proposed.

While the observation of magnetic monopoles has defied all experimental attempts in high-energy physics and astrophysics, sound theoretical approaches predict they should exist, and they have indeed been observed as quasiparticle excitations in certain condensed-matter systems. This indicates that, even though they are not ubiquitous contrary to electrons, it is possible to get them as excitations above a ground state. In this report, we show that phonons or lattice shear strain generate topological monopoles in some low-dimensional quantum antiferromagnets. For the Heisenberg ladder, phonons are found to generate topological monopoles with nonzero density due to quantum spin fluctuations. For the four-leg Heisenberg tube, longitudinal shear stress generates topological monopoles with density proportional to the strain deformation. The present theory is based on mapping the spin degrees of freedom onto spinless fermions using the generalized Jordan-Wigner transformation in dimensions higher than one. The effective magnetic field generated by the motion of the spinless fermions has non-zero divergence when phonons or shear stress are present. A possible system where the present kind of monopoles could be observed is BiCu$_2$PO$_6$.

In this paper, it is introduced the notion of r-fuzzy β-T_i, i = 0, 1, 2 separation axioms related to a fuzzy operator β on the initial set X which is a generalization of previous fuzzy separation axioms. An r-fuzzy α-connectedness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of r-fuzzy connectedness. An r-fuzzy α-compactness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of fuzzy compactness.

This work aims to generate some types of M_(j )–neighborhoods. Relationships among these M_(j )-neighborhoods and some other types of neighborhoods are discussed. Additionally, M_(j )-lower, M_(j )-upper approximations and M_(j )-accuracy in terms of M_(j )-neighborhoods are presented. Their properties, with some examples, are investigated. Finally, We addressed the comparisons among M_(j )approach and other approaches.

Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the ev-degree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches . In this paper we define the ve-degree and ev-degree Narumi–Katayama indices, investigate the predicting power of these novel indices and extremal graphs with respect to these novel topological indices. Also we give some basic mathematical properties of ev-degree and ve-degree Narumi-Katayama and Zagreb indices.

Density functional theory (DFT) calculations of hydrogen adsorption on titanium nitride had previously shown that hydrogen may adsorb on both titanium and nitrogen sites with a moderate adsorption energy. Further, the diffusion barrier was also found to be low. These findings may qualify TiN, a versatile multifunctional material with electronic conductivity, as electrode material for the hydrogen evolution reaction (HER). This was the main impetus of this work which aims to experimentally and theoretically investigate the electrocatalytic properties of TiN-layers that were processed on Ti substrate using reactive ion sputtering. The properties are discussed focusing on the role of oxygen defects introduced during the sputtering process on the HER. Based on DFT calculations, it is shown that these oxygen defects alter the electronic environment of the Ti atoms which entails a low hydrogen adsorption energy in the range of -0.1 eV; this leads to HER performances that match those of Pt-NPs in acidic media. When a few nanometr thick layer of Pd-NPs is sputtered on-top of the TiN-layer, the performance is drastically reduced. This is interpreted in terms of oxygen defects being scavenged by the Pd-NPs near the surface which is thought to reduce the hydrogen adsorption sites.

Starting from unidentified objects moving inside a two-dimensional Euclidean manifold, we propose a simple method to detect the topological changes that occur during their reciprocal interactions and shape morphing. This method, which allows the detection of topological holes development and disappearance, makes it possible to solve the uncertainty due to disconnectedness, lack of information and absence of objects’ sharp boundaries, i.e., the three troubling issues which prevent scientists to select the required proper sets/subsets during their experimental assessment of natural and artificial dynamical phenomena, such as fire propagation, wireless sensor networks, migration flows, neural networks’ and cosmic bodies’ analysis.

Physical measurements might display range values extending towards infinite. The occurrence of infinity in physical equations, such as the black hole singularities, is a troublesome issue that causes many theories to break down when assessing extreme events. Different methods, such as re-normalization, have been proposed to avoid detrimental infinity. Here a novel technique is proposed, based on physical geometrical considerations and the Alexander Horned sphere, that permits to undermine infinity in physical equations. In this unconventional approach, a continuous monodimensional line becomes an assembly of countless bidimensional lines that superimpose in quantifiable knots and bifurcations.

3D city models are being extensively used in applications such as evacuation scenarios and energy consumption estimation. The main standard for 3D city models is the CityGML data model which can be encoded through the CityJSON data format. CityGML and CityJSON use polygonal modelling in order to represent geometries. True topological data structures have proven to be more computationally efficient for geometric analysis compared to polygonal modelling. In a previous study, we have introduced a method to topologically reconstruct CityGML models while maintaining the semantic information of the dataset, based solely on the combinatorial map (C-Map) data structure. As a result of the limitations of C-Map's semantic representation mechanism, the resulting datasets could suffer either from semantic information loss or the redundant repetition of them. In this article, we propose a solution for a more efficient representation of both geometry, topology and semantics by incorporating the C-Map data structure in the CityGML data model and implementing a CityJSON extension to encode the C-Map data. In addition, we provide an algorithm for the topological reconstruction of CityJSON datasets to append them according to this extension. Finally, we apply our methodology to three open datasets in order to validate our approach when applied to real-world data. Our results show that the proposed CityJSON extension can represent all geometric information of a city model in a lossless way, providing additional topological information for the objects of the model.

Defect detection and identification from fruits and vegetables are particularly challenging for Indian agriculture. Defect Detection is a process to identify the defects or damages in vegetables and fruits, based on the shapes, colors and textures. The local market finds it difficult to cope with the defects and other infections in fruits and vegetables as quality evaluations and classification of vegetables and fruits have become tedious process. Recently, several approaches based on Image processing, Machine Learning and Artificial Intelligence methods have been proposed for the purpose of defect detection. On the basis of classifying the types of defects, related pathogens, and physical and morphological characteristics descriptors, we review the different approaches based on a corpus of 57 articles between 2016 and 2021. In the process of describing the defect analysis, steps from the target articles, algorithms, and methods including qualitative and quantitative evaluation are mainly summarized. The aim of this current review work is to present-day novel images and collects recent defective area calculation methods to detect surface defects of fruits and vegetables using RGB images and to classify whether the fruit is defected or fresh. A rigorous evaluation of many new algorithms provided for quality assurance by researcher’s probes of vegetables and fruits have been conducted in this work. This review work conveys that using the recent identification features will help to decrease the disadvantages in fruit storeroom owing to storage of the affected vegetables and fruits, ie. Preventing the spread of defects and other infections from the infected fruits and vegetables to the fresh ones.

A topological quantum interplay between the magnetic flux and the mass has been investigated, for the case of an electron, by evaluating a gauge-invariant phase factor (a Wilson loop) linked to the electromagnetic gauge field of the particle. In particular, from this phase factor and the quantization of the magnetic flux variations, a relationship between the mass at rest of the electron and its self-energy , arising from radiative corrections, has been obtained also within a QED approach. Besides, a formulation of an energy scale comparable to the energy at rest of an electron-positron pair is proposed. Remarkably, a reckoning of the Bohr energy of a W⁺ W^- pair is compatible with constants and parameters usually employed within the electroweak theory and comparable to the energy at rest of an electron-positron pair.

In this work the general problem of the characterization of the topological phase of an open quantum system is addressed. In particular, we study the topological properties of Kitaev chains and ladders under the perturbing effect of a current flux injected into the system using an external normal lead and derived from it via a superconducting electrode. After discussing the topological phase diagram of the isolated systems, using a scattering technique within the Bogoliubov-de Gennes formulation, we analyze the differential conductance properties of these topological devices as a function of all relevant model parameters. The relevant problem of implementing local spectroscopic measurements to characterize topological systems is also addressed by studying the system electrical response as a function of the position and the distance of the normal electrode (tip). The results show how the signatures of topological order affect the electrical response of the analyzed systems, a subset of such signatures being robust also against the effects of a moderate amount of disorder. The analysis of the internal modes of the nanodevices demonstrates that topological protection can be lost when quantum states of an initially isolated topological system are hybridized with those of the external reservoirs. The conclusions of this work could be useful in understanding the topological phases of nanowire-based mesoscopic devices.

The topological index is a numerical quantity based on the characteristics of various invariants or molecular graph. For ease of discussion, these indices are classified according to their logical derivation from topological invariants rather than their temporal development. Degree based topological indices depends upon the degree of vertices. This paper computes degree based topological indices of Bismuth Tri-Iodide chains and sheets with the help of M-polynomial.

In the study of QSAR/QSPR, due to high degree of predictability of pharmaceutical properties, the eccentric-connectivity index has very important place among the other topological descriptors, In this paper, we compute the exact formulas of eccentric-connectivity index and its corresponding polynomial, total eccentric-connectivity index and its corresponding polynomial, first Zagreb eccentricity index, augmented eccentric-connectivity index, modified eccentric-connectivity index and its corresponding polynomial for a class of phosphorus containing dendrimers.

Topological data analysis (TDA) is a recent approach for analyzing and interpreting complex data sets, based on ideas a branch of mathematics called algebraic topology. TDA has proven useful to disentangle non-trivial data structure in a broad range of data analytics problems including the study of cardiovascular signals. This review aims to provide an overview of the application of TDA to cardiovascular signals and its potential to enhance the understanding of cardiovascular diseases and their treatment. We first introduce the concept of TDA and its key techniques, including persistent homology, Mapper, and multidimensional scaling. We then discuss the use of TDA in analyzing various cardiovascular signals, including electrocardiography, photoplethysmography, and arterial stiffness. We also discuss the potential of TDA to improve the diagnosis and prognosis of cardiovascular diseases, as well as its limitations and challenges. Finally, we outline future directions for the use of TDA in cardiovascular signal analysis and its potential impact on clinical practice. Overall, TDA has shown great promise as a powerful tool for the analysis of complex cardiovascular signals and may offer significant insights into the understanding and management of cardiovascular diseases.

The study of photonic crystals has emerged as an attractive area of research in nanoscience in the last years. In this work we study the properties of a two-dimensional photonic crystal composed of dielectric rods. The unit cell of the system is composed of six rods organized on the sites of a C6 triangular lattice. We induce a topological phase by introducing an angular perturbation ϕ in the pristine system. The topology of the system is then determined by using the so-called k.p perturbed model. Our results show that the system presents a topological and a trivial phases, depending on the sign of the angular perturbation ϕ. The topological character of the system is probed by evaluating the electromagnetic energy density and analyzing its distribution in the real space, in particular on the maximal Wyckoff points. We also find two edge modes at the interface between the trivial and topological photonic crystals, which present a pseudospin topological behavior. By applying the Bulk-Edge correspondence, we study the pseudospin edge modes and conclude that they are robust against defects, disorder and reflection. Moreover, the localization of the edge modes leads to the confinement of light and the interface behaves as a waveguide for the propagation of electromagnetic waves. Finally, we show that the two edge modes present energy flux propagating in opposite directions, which is the photonic analogue of the quantum spin Hall effect.

In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties in many fields of applied sciences. In 2011, Shabir and Naz introduced and studied the notion of soft topological spaces, also defining and investigating many new soft properties as generalization of the classical ones. In this paper, we introduce the notions of soft separation between soft points and soft closed sets in order to obtain a generalization of the well-known Embedding Lemma to the class of soft topological spaces.

It is very difficult to repair large bone defects, especially when they have a complex shape. We have developed a new technique to make a desired copy of rabbit bones. A rabbit distal femur was scanned by computed tomography (CT), and a rectangular-shaped beta-tricalcium phosphate (β-TCP) block with 75% porosity was automatically machined using milling tools into a half-scale copy of the distal femur based on the CT data. The β-TCP block was seeded with bone morphogenetic protein-2 and bone marrow cells obtained from the femur and implanted on the periosteum of the femur. At 10 weeks after implantation, most of the β-TCP block had been replaced by bone and a complete copy of the distal femur was reconstructed. Our findings indicate that this technique will be useful in the clinical setting. We also report the representative clinical results of treatment with β-TCP graft in patients with bone defects since 1989.

In this paper, we introduce a new class of open sets that is called is*-open set . Also, we present the notion of is*-continuous, is*-open, is*-irresolute, is*-totally continuous, and is-contra-continuous mappings, and we investigate some properties of these mappings. Furthermore, we introduce some is*-separation axioms, and is*-mappings are related with is*-separation axioms. . .

We discuss a possible scale of gravitational origin at around 10 MeV, or 10⁻¹² cm, which arises in the MacDowell-Mansouri formalism of gravity due to the topological Gauss-Bonnet term in the action, as pointed out by Bjorken several years ago.~A length scale of the same size emerges also in the Kodama solution in gravity, which is known to be closely related to the MacDowell-Mansouri formulation. We particularly draw attention to the intriguing incident that existence of six compact extra dimensions originated from TeV-scale quantum gravity as well points to a length scale of 10⁻¹² cm, as the compactification scale. The presence of six such extra dimensions is also in remarkable consistency with the MacDowell-Mansouri formalism; it provides a possible explanation for the factor of ~10¹²⁰ multiplying the Gauss-Bonnet term in the action. We also comment on the relevant implications of such a scale regarding the thermal history of the universe motivated by the fact that it is considerably close to 1–2 MeV below which the weak interactions freeze out, leading to Big Bang Nucleosynthesis.

This paper first discusses a fractional-order Liu system of order as low as 2.7 and shows its chaotic characteristics by carrying out numerical simulations such as Lyapunov exponents, bifurcation diagrams and phase portraits. Then, by using the topological horseshoe theory and computer-assisted proof, the existence of chaos in the system is verified theoretically. Finally, the fractional-order system is implemented on a Field Programmable Gate Array (FPGA) and the results obtained show that the fractional-order Liu system is indeed chaotic.

. In this paper, we introduce a series of definitions of generalized affine functions for vector-valued functions. We prove that our generalized affine functions have some similar properties with generalized convex functions. We present examples to show that our generalized affinenesses are different from one another, and also provide an example to show that our definition of presubaffinelikeness is non-trivial; presubaffinelikeness is the weakest generalized affineness introduced in this article. We work with optimization problems that are defined and taking values in linear topological spaces. We devote to the study of constraint qualifications, and derive some optimality conditions as well as a strong duality theorem. Our optimization problems have inequality constraints, equality constrains and abstract constraints; our inequality constraints are generalized convex functions and equality constraints are generalized affine functions.

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

The entangled antipodal points on black hole surfaces, recently described by t’Hooft, display an unnoticed relationship with the Borsuk-Ulam theorem. Taking into account this observation and other recent claims, suggesting that quantum entanglement takes place on the antipodal points of a S³ hypersphere, a novel framework can be developed, based on algebraic topological issues: a feature encompassed in an S² unentangled state gives rise, when projected one dimension higher, to two entangled particles. This allows us to achieve a mathematical description of the holographic principle occurring in S². Furthermore, our observations let us to hypothesize that a) quantum entanglement might occur in a four-dimensional spacetime, while disentanglement might be achieved on a motionless, three-dimensional manifold; b) a negative mass might exist on the surface of a black hole.

Assuming the Multiple Point Principle (MPP) as a new law of Nature, we considered the existence of the two degenerate vacua of the Universe: a) the first Electroweak (EW) vacuum at $v_1\approx 246$ GeV—“true vacuum”, and b) the second Planck scale “false vacuum” at $v_2 \sim 10^{18}$ GeV. In these vacua, we investigated different topological defects. The main aim of the paper is an investigation of the black-hole-hedgehogs configurations as defects of the false vacuum. In the framework of the $f(R)$ gravity, described by the Gravi-Weak unification model, we considered a black-hole solution, which corresponds to a “hedgehog”—global monopole, that has been “swallowed” by the black-hole with mass core $M_{BH}\sim 10^{18}$ GeV and radius $\delta\sim 10^{-21}$ GeV$^{-1}$. Considering the results of the hedgehog lattice theory in the framework of the $SU(2)$ Yang-Mills gauge-invariant theory with hedgehogs in the Wilson loops, we have used the critical value of temperature for the hedgehogs’ confinement phase ($T_c\sim 10^{18}$ GeV). This result gave us the possibility to conclude that the SM shows a new physics (with contributions of the $SU(2)$-triplet Higgs bosons) at the scale $\sim 10$ TeV. This theory predicts the stability of the EW-vacuum and the accuracy of the MPP.

Background: Kidney damage is considered to be one of the risk factors for severity and mortality among COVID-19 patients. However, molecular nature of such observations remains unknown. Hypothesis: Altered gene expressions due to infection and in chronic kidney disease could explain severity in COVID-19 with kidney defects. Methods: We collected gene expression data from publicly available resources Gene Expression Omnibus CKD, Enrichr for deregulated genes in SARS-CoV infected cells in vitro, DisGeNET and others and carried out enrichment analysis using Enrichr. Result: Number of common genes altered in chronic kidney disease (CKD) and SARS-CoV infected cells was 2834. Enrichment analysis revealed that biological processes related viral life cycle and growth, cytokines, immunity, interferon, inflammation, apoptosis, autophagy, oxidative stress and others were significantly enriched with common deregulated genes. Similarly, significantly enriched pathways related to viral and bacterial infections, immunity and inflammation, cell cycle, ubiquitin mediated proteolysis, signaling pathways like Relaxin signaling pathway, mTOR signaling pathway, IL-17 signaling pathway, NF-kappa B signaling pathway were enriched with the common deregulated genes. These processes and pathways are known to be related to kidney damage. DisGeNET terms enriched include and related to Dengue fever, chronic Hepatitis, measles, retroviridae infections, respiratory syncytial virus Infections and many others. Kidney dysfunction related terms ischemia of kidney, renal fibrosis and diabetic nephropathy. Conclusion: Common deregulated genes in SARS-CoV infected cells and chronic kidney disease, as well as their enrichment with molecular processes and pathways relevant for viral pathogenesis and renal dysfunctions, could explain the severity of COVID-19 with kidney disease. This observation not only provides molecular relation of severity in COVID-19 with renal dysfunctions but might also help in the management and treatment targets for these cases.

Protrusive defects on the color filter of thin-film transistor (TFT) liquid crystal displays (LCDs) frequently damage the valuable photomask. An fast method using side-view illuminations associated with digital charge-couple devices (CCDs) to detect the protrusive defect in the four substrates, which are the black matrix (BM), red, green, and blue. Between the photomask and substrate, the depth of field (DOF) is normally 300 μm for the proximity-type aligner; we select the four substrates to evaluate the detectability in the task. The experiment is capable of detecting measurements of 300 μm and even lower than 100 μm can be assessed successfully. The maximum error of the measurement is within 6% among the four samples. Furthermore, the uncertainty analysis of three standard deviations is conducted. Thus, the method is cost-effective to prevent damage for valuable photomasks in the flat panel display industry.

The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. Identification of fields in the quantized theory is occurred directly as usual in terms of superconnection and its supercurvature components with the double covering of the general affine group GA¯(4,R). Then, by means of an appropriate decomposition of the metalinear double-covering group SL¯(5,R) with respect to the general linear double-covering group GL¯(4,R) one can easily obtain the enlargements of the fields while remaining consistent with the BRST algebra. This leads to the descent equations allowing us to build the observables of the theory by means of the BRST algebra constructed using a sa¯(5,R) algebra-valued superconnection. In particular, we discuss the construction of topological invariants with torsion.

Graph theory plays a crucial role in modeling and designing of chemical structure or chemical network. Chemical Graph theory helps to understand the molecular structure of molecular graph. The molecular graph consists of atoms as vertices and bonds as edges. Topological indices capture symmetry of molecular structures and give it a mathematical language to predict properties such as boiling points, viscosity, the radius of gyrations etc. In this article, we study the chemical graph of carbon Crystal structure of graphite and cubic carbon and compute several degree-based topological indices. Firstly we compute M-Polynomials of these structures and then from these M-polynomials we recover nine degree-based topological indices.

The electronic properties of calcium intercalated graphite (CaC6) as a function of pressure are revisited using density functional theory (DFT). The electronic band structures of CaC6, like many other layered superconducting materials, display cosine-shaped bands at or near the Fermi level (FL). Such bands encompass bonding/antibonding information with a strong connection to superconducting properties. Using an hexagonal cell representation for CaC6, construction of a double supercell in the c-direction effects six-folding in reciprocal space of the full cosine function, explicitly revealing the bonding/antibonding relationship divide at the cosine midpoint. Similarly, folding of the Fermi surface (FS) reveals physical phenomena relevant to electronic topological transitions (ETT) with application of pressure. For CaC6, the peak value for the superconducting transition temperature, Tc, occurs at about 7.5 GPa, near to the observed pressure of the calculated ETT. At this pressure, the radius of the nearly spherical Ca 4s-orbital FS coincides with three times the distance from the G centre point to the Brillouin zone (BZ) boundary of the 2c supercell (which is equal to half the identically defined distance for the primitive rhombohedral BZ). In addition, the ETT coincides with alignment of the non-bonding (inflection) point of the cosine band (the point at which the sign of the cosine amplitude modulation is reversed) with the FL. At other calculated pressure conditions, the Ca 4s-orbital FS undergoes topological changes that correspond and can be correlated to experimentally determined changes in Tc. The ETT is a key mechanism that circumscribes the known significant drop in Tc for CaC6 as a function of increasing pressure.

Data can be illustrated in shapes, and the shapes could provide insight for data modeling and information extraction. Topological data analysis provides an alternative insight in biomedical data analysis and knowledge discovery with the algebra topology tools. In present work, we study the application of topological data analysis for personalized electrocardiographic signal classification toward arrhythmia analysis. Using phase space reconstruction technique, the signal samples are converted into point clouds for topological analysis facility. With topological techniques the persistence landscapes from the point clouds are extracted as features to perform the arrhythmia classification task. We find that the proposed method is robust to the training set size, with only a training set size of 20% percents, the normal heartbeat class are 100% recognized, ventricular beats for 97.13%, supra-ventricular beats for 94.27% and fusion beats for 94.27% within the corresponding experiments. The property of keeping high performance when using smaller training sample proves that the proposed method is especially applicable to personalized analysis. With the present study, we show that the topological data analysis technique could be a useful tool in biomedical signal analysis, and provide powerful ability in personalized analysis.

We characterize the form of the order divisor graph of cyclic groups based on the group order. Furthermore, we describe some topological indices of the order divisor graph of cyclic groups, including the Wiener index, Harary index, first Zagreb index, and second Zagreb index.

Spatially uniform optical excitations can induce Floquet topological band structures within insulators which can develop similar or equal characteristics as are known from three-dimensional topological insulators. We derive in this article theoretically the development of Floquet topological quantum states for electromagnetically driven semiconductor bulk matter and we present results for the lifetime of these states and their occupation in the non-equilibrium. The direct physical impact of the mathematical precision of the Floquet-Keldysh theory is evident when we solve the driven system of a generalized Hubbard model with our framework of dynamical mean field theory (DMFT) in the non-equilibrium for a case of ZnO. The physical consequences of the topological non-equilibrium effects in our results for correlated systems are explained with their impact on optoelectronic applications.

We measured the anelastic, dielectric and structural properties of the metal-free molecular perovskite (ABX$_{3}$) (MDABCO)(NH$_{4}$)I$_{3}$, which has already been demonstrated to become ferroelectric below $T_{\text{C}}=$ 448~K. Both the dielectric permittivity measured in air on discs pressed from powder and the complex Young's modulus measured on resonating bars in vacuum show that the material starts deteriorating with loss of mass just above $T_{\text{C}}$, introducing defects and markedly lowering $T_{\text{C}}$. The elastic modulus softens of 50\% when heating through the initial $T_{\mathrm{C}}$, contrary to usual ferroelectrics, which are stiffer in the paraelectric phase. This suggests improper ferroelectricity, where the primary order parameter of the transition is not the electric polarization, but the orientational order of the MDABCO molecules. The degraded material presents thermally activated relaxation peaks in the elastic energy loss, whose intensities increase together with the decrease of ~$T_{\mathrm{C}}$. The peaks are much broader than pure Debye, due to the general loss of crystallinity, also apparent from X-ray diffraction, but their relaxation times have parameters typical of point defects. It is argued that the major defects should be of the Schottky type, mainly due to the loss of (MDABCO)$^{2+} $ and I$^{-}$, leaving charge neutrality, and possibly also (NH$_{4}$)$^{+}$ vacancies. The focus is on an anelastic relaxation process peaked around 200~K at $\sim 1$~kHz, whose relaxation time follows the Arrhenius law with $\tau $$_{0}$~$\sim $\ $10^{-13}$\ s and $E\simeq 0.4$~eV. This peak is attributed to I vacancies (V$_{\text{X}}$) hopping around MDABCO vacancies (V$_{\text{A}}$) and its intensity presents a peculiar dependence on temperature and content of defects. The phenomenology is thoroughly discussed in terms of lattice disorder introduced by defects and of partition of V$_{\text{X}}$ among sites that are far from and close to the cation vacancies. A method is proposed for calculating the relative concentrations of V$_{\text{X}}$, that are untrapped, paired with V$_{\text{A}}$ or forming V$_{\text{X}}$--V$_{\text{A}}$--V$_{\text{X}}$ complexes.

The surface defects of shield subway tunnel can significantly affect the serviceability of the tunnel structure and may compromise the operation safety. To effectively detect the multiple surface defects, this research employs a tunnel inspection trolley (TIT) based on the mobile laser scanning technique. By conducting the inspection of the shield tunnel on a metro line section, various surface defects are identified by the TIT, including water leakage defect, dislocation, spalling, cross-section deformation, etc. To explore the root causes of the surface defects, the association rules between different defects are calculated via an improved Apriori algorithm. Results show that: i) there are significant differences in different association rules of various surface defects of the shield tunnel; ii) the average confidence of the association rule “dislocation &amp; spalling → water leakage” is as high as 57.78%, indicating that most of the water leakage defects are caused by dislocation and spalling of the shield tunnel in the sections being inspected; iii) the weakest rule appears at “water leakage → spalling”, with the average confidence of 13%. The association analysis can be used in predicting the critical defects influencing the structural reliability and operation safety, such as water leakage, and optimizing the construction and maintenance work for the shield subway tunnel.

Advancements in genomics, bioinformatics and genome editing have uncovered new dimensions in gene regulation. Post-transcriptional modifications by the alternative splicing of mRNA transcripts are critical regulatory mechanisms of mammalian gene expression. In the heart, there is an expanding interest in elucidating the role of alternative splicing in transcriptome regulation. Substantial efforts have been directed towards investigating this process in heart development and failure. However, few studies have shed light on alternative splicing products and their dysregulation in congenital heart defects (CHDs). While elegant reports have shown the crucial roles of RNA binding proteins (RBPs) in orchestrating splicing transitions during heart development and failure, the impact of RBPs dysregulation or genetic variation on CHDs has not been fully addressed. Herein, we review the current understanding of alternative splicing and RBPs’ roles in heart development and CHDs and discuss the impacts of perinatal splicing transition and its dysregulation in CHDs. We further summarize discoveries made of causal splicing variants in key transcription factors that have been implicated in CHDs. Improved understanding of the roles of alternative splicing in heart development and CHDs may potentially inform novel preventive and therapeutic advancements for newborn infants with CHDs.

Urban trees are often more sun- and wind-exposed than their forest-grown counterparts. These environmental differences can impact how many species grow – impacting trunk taper, crown spread, branch architecture, and other aspects of tree form. Given these differences, windthrow models derived from traditional forest production data sources may not be appropriate for urban forest management. Additionally, visual abnormalities historically labeled as “defects” in timber production may not have a significant impact on tree failure potential. In this study, we look at urban tree failures associated with Hurricane Irma in Tampa, Florida, USA. We used spatial analysis to determine if patterns of failure existed among our inventoried trees. We also looked at risk assessment data to determine which visual defects were the most common and the most likely to be associated with branch or whole-tree failure. Results indicate that there was no spatial pattern associated with the observed tree failures – trees failed or withstood the storm as individuals. While some defects like decay and dead wood were associated with increased tree failure, other defects like weak branch unions and poor branch architecture were less problematic.

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.

LSM4 is an essential yeast gene encoding a component of different LSM complexes involved in the regulation of mRNA splicing, stability and translation. In previous papers we reported that the expression in S. cerevisiae of the K. lactis Lsm4 gene lacking the C-terminal Q/N-rich domain in a Lsm4 null strain S. cerevisiae (Sclsm4D1) restored cell viability. Nevertheless, in this transformed strain we observed some phenotypes which are typical markers of regulated cell death, Reactive Oxygen Species and oxidated RNA accumulation. In this paper we report that a similar truncation operated in the S. cerevisiae LSM4 gene confers to cells the same phenotypes observed with the K.lactis LSM4D1 gene. Up to now there was no evidence on the direct involvement of LSM4 in autophagy. Here we found that the Sclsm4D1 mutant showed defects in the induction of autophagy and it was very sensitive to nitrogen starvation or treatment with low doses of rapamycin, an inducer of autophagy. Moreover, both during nitrogen starvation and ageing, the Sclsm4D1 mutant accumulated cytoplasmic autophagy-related structures, suggesting a role of Lsm4 in Phagophore Assembly Site (PAS) processing and/or vacuolar autophagosome internalization

Clients are increasingly looking for fast and effective means to quickly and frequently survey and communicate the condition of their buildings so that essential repairs and maintenance work can be done in a proactive and timely manner before it becomes too dangerous and expensive. Traditional methods for this type of work commonly comprise of engaging building surveyors to undertake a condition assessment which involves a lengthy site inspection to produce a systematic recording of the physical condition of the building elements, including cost estimates of immediate and projected long-term costs of renewal, repair and maintenance of the building. Current asset condition assessment procedures are extensively time consuming, laborious, and expensive and pose health and safety threats to surveyors, particularly at height and roof levels which are difficult to access. We propose a method for automated detection and localisation of key building defects from images using deep learning and convolution neural networks. The proposed model is based on a pre-trained VGG-16 classifier with Class Activation Mapping (CAM) for object localisation. The model has proven to be robust and able to accurately detect and localise mould growth, stains, and paint deterioration defects arising from dampness in buildings. The approach is being developed with potentials to scale-up to support automated detection of defects and deterioration of buildings in real-time using mobile devices and drones.

In this article, we first introduced new types of higher separation axioms called (r,s)-GFS-regular and (r,s)-GFS-normal spaces with the help of (r,s)-generalized fuzzy semi-closed sets (briefly, (r,s)-gfsc sets) and discussed some topological properties of them. Thereafter, we defined a stronger form of (r,s)-gfsc sets called (r,s)-g*fsc sets and investigated some of its features. Moreover, we showed that (r,s)-fsc set → (r,s)-g*fsc set → (r,s)-gfsc set, but the converse may not be true. In addition, we explored new types of fuzzy generalized mappings between double fuzzy topological spaces (U, τ, τ*) and (V, η, η*), and the relationships between these classes of mappings were examined with the help of some illustrative examples. Finally, some new types of compactness via (r,s)-gfso sets were defined and the relationships between them were introduced.

This paper establishes methods that quantify the structure of statistical interactions within a given data set using the characterization of information theory in cohomology by finite methods, and provides their expression in terms of statistical physic and machine learning. Following [1–3], we show directly that k multivariate mutual-informations (I_k) are k-coboundaries. The k-cocycles are given by I_k = 0, which generalize statistical independence to arbitrary dimension k. The topological approach allows to investigate Shannon’s information in the multivariate case without the assumptions of independent identically distributed variables. We develop the computationally tractable subcase of simplicial information cohomology represented by entropy H_k and information I_k landscapes. The I₁ component defines a self-internal energy functional U_k, and (−1)^k I_k,k≥2 components define the contribution to a free energy functional G_k of the k-body interactions. The set of information paths in simplicial structures is in bijection with the symmetric group and random processes, provides a topological expression of the 2nd law and points toward a discrete Noether theorem (1st law). The local minima of free-energy, related to conditional information negativity and the non-Shannonian cone of Yeung [4], characterize a minimum free energy complex. This complex formalizes the minimum free-energy principle in topology, provides a definition of a complex system, and characterizes a multiplicity of local minima that quantifies the diversity observed in biology. Finite data size effects and estimation bias severely constrain the effective computation of the information topology on data, and we provide simple statistical tests for the undersampling bias and for the k-dependences following [5]. We give an example of application of these methods to genetic expression and cell-type classification. The maximal positive I_k identifies the variables that co-vary the most in the population, whereas the minimal negative I_k identifies clusters and the variables that differentiate-segregate the most. The methods unravel biologically relevant I₁₀ with a sample size of 41. It establishes generic methods to quantify the epigenetic information storage and a unified epigenetic unsupervised learning formalism.

Defectively manufactured and deliberately damaged composite laminates fabricated with different continuous reinforcing fibres (respectively, carbon and glass) and polymer matrices (respectively, thermoset and thermoplastic) were inspected in magnetic resonance imaging equipment. Two pulse sequences were evaluated during non-destructive examination conducted in saline solution-immersed samples to simulate load-bearing orthopaedic implants permanently in contact with biofluids. The orientation, positioning, shape, and especially the size of translaminar and delamination fractures were determined according to stringent structural assessment criteria. The spatial distribution, shape, and contours of water-filled voids were sufficiently delineated to infer the amount of absorbed water if thinner image slices than this study were used. The surface texture of composite specimens featuring roughness, waviness, indentation, crushing, and scratches was outlined, with fortuitous artefacts not impairing the image quality and interpretation. Low electromagnetic shielding glass fibres delivered the highest, while electrically conductive carbon fibres produced the poorest quality images, particularly when blended with thermoplastic polymer, though reliable image interpretation was still attainable.

Nowadays, diamonds are widely used in science and technology. However, the properties of diamonds due to their defects are not fully understood. In addition to optical methods, positron annihilation spectroscopy (PAS) can be successfully used to study defects in diamonds. Positrons are capable of detecting vacancies, small and large clusters of vacancies induced by irradiation, by providing information about their size, concentration, and chemical environment. By mapping in the infrared (IR) range, it is possible to consider the admixture composition of the main inclusions of the whole plate. The article presents the results of the study of defects in synthetic diamond plates, one of which was irradiated by electrons. Presents data about the distribution of the defect concentration obtained by Infrared spectroscopy. PAS with a monochromatic positron beam can be used as a non-destructive technique of detecting defects (vacancy) distribution over the depth of diamond plates.

We review the topological gauge theory description of Josephson junction arrays (JJA), fabricated systems which exhibit the superconductor to insulator transition (SIT). This description revealed the topological nature of the phases appearing at the SIT and lead to the discovery of a new state of matter, the superinsulator, characterized by an infinite resistance, even at finite temperature, due to linear confinement of electric charges. This discovery is particularly relevant for the physics of superconducting films with emergent granularity, which are modeled by JJA, and share the same phase diagram.

We study factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let $D=\prod_{i\in I}D_i$ be a product of paratopological groups, $S$ be a dense subgroup of $D$, and $\chi$ a continuous character of $S$. Then one can find a finite set $E\subset I$ and continuous characters $\chi_i$ of $D_i$, for $i\in E$, such that $\chi=\big(\prod_{i\in E} \chi_i\circ p_i\big)\hs1\res\hs1 S$, where $p_i\colon D\to D_i$ is the projection.

This study presents a computational simulation to explore the distinctive patterns of neural connectivity in Autism Spectrum Disorder (ASD), focusing on the concepts of spatial and topological proximities. ASD is characterized by unique cognitive and behavioral profiles, often attributed to atypical neural development and connectivity. Our simulation employs a two-pronged approach: first, by modeling spatial proximity through the generation of clustered 3D node positions, we mimic the observed over-connectivity in localized brain regions in ASD. Second, we construct a topological network to represent the complex interplay of under-connectivity and over-connectivity in functional brain networks, a hallmark of ASD's neural landscape. The spatial model demonstrates pronounced clustering, reflecting the structural brain differences and atypical growth patterns reported in neuroimaging studies of individuals with ASD. In contrast, the topological model reveals a network with a mix of sparse and dense connections, simulating the diverse and often contradictory findings of functional connectivity in ASD, such as reduced long-range connections and increased local connections. Our simulation provides a visual and conceptual framework for understanding the altered neural connectivity in ASD. It underscores the importance of considering both physical (spatial) and functional (topological) aspects of brain connectivity to grasp the full extent of neurodevelopmental deviations in ASD. This approach not only aids in elucidating the neural underpinnings of ASD's core symptoms but also offers a foundation for developing targeted interventions. Future research, integrating more complex and individual-specific data, could further refine this model, enhancing our understanding of ASD's neural dynamics and contributing to personalized therapeutic strategies.

We show that the compound samarium hexaboride is a strong topological insulator using the eigenvalues of the space inversion operator in the low-energy limit of the periodic Anderson model. Additionally, we assume the presence of the ferromagnetic exchange interaction (M). A Dirac cone like feature in the surface state energy spectra is observed for M equals zero in a certain parameter range. For M not equal to zero, there is no Kramers degeneracy. We have been able to show that this phase corresponds to the quantum anomalous Hall state by calculating Berry curvature and the Chern number. Using Floquet theory, we further show that the access to a novel state with broken time reversal symmetry is possible due to the normal incidence of circularly polarized optical field on the surface of the compound despite M being absent.

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to a HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here, we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states which are also BICs in a laser-written second-order topological lattice, and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such an HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

Majorana bound states in topological superconductors have attracted intense research activity in view of applications in topological quantum computation. However, they are not the only example of topological bound states that can occur in such systems. We here study a model in which both Majorana and Tamm bound states compete. We show both numerically and analytically that, surprisingly, the Tamm state remains partially localized even when the spectrum becomes gapless. Despite this fact, we demonstrate that the Majorana polarization shows a clear transition between the two regimes.

The recent growth of high-resolution spatial data, especially in developing urban environments, is enabling new approaches to civic activism, urban planning and the provision of services necessary for sustainable development. A special area of great potential and urgent need deals with urban expansion through informal settlements (slums). These neighborhoods are too often characterized by a lack of connections, both physical and socioeconomic, with detrimental effects to residents and their cities. Here, we show how a scalable computational approach based on the topological properties of digital maps can identify local infrastructural deficits and propose context-appropriate minimal solutions. We analyze 1 terabyte of OpenStreetMap (OSM) crowdsourced data to create worldwide indices of street block accessibility and local cadastral maps and propose infrastructure extensions with a focus on 120 Low and Middle Income Countries (LMIC) in the Global South. We illustrate how the lack of physical accessibility can be identified in detail, how the complexity and costs of solutions can be assessed and how detailed spatial proposals are generated. We discuss how these diagnostics and solutions provide a multiscalar set of new capabilities – from individual neighborhoods to global regions – that can coordinate local community knowledge with political agency, technical capability, and further research.

Anyon is collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. So far, anyons with serial fractional charges only exist in fractional quantum Hall effect. It is still a challenge to find new serial of fractional charges in other physical system and develop an unified mathematical physics theory based on the same root. Here a topological path fusion theory of propagating electrons in magnetic flux lattice is proposed to explore the physical origin of fractional charges based on a generalization of Feynman's path integral theory and Thurston's train track theory. This mathematical physics theory generated the existed serial of fractional charges in fractional quantum Hall effect and predicted new serial of fractional charges. A serial of irrational charges are predicted in one dimensional lattice of magnetic fluxes. Fractionally charged anyons are also generated in two dimensional and three dimensional lattice of train tracks of electric currents, revealing an exact correspondence between knot lattice model and train track model. A new explanation for the modular symmetry of complex Hall conductance and composite fermion in fractional quantum Hall effect is also derived from this topological path fusion theory. Experimental observation of anyon in three dimensions can be realized by constructing three dimensional interlocking magnetic fluxes or mapping magnetic fluxes into forbidden zones in multi-connected space filled by solid state material. A photonic crystal with porous nano-structures is a promising system for detecting fractional charges and paves a new way for topological quantum computation.

Sample size using prevalence has been one of the most important medical research methodologies and has been used in original articles more often than any other statistical tool available. The simple formula consists of variables interdependent and it is as important to understand how they influence each other as it is to learn to use the formula to calculate the sample size. With the choice of different amounts of precision and levels of confidence available to a medical researcher, it should be of paramount importance to understand what a slight change in choosing the parameter would mean at the end of the research. Understanding of different Z values, Levels of precision, and ranging Prevalence is required to understand the effect on the sample size and subsequently on the research. Topological representation using parameter ranges can be used to demonstrate this relationship.

The radiation-induced optical absorption at 1.5-5.5 eV (up to the beginning of fundamental absorption) has been analyzed in CVD diamond disks exposed to 231-MeV 132Xe ions with four fluences from 1012 to 3.81013 cm-2. The 5-mm diameter samples (thickness 0.4 mm) were prepared by Diamond Materials, Freiburg (Germany), average grain size at growth site was around 80 m, the range of xenon ions was R= 11.5 m. The intensity of several bands grows with ion fluence thus confirming radiation-induced origin of the defects responsible for these bands. The recovery of radiation damage has been investigated via isochronal (stepwise) thermal annealing procedure up to 650°C, while all spectra were measured at room temperature. Based on these spectra, the annealing kinetics of several defects, in particular carbon vacancies (GR1 centers with a broad band 2 eV) and complementary C-interstitial-related defects ( 4 eV), as well as vacancies located nearby nitrogen substitutional atoms (narrow bands around 2.5 eV) have been constructed. The experimental kinetics have also been analyzed in terms of the diffusion-controlled bimolecular reactions. The migration energies of tentatively interstitial atoms (mobile components in recombination process) are obtained, their dependence on the irradiation fluences is discussed.

Nemaline myopathy (NM) is one of the most common forms of congenital myopathy and it is identified by the presence of "nemaline bodies" (rods) in muscle fibers by histopathological exam-ination. The most common forms of NM are caused by mutations in the ACTA1 (Actin Alpha 1) and NEB (Nebulin) genes. Clinical features include hypotonia and muscle weakness. Unfortunate-ly, there is no curative treatment and the pathogenetic mechanisms remains unclear. In this man-uscript, we examined the pathophysiological alterations in NM using dermal fibroblasts derived from patients with mutations in ACTA1 and NEB genes. Patients’ fibroblasts were stained with rhodamine phalloidin to analyze the polymerization of actin filaments by fluorescence microsco-py. We found that patients' fibroblasts showed incorrect actin filament polymerization compared to control fibroblasts. Actin filament polymerization defects was associated with mitochondrial dysfunction. Furthermore, we identified two mitochondrial boosting compounds, linoleic acid (LA) and L-carnitine (LCAR), that improved the formation of actin filaments in mutant fibro-blasts and corrected mitochondrial bioenergetics. Our results indicate that cellular models can be useful to study the pathophysiological mechanisms involved in NM and to find new potential therapies. Furthermore, targeting mitochondrial dysfunction with LA and LCAR can revert the pathological alterations in NM cellular models.

The cast defects strongly degrade the mechanical properties in cast alloys. The effect of Sn addition on Al-Si alloys was investigated by 3D computed tomography, SEM and TEM. Amorphous Sn oxides are found near the alumina film, cause more shrinkage pores, initiate cracks and deteriorate mechanical properties. This work suggests not adding Sn in various Al alloys used in cast state.

Mitochondrial disorders, although heterogeneous, are traditionally described as conditions characterized by encephalomyopathy, hypotonia and progressive postnatal organ failure. Here we provide a systematic review of Linear Skin Defects with Multiple Congenital Anomalies (LSDMCA), a rare unconventional mitochondrial disorder which presents as a developmental disease; its main clinical features include microphthalmia with different degrees of severity, linear skin lesions, and central nervous system malformations. The molecular basis of this disorder has been elusive for several years. Mutations were eventually identified in three X-linked genes, i.e., HCCS, COX7B, and NDUFB11, which are all endowed with defined roles in the mitochondrial respiratory chain. A peculiar feature of this condition is its inheritance pattern: X-linked dominant male-lethal. Only female or XX male individuals can be observed, implying that nullisomy for these transcripts is incompatible with normal embryonic development in mammals. All three genes undergo X-inactivation that, according to our hypothesis, may contribute to the extreme variable expressivity observed in this condition. We propose that mitochondrial dysfunction should be considered as an underlying cause in developmental disorders. Moreover, LSDMCA should be taken into consideration by clinicians when dealing with patients with microphthalmia with or without associated skin phenotypes.

Existing methods for detecting magnetic leakage signals from damaged wire ropes require axial saturation magnetisation, and the accuracy of the detection equipment depends on the saturation degree of magnetisation. Moreover, the expected magnetisation effect is usually difficult to achieve owing to the special characteristics of the rope structure, diameter, and operating environment of the wire rope. Consequently, in addition to other issues, the detection accuracy and versatility of the equipment are low. In this study, a method based on spatial multidimensional orthogonal array loop magnetisation for detecting mine wire rope defects is proposed. Firstly, a new sensor excitation structure model is developed. Then a method of radiant magnetic flux of permanent magnet array is analysed, and the influence law of the number of permanent radiant magnetic blocks on the magnetisation effect is studied. In addition, a method of wire rope detection based on the principle of clustering is investigated, according to which the influence law of the shape, structure, and size of the polyurethane device on the effect of magnetisation is discussed. Finally, through laboratory experiments, the test model and proposed method are verified. The results show that the magnetisation effect is better and more cost-effective when the number of permanent magnet radiation magnetic block is n=8, and the proposed detection method can effectively distinguish damaged wire rope joints. Furthermore, the proposed equipment achieved signal-to-noise ratio of the signals, improving the reliability of damage detection.

This article discusses the application of thermal quality control methods for plant tissues. The purpose of the work is to determine the optimal parameters of thermal impact on a spherical-shaped plant control object, ensuring the detection of surface and subsurface defects. The authors of the work proposed mathematical models of the temperature field for a spherical body with defects and a flat sample when exposed to the thermal influence of a pulsed source. As a result of the use of mathematical models, the thermophysical characteristics of plant tissues of varying degrees of disease damage were obtained, which made it possible to simulate the temperature field of the control object and obtain an image of classified tissues. The developed recommendations made it possible to select the optimal parameters of the thermal effect on the test object.

This study investigates the effect of scaffold architecture on bone regeneration, focusing on 3D-printed polylactic acid-bioceramic calcium phosphate (PLA-bioCaP) composite scaffolds in rabbit femoral condyle critical defects. To assess their influence on bone healing and scaffold performance, we explored two distinct scaffold designs, alternate and helical laydown patterns. The scaffolds were meticulously characterized for pore size, strut thickness, porosity, pore accessibility, and mechanical properties. The in vivo efficacy of these scaffolds was evaluated using a rabbit femoral condyle critical defect model. Our findings indicate that both scaffold architectures are biocompatible and support bone formation. The helical scaffolds, characterized by larger pore sizes and higher porosity, demonstrated significantly greater bone regeneration than the alternate structures. However, their lower mechanical strength presented limitations for use in load-bearing sites. This study highlights the importance of scaffold architecture in bone tissue engineering and underscores the need to balance porosity and mechanical strength for optimal bone regeneration. The findings provide crucial insights for the design of 3D- printed scaffolds in clinical applications, particularly in the context of critical-sized bone defects. The study also outlines potential areas for future research, including exploring hybrid scaffold designs to achieve optimal porosity without compromising mechanical integrity.

AlphaFold is a groundbreaking Deep Learning tool for protein structure prediction. It achieved remarkable accuracy in modeling the many 3D structures while taking as the input only the known amino acid sequence of proteins in question. Intriguingly though, in the early steps of each individual structure prediction procedure, AlphaFold is not respecting topological barriers that in real proteins result from the reciprocals impermeability of polypeptide chains. This study aims to investigate how this non-respecting of topological barriers affects AlphaFold predictions with respect to the topology of protein chains. We focus on such classes of proteins that during their natural folding form reproducibly the same knot type on their linear polypeptide chain as revealed by their crystallographic analysis. We use partially artificial test constructs in which the mutual non-permeability of polypeptide chains should not permit the formation of such knots during natural protein folding. We find that despite the formal impossibility that the protein folding process could produce such knots, AlphaFold predicts these proteins to be knotted. Our study underscores the necessity for cautious interpretation and further validation of topological features in protein structures predicted by AlphaFold.

We report on comparison between temperature-dependent magneto¬absorption and magnetotransport spectroscopy of HgTe/CdHgTe quantum wells in terms of detection of phase transition between topological insulator and band insulator states. Our results demonstrate that temperature-dependent magnetospectroscopy is a powerful tool to discriminate trivial and topological insulator phases, yet magnetotransport method is shown to have advantages for clear manifestation of the phase transition with accurate quantitative values of transition parameter (i.e. critical magnetic field Bc).

Topological Data Analysis (TDA) refers to a collection of methods that find the structure of shapes in data. Although recently, TDA methods have been used in many areas of data mining, it has not been widely applied to text mining tasks. In most text processing algorithms, the order in which different entities appear or co-appear is being lost. Assuming these lost orders are informative features of the data, TDA may play a significant role in the resulted gap on text processing state of the art. Once provided, the topology of different entities through a textural document may reveal some additive information regarding the document that is not reflected in any other features from traditional text processing methods. In this paper, we introduce a novel approach that hires TDA in text processing in order to capture and use the topology of different same-type entities in textural documents. First, we will show how to extract some topological signatures in the text using persistent homology-i.e., a TDA tool that captures topological signature of data cloud. Then we will show how to utilize these signatures for text classification.

When an edge is removed, a cycle graph Cn becomes a n-1 tree graph. This observation from extremal set theory leads us to the realm of set theory, in which a topological manifold of genus-1 turns out to be of genus-0. Starting from these premises, we prove a theorem suggesting that a manifold with disjoint points must be of genus-0, while a manifold of genus-1 cannot encompass disjoint points.

This paper focuses on the impact of defects density and carrier capture cross-section area in the electron transport material (ETM), hole transport material (HTM), and absorber layers on the performance of perovskite solar cells and quantum efficiency (QE). Furthermore, the impact of defects density at the interface between ETM/absorber and absorber/HTM is also studied. SCAPS-1D software is used in the current study in determining solar cell performance. The proposed perovskite solar cell structure is a planar FTO/TiO2/ CH3NH3PbI3/ Cu2O. The results indicated that increasing the defect density in the absorber layer significantly affects cell performance, while in ETM and HTM layers, the cell parameters remain unaffected. It is also found that the defect capture cross-section has a similar behavior to the defect density in the main layers (ETM, absorber, and HTM). In addition, it is observed that by increasing the defects density in the ETM/absorber and absorber/HTM interfaces layer, the cell parameters FF, Jsc, and PCE have been slightly decreased, with no effect on Voc. Moreover, it is also noted that the quantum efficiency QE is sharply reduced. Finally, this paper introduced the correlation between the defect density and the capture cross-section, which is the first attempt to find such a relationship in perovskite solar cells to the knowledge of the authors.

We explore the implementation of specific optical properties of armchair graphene nanoribbons (AGNRs) through edge-defect manipulation. This technique employs the tight-binding model in conjunction with the calculated absorption spectral function. Modification of the edge states gives rise to the diverse electronic structures with striking changes in the band gap and special flat bands at low energy. The optical-absorption spectra exhibit exotic excitation peaks and they strongly depend on the type and period of the edge extension. Remarkably, there exist the unusual transition channels associated with the flat bands for selected edge-modified systems. We discover the special rule governing how the edge-defect influences the electronic and optical properties in AGNRs. Our theoretical prediction demonstrates an efficient way to manipulate the optical properties of AGNRs. This might be of importance in the search for suitable materials designed to have possible technology applications in nano-optical, plasmonic and optoelectronic devices.

Aluminum profile surface defects can greatly affect the performance, safety and reliability of products. Traditional human-based visual inspection is low accuracy and time consuming, and machine vision-based methods depend on hand-crafted features which need to be carefully designed and lack robustness. To recognize the multiple types of defects with various size on aluminum profiles, a multiscale defect detection network based on deep learning is proposed. Then, the network is trained and evaluated using aluminum profile surface defects images. Results show 84.6%, 48.5%, 96.9%, 97.9%, 96.9%, 42.5%, 47.2%, 100%, 100%, 43.3% average precision(AP) for the ten defect categories, respectively, with a mean AP of 75.8%, which illustrate the effectiveness of the network in aluminum profile surface defects detection. In addition, saliency maps also show the feasibility of the proposed network.

Iron is the most abundant micronutrient in plant mitochondria and it has a crucial role in biochemical reactions involving electron transfer. It has been described in Oryza sativa that Mitochondrial Iron Transporter (MIT) is an essential gene and that knockdown mutant rice plants have a decreased amount of iron in mitochondria, strongly suggesting that OsMIT is involved in mitochondrial iron uptake. In Arabidopsis thaliana, two genes encode MIT homologues. In this study, we analyzed different AtMIT1 and AtMIT2 mutant alleles, confirming that individually AtMIT1 nor AtMIT2 genes are essential. When we generated crosses between Atmit1 and Atmit2 alleles we were able to isolate homozygous double mutant plants. Interestingly, homozygous double mutant plants were obtained only when mutant alleles of Atmit2 with the T-DNA insertion in the intron region were used for crossings, and in these cases a correctly spliced AtMIT2 mRNA was generated, although at a low level. Atmit1 Atmit2 double homozygous mutant plants, which were knockout for AtMIT1 and knockdown for AtMIT2, were grown and chacterised in iron sufficient conditions. Pleiotropic developmental defects were observed including abnormal seeds, increased number of cotyledons, slow growth rate, pinoid stems, defects in flower structures and reduced seed set. We observed a possible phenomenon of T-DNA suppression in the next generation of Atmit1 Atmit2 double homozygous mutant plants, correlating with an increased splicing of the AtMIT2 intron containing the T-DNA. Molecular analysis of gene expression markers for mitochondrial and oxidative stress showed that Atmit1 Atmit2 double homozygous mutant plants express a degree of mitochondrial perturbation. A RNA-Seq study was performed and we could identify more than 760 genes differentially expressed in Atmit1 Atmit2, including genes involved in iron transport, coumarin metabolism, and hormones metabolism, transport and signaling. Our data suggest that some of the phenotypes observed in Atmit1 Atmit2 double homozygous mutant plants are mediated by defects in auxin homeostasis.

The material flow dynamic and velocity distribution on the melted domain surface play a crucial role on the joint quality and formation of welding defects. In this study, authors investigated the effects of the low and high currents of plasma arc welding on the material flow and thermodynamics of molten pool and its relationship to the welding defects. The high-speed video camera (HSVC) was used to observe the convection of the melted domain and welded-joint appearance. Furthermore, to consider the Marangoni force activation, the temperature on the melted domain was measured by a thermal HSVC. The results revealed that the velocity distribution on the weld surface was higher than that inside the molten weld pool due to the difference of the massive density between the air and the steel. Moreover, in the case of low welding current (80A) the convection speed of molten was faster than that of the high welding current case (160A) owing to the difference of main driving forces direction and strength, which leading to undercut and humping defects on the weld surface and excessive convex (burn-through) defect at the bottom weld side, respectively. The medium welding current (120A) had two convection patterns with the main flow in backward direction, which resulted in better welding quality without defect. The interaction between the shear force and Marangoni force played a solid state on the convection and heat transportation processes in the plasma arc welding process.

During the last decades the quantitative description of electrical and magnetotransport properties of solid-state materials has been a remarkable challenge in materials science. Recently, the discovery of a novel class of materials, the topological semimetals, has led to a growing interest for the full understanding of their magnetotransport properties. In this review, the strong interplay among topology, band structure and carrier mobility in recently discovered high carriers mobility topological semimetals is discussed and their effect on their magnetotransport properties is outlined. The huge magnetoresistance effect, especially in the Hall transverse configuration, and a new version of a three-dimensional quantum Hall effect observed in high-mobility Weyl and Dirac semimetals are reviewed. The design of novel quantum sensors based on solid-state semimetals is also encouraged.

Sparse training (ST) aims to ameliorate deep learning by replacing fully connected artificial neural networks (ANNs) with sparse or ultra-sparse ones, such as brain networks are, therefore it might benefit to borrow brain-inspired learning paradigms from complex network intelligence theory. Here, we launch the ultra-sparse advantage challenge, whose goal is to offer evidence on the extent to which ultra-sparse (around 1% connection retained) topologies can achieve any leaning advantage against fully connected. Epitopological learning is a field of network science and complex network intelligence that studies how to implement learning on complex networks by changing the shape of their connectivity structure (epitopological plasticity). One way to implement Epitopological (epi- means new) Learning is via link prediction: predicting the likelihood of non-observed links to appear in the network. Cannistraci-Hebb learning theory inspired the CH3-L3 network automata rule for link prediction which is effective for general-purpose link prediction. Here, starting from CH3-L3 we propose Epitopological Sparse Meta-deep Learning (ESML) to apply Epitopological Learning to sparse training. In empirical experiments, we find that ESML learns ANNs with ultra-sparse hyperbolic (epi-)topology in which emerges a community layer organization that is meta-deep (meaning that each layer also has an internal depth due to power-law node hierarchy). Furthermore, we discover that ESML can in many cases automatically sparse the neurons during training (arriving even to 30% neurons left in hidden layers), this process of node dynamic removal is called percolation. Starting from this network science evidence, we design Cannistraci-Hebb training (CHT), a 4-step training methodology that puts ESML at its heart. We conduct experiments on 7 datasets and 5 network structures comparing CHT to dynamic sparse training SOTA algorithms and the fully connected counterparts. The results indicate that, with a mere 1% of links retained during training, CHT surpasses fully connected networks on VGG16, GoogLeNet, ResNet50, and ResNet152. This key finding is an evidence for ultra-sparse advantage and signs a milestone in deep learning. CHT acts akin to a gradient-free oracle that adopts CH3-L3-based epitopological learning to guide the placement of new links in the ultra-sparse network topology to facilitate sparse-weight gradient learning, and this in turn reduces the convergence time of ultra-sparse training. Finally, CHT offers the first examples of parsimony dynamic sparse training because, in many datasets, it can retain network performance by percolating and significantly reducing the node network size. Our code is available at: https://github.com/biomedical-cybernetics/Cannistraci-Hebb-training.

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randić and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randić and the Zagreb indices are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study we define ev-degree Zagreb index, ve-degree Zagreb indices and ve-degree Randić index by using these new graph invariants as parallel to their corresponding classical degree versions. We compare these new group ev-degree and ve-degree indices with the other well-known and most used topological indices in literature such as; Wiener, Zagreb and Randić indices by modelling some physicochemical properties of octane isomers. We show that the ev-degree Zagreb index, the ve-degree Zagreb and the ve-degree Randić indices give better correlation than Wiener, Zagreb and Randić indices to predict the some specific physicochemical properties of octanes. We investigate the relations between the second Zagreb index and ev-degree and ve-degree Zagreb indices and some mathematical properties of ev-degree and ve-degree Zagreb indices.

A quantitative method is proposed to determine of Stone-Wales defects for carbon nanostructures with sp2 hybridization of carbon atoms. The technique is based on the diene synthesis reaction (Diels-Alder reaction). The proposed method was used to determine Stone-Wales defects in the few-layer graphene (FLG) nanostructures synthesized by the self-propagating high-temperature synthesis (SHS) process, in reduced graphene oxide (rGO) synthesized based on the method of Hammers and in the single-walled carbon nanotubes (SWCNT) TUBAL trademark, Russia. Our research has shown that the structure of FLG is free of Stone-Wales defects, while the surface concentration of Stone-Wales defects in TUBAL carbon nanotubes is 1.1×10-5 mol/m2 and 3.6×10-5 mol/m2 for rGO.

In addition to image filtering in the spatial and frequency domains, fractal characteristics induced algorithms offers considerable flexibility in the design and implementations of image processing solutions in areas such as image enhancement, image restoration, image data compression and spectrum of applications of practical interests. Facing up to a real-world problem of identifying workpiece surface defects, a generic adaptive fractal filtering algorithm is proposed, which shows advantages on the problems of target recognition, feature extraction and image denoising at multiple scales. First, we reveal the physical principles underlying between signal SNR and its representative fractal dimension indicative parameters, validating that the fractal dimension can be used to adaptively obtain the image features. Second, an adaptive fractal filtering algorithm (Abbreviated as AFFA) is proposed according to the identified correlation between the image fractal dimensions and the scales of objects, and it is verified by a benchmarking image processing case study. Third, by using the proposed fractal filtering algorithm, surface defects on a flange workpiece are identified. Compared to conventional image processing algorithms, the proposed algorithm shows superior computing simplicity and better performance Numerical analysis and engineering case studies show that the fractal dimension is eligible for deriving an adaptive filtering algorithm for diverse-scale object identification, and the proposed AFFA is feasible for general application in workpiece surface defect detection.

An effective method to inspect inaccessible nuclear power facility by interface wave which propagate along the shrink fit boundary of reactor head is proposed in this study. Reactor head is relatively thick to inspect from the outside of reactor by conventional ultrasonic testing. The proposed interface wave can propagate a long distance from the fixed transducer position. The inside of nuclear reactor is limited to access due to the high radiation, so transducers are located at outside of nuclear facility and interface wave propagates into the nuclear reactor for defect detection. The numerical simulation and experiments were carried out to validate the effectiveness of the proposed interface wave inspection method. Various defect cases simulating field failures are also presented with satisfactory detectability by the proposed technique with the features for defect classification.

Statistical modeling lies at the heart of product design and development throughout numerous engineering disciplines, especially since processing large amounts of data has become increasingly ubiquitous. While mathematical statistics provide elegant guidance pertaining to the question of whether or not some particular underlying modeling assumptions are justified and appropriate, when pursuing a more comprehensive assessment of product design and development other considerations often increase in significance. Therefore, we will examine and analyze the tedious interactions and implications of statistical modeling choices and product liability exposure. To the best of our knowledge, this paper is the first to draw attention to and explore some often overlooked or oversimplified dangers and pitfalls that enter the equation when product design heavily relies on statistical modeling. In particular, through a diligent analysis of both statistical and legal aspects we will explore how statistically optimal procedures may yield far from optimal outcomes in terms of product liability when applied to actual real life problems and why suboptimal nonparametric or robust approaches may constitute better alternatives.

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. Closed forms of multiplicative degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned molecular compound. In this article, we compute and analyze many multiplicative degree-based topological indices of silicon-carbon Si₂C₃-I[p,q] and Si₂C₃-II[p,q].

Cytokinesis is accomplished in higher plants by the phragmoplast, creating and conducting the cell plate, to separate daughter nuclei by a new cell wall. The microtubule-severing enzyme p60-katanin plays an important role in the centrifugal expansion and timely disappearance of phragmoplast microtubules. Consequently, aberrant structure and delayed expansion rate of the phragmoplast occur in p60-katanin mutants. Here, the consequences of p60-katanin malfunction in cell plate/daughter wall formation were investigated by transmission electron microscopy (TEM), while deviations in the chemical composition of cell plate/new cell wall were identified by immunolabeling and confocal microscopy, in root cells of the fra2 Arabidopsis thaliana mutant. It was found that, apart from defective phragmoplast microtubule organization, cell plates/new cell walls appeared also faulty in structure, being unevenly thick and perforated by large gaps. In addition, demethylesterified homogalacturonans were prematurely present in fra2 cell plates, while callose content was significantly lower than in the wild-type. Furthermore, KNOLLE syntaxin disappeared from newly formed cell walls in fra2 earlier than in the wild-type. Taken together, these observations indicate that delayed cytokinesis, due to faulty phragmoplast organization and expansion, results in a loss of synchronization between cell plate growth and its chemical maturation.

Defects are considered one of the wastes in manufacturing systems that negatively affect the delivery times, cost and quality of products leading to manufacturing companies facing a critical situation with the customers and to not comply with the IPC-A-610E standard for the acceptability of electronic components. This is the case is a manufacturing company located in Tijuana, Mexico. Due to an increasing demand on the products manufactured by this company, several defects have been detected in the welding process of electronic boards, as well as in the components named Thru-Holes. It is for this reason that this paper presents a lean manufacturing application case study. The objective of this research is to reduce at least 20% the defects generated during the welding process. In addition, it is intended to increase 20% the capacity of 3 double production lines where electronic boards are processed. As method, the PDCA cycle, is applied. The Pareto charts and the flowchart are used as support tools. As results, defects decreased 65%, 79% and 77% in three analyzed product models. As conclusion, the PDCA cycle, the Pareto charts, and the flowchart are excellent quality tools that help decrease the number of defective components.

This study investigated defect formation and strain distribution in high Mg content Al-Mg alloys during normal rolling and cross-rolling processes. The finite element analysis (FEA) revealed the presence of wave defects and strain localization-induced zipper cracks in normal cold rolling, which were confirmed by experimental results. The concentration of shear strain played a significant role in crack formation and propagation. However, the influence of wave defects was minimal in the cross-rolling process, which exhibited a relatively uniform strain distribution. Nonetheless, strain concentration at the edge and center regions led to the formation of zipper cracks and edge cracks, with more pronounced propagation observed in the experiments compared to FEA predictions. Furthermore, texture evolution was found to be a crucial factor affecting crack propagation, particularly with the development of the Goss texture component which is observed by electron backscattered diffraction analysis at bending points. The Goss texture hindered crack propagation, while the Brass texture allowed cracks to pass through. This phenomenon was consistent with both FEA and experimental observations. To mitigate edge crack formation and propagation, potential strategies involve promoting the formation of the Goss texture at the edge through alloy and process conditions, as well as implementing intermediate annealing to alleviate stress accumulation. These measures can enhance the overall quality and reliability of Al-Mg alloys during cross-rolling processes. In summary, understanding the mechanisms of defect formation and strain distribution in Al-Mg alloys during rolling processes is crucial for optimizing their mechanical properties. The findings of this study provide insights into the challenges associated with wave defects, strain localization, and crack propagation. Future research and optimization efforts should focus on implementing strategies to minimize defects and improve the overall quality of Al-Mg alloys in industrial applications.

Quantification of bone loss for follow-up comparisons has not been routinely performed in patients with parietal thinning so far. This study compares different methodological approaches including both 2- and 3-dimensional methods in computerized tomographies of a single patient. The 2-dimensional method provides accurate measurements of bone thickness, while the 3-dimensional method allows for a more comprehensive view of the bone's structure, including parameters like shape, size, and thickness. The techniques provided valuable data for the treating physician and suggest a possible effect of corticosteroids in this individual patient. The study concludes that 3-dimensional reconstruction of computerized tomographies with subsequent 2-dimensional analyses appears justified for routine radiological practice to increase clinical awareness of the size of the parietal bone defects and allow for quantification of bone loss during long-term follow-ups. Further validation of the proposed analytical approaches is warranted in larger studies to investigate patterns of bone thinning across the skull and changes in bone volumes over time, with specialized software to be approved for such analyses.

When bone substitutes materials are used, the increased risk of infection due to the none-autogenic graft is often discussed. The treatment of large bone defects in geriatric patients, often with osteoporotic bone, often presents major challenges to surgery. Bone substitutes materials are available indefinitely without the risk of additional surgery in each patient. Can bone substitutes materials be used without hesitation in the geriatric patient?Eighty-three patients suffered traumatic fractures of the distal radius, proximal humerus, and proximal tibia. The defect zones were filled with bone substitute material based on nanocrystalline hydroxyapatite (NHA) or calcium phosphate (CP). For comparison, a reference group without the void filling with a bone graft substitute (void defects, ED) was studied. All patients over the age of 64 years were retrospectively evaluated for complications and radiological outcomes. Results: 106 patients sustained traumatic fractures of the distal radius (68.9%), proximal humerus (5.7%), and proximal tibia (22.6%). No differences in infections were found when comparing the groups (p=1.0). retrospectively evaluated. The KEM group had a nonsignificantly lower rate of pseudarthrosis (p=0.09). A relative risk (RR) reduction of complications of 32.64% was observed when bone grafting material was used. The NNT for the prevention of complications was 5.99. When bone healing was assessed by radiological images, some follow-up studies showed significant differences in fracture bridging (p<0.001).Conclusions: In contrast to previous studies, bone substitutes materials can support the healing process in geriatric patients without relevant disadvantages. With an NNT of 6 regarding complications, many patients could benefit from bone graft augmentation. No increased infection rate was observed.

When bone substitutes materials are used, the increased risk of infection due to the none-autogenic graft is often discussed. The treatment of large bone defects in geriatric patients, often with osteoporotic bone, often presents major challenges to surgery. Bone substitutes materials are available indefinitely without the risk of additional surgery in each patient. Can bone substitutes materials be used without hesitation in the geriatric patient? Eighty-three patients suffered traumatic fractures of the distal radius, proximal humerus, and proximal tibia. The defect zones were filled with bone substitute material based on nanocrystalline hydroxyapatite (NHA) or calcium phosphate (CP). For comparison, a reference group without the void filling with a bone graft substitute (void defects, ED) was studied. All patients over the age of 64 years were retrospectively evaluated for complications and radiological outcomes. Results: 106 patients sustained traumatic fractures of the distal radius (68.9%), proximal humerus (5.7%), and proximal tibia (22.6%). No differences in infections were found when comparing the groups (p=1.0). retrospectively evaluated. The KEM group had a nonsignificantly lower rate of pseudarthrosis (p=0.09). A relative risk (RR) reduction of complications of 32.64% was observed when bone grafting material was used. The NNT for the prevention of complications was 5.99. When bone healing was assessed by radiological images, some follow-up studies showed significant differences in fracture bridging (p<0.001). Conclusions: In contrast to previous studies, bone substitutes materials can support the healing process in geriatric patients without relevant disadvantages. With an NNT of 6 regarding complications, many patients could benefit from bone graft augmentation. No increased infection rate was observed.

In recent years, there has been a wave of research on complex networks. The purpose of this paper is to study the graph theoretic mathematical properties of random cyclooctatetraene chain. We obtain the explicit analytical expressions for the variances of the Gutman index, Schultz index, multiplicative degree-Kirchhoff index and additive degree-Kirchhoff index of a random cyclooctatetraene chain with $n$ octagons, which plays a crucial role in the research and application of topological indices.

In this paper, the existence of optimal solutions for problems governed by differential equations involving feedback controls is established, when the problem must account for a Volterra-type distributed delay and is subject to the action of impulsive external forces. The problem is reformulated within the class of impulsive semilinear integro-differential inclusions in Banach spaces and is studied using topological methods and multivalued analysis. The paper concludes with an application to a population dynamics model.