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.

Vertex-degree-based (VDB) topological indices have been applied in QSPR/QSAR. As an important category, the general logarithmic VDB topological index $T_{lnf}(G)$, is defined as the summation of $ln{f(d(u),d(v))}$, where the summation over all $uv\in E(G)$. In this paper, we give the sufficient conditions for that (1) the path $P_{n}$ is the only tree with the minimal $T_{lnf}$; (2) the star $S_n$ is the only tree with the maximal and the minimal $T_{lnf}$, respectively. As applications, the minimal and maximal trees of some logarithmic VDB indices are determined.

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.

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.

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.

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.

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.

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.

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].

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.

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).

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.

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.

Background: In recent years, whole blood parameters and derivatives have been used as prognostic criteria in the course of the disease in various diseases. The prognostic nutritional index (PNI), the systemic immune-inflammation index (SII), the neutrophil-lymphocyte ratio (NLR) have been adapted as an indicator of inflammation and have been widely studied to define the severity of inflammation in some diseases. The aim of this study was to evaluate the relationship between parameters such as NLR, SII, PNI, controlling nutritional status (CONUT) score, nutritional risk index (NRI) and with immunonutrition status and disease activity in patients with ischemic stroke of small vessel, large vessel and other etiologies. Methods: We retrospectively evaluated the records of 1454 consecutive ischemic stroke patients hospitalized in the emergency department of Gaziosmanpasa Education and Research Hospital from 2019 to 2023. Results: Of the 1350 SVO patients included in the study, 58.8% had small vessel, 29.3% had large vessel and 11.9% had other etiologies. There was a significant difference between the 3 etiology groups for PNI and CONUT. The median PNI was 47.03 (41.33-52.85) in the other etiology group, 35.29 (33.69-37.25) in the small vessel group, and 34.11 (30.23-36.87) in the large vessel group. The CONUT median was 5(5-6) in the small vessel group, 5(4-6) in the large vessel group and 4(4-4) in the other etiology group. In addition, CONUT and PNI were also found to be independent risk factors for death. A negative significant correlation was observed between PNI and NLR (r:-0.692), SII (r:-0.591), CONUT (r:-0.685). Significant correlations were observed between CONUT and NLR (r:0.402), SII (r:0.312). Conclusion: PNI and SII were significantly associated with disease activity. PNI, CONUT and NRI as a more accurate prognostic indicator of nutritional status in patients with ischemic stroke of small vessel, large vessel and other etiologies. NLR and SII may be important predictive markers in the course and prognosis of stroke.

Drought affects human and natural systems, human and animal life and health, and socioeconomic activities. Drought consequences depend on its type and class, but also on the preparedness and resistance of communities to this climate disturbance. In the last decades, droughts accounted for about 16% of the total number of disasters but were responsible for 95% of the number of deaths and 26% of economic losses in Africa. This study aims to assess the drought regime in Southern Africa based on drought and vegetation indices. The SPI and SPEI were calculated at different timescales, using ERA5 data for the 1971 – 2020 period. The spatiotemporal distribution of drought descriptors was analyzed and compared with the patterns of the NDVI, EVI and VCI vegetation indices. The results reveal (i) the occurrence of droughts of various classes and at different timescales throughout the study period and region, (ii) high spatial variability in the number, duration, severity and intensity of drought, which tends to decrease with increasing timescale, (iii) high spatial-temporal agreement between drought and vegetation indices that confirm the dryness of vegetation during drought. These results aim to support policymakers in defining legislation to manage drought and water resources.

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.

Detecting and monitoring changes in soil salinity through remote sensing provides an opportunity for field assessment in regions where on-site measurements are limited. This investigation, carried out in Siwa Oasis, Egypt, aimed to assess the efficacy of several soil salinity indices derived from Landsat 5 and 7 satellite images. To achieve this, 56 on-site ground measurements were utilized for evaluation purposes. The study aimed to improve the correlation between EC and index values and explore the relationship between salinity and changes in land cover. Eleven spectral indices were calculated for nine scenes captured in different months from August to December. The first approach involved stacking the data to identify the index with the strongest correlation with ground EC values, without the need for complex analysis or EC value ranging. In the second approach, the ground EC measurements were classified into seven different salinity categories, and the correlation coefficient was calculated between each index and each salinity category. The third approach analyzed the data temporally, considering different salinity levels. Lastly, a spatial correlation analysis was conducted between EC and index values in the fourth scenario. The initial approach revealed a weak correlation due to substantial variation in EC values. However, the SI index demonstrated the highest correlation coefficient of 0.38. In the second scenario, the S2 index exhibited the highest correlation of 0.96 for moderate salinity samples. The third scenario showed that the S1 index achieved the highest correlation value of 0.99 for moderately saline areas. In the fourth scenario, the SI index exhibited the strongest correlation among all four ponds with correlation coefficients of 0.23, 0.23, 0.18, and 0.61. Notably, the correlations observed in the second and third scenarios demonstrated higher correlation coefficients compared to both the first and fourth scenarios. The study highlighted significant variations in EC levels related to land cover types and pond elevation. Additionally, remote sensing methods detected a 48% increase in total vegetated area over 17 years, showing the potential of remote sensing techniques in salinity monitoring for expanding agriculture and improving land management.

People have always hoped to be able to fill an entire plane with ``single unit cells'' without periodicity. This wish was realized after the mathematician discovered a 13-sided ``single unit cell'' named `einstein'. These non-periodic tessellations generally exhibit anisotropic properties, making them superior in terms of mechanical performance compared to periodic structures. From the perspective of information entropy, the reason behind the improved mechanical properties of these structures is the higher entropy associated with non-periodic configurations. To quantify the disorder of non-periodic structures, we propose an entropy expression for the `einstein' metamaterial. To demonstrate the mechanical properties of these high-entropy structures, we fabricate specimens using 3D printing and conducte mechanical experiments. For comparative analysis, we also use ABAQUS to perform finite element analysis of the problem. The research results reveal that the mechanical properties of high-entropy structures created by the non-periodic stacking of cells are significantly improved compared to those of low-entropy structures created by periodic stacking. The conclusions drawn from the study of individual issues are generalizable and may be of assistance in future material and structural design.

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.

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.

Although vitamin D deficiency has been correlated with an increased risk of cardiovascular disease (CVD), there are few data on the association between 25-hydroxyvitamin D (25(OH) D) and atherogenic indices predictive of CVD. This study aimed to investigate the relationship of vitamin D status with lipid profile and atherogenic indices in adult women in Morocco. Three hundred healthy women, aged 18 to 50 years, from Meknes were included. Fasting 25(OH) D and lipid concentrations were determined using a one-step electrochemiluminescence-based immunoassay and an enzymatic method, respectively. Atherogenic indices (Atherogenic index of plasma (AIP), non-HDL cholesterol (Non-HDL-C), Atherogenic coefficient (AC), Castelli risk indices I and II (CRI-I and II), and CHOLIndex (CI)) were calculated using conventional lipid parameters. Logistic regression models and operating characteristic curve (ROC) analysis were used to assess the relationship of the variables and estimate the threshold of 25(OH) D levels associated with high atherogenic indices. 25(OH) D below 20 ng/ml was significantly associated with an enhanced risk of hypertriglyceridemia and elevated values of AIP, AC, Non-HDL-C, and CRI-I with an OR (95% CI) of 4.904 (1.856-12.959); 3.637(2.149-6.158); 3.589(1.673-7.700); 2.074(1.215-3.540), and 2.481(1.481-4.123), respectively. According to ROC analysis, the likelihood of hypertriglyceridemia and high values of AIP, AC, Non-HDL-C, and CRI-I were associated with 25(OH)D thresholds ≤15.15 ng/ml, ≤ 17.5 ng/ml, ≤ 19.8 ng/ml, ≤ 20.1 ng/ml and ≤ 19.5 ng/ml, respectively, all p &lt; 0.01. Based on atherogenic indices, this study indicates that vitamin D below 20 ng/ml may increase the risk of cardiovascular disease in adult women. Additional health efforts are needed to raise awareness among women and healthcare providers in preventing and controlling cardiovascular risk factors.

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.

(1) Background: Depressional wetlands are highly vulnerable to changes in temperature and rainfall, affecting littoral vegetation, thus HydroGeoMorphic (HGM) wetland types. This study aimed to assess the utility of Sentinel-2A vegetation indices in enhancing delineation and sub-classify depressional HGM types. (2) Methods: We sampled 84 pairs of four vegetation indices from 10x10m plots along 14 belt transects in eight depressional wetlands in Mpumalanga, South Africa. We evaluated vegetation index differences between and within wetlands, focusing on lit-toral gradients. (3) Results: Significant differences (Bonferroni p

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.

Objective. The present study examined the potential use of computed tomography panoramic mandibular indices on cone beam CT (CBCT) for the assessment of bone density in postmenopausal women with low bone mass. Study design. We enrolled 104 postmenopausal women who performed dual energy X-ray absorptiometry (DXA) using a DXA scanner and mental foramen region CBCT using NewTom VGi EVO Cone Beam 3D system. We assessed the relationship between DXA parameters: lumbar, femoral neck and total hip T score, bone mineral density (BMD), and lumbar trabecular bone score (TBS) and the panoramic mandibular indices: computed tomography mandibular index superior (CTI(S)), computed tomography mandibular index inferior (CTI(I)) and computed tomography mental index (CTMI). Results. We found important correlations between the CTI(I), CTI(S) and CTMI and bone mass, quantitative evaluated as BMD and T-score and also quality using TBS score. Conclusion. CBCT measured indices CTI(S), CTI(I), CTMI are useful in assessing patients with low bone mass.

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.

Our aim is at three feels: i) study safe haven properties of sectoral CDS; ii) study hedging effectiveness and measure the diversification benefits of introducing them in both Conventional and Islamic stock markets portfolios and iii) compare these results with VSTOXX, Gold and Bitcoin indices. To do this, we estimate time varying hedge ratio using (A)DCC and GOGARCH models and then deduce hedging effectiveness.. We follow the same methodology for each sub-period and each refit to test the effect of bubble crypto currency and COVID-19 pandemic on hedging effectiveness. Empirical results show the superiority of industrial CDS sectoral index to hedge both conventional and Islamic stock markets whether long or short term despite that their performances were reduced slightly during the second and third periods. VSTOXX and Others sectoral CDS indices offers Hedging performances that are generally better than Bitcoin and gold.

A method for estimating river water surface elevation (WSE) from Landsat imagery using the river inundation area - water surface elevation (RIA-WSE) rating curve constructed from the U.S. Geological Survey Topobathymetric Elevation Model (TEM) data was developed and tested at six gauging stations along the upper Mississippi River. The Otsu's automatic threshold selection algorithm was employed for the image classification and estimation of inundation areas within each pre-defined polygon around each gauging station. In addition to the commonly used green-band based water indices, Landsat 8 and 9 OLI's ultra-blue, blue, and red band-based water indices were also tested in this study, which resulted in twenty different water indices: NDWIv (Normalized Difference Water Index), MNDWI1v and MNDWI2v (Modified Normalized Difference Water Index), AWEIsv (Automatic Water Extraction Index with shadow), and AWEInsv (AWEI without shadow), where v represents the visible light band used in the water index. At each station, about 60-80 Landsat 8 or 9 images during 2013-2023 were used for assessing the performances of the twenty water indices through comparing the estimated WSEs with the measured WSEs. Results showed that the ultra-blue or red band-based AWEIs yielded the most accurate estimations of WSEs among the twenty tested water indices.

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.

Topological interlocking assembly (TIA) and computational architecture treat form as an emergent property of a material system, where the final shape results from the interplay of geometries and geometric interdependencies influenced by material, structural, and fabrication constraints. This paper posits that TIA is an ideal pedagogical tool for introducing students to computational architecture, its theoretical foundations and design principles. Specifically, defining TIA as a material system provides a robust educational approach for engaging students with computation, fostering design processes through bottom-up, hands-on investigations and procedural logic, understanding generative geometric rules, and exploring the flexibility of parametric variations. The methodology is illustrated through a Design Workshop and study unit from the Bachelor’s and Master’s programs at the Faculty for the Built Environment, University of Malta. The paper presents four investigations of defining a material system based on TIA - of tetrahedra, cones, octahedra, and osteomorphic blocks—as case studies to demonstrate how these exercises introduce students to computational thinking, parametric design, and fabrication techniques. Finally, the paper discusses the advantages and limitations of this pedagogical methodology.

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.

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 growing concerns about floods have highlighted the need for accurate and detailed precipitation data as extreme precipitation occurrences can lead to catastrophic floods, resulting in significant economic losses and casualties. Integrated Multi-satellitE Retrievals for the Global Precipitation Measurement (GPM-IMERG) is a commonly used high-resolution gridded precipitation dataset and is recognized as trustworthy alternative sources of precipitation data. The aim of this study is to comprehensively evaluate the performance of GPM IMERG Early (IMERG-E), Late (IMERG-L), and Run Final (IMERG-F) in precipitation estimation and their capability in detecting extreme rainfall indices over southwestern Iran during 2001-2020. The Asfezari gridded precipitation data which are developed using a dense of ground-based observation were utilized as the reference dataset. The findings indicate that the IMERG-F performs reasonably well in capturing many extreme precipitation events (defined by various indices). All the three products showed a better performance in capturing fixed and non-threshold precipitation indices across the study region. The findings also revealed that both IMERG-E and IMERG-L have problems in rainfall estimation over elevated areas showing values of overestimations. Examining the effect of land cover type on the accuracy of the precipitation products suggest that both IMERG-E and IMERG-L show large and highly unrealistic overestimations over inland water bodies and permanent wetlands. The results of the current study highlight the potential of IMERG-F as a valuable source of data for precipitation monitoring in the region.

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.

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: S degree. And also we define S indices of a simple connected graph by using the S degree concept. We compute the S indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.

Drought monitoring and early detection have improved greatly in recent decades through the development and refinement of numerous indices and indicators. However, a lack of guidance, based on user experience, exists as to which drought monitoring tools are most appropriate in a given location. This review paper summarizes the results of targeted user engagement and the published literature to improve the understanding of drought across North America, and to enhance the utility of drought monitoring tools. Workshops and surveys were used to assess and make general conclusions about the perceived performance of drought indicators, indices and impacts information used for monitoring drought in the five main Köppen climate types (Tropical, Temperate, Continental, Polar Tundra, Dry) found across Canada, Mexico, and the United States. In Tropical, humid Temperate, and southerly Continental climates, droughts are perceived to be more short-term (less than 6 months) in duration rather than long-term (more than 6 months). In Polar Tundra climates, Dry climates, Temperate climates with dry warm seasons, and northerly Continental climates, droughts are perceived to be more long-term than short-term. In general, agricultural and hydrological droughts were considered to be the most important drought types. Drought impacts related to agriculture, water supply, ecosystem, and human health were rated to be of greatest importance. Users identified the most effective indices and indicators for monitoring drought across North America to be the U.S. Drought Monitor (USDM) and Standardized Precipitation Index (SPI) (or another measure of precipitation anomaly), followed by the Normalized Difference Vegetation Index (NDVI) (or another satellite-observed vegetation index), temperature anomalies, crop status, soil moisture, streamflow, reservoir storage, water use (demand), and reported drought impacts. Users also noted the importance of indices that measure evapotranspiration, evaporative demand, and snow water content. Drought indices and indicators were generally thought to perform equally well across seasons in Tropical and the colder Continental climates, but their performance was perceived to vary seasonally in Dry, Temperate, Polar Tundra, and the warmer Continental climates, with improved performance during warm and wet times of the year. The drought indices and indicators, in general, were not perceived to perform equally well across geographies. This review paper provides guidance on when (time of year) and where (climate zone) the more popular drought indices and indicators should be used. The paper concludes by noting the importance of understanding how drought, its impacts, and indicators are changing over time as the climate warms, and by recommending ways to strengthen the use of indices and indicators in drought decision-making.

This article explores the use of vegetation indices (VIs) in remote sensing for estimating standing wood volume and volume increments in forest ecosystems. The study investigates the correlations between various VIs and wood volume across different forest stand age classes, focusing on the effectiveness of commonly used indices such as Squared Ratio Simple Red Edge (SQSR) and Red-Edge Ratio Vegetation Index (RERVI), as well as other typical indicators including Enhanced Vegetation Index (EVI), Red-Edge EVI (RE-EVI), and Green Normalized Difference Vegetation Index (GNDVI). Additionally, the analysis considers a pair of indicators based on blue and near-infrared channels, resembling the Blue-normalized Difference Vegetation Index (BNDVI). The research reveals that quadratic and power-law models of SQSR and RERVI demonstrate higher correlations (>0.40) with wood volume, especially in younger forest stands (>0.80). Furthermore, the study highlights the potential of NDII and NDWI indices for estimating volume increments in certain classes of forest stands (0.70). However, correlations vary across different forest stand classes, suggesting the need for further investigation into the reliability of VIs for monitoring wood volume and volume increments in forest ecosystems. Overall, this research contributes to the understanding of the applicability of VIs in remote sensing for forest management and ecosystem monitoring.

Background/Objectives: The primary life-threatening complication in Spinal-bulbar muscular atrophy (SBMA) is ventilatory failure, which results from the weakening of the bulbar and respiratory muscles. However, systematic studies assessing respiratory function over the long-term have not been performed. The present study analyzes the longitudinal patterns of respiratory function tests over a follow-up of 11 years, aiming to identify any potential, sustained decline during this time. Furthermore, we explored possible correlations between respiratory function tests and clinical and biochemical serum indices. Methods: We collected data from 9 genetically confirmed SBMA patients and conducted spirometric measurements twice a year for eleven years. The spirometric data included maximum inspiratory pressure (MIP), maximum expiratory pressure (MEP), and forced vital capacity (FVC)]. Additionally, we measured serum biochemical indices and SBMA functional rating scale (SBMAFRS) for clinical analysis. Results: All three respiratory function tests showed a descending trend. A major decrease was observed for MEP (52%) and MIP (42%), while this was minor for FVC (25%). SBMAFRS score correlated with the three pulmonary function tests. MIP and MEP correlated with creatine phosphokinase and creatinine levels, and FVC correlated with serum level of transaminases. Conclusions: This longitudinal study shows a progressive decline of spirometric data throughout life in patients with SBMA. Spirometric measures relative to maximal strength of the respiratory muscles (MIP and MEP) may have a better predictive value for pulmonary and muscular decline than FVC.

The objective of this study was to investigate the impact of adding fermented herbal extracts (FHE) derived from mulberry leaf (Morus alba), Javanese turmeric (Curcuma xanthorrhiza), and fingerroot (Boesenbergia rotunda) to the diet of tiger shrimp (Penaeus monodon) on their growth, moulting performance, feed efficiency, and nutrient retention. The main feed used in this trial was a commercially manufactured pellet, then five different doses of FHE supplementation were used: 0 mg/kg feed (P0, control), 50 mg/kg feed (P1), 100 mg/kg feed (P2), 150 mg/kg feed (P3), and 200 mg/kg feed (P4). Weight gain, average daily gain, and length gain of shrimps fed P2 was significantly higher than that of those fed the control diet. Similar result was observed in moulting performance. The application of P2 showed superior results in enhancing the FE of cultured shrimp. Thus, the protein and energy retention of P. monodon was significantly better in P2 treatment groups. P0 had the lowest crude protein, while shrimp given P2 and P3 diets had the highest crude protein content of any treatment group. Based on the findings, it is recommended that the juvenile tiger shrimp diet contain 100 mg/kg of FHE for the best effects.

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.

Financial stress can have significant implications for individuals, businesses, asset prices and the economy as a whole. This study examines the nonlinear structure and dynamic changes in the multifractal behavior of cross-correlation between the financial stress index (FSI) and four well-known commodity indices, namely Commodity Research Bureau Index (CRBI), Baltic Dry Index (BDI), London Metal Index (LME) and Brent Oil prices (BROIL), using multifractal detrended cross correlation analysis (MFDCCA). For analysis, we utilized daily values of FSI and commodity index prices from 16th June 2016 to 9th July 2023. The following are the most important empirical findings: (I) All of the chosen commodity market indices show cross correlations with the FSI and have notable multifractal characteristics. (II) The presence of power law cross-correlation implies that a noteworthy shift in FSI is likely to coincide with a considerable shift in the commodity indices. (III) The multifractal cross-correlation is highest between FSI and Brent Oil (BROIL) and lowest with LME. (IV) The rolling windows analysis reveals a varying degree of persistency between FSI and commodity markets. The findings of this study have a number of important implications for commodity market investors and policymakers.

In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced reciprocal Randic index, Narumi-Katayama index and symmetric division index a graph using solely the vertex degrees. Then we obtain upper and lower bounds for these indices for the complete graphs, path graphs and Fibonacci-sum graphs. Finally, we compared the bounds of these indices for a general graph and some special graphs.

Lake Chapala is a natural ecosystem of Mexico, declared Ramsar site, currently, is an area with importance in the agricultural sector, tourism, and important source of drinking water in the Metropolitan area of Guadalajara, considered as a thermo regulatory body. This study used tools such as Rhtest, as well as analyzing extreme climate indices using RClimdex. In addition, the relationship with the change in water surface of Lake Chapala was assessed through the NDWI index, using Landsat images, between 1985 and 2018. According to the obtained results, the signs of climatic variability are detected in the study region, which, directly affects the basin runoff and water levels in the lake, as well as, the factor of water overexploitation in the basin, so it is considered that the lake conditions mostly depend on the type of management that is given to the resource. Finally, the results will help the understanding of climate variability and its water resources influence of the Lerma Chapala basin, which will assist in future research.

Vegetation indexes help perform precision farming because they provide useful information regarding moisture, nutrient content, and crop health. Primary sources of those indexes are satellites and unmanned aerial vehicles equipped with expensive multispectral sensors. Reducing the price of obtaining such information would increase the availability of precision farming for small farms. Several studies have proposed deep neural network methods to estimate the indexes from RGB color images. However, these methods report relatively large errors for mature plants when highly non-linear relationships of images and vegetation indexes arise. One could apply multilayer random forest-based models (Deep Forests) to solve this problem, but the discriminative power of such models is limited: they cannot catch complex dependencies between image features. In this paper, we propose a method that combines ideas of deep forests, random forests of kernel trees, and global pruning of random forests to tackle the problem. As a result, the method considers the properties of objects with a complex structure: the presence of relationships between groups of features, displacement, and scaling of objects. The experimental results show that the proposed method outperforms neural network-based solutions in several datasets.

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.

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 paper, we explore the hypothesis that topological defects formed in the quark-gluon plasma (QGP) of the early universe, specifically flux tubes and domain walls, could serve as stable dark matter candidates. Theoretical analysis of the QCD vacuum structure reveals that these defects can form due to nontrivial topological configurations, with the Lagrangian density incorporating topological terms. We model the formation and stability of flux tubes and domain walls, estimating their energy densities and dynamics within the QGP. Flux tubes, with energy per unit length approximately given by $\mu \approx \frac{\sigma}{g_s^2}$, and domain walls, characterized by a surface energy density $\sigma_{\text{DW}} \sim \Lambda_{\text{QCD}}^3$, exhibit unique gravitational signatures. These signatures include distinct gravitational lensing patterns due to their linear and planar mass distributions, making them detectable through astrophysical surveys. Furthermore, their minimal interaction with conventional matter aligns well with observational constraints on dark matter properties. We discuss potential experimental approaches for detecting these defects, including high-energy collider experiments and detailed analysis of gravitational lensing data. Our findings suggest that topological defects in the QGP provide a compelling and novel solution to the dark matter problem, offering a new direction for both theoretical investigation and experimental verification.

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.

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.

Non-destructive, accurate, and timely approach for crop yield prediction at field scale is vital for precision agriculture. This study aimed to investigate the appropriate wavelengths and their combinations to explore the new SIs derived from UAV hyperspectral images in predicting yield during the growing season of spring maize. The best wavelengths and new SIs, including the difference spectral index, ratio spectral index, and normalized difference spectral index forms, were obtained by the contour maps constructed by the coefficient of determination (R2) from the linear regression models between the yield and all possible SIs screening out from the 450-950 nm wavelengths. The results showed that the most sensitive wavelengths were 640-714 nm at WJQ, 450-650 nm and 750-950 nm at SKS, and 450-700 nm and 750-950 nm at FJJ. The new SIs established here were different across the three experimental fields, and their performance on maize yield prediction were generally better than that of the published SIs. In addition, the new SIs presented different response to various N fertilization levels. This study demonstrated the potential of exploring new spectral characteristics from remote sensing technology for predicting field-scale crop yield in spring maize cropping systems before harvest.

The socioeconomic sectors increasingly rely on prompt and affordable tools to predict climatic conditions. This study uses a decision tree classifier model to identify similar monthly ENSO 3.4 indices from March 2001 to February 2011 through monthly historical ENSO3.4 indices (December 1950 – February 2001). Historical monthly ENSO3.4 indices were used to extract available high-resolution monthly historical precipitation grids (1950-2001) for Mexico and constructed monthly ensembles (March 2001 – February 2011 hindcasts). Formerly, a precipitation categorization of monthly observed and simulated precipitation (2001-2011 hindcasts) was employed. Thereafter, global vector data and spatial map assessments were performed seasonally (winter, spring, summer, and fall). Global KSS and HSS metrics indicated the model approach has skill, especially in the spring and fall. Spatial metrics exposed large areas with hit rates > 0.60 in winter and spring, though in winter and spring (dry seasons), it was due to the precipitation categorization hindcast and observed were within the first classification. Lower hit rates, but still acceptable (> 0.40), were detected in summer and fall (during the rainy season and at the end, respectively) because more precipitation classifications were tested and prone to miss. Spatial Spearman correlations provided specific areas of significant model performances and found that high hit rates during the winter and spring are spurious. Meanwhile, it was also found that during the fall the model approach is reliable in most of Mexico, followed by the spring, and in constraint areas in summer and winter across the country. It also appears that dominant ENSO neutral events followed by balanced ENSO cooling and warming events do not prefer the model skill. Overall, the empirical method shows promise (low-cost human and computational resources if ENSO indices expose certainty in its Lead months to forecast) and has the potential to be used in other developing countries influenced by El Niño phenomena.

The purpose of this article is to analyze urban form through the mapping of morphological indices, namely impervious surface fraction, building density, verticality, height/width ratio, roughness length, and porosity, to support urban planning in the city of João Pessoa, PB, in northeastern Brazil. The application of this study identifies and calculates such significant indices for the city's urban space from a Geographic Information System (GIS) model. The spatial indices play notable roles in climate at different scales, developing guidelines to maximize environmental quality, promote improvements to thermal comfort, minimize the urban heat island in the city of João Pessoa, and provide relevant data (considering microclimate aspects), guiding decisions related to the planning process.

This study presents a novel approach to understanding evolutionary dynamics through topological analysis of genotypic structures. We model the genome of a simple organism as a topological torus undergoing mutations at a constant rate of 1% per generation. Employing persistent homology and other topological data analysis techniques, we investigate how these mutations influence the overall topology of the genomic structure over time. Our simulations reveal that specific critical mutations lead to significant changes in the homotopic and homologic properties of the torus. We interpret these topological shifts as potential markers for the formation of new subspecies. By identifying the precise points of topological "breaks" within the toroidal genomic representation, our model provides a quantitative framework for observing the incremental transformations that underpin major evolutionary developments. The results offer new insights into the thresholds of speciation and adaptation, demonstrating how gradual genetic changes can accumulate to produce qualitative shifts in organismal traits. This approach bridges the gap between microscopic genetic mutations and macroscopic evolutionary outcomes, potentially revolutionizing our understanding of evolutionary processes. Our findings have implications for various fields, including theoretical biology, genetic engineering, and conservation biology. The model provides a novel perspective on genetic resilience and adaptability, offering a foundation for future research on the relationship between genomic topology and evolutionary trajectories. It also emphasizes the innovative nature of the research and its potential impact on multiple fields of study.

A topological representation theory of chiral spin liquid is proposed to unify the integral and fractional quantum Hall fluid based on hyperbolic geometry, knot lattice and Thurston's train track theory. The integral and fractional Hall resistivity obeys an exact unified equation, $R_{xy} = (h/e^2)B_{e}$, $B_{e} = (n+\nu)^{-1}$, with respect to the bulk energy gap ${\Delta}E = {\hbar{e}B_{e}}/{Mc}$. The Wen-Zee matrix formulation of topological fluid for quantum Hall effect is constructed by topological surgery and train track. The chirality of spin liquid is spontaneously distinguished by Jones polynomial. The integral Chern number for Hall conductance is fractionalized by generalizing Thurston's train track to folding laminations in three dimensions, which spontaneously bring fractional quantum Hall fluid and anyons into three dimensions and provided an theoretical explanation on the competing fractional quantum Hall states. The many body system of interacting fermions or bosons are mapped into many interacting liquid droplets that interwind into knot lattice, which provide an effective topological representation for superfluid and superconductor, the strange metal state in superconductor is explained by topological dislocation and topological surgery. The Kauffman decomposition rule in knot theory is extended to describe the topological relations between different two dimensional manifolds, which further reveals the non-trivial relationship between the partition functions of pairing fermions and free electrons. The minimal energy state is the most stable topological state, even thought it maybe shares the same topological number with the excited states. The topological representation theory predicts a circular motion of electrons in hyperbolic space, that is implementable and testable by inhomogeneous magnetic field in three dimensions. The folding lamination representation of topological quantum fluid provides an promising implementation of string theory in high energy physics.

In the realm of molecular science, intricate relationships between molecular structures and their biomedical and pharmacological characteristics have been revealed through empirical experiments. This exploration hinges on the application of numerical descriptors, known as Topological Indices, which illuminate the inherent properties of diverse molecular structures. With particular significance in the medical and pharmaceutical domains, these indices facilitate the prediction of biological features for new chemical compounds and drugs by quantifying weighted entropies. In the context of this paper, we delve into the concept of graph entropy, weaving it intricately with the topological properties of the crystalline framework of the copper oxide molecule, denoted as Cu\textsubscript{2}O$[i,j,t]$. Our primary objective is to unravel the mathematical symphony underlying the structural intricacies of Cu\textsubscript{2}O$[i,j,t]$ and to imbue it with the conceptual essence of entropy. We accomplish this through the computation of entropy, leveraging various topological indices, including weight. In addition to our analytical journey, we present a graphical comparison that juxtaposes the computed indices and entropies, shedding light on the interplay between mathematical analysis and the structural elegance of Cu\textsubscript{2}O$[i,j,t]$. This endeavor contributes to a deeper understanding of the material's multifaceted applications, spanning domains from chemical sensors to solar cells, photocatalysis, and batteries, where Cu\textsubscript{2}O's crystallographic structure plays a pivotal role.

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.

Increased exposure to artificial light at night can affect human health including disruption of melatonin production and circadian rhythms and extend to increased risks of hormonal cancers and other serious diseases. In addition, multiple negative impacts on fauna and flora are well documented, and it is a matter of fact that artificial light at night is a nuisance for ground-based astronomy. These impacts are frequently linked to the colour of the light or more specifically to its spectral content. Artificial light at night is often mapped by using space borne sensors, but most of them are panchromatic and thus insensitive to the colour. In this paper, we suggest a method that allows high resolution mapping of the Artificial light at night by using ground-based measurements with the LANcube system. The device separates the light detected in four bands (Red, Green, Blue, and Clear) and provides this information for six faces of a cube. We found relationships between the LANcube’s colour ratios and 1- the Melatonin Suppression Index, 2- the StarLight Index and 3- the Induced Photosynthesis Index. We show how such relationships combined with data acquisition from a LANcube positioned on the top of a car can be used to produce spectral indices maps of a whole city in a few hours.

We explore the concept of Euclidean locality within treonic topological spaces. Our study establishes a foundational theoretical framework, elucidating the properties of continuity, homeomorphisms, and compactness in these spaces. We assess the Euclidean locality of treonic spaces through the analysis of specific homeomorphisms, which enables us to define manifolds in treonic spaces and extend recent research on Bermejo Algebras. For the first time, we characterize treonic manifolds by incorporating the property of Euclidean locality alongside previously studied properties such as Hausdorff spaces and second countable spaces. Our findings advance the understanding of the topological and geometric properties of treonic spaces, providing significant insights for advanced mathematical research.

The dynamic beam equations provide an analytical model and a generic solution for continuous systems. The constants for amplitudes and frequencies are given by the boundary conditions, which are here considered looped, in order to represent a closed element, by topological closure. This type of model is applied to the representation of a semicircular canal. This approach addresses the deformability of this anatomical element, both in Lagrangian solid parts (bone, membranes, intermediate materials) and in fluids (Eulerian pressure waves). The model is proposed for both physiological representation and pathology modeling. The latter is represented by a passive or retroactive singularity. An original analytical approach is thus developed for each segment, representing physiological modes – nodes and bellies - and possible disturbances. The damping entropy is also the subject of a special segmented treatment, to take account of fluid-solid interactions, providing a coherent model. The result is a simplified but robust model that both reproduces the vibro-acoustic modes of the semicircular canal and anticipates the effects of a singular pathology, such as a third window or neuritis. Mathematically, this model opens the way to structural analytical models of the inner ear, and to possible dynamic couplings between equilibration and acoustics.

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 two interconnected mathematical models: one describing the stability and bifurcation dynamics of ecological biomes, and another simulating the progressive deformation and structural failure of a toroidal object. Both models explore topological changes in complex systems, bridging concepts from ecology, materials science, and mathematical physics. The first part introduces a dynamic model of ecological biomes, incorporating seasonal oscillations and external pressures. We define equations for topology updates, seasonal effects, and pressure impacts, culminating in a bifurcation condition that represents a critical shift in the biome's equilibrium state. This model provides insights into the resilience and tipping points of ecological systems under varying environmental stresses.The second part extends these concepts to a three-dimensional toroidal structure. We present parametric equations describing the torus geometry and develop a time-dependent deformation model that includes both stochastic and deterministic elements. A novel twisting deformation component enhances the realism of the structural changes. We define a critical threshold for maximum displacement, beyond which the torus undergoes structural failure, analogous to the bifurcation point in the biome model. Both models are implemented computationally, providing visual representations of the systems' evolution over time. The biome model illustrates the path to and consequences of bifurcation, while the torus simulation depicts the stages of deformation leading to structural break. This work contributes to the understanding of topological changes and critical transitions in both ecological and physical systems. By presenting these models in parallel, we highlight the universal nature of stability, bifurcation, and failure across different domains. The methodologies presented here have potential applications in ecology, materials science, structural engineering, and theoretical physics, offering a framework for studying the limits of system integrity under stress.

Haemodynamic indices are widely used in clinical practice for deciding on a particular type of treatment. Low quality of the CT data and tachycardia complicate interpretation of the measured or simulated values. In this work, we present a novel approach for evaluating resistances in terminal coronary arteries. Using 14 measurements from 10 patients, we show that this algorithm retains the accuracy of 1D haemodynamic simulations in less detailed (truncated) geometric models of coronary networks. We also apply the variable systole fraction model to study the effect of elevated heart rate on the values of FFR, CFR and iFR. We conclude that tachycardia may produce both overestimation or underestimation of coronary stenosis significance.

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.

. (1) Background: The aim of this study was to verify the differences in body composition, power and lower limb muscle strength in futsal players from three competitive levels. (2) Methods: The study involved 68 players (24.26 ± 4.63 years), divided into three competitive levels: elite, sub-elite and amateur. To assess physical condition, we used the Inbody270, the ChronoJump and the Isokinetic Dynamometer and used the non-parametric Kruskal-Wallis test to compare the three independent variables. (3) Results: There were no differences in body composition between the players at the three competitive levels. With regard to lower limb muscle power and strength, the elite group showed, on average, better performance and capabilities, especially when compared to the amateur group, and all groups showed an H/Q ratio &gt; 60%. (4) Conclusions: We conclude that there are not many differences in physical condition between the three competitive levels of futsal, despite the unequal sporting demands between them. However, the elite group has greater power and muscle strength, and both groups showed a high probability of lower limb muscle injury at this stage of the sporting season, alerting sports training professionals to the importance of individualized analysis of physical condition and performance capacity.

In this study, we performed periodicity analyzes of selected daily solar (FI, CI), geomagnetic (Ap, Dst, Scalar B) and cosmic (CRI) activity indices for the last solar Cycle 24 (December 2008 to December 2019). To investigate the periodic variations of above selected data sets the Multi Taper Method (MTM), Morlet wavelet, Cross Wavelet Transform (XWT), and Wavelet Coherence (WTC) analysis techniques were used. In results of our analysis we found that i) the 25-33 and 2048-day periodicities exist in all data sets without any exception, while all other detected periodicities have data preferences, ii) all detected periods located around the maximum phase of the cycle (Cycle 24), iii) the phase relations between compared data sets periodicities are gradually changing from small periods to large ones; there are no phase relations between small periodicities and they show mixed phases, while they are completely in phase/antiphase for large periodicities, iv) all detected FI periodicities, except 2048 days periodicity, are common periodicities with all other data sets used in this study.

The urban environment induces stress on trees and the impact can be identified by observing the condition of the crown. The aim of this study is to correlate the variables crown density (Cdn), crown transparency (Ctr) and dieback (Cdie) with the following vegetation indices: normalized difference vegetation index (NDVI), enhanced vegetation index (EVI2), blue normalized difference vegetation index (BNDVI), green normalized difference vegetation index (GNDVI), green-red vegetation Index (GRVI) and red-green-blue vegetation index (RGBVI) of the tree crown located in urban green areas, as well as chlorophyll fluorescence (Fv/Fm) as an indirect indicator of tree health condition. A total of 549 trees were evaluated, represented in 24 families, 36 genera and 53 species; the variables had average values of 67.96 % in Cdn, 35.19 % in Ctr and 1 % in Cdie. Correlations were found between Fv/Fm, NDVI and BNDVI. NDVI and BNDVI correlated with variables such as Cdn and Ctr, mainly in species such as Ligustrum lucidum, Jacaranda mimosifolia and Fraxinus uhdei. Therefore, it is possible to evaluate tree health condition of trees in urban green environments through the identification of unfavorable conditions at the crown level by using vegetation indices for some of the species studied.

Air pollution is responsible for any adverse effects on human beings. Thermal discomfort, on the other hand, is able to overload the human body and eventually provoke health implications due to the heat imbalance. Methods: The aim of the present work is to study the behavior of two bio-climatic indexes and statistical characteristics of the air quality index for Sofia city - the capital of Bulgaria for the period 2008 - 2014. The study is based on WRF-CMAQ model system simula-tions with a spatial resolution of 1 kilometer. The air quality is estimated by the air quality index, taking into account the influence of different pollutants and the thermal conditions by two indi-ces, respectively, for hot and cold weather. Results: It was found that half of the heat and cold index categories are present in the simulations. Their distribution has some spatial features. All air quality categories are present in the domain, with dominance only of the O3 and PM10. Conclu-sions: It was found that Sofia is not so hot and air polluted place, but in some situations, people have to have some concerns when intend to be outdoors for a prolonged time.

The use of heart rate variability (HRV) in research has been greatly popularized over the past decades due to the ease and affordability of HRV collection, coupled with its clinical relevance and significant relationships with psychophysiological constructs and psychopathological disorders. Despite the wide use of electrocardiogram (ECG) in research and advancement in sensors technology, the analytical approach and steps applied to obtain HRV measures can be seen as complex. Thus, posing a challenge to users who may not have the adequate background knowledge to obtain the HRV indices reliably. To maximize the impact of HRV-related research and its reproducibility, parallel advances in users’ understanding of the indices and the standardization of analysis pipelines in its utility will be crucial. This paper addresses this gap and aims to provide an overview of the most up-to-date and commonly used HRV indices, as well as common research areas that these indices have shown to be very useful, particularly in psychology. In addition, we also provide a step-by-step guide on how to perform HRV analysis using an integrative neurophysiological toolkit, NeuroKit2.

This paper explores a novel approach to establishing the topological equivalence of manifolds embedded in ℝ

This study aims to refine our understanding of evolutionary processes, particularly as they apply to complex organisms, using an innovative graph-based simulation approach. We model the topological evolution of simple (5-node ring graph) and complex (20-node dense random graph) organisms over 10 generations, applying different mutation rates to reflect biological realities. Our results provide intriguing insights into the potentially different evolutionary dynamics at play in simple versus complex organisms. While simple organisms demonstrate high topological flexibility and rapid adaptability, aligning with classical evolutionary models, complex organisms exhibit a surprising degree of structural stability. This stability persists even under mutation rates that would typically drive significant changes in simpler systems. The simulation highlights an important consideration: the intricate, interdependent networks characteristic of complex organisms may create a form of evolutionary buffering. This buffering could modulate the impact of random mutations and natural selection – processes that are cornerstones of evolutionary theory. Our findings suggest that the high degree of complexity in advanced life forms may necessitate a more nuanced view of how evolutionary processes operate across different levels of biological organization. Furthermore, the emergence of new structural motifs in simple organisms, contrasted with the relative conservation in complex topologies, indicates that evolutionary mechanisms may manifest differently across the spectrum of biological complexity. This observation invites a more detailed exploration of how evolutionary principles apply to diverse life forms.These results contribute to the ongoing refinement of evolutionary theory, especially in its application to complex organisms. They suggest that additional mechanisms, such as constrained mutations, epigenetic changes, or higher-order organizational principles, may play significant roles alongside random mutations and natural selection in the evolution of complex life forms.

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.

The intricate relationship between genomic mutations and proteomic network topology represents a frontier in understanding cellular resilience and disease mechanisms. This study presents a novel approach to analyzing how proteomic topological structures evolve and potentially break down in response to accumulating genomic mutations, offering insights into the complex interplay between genetic alterations and protein interaction networks. We developed a computational model simulating a network of ten key proteins (A-J) over 20 discrete time points, each representing a state of increasing genomic mutation load. Our model incorporates dynamic protein interaction strengths that fluctuate in response to simulated genomic alterations and a topological representation of the protein network, allowing for visualization of structural changes. Not forgetting a quantitative measure of network integrity, correlating with the system's ability to maintain function under mutational stress. Our Key findings include: visualization of proteomic network evolution through a series of topological graphs, revealing how genomic mutations progressively alter protein interaction patterns and identification of a critical "breakage point" in the network topology, signifying a threshold where genomic mutations overwhelm the protein network's ability to maintain its functional structure. And also quantification of network properties, including interaction strengths and overall network density, demonstrating the non-linear relationship between genomic mutations and proteomic topological integrity.The observed breakage point may represent a critical threshold in disease progression, where the accumulation of genomic mutations leads to a collapse in the proteomic interaction network, potentially triggering pathological states. This methodology offers a new perspective on the genotype-phenotype relationship, viewing it through the lens of protein network topology. Our approach provides a framework for future studies to analyze how specific genomic mutations might impact proteomic structures, potentially leading to new insights in cancer research, neurodegenerative disorders, and other mutation-driven diseases. It also suggests that maintaining proteomic topological integrity could be a key factor in cellular resilience against genomic instability.

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.

This study addresses the gap in methodological guidelines for Neuroergonomic attention assessment in safety-critical tasks, focusing on validating EEG indices including the Engagement Index (EI) and Beta/Alpha ratio alongside subjective ratings. A novel task-embedded reaction time paradigm was developed to evaluate the sensitivity of these metrics to dynamic attentional demands in a more naturalistic multitasking context. By manipulating attention levels through varying secondary tasks in the NASA MATB-II task while maintaining a consistent primary reaction-time task, the study successfully demonstrated the effectiveness of the paradigm. Results indicate that both Beta/Alpha ratio and EI are sensitive to changes in attentional demands, with Beta/Alpha being more responsive to dynamic variations in attention, and EI reflecting more the overall effort required to sustain performance, especially in conditions where maintaining attention is challenging. The potential for predicting the attention lapses through integration of performance metrics, EEG measures, and subjective assessments was demonstrated, providing a more nuanced understanding of dynamic fluctuations of attention in multitasking scenarios, mimicking those in real-world safety-critical tasks. These findings provide a foundation for advancing methods to accurately monitor attention fluctuations and mitigate risks in critical scenarios, such as train-driving or automated vehicle operation, where maintaining high attention level is crucial.

The current echocardiography reference values are derived primarily from populations in North America and Europe. It becomes necessary to study ethnically different groups of the population, which often have different living conditions, food habits and lifestyle. The aim of the study was to compare echocardiography indicators in urbanized patients with arterial hypertension of the Shor and non-indigenous ethnic groups living in the Gornaya Shoria region. The study included patients with arterial hypertension: 58 Shors (20 men and 38 women) and 50 non-indigenous residents (15 men and 35 women) of Gornaya Shoria. All underwent an echocardiographic study with an assessment of the left heart parameters. We assessed the left ventricular hypertrophy (LVH) severity, LV geometry and diastolic function in the ethnic and sex groups. Shor with hypertension no showed a significant difference in left ventricular dimensions compared to Caucasian. Severe abnormal LVH was associated in the Shors with glucose levels (OR 3.24, 95%CI 1.56-6.7, p=0,001), and in Caucasians with systolic (p=0.021) and diastolic (p=0.011) blood pressure, and heart rate (p=0.033). The Shor men were more likely to have normal LV diastolic function (p=0.029) and LV concentric remodeling (p=0.023), and less often to have normal LV geometry (p=0.015) compared to non-indigenous men. Thus, this study can be useful in assessing the impact of the development of arterial hypertension, as well as the impact of changing the lifestyle of the Shors when moving to the city from rural areas on ethnic differences in echocardiography.

We assessed how close human perceptions of landscape modification matched a multivariate index based on remotely sensed data of the same locations. Using a Human Footprint (HF) map of the continental U.S. (scaled 0-100), we created three series of aerial images, each with ten images distributed evenly across the 10 deciles of HF score. Using a web-based survey, 290 members of the global public ranked the images in one series based on their perception of the degree of human modification. Respondents also reported age, sex, and country. The degree of correspondence between rankings by respondents and by HF score was high, an average of 1.29 units of difference out of a maximum possible of 5.0. Differences among respondents were not explained by age, sex, or general geographic location. These results suggest that human perception of relative landscape modification conforms closely with the relative ranking made by a multivariate, analytical index.

This study assesses Human Thermal Comfort in two selected areas: a Green Infrastructure (GI) area represented by a garden and a high-rise building area, in the Central Business District (CBD) of Melbourne, Australia. Three-dimensional microclimatic modelling software, ENVI-met version 4 was used to simulate the microclimate. The indices of Predicted Mean Vote (PMV), Physiological Equivalent Temperature (PET) and Universal Temperature Climate Index (UTCI) were used to quantify the level of thermal comfort in the research areas. The simulation results showed that at midday, the difference in temperature between the garden area and the high-rise building area was approximately 1°C. Increasing temperatures at midday led to a change in the level of thermal comfort for both the areas, even though it was not significant. In general, the thermal perception in the GI area was slightly ‘cooler’ than in the high-rise building area. The results of the study indicated the important role of GI in improving the thermal comfort in urban areas.

Increasing demand for electricity and modernization of power systems within competitive markets induce power systems to operate close to their stability limits. Therefore, a power system continuous monitoring and control by using voltage stability indices are known exigence. This is the first-ever effort, examined more than 40 voltage stability indices thorough an exhaustive study based in on their formulation, application, performance, and assessment measures. Which is conducted based on a logical and chronological order considering the most recent worldwide applied voltage stability indices. However, the generalizability of such an immense diversity of these indices in term of multivariable objectives subjects to a certain limitation to summate into a deciphered outcome. Despite all these obstacles, this study systematically reviews available indices in the literature within the past three decades to set out an integrated knowledge with an insight up-to-date exposition. That followed with a comparative analysis in term of their similarity, functionality, applicability, formulation, merit, demerit, and overall performances. Also, a broad categorization of voltage stability indices is addressed. This study with an immediate implication in practice as an exhaustive roadmap can be counted a planning and operation reference in the context of voltage stability for students, researchers, scholars, and practitioners.

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In this paper, bounds for the Randić, general Randić, sum-connectivity, the general sum-connectivity and harmonic indices for tensor product of graphs are determined by using the combinatorial inequalities and combinatorial computing.

Collatz conjecture states that an integer $n$ reduces to $1$ when certain simple operations are applied to it. Mathematically, the Collatz function is written as $f^k(n) = \frac{3^kn + C}{2^{z}}$, where $z, k, C \geq 1$. Suppose the integer $n$ violates Collatz conjecture by reappearing as $2^in$, where $i \geq 1$, then the equation modifies to $n \left(1 - \frac{3^k}{2^{z}2^i}\right) = \frac{C}{2^{z}2^i}$. The article takes an elementary approach to this problem by calculating the bounds on the values of $\frac{C}{2^{z}2^i}$ and $1 - \frac{3^k}{2^{z}2^i}$. Correspondingly, an upper limit on the integer $n$ is placed that can re-appear in the sequence. The integer $n$ lies in the $(-\infty, 5)$ range, and the limit on the number of odd steps is $k < 3$. Finally, it is shown that no integer chain exists that does not lead to 1.

The importance of small urban green areas has increased in the context of rapid urbanization and densification of the urban tissue. The analysis of these areas through remote sensing has been limited due to the low spatial resolution of freely available satellite images. We propose a timeseries analysis on 3 m resolution Planet images, using GEOBIA and vegetation indices, with the aim of extracting and assessing the quality of small urban green areas in two different climatic and biogeographical regions – temperate (Bucharest, Romania) and mediterranean (Athens, Greece). Our results have shown high accuracy (over 91%) regarding the extraction of small urban green areas in both cities, across all analysed images. The timeseries analysis showed consistency in location for around 55% of the identified surfaces throughout the entire period. The vegetation indices registered higher values in the temperate region, due to the vegetation characteristics and the planning of the two cities. For the same reasons, the increase in vegetation density and quality, as a result of the distance from the city centre and the decrease in the density of built-up areas is more obvious in Athens. The proposed method provides valuable insights in the distribution and quality of small urban green areas at city level and can represent the ground basis for many analyses, currently limited by poor spatial resolution.

Polycystic ovary syndrome (PCOS) is a complex hormonal disorder which impair ovarian function. The adherence to healthy dietary patterns and physical exercise are the first line of recommended treatment for PCOS patients, but it is no clear what type of diet is more adequate. In this case-control study, we explore the association between the adherence to five dietary quality indices widely used and PCOS. We enrolled 126 cases of PCOS and 159 controls (Murcia, Spain). Diagnostic of PCOS and its phenotypes were established following the Rotterdam criteria [hyperandrogenism (H), oligoanovulation (O), polycystic ovaries morphology (POM)]. We used a validated food frequency questionnaires to calculate the scores for five dietary indices: alternate Healthy Eating index (AHEI), AHEI-2010, relative Mediterranean Dietary Score (rMED), alternate Mediterranean Dietary Score (aMED) and Dietary Approaches to Stop Hypertension (DASH). We used multivariable logistic regression to estimate adjusted odds ratios and confidence intervals. In the multivariable analysis, AHEI-2010 index was inversely associated with “H+O” PCOS’ phenotype (ORQ3 VS Q1= 0.1; 95% CI :(0.0; 0.9); P for trend= 0.02). In conclusion, we did not find any statistical significative association between dietary indices and total, anovulatory and ovulatory PCOS, but it seems interesting explore these association among the diverse phenotypes of PCOS in studies with higher sample size.