An odd-dimensional sphere admits a killing vector field, induced by the transform of the unit normal by the complex structure of the ambiant Euclidean space. In this paper, we study orientable hypersurfaces in a Euclidean space those admit a unit Killing vector field and find two characterizations of odd-dimensional spheres. In first result, we show that a complete and simply connected hypersurface of Euclidean space Rn+1, n>1 admits a unit Killing vector field ξ that leaves the shape operator S invariant and has sectional curvatures of plane sections containing ξ positive satisfies S(ξ)=αξ, α mean curvature if and only if n=2m−1, α is constant and the hypersurfaces is isometric to the sphere S2m−1(α2). Similarly, we find another characterization of unit sphere S2(α2) using the smooth function σ=g(S(ξ),ξ) on the hypersurface.

We obtain some generalised Minkowski-type integral formulas for compact Riemannian (resp. spacelike) hypersurfaces in Riemannian (resp. Lorentzian) manifolds admitting an arbitrary vector field that we assume to be timelike in the case where the ambient space is Lorentzian. Some of these formulas generalize existing formulas in the case of conformal and Killing vector fields. We apply these integral formulas to obtain interesting results concerning the characterization of such hypersurfaces in some particular cases such as when the ambient space is Einstein admitting an arbitrary (in particular, conformal or Killing) vector field, and when the hypersurface has constant mean curvature.

In this paper, we define Ulisse Dini-type helicoidal hypersurface with spacelike axis in Minkowski 4-space ${\mathbb{E}}_1^4$ . We compute the Gaussian and the mean curvature of the hypersurface. Moreover, we obtain some special symmetry to the curvatures when they are flat and maximal.

This article investigates the fundamental principles that establish universal limits in physical phenomena, such as the uniformity of physical laws and Energy conservation, leading to the concepts of maximum speed, locality, and maximum density. These principles guide me to explore Quantum Black Holes—relativistically rotating, miniature charged black holes with a singular core at the highest possible density. Uniquely, these Quantum Black Holes maintain all quantized charges, including gravitational ones. The study further demonstrates that quarks and leptons are composed of these Quantum Black Holes, redefining them as the actual elementary particles.Exploring these particles reveals that they emit Energy outward, modifying the curvature of nearby space-time. This discovery provides new insights into local space-time dynamics, characterized by a single equation that includes the influence of all charges and hidden Energy. By the conclusion of this article, I show that Quantum Black Holes offer explanations for several Standard Model deficiencies: the nature of luminous, dark, and anti-Matter; the mass, size, and quantized charges of all elementary particles (including gravitational); the nature of neutrino oscillations; and the mechanism by which electric charges remain bound even though the same type of electric charge components must repeal each other.

Resonance inductive coupling is widely used for wireless power transfer (WPT) in medical applications. In this paper, we analyze the LCL-compensated WPT structure and propose a novel constant voltage transmission system based on gain estimation, without any extra feedback from the receiver. The system is capable for implant neural stimulation where the load impedance and the coupling coefficient are both variable. Compared to existing methods for constant voltage transmission, our approach offers advantages in compact size and the compatibility with the industrial, scientific and medical (ISM) band. We validate the load-independent resonant characteristic and the feasibility of constant voltage transmission using an experimental prototype working at 6.78MHz. Finally, we discuss the structure of the implant stimulator and methods of applying the proposed WPT system.

I want to find an extension of the Hausdorff Measure and Fractal Measure which allows me to compute a unique, satisfying average for functions defined on non-fractal, measurable sets in the sense of Carathedory which has no gauge function.

This study aimed to characterize the antioxidant, mechanical and physical properties of chicken skin gelatin/CMC/Centella asiatica blended film. The influence of Centella asiatica at 0.3% and 0.7% on antioxidant activities; mechanical properties and physical properties of chicken skin gelatin/CMC/Centella asiatica film were investigated. Characterization of the blended films with 0.7% Centella asiatica extract shows higher antioxidant activities with a total phenolic content of 0.36 mg/g of GAE, DPPH of 89.26%, and reducing power of 0.80 nm compared to 0.3% Centella asiatica extract. The addition of 0.3% of Centella extract provide higher value in tensile strength (5.0 × 10⁻² MPa), elongation at break (281%), melting point (131.31 °C), transparency (0.86) but lower UV-light penetration. While the addition of 0.7% Centella extract contribute to higher value in WVP (1.13 × 10⁻⁴ g m⁻¹s⁻¹Pa⁻¹) and puncture test (0.06 N). There are no significant differences between functional groups obtained from this blended film as evaluated by FTIR analysis (p > 0.05). Furthermore, XRD analysis showed the addition of extract decrease the crystallinity of film. In conclusion, the incorporation of Centella asiatica extracts on film greatly increased antioxidant levels and improved some of the mechanical and physical properties of the film blends.

Various means (the arithmetic mean, the geometric mean, the harmonic mean, the power means) are often used as central tendency statistics. A new statistic of such type is offered for a sample from a distribution on the positive semi-axis, the gamma-weighted geometric mean. This statistic is a certain weighted geometric mean with adaptive weights.

The recent Planck Legacy release confirmed the existence of an enhanced lensing amplitude in the cosmic microwave background (CMB) power spectra, which endorses the positive curvature of the early Universe with a confidence level exceeding 99%. In this study, the pre-existing curvature is incorporated to extend the field equations where the derived wave function of the Universe is utilized to model Universe evolution with reference to the scale factor of the early Universe and its radius of curvature upon the emission of the CMB. The wave function reveals both positive and negative solutions, implying that matter and antimatter of early Universe plasma evolve in opposite directions as distinct Universe sides. The wave function indicates that a nascent hyperbolic expansion is followed by a first phase of decelerating expansion away from early plasma during the first 10 Gyr, and then, a second phase of accelerating expansion in reverse directions, whereby both Universe sides free-fall towards each other under gravitational acceleration. Simulations of the predicted conformal curvature evolution demonstrate the fast orbital speed of outer stars owing to the external fields exerted on galaxies as they travel through conformally curved space-time. Finally, the wave function predicts an eventual time-reversal phase comprising rapid spatial contraction that culminates in a Big Crunch, signalling a cyclic Universe. These findings reveal that early plasma could have separated and evolved into distinct sides that collectively and geometrically influencing the Universe evolution, physically explanting the effects attributed to dark matter and energy.

Geometry deals both with analogical thinking and physical/biological observables. Naïve, common-sense descriptions of objects’ shapes and systems’ trajectories in geometric phase spaces may help experimental investigation. For example, very different biological dynamics, as the developmental growth patterns of the oldest known animal (the extinct Dickinsonia) and the human brain electric oscillations, display a striking analogy: when encompassed in abstract geometric spaces, their paths describe the same changes in curvature: from convex, to flat, to concave and vice versa. This dynamical behavior, anticipated by Nicholas de Cusa in his analogical account of “coincidentia oppositorum” (1440), helps to describe widespread biological paths in the manageable terms of concave, flat and convex curves on donut-like structures. Every trajectory taking place on such toroidal manifolds can be located, through a topological technique called Hopf fibration, into a four-dimensional space. We discuss how the correlation between Hopf fibration and Navier-Stokes equations allows us to treat the above-mentioned biological and neuroscientific curved paths in terms of flows taking place into a viscous fluid medium that can be experimentally assessed and quantified.

Taiwan developing offshore wind power to promote green energy and self-electricity production. In this study, a Light Detection and Ranging (Lidar) was set up at Chang-Hua development zone one on the sea and 10km away from the seashore. At Lidar location, WRF (3.33km & 2km grid lengths) model and WAsP were used to simulate the wind speed at various elevations. Three days mean wind speed of simulated results were compared with Lidar data. From the four wind data sets, developed five different comparisons to find an error% and R-Squared values. Comparison between WAsP and Floating Lidar was shown good consistency. Lukang meteorological station 10 years wind observations at 5m height were used for wind farm energy predictions. The yearly variation of energy predictions of traditional and TGC wind farm layouts are compared under purely neutral and stable condition. The one-year cycle average surface heat flux over the Taiwan Strait is negative (-72.5 (W/m2) and 157.13 STD), which represents stable condition. At stable condition TGC (92.39%) and 600(92.44%), wind farms were shown higher efficiency. The Fuhai met mast wind data was used to estimate roughness length and power law exponent. The average roughness lengths are very small and unstable atmosphere.

The scope of this study was twofold: first, to introduce a new method in examining measurement invariance, especially with large-scale studies where a large number of group comparisons are involved: the alignment approach, where only configural invariance is necessary to achieve measurement invariance. Second, to evaluate the psychometric robustness of this approach using real-life data. Particularly, we applied this approach to examine whether the factor structure of a cognitive ability test (PGAT) exhibits measurement invariance across the 26 universities of the Kingdom of Saudi Arabia. The sample consisted of 9,849 graduate students from 26 universities around the Kingdom. The results indicated a robust configural model suggesting that the P-GAT subscales were invariant across the 26 universities. Finally, the aligned factor mean values were estimated, and factor mean comparisons of every group’s mean with all other group means were conducted for both cognitive domains (Verbal and Quantitative). In both domains, King Saud University had the highest mean score among all universities. Moreover, its mean factor score was significantly higher than any other university besides Dammam University. On the other hand, several universities allocated at the northern and Southern borders of the country exhibited the lowest factor mean scores.

The dielectric constant (ε) reflects the ability of a material to align and orient electrical dipoles within its structure in response to an externally applied electric field; the greater the polarizability of molecules, the greater the value of dielectric constant. In this study a data set of 86 polymers was investigated to develop a structure-property quantitative relations (QSPR) model to predict the dielectric constant in polymers. An initial set of 1273 descriptors was used to select a best set of descriptors and to construct two machine learning models with Gradient Boosting Regressor (GB_A and GB_B). The best performing model (GB_A) with 8 descriptors, exhibited a performance of (R2train) = 0.938 and (R2test) = 0.802. The models were internally validated by 5 folds cross-validation, demonstrating robustness. Additionally, using the Accumulative Local Effect (ALE) technique, we analyzed the relationship between the 8 descriptors involved and the impact of these descriptors to dielectric constant of polymers.

When generalized noncommutative Heisenberg algebra accommodating impacts of finite gravitational fields as specified by loop quantum gravity, doubly–special relativity, and string theory, for instance, is thoughtfully applied to the eight-dimensional manifold (M8), the generalization of the Riemannian manifold becomes imminent. By constructing the deformed affine connections on a four-dimensional Riemannian manifold, we have determined the minimal length deformation of Riemann curvature tensor and its contractions, the Ricci curvature tensor, and Ricci scalar. Consequently, we have been able to construct the deformed Einstein tensor. As in Einstein’s classical theory of general relativity, we have proved that the covariant derivative of the deformed Einstein tensor vanishes, as well. We conclude that the minimal length correction suggests a correction to the spacetime curvature which is manifest in the additional curvature terms of the corrected Riemann tensor and its contractions. Accordingly, the spacetime curvature endows additional curvature and geometrical structure.

Hubble expansion may be considered as a velocity per photon travel time rather than as velocity or redshift per distance. Dimensionally, this is an acceleration and will have an associated curvature of space under general relativity. This paper explores this theoretical curvature as an extension to the spacetime manifold of general relativity, generating a modified solution with three additional non-zero Christoffel symbols, and a reformulated Ricci tensor and curvature. The observational consequences of this reformulation were compared with the ΛCDM model for luminosity distance using the extensive type Ia supernovae (SNe Ia) data with redshift corrected to the CMB, and for angular diameter distance with the recent baryonic acoustic oscillation (BAO) data. For the SNe Ia data, the modified GR and ΛCDM models differed by −0.15+0.11μB mag. over zcmb=0.01−1.3, with overall weighted RMS errors of ±0.136μB mag for modified GR and ±0.151μB mag for ΛCDM espectively. The BAO measures spanned a range z=0.106−2.36, with weighted RMS errors of ±0.034 Mpc with H0=67.6±0.25 for the modified GR model, and ±0.085 Mpc with H0=70.0±0.25 for the ΛCDM model. The derived GR metric for this new solution describes both the SNe Ia and the BAO observations with comparable accuracy to ΛCDM without requiring the inclusion of dark matter or w’-corrected dark energy.

We provide a detailed analysis of the electronic properties of graphene-like materials with charge carriers living on a curved substrate, focusing in particular on constant negative-curvature spacetime. An explicit parametrization is also worked out in the remarkable case of Beltrami geometry, with an analytic solution for the pseudoparticles modes living on the curved bidimensional surface. We will then exploit the correspondent massless Dirac description, to determine how it affects the sample local density of states.

This paper propose a kernel geometric mean metric learning (KGMML) algorithm. The basic idea is to obtain the closed-form solution of the geometric mean metric learning (GMML) algorithm in the high-dimensional feature space determined by the kernel function. Then, the solution is generalized as a form of kernel matrix by using the integral representation of the weighted geometric mean and the Woodbury matrix in this new feature space. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.

Background: Fold change is widely used in biomedical research to quantify the magnitude of group differences in omics variables. However, the exact calculation method is often not reported, leading to inconsistent results. This study re-evaluates different fold-change calculation methods and provides a clear preference. Methods: Data scenarios with different distributions of treatment/test and reference data were created to challenge the assumption of interchangeable calculation methods. The main difference lies in the definition of the expected values of the groups used to calculate the log ratio, which is the basis of the fold change calculation. In addition, a multi-omics biomedical dataset was analyzed. Results: Using the arithmetic mean as the expected value for the treatment and reference groups resulted in incorrect fold change values more frequently than other methods, especially when the standard deviations between subgroups differed widely. Conclusions: The inferior arithmetic mean method is often perceived as the standard, although mathematically different equations are possible that differ mainly in the estimation of the expected value. Alternatives that define expectation by median, geometric mean, or paired fold change combinations are less susceptible to violations of equal variances or similar treatment/reference distributions.

Induction heating is a fast, reproducible, and efficient heating method used in various manufacturing processes. However, there is no established additive manufacturing (AM) process based on induction heating using wire as feedstock. This study investigates a novel approach to AM based on inductive heating, where a steel wire is melted and droplets are detached periodically using a two-winding induction coil. The process parameters and energy input into the droplets are characterized. The induction generator exhibits sluggish response to the excitation voltage, resulting in a lag in the coil current. The process is captured using a high-speed camera, revealing regular droplet formation and uniform size and shape when operated within an appropriate process window. Larger drops and increased spatter formation occur outside this window. The proposed method allows for the production of droplets with almost spherical shapes. Further analysis and characterization of droplet formation and energy input provide insights into process optimization and overall efficiency.

This study explores students’ understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.

Clustering, or otherwise known as cluster analysis, is a learning problem that takes place without any human supervision. This technique has often been utilized, much efficiently, in data analysis, and serves for observing and identifying interesting, useful, or desired patterns in the said data. The clustering technique functions by performing a structured division of the data involved, in similar objects based on the characteristics that it identifies. This process results in the formation of groups, and each group that is formed, is called a cluster. A single said cluster consists of objects from the data, that have similarities among other objects found in the same cluster, and resemble differences when compared to objects identified from the data that now exist in other clusters. The process of clustering is very significant in various aspects of data analysis, as it determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data. A textbook or otherwise said, good criteria, does not exist in this method of cluster analysis. That is because this process is so different and so customizable for every user, that needs it in his/her various and different needs. There is no outright best clustering algorithm, as it massively depends on the user’s scenario and needs. This paper is intended to compare and study two different clustering algorithms. The algorithms under investigation are k-mean and mean shift. These algorithms are compared according to the following factors: time complexity, training, prediction performance and accuracy of the clustering algorithms.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

This article presents a novel approach to understanding the influence of electric Energy on space-time curvature. EFE actual calculations refer solely to gravitational charges. In this article, I expand them to include the electric charge with calculations carried specifically for electric charges, with exciting results. The article leverages the universal consistency of physical laws, applying the known effects of gravitational charges on space-time curvature to electric charges. The research focuses on calculating the specific impact of electric charges on space-time curvature, rooted in the principle that space-time curvature is omnipresent. The findings reveal that space-time curvature's alteration due to an electric charge is influenced by various factors, including the charge's location, magnitude, mass, density, associated electric field, and its motion through space-time. Notably, the conversion factor for electric charges differs from the conversion factor for gravitational charges. These insights significantly enhance our understanding of electromagnetism and general relativity, paving the way for a more profound comprehension of electric charges.

The conventional rolled-up model for carbon nanocones assumes that the cone is constructed from a rolled-up graphene sheet joined seamlessly, which predicts five distinct vertex angles. This model completely ignores any effects due to the changing curvature and all bond lengths and bond angles are assumed to be those for the planar graphene sheet. Clearly curvature effects will become more important closest to the cone vertex, and especially so for the cones with the smaller apex angles. Here we construct carbon nanocones which in the assembled cone are assumed to comprise bond lengths and bond angles which are, as far as possible, equal throughout the structure at the same distance from the conical apex. Predicted bond angles and bond lengths are shown to agree well with those obtained by relaxing the conventional rolled-up model using the LAMMPS software. The major objective here is not simply to model physically realisable carbon nanocones for which numerical procedures are far superior, but rather to produce an improved model that takes into account curvature effects close to the vertex, and from which we may determine an analytical formula which represents an improvement on that for the conventional rolled-up model.

The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs since the FIM only accounts for the linear variation of the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO) MBDOE, where model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of Baker's yeast.

In recent times, there has been a growing interest in the use of control charts as a feedback process monitoring technique. Particularly, CUSUM schemes have been proven to be efficient for monitoring processes where the magnitude of the sustained mean shifts is small or moderate. However, because of the constant control limits, the detection ability of CUSUM schemes becomes slow at the initial set-up of the process. The fast initial response FIR feature has often been used to enhance it at the process startup. Meanwhile, the dynamism of real-life problems has always encouraged a more sensitive CUSUM scheme capable of detecting process shifts more rapidly. In this paper, an improved CUSUM scheme for monitoring process mean is proposed. This scheme will be substantial for monitoring processes whose observations are obtained at a distant time interval for example hourly, daily or weekly and where the sustained shifts are assumed to be small or moderate. To demonstrate the practical applications of the proposed scheme, we present its real-life application using datasets from a bottling company and petroleum refinery laboratory.

In the paper, by virtue of a Lévy–Khintchine representation and an alternative integral representation for the weighted geometric mean, the authors establish a Lévy–Khintchine representation and an alternative integral representation for the Toader–Qi mean. Moreover, the authors also collect an probabilistic interpretation and applications in engineering of the Toader–Qi mean.

A novel chemically cross-linked hydrogel was prepared through the utilization of the nor-bornene (Nb)-methyl tetrazine (mTz) click reaction, derived from carboxymethyl cellulose (CMC) and alginate (Alg). The hydrogel was designed to generate reactive oxygen species (ROS) from NIR-dye, indocyanine green (ICG) for a combined photothermal and photodynamic ther-apy (PTT/PDT). The cross-linking of Nb and mTz moieties occurred via an inverse elec-tron-demand Diels-Alder reaction under physiological conditions avoiding the need for a cata-lyst. The resulting hydrogels exhibited viscoelastic properties (G′ ~ 492-270 Pa) and high porosi-ty. The hydrogels were found to be injectable with tunable mechanical characteristics. The ICG encapsulated hydrogels demonstrated ROS generation ability under NIR exposure. The ROS production was investigated through DPBF assays to access photodynamic effect (with NIR irra-diation at 1-2W for 5-15 min). The temperature of the ICG-loaded hydrogels was also raised up-on the NIR irradiation to eradicate tumor cells photothermally. In vitro cytocompatibility as-sessments revealed the non-toxic nature of CMC-Nb and Alg-mTz towards HEK-293 cells. Fur-thermore, the ICG-loaded hydrogels effectively inhibited the metabolic activity of Hela cells following NIR exposure. This innovative hydrogel system holds promise for applications in combined PTT and PDT.

This paper is devoted to study the gravitational lensing for Curvature-coupled antisymmetric wormhole solution to compute the bending angle of light by utilizing the Gibbons and Werner technique. To achieve this, we find the Gaussian optical curvature and then apply Gauss-Bonnet theorem in the weak field limits. We also study the effects of plasma as well as dark matter mediums on the bending angle. Moreover, we analyze the graphical behaviour of the deflection angle $\alpha$ with respect to the impact parameter $\sigma$ and minimal radius $r_{0}$ in non-plasma and plasma mediums. We examine that deflection angle shows direct relation with $r_{0}$ such that large values of $r_{0}$ gives large deflection angle and small values of $r_{0}$ gives small deflection angle. For impact parameter $\sigma$, deflection angle $\alpha$ shows inverse relation. Additionally, we derive the deflection angle of light by using Keeton and Petters method and compare with the previous results.

Planck's constant plays an important role in quantum mechanics but has little physical meaning apart from its contribution to the formulas. Evaluating each of the constant's unit dimensions gives a more granular account of the physical phenomena described by the equations. These formulas show how classical and quantum mechanical equations are related, and they give consistent descriptions of phenomena like momentum and energy in classical and quantum systems.

Background and objectives: sickle cell disease is the most common hemoglobinopathy in the world. It is considered to be a real public health problem. Sickle cell patients are subjected to several factors causing inflammation such as iron metabolism. The study aimed to look for inflammation in children with sickle cell disease in Cameroon, identify the factors associated with inflammation, and raise the consequences for the patient including the iron profile and the profile of the hemogram. Materials and methods: We conducted an analytical cross-sectional study for 03 months. The sickle cell disease patients coming and/or followed at the Hematology Department of the Regional Hospital of Bafoussam and the Central Hospital of Yaoundé have been recruited. The exploration of inflammation was made by determining CRP, IL6, and ferritin concentrations. The hematological parameters and iron profile were evaluated using standard methods. Statistical analysis of the data was performed; Univariate and multivariate logistic regression analyses allowed to identification of factors associated with inflammation in patients, using the statistical tool R version 4.1.1.. The proportions were compared with the chi-square test when the expected numbers were greater than 5 and the Fisher test when not. Results: The frequency of inflammation in the population was 42.3%. Hyperferritinemia was significantly greater (p<0.001) in patients with inflammation compared to the non-inflammatory patients (96.8% and 76.7% respectively). Patients with inflammation showed a significant elevation of iron parameters (p<0.05). In addition, ferritin and IL6 elevation were associated with inflammation during sickle cell disease respectively (Or = 4.96; 95% CI [1.15-36.42]; p=0.056) and (Or =6.23; 95% CI [1.43-45.96]; p=0.030). Conclusions: The elevated iron in plasma is an effect of inflammation in sickle cell patients. Hence the need of controlling inflammation and iron in the latter is necessary.

This paper presents a control algorithm for soft-switching series LC converters. The conventional voltage-to-voltage controller is split into a master and a slave controller. The master controller implements constant-current-constant-voltage (CCCV) control, required for demanding applications, i.e. lithium battery charging or laboratory power supplies. It defines the set-current for the open-loop current slave controller, which generates the PWM parameters. The power supply achieves fast large-signal responses, e.g. from 5 V to 24 V, where 95% of the target value is reached in less than 400 µs. The design is evaluated extensively in simulation and on a prototype. A consensus between simulation and measurement is achieved.

Despite the successful reconciliation of special relativity and quantum mechanics (QM), a good century ago, general relativity (GR) in its current classical formulation still does not compile with QM. While GR gives precise sensical predictions at large scales, QM is obviously dominated at small scales! We think that the everlasting battle for exploring and understanding the Universe and for privileging a consistent perception of reality is therefore awaiting a consolidator rather than a conqueror. This should be capable of either unifying the two different benchmarks or at least bringing one closer to the other! The latter describes the consolidating approach, which is based on extending QM to relativistic energies and gravitational fields and generalizing Riemann to discretized Finsler geometry. Some properties of the additional geometric structures and curvatures which are disclosed by the proposed quantization and apparently overlooked in Einstein's GR, are analytically and numerically characterized. The analytical analyses introduce dynamics with possible nonlinear connections. We conclude that i) additional geometric structures and curvatures are intrinsic essential and ii) the spacetime at the quantum scale is no longer smooth or continuous. A maximal proper force is predicted, which maximally gravitationally accelerates a test particle and importantly manifests the quantum geometric nature of the generalized spacetime curvature.

The Einstein-Lovelock theory contains an infinite series of corrections to the Einstein term with an increasing power of the curvature. It is well-known that for large black holes the lowest (Gauss-Bonnet) term is the dominant one, while for smaller black holes higher curvature corrections become important. We will show that if one is limited by positive values of the coupling constants, then the dynamical instability of black holes serves as an effective cut-off of influence of higher curvature corrections in the 4D Einstein-Lovelock approach: the higher is the order of the Lovelock term, the smaller is the maximal value of the coupling constant allowing for stability, so that effectively only a first few orders can deform the observable values seemingly. For negative values of coupling constants this is not so, and, despite some suppression of higher order terms also occurs due to the decreasing threshold values of the coupling constant, this does not lead to an noticeable opportunity to neglect higher order corrections. In the case a lot of orders of Lovelock theory are taken into account, so that the black-hole solution depends on a great number of coupling constants, we propose a compact description of it in terms of only two or three parameters encoding all the observable values.

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

The biophysical consequences of nanoscale curvature have been challenging to resolve due to size-dependent membrane behavior and the experimental resolution limits imposed by optical diffraction. Recent advances in nanoengineering and super-resolution techniques have enabled new capabilities for creating and observing curvature. In particular, draping supported lipid bilayers over lithographically patterned substrates provides a model system for endocytic pits. The experiments and simulations presented below describe the possible detection of membrane curvature through fluorescence recovery after photobleaching (FRAP), fluorescence correlation spectroscopy (FCS), single particle tracking (SPT), and polarized localization microscopy (PLM). FRAP and FCS depend on diffraction-limited illumination and detection. In particular, a simulation of FRAP shows no effects on lipids diffusion due to a 50 nm diameter membrane bud at any stage in the budding process. Simulated FCS demonstrated small effects due to a 50 nm radius membrane bud that was amplified with curvature-dependent lipid mobility changes. However, PLM and SPT achieve sub-diffraction-limited resolution of membrane budding and lipid mobility through the identification of the single-lipid positions with ≤15 nm spatial and ≤20 ms temporal resolution. By mapping the single-lipid step lengths to locations on the membrane, the effects of curvature on lipid behavior have been resolved.

In modern physics, it is assumed that the Planck length is a derived constant from Newton's gravitational constant, the Planck constant and the speed of light, $l_p=\sqrt{\frac{G\hbar}{c^3}}$. This was first discovered by Max Planck in 1899. We suggest a way to find the Planck length independent of any knowledge of Newton's gravitational constant or the Planck constant, but still dependent on the speed of light (directly or indirectly).

(1) Background: Malaria remains a global public health problem. Unfortunately, the resistance of malaria vectors to insecticides commonly used threatens disease control and elimination efforts. Molecular mechanisms helping some malaria vectors to now survive to greater doses of insecticides remains poorly understood. Here, we elucidated the pattern of resistance escalation in the main malaria vector Anopheles gambiae in a pesticide-driven agricultural hotspot in Cameroon and its impact on vector control tools; (2) Methods: Larval stages and indoor blood-fed females (F0) were collected in Mangoum in May and November and forced to lay eggs; the emerging mosquitoes were used for WHO tube, synergist and cone tests. Molecular identification was done using SINE PCR whereas TaqMan-based PCR was used for genotyping of L1014F/S and N1575Y kdr and the G119S-ACE1 resistance markers. Transcription profile of candidate resistance genes was performed using qRT-PCR methods. Characterization of the breeding water and soil from Mangoum was also performed using HPLC technique; (3) Results: An. gambiae s.s. was the only species in Mangoum with 4.10 % infection with Plasmodium. These mosquitoes were resistant to all the four classes of insecticides with mortality rates &lt;7% for pyrethroids and DDT and &lt;54% for carbamates and organophophates. This population also exhibited high resistance intensity to pyrethroids (permethrin, alpha-cypermethrin and deltamethrin) after exposure to 5X and 10X discriminating doses and Synergist assays with PBO revealed only a partial recovery of susceptibility to permethrin, alpha-cypermethrin and deltamethrin. Only PBO-based nets (Olyset plus and permaNet 3.0) and Royal Guard showed an optimal efficacy. A high amount of alpha-cypermethrin was detected in breeding sites (5.16 fold LOD) suggesting ongoing selection from agricultural pesticides. The 1014F-kdr allele was fixed (100%) whereas the 1575Y-kdr (37.5%) and the 119S Ace-1R (51.1%) are moderately present. Elevated expression of P450s respectively in permethrin and deltamethrin resistant mosquitoes [CYP6M2 (10 and 34-fold), CYP6Z1(17 and 29-fold), CYP6Z2 (13 and 65-fold), CYP9K1 (13 and 87-fold)] supports their role in the observed resistance besides other mechanisms including chemosensory genes as SAP1 (28 and 13-fold), SAP2 (5 and 5-fold),SAP3 (24 and 8-fold) and cuticular genes as CYP4G16 (6 and 8-fold) and CYP4G17 (5 and 27-fold). However, these candidate genes were not associated with resistance escalation as expression level did not differ significantly between 1x, 5x and 10x surviving mosquitoes. (4) Conclusions: Intensive and multiple resistance is being selected in malaria vectors from pesticide-based agricultural hotspot of Cameroon leading to loss of efficacy of pyrethroid-only nets. Further studies are needed to decipher the molecular basis underlying such resistance escalation to better assess its impact on control interventions.

In this study, we investigate the behavior of randomly moving particles with a defined average energy, focusing on their biased motion around a specific point. These particles' velocity magnitudes follow a Maxwell distribution with a specific scale parameter. Our analysis derives the stochastic rotation rules for these particles and introduces the Ito equation conditions for biased stochastic rotation at a given curl value. We also consider the special relativistic-like effects in this context. The findings are validated through a representative example.

In this paper, we investigate the effects of mean stress, multiaxial loading, and residual stresses on the fatigue life of springs. We study the fatigue life of a homogeneously stressed material subjected to cyclic loading with nonzero mean stress. Traditional methods for estimating fatigue life are based on Goodman and HAIGH diagrams. The formal analytical descriptions, namely "stress-life" and "strain-life" approaches, are found to be more suitable for the numerical methods. The fatigue analysis method described above, which describes crack growth per cycle, is extended. The extensions allow consideration of the mean stress of a load cycle. Closed-form expressions for crack length versus number of cycles are derived. The complementary effects on the fatigue life of springs, which ultimately have a significant influence on the fatigue life of springs, are summarized. For the proposed unified fatigue life functions, the ranges for the stress loading factor are extended by introducing the effective stress intensity. The solution leads to the factor range for the effective stress intensity, the effective mean value of the stress intensity factor and the effective stress ratio. The developed method assumes the homogeneous stress state in the whole spring element. For the non-homogeneously loaded structural elements, the weak-link concept is applied to account for fatigue.

Despite the efforts made to stop the tuberculosis (TB) epidemic, it still remains one of the leading causes of death from an infectious disease. Previous work in the group uncovered a new family of amides which showed promising activities against Mycobacterium tuberculosis. A closer look at the literature showed that these compounds are structurally related to the DNB family of DprE1 inhibitors, so, we decided to study a wide range of substituted amides and determine their activity, focusing on unexplored structures related to the dinitrobenzamides (DNB) found in the literature. To synthesize our library of compounds we started from 3,5-dinitrobenzoic acid to form the nitroaromatic core that is characteristic of the DNB’s, to which we then added linear or cyclic amine moieties. Additionally, the impact of terminal aromatic moieties was also assessed for some derivatives, via an ether, ester, or amide bond. In order to obtain the desired derivatives, multiple synthetic approaches were used, mainly focused on nucleophilic addition/elimination reactions, SN2 reactions and Mitsunobu reactions. The activity was impacted mainly by two structural features, the addition of an aromatic moiety as a terminal group and the type of the linker. The most interesting compounds exhibited activities comparable to isoniazid and DNB1. Computational studies were also performed aimed at understanding their possible interactions with DprE1. The most active compounds are a good starting point for further development, and we plan to study an extended family of compounds based in those structures.

In document forensic, Ink mismatch relays very important information about forgeries in this way we can find out the authenticity of documents. Finding out and distinguishing these unique inks from the multispectral document is very challenging task. In this paper we proposed the method to identify the inks using clustering. We used K-Mean clustering instead of widely known Fuzzy C-Means Clustering (FCM) and successfully identity the number of inks. For the purpose of optimizing and improving our results we used two optimization techniques such as Elbow and silhouette optimization techniques.

The formulation and analytic solution of a new mathematical model with constitutive curvature for analysis of tunnel ventilation shaft wall is proposed. Based on the Mindlin-Reissner theory for thick shells, this model also takes into account the shell constitutive curvature and considers an expression of the shear correction factor variable (αn) in terms of the thickness (h) and the radius of curvature (R). The main advantage of the proposed model is that it has the possibility to analyze thin, medium and thick tunnel ventilation shafts. As a result, two comparisons were made: the first one, between the new model and the Mindlin-Reissner model without constitutive curvature with the shear correction factor (α_n=6/5) as a constant, and the other, between the new model and the tridimensional numerical models (solids and shells) obtained by finite element method for different slenderness ratios (h/R). The limitation of the proposed model is that it is to be formulated for a general linear-elastic and axial-symmetrical state with continuous distribution of the mass.

This paper attempts to address the phenomenon of normal vibrations, (referred to as dynamic vibrations) occurring on a surface which is already in vibrational motion due to other kinematic phenomena. Such a surface will have a metric tensor, normal, and ambient velocity which diverges from the surface’s original various dynamic tensorial descriptors. This paper formulates the wave equation defined in a coordinate space, and extends the equation to observe vibrations on a surface with the use of the Laplace-Beltrami operator in a tensorial fashion drawing on conventions from the newly established Calculus of Moving Surfaces (CMS). The Paper then identifies the way which these normal vibrations will manifest within ambient space. Finally, a counter-intuitive relation between the magnitude of such dynamic vibrations and dynamic surface’s time-dependent mean curvature presents itself, for which dynamic vibrations superimposed on original dynamic motion will eliminate the other, and the surface remains static under an arbitrary initial motion. From this condition, resubstitution within the wave equation yields a novel coupled PDE system which within contains the time-evolution of the surface’s mean curvature and its dynamic vibrations. This analysis can have application for algorithms designed for mechanical stabilization during seismic activity, as well as analyzing stabilization algorithms for other various applications and can also have application with respect to biotechnological innovations for analyzing properties defined on the surface of cell-Like biological entities such as metabolism, lipid content, and actin dynamics.

This paper employs the two-step procedure developed by Cheung and Ng (1996) to analyze the causality-in-mean and causality-in-variance between the housing and stock markets of the UK. The empirical findings make two key contributions. First, although previous studies have indicated a one-way causal relation from the housing market to the stock market in the UK, this paper discovered a two-way causal relation between them. Second, a causality-in-variance as well as a causality-in-mean was detected from the housing market to the stock market.

With reference to our earlier published views on large nuclear gravitational constant , nuclear elementary charge and strong coupling constant , in this paper, we present simple relations for nuclear stability range, binding energy of isotopes and magic proton numbers.

We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model (NLSM). We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued (2/π)ρ_c0 (ρ_c0 the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant 2/π in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. The equivalence principle is also generalized to the quantum level.

In a particle swarm with a fixed kinetic energy, the constituent particles move randomly and their velocity magnitudes follow a Maxwell distribution characterized by specific parameters. Within a certain time frame, particles in a sub-swarm may exhibit a bias in their movement direction. Thus, the particles may exhibit a special characteristic (biased random motion), where the group velocity in a particular direction remains constant u. For this biased particle swarm, composed of randomly moving particles with a fixed average speed c, particles have a higher probability of moving in a specific direction. Conversely, their likelihood of moving in all other directions is equally reduced. This study starts from the perspective of biased random walks and using Mathematica software proves that the diffusion rate of particles (in the reference frame R_u observed from R₀) in all directions is slower than that of an unbiased particle swarm with the same average speed c. Specifically, the degree of reduction is determined by the Lorentz-like factor. Lastly, we present the Ito equation for this biased random motion and provide associated verification examples. This study aims to serve as a reference for comprehending the underlying principles of the special relativity effect.

Measurement uncertainty is typically expressed in terms of a symmetric interval , where denotes the measurement result and the expanded uncertainty. However, in the case of heteroscedasticity, symmetric uncertainty intervals can be misleading. In this paper, a different approach for the calculation of uncertainty intervals is introduced. This approach is applicable when a validation study has been conducted with samples with known concentrations. It will be shown how, under certain circumstances, asymmetric uncertainty intervals arise quite naturally and lead to more reliable uncertainty intervals.

Functional Data Analysis (FDA) is a relatively new field of statistics dealing with data expressed in the form of functions. FDA methodologies can be easily extended to the study of imaging data, an application proposed in Wang et al. (2020), where the authors settle the mathematical groundwork and properties of the proposed estimators. This methodology allows for the estimation of mean functions and simultaneous confidence corridors (SCC), also known as simultaneous confidence bands, for imaging data and for the difference between two groups of images. This is especially relevant for the field of medical imaging, as one of the most extended research setups consists on the comparison between two groups of images, a pathological set against a control set. FDA applied to medical imaging presents at least two advantages compared to previous methodologies: it avoids loss of information in complex data structures and avoids the multiple comparison problem arising from traditional pixel-to-pixel comparisons. Nonetheless, computing times for this technique have only been explored in reduced and simulated setups (Arias-López et al., 2021). In the present article, we apply this procedure to a practical case with data extracted from open neuroimaging databases and then measure computing times for the construction of Delaunay triangulations, and for the computation of mean function and SCC for one-group and two-group approaches. The results suggest that previous researcher has been too conservative in its parameter selection and that computing times for this methodology are reasonable, confirming that this method should be further studied and applied to the field of medical imaging.

This study evaluates the historical mean surface temperature (hereafter T2m) and examines how T2m changes over East Africa (EA) in the 21^st century using CMIP6 models. An evaluation was conducted based on mean state, trends, and statistical metrics (Bias, Correlation Coefficient, Root Mean Square Difference, and Taylor skill score). For future projections over EA, five best performing CMIP6 models (based on their performance ranking in historical mean temperature simulations) under the shared socioeconomic pathways SSP2-4.5 and SSP5-8.5 scenarios were employed. The historical simulations reveal an overestimation of the mean annual T2m cycle over the study region with fewer models depicting underestimations. Further, CMIP6 models reproduce the spatial and temporal trends within the observed range proximity. Overall, the best performing models are as follows: FGOALS-g3, HadGEM-GC31-LL, MPI-ESM2-LR, CNRM-CM6-1, and IPSL-CM6A-LR. During the three-time slice under consideration, the Multi Model Ensemble (MME) project many changes during the late period (2080 – 2100) with expected mean changes at 2.4 °C for SSP2-4.5 and 4.4 °C for the SSP5-8.5 scenario. The magnitude of change based on Sen’s slope estimator and Mann-Kendall test reveal significant increasing tendencies with projections of 0.24°C decade-1 (0.65°C decade-1) under SSP2-4.5 (SSP5-8.5) scenarios. The findings from this study illustrate higher warming in the latest model outputs of CMIP6 relative to its predecessor, despite identical instantaneous radiative forcing.

Hamacher operation which is generalization of the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments or different criteria and don’t make calculation redundancy, meanwhile, the normal intuitionistic fuzzy numbers (NIFNs) can depict distinctively normal distribution information in practical decision making. In this paper, a multi-criteria group decision-making (MCGDM) problem is researched under the NIFNs environment, and a new MCGDM approach is introduced on the basis of the Hamacher operation. Firstly, according to Hamacher t-conorm and t-norm, some operational laws of NIFNs are presented. Secondly, it is noticed that Heronian mean can’t only once take into account mutual relation between attribute values once, but also consider the correlation between input argument and itself. Therefore, we develop some operators and study their properties in order to aggregate normal intuitionistic fuzzy numbers information, these operators include Hamacher Heronian mean (NIFHHM), Hamacher weighted Heronian mean (NIFHWHM), Hamacher geometric Heronian mean (NIFHGHM) and Hamacher weighted geometric Heronian mean (NIFHWGHM). Furthermore, we apply the proposed operators to the MCGDM problem and present a new method. The main characteristics of this new method involve that: (1) it is suitable to make decision under the normal intuitionistic fuzzy numbers environment and more reliable and reasonable to aggregate the normal distribution information. (2) it utilizes Hamacher operation which can provide more reliable and flexible decision-making results and offer an effective and powerful mathematic tool for the MAGDM under uncertainty. (3) it uses the Heronian mean operator which can considers relationships between the input arguments or the attributes and don’t brings subsequently about redundancy. Lastly, an application is given for showing the feasibility and effectiveness of the presented method in this paper.

Recent observations of the dark energy density have demonstrated the fine-tuning problem, and the challenges faced by theoretical modeling. In this study, we apply the self-similar symmetry (SSS) model, describing the hierarchical structure of the universe based on the Dirac large numbers hypothesis, to Einstein's cosmological term. We introduce a new similarity dimension, D_B, in the SSS model. Using the D_B SSS model, the cosmological constant Λ is simply expressed as a function of the cosmic microwave background (CMB) temperature. The result shows that both the gravitational constant G and Λ are coupled with the CMB temperature, which simplifies the solution of Einstein's field equations for the variable Λ-G model.

We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. A change of variables, introduced in [13], transforms the Mean Field Games system into a system of two coupled kinetic Fokker-Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.

We show that the implementation of the 1/c² transverse current-current interaction between electrons into the standard self-consistent electron BCS model in bulk under thermal equilibrium ensures in the stable superconductive phase the full compensation of a constant external magnetic field by the internal magnetic field created by the electrons i.e. one has an ideal diamagnet. However, no proof of the phenomenological London equation emerges within the bulk approach.

The stage of a super-early scale-invariant Universe is considered on the basis of the Poincaré–Weyl gauge theory of gravity in a Cartan–Weyl space-time. An approximate solution has been found that demonstrates an inflationary behavior of the scale factor and, at the same time, a sharp exponential decrease in the effective cosmological constant from a huge value at the beginning of the Big Bang to an extremely small (but not zero) value in the modern era, which solves the well-known “cosmological constant problem”.

In this work, the author employs the quantum hydrodynamic formalism to achieve the geometrization of spacetime for describing the gravitational interaction within the framework of quantum theory. This approach allows for the development of an equation of gravity that is mathematically connected to the fermion and boson fields. This achievement is accomplished by incorporating two fundamental principles: covariance of the quantum field equations and the principle of least action. By considering these principles, a theory is established that enables the calculation of gravitational corrections to Quantum Electrodynamics, and potentially, to the standard model of particle physics as well. The theory also provides an explanation for two phenomena: the existence of a cosmological pressure density similar to quintessence, that is compatible with the small value of the observed cosmological constant, and the breaking of matter-antimatter symmetry at high energies offering insights into why there is an imbalance between the two in the early universe. In the cosmological modeling of the theory, there exists a proposal to account for the formation of supermassive black holes that are accompanied by their own surrounding galaxies, without relying on the process of mass accretion. The model, in accordance with recent observations conducted by the James Webb Space Telescope, supports the notion that galactic configurations were established relatively early in the history of the universe, shortly after the occurrence of the Big Bang.

Here we will model the curvature and contraction of space-time using as a basis the equation of state of an ideal gas and the Hawking´s equation for the temperature of a black hole. We will use this mathematical model to hypothesize that the Boltzmann´s constant depends on the state of matter, that is, there is a known Boltzmann´s constant for flat space-time and an effective Boltzmann´s constant for curved space-time. This model will allow us to quantify the structure of space-time and will serve as a basis to determine the origin of gravity and the origin of elementary particles. Using the Shannon-Boltzmann-Gibbs entropy relation, we will demonstrate that information is not lost and depends on the state of matter, the information is encoded and depends on the effective Boltzmann´s constant.

This study examines the improvement in coupled intercomparison project phase six (CMIP6) models against the predecessor CMIP5 in simulating mean and extreme precipitation over the East Africa region. The study compares the climatology of the precipitation indices simulated by the CMIP models with the CHIRPS dataset using robust statistical techniques for 1981 – 2005. The results display the varying performance of the general circulation models (GCMs) in the simulation of annual and seasonal precipitation climatology over the study domain. CMIP6-MME shows improved performance in the local annual mean cycle simulation with a better representation of two peaks, especially the MAM rainfall relative to its predecessor. Moreover, simulation of extreme indices is well captured in CMIP6 models relative to its predecessor. The CMIP6-MME performed better than the CMIP5-MME with lesser biases in simulating SDII, CDD, and R20mm over East Africa. Remarkably, most CMIP6 models are unable to simulate extremely wet days (R95p). A few CMIP6 models (e.g., NorESM2-MM and CNRM-CM6-1) depicts robust performance in reproducing the observed indices across all analyses. Conversely, OND season shows the overestimation of some indices (i.e., R95p, PRCPTOT), except for SDII, CDD, and R20mm. Consistent with other studies, the mean ensemble performance for both CMIP5/6 shows better performance due to the cancellation of some systematic errors in the individual models. Generally, the CMIP6 depicts improved performance in the simulation of MAM season akin CMIP5 models. However, the new model generation is still marred with uncertainty, thereby depicting substandard performance over the East Africa domain. This calls for further investigation of attribution studies into the sources of persistent systematic biases and a prerequisite for identifying individual models with robust features that can accurately simulate observed patterns for future usage.

Noise reduction in medical images is a perplexing undertaking for the researchers in digital image processing. Noise generates maximum critical disturbances as well as touches the medical images quality, ultrasound images in the field of biomedical imaging. The image is normally considered as gathering of data and existence of noises degradation the image quality. It ought to be vital to reestablish the original image noises for accomplishing maximum data from images. Medical images are debased through noise through its transmission and procurement. Image with noise reduce the image contrast and resolution, thereby decreasing the diagnostic values of the medical image. This paper mainly focuses on Gaussian noise, Pepper noise, Uniform noise, Salt and Speckle noise. Different filtering techniques can be adapted for noise declining to improve the visual quality as well as reorganization of images. Here four types of noises have been undertaken and applied on medical images. Besides numerous filtering methods like Gaussian, median, mean and Weiner applied for noise reduction as well as estimate the performance of filter through the parameters like mean square error (MSE), peak signal to noise ratio (PSNR), Average difference value (AD) and Maximum difference value (MD) to diminish the noises without corrupting the medical image data.

An approach to the assessment of probabilistic inference is described which quantifies the performance on the probability scale. From both information and Bayesian theory, the central tendency of an inference is proven to be the geometric mean of the probabilities reported for the actual outcome and is referred to as the “Accuracy.” Upper and lower error bars on the accuracy are provided by the arithmetic mean and the -2/3 mean. The arithmetic is called the “Decisiveness” due to its similarity with the cost of a decision and the -2/3 mean is called the “Robustness”, due to its sensitivity to outlier errors. Visualization of inference performance is facilitated by plotting the reported model probabilities versus the histogram calculated source probabilities. The visualization of the calibration between model and source is summarized on both axes by the arithmetic, geometric, and -2/3 means. From information theory, the performance of the inference is related to the cross-entropy between the model and source distribution. Just as cross-entropy is the sum of the entropy and the divergence; the accuracy of a model can be decomposed into a component due to the source uncertainty and the divergence between the source and model. Translated to the probability domain these quantities are plotted as the average model probability versus the average source probability. The divergence probability is the average model probability divided by the average source probability. When an inference is over/under-confident, the arithmetic mean of the model increases/decreases, while the -2/3 mean decreases/increases, respectively.

We propose a promising model of discrete spacetime based on nonassociative geometry and complex networks. Our approach treats space as a simplicial 3-complex (or complex network), built from "atoms" of spacetime and entangled states forming n-dimensional simplices (n=1,2,3). At large scales, a highly connected network is a coarse, discrete representation of a smooth spacetime. We show that for high temperatures, the network describes disconnected discrete space. At the Planck temperature, the system experiences the phase transition, and for low temperatures, the space becomes a triangulated discrete space. We show that the cosmological constant depends on the universe’s topology. The "foamy" structure, analogous to Wheeler’s "spacetime foam," significantly contributes to the effective cosmological constant, which is determined by the Euler characteristic of the universe.

Although the presence of dark energy is well established from various observations, its true nature is still not well understood. The cosmological constant term seems to be the preferred candidate. In earlier work we had a constant cosmological constant term to limit the sizes of large-scale structures at lower redshifts. In this work, we extend this to large scale structures at higher redshifts. Here we invoke a time varying cosmological constant to set constraints on sizes of galaxies at high redshifts and see that they are consistent with their observed sizes. The time-varying cosmological constant also provides a possible solution to the puzzle of structure formation of large disk galaxies (like the Wolfe disk) observed at very early stages of the Universe. Future observations of galaxies at even higher redshifts could support our approach.

A study of curvature along the contour provides important sources of information about the shape of an object. Knowledge of contour curvature allows for the perception of and interaction with 3D objects. In this review, we will explore the value of contour curvature in the field of neurophysiology, psychophysics, computer vision, and psychology. The serial consolidation of disjoint edges, oriented in a particular manner, into composited curves allows building of identifiable shapes in occluded natural environments [Hess1999, Wertheimer1923, Zucker1989, Feldman2001]. Examples are our ability to pick objects, sort and manage shapes otherwise hidden or confounded by occlusion in messy natural environments. Contour curvature has been intensively studied in psychology as it forms the first steps in 2D shape building which eventually becomes 3D object recognition in the human brain.

In this work, the analytical Lagrange-Kirchhoff model for the deformation for a taiko plate silicon is proposed. Under the conditions of validity of the linear theory of thin plates, the model is in agreement with the experimental data.

Assuming a geometrically closed universe, we predict a value for the cosmic curvature, , a value within current observational bounds. We also propose a thermodynamic heat engine model for the universe, which bypasses the need for an inflaton field. Our model is based on a Carnot Cycle where we have isothermal expansion, followed by adiabatic expansion, followed by isothermal contraction, followed by adiabatic contraction, bringing us back to our original starting point. For the working substance, we focus specifically on the CMB radiation filling the collective voids in the universe. Using this construct, we identify cosmic inflation as the isothermal expansion phase, which lasts just under, . The collective CMB volume we see today only increases by a factor of 5.65 times during this process, and homogeneity and perturbations in the CMB are explained. The singularity problem is avoided and we have a clear mechanism for the work done by the cosmos in causing expansion, and later contraction. For scaling laws with respect to the density parameters in Friedmann’s equations, we will assume a susceptibility model for space, where, , the smeared cosmic susceptibility, decreases with increasing cosmic scale parameter, . Within this framework, we can predict a maximum Hubble volume with minimum CMB temperature for the voids before contraction begins, as well as a minimum volume with maximum CMB temperature when expansion starts. The thermodynamic heat cycle deviates from efficiency in converting heat energy into mechanical energy (expansion) by a minuscule amount, namely, . The significance of this number is not known.

Group IV phospholipase A₂α (cPLA₂α) regulates the production of prostaglandins and leukotrienes via the formation of arachidonic acid from membrane phospholipids. The targeting and membrane binding of cPLA₂α to the Golgi involves the N-terminal C2 domain whereas the catalytic domain produces arachidonic acid. Although most studies of cPLA₂α concern its catalytic activity, it is also linked to homeostatic processes involving the generation of vesicles that traffic material from the Golgi to the plasma membrane. Here we investigate how membrane curvature influences the homeostatic role of cPLA₂α in vesicular trafficking. The cPLA₂α C2 domain is known to induce changes in positive membrane curvature, a process which is dependent on cPLA₂α membrane penetration. We show that cPLA₂α undergoes C2 domain-dependent oligomerization on membranes in vitro and in A549 cells. We found that the association of the cPLA₂α C2 domain with membranes is limited to membranes with positive curvature, and enhanced C2 domain oligomerization was observed on vesicles ~50 nm in diameter. We demonstrated that the cPLA₂α C2 domain generates cholesterol enriched Golgi-derived vesicles independently of cPLA₂α catalytic activity. Our results therefore provide novel insight into the molecular forces that mediate C2 domain-dependent membrane localization in vitro and in cells.

This paper presents a new discrete counterpart of the mixture exponential distribution by utilizing the survival discretization method. The moment-generating function and associated moment measures are discussed. The distribution’s hazard rate function can assume increasing or decreasing forms, making it adaptable for diverse fields requiring count data modelling. The paper explores four distinct parameter estimation methods and assesses their performance through Monte Carlo simulations. The applicability of this distribution extends to time series analysis, particularly within the framework of the first-order integer-valued autoregressive process. Additionally, the paper explores quality control applications, addressing serial dependence challenges in count data encountered in production and market management. The performance of two distinct control charts, the cumulative sum chart and the exponentially weighted moving average chart, is evaluated for their effectiveness in detecting shifts in the process means under various models. A bivariate Markov chain approach is used to estimate the average run lengths of these charts, offering valuable insights for implementation. Design recommendations for achieving robustness in-control chart applications are provided. The effectiveness of the proposed models and charts is illustrated using a real data, demonstrating their practical superiority.

Using a theorem of Ulam and Hyers, we will prove the Hyers-Ulam stability of two-dimensional Lagrange's mean value points $(\eta, \xi)$ which satisfy the equation, $f(u, v) - f(p, q) = (u-p) f_x(\eta, \xi) + (v-q) f_y(\eta, \xi)$, where $(p, q)$ and $(u, v)$ are distinct points in the plane. Moreover, we introduce an efficient algorithm for applying our main result in practical use.

We introduce two symmetric concepts to physics: “distance” (space and time in one) and “wavematter” (electromagnetic wave packet and matter in one). We claim that physics has chosen the wrong concept of time: It is not aware that the time of a moving object flows in a direction other than my time. We provide 15 proofs for our claim by solving 15 mysteries of physics graphically! For example, we prove that length contraction and time dilation are actually geometrical effects in a 4D manifold that we call “Euclidean spacetime” (ES). We prove that the discrepancy in calculating the Hubble constant stems from a systematic error in the redshift measurement. We prove that what I deem wave, deems itself matter, which solves wave–particle duality. We even untangle quantum entanglement without the issue of non-locality. We finally understand why alternative theories of Euclidean relativity have failed: They are all based on four dimensions of space rather than distance. A huge amount of energy was injected into ES at a point that we take as origin. Ever since has this energy been moving radially away at the speed of light. We live in the 3D hypersurface of an expanding 4D hypersphere. Hyperspherical coordinates have the great advantage that they reduce all that is ever happening to just one formula. So, it is the Theory of Everything in these coordinates: “Energy is covering radial distance which, divided by Euclidean time, is equal to the speed of light.” Acceleration and force like gravitation emerge from a rotation of objects in ES and a subsequent projection to 3D space. Matching the symmetry simplifies physics.

The cosmological constant problem is examined by taking an Einstein--scalar with a Higgs-type potential and scrutinizing the infrared structure induced by finite temperature effects. A variant optimal perturbation theory is implemented in the recently proposed quantum-gravitational framework. The optimized renormalized mass, i.e., the renormalized mass determined by the variant optimal perturbation theory, of the scalar field turns out to be on the order of the temperature. This shifts the cosmological constant problem to compatibility of the consequent perturbative analysis. The compatibility is guaranteed essentially by renormalization group invariance of physical quantities. We point out the resummation behind the invariance.

Iterations of continuous maps are the simplest models of generic dynamical systems. In particular, circle maps display several key properties of complex dynamics, such as phase-locking and the quasi-periodicity route to chaos. Our work points out that Planck’s constant may be derived from the scaling behavior of circle maps in the asymptotic limit.

To account for the very low mass density associated with Dark Energy and the Cosmological Constant, a new approach to the ground state of empty space is presented. The resulting model for the vacuum state associated with empty space proposes a crystalline-like texture for the chromatic structure of empty space. This vacuum state has the appropriate mass density and predicts acceleration for the Universe expansion. Furthermore, the model predicts that this texture is anisotropic and may lead to measurable changes in the production of electron and positron pairs by gamma rays incident on a solid crystal of low mass density such as graphite.

In this article it is shown how Milgrom’s acceleration constant is related with the Ω_Λ, Ω_m and Ω_B values of the matter distribution within observable universe as defined in the Standard Model of Cosmology, established by the Planck Collaboration Group. The result is a two-parameter model for the observable universe. The two parameters are the age of the universe and Milgrom’s acceleration constant. It is shown that these are sufficient to calculate the amounts of matter and dark energy in the universe, as well as the contributions of dark matter and baryonic matter in the matter part. The numerical results are in agreement with those of the Lamda-CDM model.

Background: Many clinical conditions are affected by meteorological factors and climate changes. Psychiatric disorders are large contributors to the global disease burden, but the literature on the impact of climate changes on mental health is limited. The aim of this study is to investigate the correlation between rising temperatures and admissions for acute exacerbations of psychiatric disorders. Methods: Data were collected for summer months of years 2013 to 2022. Mean monthly tempera-tures were obtained from the meteorological station of the Department of Physics of the Universi-ty of Turin. Data on patients admitted to the acute psychiatric unit of San Luigi Gonzaga Univer-sity Hospital (Turin, Italy) were extracted from the hospital registry. Linear regression analyses were used to investigate the correlation between temperature and number of admissions. Results: A total of 1600 admissions to our psychiatric ward were recorded. Mean monthly temper-ature and monthly number of admissions were directly correlated (P = 0.0020). The correlation between temperature and admissions was significant for the subgroup of admissions due to Bipo-lar Disorders (BD) (P=0.0011), but not for Schizophrenia (P=0.6070) (SCZ) or Major Depressive Disorder (MDD) (P=0.0588). Conclusions: These results confirm the impact of meteorological factors on mental disorders, and in particular on the course of BD. This provides new insights into etiopathological mechanisms and can contribute to improved follow up and relapse prevention.

In order to better understand the extent to which global climate variability is linked to the frequency and intensity of heat waves and overall changes in temperature throughout the United States (US), correlations between long-term monthly mean, minimum, and maximum temperatures measured at sites throughout the contiguous US and low-frequency variability of multiple climate indices (CIs) are analyzed over the period 1948 to 2018 using correlation analysis. The Pearson’s correlation coefficient is used to assess correlation strength, while Leave-One-Out Cross-Validation and a bootstrapping technique (p-value) are used to address potential serial and spurious correlation and assess the significance of each correlation. Three parameters defined the sliding windows over which surface temperature and CI values were averaged: window size, lag time between the temperature and CI windows, and the beginning month of the temperature window. A 60-month sliding window size and 0 lag time resulted in the strongest correlations overall; beginning months were optimized on an individual site basis. Strong (r &gt;= 0.60) and significant (p-value &lt;= 0.05) correlations were identified. The Western Hemisphere Warm Pool (WHWP) and El Niño/Southern Oscillation (ENSO) exhibited the strongest links to temperatures in the western US, tropical Atlantic sea surface temperatures to temperatures in the central US, the WHWP to temperatures throughout much of the eastern US, and atmospheric patterns over the northern Atlantic to temperatures in the Northeast and Southeast. The final results were compared to results from previous studies focused on precipitation and coastal sea levels. Regional consistency was found regarding links between the northern Atlantic and overall weather and coastal sea levels in the Northeast and Southeast as well as on weather in the upper Midwest. Though the MJO and WHWP revealed dominant links with precipitation and temperature, respectively, throughout the West, ENSO revealed consistent links to sea levels and surface temperatures along the West Coast. These results help focus future research regarding specific mechanisms of climate variability that appear the exhibit strong links to US regional weather and sea level variability and prediction.

The centrifugal force field in the hydrocyclone was affected by the concave-wall curvature radius R0, the mechanism of droplet deformation was closely related to the mass transfer efficiency. Numerical simulation and experimental data were collected to reveal the deformation characteristics and mechanism of single droplet crossing concave-wall jet. Normalized interfacial energy γ and stretching performance were provided to investigate the droplet deformation process. The results showed that the droplet was stretched along the streamwise and shrank along the spanwise in the concave-wall jet. The droplet interfacial energy and deformation were the largest when the droplet crossed the jet boundary at t = 0.20 s. Maximum γ value increased with the increase of R0 by 57.3% to 71.4%, and the distance between droplet and concave-wall increased with R0. Q-criterion was exported to show the vortex strength increasing as the decrease of R0 in the jet boundary. The pressure distribution inside the droplet showed that the pressure decreased as R0 increased, while the pressure difference increased along the streamwise and wall-normal direction. The study suggested that the droplet breakup was more difficult for the smaller R0, which was beneficial for liquid-liquid heterogeneous separation.

In this paper a high-power and propellant-free electromagnetic propulsion is proposed based on the General Relativity and nuclear fusion technology. We find that Riemann curvature vanish and geodesic motion is free from gravitational field locally in a special space-time, which demonstrates the feasibility of propellant-free electromagnetic propulsion. To achieve high-power propulsion in Schwarzschild background, we choose current loop as axisymmetric field source and obtain exact solution of Einstein-Maxwell field equation using Killing symmetry and Ernst generation technique. An implementation with superconductor shield is given according to the Meissner effect, calculation implies that the device can be sufficiently free from gravitational field with the aid of existing nuclear fusion engineering.

The constant ħ is elevated to a dynamical field, coupling to other fields, and itself, through the Lagrangian density derivative terms. The spatial and temporal dependence of ħ falls directly out of the field equations themselves. Three solutions are found: a free field with a tadpole term; a standing-wave non-propagating mode; a non-oscillating non-propagating mode. The first two could be quantized. The third corresponds to a zero-momentum classical field that naturally decays spatially to a constant with no ad-hoc terms added to the Lagrangian. An attempt is made to calibrate the constants in the third solution based on experimental data. The three fields are referred to as actons. It is tentatively concluded that the acton origin coincides with a massive body, or point of infinite density, though is not mass dependent. An expression for the positional dependence of Planck’s constant is derived from a field theory in this work that matches in functional form that of one derived from considerations of Local Position Invariance violation in GR in another paper by this author. Astrophysical and Cosmological interpretations are provided. A derivation is shown for how the integrand in the path integral exponent becomes Lc/ħ(r), where Lc is the classical action. The path that makes stationary the integral in the exponent is termed the “dominant” path, and deviates from the classical path systematically due to the position dependence of ħ. The meaning of variable ħ is seen to be related to the rate of time passage along each path increment. The changes resulting in the Euler-Lagrange equation, Newton’s first and second laws, Newtonian gravity, Friedmann equation with a Cosmological Constant, and the impact on gravitational radiation for the dominant path are shown and discussed.

The thermodynamics of black holes is discussed for the case, when the Newton constant G is not a constant, but is the thermodynamic variable. This gives for the first law of the Schwarzschild black hole thermodynamics: d S BH = − A d K + d M T BH , where the gravitational coupling K = 1 / 4 G , M is the black hole mass, A is the area of horizon, and T BH is Hawking temperature. From this first law it follows that the dimensionless quantity M 2 / K is the adiabatic invariant, which in principle can be quantized if to follow the Bekenstein conjecture. From the Euclidean action for the black hole it follows that K and A serve as dynamically conjugate variables. This allows us to calculate the quantum tunneling from the black hole to the white hole, and determine the temperature and entropy of the white hole.

In this paper we show that the Schwarzschild radius can be extracted easily from any gravitationally-linked phenomena without having knowledge of the Newton gravitational constant or the mass size of the gravitational object. Further, the Schwarzschild radius can be used to predict any gravity phenomena accurately, again without knowledge of the Newton gravitational constant and also without knowledge of the size of the mass, although this may seem surprising at first. Hidden within the Schwarzschild radius are the mass of the gravitational object, the Planck mass (their relative mass), and the Planck length. We do not claim to have all the answers, but this seems to indicate that gravity is quantized, even at a cosmological scale, and this quantization is directly linked to the Planck units. This also supports our view that the Newton gravitational constant is a universal composite constant of the form $G=\frac{l_p^2{c}^3}{\hslash }$ , rather than relying on the Planck units as a function of G. This does not mean that Newton’s gravitational constant is not a universal constant, but that it is instead a composite universal constant that depends on the Planck length, the speed of light, and the Planck constant. Further, $\frac{G\times 1\hspace{0.17em}\mathrm{weight}\hspace{0.17em}\mathrm{unit}}{c^2}=\frac{G}{c^2}$ is the Schwarzschild radius off one weight unit. So G is only needed when we want to use gravity to find the weight of an object, such as weighing the Earth. This is, to our knowledge, the first paper that shows how a long series of major gravity predictions and measurements can be completed without any knowledge of the mass size of the object, or Newton’s gravitational constant. As a minimum we think it provides an interesting new angle for evaluating existing gravity theories, and it may even give us a small hint on how to combine quantum gravity with Newton and Einstein gravity.

3D measurement is a high-throughput method that can record a large amount of information. In this study, we have developed new methods that could be used for morphological analysis of plants from the information contained in 3D data. Specifically, we investigated characteristics that can be measured by scale (dimension) and/or visual assessment by humans. The characteristics that can be measured on a scale-related dimension were tested based on the bounding box, convex hull, column solid, and voxel. Furthermore, for characteristics that can be evaluated by visual assessment, we propose a new method using normal vectors and local curvature (LC) data. For these examinations, we used our highly accurate all-around 3D plant modelling system. The correlation coefficients between manual measurements and the scale-related methods were all above 0.9. In particular, the differences in LC calculated from the normal vector data allowed us to visualize and quantify the concavity and convexity of leaves. Furthermore, we also found a difference in the time point at which leaf blistering began to develop among the cultivars. The precise 3D model made it possible to perform quantitative measurements of lettuce size and morphological characteristics. In addition, the newly proposed LC-based analysis method made it possible to quantify the characteristics that rely on visual assessment.

Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system’s evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system.This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata.

The Oxford English Dictionary includes 17 definitions for the word “model” as a noun and other 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For in-stance, “model railways” refer to replicas of railways and trains at a smaller scale and a “model student” refers to an exemplar individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning of a model. Even if the context is narrowed, specifically to the research related to the tumour microenvironment, a “model” can be understood in a wide variety of ways, from an animal model, to a mathematical expression. This paper presents a review of the different “models” of the tumour microenvironment grouped by the different def-initions of the word into four categories: model organisms, in vitro models, mathematical models, and computational models. Then, the frequency of different meanings of the word “model” related to the tumour microenvironment is measured from the number of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequency of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, in particular xenografts and mouse models are the most common used “models”, the number of entries have been slowly de-creasing. Mathematical models, prognostic and risk models follow in frequency and these have been growing in use.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

We study the divisibility properties of the constant terms of certain meromorphic modular forms for Hecke groups. We relate those properties to those of some sequences that have already appeared in the literature. For possible use in later drafts, we show how to invert the map taking a Laurent series $f(x) = 1/x + \sum_{n=0}^{\infty}a_{n+1} x^n$ to the sequence of constant terms of its positive powers. At the end of the article, we construct from elementary arithmetic functions some meromorphic but not necessarily modular functions and study their constant terms.

Care coordination (CC) for children with special healthcare needs and medical complexity (CSHCN-CMC) is challenging, and medication management is especially difficult for providers, parents/caregivers, and patients alike. While numerous strategies for CC have been suggested and implemented, barriers to medication optimization remain. The report describes the creation of a pediatric clinical pharmacotherapy practice, related standard operating procedures to assure consistent application of screening tools and care provision through comprehensive medication management (CMM), and establishment of a collaborative practice agreement (CPA) to guide drug therapy delegation, monitoring, and modification. The methodology of a prospective case series is also presented to highlight drug therapy problems and their resolution in CSHCN-CMC. Future opportunities to expand the practice for engagement in population health management as well as prior authorization activities on behalf of physicians will be discussed.

Background The Delta Neutrophil Index (DNI), a prodiagnostic marker for sepsis, utilizes leukocyte count. Platelet activation, similar to leukocytes, plays a crucial role in host defence against pathogens and may serve as a predictor of sepsis outcome. However, the combined evaluation of Mean Platelet Component (MPC) and DNI in assessing sepsis has been rarely used. Methods To assess the prodiagnostic validity of simultaneous utilization of DNI and MPC in cases of human febrile sepsis, we conducted measurements of cellular indices, including DNI and MPC, as well as molecular biomarkers such as procalcitonin (PCT) and C-reactive protein (CRP). This study was carried out on patients admitted to the emergency department with suspected sepsis. Results Using a cutoff value of 2.65%, the sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) of DNI in sepsis were found to be 69%, 73.9%, 77.9%, and 64.1%, respectively. Furthermore, significant differences in DNI and MPC levels were observed between the sepsis and non-sepsis groups (6.7±7.8% versus 2.1±2.2%, P=0.000 and 26.0±1.9 g/dl versus 26.8±1.4 g/dl, P=0.002), respectively. Notably, there was a negative correlation between DNI and MPC, with the strength of the correlation varying based on the cause of sepsis. By setting the cutoff value for DNI at 6.2%, the sensitivity, specificity, and NPV improved to 100%, 80.3%, and 100%, respectively, although the PPV remained at 10.6%. Importantly, the DNI≥6.2 group exhibited a higher incidence of death (10.9%, 5/46) and multiorgan failure (19.6%, 9/46) compared to the DNI<6.2 group (0.0%, 0/46 and 0.0%, 0/167, respectively) (P=0.000 and P=0.000, respectively). Conclusions In our study, DNI demonstrates superior effectiveness compared to other molecular biomarkers such as CRP and procalcitonin in distinguishing febrile septic patients from febrile nonseptic patients and predicting prognosis. Additionally, there exists a negative correlation between MPC and DNI, making MPC a valuable marker for differentiating the etiology of sepsis. These findings hold significant clinical implications as DNI/MPC is a cost-effective and readily applicable approach in various impending sepsis scenarios. Notably, this study represents the first examination of the prodiagnostic validity of simultaneously employing DNI and MPC in human cases of febrile sepsis.

In the paper, by convolution theorem for the Laplace transforms and analytic techniques, the author finds necessary and sufficient conditions for complete monotonicity, monotonicity, and inequalities of several functions involving polygamma functions. By these results, the author derives a lower bound of a function related to the sectional curvature of the manifold of the beta distributions. Finally, the author poses several guesses and open problems related to monotonicity, complete monotonicity, and inequalities of several functions involving polygamma functions.

Motivated by important applications to the analysis of complex noise-induced phenomena, a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise is considered. Using apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noise. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with the example of the van der Pol oscillator with hard excitement.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

Resonance inductive coupling is widely used for wireless power transfer (WPT) in medical applications. In this paper, we analyze the LCL-compensated WPT structure and propose a novel constant voltage transmission system based on gain estimation, without any extra feedback from the receiver. The system is capable for amplitude-modulated implant neural stimulation where the load impedance and the coupling coefficient are both variable. Compared to existing methods for constant voltage transmission, our approach offers advantages in compact size and the compatibility with the industrial, scientific and medical (ISM) band. We validate the load-independent resonant characteristic and the feasibility of constant voltage transmission using an experimental prototype working at 6.78MHz. Finally, we discuss the structure of the implant stimulator and methods of applying the proposed WPT system.

To understand the mystery of final unification, in our earlier publications, we proposed that there exist three atomic gravitational constants associated with electroweak, strong and electromagnetic interactions. During cosmic evolution, if one is willing to give equal importance to Higgs boson and Planck mass in understanding the massive origin of elementary particles, then it seems quite logical to expect a common relation in between Planck scale and Electroweak scale. Based on these two points, we noticed that, electroweak field seems to be operated by a primordial massive fermion of rest energy 585 GeV. It can be considered as the zygote of all elementary particles and galactic dark matter. H-bar seems to be a characteristic outcome of unified electroweak gravity. Electron rest mass seems to be a characteristic outcome of electroweak and strong gravity. Proton rest mass seems to be a characteristic outcome of electroweak, strong and electromagnetic gravity. Recently observed 3.5 keV photon seems to be an outcome of annihilation of charged baby lepton of rest energy 1.75 keV. Interesting point to be noted is that, Schwarzschild radius of electron is 0.48 nanometer and it needs further investigation with respect to emerging nano-science and technology. Proceeding further, by considering electromagnetic and weak gravitational constants, neutron life time can be understood.

We will demonstrate how the CMB temperature simply can be predicted from what we will call geometric mean Planck gravitational potential energy in the universe. This falls nicely in line with the recent discovery that the CMB temperature also is a geometric mean of the minimum and maxium temerature in the Hubble sphere, and also that the CMB tem- perature can be derived from the Stefan-Boltzman law. Since the Coulomb force for Planck charges are identical to the Newton force for two Planck mass particles this also seems to give a potential connection between electrostatic force and the CMB temperature.

Humeral resurfacing arthroplasty (HRA) entails the substitution of the articular surface alone with a prosthetic cap without stem. It is a more conservative procedure which can be easily converted in a total arthroplasty if necessary. The present study aimed to evaluate the clinical and radiographical outcomes in a series of patients treated with HRA. 33 patients with a mean fol-low-up of 11 years were clinically (Constant score; Disability of the Arm, Shoulder and Hand score, DASH) and radiographically assessed before and after surgery. Constant and DASH score improved significantly after surgery, and only 2 cases needed revision surgery. HRA represents a valid therapeutic option in selected cases to improve the quality of life and delaying the need for more invasive procedures.

Background: Peyronie’s disease (PD) represents a challenging urological disease, due to not optimal post-operative surgical outcomes. We aim to evaluate if vacuum erection devices (VED) treatment before pe-nile curvature surgery is able to improve the post-operative surgical outcomes. Methods: All enrolled patients were assigned to the following groups: a) treatment group, VED treatment (3 times per week) starting 3 months before surgery and (3 times per week) one months after surgery and b) control group, VED treatment (3 times per week) one months after surgery. Follow-up urologic visits were scheduled at 3 and 6 months after surgery and the two groups were compared. Results: Thirty-eight patients have been enrolled (median age 67 years, 57-74, IQR), 20 in the treatment group and 18 in the control group. At the follow-up visits, the two groups are different in terms of IIEF-5 (26 vs 24; p=0.02), ‘yes’ to SEP2 and 3 (85% vs 55%; p<0.001, 85% vs 50%; p<0.001, respectively) and PDQ (-16 vs -11; p=0.03). Complete correction of penile curvature was achieved in 36 patients (94.7%). In the treatment group, no hourglass deformity has been reported, while in the control group 1 patient reported a mild hourglass deformity. In the treatment group, we obtained a longer total penile length (median +1.5 cm). The overall satisfaction rate was 98% in the treatment group and 96% in the control group. Conclusions: The VED treatment before penile curvature surgery in patients affected by PD is able to improve the post-operative surgery.

Single particle tracking is a powerful technique to investigate the motion of molecules or particles. Here we review methods for analyzing the reconstructed trajectories, step needed for deciphering the underlying mechanisms driving the motion. First, we review the traditional analysis based on the mean square displacement (MSD), highlighting sometimes-neglected factors potentially affecting results accuracy. We then report methods that exploit distributions of parameters other than displacements, e.g. angles, velocities, and times and probabilities of reaching a target, discussing how they are more sensitive in characterizing heterogeneities and transient behaviors masked in MSD analysis. Hidden Markov Models are also used for this purpose, and these allow identifying different states, their populations and the switching kinetics. Finally, we discuss a rapidly expanding field: trajectory analysis based on machine learning. Various approaches, from random forest to deep learning, are used to classify trajectory motions, which can be identified by motion models or by model-free sets of trajectory features, either previously defined or automatically identified by the algorithms. We also review free software available for some of the analysis methods. We emphasize that approaches based on combined different methods, including classical statistics and machine learning, may be the way to obtain the most informative and accurate results.

Measured values of the electron mass and Compton wavelength produce a value of Planck's constant with a relative standard uncertainty of 3 x 10^-10. This is only slightly larger than the 1.3 x 10^-10 relative standard uncertainty in measurements performed using the Kibble balance. Compton scattering represents an alternative pathway to improving the value of Planck's constant in the future. Natural units of length, mass, and time offer new pathways to improving the values of physical constants. While extensive values of the Planck units lie beyond the reach of present-day instrumentation, certain product and quotient pairs of Planck units such as the speed of light can be measured with relatively high precision. Better measurements of certain unit pairs will improve the value of the gravitational constant.

We study a localization of gravity through the matching point between non-inertial frames and local inertial frames. This localization of gravity is done through defining relative gravitational red-shift. This lead to an emergence of a timeless state in a mathematically consistent way. In this timeless state of gravity, we find a geometric interpretation of the speed of light and mass. The experimental support of the timeless state is the quantum entanglement and internal symmetries that are independent of time. Therefore gravity would be responsible for measurements independent of time including quantum entanglement. Timeless state in that sense explain why do we have gravity/gauge correspondence. We conjecture that the universe emerged from a black hole with a global $SU(3)\times SU(2)\times U(1)$ symmetry on its event horizon that produces gauge fields Electromagnetism, weak and strong nuclear force through localization of this global symmetry. Through the localization in the gravity field, the timeless measurements such as spin will be correlated with the varying of timeless measurement which is relative gravitational red-shift. We present a gravitational or geometric interpretation of spin-0, spin-1, and spin-1/2 states. We present an interpretation of why do we measure matter rather than anti-matter. We found that the Higgs scalar field is represented by the gravitational red-shift at every point in the space around the black hole. We derive the numerical value of the cosmological constant that agrees with experimental observations.

In 1895, Korteweg and de Vries (KdV), derived their celebrated equation describing the motion of waves of long wavelength in shallow water. In doing so they made a number of quite reasonable assumptions, incompressibility of the water and irrotational fluid. The resulting equation, the celebrated KdV equation, has been shown to be a very reasonable description of real water waves. However there are other phenomena which have an impact on the shape of the wave, that of vorticity and viscosity. This paper examines how a constant vorticity affects the shape of waves in electrohydrodynamics. For constant vorticity, the vertical component of the velocity obeys a Laplace equation and also has the usual lower boundary condition. In making the vertical component of the velocity take central stage, the Burns condition can be thus bypassed.